Finite Group Databasebeta

← #26425679

Subgroups — #26425679

Order 12032.

1666 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251701C211yesmaximal, characteristic
2#20251694C211yesmaximal, characteristic, complemented
3#20251267C211yesmaximal, characteristic, complemented
4#20251142C211yesmaximal, characteristic, complemented
5#20250797C211yesmaximal, characteristic, complemented
6#20250789C211yesmaximal, characteristic, complemented
7#20250747C211yesmaximal, characteristic, complemented
8#20250745C211yesmaximal, characteristic, complemented
9#20250702C211yesmaximal, characteristic, complemented
10#20250679C211yesmaximal, characteristic, complemented
11#20250221C211yesmaximal, characteristic, complemented
12#20250220C211yesmaximal, characteristic, complemented
13#20250174C211yesmaximal, characteristic, complemented
14#20250168C211yesmaximal, characteristic, complemented
15#20250039C211yesmaximal, characteristic, complemented
16#20249964C211yesmaximal, characteristic, complemented
17#20249859C211yesmaximal, characteristic, complemented
18#20249845C211yesmaximal, characteristic, complemented
19#20249358C211yesmaximal, characteristic, complemented
20#20248614C211yesmaximal, characteristic, complemented
21#20248572C211yesmaximal, characteristic
22#20247946C211yesmaximal, characteristic
23#20247887C211yesmaximal, characteristic, complemented
24#20247654C211yesmaximal, characteristic
25#20247536C211yesmaximal, characteristic, complemented
26#20247030C211yesmaximal, characteristic, complemented
27#20246750C211yesmaximal, characteristic
28#20246119C211yesmaximal, characteristic, complemented
29#20246014C211yesmaximal, characteristic
30C2×#15689027C211yesmaximal, characteristic, complemented
31C47×#2643C211yesmaximal, characteristic
32C23×Dic94C2211yescharacteristic
33C2×#13094023C2211yescharacteristic
34C2×#13094023C2211yescharacteristic
35C2×#13094017C2211yescharacteristic
36C2×#13094017C2211yescharacteristic
37C2×#13094015C2211yescharacteristic
38C2×#13094014C2211yescharacteristic
39C2×#13094001C2211yescharacteristic
40C2×#13094001C2211yescharacteristic
41C2×#13094001C2211yescharacteristic
42C2×D4×Dic47C2211yescharacteristic
43C22×Dic47⋊C4C2211yescharacteristic
44C22×C4×Dic47C2211yescharacteristic
45C47⋊#401C2211yescharacteristic
46#15689065C2211yescharacteristic
47#15689065C2211yescharacteristic
48#15689065C2211yescharacteristic
49#15689065C2211yescharacteristic
50#15689065C2211yescharacteristic
51#15689065C2211yescharacteristic
52#15689064C2211yescharacteristic
53#15689064C2211yescharacteristic
54#15689064C2211yescharacteristic
55#15689064C2211yescharacteristic
56#15689064C2211yescharacteristic
57#15689063C2211yescharacteristic
58#15689061C2211yescharacteristic
59#15689061C2211yescharacteristic
60#15689059C2211yescharacteristic
61#15689057C2211yescharacteristic
62#15689057C2211yescharacteristic
63#15689057C2211yescharacteristic
64#15689057C2211yescharacteristic
65#15689057C2211yescharacteristic
66#15689056C2211yescharacteristic
67#15689056C2211yescharacteristic
68#15689055C2211yescharacteristic
69#15689054C2211yescharacteristic
70#15689053C2211yescharacteristic
71#15689051C2211yescharacteristic
72#15689051C2211yescharacteristic
73#15689051C2211yescharacteristic
74#15689046C2211yescharacteristic
75#15689044C2211yescharacteristic
76#15689044C2211yescharacteristic
77#15689044C2211yescharacteristic
78#15689044C2211yescharacteristic
79#15689044C2211yescharacteristic
80#15689043C2211yescharacteristic
81#15689043C2211yescharacteristic
82#15689035C2211yescharacteristic
83#15689035C2211yescharacteristic
84#15689035C2211yescharacteristic
85#15689028C2211yescharacteristic
86#15689027C2211yescharacteristic
87#15689027C2211yescharacteristic
88#15689027C2211yescharacteristic
89#15689027C2211yescharacteristic
90#15689027C2211yescharacteristic
91#15689027C2211yescharacteristic
92#15689027C2211yescharacteristic
93#15689027C2211yescharacteristic
94#15689027C2211yescharacteristic
95#15689027C2211yescharacteristic
96#15689027C2211yescharacteristic
97#15689027C2211yescharacteristic
98#15689027C2211yescharacteristic
99#15689020C2211yescharacteristic
100#15689019C2211yescharacteristic
101#15689019C2211yescharacteristic
102#15689018C2211yescharacteristic
103#15689018C2211yescharacteristic
104#15689018C2211yescharacteristic
105#15689017C2211yescharacteristic
106#15689017C2211yescharacteristic
107#15689017C2211yescharacteristic
108#15689016C2211yescharacteristic
109#15689011C2211yescharacteristic
110#15689011C2211yescharacteristic
111#15689011C2211yescharacteristic
112#15689011C2211yescharacteristic
113#15689010C2211yescharacteristic
114#15689010C2211yescharacteristic
115#15689010C2211yescharacteristic
116#15689010C2211yescharacteristic
117#15689009C2211yescharacteristic
118#15689009C2211yescharacteristic
119#15689008C2211yescharacteristic
120#15689008C2211yescharacteristic
121#15689008C2211yescharacteristic
122#15689008C2211yescharacteristic
123#15689008C2211yescharacteristic
124#15689006C2211yescharacteristic
125#15689006C2211yescharacteristic
126#15689006C2211yescharacteristic
127#15689005C2211yescharacteristic
128#15689005C2211yescharacteristic
129#15689005C2211yescharacteristic
130#15689005C2211yescharacteristic
131#15689005C2211yescharacteristic
132#15689005C2211yescharacteristic
133#15689005C2211yescharacteristic
134#15689005C2211yescharacteristic
135#15689004C2211yescharacteristic
136#15689004C2211yescharacteristic
137#15689004C2211yescharacteristic
138#15689004C2211yescharacteristic
139#15689003C2211yescharacteristic
140#15689003C2211yescharacteristic
141#15689003C2211yescharacteristic
142#15688998C2211yescharacteristic
143#15688998C2211yescharacteristic
144#15688998C2211yescharacteristic
145#15688996C2211yescharacteristic
146#15688996C2211yescharacteristic
147#15688996C2211yescharacteristic
148#15688996C2211yescharacteristic
149#15688995C2211yescharacteristic
150#15688995C2211yescharacteristic
151#15688995C2211yescharacteristic
152#15688995C2211yescharacteristic
153#15688990C2211yescharacteristic
154#15688990C2211yescharacteristic
155#15688990C2211yescharacteristic
156#15688987C2211yescharacteristic
157#15688987C2211yescharacteristic
158#15688987C2211yescharacteristic
159#15688984C2211yescharacteristic
160#15688983C2211yescharacteristic
161#15688983C2211yescharacteristic
162#15688981C2211yescharacteristic
163#15688981C2211yescharacteristic
164#15688981C2211yescharacteristic
165#15688981C2211yescharacteristic
166C22⋊C4×Dic47C2211yescharacteristic
167C22⋊C4×Dic47C2211yescharacteristic
168C22⋊C4×Dic47C2211yescharacteristic
169C2×C47⋊#95C2211yescharacteristic
170C2×C47⋊#95C2211yescharacteristic
171C2×C47⋊#95C2211yescharacteristic
172C47×#401C2211yescharacteristic
173C47×#400C2211yescharacteristic
174C47×#400C2211yescharacteristic
175C47×#400C2211yescharacteristic
176C47×#397C2211yescharacteristic
177C47×#397C2211yescharacteristic
178C47×#397C2211yescharacteristic
179C47×#396C2211yescharacteristic
180C47×#386C2211yescharacteristic
181C47×#386C2211yescharacteristic
182C47×#386C2211yescharacteristic
183C47×#385C2211yescharacteristic
184C47×#385C2211yescharacteristic
185C47×#385C2211yescharacteristic
186C2×#95×C47C2211yescharacteristic
187C22×Dic94—24no—
188C22×Dic94—42no—
189C22×Dic94—42no—
190C22×Dic94C2311yescharacteristic
191C22×Dic94C2311yescharacteristic
192C22×Dic94C2311yescharacteristic
193C22×Dic94C2311yescharacteristic
194C22×Dic94C2311yescharacteristic
195C23×Dic47C2311yescharacteristic
196C23×Dic47C2311yescharacteristic
197C23×Dic47C2311yescharacteristic
198C23×Dic47C2311yescharacteristic
199C23×Dic47C2311yescharacteristic
200#13094023—42no—
201#13094023—42no—
202#13094017—42no—
203#13094017—42no—
204#13094015—42no—
205#13094014—42no—
206#13094001—24no—
207#13094001—42no—
208#13094001—42no—
209D4×Dic47—24no—
210C2×C4⋊Dic47C2311yescharacteristic
211C2×C4⋊Dic47C2311yescharacteristic
212C2×C4⋊Dic47C2311yescharacteristic
213C2×C4⋊Dic47C2311yescharacteristic
214C2×C4⋊Dic47C2311yescharacteristic
215C2×C4⋊Dic47C2311yescharacteristic
216C2×C4⋊Dic47C2311yescharacteristic
217C2×C4⋊Dic47C2311yescharacteristic
218C2×C4⋊Dic47C2311yescharacteristic
219C2×C4⋊Dic47C2311yescharacteristic
220C2×Dic47⋊C4—42no—
221C2×Dic47⋊C4C2311yescharacteristic
222C2×Dic47⋊C4C2311yescharacteristic
223C2×Dic47⋊C4C2311yescharacteristic
224C2×Dic47⋊C4C2311yescharacteristic
225C2×Dic47⋊C4C2311yescharacteristic
226C2×Dic47⋊C4C2311yescharacteristic
227C2×Dic47⋊C4C2311yescharacteristic
228C2×Dic47⋊C4C2311yescharacteristic
229C2×Dic47⋊C4C2311yescharacteristic
230C2×Dic47⋊C4C2311yescharacteristic
231C2×Dic47⋊C4C2311yescharacteristic
232C2×Dic47⋊C4C2311yescharacteristic
233C2×Dic47⋊C4C2311yescharacteristic
234C2×Dic47⋊C4C2311yescharacteristic
235C2×Dic47⋊C4C2311yescharacteristic
236C2×Dic47⋊C4C2311yescharacteristic
237C2×Dic47⋊C4C2311yescharacteristic
238C2×Dic47⋊C4C2311yescharacteristic
239C2×Dic47⋊C4C2311yescharacteristic
240C2×Dic47⋊C4C2311yescharacteristic
241C2×Dic47⋊C4C2311yescharacteristic
242C2×Dic47⋊C4C2311yescharacteristic
243C2×Dic47⋊C4C2311yescharacteristic
244C2×Dic47⋊C4C2311yescharacteristic
245C2×Dic47⋊C4C2311yescharacteristic
246C2×Dic47⋊C4C2311yescharacteristic
247C2×C22⋊Dic47C2311yescharacteristic
248C2×C22⋊Dic47C2311yescharacteristic
249C2×C22⋊Dic47C2311yescharacteristic
250C2×C22⋊Dic47C2311yescharacteristic
251C2×C22⋊Dic47C2311yescharacteristic
252C2×C22⋊Dic47C2311yescharacteristic
253C2×C22⋊Dic47C2311yescharacteristic
254C2×C22⋊Dic47C2311yescharacteristic
255C2×C22⋊Dic47C2311yescharacteristic
256C2×C22⋊Dic47C2311yescharacteristic
257C2×C22⋊Dic47C2311yescharacteristic
258C2×C4×Dic47—42no—
259C2×C4×Dic47C2311yescharacteristic
260C2×C4×Dic47C2311yescharacteristic
261C2×C4×Dic47C2311yescharacteristic
262C2×C4×Dic47C2311yescharacteristic
263C2×C4×Dic47C2311yescharacteristic
264C2×C4×Dic47C2311yescharacteristic
265C2×C4×Dic47C2311yescharacteristic
266C2×C4×Dic47C2311yescharacteristic
267C2×C4×Dic47C2311yescharacteristic
268C2×C4×Dic47C2311yescharacteristic
269C2×C4×Dic47C2311yescharacteristic
270C47⋊#95C2311yescharacteristic
271C47⋊#95C2311yescharacteristic
272C47⋊#95C2311yescharacteristic
273C47⋊#95C2311yescharacteristic
274C47⋊#95C2311yescharacteristic
275C47⋊#95C2311yescharacteristic
276C47⋊#95C2311yescharacteristic
277C47⋊#95C2311yescharacteristic
278C47⋊#95C2311yescharacteristic
279C47⋊#95C2311yescharacteristic
280C47⋊#95C2311yescharacteristic
281C47⋊#95C2311yescharacteristic
282C47⋊#95C2311yescharacteristic
283C47⋊#95C2311yescharacteristic
284C47⋊#95C2311yescharacteristic
285C47⋊#95C2311yescharacteristic
286C47⋊#95C2311yescharacteristic
287C47⋊#95C2311yescharacteristic
288C47⋊#95C2311yescharacteristic
289C47⋊#95C2311yescharacteristic
290C47⋊#95C2311yescharacteristic
291C47⋊#95C2311yescharacteristic
292C47⋊#95C2311yescharacteristic
293C47⋊#95C2311yescharacteristic
294C47⋊#95C2311yescharacteristic
295C47⋊#95C2311yescharacteristic
296C47⋊#95C2311yescharacteristic
297C47⋊#95C2311yescharacteristic
298C47⋊#95C2311yescharacteristic
299C47⋊#95C2311yescharacteristic
300C47⋊#95C2311yescharacteristic
301C47⋊#95C2311yescharacteristic
302C47⋊#95C2311yescharacteristic
303C47⋊#95C2311yescharacteristic
304C47⋊#95C2311yescharacteristic
305C47⋊#95C2311yescharacteristic
306C47⋊#95C2311yescharacteristic
307C47⋊#95C2311yescharacteristic
308C47⋊#95C2311yescharacteristic
309C47⋊#95C2311yescharacteristic
310C47⋊#95C2311yescharacteristic
311C47⋊#95C2311yescharacteristic
312C47⋊#95C2311yescharacteristic
313C47⋊#95C2311yescharacteristic
314C47⋊#95C2311yescharacteristic
315C47⋊#95C2311yescharacteristic
316C47⋊#95C2311yescharacteristic
317C47⋊#95C2311yescharacteristic
318C47⋊#95C2311yescharacteristic
319C47⋊#95C2311yescharacteristic
320C47⋊#95C2311yescharacteristic
321C47⋊#95C2311yescharacteristic
322C22×D4×C47C2311yescharacteristic
323C23×C4×C47C2311yescharacteristic
324C23×C4×C47C2311yescharacteristic
325C23×C4×C47C2311yescharacteristic
326C2×C4⋊C4×C47C2311yescharacteristic
327C2×C4⋊C4×C47C2311yescharacteristic
328C2×C4⋊C4×C47C2311yescharacteristic
329C2×C4⋊C4×C47C2311yescharacteristic
330C2×C4⋊C4×C47C2311yescharacteristic
331C2×C4⋊C4×C47C2311yescharacteristic
332C2×C22⋊C4×C47C2311yescharacteristic
333C2×C22⋊C4×C47C2311yescharacteristic
334C2×C22⋊C4×C47C2311yescharacteristic
335C2×C22⋊C4×C47C2311yescharacteristic
336C2×C22⋊C4×C47C2311yescharacteristic
337C2×C22⋊C4×C47C2311yescharacteristic
338C2×C22⋊C4×C47C2311yescharacteristic
339C2×C22⋊C4×C47C2311yescharacteristic
340C2×C22⋊C4×C47C2311yescharacteristic
341#95×C47C2311yescharacteristic
342#95×C47C2311yescharacteristic
343#95×C47C2311yescharacteristic
344#95×C47C2311yescharacteristic
345#95×C47C2311yescharacteristic
346#95×C47C2311yescharacteristic
347#95×C47C2311yescharacteristic
348#95×C47C2311yescharacteristic
349#95×C47C2311yescharacteristic
350#95×C47C2311yescharacteristic
351#95×C47C2311yescharacteristic
352#95×C47C2311yescharacteristic
353#95×C47C2311yescharacteristic
354#95×C47C2311yescharacteristic
355#95×C47C2311yescharacteristic
356#95×C47C2311yescharacteristic
357C24×C47C2411yescharacteristic
358C24×C47C2411yescharacteristic
359C2×D4×C47—22no—
360C2×D4×C47—22no—
361C2×D4×C47—22no—
362C22×C4×C47—22no—
363C22×C4×C47—22no—
364C22×C4×C47—22no—
365C22×C4×C47—41no—
366C22×C4×C47—41no—
367C22×C4×C47—41no—
368C22×C4×C47—41no—
369C22×C4×C47—41no—
370C22×C4×C47—41no—
371C22×C4×C47C2411yescharacteristic
372C22×C4×C47C2411yescharacteristic
373C22×C4×C47C2411yescharacteristic
374C22×C4×C47C2411yescharacteristic
375C22×C4×C47C2411yescharacteristic
376C22×C4×C47C2411yescharacteristic
377C22×C4×C47C2411yescharacteristic
378C22×C4×C47C2411yescharacteristic
379C22×C4×C47C2411yescharacteristic
380C22×C4×C47C2411yescharacteristic
381C22×C4×C47C2411yescharacteristic
382C22×C4×C47C2411yescharacteristic
383C22×C4×C47C2411yescharacteristic
384C22×Dic47—22no—
385C22×Dic47—22no—
386C22×Dic47—22no—
387C22×Dic47—22no—
388C22×Dic47—22no—
389C22×Dic47—22no—
390C22×Dic47—22no—
391C22×Dic47—41no—
392C22×Dic47—41no—
393C22×Dic47—41no—
394C22×Dic47—41no—
395C22×Dic47—41no—
396C22×Dic47—41no—
397C22×Dic47—41no—
398C22×Dic47#4114yes—
399C22×Dic47C2411yescharacteristic
400C22×Dic47C2411yescharacteristic
401C22×Dic47C2411yescharacteristic
402C22×Dic47C2411yescharacteristic
403C22×Dic47C2411yescharacteristic
404C22×Dic47C2411yescharacteristic
405C22×Dic47C2411yescharacteristic
406C22×Dic47C2411yescharacteristic
407C22×Dic47C2411yescharacteristic
408C22×Dic47C2411yescharacteristic
409C22×Dic47C2411yescharacteristic
410C22×Dic47C2411yescharacteristic
411C22×Dic47C2411yescharacteristic
412C22×Dic47C2411yescharacteristic
413C22×Dic47C2411yescharacteristic
414C22×Dic47C2411yescharacteristic
415C2×Dic94—22no—
416C2×Dic94—22no—
417C2×Dic94—22no—
418C2×Dic94—22no—
419C2×Dic94—22no—
420C2×Dic94—22no—
421C2×Dic94—22no—
422C2×Dic94—22no—
423C2×Dic94—22no—
424C2×Dic94—41no—
425C2×Dic94—41no—
426C2×Dic94—41no—
427C2×Dic94—41no—
428C2×Dic94—416no—
429C2×Dic94—41no—
430C2×Dic94—41no—
431C4⋊C4×C47—41no—
432C4⋊C4×C47—41no—
433C4⋊C4×C47—41no—
434C4⋊C4×C47—41no—
435C4⋊C4×C47—41no—
436C4⋊C4×C47—41no—
437C22⋊C4×C47—22no—
438C22⋊C4×C47—22no—
439C22⋊C4×C47—22no—
440C22⋊C4×C47—41no—
441C22⋊C4×C47—41no—
442C22⋊C4×C47—41no—
443C22⋊C4×C47—41no—
444C22⋊C4×C47—41no—
445C22⋊C4×C47—41no—
446C22⋊Dic47—22no—
447C22⋊Dic47—22no—
448C22⋊Dic47—22no—
449C22⋊Dic47—22no—
450C22⋊Dic47—22no—
451C22⋊Dic47—22no—
452C22⋊Dic47—22no—
453C22⋊Dic47—22no—
454C22⋊Dic47—41no—
455C22⋊Dic47—41no—
456C22⋊Dic47—41no—
457C4⋊Dic47—22no—
458C4⋊Dic47—22no—
459C4⋊Dic47—22no—
460C4⋊Dic47—22no—
461C4⋊Dic47—22no—
462C4⋊Dic47—22no—
463C4⋊Dic47—41no—
464C4⋊Dic47—41no—
465C4⋊Dic47—41no—
466C4⋊Dic47—41no—
467Dic47⋊C4—22no—
468Dic47⋊C4—22no—
469Dic47⋊C4—22no—
470Dic47⋊C4—22no—
471Dic47⋊C4—22no—
472Dic47⋊C4—22no—
473Dic47⋊C4—22no—
474Dic47⋊C4—22no—
475Dic47⋊C4—22no—
476Dic47⋊C4—41no—
477Dic47⋊C4—41no—
478Dic47⋊C4—41no—
479Dic47⋊C4—41no—
480Dic47⋊C4—41no—
481Dic47⋊C4—41no—
482Dic47⋊C4—41no—
483Dic47⋊C4—41no—
484Dic47⋊C4—41no—
485Dic47⋊C4—41no—
486Dic47⋊C4—41no—
487Dic47⋊C4—41no—
488Dic47⋊C4—41no—
489Dic47⋊C4—41no—
490Dic47⋊C4—41no—
491Dic47⋊C4—41no—
492Dic47⋊C4—41no—
493C4×Dic47—22no—
494C4×Dic47—22no—
495C4×Dic47—22no—
496C4×Dic47—41no—
497C4×Dic47—41no—
498C4×Dic47—41no—
499C4×Dic47—41no—
500C4×Dic47—41no—
501C4×Dic47—41no—
502C4×Dic47—41no—
503C4×Dic47—41no—
504C23×C47—21no—
505C23×C47—21no—
506C23×C47—21no—
507C23×C47—21no—
508C23×C47—21no—
509C23×C47—21no—
510C23×C47—21no—
511C23×C47—21no—
512C23×C47—21no—
513C23×C47—21no—
514C23×C47—21no—
515C23×C47C2×#4112yes—
516C23×C472−1+412yes—
517C23×C472−1+412yes—
518C23×C47C2511yescharacteristic
519D4×C47—44no—
520C2×C4×C47—21no—
521C2×C4×C47—21no—
522C2×C4×C47—21no—
523C2×C4×C47—21no—
524C2×C4×C47—21no—
525C2×C4×C47—21no—
526C2×C4×C47—21no—
527C2×C4×C47—21no—
528C2×C4×C47—21no—
529C2×C4×C47—21no—
530C2×C4×C47—21no—
531C2×C4×C47—21no—
532C2×C4×C47—21no—
533C2×C4×C47—21no—
534C2×C4×C47—21no—
535C2×C4×C47—21no—
536C2×C4×C47—21no—
537C2×C4×C47—21no—
538C2×C4×C47—21no—
539C2×C4×C47—21no—
540C2×C4×C47—21no—
541C2×C4×C47—21no—
542C2×C4×C47—21no—
543C2×C4×C47—21no—
544C2×C4×C47—21no—
545C2×C4×C47—21no—
546C2×C4×C47—21no—
547C2×C4×C47—21no—
548C2×C4×C47—21no—
549C2×C4×C47—21no—
550C2×C4×C47—21no—
551C2×C4×C47—21no—
552C2×C4×C47—21no—
553C2×C4×C47—21no—
554C2×C4×C47—21no—
555C2×C4×C47—21no—
556C2×C4×C47—21no—
557C2×C4×C47—21no—
558C2×C4×C47—21no—
559C2×C4×C47—44no—
560C2×C4×C47—44no—
561C2×C4×C47—82no—
562C2×Dic47—28no—
563C2×Dic47—21no—
564C2×Dic47—21no—
565C2×Dic47—21no—
566C2×Dic47—21no—
567C2×Dic47—21no—
568C2×Dic47—21no—
569C2×Dic47—21no—
570C2×Dic47—21no—
571C2×Dic47—21no—
572C2×Dic47—21no—
573C2×Dic47—21no—
574C2×Dic47—21no—
575C2×Dic47—21no—
576C2×Dic47—21no—
577C2×Dic47—21no—
578C2×Dic47—21no—
579C2×Dic47—21no—
580C2×Dic47—21no—
581C2×Dic47—21no—
582C2×Dic47—21no—
583C2×Dic47—21no—
584C2×Dic47—21no—
585C2×Dic47—21no—
586C2×Dic47—21no—
587C2×Dic47—21no—
588C2×Dic47—21no—
589C2×Dic47—21no—
590C2×Dic47—21no—
591C2×Dic47—21no—
592C2×Dic47—21no—
593C2×Dic47—21no—
594C2×Dic47—21no—
595C2×Dic47—21no—
596C2×Dic47—21no—
597C2×Dic47—21no—
598C2×Dic47—21no—
599C2×Dic47—21no—
600C2×Dic47—21no—
601C2×Dic47—21no—
602C2×Dic47—21no—
603C2×Dic47—21no—
604C2×Dic47—21no—
605C2×Dic47—21no—
606C2×Dic47—44no—
607C2×Dic47—44no—
608C2×Dic47—82no—
609C2×Dic47—82no—
610C2×Dic47C2×#4112yes—
611C2×Dic47C2×#4112yes—
612C2×Dic47H(5,𝔽2)12yes—
613C2×Dic47H(5,𝔽2)12yes—
614C2×Dic472−1+412yes—
615Dic94—44no—
616Dic94—44no—
617Dic94—44no—
618Dic94—44no—
619Dic94—82no—
620#36810—471nomaximal, Sylow
621C22×C47—22no—
622C22×C47—22no—
623C22×C47—22no—
624C22×C47—22no—
625C22×C47—22no—
626C22×C47—22no—
627C22×C47—41no—
628C22×C47—41no—
629C22×C47—41no—
630C22×C47—41no—
631C22×C47—41no—
632C22×C47—41no—
633C22×C47—41no—
634C22×C47#54114yes—
635C22×C47C22×#4111yescharacteristic
636C22×C47C2×H(5,𝔽2)11yescharacteristic
637C22×C47C2×H(5,𝔽2)11yescharacteristic
638C22×C47C2×2−1+411yescharacteristic
639C22×C47C2×2−1+411yescharacteristic
640C22×C47C2×2−1+411yescharacteristic
641C22×C47#58511yescharacteristic
642C4×C47—41no—
643C4×C47—41no—
644C4×C47—41no—
645C4×C47—41no—
646C4×C47—41no—
647C4×C47—41no—
648C4×C47—41no—
649C4×C47—41no—
650C4×C47—41no—
651C4×C47—41no—
652C4×C47—41no—
653C4×C47—41no—
654C4×C47—41no—
655Dic47—22no—
656Dic47—22no—
657Dic47—22no—
658Dic47—22no—
659Dic47—22no—
660Dic47—41no—
661Dic47—41no—
662Dic47—41no—
663Dic47—41no—
664Dic47—41no—
665Dic47—41no—
666Dic47—41no—
667Dic47—41no—
668Dic47—41no—
669Dic47—41no—
670Dic47—41no—
671#2852—471no—
672#2851—471no—
673#2798—471no—
674#2789—471no—
675#2762—471no—
676#2762—471no—
677#2758—471no—
678#2758—471no—
679#2755—471no—
680#2754—471no—
681#2716—471no—
682#2716—471no—
683#2713—471no—
684#2713—471no—
685#2704—471no—
686#2698—471no—
687#2690—471no—
688#2689—471no—
689#2646—471no—
690#2643D4711yescharacteristic
691#2569—471no—
692#2564—471no—
693#2510—471no—
694#2505—471no—
695#2481—471no—
696#2473—471no—
697#2434—471no—
698#2409—471no—
699#2329—471no—
700#2318—471no—
701C2×#391—471no—
702C2×C47—24no—
703C2×C47—81no—
704C2×C47C2×#54111yescharacteristic
705C2×C47#349011yescharacteristic
706C2×C47#350711yescharacteristic
707C2×C47#353811yescharacteristic
708C2×C47#354111yescharacteristic
709C2×C47#355211yescharacteristic
710C2×C47#356111yescharacteristic
711C23×Q8—471no—
712C2×C4⋊Q8—471no—
713C2×C4⋊Q8—471no—
714C2×#126—471no—
715C2×#126—471no—
716C2×#125—471no—
717C2×#125—471no—
718C2×C22⋊Q8—471no—
719C2×C22⋊Q8—471no—
720C2×C22⋊Q8—471no—
721C2×C4×D4—471no—
722C22×C4⋊C4—471no—
723C22×C42—471no—
724#401—471no—
725#401C2×D4711yescharacteristic
726#400—471no—
727#400—471no—
728#400—471no—
729#400—471no—
730#400—471no—
731#400—471no—
732#400—471no—
733#400—471no—
734#400—471no—
735#400—471no—
736#400—471no—
737#400—471no—
738#400—471no—
739#400—471no—
740#400C2×D4711yescharacteristic
741#400C2×D4711yescharacteristic
742#400C2×D4711yescharacteristic
743#399—471no—
744#398—471no—
745#398—471no—
746#398—471no—
747#398—471no—
748#398—471no—
749#398—471no—
750#398—471no—
751#398—471no—
752#398—471no—
753#398—471no—
754#397—471no—
755#397—471no—
756#397—471no—
757#397C2×D4711yescharacteristic
758#397C2×D4711yescharacteristic
759#397C2×D4711yescharacteristic
760#396—471no—
761#396C2×D4711yescharacteristic
762#395—471no—
763#395—471no—
764#395—471no—
765#395—471no—
766#395—471no—
767#395—471no—
768#395—471no—
769#393—471no—
770#393—471no—
771#393—471no—
772#391—471no—
773#391—471no—
774#391—471no—
775#391—471no—
776#391—471no—
777#391—471no—
778#391—471no—
779#391—471no—
780#391—471no—
781#391—471no—
782#391—471no—
783#391—471no—
784#391—471no—
785#391—471no—
786#389—471no—
787#389—471no—
788#389—471no—
789#389—471no—
790#389—471no—
791#389—471no—
792#388—471no—
793#388—471no—
794#388—471no—
795#388—471no—
796#388—471no—
797#388—471no—
798#388—471no—
799#388—471no—
800#387—471no—
801#387—471no—
802#387—471no—
803#387—471no—
804#387—471no—
805#387—471no—
806#387—471no—
807#387—471no—
808#387—471no—
809#387—471no—
810#387—471no—
811#387—471no—
812#387—471no—
813#387—471no—
814#387—471no—
815#387—471no—
816#387—471no—
817#387—471no—
818#387—471no—
819#387—471no—
820#387—471no—
821#387—471no—
822#387—471no—
823#387—471no—
824#387—471no—
825#387—471no—
826#386—471no—
827#386—471no—
828#386—471no—
829#386C2×D4711yescharacteristic
830#386C2×D4711yescharacteristic
831#386C2×D4711yescharacteristic
832#385—471no—
833#385—471no—
834#385—471no—
835#385—471no—
836#385—471no—
837#385—471no—
838#385—471no—
839#385—471no—
840#385—471no—
841#385—471no—
842#385—471no—
843#385C2×D4711yescharacteristic
844#385C2×D4711yescharacteristic
845#385C2×D4711yescharacteristic
846#383—471no—
847#383—471no—
848#383—471no—
849#382—471no—
850#382—471no—
851#382—471no—
852#381—471no—
853#380—471no—
854#380—471no—
855#380—471no—
856#380—471no—
857#380—471no—
858#380—471no—
859C4×C22⋊C4—471no—
860C4×C22⋊C4—471no—
861C4×C22⋊C4—471no—
862C2×#95—471no—
863C2×#95—471no—
864C2×#95—471no—
865C2×#95C2×D4711yescharacteristic
866C47#3681011yescharacteristic, complemented, Sylow
867C22×Q8—471no—
868C22×Q8—471no—
869C22×Q8—471no—
870C22×Q8—471no—
871C22×Q8—471no—
872C22×Q8—944no—
873C22×Q8—1882no—
874C22×Q8—1882no—
875C22×D4C22×D4711yescharacteristic
876C23×C4—471no—
877C23×C4—471no—
878C23×C4—471no—
879C23×C4—471no—
880C23×C4—471no—
881C23×C4C22×D4711yescharacteristic
882C23×C4C22×D4711yescharacteristic
883C23×C4C22×D4711yescharacteristic
884C4⋊Q8—1882no—
885C4⋊Q8—1882no—
886#126—1882no—
887#126—1882no—
888#125—1882no—
889#125—1882no—
890C22⋊Q8—944no—
891C22⋊Q8—1882no—
892C22⋊Q8—1882no—
893C4×D4—944no—
894C2×C4⋊C4—471no—
895C2×C4⋊C4—471no—
896C2×C4⋊C4—471no—
897C2×C4⋊C4—471no—
898C2×C4⋊C4—471no—
899C2×C4⋊C4—471no—
900C2×C4⋊C4—471no—
901C2×C4⋊C4—471no—
902C2×C4⋊C4—471no—
903C2×C4⋊C4—471no—
904C2×C4⋊C4—471no—
905C2×C4⋊C4—471no—
906C2×C4⋊C4—471no—
907C2×C4⋊C4—471no—
908C2×C4⋊C4—471no—
909C2×C4⋊C4—471no—
910C2×C4⋊C4—471no—
911C2×C4⋊C4—471no—
912C2×C4⋊C4—471no—
913C2×C4⋊C4—471no—
914C2×C4⋊C4—471no—
915C2×C4⋊C4—471no—
916C2×C4⋊C4—471no—
917C2×C4⋊C4—471no—
918C2×C4⋊C4—471no—
919C2×C4⋊C4—471no—
920C2×C4⋊C4—471no—
921C2×C4⋊C4—471no—
922C2×C4⋊C4—471no—
923C2×C4⋊C4—471no—
924C2×C4⋊C4—471no—
925C2×C4⋊C4—471no—
926C2×C4⋊C4—471no—
927C2×C4⋊C4—471no—
928C2×C4⋊C4—471no—
929C2×C4⋊C4—471no—
930C2×C4⋊C4—1882no—
931C2×C4⋊C4C22×D4711yescharacteristic
932C2×C4⋊C4C22×D4711yescharacteristic
933C2×C4⋊C4C22×D4711yescharacteristic
934C2×C4⋊C4C22×D4711yescharacteristic
935C2×C4⋊C4C22×D4711yescharacteristic
936C2×C4⋊C4C22×D4711yescharacteristic
937C2×C22⋊C4—471no—
938C2×C22⋊C4—471no—
939C2×C22⋊C4—471no—
940C2×C22⋊C4—471no—
941C2×C22⋊C4—471no—
942C2×C22⋊C4—471no—
943C2×C22⋊C4—471no—
944C2×C22⋊C4—471no—
945C2×C22⋊C4—471no—
946C2×C22⋊C4—471no—
947C2×C22⋊C4—471no—
948C2×C22⋊C4C22×D4711yescharacteristic
949C2×C22⋊C4C22×D4711yescharacteristic
950C2×C22⋊C4C22×D4711yescharacteristic
951C2×C22⋊C4C22×D4711yescharacteristic
952C2×C22⋊C4C22×D4711yescharacteristic
953C2×C22⋊C4C22×D4711yescharacteristic
954C2×C22⋊C4C22×D4711yescharacteristic
955C2×C22⋊C4C22×D4711yescharacteristic
956C2×C22⋊C4C22×D4711yescharacteristic
957C2×C42—471no—
958C2×C42—471no—
959C2×C42—471no—
960C2×C42—471no—
961C2×C42—471no—
962C2×C42—471no—
963C2×C42—471no—
964C2×C42—471no—
965C2×C42—471no—
966C2×C42—471no—
967C2×C42—471no—
968C2×C42—1882no—
969#95—471no—
970#95—471no—
971#95—471no—
972#95—471no—
973#95—471no—
974#95—471no—
975#95—471no—
976#95—471no—
977#95—471no—
978#95—471no—
979#95—471no—
980#95—471no—
981#95—471no—
982#95—471no—
983#95—471no—
984#95—471no—
985#95—471no—
986#95—471no—
987#95—471no—
988#95—471no—
989#95—471no—
990#95—471no—
991#95—471no—
992#95—471no—
993#95—471no—
994#95—471no—
995#95—471no—
996#95—471no—
997#95—471no—
998#95—471no—
999#95—471no—
1000#95—471no—
1001#95—471no—
1002#95—471no—
1003#95—471no—
1004#95—471no—
1005#95—471no—
1006#95—471no—
1007#95—471no—
1008#95—471no—
1009#95—471no—
1010#95—471no—
1011#95—471no—
1012#95—471no—
1013#95—471no—
1014#95—471no—
1015#95—471no—
1016#95—471no—
1017#95—471no—
1018#95—471no—
1019#95—471no—
1020#95—471no—
1021#95C22×D4711yescharacteristic
1022#95C22×D4711yescharacteristic
1023#95C22×D4711yescharacteristic
1024#95C22×D4711yescharacteristic
1025#95C22×D4711yescharacteristic
1026#95C22×D4711yescharacteristic
1027#95C22×D4711yescharacteristic
1028#95C22×D4711yescharacteristic
1029#95C22×D4711yescharacteristic
1030#95C22×D4711yescharacteristic
1031#95C22×D4711yescharacteristic
1032#95C22×D4711yescharacteristic
1033#95C22×D4711yescharacteristic
1034#95C22×D4711yescharacteristic
1035#95C22×D4711yescharacteristic
1036#95C22×D4711yescharacteristic
1037C24C23×D4711yescharacteristic
1038C24C23×D4711yescharacteristic
1039C2×Q8—942no—
1040C2×Q8—942no—
1041C2×Q8—942no—
1042C2×Q8—942no—
1043C2×Q8—942no—
1044C2×Q8—942no—
1045C2×Q8—942no—
1046C2×Q8—942no—
1047C2×Q8—942no—
1048C2×Q8—1881no—
1049C2×Q8—1881no—
1050C2×Q8—1881no—
1051C2×Q8—1881no—
1052C2×Q8—1881no—
1053C2×Q8—1881no—
1054C2×Q8—18816no—
1055C2×D4—22no—
1056C2×D4—22no—
1057C2×D4—22no—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—22no—
1061C22×C4—41no—
1062C22×C4—41no—
1063C22×C4—41no—
1064C22×C4—41no—
1065C22×C4—41no—
1066C22×C4—41no—
1067C22×C4—471no—
1068C22×C4—471no—
1069C22×C4—471no—
1070C22×C4—471no—
1071C22×C4—471no—
1072C22×C4—474no—
1073C22×C4—471no—
1074C22×C4—471no—
1075C22×C4—471no—
1076C22×C4—471no—
1077C22×C4—471no—
1078C22×C4—471no—
1079C22×C4—471no—
1080C22×C4—471no—
1081C22×C4—471no—
1082C22×C4—471no—
1083C22×C4—471no—
1084C22×C4—942no—
1085C22×C4—942no—
1086C22×C4—942no—
1087C22×C4—942no—
1088C22×C4—942no—
1089C22×C4—942no—
1090C22×C4—942no—
1091C22×C4—1881no—
1092C22×C4—1881no—
1093C22×C4—1881no—
1094C22×C4—1881no—
1095C22×C4—1881no—
1096C22×C4—1881no—
1097C22×C4—1881no—
1098C22×C4C23×D4711yescharacteristic
1099C22×C4C23×D4711yescharacteristic
1100C22×C4C23×D4711yescharacteristic
1101C22×C4C23×D4711yescharacteristic
1102C22×C4C23×D4711yescharacteristic
1103C22×C4C23×D4711yescharacteristic
1104C22×C4C23×D4711yescharacteristic
1105C22×C4C23×D4711yescharacteristic
1106C22×C4C23×D4711yescharacteristic
1107C22×C4C23×D4711yescharacteristic
1108C22×C4C23×D4711yescharacteristic
1109C22×C4C23×D4711yescharacteristic
1110C22×C4C23×D4711yescharacteristic
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—41no—
1114C4⋊C4—41no—
1115C4⋊C4—41no—
1116C4⋊C4—41no—
1117C4⋊C4—942no—
1118C4⋊C4—942no—
1119C4⋊C4—942no—
1120C4⋊C4—942no—
1121C4⋊C4—942no—
1122C4⋊C4—942no—
1123C4⋊C4—942no—
1124C4⋊C4—942no—
1125C4⋊C4—942no—
1126C4⋊C4—942no—
1127C4⋊C4—942no—
1128C4⋊C4—942no—
1129C4⋊C4—942no—
1130C4⋊C4—942no—
1131C4⋊C4—942no—
1132C4⋊C4—1881no—
1133C4⋊C4—1881no—
1134C4⋊C4—1881no—
1135C4⋊C4—1881no—
1136C4⋊C4—1881no—
1137C4⋊C4—1881no—
1138C4⋊C4—1881no—
1139C4⋊C4—1881no—
1140C4⋊C4—1881no—
1141C4⋊C4—1881no—
1142C4⋊C4—1881no—
1143C4⋊C4—1881no—
1144C4⋊C4—1881no—
1145C4⋊C4—1881no—
1146C4⋊C4—1881no—
1147C4⋊C4—1881no—
1148C4⋊C4—1881no—
1149C4⋊C4—1881no—
1150C4⋊C4—1881no—
1151C4⋊C4—1881no—
1152C4⋊C4—1881no—
1153C22⋊C4—22no—
1154C22⋊C4—22no—
1155C22⋊C4—22no—
1156C22⋊C4—41no—
1157C22⋊C4—41no—
1158C22⋊C4—41no—
1159C22⋊C4—41no—
1160C22⋊C4—41no—
1161C22⋊C4—41no—
1162C22⋊C4—942no—
1163C22⋊C4—942no—
1164C22⋊C4—942no—
1165C22⋊C4—942no—
1166C22⋊C4—942no—
1167C22⋊C4—942no—
1168C22⋊C4—942no—
1169C22⋊C4—942no—
1170C22⋊C4—1881no—
1171C22⋊C4—1881no—
1172C22⋊C4—1881no—
1173C42—942no—
1174C42—942no—
1175C42—942no—
1176C42—1881no—
1177C42—1881no—
1178C42—1881no—
1179C42—1881no—
1180C42—1881no—
1181C42—1881no—
1182C42—1881no—
1183C42—1881no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23#41×D4712yes—
1196C23#1309407112yes—
1197C23#1309407112yes—
1198C23C24×D4711yescharacteristic
1199Q8—3762no—
1200Q8—1884no—
1201Q8—1884no—
1202Q8—1884no—
1203Q8—1884no—
1204D4—44no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—44no—
1245C2×C4—44no—
1246C2×C4—82no—
1247C2×C4—472no—
1248C2×C4—472no—
1249C2×C4—472no—
1250C2×C4—472no—
1251C2×C4—472no—
1252C2×C4—948no—
1253C2×C4—941no—
1254C2×C4—941no—
1255C2×C4—941no—
1256C2×C4—941no—
1257C2×C4—941no—
1258C2×C4—941no—
1259C2×C4—941no—
1260C2×C4—941no—
1261C2×C4—941no—
1262C2×C4—941no—
1263C2×C4—941no—
1264C2×C4—941no—
1265C2×C4—941no—
1266C2×C4—941no—
1267C2×C4—941no—
1268C2×C4—941no—
1269C2×C4—941no—
1270C2×C4—941no—
1271C2×C4—941no—
1272C2×C4—941no—
1273C2×C4—941no—
1274C2×C4—941no—
1275C2×C4—941no—
1276C2×C4—941no—
1277C2×C4—941no—
1278C2×C4—941no—
1279C2×C4—941no—
1280C2×C4—941no—
1281C2×C4—941no—
1282C2×C4—941no—
1283C2×C4—941no—
1284C2×C4—941no—
1285C2×C4—941no—
1286C2×C4—941no—
1287C2×C4—941no—
1288C2×C4—941no—
1289C2×C4—941no—
1290C2×C4—941no—
1291C2×C4—941no—
1292C2×C4—941no—
1293C2×C4—941no—
1294C2×C4—941no—
1295C2×C4—941no—
1296C2×C4—3762no—
1297C2×C4—3762no—
1298C2×C4—1884no—
1299C2×C4—1884no—
1300C22—22no—
1301C22—22no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22#1568973014yes—
1314C22C2×#41×D4711yescharacteristic
1315C22H(5,𝔽2)×D4711yescharacteristic
1316C22H(5,𝔽2)×D4711yescharacteristic
1317C222−1+4×D4711yescharacteristic
1318C22C2×#1309407111yescharacteristic
1319C22C2×#1309407111yescharacteristic
1320C22#1568995811yescharacteristic
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—942no—
1335C4—942no—
1336C4—942no—
1337C4—942no—
1338C4—942no—
1339C4—1881no—
1340C4—1881no—
1341C4—1881no—
1342C4—1881no—
1343C4—1881no—
1344C4—1881no—
1345C4—1881no—
1346C4—1881no—
1347C4—1881no—
1348C4—1881no—
1349C4—1881no—
1350C2—24no—
1351C2—81no—
1352C2C2×#1568973011yescharacteristic
1353C2#2025707411yescharacteristic
1354C2#2025724811yescharacteristic
1355C2#2025763511yescharacteristic
1356C2#2025766811yescharacteristic
1357C2#2025782111yescharacteristic
1358C2#2025794811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2643C2
prime radicalC22×D4×C47C23
hypercenter#2643D47
hypocenterC47#36810
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2643

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20251694C2semidirect
3. #20251267C2semidirect
4. #20251142C2semidirect
5. #20250797C2semidirect
6. #20250789C2semidirect
7. #20250747C2semidirect
8. #20250745C2semidirect
9. #20250702C2semidirect
10. #20250679C2semidirect
11. #20250221C2semidirect
12. #20250220C2semidirect
13. #20250174C2semidirect
14. #20250168C2semidirect
15. #20250039C2semidirect
16. #20249964C2semidirect
17. #20249859C2semidirect
18. #20249845C2semidirect
19. #20249358C2semidirect
20. #20248614C2semidirect
23. #20247887C2semidirect
25. #20247536C2semidirect
26. #20247030C2semidirect
28. #20246119C2semidirect
30. C2×#15689027C2semidirect
866. C47#36810semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202517012
#202516942
#202512672
#202511422
#202507972
#202507892
#202507472
#202507452
#202507022
#202506792
#202502212
#202502202
#202501742
#202501682
#202500392
#202499642
#202498592
#202498452
#202493582
#202486142
#202485722
#202479462
#202478872
#202476542
#202475362
#202470302
#202467502
#202461192
#202460142
C2×#156890272
C47×#26432
#3681047