Finite Group Databasebeta

← #26430799

Subgroups — #26430799

Order 12032.

1526 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251724C211yesmaximal, characteristic, complemented
2#20251713C211yesmaximal, characteristic
3#20251379C211yesmaximal, characteristic, complemented
4#20251373C211yesmaximal, characteristic, complemented
5#20251302C211yesmaximal, characteristic, complemented
6#20251264C211yesmaximal, characteristic, complemented
7#20251208C211yesmaximal, characteristic, complemented
8#20251193C211yesmaximal, characteristic, complemented
9#20251169C211yesmaximal, characteristic, complemented
10#20251154C211yesmaximal, characteristic, complemented
11#20251145C211yesmaximal, characteristic, complemented
12#20251114C211yesmaximal, characteristic, complemented
13#20251076C211yesmaximal, characteristic, complemented
14#20250971C211yesmaximal, characteristic, complemented
15#20250962C211yesmaximal, characteristic, complemented
16#20250902C211yesmaximal, characteristic, complemented
17#20250848C211yesmaximal, characteristic, complemented
18#20250543C211yesmaximal, characteristic, complemented
19#20249360C211yesmaximal, characteristic, complemented
20#20249344C211yesmaximal, characteristic
21#20247891C211yesmaximal, characteristic, complemented
22#20247826C211yesmaximal, characteristic
23#20247775C211yesmaximal, characteristic, complemented
24#20247671C211yesmaximal, characteristic, complemented
25#20247214C211yesmaximal, characteristic
26#20247058C211yesmaximal, characteristic, complemented
27#20246867C211yesmaximal, characteristic
28#20246789C211yesmaximal, characteristic
29#20246057C211yesmaximal, characteristic
30C2×#15689004C211yesmaximal, characteristic, complemented
31C47×#2317C211yesmaximal, characteristic, complemented
32C2×#13094008C2211yescharacteristic
33C2×#13094007C2211yescharacteristic
34C2×#13094001C2211yescharacteristic
35C2×C4×C22⋊D47C2211yescharacteristic
36C22×Dic47⋊C4C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38C47⋊#401C2211yescharacteristic
39C47⋊#401C2211yescharacteristic
40#15689065C2211yescharacteristic
41#15689065C2211yescharacteristic
42#15689065C2211yescharacteristic
43#15689064C2211yescharacteristic
44#15689064C2211yescharacteristic
45#15689064C2211yescharacteristic
46#15689064C2211yescharacteristic
47#15689063C2211yescharacteristic
48#15689063C2211yescharacteristic
49#15689062C2211yescharacteristic
50#15689062C2211yescharacteristic
51#15689062C2211yescharacteristic
52#15689061C2211yescharacteristic
53#15689061C2211yescharacteristic
54#15689061C2211yescharacteristic
55#15689061C2211yescharacteristic
56#15689061C2211yescharacteristic
57#15689061C2211yescharacteristic
58#15689061C2211yescharacteristic
59#15689058C2211yescharacteristic
60#15689057C2211yescharacteristic
61#15689056C2211yescharacteristic
62#15689056C2211yescharacteristic
63#15689056C2211yescharacteristic
64#15689056C2211yescharacteristic
65#15689054C2211yescharacteristic
66#15689054C2211yescharacteristic
67#15689054C2211yescharacteristic
68#15689054C2211yescharacteristic
69#15689054C2211yescharacteristic
70#15689053C2211yescharacteristic
71#15689053C2211yescharacteristic
72#15689053C2211yescharacteristic
73#15689053C2211yescharacteristic
74#15689052C2211yescharacteristic
75#15689052C2211yescharacteristic
76#15689050C2211yescharacteristic
77#15689049C2211yescharacteristic
78#15689049C2211yescharacteristic
79#15689049C2211yescharacteristic
80#15689045C2211yescharacteristic
81#15689045C2211yescharacteristic
82#15689045C2211yescharacteristic
83#15689045C2211yescharacteristic
84#15689043C2211yescharacteristic
85#15689036C2211yescharacteristic
86#15689029C2211yescharacteristic
87#15689027C2211yescharacteristic
88#15689027C2211yescharacteristic
89#15689027C2211yescharacteristic
90#15689021C2211yescharacteristic
91#15689021C2211yescharacteristic
92#15689021C2211yescharacteristic
93#15689020C2211yescharacteristic
94#15689018C2211yescharacteristic
95#15689018C2211yescharacteristic
96#15689018C2211yescharacteristic
97#15689018C2211yescharacteristic
98#15689014C2211yescharacteristic
99#15689014C2211yescharacteristic
100#15689014C2211yescharacteristic
101#15689014C2211yescharacteristic
102#15689013C2211yescharacteristic
103#15689013C2211yescharacteristic
104#15689013C2211yescharacteristic
105#15689013C2211yescharacteristic
106#15689012C2211yescharacteristic
107#15689012C2211yescharacteristic
108#15689010C2211yescharacteristic
109#15689010C2211yescharacteristic
110#15689010C2211yescharacteristic
111#15689009C2211yescharacteristic
112#15689009C2211yescharacteristic
113#15689009C2211yescharacteristic
114#15689009C2211yescharacteristic
115#15689009C2211yescharacteristic
116#15689009C2211yescharacteristic
117#15689009C2211yescharacteristic
118#15689009C2211yescharacteristic
119#15689007C2211yescharacteristic
120#15689007C2211yescharacteristic
121#15689007C2211yescharacteristic
122#15689007C2211yescharacteristic
123#15689007C2211yescharacteristic
124#15689007C2211yescharacteristic
125#15689007C2211yescharacteristic
126#15689007C2211yescharacteristic
127#15689006C2211yescharacteristic
128#15689005C2211yescharacteristic
129#15689005C2211yescharacteristic
130#15689004C2211yescharacteristic
131#15689004C2211yescharacteristic
132#15689004C2211yescharacteristic
133#15689004C2211yescharacteristic
134#15689004C2211yescharacteristic
135#15689004C2211yescharacteristic
136#15689004C2211yescharacteristic
137#15689004C2211yescharacteristic
138#15689004C2211yescharacteristic
139#15689004C2211yescharacteristic
140#15689004C2211yescharacteristic
141#15689004C2211yescharacteristic
142#15689002C2211yescharacteristic
143#15689000C2211yescharacteristic
144#15689000C2211yescharacteristic
145#15689000C2211yescharacteristic
146#15688998C2211yescharacteristic
147#15688998C2211yescharacteristic
148#15688996C2211yescharacteristic
149#15688995C2211yescharacteristic
150#15688995C2211yescharacteristic
151#15688995C2211yescharacteristic
152#15688994C2211yescharacteristic
153#15688994C2211yescharacteristic
154#15688994C2211yescharacteristic
155#15688994C2211yescharacteristic
156#15688990C2211yescharacteristic
157#15688987C2211yescharacteristic
158#15688986C2211yescharacteristic
159#15688985C2211yescharacteristic
160#15688984C2211yescharacteristic
161#15688984C2211yescharacteristic
162#15688984C2211yescharacteristic
163#15688982C2211yescharacteristic
164#15688981C2211yescharacteristic
165#15688981C2211yescharacteristic
166#15688981C2211yescharacteristic
167C4×C22⋊Dic47C2211yescharacteristic
168C2×C47⋊#95C2211yescharacteristic
169C2×C47⋊#95C2211yescharacteristic
170C2×C47⋊#95C2211yescharacteristic
171C2×C47⋊#95C2211yescharacteristic
172C2×#117×C47C2211yescharacteristic
173C2×#117×C47C2211yescharacteristic
174C22×C4⋊C4×C47C2211yescharacteristic
175C47×#389C2211yescharacteristic
176C47×#389C2211yescharacteristic
177C47×#389C2211yescharacteristic
178C47×#389C2211yescharacteristic
179C47×#385C2211yescharacteristic
180C47×#385C2211yescharacteristic
181C47×#385C2211yescharacteristic
182C47×#385C2211yescharacteristic
183C47×#384C2211yescharacteristic
184C47×#384C2211yescharacteristic
185C47×#382C2211yescharacteristic
186C47×#382C2211yescharacteristic
187C22×Dic94C2311yescharacteristic
188C22×C22⋊D47C2311yescharacteristic
189C23×Dic47C2311yescharacteristic
190C23×Dic47C2311yescharacteristic
191C23×Dic47C2311yescharacteristic
192C23×Dic47C2311yescharacteristic
193C22×C4×D47C2311yescharacteristic
194#13094008—42no—
195#13094007—24no—
196#13094001—42no—
197C4×C22⋊D47—42no—
198C2×C4⋊Dic47C2311yescharacteristic
199C2×C4⋊Dic47C2311yescharacteristic
200C2×C4⋊Dic47C2311yescharacteristic
201C2×C4⋊Dic47C2311yescharacteristic
202C2×C4⋊Dic47C2311yescharacteristic
203C2×C4⋊Dic47C2311yescharacteristic
204C2×C4⋊Dic47C2311yescharacteristic
205C2×Dic47⋊C4—24no—
206C2×Dic47⋊C4C2311yescharacteristic
207C2×Dic47⋊C4C2311yescharacteristic
208C2×Dic47⋊C4C2311yescharacteristic
209C2×Dic47⋊C4C2311yescharacteristic
210C2×Dic47⋊C4C2311yescharacteristic
211C2×Dic47⋊C4C2311yescharacteristic
212C2×Dic47⋊C4C2311yescharacteristic
213C2×Dic47⋊C4C2311yescharacteristic
214C2×Dic47⋊C4C2311yescharacteristic
215C2×Dic47⋊C4C2311yescharacteristic
216C2×Dic47⋊C4C2311yescharacteristic
217C2×Dic47⋊C4C2311yescharacteristic
218C2×Dic47⋊C4C2311yescharacteristic
219C2×Dic47⋊C4C2311yescharacteristic
220C2×Dic47⋊C4C2311yescharacteristic
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×C22⋊Dic47C2311yescharacteristic
230C2×C22⋊Dic47C2311yescharacteristic
231C2×C22⋊Dic47C2311yescharacteristic
232C2×(C2×D47)⋊C4C2311yescharacteristic
233C2×(C2×D47)⋊C4C2311yescharacteristic
234C2×(C2×D47)⋊C4C2311yescharacteristic
235C2×(C2×D47)⋊C4C2311yescharacteristic
236C2×(C2×D47)⋊C4C2311yescharacteristic
237C2×(C2×D47)⋊C4C2311yescharacteristic
238C2×(C2×D47)⋊C4C2311yescharacteristic
239C2×(C2×D47)⋊C4C2311yescharacteristic
240C2×(C2×D47)⋊C4C2311yescharacteristic
241C2×(C2×D47)⋊C4C2311yescharacteristic
242C2×(C2×D47)⋊C4C2311yescharacteristic
243C2×(C2×D47)⋊C4C2311yescharacteristic
244C2×(C2×D47)⋊C4C2311yescharacteristic
245C2×C4×Dic47—42no—
246C2×C4×Dic47C2311yescharacteristic
247C2×C4×Dic47C2311yescharacteristic
248C2×C4×Dic47C2311yescharacteristic
249C2×C4×Dic47C2311yescharacteristic
250C2×C4×Dic47C2311yescharacteristic
251C2×C4×Dic47C2311yescharacteristic
252C2×C4×Dic47C2311yescharacteristic
253C47⋊#95C2311yescharacteristic
254C47⋊#95C2311yescharacteristic
255C47⋊#95C2311yescharacteristic
256C47⋊#95C2311yescharacteristic
257C47⋊#95C2311yescharacteristic
258C47⋊#95C2311yescharacteristic
259C47⋊#95C2311yescharacteristic
260C47⋊#95C2311yescharacteristic
261C47⋊#95C2311yescharacteristic
262C47⋊#95C2311yescharacteristic
263C47⋊#95C2311yescharacteristic
264C47⋊#95C2311yescharacteristic
265C47⋊#95C2311yescharacteristic
266C47⋊#95C2311yescharacteristic
267C47⋊#95C2311yescharacteristic
268C47⋊#95C2311yescharacteristic
269C47⋊#95C2311yescharacteristic
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
313C23×C4×C47C2311yescharacteristic
314C23×C4×C47C2311yescharacteristic
315C23×C4×C47C2311yescharacteristic
316#117×C47—24no—
317#117×C47—42no—
318C2×C4⋊C4×C47—42no—
319C2×C4⋊C4×C47C2311yescharacteristic
320C2×C4⋊C4×C47C2311yescharacteristic
321C2×C4⋊C4×C47C2311yescharacteristic
322C2×C4⋊C4×C47C2311yescharacteristic
323C2×C4⋊C4×C47C2311yescharacteristic
324C2×C4⋊C4×C47C2311yescharacteristic
325C2×C4⋊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×C4⋊C4×C47C2311yescharacteristic
333C2×C4⋊C4×C47C2311yescharacteristic
334C2×C4⋊C4×C47C2311yescharacteristic
335C2×C22⋊C4×C47C2311yescharacteristic
336C2×C22⋊C4×C47C2311yescharacteristic
337C2×C22⋊C4×C47C2311yescharacteristic
338C2×C22⋊C4×C47C2311yescharacteristic
339C2×C42×C47C2311yescharacteristic
340C2×C42×C47C2311yescharacteristic
341C2×C42×C47C2311yescharacteristic
342C2×C42×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
351C24×C47C2411yescharacteristic
352C23×D47C2411yescharacteristic
353C22×C4×C47—22no—
354C22×C4×C47—22no—
355C22×C4×C47—22no—
356C22×C4×C47—22no—
357C22×C4×C47—41no—
358C22×C4×C47—41no—
359C22×C4×C47—41no—
360C22×C4×C47—41no—
361C22×C4×C47#4114yes—
362C22×C4×C47C2411yescharacteristic
363C22×C4×C47C2411yescharacteristic
364C22×C4×C47C2411yescharacteristic
365C22×C4×C47C2411yescharacteristic
366C22×C4×C47C2411yescharacteristic
367C22×C4×C47C2411yescharacteristic
368C22×C4×C47C2411yescharacteristic
369C22×C4×C47C2411yescharacteristic
370C22×C4×C47C2411yescharacteristic
371C22×C4×C47C2411yescharacteristic
372C22×C4×C47C2411yescharacteristic
373C22×C4×C47C2411yescharacteristic
374C22×C4×C47C2411yescharacteristic
375C22×C4×C47C2411yescharacteristic
376C2×C22⋊D47—22no—
377C2×C22⋊D47—22no—
378C2×C22⋊D47—22no—
379C22×Dic47—22no—
380C22×Dic47—22no—
381C22×Dic47—22no—
382C22×Dic47—22no—
383C22×Dic47—22no—
384C22×Dic47—22no—
385C22×Dic47—22no—
386C22×Dic47—41no—
387C22×Dic47—41no—
388C22×Dic47—41no—
389C22×Dic47—41no—
390C22×Dic47—41no—
391C22×Dic47C2411yescharacteristic
392C22×Dic47C2411yescharacteristic
393C22×Dic47C2411yescharacteristic
394C22×Dic47C2411yescharacteristic
395C22×Dic47C2411yescharacteristic
396C22×Dic47C2411yescharacteristic
397C22×Dic47C2411yescharacteristic
398C22×Dic47C2411yescharacteristic
399C22×Dic47C2411yescharacteristic
400C22×Dic47C2411yescharacteristic
401C22×Dic47C2411yescharacteristic
402C22×Dic47C2411yescharacteristic
403C22×Dic47C2411yescharacteristic
404C22×Dic47C2411yescharacteristic
405C22×Dic47C2411yescharacteristic
406C2×C4×D47—41no—
407C2×C4×D47—41no—
408C2×C4×D47—41no—
409C2×Dic94—22no—
410C2×Dic94—41no—
411C2×Dic94—41no—
412C4⋊C4×C47—22no—
413C4⋊C4×C47—22no—
414C4⋊C4×C47—41no—
415C4⋊C4×C47—41no—
416C4⋊C4×C47—41no—
417C4⋊C4×C47—41no—
418C4⋊C4×C47—41no—
419C4⋊C4×C47—41no—
420C4⋊C4×C47—41no—
421C4⋊C4×C47—41no—
422C4⋊C4×C47—41no—
423C4⋊C4×C47—41no—
424C4⋊C4×C47—41no—
425C4⋊C4×C47—41no—
426C4⋊C4×C47—41no—
427C4⋊C4×C47—41no—
428C22⋊C4×C47—22no—
429C22⋊C4×C47—22no—
430C22⋊C4×C47—22no—
431C22⋊C4×C47—22no—
432C42×C47—22no—
433C42×C47—22no—
434C42×C47—41no—
435C42×C47—41no—
436C22⋊Dic47—22no—
437C22⋊Dic47—22no—
438C22⋊Dic47—22no—
439(C2×D47)⋊C4—22no—
440(C2×D47)⋊C4—22no—
441(C2×D47)⋊C4—22no—
442(C2×D47)⋊C4—41no—
443(C2×D47)⋊C4—41no—
444(C2×D47)⋊C4—41no—
445(C2×D47)⋊C4—41no—
446(C2×D47)⋊C4—41no—
447(C2×D47)⋊C4—41no—
448(C2×D47)⋊C4—41no—
449(C2×D47)⋊C4—41no—
450(C2×D47)⋊C4—41no—
451(C2×D47)⋊C4—41no—
452C4⋊Dic47—41no—
453C4⋊Dic47—41no—
454C4⋊Dic47—41no—
455C4⋊Dic47—41no—
456C4⋊Dic47—41no—
457C4⋊Dic47—41no—
458C4⋊Dic47—41no—
459Dic47⋊C4—22no—
460Dic47⋊C4—22no—
461Dic47⋊C4—22no—
462Dic47⋊C4—22no—
463Dic47⋊C4—22no—
464Dic47⋊C4—22no—
465Dic47⋊C4—22no—
466Dic47⋊C4—22no—
467Dic47⋊C4—41no—
468Dic47⋊C4—41no—
469Dic47⋊C4—41no—
470Dic47⋊C4—41no—
471Dic47⋊C4—41no—
472Dic47⋊C4—41no—
473Dic47⋊C4—41no—
474Dic47⋊C4—41no—
475Dic47⋊C4—41no—
476Dic47⋊C4—41no—
477Dic47⋊C4—41no—
478Dic47⋊C4—41no—
479Dic47⋊C4—41no—
480Dic47⋊C4—41no—
481Dic47⋊C4—41no—
482C4×Dic47—41no—
483C4×Dic47—41no—
484C4×Dic47—41no—
485C4×Dic47—41no—
486C4×Dic47—41no—
487C4×Dic47—41no—
488C4×Dic47—41no—
489C23×C47—21no—
490C23×C47—21no—
491C23×C47—21no—
492C23×C47—21no—
493C23×C47C2×#4112yes—
494C23×C47H(5,𝔽2)12yes—
495C23×C472−1+412yes—
496C23×C47C2511yescharacteristic
497C22×D47—21no—
498C22×D47—21no—
499C22×D47—21no—
500C22×D47—21no—
501C22×D47—21no—
502C22×D47—21no—
503C22×D47—21no—
504C2×C4×C47—28no—
505C2×C4×C47—21no—
506C2×C4×C47—21no—
507C2×C4×C47—21no—
508C2×C4×C47—21no—
509C2×C4×C47—21no—
510C2×C4×C47—21no—
511C2×C4×C47—21no—
512C2×C4×C47—21no—
513C2×C4×C47—21no—
514C2×C4×C47—21no—
515C2×C4×C47—21no—
516C2×C4×C47—21no—
517C2×C4×C47—21no—
518C2×C4×C47—21no—
519C2×C4×C47—21no—
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—44no—
546C2×C4×C47—82no—
547C2×C4×C47C2×#4112yes—
548C2×C4×C47C2×#4112yes—
549C22⋊D47—44no—
550C2×Dic47—21no—
551C2×Dic47—21no—
552C2×Dic47—21no—
553C2×Dic47—21no—
554C2×Dic47—21no—
555C2×Dic47—21no—
556C2×Dic47—21no—
557C2×Dic47—21no—
558C2×Dic47—21no—
559C2×Dic47—21no—
560C2×Dic47—21no—
561C2×Dic47—21no—
562C2×Dic47—21no—
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—44no—
595C2×Dic47—44no—
596C2×Dic47—44no—
597C2×Dic47—82no—
598C2×Dic472−1+412yes—
599C4×D47—82no—
600Dic94—82no—
601#36998—471nomaximal, Sylow
602C22×C47—22no—
603C22×C47—22no—
604C22×C47—22no—
605C22×C47—22no—
606C22×C47—22no—
607C22×C47—22no—
608C22×C47#53914yes—
609C22×C47C22×#4111yescharacteristic
610C22×C47C2×H(5,𝔽2)11yescharacteristic
611C22×C47C2×2−1+411yescharacteristic
612C22×C47C2×2−1+411yescharacteristic
613C22×C47#58511yescharacteristic
614C22×C47#58511yescharacteristic
615C22×C47#58511yescharacteristic
616C2×D47—41no—
617C2×D47—41no—
618C2×D47—41no—
619C2×D47—41no—
620C2×D47—41no—
621C2×D47—41no—
622C2×D47—41no—
623C4×C47—22no—
624C4×C47—22no—
625C4×C47—41no—
626C4×C47—41no—
627C4×C47—41no—
628C4×C47—41no—
629C4×C47—41no—
630C4×C47—41no—
631C4×C47—41no—
632C4×C47—41no—
633C4×C47—41no—
634C4×C47—41no—
635C4×C47—41no—
636C4×C47—41no—
637Dic47—22no—
638Dic47—41no—
639Dic47—41no—
640Dic47—41no—
641Dic47—41no—
642Dic47—41no—
643Dic47—41no—
644Dic47—41no—
645Dic47—41no—
646Dic47—41no—
647Dic47—41no—
648Dic47—41no—
649Dic47—41no—
650Dic47—41no—
651Dic47—41no—
652#2855—471no—
653#2853—471no—
654#2810—471no—
655#2809—471no—
656#2802—471no—
657#2798—471no—
658#2794—471no—
659#2793—471no—
660#2791—471no—
661#2790—471no—
662#2789—471no—
663#2787—471no—
664#2783—471no—
665#2776—471no—
666#2775—471no—
667#2771—471no—
668#2767—471no—
669#2744—471no—
670#2646—471no—
671#2643—471no—
672#2505—471no—
673#2498—471no—
674#2493—471no—
675#2484—471no—
676#2450—471no—
677#2438—471no—
678#2419—471no—
679#2413—471no—
680#2322—471no—
681#2317D4711yescharacteristic, complemented
682C2×#387—471no—
683C2×C47—24no—
684C2×C47C2×#53911yescharacteristic
685C2×C47#349311yescharacteristic
686C2×C47#350711yescharacteristic
687C2×C47#353311yescharacteristic
688C2×C47#353511yescharacteristic
689C2×C47#356311yescharacteristic
690C2×C47#356411yescharacteristic
691D47—81no—
692C2×#123—471no—
693C2×#123—471no—
694C2×C22⋊Q8—471no—
695C2×C4×D4—471no—
696C2×#117C2×D4711yescharacteristic
697C2×#117C2×D4711yescharacteristic
698C22×C4⋊C4—471no—
699C22×C4⋊C4C2×D4711yescharacteristic
700C22×C42—471no—
701#401—471no—
702#401—471no—
703#400—471no—
704#400—471no—
705#400—471no—
706#400—471no—
707#400—471no—
708#400—471no—
709#400—471no—
710#400—471no—
711#400—471no—
712#400—471no—
713#400—471no—
714#400—471no—
715#400—471no—
716#400—471no—
717#400—471no—
718#400—471no—
719#400—471no—
720#400—471no—
721#400—471no—
722#399—471no—
723#398—471no—
724#398—471no—
725#398—471no—
726#398—471no—
727#398—471no—
728#398—471no—
729#398—471no—
730#398—471no—
731#398—471no—
732#398—471no—
733#398—471no—
734#398—471no—
735#398—471no—
736#398—471no—
737#397—471no—
738#397—471no—
739#397—471no—
740#397—471no—
741#397—471no—
742#397—471no—
743#396—471no—
744#396—471no—
745#396—471no—
746#396—471no—
747#395—471no—
748#393—471no—
749#391—471no—
750#391—471no—
751#391—471no—
752#391—471no—
753#389—471no—
754#389—471no—
755#389—471no—
756#389—471no—
757#389—471no—
758#389—471no—
759#389—471no—
760#389—471no—
761#389C2×D4711yescharacteristic
762#389C2×D4711yescharacteristic
763#389C2×D4711yescharacteristic
764#389C2×D4711yescharacteristic
765#388—471no—
766#388—471no—
767#388—471no—
768#388—471no—
769#388—471no—
770#388—471no—
771#388—471no—
772#388—471no—
773#388—471no—
774#388—471no—
775#387—471no—
776#387—471no—
777#387—471no—
778#387—471no—
779#387—471no—
780#387—471no—
781#387—471no—
782#387—471no—
783#387—471no—
784#387—471no—
785#387—471no—
786#387—471no—
787#387—471no—
788#387—471no—
789#387—471no—
790#387—471no—
791#387—471no—
792#387—471no—
793#387—471no—
794#387—471no—
795#387—471no—
796#387—471no—
797#387—471no—
798#387—471no—
799#387—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#386—471no—
810#386—471no—
811#386—471no—
812#386—471no—
813#385—471no—
814#385—471no—
815#385—471no—
816#385—471no—
817#385—471no—
818#385—471no—
819#385—471no—
820#385—471no—
821#385—471no—
822#385—471no—
823#385C2×D4711yescharacteristic
824#385C2×D4711yescharacteristic
825#385C2×D4711yescharacteristic
826#385C2×D4711yescharacteristic
827#384C2×D4711yescharacteristic
828#384C2×D4711yescharacteristic
829#383—471no—
830#382—471no—
831#382C2×D4711yescharacteristic
832#382C2×D4711yescharacteristic
833#381—471no—
834#381—471no—
835#381—471no—
836#381—471no—
837#381—471no—
838#380—471no—
839#380—471no—
840#380—471no—
841#380—471no—
842C4×C22⋊C4—471no—
843C2×#95—471no—
844C2×#95—471no—
845C2×#95—471no—
846C2×#95—471no—
847C47#3699811yescharacteristic, complemented, Sylow
848C22×Q8—471no—
849C22×D4—471no—
850C23×C4—471no—
851C23×C4—471no—
852C23×C4—471no—
853C23×C4—471no—
854C23×C4—471no—
855C23×C4C22×D4711yescharacteristic
856C23×C4C22×D4711yescharacteristic
857C23×C4C22×D4711yescharacteristic
858#123—944no—
859#123—1882no—
860C22⋊Q8—1882no—
861C4×D4—1882no—
862#117—24no—
863#117—42no—
864C2×C4⋊C4—42no—
865C2×C4⋊C4—471no—
866C2×C4⋊C4—471no—
867C2×C4⋊C4—471no—
868C2×C4⋊C4—471no—
869C2×C4⋊C4—471no—
870C2×C4⋊C4—471no—
871C2×C4⋊C4—471no—
872C2×C4⋊C4—471no—
873C2×C4⋊C4—471no—
874C2×C4⋊C4—471no—
875C2×C4⋊C4—471no—
876C2×C4⋊C4—471no—
877C2×C4⋊C4—471no—
878C2×C4⋊C4—471no—
879C2×C4⋊C4—471no—
880C2×C4⋊C4—471no—
881C2×C4⋊C4—471no—
882C2×C4⋊C4—471no—
883C2×C4⋊C4—471no—
884C2×C4⋊C4—471no—
885C2×C4⋊C4—471no—
886C2×C4⋊C4—471no—
887C2×C4⋊C4—471no—
888C2×C4⋊C4—471no—
889C2×C4⋊C4—471no—
890C2×C4⋊C4—471no—
891C2×C4⋊C4—471no—
892C2×C4⋊C4—471no—
893C2×C4⋊C4—471no—
894C2×C4⋊C4—471no—
895C2×C4⋊C4—944no—
896C2×C4⋊C4C22×D4711yescharacteristic
897C2×C4⋊C4C22×D4711yescharacteristic
898C2×C4⋊C4C22×D4711yescharacteristic
899C2×C4⋊C4C22×D4711yescharacteristic
900C2×C4⋊C4C22×D4711yescharacteristic
901C2×C4⋊C4C22×D4711yescharacteristic
902C2×C4⋊C4C22×D4711yescharacteristic
903C2×C4⋊C4C22×D4711yescharacteristic
904C2×C4⋊C4C22×D4711yescharacteristic
905C2×C4⋊C4C22×D4711yescharacteristic
906C2×C4⋊C4C22×D4711yescharacteristic
907C2×C4⋊C4C22×D4711yescharacteristic
908C2×C4⋊C4C22×D4711yescharacteristic
909C2×C4⋊C4C22×D4711yescharacteristic
910C2×C4⋊C4C22×D4711yescharacteristic
911C2×C4⋊C4C22×D4711yescharacteristic
912C2×C22⋊C4—471no—
913C2×C22⋊C4—471no—
914C2×C22⋊C4—471no—
915C2×C22⋊C4—471no—
916C2×C22⋊C4—471no—
917C2×C22⋊C4—471no—
918C2×C22⋊C4—471no—
919C2×C22⋊C4—471no—
920C2×C22⋊C4—471no—
921C2×C22⋊C4—471no—
922C2×C22⋊C4—471no—
923C2×C22⋊C4—471no—
924C2×C22⋊C4—471no—
925C2×C22⋊C4—471no—
926C2×C22⋊C4—471no—
927C2×C22⋊C4—471no—
928C2×C22⋊C4C22×D4711yescharacteristic
929C2×C22⋊C4C22×D4711yescharacteristic
930C2×C22⋊C4C22×D4711yescharacteristic
931C2×C22⋊C4C22×D4711yescharacteristic
932C2×C42—471no—
933C2×C42—471no—
934C2×C42—471no—
935C2×C42—471no—
936C2×C42—471no—
937C2×C42—471no—
938C2×C42—471no—
939C2×C42—1882no—
940C2×C42C22×D4711yescharacteristic
941C2×C42C22×D4711yescharacteristic
942C2×C42C22×D4711yescharacteristic
943C2×C42C22×D4711yescharacteristic
944#95—471no—
945#95—471no—
946#95—471no—
947#95—471no—
948#95—471no—
949#95—471no—
950#95—471no—
951#95—471no—
952#95—471no—
953#95—471no—
954#95—471no—
955#95—471no—
956#95—471no—
957#95—471no—
958#95—471no—
959#95—471no—
960#95—471no—
961#95—471no—
962#95—471no—
963#95—471no—
964#95—471no—
965#95—471no—
966#95—471no—
967#95—471no—
968#95—471no—
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#95C22×D4711yescharacteristic
1005#95C22×D4711yescharacteristic
1006#95C22×D4711yescharacteristic
1007#95C22×D4711yescharacteristic
1008#95C22×D4711yescharacteristic
1009#95C22×D4711yescharacteristic
1010#95C22×D4711yescharacteristic
1011#95C22×D4711yescharacteristic
1012C24—471no—
1013C24C23×D4711yescharacteristic
1014C2×Q8—942no—
1015C2×Q8—1881no—
1016C2×Q8—1881no—
1017C2×D4—942no—
1018C2×D4—942no—
1019C2×D4—942no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—41no—
1025C22×C4—41no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—471no—
1029C22×C4—471no—
1030C22×C4—471no—
1031C22×C4—471no—
1032C22×C4—471no—
1033C22×C4—471no—
1034C22×C4—471no—
1035C22×C4—471no—
1036C22×C4—471no—
1037C22×C4—471no—
1038C22×C4—471no—
1039C22×C4—471no—
1040C22×C4—471no—
1041C22×C4—471no—
1042C22×C4—471no—
1043C22×C4—942no—
1044C22×C4—942no—
1045C22×C4—942no—
1046C22×C4—942no—
1047C22×C4—942no—
1048C22×C4—942no—
1049C22×C4—942no—
1050C22×C4—1881no—
1051C22×C4—1881no—
1052C22×C4—1881no—
1053C22×C4—1881no—
1054C22×C4—1881no—
1055C22×C4—1881no—
1056C22×C4—1881no—
1057C22×C4—1881no—
1058C22×C4#1062535014yes—
1059C22×C4C23×D4711yescharacteristic
1060C22×C4C23×D4711yescharacteristic
1061C22×C4C23×D4711yescharacteristic
1062C22×C4C23×D4711yescharacteristic
1063C22×C4C23×D4711yescharacteristic
1064C22×C4C23×D4711yescharacteristic
1065C22×C4C23×D4711yescharacteristic
1066C22×C4C23×D4711yescharacteristic
1067C22×C4C23×D4711yescharacteristic
1068C22×C4C23×D4711yescharacteristic
1069C22×C4C23×D4711yescharacteristic
1070C22×C4C23×D4711yescharacteristic
1071C22×C4C23×D4711yescharacteristic
1072C22×C4C23×D4711yescharacteristic
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—942no—
1090C4⋊C4—942no—
1091C4⋊C4—942no—
1092C4⋊C4—942no—
1093C4⋊C4—942no—
1094C4⋊C4—942no—
1095C4⋊C4—942no—
1096C4⋊C4—942no—
1097C4⋊C4—1881no—
1098C4⋊C4—1881no—
1099C4⋊C4—1881no—
1100C4⋊C4—1881no—
1101C4⋊C4—1881no—
1102C4⋊C4—1881no—
1103C4⋊C4—1881no—
1104C4⋊C4—1881no—
1105C4⋊C4—1881no—
1106C4⋊C4—1881no—
1107C4⋊C4—1881no—
1108C4⋊C4—1881no—
1109C4⋊C4—1881no—
1110C4⋊C4—1881no—
1111C4⋊C4—1881no—
1112C4⋊C4—1881no—
1113C4⋊C4—1881no—
1114C4⋊C4—1881no—
1115C4⋊C4—1881no—
1116C4⋊C4—1881no—
1117C4⋊C4—1881no—
1118C4⋊C4—1881no—
1119C22⋊C4—22no—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—22no—
1123C22⋊C4—942no—
1124C22⋊C4—942no—
1125C22⋊C4—942no—
1126C22⋊C4—942no—
1127C22⋊C4—942no—
1128C22⋊C4—942no—
1129C22⋊C4—1881no—
1130C22⋊C4—1881no—
1131C22⋊C4—1881no—
1132C22⋊C4—1881no—
1133C22⋊C4—1881no—
1134C22⋊C4—1881no—
1135C22⋊C4—1881no—
1136C22⋊C4—1881no—
1137C22⋊C4—1881no—
1138C22⋊C4—1881no—
1139C42—22no—
1140C42—22no—
1141C42—41no—
1142C42—41no—
1143C42—1881no—
1144C42—1881no—
1145C42—1881no—
1146C42—1881no—
1147C42—1881no—
1148C42—1881no—
1149C42—1881no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—941no—
1155C23—941no—
1156C23—941no—
1157C23—941no—
1158C23—941no—
1159C23—941no—
1160C23—941no—
1161C23C2×#1062535012yes—
1162C23#1309406912yes—
1163C23#1309407212yes—
1164C23C24×D4711yescharacteristic
1165Q8—3762no—
1166D4—1884no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—28no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—44no—
1209C2×C4—82no—
1210C2×C4—472no—
1211C2×C4—941no—
1212C2×C4—941no—
1213C2×C4—941no—
1214C2×C4—941no—
1215C2×C4—941no—
1216C2×C4—941no—
1217C2×C4—941no—
1218C2×C4—941no—
1219C2×C4—941no—
1220C2×C4—941no—
1221C2×C4—941no—
1222C2×C4—941no—
1223C2×C4—941no—
1224C2×C4—941no—
1225C2×C4—941no—
1226C2×C4—941no—
1227C2×C4—941no—
1228C2×C4—941no—
1229C2×C4—941no—
1230C2×C4—941no—
1231C2×C4—941no—
1232C2×C4—941no—
1233C2×C4—941no—
1234C2×C4—941no—
1235C2×C4—941no—
1236C2×C4—941no—
1237C2×C4—941no—
1238C2×C4—941no—
1239C2×C4—941no—
1240C2×C4—941no—
1241C2×C4—941no—
1242C2×C4—941no—
1243C2×C4—941no—
1244C2×C4—941no—
1245C2×C4—941no—
1246C2×C4—941no—
1247C2×C4—941no—
1248C2×C4—941no—
1249C2×C4—941no—
1250C2×C4—941no—
1251C2×C4—941no—
1252C2×C4—941no—
1253C2×C4—941no—
1254C2×C4—941no—
1255C2×C4—3762no—
1256C2×C4—3762no—
1257C2×C4—1884no—
1258C2×C4—1884no—
1259C2×C4—1884no—
1260C2×C4C2×#1062535012yes—
1261C2×C4C2×#1062535012yes—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—1881no—
1269C22—1881no—
1270C22—1881no—
1271C22—1881no—
1272C22—1881no—
1273C22—1881no—
1274C22—1881no—
1275C22#1568972014yes—
1276C22C22×#1062535011yescharacteristic
1277C22C2×#1309406911yescharacteristic
1278C222−1+4×D4711yescharacteristic
1279C22C2×#1309407211yescharacteristic
1280C22#1568995811yescharacteristic
1281C22#1568995811yescharacteristic
1282C22#1568996011yescharacteristic
1283C4—22no—
1284C4—22no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—942no—
1298C4—1881no—
1299C4—1881no—
1300C4—1881no—
1301C4—1881no—
1302C4—1881no—
1303C4—1881no—
1304C4—1881no—
1305C4—1881no—
1306C4—1881no—
1307C4—1881no—
1308C4—1881no—
1309C4—1881no—
1310C4—1881no—
1311C4—1881no—
1312C2—24no—
1313C2—3761no—
1314C2C2×#1568972011yescharacteristic
1315C2#2025710111yescharacteristic
1316C2#2025724611yescharacteristic
1317C2#2025756111yescharacteristic
1318C2#2025758711yescharacteristic
1319C2#2025798711yescharacteristic
1320C2#2025800911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2317C2
prime radicalC22×C22⋊D47C23
hypercenter#2317D47
hypocenterC47#36998
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2317

Complements

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

NH ≅ G/Ntype
1. #20251724C2semidirect
3. #20251379C2semidirect
4. #20251373C2semidirect
5. #20251302C2semidirect
6. #20251264C2semidirect
7. #20251208C2semidirect
8. #20251193C2semidirect
9. #20251169C2semidirect
10. #20251154C2semidirect
11. #20251145C2semidirect
12. #20251114C2semidirect
13. #20251076C2semidirect
14. #20250971C2semidirect
15. #20250962C2semidirect
16. #20250902C2semidirect
17. #20250848C2semidirect
18. #20250543C2semidirect
19. #20249360C2semidirect
21. #20247891C2semidirect
23. #20247775C2semidirect
24. #20247671C2semidirect
26. #20247058C2semidirect
30. C2×#15689004C2semidirect
31. C47×#2317C2semidirect
681. #2317D47semidirect
847. C47#36998semidirect

Maximal subgroups

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

subgroupindex
#202517242
#202517132
#202513792
#202513732
#202513022
#202512642
#202512082
#202511932
#202511692
#202511542
#202511452
#202511142
#202510762
#202509712
#202509622
#202509022
#202508482
#202505432
#202493602
#202493442
#202478912
#202478262
#202477752
#202476712
#202472142
#202470582
#202468672
#202467892
#202460572
C2×#156890042
C47×#23172
#3699847