Finite Group Databasebeta

← #26430902

Subgroups — #26430902

Order 12032.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251779C211yesmaximal, characteristic
2#20251771C211yesmaximal, characteristic, complemented
3#20251268C211yesmaximal, characteristic, complemented
4#20251253C211yesmaximal, characteristic
5#20251211C211yesmaximal, characteristic, complemented
6#20251196C211yesmaximal, characteristic
7#20251187C211yesmaximal, characteristic, complemented
8#20251166C211yesmaximal, characteristic, complemented
9#20251148C211yesmaximal, characteristic, complemented
10#20251138C211yesmaximal, characteristic
11#20251134C211yesmaximal, characteristic
12#20250890C211yesmaximal, characteristic
13#20250889C211yesmaximal, characteristic
14#20250880C211yesmaximal, characteristic, complemented
15#20250795C211yesmaximal, characteristic, complemented
16#20250748C211yesmaximal, characteristic
17#20250733C211yesmaximal, characteristic, complemented
18#20250673C211yesmaximal, characteristic
19#20249485C211yesmaximal, characteristic, complemented
20#20249410C211yesmaximal, characteristic
21#20249036C211yesmaximal, characteristic, complemented
22#20248965C211yesmaximal, characteristic
23#20248899C211yesmaximal, characteristic
24#20248829C211yesmaximal, characteristic, complemented
25#20248580C211yesmaximal, characteristic, complemented
26#20248270C211yesmaximal, characteristic, complemented
27#20248255C211yesmaximal, characteristic
28#20246194C211yesmaximal, characteristic, complemented
29#20245997C211yesmaximal, characteristic
30#20245860C211yesmaximal, characteristic, complemented
31C47×#2611C211yesmaximal, characteristic
32C2×C4×Dic94C2211yescharacteristic
33C47⋊#401C2211yescharacteristic
34C47⋊#401C2211yescharacteristic
35#15689065C2211yescharacteristic
36#15689065C2211yescharacteristic
37#15689065C2211yescharacteristic
38#15689065C2211yescharacteristic
39#15689064C2211yescharacteristic
40#15689064C2211yescharacteristic
41#15689064C2211yescharacteristic
42#15689063C2211yescharacteristic
43#15689063C2211yescharacteristic
44#15689063C2211yescharacteristic
45#15689063C2211yescharacteristic
46#15689062C2211yescharacteristic
47#15689062C2211yescharacteristic
48#15689062C2211yescharacteristic
49#15689061C2211yescharacteristic
50#15689061C2211yescharacteristic
51#15689057C2211yescharacteristic
52#15689057C2211yescharacteristic
53#15689056C2211yescharacteristic
54#15689056C2211yescharacteristic
55#15689056C2211yescharacteristic
56#15689056C2211yescharacteristic
57#15689056C2211yescharacteristic
58#15689055C2211yescharacteristic
59#15689054C2211yescharacteristic
60#15689053C2211yescharacteristic
61#15689053C2211yescharacteristic
62#15689051C2211yescharacteristic
63#15689051C2211yescharacteristic
64#15689048C2211yescharacteristic
65#15689048C2211yescharacteristic
66#15689048C2211yescharacteristic
67#15689046C2211yescharacteristic
68#15689046C2211yescharacteristic
69#15689044C2211yescharacteristic
70#15689044C2211yescharacteristic
71#15689044C2211yescharacteristic
72#15689044C2211yescharacteristic
73#15689043C2211yescharacteristic
74#15689035C2211yescharacteristic
75#15689035C2211yescharacteristic
76#15689035C2211yescharacteristic
77#15689029C2211yescharacteristic
78#15689029C2211yescharacteristic
79#15689028C2211yescharacteristic
80#15689028C2211yescharacteristic
81#15689028C2211yescharacteristic
82#15689028C2211yescharacteristic
83#15689027C2211yescharacteristic
84#15689027C2211yescharacteristic
85#15689027C2211yescharacteristic
86#15689027C2211yescharacteristic
87#15689027C2211yescharacteristic
88#15689027C2211yescharacteristic
89#15689022C2211yescharacteristic
90#15689022C2211yescharacteristic
91#15689022C2211yescharacteristic
92#15689020C2211yescharacteristic
93#15689020C2211yescharacteristic
94#15689020C2211yescharacteristic
95#15689019C2211yescharacteristic
96#15689018C2211yescharacteristic
97#15689017C2211yescharacteristic
98#15689017C2211yescharacteristic
99#15689017C2211yescharacteristic
100#15689016C2211yescharacteristic
101#15689016C2211yescharacteristic
102#15689016C2211yescharacteristic
103#15689016C2211yescharacteristic
104#15689016C2211yescharacteristic
105#15689016C2211yescharacteristic
106#15689011C2211yescharacteristic
107#15689011C2211yescharacteristic
108#15689011C2211yescharacteristic
109#15689011C2211yescharacteristic
110#15689011C2211yescharacteristic
111#15689010C2211yescharacteristic
112#15689010C2211yescharacteristic
113#15689010C2211yescharacteristic
114#15689010C2211yescharacteristic
115#15689010C2211yescharacteristic
116#15689009C2211yescharacteristic
117#15689009C2211yescharacteristic
118#15689009C2211yescharacteristic
119#15689009C2211yescharacteristic
120#15689009C2211yescharacteristic
121#15689009C2211yescharacteristic
122#15689009C2211yescharacteristic
123#15689009C2211yescharacteristic
124#15689009C2211yescharacteristic
125#15689009C2211yescharacteristic
126#15689009C2211yescharacteristic
127#15689009C2211yescharacteristic
128#15689009C2211yescharacteristic
129#15689008C2211yescharacteristic
130#15689008C2211yescharacteristic
131#15689008C2211yescharacteristic
132#15689007C2211yescharacteristic
133#15689007C2211yescharacteristic
134#15689007C2211yescharacteristic
135#15689007C2211yescharacteristic
136#15689006C2211yescharacteristic
137#15689006C2211yescharacteristic
138#15689006C2211yescharacteristic
139#15689006C2211yescharacteristic
140#15689006C2211yescharacteristic
141#15689006C2211yescharacteristic
142#15689005C2211yescharacteristic
143#15689004C2211yescharacteristic
144#15689004C2211yescharacteristic
145#15689004C2211yescharacteristic
146#15689004C2211yescharacteristic
147#15689004C2211yescharacteristic
148#15689004C2211yescharacteristic
149#15689004C2211yescharacteristic
150#15689004C2211yescharacteristic
151#15688996C2211yescharacteristic
152#15688996C2211yescharacteristic
153#15688993C2211yescharacteristic
154#15688992C2211yescharacteristic
155#15688991C2211yescharacteristic
156#15688990C2211yescharacteristic
157#15688990C2211yescharacteristic
158#15688990C2211yescharacteristic
159#15688990C2211yescharacteristic
160#15688989C2211yescharacteristic
161#15688988C2211yescharacteristic
162#15688983C2211yescharacteristic
163#15688983C2211yescharacteristic
164C4⋊C4×Dic47C2211yescharacteristic
165C4⋊C4×Dic47C2211yescharacteristic
166C4×Dic47⋊C4C2211yescharacteristic
167C4×Dic47⋊C4C2211yescharacteristic
168C4×C4⋊Dic47C2211yescharacteristic
169C4×C4⋊Dic47C2211yescharacteristic
170#15688969C2211yescharacteristic
171C42×Dic47C2211yescharacteristic
172C2×#125×C47C2211yescharacteristic
173C2×#117×C47C2211yescharacteristic
174C47×#400C2211yescharacteristic
175C47×#399C2211yescharacteristic
176C47×#398C2211yescharacteristic
177C47×#397C2211yescharacteristic
178C47×#389C2211yescharacteristic
179C47×#389C2211yescharacteristic
180C47×#388C2211yescharacteristic
181C47×#388C2211yescharacteristic
182C47×#387C2211yescharacteristic
183C47×#387C2211yescharacteristic
184C47×#385C2211yescharacteristic
185C47×#385C2211yescharacteristic
186C47×#376C2211yescharacteristic
187C22×Dic94C2311yescharacteristic
188C22×Dic94C2311yescharacteristic
189C22×Dic94C2311yescharacteristic
190C4×Dic94—24no—
191C2×C4⋊Dic47C2311yescharacteristic
192C2×C4⋊Dic47C2311yescharacteristic
193C2×C4⋊Dic47C2311yescharacteristic
194C2×C4⋊Dic47C2311yescharacteristic
195C2×C4⋊Dic47C2311yescharacteristic
196C2×C4⋊Dic47C2311yescharacteristic
197C2×C4⋊Dic47C2311yescharacteristic
198C2×C4⋊Dic47C2311yescharacteristic
199C2×C4⋊Dic47C2311yescharacteristic
200C2×C4⋊Dic47C2311yescharacteristic
201C2×C4⋊Dic47C2311yescharacteristic
202C2×C4⋊Dic47C2311yescharacteristic
203C2×C4⋊Dic47C2311yescharacteristic
204C2×C4⋊Dic47C2311yescharacteristic
205C2×C4⋊Dic47C2311yescharacteristic
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×C22⋊Dic47C2311yescharacteristic
225C2×C22⋊Dic47C2311yescharacteristic
226C2×C22⋊Dic47C2311yescharacteristic
227C2×C22⋊Dic47C2311yescharacteristic
228C2×C22⋊Dic47C2311yescharacteristic
229C2×C22⋊Dic47C2311yescharacteristic
230C2×C22⋊Dic47C2311yescharacteristic
231C2×C22⋊Dic47C2311yescharacteristic
232C2×C4×Dic47C2311yescharacteristic
233C2×C4×Dic47C2311yescharacteristic
234C2×C4×Dic47C2311yescharacteristic
235C2×C4×Dic47C2311yescharacteristic
236C2×C4×Dic47C2311yescharacteristic
237C2×C4×Dic47C2311yescharacteristic
238C2×C4×Dic47C2311yescharacteristic
239C2×C4×Dic47C2311yescharacteristic
240C2×C4×Dic47C2311yescharacteristic
241C2×C4×Dic47C2311yescharacteristic
242C2×C4×Dic47C2311yescharacteristic
243C2×C4×Dic47C2311yescharacteristic
244C2×C4×Dic47C2311yescharacteristic
245C2×C4×Dic47C2311yescharacteristic
246C47⋊#95C2311yescharacteristic
247C47⋊#95C2311yescharacteristic
248C47⋊#95C2311yescharacteristic
249C47⋊#95C2311yescharacteristic
250C47⋊#95C2311yescharacteristic
251C47⋊#95C2311yescharacteristic
252C47⋊#95C2311yescharacteristic
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
308C23×C4×C47C2311yescharacteristic
309#125×C47—24no—
310#117×C47—24no—
311C2×C4⋊C4×C47C2311yescharacteristic
312C2×C4⋊C4×C47C2311yescharacteristic
313C2×C4⋊C4×C47C2311yescharacteristic
314C2×C4⋊C4×C47C2311yescharacteristic
315C2×C4⋊C4×C47C2311yescharacteristic
316C2×C4⋊C4×C47C2311yescharacteristic
317C2×C4⋊C4×C47C2311yescharacteristic
318C2×C4⋊C4×C47C2311yescharacteristic
319C2×C4⋊C4×C47C2311yescharacteristic
320C2×C4⋊C4×C47C2311yescharacteristic
321C2×C4⋊C4×C47C2311yescharacteristic
322C2×C4⋊C4×C47C2311yescharacteristic
323C2×C22⋊C4×C47C2311yescharacteristic
324C2×C22⋊C4×C47C2311yescharacteristic
325C2×C22⋊C4×C47C2311yescharacteristic
326C2×C22⋊C4×C47C2311yescharacteristic
327C2×C22⋊C4×C47C2311yescharacteristic
328C2×C22⋊C4×C47C2311yescharacteristic
329C2×C42×C47C2311yescharacteristic
330C2×C42×C47C2311yescharacteristic
331C2×C42×C47C2311yescharacteristic
332C2×C42×C47C2311yescharacteristic
333#95×C47C2311yescharacteristic
334#95×C47C2311yescharacteristic
335#95×C47C2311yescharacteristic
336#95×C47C2311yescharacteristic
337#95×C47C2311yescharacteristic
338#95×C47C2311yescharacteristic
339#95×C47C2311yescharacteristic
340#95×C47C2311yescharacteristic
341#95×C47C2311yescharacteristic
342#95×C47C2311yescharacteristic
343#95×C47C2311yescharacteristic
344#95×C47C2311yescharacteristic
345C24×C47C2411yescharacteristic
346C22×C4×C47—22no—
347C22×C4×C47—41no—
348C22×C4×C47—41no—
349C22×C4×C47C2411yescharacteristic
350C22×C4×C47C2411yescharacteristic
351C22×C4×C47C2411yescharacteristic
352C22×C4×C47C2411yescharacteristic
353C22×C4×C47C2411yescharacteristic
354C22×C4×C47C2411yescharacteristic
355C22×C4×C47C2411yescharacteristic
356C22×C4×C47C2411yescharacteristic
357C22×C4×C47C2411yescharacteristic
358C22×C4×C47C2411yescharacteristic
359C22×C4×C47C2411yescharacteristic
360C22×C4×C47C2411yescharacteristic
361C22×C4×C47C2411yescharacteristic
362C22×C4×C47C2411yescharacteristic
363C22×Dic47C2411yescharacteristic
364C22×Dic47C2411yescharacteristic
365C22×Dic47C2411yescharacteristic
366C22×Dic47C2411yescharacteristic
367C22×Dic47C2411yescharacteristic
368C22×Dic47C2411yescharacteristic
369C22×Dic47C2411yescharacteristic
370C22×Dic47C2411yescharacteristic
371C22×Dic47C2411yescharacteristic
372C22×Dic47C2411yescharacteristic
373C22×Dic47C2411yescharacteristic
374C22×Dic47C2411yescharacteristic
375C22×Dic47C2411yescharacteristic
376C22×Dic47C2411yescharacteristic
377C22×Dic47C2411yescharacteristic
378C22×Dic47C2411yescharacteristic
379C2×Dic94—22no—
380C2×Dic94—22no—
381C2×Dic94—22no—
382C2×Dic94—41no—
383C2×Dic94—41no—
384C2×Dic94—41no—
385C2×Dic94—41no—
386C2×Dic94—41no—
387C2×Dic94—41no—
388C4⋊C4×C47—22no—
389C4⋊C4×C47—22no—
390C4⋊C4×C47—22no—
391C4⋊C4×C47—22no—
392C4⋊C4×C47—22no—
393C4⋊C4×C47—22no—
394C4⋊C4×C47—22no—
395C4⋊C4×C47—22no—
396C4⋊C4×C47—22no—
397C4⋊C4×C47—41no—
398C4⋊C4×C47—41no—
399C4⋊C4×C47—41no—
400C22⋊C4×C47—22no—
401C22⋊C4×C47—22no—
402C22⋊C4×C47—22no—
403C22⋊C4×C47—41no—
404C22⋊C4×C47—41no—
405C22⋊C4×C47—41no—
406C42×C47—22no—
407C42×C47—22no—
408C42×C47—41no—
409C42×C47#4114yes—
410C22⋊Dic47—22no—
411C22⋊Dic47—41no—
412C22⋊Dic47—41no—
413C22⋊Dic47—41no—
414C22⋊Dic47—41no—
415C22⋊Dic47—41no—
416C22⋊Dic47—41no—
417C22⋊Dic47—41no—
418C4⋊Dic47—22no—
419C4⋊Dic47—41no—
420C4⋊Dic47—41no—
421C4⋊Dic47—41no—
422C4⋊Dic47—41no—
423C4⋊Dic47—41no—
424C4⋊Dic47—41no—
425C4⋊Dic47—41no—
426C4⋊Dic47—41no—
427C4⋊Dic47—41no—
428C4⋊Dic47—41no—
429C4⋊Dic47—41no—
430C4⋊Dic47—41no—
431C4⋊Dic47—41no—
432C4⋊Dic47—41no—
433Dic47⋊C4—22no—
434Dic47⋊C4—22no—
435Dic47⋊C4—22no—
436Dic47⋊C4—22no—
437Dic47⋊C4—22no—
438Dic47⋊C4—41no—
439Dic47⋊C4—41no—
440Dic47⋊C4—41no—
441Dic47⋊C4—41no—
442Dic47⋊C4—41no—
443Dic47⋊C4—41no—
444Dic47⋊C4—41no—
445Dic47⋊C4—41no—
446Dic47⋊C4—41no—
447Dic47⋊C4—41no—
448Dic47⋊C4—41no—
449Dic47⋊C4—41no—
450Dic47⋊C4—41no—
451C4×Dic47—22no—
452C4×Dic47—22no—
453C4×Dic47—22no—
454C4×Dic47—41no—
455C4×Dic47—41no—
456C4×Dic47—41no—
457C4×Dic47—41no—
458C4×Dic47—41no—
459C4×Dic47—41no—
460C4×Dic47—41no—
461C4×Dic47—41no—
462C4×Dic47—41no—
463C4×Dic47—41no—
464C4×Dic47—41no—
465C23×C47—21no—
466C23×C47—21no—
467C23×C47—21no—
468C23×C47—21no—
469C23×C47—21no—
470C23×C47—21no—
471C23×C47—21no—
472C23×C47C2511yescharacteristic
473C2×C4×C47—21no—
474C2×C4×C47—21no—
475C2×C4×C47—21no—
476C2×C4×C47—21no—
477C2×C4×C47—21no—
478C2×C4×C47—21no—
479C2×C4×C47—21no—
480C2×C4×C47—21no—
481C2×C4×C47—21no—
482C2×C4×C47—21no—
483C2×C4×C47—21no—
484C2×C4×C47—21no—
485C2×C4×C47—21no—
486C2×C4×C47—21no—
487C2×C4×C47—21no—
488C2×C4×C47—21no—
489C2×C4×C47—21no—
490C2×C4×C47—21no—
491C2×C4×C47—21no—
492C2×C4×C47—21no—
493C2×C4×C47—21no—
494C2×C4×C47—21no—
495C2×C4×C47—21no—
496C2×C4×C47—21no—
497C2×C4×C47—21no—
498C2×C4×C47—21no—
499C2×C4×C47—21no—
500C2×C4×C47—21no—
501C2×C4×C47—21no—
502C2×C4×C47—21no—
503C2×C4×C47—21no—
504C2×C4×C47—21no—
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—44no—
512C2×C4×C47C2×#4112yes—
513C2×C4×C47C2×#4112yes—
514C2×C4×C47C2×#4112yes—
515C2×C4×C472−1+412yes—
516C2×Dic47—21no—
517C2×Dic47—21no—
518C2×Dic47—21no—
519C2×Dic47—21no—
520C2×Dic47—21no—
521C2×Dic47—21no—
522C2×Dic47—21no—
523C2×Dic47—21no—
524C2×Dic47—21no—
525C2×Dic47—21no—
526C2×Dic47—21no—
527C2×Dic47—21no—
528C2×Dic47—21no—
529C2×Dic47—21no—
530C2×Dic47—21no—
531C2×Dic47—21no—
532C2×Dic47—21no—
533C2×Dic47—21no—
534C2×Dic47—21no—
535C2×Dic47—21no—
536C2×Dic47—21no—
537C2×Dic47—21no—
538C2×Dic47—21no—
539C2×Dic47—21no—
540C2×Dic47—21no—
541C2×Dic47—21no—
542C2×Dic47—21no—
543C2×Dic47—21no—
544C2×Dic47—21no—
545C2×Dic47—21no—
546C2×Dic47—21no—
547C2×Dic47—21no—
548C2×Dic47—21no—
549C2×Dic47—21no—
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×Dic472−1+412yes—
564Dic94—44no—
565Dic94—82no—
566Dic94—82no—
567#37001—471nomaximal, Sylow
568C22×C47—41no—
569C22×C47—41no—
570C22×C47—41no—
571C22×C47—41no—
572C22×C47—41no—
573C22×C47—41no—
574C22×C47—41no—
575C22×C47C22×#4111yescharacteristic
576C22×C47C2×2−1+411yescharacteristic
577C22×C47C2×2−1+411yescharacteristic
578C22×C47#58511yescharacteristic
579C22×C47#58511yescharacteristic
580C22×C47#58511yescharacteristic
581C22×C47#58511yescharacteristic
582C4×C47—22no—
583C4×C47—22no—
584C4×C47—22no—
585C4×C47—22no—
586C4×C47—41no—
587C4×C47—41no—
588C4×C47—41no—
589C4×C47—41no—
590C4×C47—41no—
591C4×C47—41no—
592C4×C47—41no—
593C4×C47—41no—
594C4×C47—41no—
595C4×C47—41no—
596Dic47—22no—
597Dic47—41no—
598Dic47—41no—
599Dic47—41no—
600Dic47—41no—
601Dic47—41no—
602Dic47—41no—
603Dic47—41no—
604Dic47—41no—
605Dic47—41no—
606Dic47—41no—
607Dic47—41no—
608Dic47—41no—
609Dic47—41no—
610Dic47—41no—
611Dic47—41no—
612#2866—471no—
613#2863—471no—
614#2799—471no—
615#2798—471no—
616#2794—471no—
617#2793—471no—
618#2792—471no—
619#2791—471no—
620#2789—471no—
621#2788—471no—
622#2788—471no—
623#2770—471no—
624#2770—471no—
625#2769—471no—
626#2762—471no—
627#2759—471no—
628#2758—471no—
629#2754—471no—
630#2655—471no—
631#2650—471no—
632#2611D4711yescharacteristic
633#2605—471no—
634#2599—471no—
635#2594—471no—
636#2588—471no—
637#2565—471no—
638#2533—471no—
639#2532—471no—
640#2336—471no—
641#2314—471no—
642#2295—471no—
643C2×C47—81no—
644C2×C47#345511yescharacteristic
645C2×C47#349511yescharacteristic
646C2×C47#350711yescharacteristic
647C2×C47#355511yescharacteristic
648C2×C47#356411yescharacteristic
649C2×C47#356511yescharacteristic
650C2×C47#356611yescharacteristic
651C2×#125C2×D4711yescharacteristic
652C2×C4×Q8—471no—
653C2×#117C2×D4711yescharacteristic
654#401—471no—
655#401—471no—
656#400—471no—
657#400—471no—
658#400—471no—
659#400—471no—
660#400—471no—
661#400—471no—
662#400—471no—
663#400—471no—
664#400—471no—
665#400—471no—
666#400—471no—
667#400—471no—
668#400—471no—
669#400—471no—
670#400—471no—
671#400—471no—
672#400C2×D4711yescharacteristic
673#399C2×D4711yescharacteristic
674#398—471no—
675#398—471no—
676#398—471no—
677#398—471no—
678#398—471no—
679#398—471no—
680#398—471no—
681#398—471no—
682#398—471no—
683#398—471no—
684#398—471no—
685#398C2×D4711yescharacteristic
686#397—471no—
687#397—471no—
688#397—471no—
689#397—471no—
690#397—471no—
691#397C2×D4711yescharacteristic
692#396—471no—
693#396—471no—
694#395—471no—
695#395—471no—
696#395—471no—
697#395—471no—
698#395—471no—
699#393—471no—
700#393—471no—
701#393—471no—
702#391—471no—
703#391—471no—
704#391—471no—
705#391—471no—
706#391—471no—
707#391—471no—
708#391—471no—
709#391—471no—
710#391—471no—
711#391—471no—
712#391—471no—
713#391—471no—
714#389—471no—
715#389—471no—
716#389—471no—
717#389—471no—
718#389—471no—
719#389—471no—
720#389—471no—
721#389—471no—
722#389C2×D4711yescharacteristic
723#389C2×D4711yescharacteristic
724#388—471no—
725#388—471no—
726#388—471no—
727#388—471no—
728#388—471no—
729#388—471no—
730#388—471no—
731#388—471no—
732#388—471no—
733#388—471no—
734#388—471no—
735#388—471no—
736#388—471no—
737#388—471no—
738#388C2×D4711yescharacteristic
739#388C2×D4711yescharacteristic
740#387—471no—
741#387—471no—
742#387—471no—
743#387—471no—
744#387—471no—
745#387—471no—
746#387—471no—
747#387—471no—
748#387—471no—
749#387—471no—
750#387—471no—
751#387—471no—
752#387—471no—
753#387—471no—
754#387—471no—
755#387—471no—
756#387—471no—
757#387—471no—
758#387—471no—
759#387—471no—
760#387—471no—
761#387—471no—
762#387—471no—
763#387—471no—
764#387—471no—
765#387—471no—
766#387—471no—
767#387—471no—
768#387—471no—
769#387—471no—
770#387—471no—
771#387—471no—
772#387—471no—
773#387—471no—
774#387—471no—
775#387—471no—
776#387—471no—
777#387—471no—
778#387—471no—
779#387—471no—
780#387C2×D4711yescharacteristic
781#387C2×D4711yescharacteristic
782#385—471no—
783#385—471no—
784#385C2×D4711yescharacteristic
785#385C2×D4711yescharacteristic
786#384—471no—
787#384—471no—
788#383—471no—
789#383—471no—
790#383—471no—
791#383—471no—
792#383—471no—
793#382—471no—
794#382—471no—
795#380—471no—
796#380—471no—
797C4×C4⋊C4—471no—
798C4×C4⋊C4—471no—
799C4×C4⋊C4—471no—
800C4×C4⋊C4—471no—
801C4×C4⋊C4—471no—
802C4×C4⋊C4—471no—
803#376—471no—
804#376C2×D4711yescharacteristic
805C43—471no—
806C47#3700111yescharacteristic, complemented, Sylow
807C22×Q8—471no—
808C22×Q8—471no—
809C22×Q8—471no—
810C23×C4C22×D4711yescharacteristic
811#125—24no—
812C4×Q8—944no—
813#117—24no—
814C2×C4⋊C4—471no—
815C2×C4⋊C4—471no—
816C2×C4⋊C4—471no—
817C2×C4⋊C4—471no—
818C2×C4⋊C4—471no—
819C2×C4⋊C4—471no—
820C2×C4⋊C4—471no—
821C2×C4⋊C4—471no—
822C2×C4⋊C4—471no—
823C2×C4⋊C4—471no—
824C2×C4⋊C4—471no—
825C2×C4⋊C4—471no—
826C2×C4⋊C4—471no—
827C2×C4⋊C4—471no—
828C2×C4⋊C4—471no—
829C2×C4⋊C4—471no—
830C2×C4⋊C4—471no—
831C2×C4⋊C4—471no—
832C2×C4⋊C4—471no—
833C2×C4⋊C4—471no—
834C2×C4⋊C4—471no—
835C2×C4⋊C4—471no—
836C2×C4⋊C4—471no—
837C2×C4⋊C4—471no—
838C2×C4⋊C4—471no—
839C2×C4⋊C4—471no—
840C2×C4⋊C4—471no—
841C2×C4⋊C4—471no—
842C2×C4⋊C4—471no—
843C2×C4⋊C4—471no—
844C2×C4⋊C4—471no—
845C2×C4⋊C4—471no—
846C2×C4⋊C4—471no—
847C2×C4⋊C4C22×D4711yescharacteristic
848C2×C4⋊C4C22×D4711yescharacteristic
849C2×C4⋊C4C22×D4711yescharacteristic
850C2×C4⋊C4C22×D4711yescharacteristic
851C2×C4⋊C4C22×D4711yescharacteristic
852C2×C4⋊C4C22×D4711yescharacteristic
853C2×C4⋊C4C22×D4711yescharacteristic
854C2×C4⋊C4C22×D4711yescharacteristic
855C2×C4⋊C4C22×D4711yescharacteristic
856C2×C4⋊C4C22×D4711yescharacteristic
857C2×C4⋊C4C22×D4711yescharacteristic
858C2×C4⋊C4C22×D4711yescharacteristic
859C2×C22⋊C4—471no—
860C2×C22⋊C4—471no—
861C2×C22⋊C4—471no—
862C2×C22⋊C4—471no—
863C2×C22⋊C4—471no—
864C2×C22⋊C4—471no—
865C2×C22⋊C4—471no—
866C2×C22⋊C4—471no—
867C2×C22⋊C4C22×D4711yescharacteristic
868C2×C22⋊C4C22×D4711yescharacteristic
869C2×C22⋊C4C22×D4711yescharacteristic
870C2×C22⋊C4C22×D4711yescharacteristic
871C2×C22⋊C4C22×D4711yescharacteristic
872C2×C22⋊C4C22×D4711yescharacteristic
873C2×C42—471no—
874C2×C42—471no—
875C2×C42—471no—
876C2×C42—471no—
877C2×C42—471no—
878C2×C42—471no—
879C2×C42—471no—
880C2×C42—471no—
881C2×C42—471no—
882C2×C42—471no—
883C2×C42—471no—
884C2×C42—471no—
885C2×C42—471no—
886C2×C42—471no—
887C2×C42C22×D4711yescharacteristic
888C2×C42C22×D4711yescharacteristic
889C2×C42C22×D4711yescharacteristic
890C2×C42C22×D4711yescharacteristic
891#95—471no—
892#95—471no—
893#95—471no—
894#95—471no—
895#95—471no—
896#95—471no—
897#95—471no—
898#95—471no—
899#95—471no—
900#95—471no—
901#95—471no—
902#95—471no—
903#95—471no—
904#95—471no—
905#95—471no—
906#95—471no—
907#95—471no—
908#95—471no—
909#95—471no—
910#95—471no—
911#95—471no—
912#95—471no—
913#95—471no—
914#95—471no—
915#95—471no—
916#95—471no—
917#95—471no—
918#95—471no—
919#95—471no—
920#95—471no—
921#95—471no—
922#95—471no—
923#95—471no—
924#95—471no—
925#95—471no—
926#95—471no—
927#95—471no—
928#95—471no—
929#95—471no—
930#95—471no—
931#95—471no—
932#95—471no—
933#95—471no—
934#95—471no—
935#95—471no—
936#95—471no—
937#95—471no—
938#95—471no—
939#95—471no—
940#95—471no—
941#95—471no—
942#95—471no—
943#95—471no—
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#95C22×D4711yescharacteristic
954#95C22×D4711yescharacteristic
955#95C22×D4711yescharacteristic
956#95C22×D4711yescharacteristic
957#95C22×D4711yescharacteristic
958#95C22×D4711yescharacteristic
959#95C22×D4711yescharacteristic
960#95C22×D4711yescharacteristic
961#95C22×D4711yescharacteristic
962#95C22×D4711yescharacteristic
963#95C22×D4711yescharacteristic
964#95C22×D4711yescharacteristic
965C24C23×D4711yescharacteristic
966C2×Q8—942no—
967C2×Q8—942no—
968C2×Q8—942no—
969C2×Q8—1881no—
970C2×Q8—1881no—
971C2×Q8—1881no—
972C2×Q8—1881no—
973C2×Q8—1881no—
974C2×Q8—1881no—
975C22×C4—22no—
976C22×C4—41no—
977C22×C4—41no—
978C22×C4—471no—
979C22×C4—471no—
980C22×C4—471no—
981C22×C4—471no—
982C22×C4—471no—
983C22×C4—471no—
984C22×C4—471no—
985C22×C4—471no—
986C22×C4—471no—
987C22×C4—471no—
988C22×C4—471no—
989C22×C4—471no—
990C22×C4—471no—
991C22×C4—471no—
992C22×C4—471no—
993C22×C4—471no—
994C22×C4C23×D4711yescharacteristic
995C22×C4C23×D4711yescharacteristic
996C22×C4C23×D4711yescharacteristic
997C22×C4C23×D4711yescharacteristic
998C22×C4C23×D4711yescharacteristic
999C22×C4C23×D4711yescharacteristic
1000C22×C4C23×D4711yescharacteristic
1001C22×C4C23×D4711yescharacteristic
1002C22×C4C23×D4711yescharacteristic
1003C22×C4C23×D4711yescharacteristic
1004C22×C4C23×D4711yescharacteristic
1005C22×C4C23×D4711yescharacteristic
1006C22×C4C23×D4711yescharacteristic
1007C22×C4C23×D4711yescharacteristic
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
1015C4⋊C4—22no—
1016C4⋊C4—22no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—942no—
1021C4⋊C4—942no—
1022C4⋊C4—942no—
1023C4⋊C4—942no—
1024C4⋊C4—942no—
1025C4⋊C4—942no—
1026C4⋊C4—1881no—
1027C4⋊C4—1881no—
1028C4⋊C4—1881no—
1029C4⋊C4—1881no—
1030C4⋊C4—1881no—
1031C4⋊C4—1881no—
1032C4⋊C4—1881no—
1033C4⋊C4—1881no—
1034C4⋊C4—1881no—
1035C4⋊C4—1881no—
1036C4⋊C4—1881no—
1037C4⋊C4—1881no—
1038C4⋊C4—1881no—
1039C4⋊C4—1881no—
1040C4⋊C4—1881no—
1041C4⋊C4—1881no—
1042C4⋊C4—1881no—
1043C4⋊C4—1881no—
1044C4⋊C4—1881no—
1045C4⋊C4—1881no—
1046C4⋊C4—1881no—
1047C4⋊C4—1881no—
1048C4⋊C4—1881no—
1049C4⋊C4—1881no—
1050C4⋊C4—1881no—
1051C4⋊C4—1881no—
1052C4⋊C4—1881no—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—942no—
1060C22⋊C4—1881no—
1061C22⋊C4—1881no—
1062C22⋊C4—1881no—
1063C22⋊C4—1881no—
1064C22⋊C4—1881no—
1065C22⋊C4—1881no—
1066C22⋊C4—1881no—
1067C42—22no—
1068C42—22no—
1069C42—41no—
1070C42—942no—
1071C42—942no—
1072C42—942no—
1073C42—1881no—
1074C42—1881no—
1075C42—1881no—
1076C42—1881no—
1077C42—1881no—
1078C42—1881no—
1079C42—1881no—
1080C42—1881no—
1081C42—1881no—
1082C42—1881no—
1083C42—1881no—
1084C42#1062535214yes—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23C24×D4711yescharacteristic
1093Q8—3762no—
1094Q8—3762no—
1095Q8—1884no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—44no—
1135C2×C4—472no—
1136C2×C4—941no—
1137C2×C4—941no—
1138C2×C4—941no—
1139C2×C4—941no—
1140C2×C4—941no—
1141C2×C4—941no—
1142C2×C4—941no—
1143C2×C4—941no—
1144C2×C4—941no—
1145C2×C4—941no—
1146C2×C4—941no—
1147C2×C4—941no—
1148C2×C4—941no—
1149C2×C4—941no—
1150C2×C4—941no—
1151C2×C4—941no—
1152C2×C4—941no—
1153C2×C4—941no—
1154C2×C4—941no—
1155C2×C4—941no—
1156C2×C4—941no—
1157C2×C4—941no—
1158C2×C4—941no—
1159C2×C4—941no—
1160C2×C4—941no—
1161C2×C4—941no—
1162C2×C4—941no—
1163C2×C4—941no—
1164C2×C4—941no—
1165C2×C4—941no—
1166C2×C4—941no—
1167C2×C4—941no—
1168C2×C4—941no—
1169C2×C4—941no—
1170C2×C4—941no—
1171C2×C4—941no—
1172C2×C4—941no—
1173C2×C4—941no—
1174C2×C4—941no—
1175C2×C4—941no—
1176C2×C4—941no—
1177C2×C4—941no—
1178C2×C4—941no—
1179C2×C4—941no—
1180C2×C4—941no—
1181C2×C4—941no—
1182C2×C4—941no—
1183C2×C4C2×#1062535212yes—
1184C2×C4C2×#1062535212yes—
1185C2×C4C2×#1062535212yes—
1186C2×C4#1309407112yes—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—41no—
1194C22C22×#1062535211yescharacteristic
1195C222−1+4×D4711yescharacteristic
1196C22C2×#1309407111yescharacteristic
1197C22#1568995911yescharacteristic
1198C22#1568995911yescharacteristic
1199C22#1568995911yescharacteristic
1200C22#1568996011yescharacteristic
1201C4—22no—
1202C4—22no—
1203C4—22no—
1204C4—22no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—942no—
1216C4—1881no—
1217C4—1881no—
1218C4—1881no—
1219C4—1881no—
1220C4—1881no—
1221C4—1881no—
1222C4—1881no—
1223C4—1881no—
1224C4—1881no—
1225C4—1881no—
1226C4—1881no—
1227C4—1881no—
1228C4—1881no—
1229C4—1881no—
1230C4—1881no—
1231C2—81no—
1232C2#2025677611yescharacteristic
1233C2#2025713711yescharacteristic
1234C2#2025725011yescharacteristic
1235C2#2025786311yescharacteristic
1236C2#2025800811yescharacteristic
1237C2#2025801811yescharacteristic
1238C2#2025806611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2611C2
prime radicalC24×C47C24
hypercenter#2611D47
hypocenterC47#37001
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2611

Complements

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

NH ≅ G/Ntype
2. #20251771C2semidirect
3. #20251268C2semidirect
5. #20251211C2semidirect
7. #20251187C2semidirect
8. #20251166C2semidirect
9. #20251148C2semidirect
14. #20250880C2semidirect
15. #20250795C2semidirect
17. #20250733C2semidirect
19. #20249485C2semidirect
21. #20249036C2semidirect
24. #20248829C2semidirect
25. #20248580C2semidirect
26. #20248270C2semidirect
28. #20246194C2semidirect
30. #20245860C2semidirect
806. C47#37001semidirect

Maximal subgroups

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

subgroupindex
#202517792
#202517712
#202512682
#202512532
#202512112
#202511962
#202511872
#202511662
#202511482
#202511382
#202511342
#202508902
#202508892
#202508802
#202507952
#202507482
#202507332
#202506732
#202494852
#202494102
#202490362
#202489652
#202488992
#202488292
#202485802
#202482702
#202482552
#202461942
#202459972
#202458602
C47×#26112
#3700147