Finite Group Databasebeta

← #26221299

Subgroups — #26221299

Order 12032.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689657C211yesmaximal, characteristic
2C2×#15689185C211yesmaximal, characteristic, complemented
3C2×#15689080C211yesmaximal, characteristic, complemented
4#20244326C211yesmaximal, characteristic, complemented
5#20244322C211yesmaximal, characteristic, complemented
6#20244184C211yesmaximal, characteristic, complemented
7#20244180C211yesmaximal, characteristic, complemented
8#20243684C211yesmaximal, characteristic, complemented
9#20243682C211yesmaximal, characteristic, complemented
10#20243679C211yesmaximal, characteristic, complemented
11#20243677C211yesmaximal, characteristic, complemented
12#20243157C211yesmaximal, characteristic, complemented
13#20243157C211yesmaximal, characteristic, complemented
14C4×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
15C47×#1749C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18#15689657—24no—
19#15689657—24no—
20C2×#13094018C411yescharacteristic
21C2×#13094018C411yescharacteristic
22C2×#13094016C411yescharacteristic
23C2×#13094012C411yescharacteristic
24C2×#13094007C411yescharacteristic
25C2×#13094007C411yescharacteristic
26C2×#13094003C411yescharacteristic
27C2×#13093998C411yescharacteristic
28C2×C4×Dic94C2211yescharacteristic
29C2×C4×D188C2211yescharacteristic
30C2×C4×C22⋊D47C2211yescharacteristic
31C2×C4×C22⋊D47C2211yescharacteristic
32C2×#13093981C2211yescharacteristic
33C2×#13093981C2211yescharacteristic
34#15689185—24no—
35C2×Dic47⋊C8C2211yescharacteristic
36C2×Dic47⋊C8C2211yescharacteristic
37C2×C22⋊(C47⋊C8)C2211yescharacteristic
38C2×C22⋊(C47⋊C8)C2211yescharacteristic
39C2×(C2×D47)⋊C8C2211yescharacteristic
40C2×(C2×D47)⋊C8C2211yescharacteristic
41C2×(C2×D47)⋊C8C2211yescharacteristic
42C2×(C2×D47)⋊C8C2211yescharacteristic
43C2×(C2×D47)⋊C8C2211yescharacteristic
44C2×(C2×D47)⋊C8C2211yescharacteristic
45#15689080—24no—
46C2×#13093934C2211yescharacteristic
47C2×C4×C47⋊C8C2211yescharacteristic
48C2×C4×C47⋊C8C2211yescharacteristic
49C2×C8×Dic47C2211yescharacteristic
50#15688878C2211yescharacteristic
51#15688878C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C22×C42×C47C2211yescharacteristic
57C2×C22⋊C8×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×#97×C47C2211yescharacteristic
60C2×#97×C47C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Dic94C2×C411yescharacteristic
64C22×D188C2×C411yescharacteristic
65C22×C22⋊D47C2×C411yescharacteristic
66C22×C22⋊D47C2×C411yescharacteristic
67C22×C4×D47C2311yescharacteristic
68C22×C4×D47C2311yescharacteristic
69C2×#10625324—22no—
70C2×#10625324—22no—
71C2×#10625324—22no—
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C2×C8×D47—22no—
77C2×C8×D47—22no—
78C2×C8×D47—22no—
79#13094018—24no—
80#13094018—24no—
81#13094016—24no—
82#13094012—24no—
83#13094007—24no—
84#13094007—24no—
85#13094003—24no—
86#13093998—24no—
87C4×Dic94—22no—
88C4×Dic94—22no—
89C4×D188—22no—
90C4×D188—22no—
91C4×C22⋊D47—22no—
92C4×C22⋊D47—22no—
93C4×C22⋊D47—22no—
94C4×C22⋊D47—22no—
95#13093981—22no—
96#13093981—22no—
97#13093981D414yes—
98#13093981D414yes—
99C2×C4⋊Dic47C2×C411yescharacteristic
100C2×C4⋊Dic47C2×C411yescharacteristic
101C2×Dic47⋊C4C2×C411yescharacteristic
102C2×Dic47⋊C4C2×C411yescharacteristic
103C2×Dic47⋊C4C2×C411yescharacteristic
104C2×Dic47⋊C4C2×C411yescharacteristic
105C2×Dic47⋊C4C2×C411yescharacteristic
106C2×Dic47⋊C4C2×C411yescharacteristic
107C2×Dic47⋊C4C2×C411yescharacteristic
108C2×Dic47⋊C4C2×C411yescharacteristic
109C2×C22⋊Dic47C2×C411yescharacteristic
110C2×C22⋊Dic47C2×C411yescharacteristic
111C2×(C2×D47)⋊C4C2×C411yescharacteristic
112C2×(C2×D47)⋊C4C2×C411yescharacteristic
113C2×(C2×D47)⋊C4C2×C411yescharacteristic
114C2×(C2×D47)⋊C4C2×C411yescharacteristic
115C2×(C2×D47)⋊C4C2×C411yescharacteristic
116C2×(C2×D47)⋊C4C2×C411yescharacteristic
117C2×(C2×D47)⋊C4C2×C411yescharacteristic
118C2×(C2×D47)⋊C4C2×C411yescharacteristic
119C2×C4×Dic47C2311yescharacteristic
120C2×C4×Dic47C2311yescharacteristic
121Dic47⋊C8—22no—
122Dic47⋊C8—22no—
123C22⋊(C47⋊C8)—22no—
124C22⋊(C47⋊C8)—22no—
125(C2×D47)⋊C8—22no—
126(C2×D47)⋊C8—22no—
127(C2×D47)⋊C8—22no—
128(C2×D47)⋊C8—22no—
129(C2×D47)⋊C8—22no—
130(C2×D47)⋊C8—22no—
131#13093934—22no—
132C4×C47⋊C8—22no—
133C4×C47⋊C8—22no—
134C8×Dic47—22no—
135C23×C4×C47C2×C411yescharacteristic
136C23×C4×C47C2×C411yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C22×C8×C47C2311yescharacteristic
139C22×C8×C47C2311yescharacteristic
140C22×C8×C47C2311yescharacteristic
141C22×C8×C47C2311yescharacteristic
142C2×C42×C47—22no—
143C2×C42×C47—22no—
144C2×C42×C47C2×C411yescharacteristic
145C2×C42×C47C2×C411yescharacteristic
146C2×C42×C47C2311yescharacteristic
147C2×C42×C47C2311yescharacteristic
148C22⋊C8×C47—22no—
149C22⋊C8×C47—22no—
150#97×C47—22no—
151#97×C47—22no—
152C24×C47C22×C411yescharacteristic
153C23×D47C22×C411yescharacteristic
154C23×D47C22×C411yescharacteristic
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—41no—
166C22×C4×C47—41no—
167C22×C4×C47C22×C411yescharacteristic
168C22×C4×C47C22×C411yescharacteristic
169C22×C4×C47C22×C411yescharacteristic
170C22×C4×C47C22×C411yescharacteristic
171C22×C4×C47C22×C411yescharacteristic
172C22×C4×C47C2411yescharacteristic
173C2×C22⋊D47—22no—
174C2×C22⋊D47—22no—
175C2×C22⋊D47—22no—
176C2×C22⋊D47—22no—
177C2×C22⋊D47—41no—
178C2×C22⋊D47—41no—
179C22×Dic47C22×C411yescharacteristic
180C22×Dic47C22×C411yescharacteristic
181C22×Dic47C22×C411yescharacteristic
182C22×Dic47C22×C411yescharacteristic
183C22×Dic47C22×C411yescharacteristic
184C22×Dic47C22×C411yescharacteristic
185C2×D188—22no—
186C2×D188—22no—
187C2×D188—41no—
188C2×C4×D47—21no—
189C2×C4×D47—21no—
190C2×C4×D47—21no—
191C2×C4×D47—21no—
192C2×C4×D47—21no—
193C2×C4×D47—21no—
194C2×C4×D47—21no—
195C2×C4×D47—21no—
196C2×C4×D47—21no—
197C2×C4×D47—21no—
198C2×C4×D47C2×D412yes—
199C2×C4×D47C2×D412yes—
200C2×Dic94—22no—
201C2×Dic94—22no—
202C2×Dic94—41no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47#4112yes—
214C2×C8×C47#4112yes—
215C42×C47—22no—
216C42×C47—22no—
217C42×C47—21no—
218C42×C47—21no—
219C42×C47C2×D412yes—
220C42×C47C2×D412yes—
221C22⋊Dic47—22no—
222C22⋊Dic47—22no—
223(C2×D47)⋊C4—22no—
224(C2×D47)⋊C4—22no—
225(C2×D47)⋊C4—22no—
226(C2×D47)⋊C4—22no—
227(C2×D47)⋊C4—22no—
228(C2×D47)⋊C4—22no—
229(C2×D47)⋊C4C22⋊C414yes—
230(C2×D47)⋊C4C22⋊C414yes—
231C4⋊Dic47—22no—
232C4⋊Dic47—22no—
233Dic47⋊C4—22no—
234Dic47⋊C4—22no—
235Dic47⋊C4—22no—
236Dic47⋊C4—22no—
237Dic47⋊C4—22no—
238Dic47⋊C4—22no—
239Dic47⋊C4C22⋊C414yes—
240Dic47⋊C4C22⋊C414yes—
241C4×Dic47—21no—
242C4×Dic47—21no—
243C4×Dic47C2×D412yes—
244C4×Dic47C2×D412yes—
245C2×C47⋊C8—21no—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8#4112yes—
256C2×C47⋊C8#4112yes—
257#10625324—28no—
258C8×D47—28no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47#13112yes—
266C23×C47C23×C411yescharacteristic
267C22×D47—21no—
268C22×D47—21no—
269C22×D47—21no—
270C22×D47—21no—
271C22×D47—21no—
272C22×D47—21no—
273C22×D47—21no—
274C22×D47—21no—
275C22×D47—21no—
276C22×D47—21no—
277C22×D47—21no—
278C22×D47—21no—
279C22×D47—21no—
280C22×D47C2×C22⋊C412yes—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—44no—
294C2×C4×C47—44no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47C2×C22⋊C412yes—
300C2×C4×C47C2×C22⋊C412yes—
301C2×C4×C47#13112yes—
302C2×C4×C47C22×D411yescharacteristic
303C2×C4×C47C22×D411yescharacteristic
304C2×C4×C47C2×#4111yescharacteristic
305C2×C4×C47C2×#4111yescharacteristic
306C2×C4×C47C2×#4111yescharacteristic
307C2×C4×C47C2×#4111yescharacteristic
308C22⋊D47—44no—
309C22⋊D47—44no—
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47—21no—
315C2×Dic47—21no—
316C2×Dic47—21no—
317C2×Dic47—21no—
318C2×Dic47—21no—
319C2×Dic47—21no—
320C2×Dic47—21no—
321C2×Dic47—21no—
322C2×Dic47—21no—
323C2×Dic47—21no—
324C2×Dic47—21no—
325C2×Dic47C2×C22⋊C412yes—
326C2×Dic47C2×C22⋊C412yes—
327C2×Dic47C2×C22⋊C412yes—
328D188—44no—
329C4×D47—22no—
330C4×D47—22no—
331C4×D47—22no—
332C4×D47—22no—
333C4×D47—41no—
334C4×D47—41no—
335C4×D47—41no—
336C4×D47—41no—
337Dic94—44no—
338C8×C47—22no—
339C8×C47—22no—
340C8×C47—41no—
341C8×C47—41no—
342C47⋊C8—22no—
343C47⋊C8—22no—
344C47⋊C8—41no—
345C47⋊C8—41no—
346#21381—471nomaximal, Sylow
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47C22×C22⋊C411yescharacteristic
355C22×C47C4×#4111yescharacteristic
356C22×C47C4×#4111yescharacteristic
357C22×C47C2×#13111yescharacteristic
358C22×C47C2×#13111yescharacteristic
359C22×C47#56811yescharacteristic
360C22×C47#56811yescharacteristic
361C2×D47—22no—
362C2×D47—22no—
363C2×D47—22no—
364C2×D47—41no—
365C2×D47—41no—
366C2×D47—41no—
367C2×D47—41no—
368C2×D47—41no—
369C2×D47—41no—
370C2×D47—41no—
371C2×D47—41no—
372C2×D47—41no—
373C2×D47—41no—
374C2×D47—41no—
375C4×C47—22no—
376C4×C47—22no—
377C4×C47—22no—
378C4×C47—41no—
379C4×C47—41no—
380C4×C47#52511yescharacteristic
381C4×C47#52511yescharacteristic
382C4×C47#53211yescharacteristic
383C4×C47#53211yescharacteristic
384Dic47—22no—
385Dic47—22no—
386Dic47—22no—
387Dic47—41no—
388Dic47—41no—
389Dic47—41no—
390C2×#529—471no—
391C2×#433—471no—
392C2×#405—471no—
393#1985—471no—
394#1984—471no—
395#1955—471no—
396#1954—471no—
397#1870—471no—
398#1870—471no—
399#1869—471no—
400#1869—471no—
401#1750—471no—
402#1750—471no—
403#1749D4711yescharacteristic, complemented
404C4×C22⋊C8—471no—
405C2×C47—42no—
406C2×C47#229711yescharacteristic
407C2×C47#288011yescharacteristic
408C2×C47#288011yescharacteristic
409C2×C47#296611yescharacteristic
410C2×C47#296711yescharacteristic
411C2×C47#296811yescharacteristic
412C2×C47#296911yescharacteristic
413D47—42no—
414D47—81no—
415C22×M16—471no—
416C23×C8—471no—
417#529—944no—
418#529—944no—
419C2×#126—471no—
420C2×#126—471no—
421C2×#125—471no—
422C2×#124—471no—
423C2×#123—471no—
424C2×#123—471no—
425C2×C22⋊Q8—471no—
426C2×#121—471no—
427C2×C4×Q8—471no—
428C2×C4×D4—471no—
429C2×C4×D4—471no—
430C2×C4×D4—471no—
431C2×#117—471no—
432C2×#117—471no—
433C22×C42C2×D4711yescharacteristic
434#433—944no—
435C2×C4⋊C8—471no—
436C2×C4⋊C8—471no—
437C2×C22⋊C8—471no—
438C2×C22⋊C8—471no—
439C2×C22⋊C8—471no—
440C2×C22⋊C8—471no—
441C2×C22⋊C8—471no—
442C2×C22⋊C8—471no—
443C2×C22⋊C8—471no—
444C2×C22⋊C8—471no—
445C2×C22⋊C8C2×D4711yescharacteristic
446C2×C22⋊C8C2×D4711yescharacteristic
447#405—944no—
448C2×#97—471no—
449C2×#97C2×D4711yescharacteristic
450C2×#97C2×D4711yescharacteristic
451C2×C4×C8—471no—
452C2×C4×C8—471no—
453C2×C4×C8—471no—
454#336—471no—
455#336—471no—
456#336—471no—
457#336—471no—
458#336—471no—
459#336—471no—
460#336C2×D4711yescharacteristic
461#336C2×D4711yescharacteristic
462C47#2138111yescharacteristic, complemented, Sylow
463C22×Q8—471no—
464C22×D4—471no—
465C22×D4—471no—
466C22×D4—471no—
467C23×C4—471no—
468C23×C4—471no—
469C23×C4C4×D4711yescharacteristic
470C23×C4C4×D4711yescharacteristic
471C23×C4C22×D4711yescharacteristic
472C2×M16—942no—
473C2×M16—942no—
474C2×M16—942no—
475C22×C8—471no—
476C22×C8—471no—
477C22×C8—471no—
478C22×C8—471no—
479C22×C8—942no—
480C22×C8—942no—
481C22×C8—942no—
482C22×C8C22×D4711yescharacteristic
483C22×C8C22×D4711yescharacteristic
484C22×C8C22×D4711yescharacteristic
485C22×C8C22×D4711yescharacteristic
486#126—944no—
487#126—944no—
488#125—944no—
489#124—944no—
490#123—944no—
491#123—944no—
492C22⋊Q8—944no—
493#121—944no—
494C4×Q8—942no—
495C4×Q8—942no—
496C4×D4—942no—
497C4×D4—942no—
498C4×D4—942no—
499C4×D4—942no—
500C4×D4—942no—
501C4×D4—942no—
502#117—474no—
503#117—474no—
504#117—942no—
505#117—942no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—471no—
511C2×C4⋊C4—471no—
512C2×C4⋊C4—471no—
513C2×C4⋊C4—471no—
514C2×C4⋊C4—471no—
515C2×C4⋊C4—471no—
516C2×C22⋊C4—471no—
517C2×C22⋊C4—471no—
518C2×C22⋊C4—471no—
519C2×C22⋊C4—471no—
520C2×C22⋊C4—471no—
521C2×C22⋊C4—471no—
522C2×C22⋊C4—471no—
523C2×C22⋊C4—471no—
524C2×C22⋊C4—471no—
525C2×C22⋊C4—471no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—471no—
529C2×C42—471no—
530C2×C42C4×D4711yescharacteristic
531C2×C42C4×D4711yescharacteristic
532C2×C42C22×D4711yescharacteristic
533C2×C42C22×D4711yescharacteristic
534C4⋊C8—942no—
535C4⋊C8—942no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—942no—
539C22⋊C8—942no—
540C22⋊C8—942no—
541C22⋊C8—942no—
542C22⋊C8—942no—
543C22⋊C8—942no—
544C22⋊C8—942no—
545C22⋊C8—942no—
546#97—22no—
547#97—22no—
548#97—942no—
549C4×C8—942no—
550C4×C8—942no—
551C4×C8—942no—
552C24—471no—
553C24—471no—
554C24C2×C4×D4711yescharacteristic
555C2×Q8—942no—
556C2×Q8—942no—
557C2×Q8—1881no—
558C2×D4—942no—
559C2×D4—942no—
560C2×D4—942no—
561C2×D4—942no—
562C2×D4—942no—
563C2×D4—942no—
564C2×D4—1881no—
565C2×D4—1881no—
566C2×D4—1881no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—471no—
580C22×C4—471no—
581C22×C4—471no—
582C22×C4—472no—
583C22×C4—472no—
584C22×C4—471no—
585C22×C4—471no—
586C22×C4—471no—
587C22×C4—941no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4C2×C4×D4711yescharacteristic
598C22×C4C2×C4×D4711yescharacteristic
599C22×C4C2×C4×D4711yescharacteristic
600C22×C4C2×C4×D4711yescharacteristic
601C22×C4C2×C4×D4711yescharacteristic
602C22×C4C23×D4711yescharacteristic
603M16—948no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—472no—
615C2×C8—472no—
616C2×C8—948no—
617C2×C8—941no—
618C2×C8—941no—
619C2×C8—941no—
620C2×C8—941no—
621C2×C8—941no—
622C2×C8—941no—
623C2×C8—941no—
624C2×C8—941no—
625C2×C8—941no—
626C2×C8—941no—
627C2×C8#1062535012yes—
628C2×C8#1062535012yes—
629C4⋊C4—474no—
630C4⋊C4—474no—
631C4⋊C4—942no—
632C4⋊C4—942no—
633C4⋊C4—942no—
634C4⋊C4—942no—
635C4⋊C4—942no—
636C4⋊C4—942no—
637C4⋊C4—942no—
638C4⋊C4—942no—
639C22⋊C4—474no—
640C22⋊C4—474no—
641C22⋊C4—942no—
642C22⋊C4—942no—
643C22⋊C4—942no—
644C22⋊C4—942no—
645C22⋊C4—942no—
646C22⋊C4—942no—
647C22⋊C4—942no—
648C22⋊C4—942no—
649C42—22no—
650C42—22no—
651C42—21no—
652C42—21no—
653C42—472no—
654C42—472no—
655C42—941no—
656C42—941no—
657C42D4×D4712yes—
658C42D4×D4712yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—472no—
666C23—941no—
667C23—941no—
668C23—941no—
669C23—941no—
670C23—941no—
671C23—941no—
672C23—941no—
673C23—941no—
674C23—941no—
675C23—941no—
676C23—941no—
677C23—941no—
678C23—941no—
679C23#1309403212yes—
680C23C22×C4×D4711yescharacteristic
681Q8—1884no—
682D4—1884no—
683D4—1884no—
684D4—1884no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—472no—
704C2×C4—472no—
705C2×C4—472no—
706C2×C4—941no—
707C2×C4—941no—
708C2×C4—941no—
709C2×C4—941no—
710C2×C4—941no—
711C2×C4—941no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—941no—
717C2×C4—941no—
718C2×C4—941no—
719C2×C4—941no—
720C2×C4—941no—
721C2×C4—941no—
722C2×C4—941no—
723C2×C4—941no—
724C2×C4—941no—
725C2×C4—1881no—
726C2×C4—1881no—
727C2×C4—1881no—
728C2×C4—1881no—
729C2×C4C22⋊C4×D4712yes—
730C2×C4C22⋊C4×D4712yes—
731C2×C4#1309403212yes—
732C2×C4C2×D4×D4711yescharacteristic
733C2×C4C2×D4×D4711yescharacteristic
734C2×C4#41×D4711yescharacteristic
735C2×C4#41×D4711yescharacteristic
736C2×C4C2×#1062535011yescharacteristic
737C2×C4C2×#1062535011yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C8—942no—
743C8—942no—
744C8—1881no—
745C8—1881no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—942no—
754C22—942no—
755C22—942no—
756C22—1881no—
757C22—1881no—
758C22—1881no—
759C22—1881no—
760C22—1881no—
761C22—1881no—
762C22—1881no—
763C22—1881no—
764C22—1881no—
765C22—1881no—
766C22—1881no—
767C22C2×C22⋊C4×D4711yescharacteristic
768C22#1568959111yescharacteristic
769C22C4×#1062535011yescharacteristic
770C22C2×#1309403211yescharacteristic
771C22C2×#1309403211yescharacteristic
772C22#1568988911yescharacteristic
773C22#1568988911yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—41no—
778C4—41no—
779C4—942no—
780C4—942no—
781C4—942no—
782C4—1881no—
783C4—1881no—
784C4—1881no—
785C4#1568963211yescharacteristic
786C4#1568963211yescharacteristic
787C4#1568967011yescharacteristic
788C4#1568967011yescharacteristic
789C2—42no—
790C2—3761no—
791C2—1882no—
792C2#2024587411yescharacteristic
793C2#2025183811yescharacteristic
794C2#2025183811yescharacteristic
795C2#2025235711yescharacteristic
796C2#2025236811yescharacteristic
797C2#2025238211yescharacteristic
798C2#2025239211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1749C2
prime radicalC2×#13093998C4
cosocleC22×C4×C47C24
hypercenter#1749D47
hypocenterC47#21381
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C2×#15689185C2semidirect
3. C2×#15689080C2semidirect
4. #20244326C2semidirect
5. #20244322C2semidirect
6. #20244184C2semidirect
7. #20244180C2semidirect
8. #20243684C2semidirect
9. #20243682C2semidirect
10. #20243679C2semidirect
11. #20243677C2semidirect
12. #20243157C2semidirect
13. #20243157C2semidirect
14. C4×C22⋊(C47⋊C8)C2semidirect
15. C47×#1749C2semidirect
403. #1749D47semidirect
462. C47#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#156896572
C2×#156891852
C2×#156890802
#202443262
#202443222
#202441842
#202441802
#202436842
#202436822
#202436792
#202436772
#202431572
C4×C22⋊(C47⋊C8)2
C47×#17492
#2138147