Finite Group Databasebeta

← #22613461

Subgroups — #22613461

Order 9344.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556565C211yesmaximal, characteristic, complemented
2C2×#14556563C211yesmaximal, characteristic, complemented
3C2×#14556561C211yesmaximal, characteristic, complemented
4C2×#14556559C211yesmaximal, characteristic, complemented
5C22×#11924005C211yesmaximal, characteristic, complemented
6#17988509C211yesmaximal, characteristic, complemented
7#17988504C211yesmaximal, characteristic, complemented
8#17988503C211yesmaximal, characteristic, complemented
9#17988496C211yesmaximal, characteristic, complemented
10#17988489C211yesmaximal, characteristic, complemented
11#17988478C211yesmaximal, characteristic, complemented
12#17988466C211yesmaximal, characteristic, complemented
13#17988466C211yesmaximal, characteristic, complemented
14#17988462C211yesmaximal, characteristic, complemented
15C2×C4×D4×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C22×D292C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic
20C22×C22⋊D73C2211yescharacteristic
21C22×C22⋊D73C2211yescharacteristic
22C22×C22⋊D73C2211yescharacteristic, complemented
23C23×Dic73C2211yescharacteristic
24#14556565—24no—
25#14556563—24no—
26#14556561—24no—
27#14556559—24no—
28C2×C4⋊Dic73C2211yescharacteristic, complemented
29C2×C4⋊Dic73C2211yescharacteristic, complemented
30C2×#11924007C2211yescharacteristic, complemented
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic, complemented
33C2×#11924005—24no—
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic
39C2×#11924005C2211yescharacteristic
40C2×#11924005C2211yescharacteristic
41C2×#11924005C2211yescharacteristic
42C2×#11924005C2211yescharacteristic, complemented
43C2×#11924005C2211yescharacteristic, complemented
44C2×#11924005C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46#14556498C2211yescharacteristic, complemented
47#14556498C2211yescharacteristic, complemented
48#14556498C2211yescharacteristic, complemented
49C22×D4×C73C2211yescharacteristic
50C23×C4×C73C2211yescharacteristic
51C23×C4×C73C2211yescharacteristic, complemented
52C4×D4×C73—24no—
53C2×C4⋊C4×C73C2211yescharacteristic, complemented
54C2×C22⋊C4×C73C2211yescharacteristic
55C2×C22⋊C4×C73C2211yescharacteristic, complemented
56C2×C42×C73C2211yescharacteristic, complemented
57C23×D73—22no—
58C23×D73—22no—
59C23×D73—22no—
60C23×D73—22no—
61C23×D73—22no—
62C23×D73—41no—
63C23×D73—41no—
64C23×D73C2311yescharacteristic
65C23×D73C2311yescharacteristic
66C23×D73C2311yescharacteristic
67C2×D292—22no—
68C2×D292—22no—
69C2×D292—22no—
70C2×D292—22no—
71C2×D292—41no—
72C2×D292—41no—
73C2×C22⋊D73—22no—
74C2×C22⋊D73—22no—
75C2×C22⋊D73—22no—
76C2×C22⋊D73—22no—
77C2×C22⋊D73—22no—
78C2×C22⋊D73—22no—
79C2×C22⋊D73—22no—
80C2×C22⋊D73—22no—
81C2×C22⋊D73—22no—
82C2×C22⋊D73—41no—
83C2×C22⋊D73—41no—
84C2×C22⋊D73—41no—
85C22×Dic73—22no—
86C22×Dic73—22no—
87C22×Dic73—41no—
88C22×Dic73C2311yescharacteristic
89C22×Dic73C2311yescharacteristic
90C22×Dic73C2311yescharacteristic
91C22×Dic73C2311yescharacteristic
92C22×Dic73C2311yescharacteristic
93C4⋊Dic73—22no—
94C4⋊Dic73—41no—
95#11924007—22no—
96C22⋊Dic73—22no—
97C22⋊Dic73—22no—
98#11924005—22no—
99#11924005—22no—
100#11924005—22no—
101#11924005—22no—
102#11924005—22no—
103#11924005—22no—
104#11924005—22no—
105#11924005—22no—
106#11924005—22no—
107#11924005—41no—
108#11924005D414yescomplemented
109C24×C73C2311yescharacteristic
110C24×C73C2311yescharacteristic
111C2×D4×C73—22no—
112C2×D4×C73—22no—
113C2×D4×C73D414yescomplemented
114C22×C4×C73—22no—
115C22×C4×C73—22no—
116C22×C4×C73—22no—
117C22×C4×C73—22no—
118C22×C4×C73—41no—
119C22×C4×C73—41no—
120C22×C4×C73C2311yescharacteristic
121C22×C4×C73C2311yescharacteristic
122C22×C4×C73C2311yescharacteristic
123C22×C4×C73C2311yescharacteristic
124C22×C4×C73C2311yescharacteristic
125C4⋊C4×C73—22no—
126C22⋊C4×C73—22no—
127C22⋊C4×C73D414yescomplemented
128C42×C73—22no—
129C23×C73—21no—
130C23×C73—21no—
131C23×C73—21no—
132C23×C73—21no—
133C23×C73—21no—
134C23×C73—21no—
135C23×C73—21no—
136C23×C73—21no—
137C23×C73—21no—
138C23×C73—21no—
139C23×C73C2×D412yes—
140C23×C73C2×D412yes—
141C23×C73C2×D412yes—
142C23×C73#4112yes—
143C23×C73C2411yescharacteristic
144C22×D73—28no—
145C22×D73—21no—
146C22×D73—21no—
147C22×D73—21no—
148C22×D73—21no—
149C22×D73—21no—
150C22×D73—21no—
151C22×D73—21no—
152C22×D73—21no—
153C22×D73—21no—
154C22×D73—21no—
155C22×D73—21no—
156C22×D73—21no—
157C22×D73—21no—
158C22×D73—21no—
159C22×D73—21no—
160C22×D73—21no—
161C22×D73—21no—
162C22×D73—21no—
163C22×D73—21no—
164C22×D73—44no—
165C22×D73—44no—
166C22×D73—44no—
167C22×D73—44no—
168C22×D73—44no—
169C22×D73—44no—
170C22×D73C2×D412yes—
171C22×D73#4112yes—
172D4×C73—28no—
173C2×C4×C73—21no—
174C2×C4×C73—21no—
175C2×C4×C73—21no—
176C2×C4×C73—21no—
177C2×C4×C73—21no—
178C2×C4×C73—21no—
179C2×C4×C73—21no—
180C2×C4×C73—21no—
181C2×C4×C73—21no—
182C2×C4×C73—21no—
183C2×C4×C73—21no—
184C2×C4×C73—44no—
185C2×C4×C73—44no—
186C2×C4×C73C2×D412yes—
187C2×C4×C73C2×D412yes—
188C2×C4×C73C2×D412yes—
189C2×C4×C73C2×D412yes—
190C22⋊D73—44no—
191C22⋊D73—44no—
192C22⋊D73—44no—
193C22⋊D73—44no—
194C2×Dic73—21no—
195C2×Dic73—21no—
196C2×Dic73—21no—
197C2×Dic73—21no—
198C2×Dic73—21no—
199C2×Dic73—21no—
200C2×Dic73—21no—
201C2×Dic73—21no—
202C2×Dic73—21no—
203C2×Dic73—21no—
204C2×Dic73—21no—
205C2×Dic73—21no—
206C2×Dic73—21no—
207C2×Dic73—21no—
208C2×Dic73—44no—
209C2×Dic73C2×D412yes—
210D292—44no—
211D292—44no—
212C22×C73—22no—
213C22×C73—22no—
214C22×C73—22no—
215C22×C73—22no—
216C22×C73—22no—
217C22×C73—22no—
218C22×C73—22no—
219C22×C73—22no—
220C22×C73—22no—
221C22×C73—41no—
222C22×C73—41no—
223C22×C73—41no—
224C22×C73—41no—
225C22×C73#12114yescomplemented
226C22×C73C22×D411yescharacteristic
227C22×C73C22×D411yescharacteristic
228C22×C73C22×D411yescharacteristic
229C22×C73C2×#4111yescharacteristic
230C22×C73C2×#4111yescharacteristic
231C22×C73H(5,𝔽2)11yescharacteristic
232C22×C73H(5,𝔽2)11yescharacteristic
233C2×D73—22no—
234C2×D73—22no—
235C2×D73—22no—
236C2×D73—22no—
237C2×D73—22no—
238C2×D73—22no—
239C2×D73—416no—
240C2×D73—41no—
241C2×D73—41no—
242C2×D73—41no—
243C2×D73—41no—
244C2×D73—41no—
245C2×D73—41no—
246C2×D73—41no—
247C2×D73—41no—
248C2×D73—41no—
249C2×D73—41no—
250C2×D73—41no—
251C2×D73—41no—
252C2×D73—41no—
253C2×D73—41no—
254C2×D73—41no—
255C4×C73—22no—
256C4×C73—22no—
257C4×C73—22no—
258C4×C73—22no—
259C4×C73—41no—
260Dic73—22no—
261Dic73—41no—
262Dic73—41no—
263Dic73—41no—
264Dic73—41no—
265C2×C73—24no—
266C2×C73—42no—
267C2×C73C2×#12111yescharacteristic
268C2×C73#52511yescharacteristic
269C2×C73#53811yescharacteristic
270C2×C73D4211yescharacteristic
271C2×C73D4211yescharacteristic
272C2×C73#54611yescharacteristic
273C2×C73#54611yescharacteristic
274D73—42no—
275D73—42no—
276D73—81no—
277#2424—731nomaximal, Sylow
278C73#242411yescharacteristic, complemented, Sylow
279C2×#121—731no—
280C2×#121—731no—
281C2×#120—731no—
282C2×#120—731no—
283C2×C4×D4D7311yescharacteristic, complemented
284C22×C22⋊C4—731no—
285#396—731no—
286#394—731no—
287#394—731no—
288#392—731no—
289#390—731no—
290#388—731no—
291#386—731no—
292#386—731no—
293#385—731no—
294C25—731no—
295C22×D4—731no—
296C22×D4—731no—
297C22×D4—731no—
298C22×D4—731no—
299C22×D4—731no—
300C22×D4—731no—
301C22×D4C2×D7311yescharacteristic
302C23×C4—731no—
303C23×C4C2×D7311yescharacteristic
304C23×C4C2×D7311yescharacteristic, complemented
305#121—1464no—
306#121—1464no—
307#120—1464no—
308#120—1464no—
309C4×D4—24no—
310C2×C4⋊C4—731no—
311C2×C4⋊C4—731no—
312C2×C4⋊C4—731no—
313C2×C4⋊C4C2×D7311yescharacteristic, complemented
314C2×C22⋊C4—731no—
315C2×C22⋊C4—731no—
316C2×C22⋊C4—731no—
317C2×C22⋊C4—731no—
318C2×C22⋊C4—731no—
319C2×C22⋊C4—731no—
320C2×C22⋊C4—731no—
321C2×C22⋊C4—731no—
322C2×C22⋊C4—731no—
323C2×C22⋊C4—731no—
324C2×C22⋊C4—731no—
325C2×C22⋊C4—731no—
326C2×C22⋊C4—731no—
327C2×C22⋊C4—1464no—
328C2×C22⋊C4C2×D7311yescharacteristic
329C2×C22⋊C4C2×D7311yescharacteristic, complemented
330C2×C42C2×D7311yescharacteristic, complemented
331#95—731no—
332#95—731no—
333#95—731no—
334#95—731no—
335C24—2921no—
336C24—2921no—
337C24—731no—
338C24—731no—
339C24—731no—
340C24—1462no—
341C24—1462no—
342C24—1462no—
343C24—1462no—
344C24—1462no—
345C24C22×D7311yescharacteristic
346C24C22×D7311yescharacteristic
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—2921no—
350C2×D4—2921no—
351C2×D4—2921no—
352C2×D4—2921no—
353C2×D4—2921no—
354C2×D4—1462no—
355C2×D4—1462no—
356C2×D4—1462no—
357C2×D4—1462no—
358C2×D4—1462no—
359C2×D4—1462no—
360C2×D4—1462no—
361C2×D4—1462no—
362C2×D4—1462no—
363C2×D4—1462no—
364C2×D4—1462no—
365C2×D4—1462no—
366C2×D4—1462no—
367C2×D4D29214yescomplemented
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—2921no—
375C22×C4—731no—
376C22×C4—731no—
377C22×C4—731no—
378C22×C4—731no—
379C22×C4—731no—
380C22×C4—1462no—
381C22×C4—1462no—
382C22×C4C22×D7311yescharacteristic
383C22×C4C22×D7311yescharacteristic
384C22×C4C22×D7311yescharacteristic
385C22×C4C22×D7311yescharacteristic
386C22×C4C22×D7311yescharacteristic
387C4⋊C4—22no—
388C4⋊C4—2921no—
389C4⋊C4—1462no—
390C4⋊C4—1462no—
391C22⋊C4—22no—
392C22⋊C4—2921no—
393C22⋊C4—734no—
394C22⋊C4—1462no—
395C22⋊C4—1462no—
396C22⋊C4—1462no—
397C22⋊C4—1462no—
398C22⋊C4—1462no—
399C22⋊C4—1462no—
400C22⋊C4—1462no—
401C22⋊C4—1462no—
402C22⋊C4—1462no—
403C22⋊C4—1462no—
404C22⋊C4—1462no—
405C22⋊C4C22⋊D7314yescomplemented
406C42—22no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—2924no—
418C23—2924no—
419C23—2924no—
420C23—2924no—
421C23—2924no—
422C23—2924no—
423C23—732no—
424C23—732no—
425C23—1468no—
426C23—1461no—
427C23—1461no—
428C23—1461no—
429C23—1461no—
430C23—1461no—
431C23—1461no—
432C23—1461no—
433C23—1461no—
434C23—1461no—
435C23—1461no—
436C23—1461no—
437C23—1461no—
438C23—1461no—
439C23—1461no—
440C23—1461no—
441C23—1461no—
442C23—1461no—
443C23—1461no—
444C23—1461no—
445C23C2×C22⋊D7312yes—
446C23C2×D29212yes—
447C23C2×D29212yes—
448C23#1192402812yes—
449C23C23×D7311yescharacteristic
450D4—28no—
451D4—2924no—
452D4—2924no—
453D4—2924no—
454D4—2924no—
455D4—2924no—
456D4—2924no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—2924no—
471C2×C4—732no—
472C2×C4—1461no—
473C2×C4—1461no—
474C2×C4—1461no—
475C2×C4—1461no—
476C2×C4—1461no—
477C2×C4—1461no—
478C2×C4—1461no—
479C2×C4—1461no—
480C2×C4—1461no—
481C2×C4—1461no—
482C2×C4—1461no—
483C2×C4—1461no—
484C2×C4—1461no—
485C2×C4—1461no—
486C2×C4D4×D7312yes—
487C2×C4C2×C22⋊D7312yes—
488C2×C4C2×C22⋊D7312yes—
489C2×C4C2×D29212yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—29216no—
504C22—2921no—
505C22—2921no—
506C22—2921no—
507C22—2921no—
508C22—2921no—
509C22—2921no—
510C22—2921no—
511C22—2921no—
512C22—2921no—
513C22—2921no—
514C22—2921no—
515C22—2921no—
516C22—2921no—
517C22—2921no—
518C22—2921no—
519C22—1462no—
520C22—1462no—
521C22—1462no—
522C22—1462no—
523C22—1462no—
524C22—1462no—
525C22#1455656514yescomplemented
526C22C2×D4×D7311yescharacteristic
527C22C22×C22⋊D7311yescharacteristic
528C22C22×D29211yescharacteristic
529C22#41×D7311yescharacteristic
530C22C2×#1192402811yescharacteristic
531C22#1455663611yescharacteristic
532C22#1455663711yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—2921no—
539C4—2921no—
540C4—2921no—
541C4—2921no—
542C4—1462no—
543C2—24no—
544C2—42no—
545C2—2922no—
546C2—2922no—
547C2—5841no—
548C2C2×#1455656511yescharacteristic
549C2#1798909611yescharacteristic
550C2#1798917011yescharacteristic
551C2D4×C22⋊D7311yescharacteristic
552C2D4×D29211yescharacteristic
553C2#1798922511yescharacteristic
554C2#1798923211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×C4×D4×C73C2
hypercenterC2×C4×D4D73
hypocenterC73#2424
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14556565C2semidirect
2. C2×#14556563C2semidirect
3. C2×#14556561C2semidirect
4. C2×#14556559C2semidirect
5. C22×#11924005C2semidirect
6. #17988509C2semidirect
7. #17988504C2semidirect
8. #17988503C2semidirect
9. #17988496C2semidirect
10. #17988489C2semidirect
11. #17988478C2semidirect
12. #17988466C2semidirect
13. #17988466C2semidirect
14. #17988462C2semidirect
15. C2×C4×D4×C73C2semidirect
22. C22×C22⋊D73C22semidirect
28. C2×C4⋊Dic73C22semidirect
29. C2×C4⋊Dic73C22semidirect
30. C2×#11924007C22semidirect
32. C2×C22⋊Dic73C22semidirect
42. C2×#11924005C22semidirect
43. C2×#11924005C22semidirect
44. C2×#11924005C22semidirect
45. #14556498C22semidirect
46. #14556498C22semidirect
47. #14556498C22semidirect
48. #14556498C22semidirect
51. C23×C4×C73C22semidirect
53. C2×C4⋊C4×C73C22semidirect
55. C2×C22⋊C4×C73C22semidirect
56. C2×C42×C73C22semidirect
108. #11924005D4semidirect
113. C2×D4×C73D4semidirect
127. C22⋊C4×C73D4semidirect
225. C22×C73#121semidirect
278. C73#2424semidirect
283. C2×C4×D4D73semidirect
304. C23×C4C2×D73semidirect
313. C2×C4⋊C4C2×D73semidirect
329. C2×C22⋊C4C2×D73semidirect
330. C2×C42C2×D73semidirect
367. C2×D4D292semidirect
405. C22⋊C4C22⋊D73semidirect
525. C22#14556565semidirect