Finite Group Databasebeta

← #22613467

Subgroups — #22613467

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×#14556564C211yesmaximal, characteristic, complemented
3C2×#14556560C211yesmaximal, characteristic, complemented
4C2×#14556560C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊D73C211yesmaximal, characteristic, complemented
6#17988510C211yesmaximal, characteristic, complemented
7#17988502C211yesmaximal, characteristic, complemented
8#17988502C211yesmaximal, characteristic, complemented
9#17988496C211yesmaximal, characteristic, complemented
10#17988487C211yesmaximal, characteristic, complemented
11#17988480C211yesmaximal, characteristic, complemented
12#17988466C211yesmaximal, characteristic, complemented
13#17988463C211yesmaximal, characteristic, complemented
14#17988460C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C73C211yesmaximal, characteristic, complemented
16C22×D292C2211yescharacteristic, complemented
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic
20C22×C22⋊D73C2211yescharacteristic
21C22×C22⋊D73C2211yescharacteristic
22C22×C22⋊D73C2211yescharacteristic
23C22×C4×D73C2211yescharacteristic, complemented
24#14556565—24no—
25#14556564—24no—
26#14556560—24no—
27#14556560—24no—
28C4×C22⋊D73—24no—
29C2×C4⋊Dic73C2211yescharacteristic, complemented
30C2×#11924007C2211yescharacteristic, complemented
31C2×#11924007C2211yescharacteristic, complemented
32C2×#11924007C2211yescharacteristic, complemented
33C2×C22⋊Dic73C2211yescharacteristic
34C2×C22⋊Dic73C2211yescharacteristic
35C2×C22⋊Dic73C2211yescharacteristic
36C2×C22⋊Dic73C2211yescharacteristic
37C2×C22⋊Dic73C2211yescharacteristic
38C2×C22⋊Dic73C2211yescharacteristic
39C2×#11924005C2211yescharacteristic, complemented
40C2×#11924005C2211yescharacteristic, complemented
41C2×#11924005C2211yescharacteristic, complemented
42C2×#11924005C2211yescharacteristic, complemented
43C2×#11924005C2211yescharacteristic, complemented
44C2×C4×Dic73C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46#14556498C2211yescharacteristic, complemented
47#14556498C2211yescharacteristic, complemented
48#14556498C2211yescharacteristic, complemented
49C25×C73C2211yescharacteristic
50C23×C4×C73C2211yescharacteristic
51C23×C4×C73C2211yescharacteristic
52C2×C22⋊C4×C73—24no—
53C2×C22⋊C4×C73C2211yescharacteristic
54C2×C22⋊C4×C73C2211yescharacteristic
55C2×C22⋊C4×C73C2211yescharacteristic
56C2×C22⋊C4×C73C2211yescharacteristic
57C23×D73C2311yescharacteristic
58C23×D73C2311yescharacteristic
59C2×D292—22no—
60C2×D292—22no—
61C2×D292—41no—
62C2×C22⋊D73—22no—
63C2×C22⋊D73—22no—
64C2×C22⋊D73—22no—
65C2×C22⋊D73—22no—
66C2×C22⋊D73—22no—
67C2×C22⋊D73—22no—
68C2×C22⋊D73—22no—
69C2×C22⋊D73—22no—
70C2×C22⋊D73—22no—
71C2×C22⋊D73—22no—
72C2×C22⋊D73—22no—
73C2×C22⋊D73—22no—
74C2×C22⋊D73—22no—
75C2×C22⋊D73—41no—
76C2×C22⋊D73—41no—
77C2×C22⋊D73—41no—
78C2×C22⋊D73—41no—
79C2×C22⋊D73D414yescomplemented
80C22×Dic73C2311yescharacteristic
81C22×Dic73C2311yescharacteristic
82C22×Dic73C2311yescharacteristic
83C22×Dic73C2311yescharacteristic
84C22×Dic73C2311yescharacteristic
85C22×Dic73C2311yescharacteristic
86C2×C4×D73—22no—
87C2×C4×D73—22no—
88C2×C4×D73—41no—
89C4⋊Dic73—22no—
90#11924007—22no—
91#11924007—22no—
92#11924007—41no—
93C22⋊Dic73—22no—
94C22⋊Dic73—22no—
95C22⋊Dic73—22no—
96C22⋊Dic73—22no—
97C22⋊Dic73—22no—
98C22⋊Dic73D414yescomplemented
99#11924005—22no—
100#11924005—22no—
101#11924005—22no—
102#11924005—22no—
103#11924005—41no—
104C4×Dic73—22no—
105C24×C73—22no—
106C24×C73—22no—
107C24×C73—22no—
108C24×C73—22no—
109C24×C73—22no—
110C24×C73—41no—
111C24×C73—41no—
112C24×C73C2311yescharacteristic
113C24×C73C2311yescharacteristic
114C24×C73C2311yescharacteristic
115C22×C4×C73—22no—
116C22×C4×C73—22no—
117C22×C4×C73—22no—
118C22×C4×C73—22no—
119C22×C4×C73—41no—
120C22×C4×C73—41no—
121C22×C4×C73C2311yescharacteristic
122C22×C4×C73C2311yescharacteristic
123C22×C4×C73C2311yescharacteristic
124C22×C4×C73C2311yescharacteristic
125C22⋊C4×C73—22no—
126C22⋊C4×C73—22no—
127C22⋊C4×C73—22no—
128C22⋊C4×C73D414yescomplemented
129C23×C73—21no—
130C23×C73—21no—
131C23×C73—21no—
132C23×C73—21no—
133C23×C73—28no—
134C23×C73—21no—
135C23×C73—21no—
136C23×C73—21no—
137C23×C73—21no—
138C23×C73—21no—
139C23×C73—21no—
140C23×C73—21no—
141C23×C73—21no—
142C23×C73—21no—
143C23×C73—21no—
144C23×C73—21no—
145C23×C73—21no—
146C23×C73—44no—
147C23×C73—44no—
148C23×C73—44no—
149C23×C73—44no—
150C23×C73—44no—
151C23×C73—44no—
152C23×C73C2×D412yes—
153C23×C73C2×D412yes—
154C23×C73C2×D412yes—
155C23×C73#4112yes—
156C23×C73#4112yes—
157C23×C73C2411yescharacteristic
158C22×D73—21no—
159C22×D73—21no—
160C22×D73—21no—
161C22×D73—21no—
162C22×D73—21no—
163C22×D73—21no—
164C22×D73—21no—
165C22×D73—21no—
166C22×D73—21no—
167C22×D73—21no—
168C22×D73—21no—
169C22×D73—21no—
170C22×D73—21no—
171C22×D73C2×D412yes—
172C2×C4×C73—21no—
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—44no—
183C2×C4×C73—44no—
184C2×C4×C73C2×D412yes—
185C2×C4×C73C2×D412yes—
186C22⋊D73—28no—
187C22⋊D73—44no—
188C22⋊D73—44no—
189C22⋊D73—44no—
190C22⋊D73—44no—
191C22⋊D73—44no—
192C2×Dic73—21no—
193C2×Dic73—21no—
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×Dic73C2×D412yes—
208C2×Dic73C2×D412yes—
209C2×Dic73C2×D412yes—
210D292—44no—
211C4×D73—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—22no—
222C22×C73—22no—
223C22×C73—22no—
224C22×C73—416no—
225C22×C73—41no—
226C22×C73—41no—
227C22×C73—41no—
228C22×C73—41no—
229C22×C73—41no—
230C22×C73—41no—
231C22×C73—41no—
232C22×C73—41no—
233C22×C73#12114yescomplemented
234C22×C73C22×D411yescharacteristic
235C22×C73C22×D411yescharacteristic
236C22×C73C22×D411yescharacteristic
237C22×C73C2×#4111yescharacteristic
238C22×C73C2×#4111yescharacteristic
239C22×C73H(5,𝔽2)11yescharacteristic
240C22×C73H(5,𝔽2)11yescharacteristic
241C2×D73—22no—
242C2×D73—22no—
243C2×D73—22no—
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—41no—
258C4×C73—41no—
259Dic73—22no—
260Dic73—22no—
261Dic73—22no—
262Dic73—41no—
263Dic73—41no—
264Dic73—41no—
265C2×C73—24no—
266C2×C73—42no—
267C2×C73—42no—
268C2×C73C2×#12111yescharacteristic
269C2×C73#52511yescharacteristic
270C2×C73#53811yescharacteristic
271C2×C73D4211yescharacteristic
272C2×C73D4211yescharacteristic
273C2×C73#54611yescharacteristic
274C2×C73#54611yescharacteristic
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×D4—731no—
284C22×C22⋊C4D7311yescharacteristic, complemented
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—
294C25C2×D7311yescharacteristic
295C22×D4—731no—
296C22×D4—731no—
297C22×D4—731no—
298C22×D4—731no—
299C22×D4—731no—
300C22×D4—731no—
301C22×D4—731no—
302C23×C4—731no—
303C23×C4C2×D7311yescharacteristic
304C23×C4C2×D7311yescharacteristic
305#121—1464no—
306#121—1464no—
307#120—1464no—
308#120—1464no—
309C4×D4—1464no—
310C2×C4⋊C4—731no—
311C2×C4⋊C4—731no—
312C2×C4⋊C4—731no—
313C2×C4⋊C4—731no—
314C2×C22⋊C4—24no—
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⋊C4C2×D7311yescharacteristic
327C2×C22⋊C4C2×D7311yescharacteristic
328C2×C22⋊C4C2×D7311yescharacteristic
329C2×C22⋊C4C2×D7311yescharacteristic
330C2×C42—731no—
331#95—731no—
332#95—731no—
333#95—731no—
334#95—731no—
335C24—22no—
336C24—22no—
337C24—22no—
338C24—22no—
339C24—22no—
340C24—41no—
341C24—41no—
342C24—731no—
343C24—731no—
344C24C22×D7311yescharacteristic
345C24C22×D7311yescharacteristic
346C24C22×D7311yescharacteristic
347C2×D4—2921no—
348C2×D4—2921no—
349C2×D4—2921no—
350C2×D4—2921no—
351C2×D4—2921no—
352C2×D4—734no—
353C2×D4—1462no—
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×D4—1462no—
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—731no—
381C22×C4—1462no—
382C22×C4—1462no—
383C22×C4C22×D7311yescharacteristic
384C22×C4C22×D7311yescharacteristic
385C22×C4C22×D7311yescharacteristic
386C22×C4C22×D7311yescharacteristic
387C4⋊C4—2921no—
388C4⋊C4—1462no—
389C4⋊C4—1462no—
390C4⋊C4—1462no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—2921no—
395C22⋊C4—734no—
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—1462no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—28no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—44no—
425C23—44no—
426C23—44no—
427C23—44no—
428C23—44no—
429C23—44no—
430C23—732no—
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—
444C23D4×D7312yes—
445C23D4×D7312yes—
446C23C2×C22⋊D7312yes—
447C23#1192402812yes—
448C23#1192402812yes—
449C23C23×D7311yescharacteristic
450D4—2924no—
451D4—2924no—
452D4—2924no—
453D4—2924no—
454D4—2924no—
455D4—2924no—
456D4—1468no—
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—44no—
468C2×C4—44no—
469C2×C4—2924no—
470C2×C4—732no—
471C2×C4—732no—
472C2×C4—732no—
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×C4—1461no—
487C2×C4—1461no—
488C2×C4C2×C22⋊D7312yes—
489C2×C4C2×C22⋊D7312yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—416no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—2921no—
512C22—2921no—
513C22—2921no—
514C22—2921no—
515C22—2921no—
516C22—2921no—
517C22—2921no—
518C22—2921no—
519C22—2921no—
520C22—2921no—
521C22—2921no—
522C22—1462no—
523C22—1462no—
524C22—1462no—
525C22#1455656414yescomplemented
526C22C2×D4×D7311yescharacteristic
527C22C2×D4×D7311yescharacteristic
528C22C22×C22⋊D7311yescharacteristic
529C22C2×#1192402811yescharacteristic
530C22C2×#1192402811yescharacteristic
531C22#1455663611yescharacteristic
532C22#1455663611yescharacteristic
533C4—22no—
534C4—22no—
535C4—41no—
536C4—41no—
537C4—2921no—
538C4—2921no—
539C4—2921no—
540C4—1462no—
541C4—1462no—
542C4—1462no—
543C2—24no—
544C2—42no—
545C2—42no—
546C2—2922no—
547C2—5841no—
548C2C2×#1455656411yescharacteristic
549C2#1798909811yescharacteristic
550C2#1798917511yescharacteristic
551C2D4×C22⋊D7311yescharacteristic
552C2D4×C22⋊D7311yescharacteristic
553C2#1798922711yescharacteristic
554C2#1798922711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC22×C22⋊C4×C73C2
hypercenterC22×C22⋊C4D73
hypocenterC73#2424
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14556565C2semidirect
2. C2×#14556564C2semidirect
3. C2×#14556560C2semidirect
4. C2×#14556560C2semidirect
5. C2×C4×C22⋊D73C2semidirect
6. #17988510C2semidirect
7. #17988502C2semidirect
8. #17988502C2semidirect
9. #17988496C2semidirect
10. #17988487C2semidirect
11. #17988480C2semidirect
12. #17988466C2semidirect
13. #17988463C2semidirect
14. #17988460C2semidirect
15. C22×C22⋊C4×C73C2semidirect
16. C22×D292C22semidirect
23. C22×C4×D73C22semidirect
29. C2×C4⋊Dic73C22semidirect
30. C2×#11924007C22semidirect
31. C2×#11924007C22semidirect
32. C2×#11924007C22semidirect
39. C2×#11924005C22semidirect
40. C2×#11924005C22semidirect
41. C2×#11924005C22semidirect
42. C2×#11924005C22semidirect
43. C2×#11924005C22semidirect
44. C2×C4×Dic73C22semidirect
45. #14556498C22semidirect
46. #14556498C22semidirect
47. #14556498C22semidirect
48. #14556498C22semidirect
79. C2×C22⋊D73D4semidirect
98. C22⋊Dic73D4semidirect
128. C22⋊C4×C73D4semidirect
233. C22×C73#121semidirect
278. C73#2424semidirect
284. C22×C22⋊C4D73semidirect
405. C22⋊C4C22⋊D73semidirect
525. C22#14556564semidirect