Finite Group Databasebeta

← #22613463

Subgroups — #22613463

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×#14556563C211yesmaximal, characteristic, complemented
2C2×#14556562C211yesmaximal, characteristic, complemented
3C2×#14556560C211yesmaximal, characteristic, complemented
4C2×#14556551C211yesmaximal, characteristic, complemented
5C22×C22⋊Dic73C211yesmaximal, characteristic, complemented
6#17988510C211yesmaximal, characteristic, complemented
7#17988503C211yesmaximal, characteristic, complemented
8#17988501C211yesmaximal, characteristic, complemented
9#17988495C211yesmaximal, characteristic, complemented
10#17988490C211yesmaximal, characteristic, complemented
11#17988475C211yesmaximal, characteristic, complemented
12#17988467C211yesmaximal, characteristic, complemented
13#17988463C211yesmaximal, characteristic, complemented
14#17988462C211yesmaximal, characteristic, complemented
15C2×#120×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic, complemented
20C23×Dic73C2211yescharacteristic
21C23×Dic73C2211yescharacteristic
22C22×C4×D73C2211yescharacteristic, complemented
23#14556563—24no—
24#14556562—24no—
25#14556560—24no—
26#14556551—24no—
27C2×C4⋊Dic73C2211yescharacteristic, complemented
28C2×C4⋊Dic73C2211yescharacteristic, complemented
29C2×#11924007C2211yescharacteristic, complemented
30C2×#11924007C2211yescharacteristic, complemented
31C2×C22⋊Dic73—24no—
32C2×C22⋊Dic73C2211yescharacteristic
33C2×C22⋊Dic73C2211yescharacteristic
34C2×C22⋊Dic73C2211yescharacteristic
35C2×C22⋊Dic73C2211yescharacteristic
36C2×C22⋊Dic73C2211yescharacteristic
37C2×C22⋊Dic73C2211yescharacteristic
38C2×C22⋊Dic73C2211yescharacteristic
39C2×C22⋊Dic73C2211yescharacteristic, complemented
40C2×C22⋊Dic73C2211yescharacteristic, complemented
41C2×C22⋊Dic73C2211yescharacteristic, 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
50C22×D4×C73C2211yescharacteristic
51C22×D4×C73C2211yescharacteristic
52C22×D4×C73C2211yescharacteristic
53#120×C73—24no—
54C2×C22⋊C4×C73C2211yescharacteristic
55C2×C22⋊C4×C73C2211yescharacteristic
56C2×C22⋊C4×C73C2211yescharacteristic
57C23×D73C2311yescharacteristic
58C2×C22⋊D73—22no—
59C2×C22⋊D73—22no—
60C2×C22⋊D73—22no—
61C2×C22⋊D73—22no—
62C2×C22⋊D73—22no—
63C2×C22⋊D73—22no—
64C2×C22⋊D73—22no—
65C2×C22⋊D73—22no—
66C2×C22⋊D73—41no—
67C2×C22⋊D73—41no—
68C2×C22⋊D73—41no—
69C2×C22⋊D73D414yescomplemented
70C22×Dic73—22no—
71C22×Dic73—22no—
72C22×Dic73—22no—
73C22×Dic73—22no—
74C22×Dic73—41no—
75C22×Dic73—41no—
76C22×Dic73C2311yescharacteristic
77C22×Dic73C2311yescharacteristic
78C22×Dic73C2311yescharacteristic
79C22×Dic73C2311yescharacteristic
80C22×Dic73C2311yescharacteristic
81C22×Dic73C2311yescharacteristic
82C22×Dic73C2311yescharacteristic
83C2×C4×D73—22no—
84C2×C4×D73—22no—
85C2×C4×D73—41no—
86C4⋊Dic73—22no—
87C4⋊Dic73—41no—
88#11924007—22no—
89#11924007—22no—
90C22⋊Dic73—22no—
91C22⋊Dic73—22no—
92C22⋊Dic73—22no—
93C22⋊Dic73—22no—
94C22⋊Dic73—22no—
95C22⋊Dic73—22no—
96C22⋊Dic73—22no—
97C22⋊Dic73—22no—
98C22⋊Dic73—41no—
99C22⋊Dic73D414yescomplemented
100#11924005—22no—
101#11924005—22no—
102C4×Dic73—22no—
103C24×C73—22no—
104C24×C73—22no—
105C24×C73—22no—
106C24×C73—22no—
107C24×C73—22no—
108C24×C73—41no—
109C24×C73—41no—
110C24×C73C2311yescharacteristic
111C24×C73C2311yescharacteristic
112C24×C73C2311yescharacteristic
113C24×C73C2311yescharacteristic
114C2×D4×C73—22no—
115C2×D4×C73—22no—
116C2×D4×C73—22no—
117C2×D4×C73—22no—
118C2×D4×C73—22no—
119C2×D4×C73—22no—
120C2×D4×C73—22no—
121C2×D4×C73—41no—
122C2×D4×C73—41no—
123C22×C4×C73C2311yescharacteristic
124C22×C4×C73C2311yescharacteristic
125C22×C4×C73C2311yescharacteristic
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—21no—
147C23×C73—21no—
148C23×C73—21no—
149C23×C73—21no—
150C23×C73—21no—
151C23×C73—21no—
152C23×C73—21no—
153C23×C73—44no—
154C23×C73—44no—
155C23×C73—44no—
156C23×C73—44no—
157C23×C73—44no—
158C23×C73—44no—
159C23×C73C2×D412yes—
160C23×C73C2×D412yes—
161C23×C73C2×D412yes—
162C23×C73#4112yes—
163C23×C73#4112yes—
164C23×C73C2411yescharacteristic
165C22×D73—21no—
166C22×D73—21no—
167C22×D73—21no—
168C22×D73—21no—
169C22×D73—21no—
170C22×D73—21no—
171C22×D73C2×D412yes—
172D4×C73—44no—
173D4×C73—44no—
174D4×C73—44no—
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×C73C2×D412yes—
183C2×C4×C73C2×D412yes—
184C22⋊D73—28no—
185C22⋊D73—44no—
186C22⋊D73—44no—
187C22⋊D73—44no—
188C2×Dic73—21no—
189C2×Dic73—21no—
190C2×Dic73—21no—
191C2×Dic73—21no—
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—44no—
207C2×Dic73—44no—
208C2×Dic73C2×D412yes—
209C2×Dic73C2×D412yes—
210C2×Dic73C2×D412yes—
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—41no—
234C22×C73—41no—
235C22×C73—41no—
236C22×C73—41no—
237C22×C73—41no—
238C22×C73—41no—
239C22×C73—41no—
240C22×C73#12114yescomplemented
241C22×C73C22×D411yescharacteristic
242C22×C73C22×D411yescharacteristic
243C22×C73C22×D411yescharacteristic
244C22×C73C2×#4111yescharacteristic
245C22×C73C2×#4111yescharacteristic
246C22×C73H(5,𝔽2)11yescharacteristic
247C22×C73H(5,𝔽2)11yescharacteristic
248C2×D73—22no—
249C2×D73—22no—
250C2×D73—22no—
251C2×D73—41no—
252C2×D73—41no—
253C2×D73—41no—
254C2×D73—41no—
255C4×C73—22no—
256C4×C73—22no—
257C4×C73—41no—
258Dic73—22no—
259Dic73—22no—
260Dic73—22no—
261Dic73—41no—
262Dic73—41no—
263Dic73—41no—
264Dic73—41no—
265C2×C73—24no—
266C2×C73—42no—
267C2×C73—42no—
268C2×C73—81no—
269C2×C73C2×#12111yescharacteristic
270C2×C73#52511yescharacteristic
271C2×C73#53811yescharacteristic
272C2×C73D4211yescharacteristic
273C2×C73D4211yescharacteristic
274C2×C73#54611yescharacteristic
275C2×C73#54611yescharacteristic
276D73—42no—
277#2424—731nomaximal, Sylow
278C73#242411yescharacteristic, complemented, Sylow
279C2×#121—731no—
280C2×#121—731no—
281C2×#120—731no—
282C2×#120D7311yescharacteristic, complemented
283C2×C4×D4—731no—
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—
294C25C2×D7311yescharacteristic
295C22×D4—731no—
296C22×D4—731no—
297C22×D4—731no—
298C22×D4—731no—
299C22×D4C2×D7311yescharacteristic
300C22×D4C2×D7311yescharacteristic
301C22×D4C2×D7311yescharacteristic
302C23×C4—731no—
303C23×C4—731no—
304C23×C4—731no—
305#121—1464no—
306#121—1464no—
307#120—24no—
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—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—1464no—
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—
343C24C22×D7311yescharacteristic
344C24C22×D7311yescharacteristic
345C24C22×D7311yescharacteristic
346C24C22×D7311yescharacteristic
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—2921no—
357C2×D4—2921no—
358C2×D4—2921no—
359C2×D4—734no—
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—2921no—
369C22×C4—2921no—
370C22×C4—2921no—
371C22×C4—731no—
372C22×C4—731no—
373C22×C4—731no—
374C22×C4—731no—
375C22×C4—731no—
376C22×C4—731no—
377C22×C4—731no—
378C22×C4—1462no—
379C22×C4—1462no—
380C22×C4—1462no—
381C22×C4—1462no—
382C22×C4—1462no—
383C22×C4—1462no—
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—2921no—
394C22⋊C4—734no—
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—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—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—44no—
435C23—44no—
436C23—44no—
437C23—732no—
438C23—1461no—
439C23—1461no—
440C23—1461no—
441C23—1461no—
442C23—1461no—
443C23—1461no—
444C23D4×D7312yes—
445C23D4×D7312yes—
446C23C2×C22⋊D7312yes—
447C23#1192402712yes—
448C23#1192402712yes—
449C23C23×D7311yescharacteristic
450D4—44no—
451D4—44no—
452D4—44no—
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—2924no—
465C2×C4—2924no—
466C2×C4—2924no—
467C2×C4—732no—
468C2×C4—732no—
469C2×C4—732no—
470C2×C4—1461no—
471C2×C4—1461no—
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×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—41no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—2921no—
519C22—2921no—
520C22—2921no—
521C22—2921no—
522C22—1462no—
523C22—1462no—
524C22—1462no—
525C22#1455656214yescomplemented
526C22C2×D4×D7311yescharacteristic
527C22C2×D4×D7311yescharacteristic
528C22C22×C22⋊D7311yescharacteristic
529C22C2×#1192402711yescharacteristic
530C22C2×#1192402711yescharacteristic
531C22#1455663611yescharacteristic
532C22#1455663611yescharacteristic
533C4—22no—
534C4—22no—
535C4—41no—
536C4—2921no—
537C4—2921no—
538C4—2921no—
539C4—2921no—
540C4—1462no—
541C4—1462no—
542C4—1462no—
543C2—24no—
544C2—42no—
545C2—42no—
546C2—81no—
547C2—2922no—
548C2C2×#1455656211yescharacteristic
549C2#1798909311yescharacteristic
550C2#1798917211yescharacteristic
551C2#1798921911yescharacteristic
552C2D4×C22⋊D7311yescharacteristic
553C2#1798922411yescharacteristic
554C2#1798923111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#120×C73C2
hypercenterC2×#120D73
hypocenterC73#2424
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#14556563C2semidirect
2. C2×#14556562C2semidirect
3. C2×#14556560C2semidirect
4. C2×#14556551C2semidirect
5. C22×C22⋊Dic73C2semidirect
6. #17988510C2semidirect
7. #17988503C2semidirect
8. #17988501C2semidirect
9. #17988495C2semidirect
10. #17988490C2semidirect
11. #17988475C2semidirect
12. #17988467C2semidirect
13. #17988463C2semidirect
14. #17988462C2semidirect
15. C2×#120×C73C2semidirect
19. C22×C22⋊D73C22semidirect
22. C22×C4×D73C22semidirect
27. C2×C4⋊Dic73C22semidirect
28. C2×C4⋊Dic73C22semidirect
29. C2×#11924007C22semidirect
30. C2×#11924007C22semidirect
39. C2×C22⋊Dic73C22semidirect
40. C2×C22⋊Dic73C22semidirect
41. C2×C22⋊Dic73C22semidirect
42. C2×#11924005C22semidirect
43. C2×#11924005C22semidirect
44. C2×C4×Dic73C22semidirect
45. #14556498C22semidirect
46. #14556498C22semidirect
47. #14556498C22semidirect
48. #14556498C22semidirect
69. C2×C22⋊D73D4semidirect
99. C22⋊Dic73D4semidirect
128. C22⋊C4×C73D4semidirect
240. C22×C73#121semidirect
278. C73#2424semidirect
282. C2×#120D73semidirect
405. C22⋊C4C22⋊D73semidirect
525. C22#14556562semidirect