Finite Group Databasebeta

← #22612909

Subgroups — #22612909

Order 9344.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556561C211yesmaximal, characteristic
2C2×C4×D292C211yesmaximal, characteristic, complemented
3C2×#14556553C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D73C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D73C211yesmaximal, characteristic, complemented
6#17988487C211yesmaximal, characteristic, complemented
7#17988480C211yesmaximal, characteristic, complemented
8#17988465C211yesmaximal, characteristic, complemented
9#17988465C211yesmaximal, characteristic, complemented
10#17988463C211yesmaximal, characteristic, complemented
11#17988461C211yesmaximal, characteristic, complemented
12#17988458C211yesmaximal, characteristic, complemented
13C4×#11924005C211yesmaximal, characteristic, complemented
14#17988434C211yesmaximal, characteristic, complemented
15#388×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C22×D292C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic
20C22×C4×D73C2211yescharacteristic
21C22×C4×D73C2211yescharacteristic
22C22×C4×D73C2211yescharacteristic
23C22×C4×D73C2211yescharacteristic
24C22×C4×D73C2211yescharacteristic, complemented
25#14556561C418yescomplemented
26C4×D292—24no—
27#14556553—24no—
28C2×C4⋊Dic73C2211yescharacteristic, complemented
29C2×#11924007C2211yescharacteristic, complemented
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic, complemented
39C2×#11924005C2211yescharacteristic, complemented
40C2×#11924005C2211yescharacteristic, complemented
41C22⋊C4×D73—24no—
42C22⋊C4×D73—24no—
43C2×C4×Dic73C2211yescharacteristic, complemented
44C2×C4×Dic73C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46#14556498C2211yescharacteristic, complemented
47#14556498C2211yescharacteristic, complemented
48#14556498C2211yescharacteristic, complemented
49C2×C4⋊C4×C73C2211yescharacteristic, complemented
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C22⋊C4×C73C2211yescharacteristic
53C2×C42×C73C2211yescharacteristic, complemented
54#95×C73C2211yescharacteristic, complemented
55#95×C73C2211yescharacteristic, complemented
56C23×D73—22no—
57C23×D73—22no—
58C23×D73—22no—
59C23×D73—22no—
60C23×D73—41no—
61C23×D73—41no—
62C23×D73C2×C414yescomplemented
63C23×D73C2311yescharacteristic
64C23×D73C2311yescharacteristic
65C23×D73C2311yescharacteristic
66C2×D292—22no—
67C2×D292—22no—
68C2×D292—22no—
69C2×D292—22no—
70C2×D292C2×C414yescomplemented
71C2×D292C2×C414yescomplemented
72C2×C22⋊D73—41no—
73C2×C22⋊D73—41no—
74C2×C22⋊D73C2×C414yescomplemented
75C22×Dic73C2311yescharacteristic
76C22×Dic73C2311yescharacteristic
77C22×Dic73C2311yescharacteristic
78C22×Dic73C2311yescharacteristic
79C22×Dic73C2311yescharacteristic
80C2×C4×D73—22no—
81C2×C4×D73—22no—
82C2×C4×D73—22no—
83C2×C4×D73—22no—
84C2×C4×D73—22no—
85C2×C4×D73—22no—
86C2×C4×D73—22no—
87C2×C4×D73—22no—
88C2×C4×D73—22no—
89C2×C4×D73—22no—
90C2×C4×D73—41no—
91C2×C4×D73—41no—
92C2×C4×D73—41no—
93C2×C4×D73—41no—
94C2×C4×D73—41no—
95C4⋊Dic73—22no—
96#11924007—41no—
97C22⋊Dic73—22no—
98C22⋊Dic73—22no—
99#11924005—22no—
100#11924005—22no—
101#11924005—22no—
102#11924005—22no—
103#11924005—41no—
104#11924005C2×C414yescomplemented
105#11924005C2×C414yescomplemented
106#11924005D414yescomplemented
107#11924005D414yescomplemented
108C4×Dic73—22no—
109C4×Dic73—41no—
110C24×C73C2311yescharacteristic
111C22×C4×C73C2311yescharacteristic
112C22×C4×C73C2311yescharacteristic
113C22×C4×C73C2311yescharacteristic
114C22×C4×C73C2311yescharacteristic
115C22×C4×C73C2311yescharacteristic
116C22×C4×C73C2311yescharacteristic
117C4⋊C4×C73—22no—
118C22⋊C4×C73—22no—
119C22⋊C4×C73—22no—
120C22⋊C4×C73C2×C414yescomplemented
121C42×C73—22no—
122C23×C73—21no—
123C23×C73—21no—
124C23×C73—21no—
125C23×C73—21no—
126C23×C73—21no—
127C23×C73—21no—
128C23×C73C22×C412yes—
129C23×C73C2411yescharacteristic
130C22×D73—21no—
131C22×D73—21no—
132C22×D73—21no—
133C22×D73—21no—
134C22×D73—21no—
135C22×D73—21no—
136C22×D73—21no—
137C22×D73—21no—
138C22×D73—21no—
139C22×D73—21no—
140C22×D73—21no—
141C22×D73—21no—
142C22×D73—21no—
143C22×D73—21no—
144C22×D73—28no—
145C22×D73—28no—
146C22×D73—44no—
147C22×D73—44no—
148C22×D73—44no—
149C22×D73—44no—
150C22×D73—44no—
151C22×D73C22×C412yes—
152C22×D73C22×C412yes—
153C22×D73C22×C412yes—
154C22×D73C2×D412yes—
155C22×D73C2×D412yes—
156C22×D73#4112yes—
157C22×D73#4112yes—
158C2×C4×C73—21no—
159C2×C4×C73—21no—
160C2×C4×C73—21no—
161C2×C4×C73—21no—
162C2×C4×C73—21no—
163C2×C4×C73—21no—
164C2×C4×C73—21no—
165C2×C4×C73—21no—
166C2×C4×C73—21no—
167C2×C4×C73—21no—
168C2×C4×C73—21no—
169C2×C4×C73—21no—
170C2×C4×C73—21no—
171C2×C4×C73—21no—
172C2×C4×C73C22×C412yes—
173C2×C4×C73C22×C412yes—
174C2×C4×C73C2×D412yes—
175C2×C4×C73C2×D412yes—
176C22⋊D73—44no—
177C2×Dic73—21no—
178C2×Dic73—21no—
179C2×Dic73—21no—
180C2×Dic73—21no—
181C2×Dic73—21no—
182C2×Dic73—21no—
183C2×Dic73—21no—
184C2×Dic73—21no—
185C2×Dic73—21no—
186C2×Dic73—21no—
187C2×Dic73—21no—
188C2×Dic73—21no—
189C2×Dic73C22×C412yes—
190C2×Dic73C2×D412yes—
191C2×Dic73C2×D412yes—
192D292—28no—
193D292—28no—
194C4×D73—44no—
195C4×D73—44no—
196C4×D73—44no—
197C4×D73—44no—
198C4×D73—44no—
199C22×C73—22no—
200C22×C73—22no—
201C22×C73—22no—
202C22×C73—41no—
203C22×C73—41no—
204C22×C73—41no—
205C22×C73—41no—
206C22×C73C23×C411yescharacteristic
207C22×C73C22×D411yescharacteristic
208C22×C73C22×D411yescharacteristic
209C22×C73C2×#4111yescharacteristic
210C22×C73C2×#4111yescharacteristic
211C22×C73H(5,𝔽2)11yescharacteristic
212C22×C73H(5,𝔽2)11yescharacteristic
213C2×D73—22no—
214C2×D73—22no—
215C2×D73—22no—
216C2×D73—22no—
217C2×D73—22no—
218C2×D73—22no—
219C2×D73—22no—
220C2×D73—22no—
221C2×D73—22no—
222C2×D73—22no—
223C2×D73—22no—
224C2×D73—22no—
225C2×D73—22no—
226C2×D73—22no—
227C2×D73—22no—
228C2×D73—416no—
229C2×D73—41no—
230C2×D73—41no—
231C2×D73—41no—
232C2×D73—41no—
233C2×D73C4×D414yescomplemented
234C2×D73C4×D414yescomplemented
235C4×C73—22no—
236C4×C73—22no—
237C4×C73—22no—
238C4×C73—22no—
239C4×C73—41no—
240C4×C73—41no—
241Dic73—22no—
242Dic73—22no—
243Dic73—22no—
244Dic73—41no—
245Dic73—41no—
246C2×C73—42no—
247C2×C73C2×C4×D411yescharacteristic
248C2×C73C2×C4×D411yescharacteristic
249C2×C73#51811yescharacteristic
250C2×C73D4211yescharacteristic
251C2×C73#54611yescharacteristic
252C2×C73#54611yescharacteristic
253C2×C73#55111yescharacteristic
254D73—24no—
255D73—24no—
256D73—42no—
257#2358—731nomaximal, Sylow
258C73#235811yescharacteristic, complemented, Sylow
259C2×#120—731no—
260C2×C4×D4—731no—
261C2×C4×D4—731no—
262C22×C22⋊C4—731no—
263C22×C22⋊C4—731no—
264#390—731no—
265#388—731no—
266#388D7311yescharacteristic, complemented
267#386—731no—
268#386—731no—
269#386—731no—
270#385—731no—
271#385—731no—
272C4×C22⋊C4—731no—
273C4×C22⋊C4—731no—
274C25—731no—
275C22×D4—731no—
276C22×D4—731no—
277C22×D4—731no—
278C23×C4—731no—
279C23×C4—731no—
280C23×C4—731no—
281C23×C4—731no—
282C23×C4—731no—
283#120—738no—
284C4×D4—1464no—
285C4×D4—1464no—
286C2×C4⋊C4—731no—
287C2×C4⋊C4—731no—
288C2×C4⋊C4C2×D7311yescharacteristic, complemented
289C2×C22⋊C4—731no—
290C2×C22⋊C4—731no—
291C2×C22⋊C4—731no—
292C2×C22⋊C4—731no—
293C2×C22⋊C4—731no—
294C2×C22⋊C4—731no—
295C2×C22⋊C4—731no—
296C2×C22⋊C4—731no—
297C2×C22⋊C4—731no—
298C2×C22⋊C4—731no—
299C2×C22⋊C4—731no—
300C2×C22⋊C4—1464no—
301C2×C22⋊C4—1464no—
302C2×C22⋊C4C2×D7311yescharacteristic
303C2×C22⋊C4C2×D7311yescharacteristic
304C2×C22⋊C4C2×D7311yescharacteristic
305C2×C42—731no—
306C2×C42—731no—
307C2×C42C2×D7311yescharacteristic, complemented
308#95—731no—
309#95—731no—
310#95—731no—
311#95—731no—
312#95C2×D7311yescharacteristic, complemented
313#95C2×D7311yescharacteristic, complemented
314C24—2921no—
315C24—2921no—
316C24—734no—
317C24—731no—
318C24—731no—
319C24—731no—
320C24—1462no—
321C24—1462no—
322C24—1462no—
323C24—1462no—
324C24C22×D7311yescharacteristic
325C2×D4—2921no—
326C2×D4—2921no—
327C2×D4—734no—
328C2×D4—734no—
329C2×D4—734no—
330C2×D4—1462no—
331C2×D4—1462no—
332C2×D4—1462no—
333C2×D4—1462no—
334C22×C4—2921no—
335C22×C4—2921no—
336C22×C4—2921no—
337C22×C4—2921no—
338C22×C4—2921no—
339C22×C4—731no—
340C22×C4—731no—
341C22×C4—731no—
342C22×C4—731no—
343C22×C4—731no—
344C22×C4—1462no—
345C22×C4—1462no—
346C22×C4—1462no—
347C22×C4—1462no—
348C22×C4—1462no—
349C22×C4—1462no—
350C22×C4—1462no—
351C22×C4—1462no—
352C22×C4—1462no—
353C22×C4—1462no—
354C22×C4C22×D7311yescharacteristic
355C22×C4C22×D7311yescharacteristic
356C22×C4C22×D7311yescharacteristic
357C22×C4C22×D7311yescharacteristic
358C22×C4C22×D7311yescharacteristic
359C22×C4C22×D7311yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—2921no—
362C4⋊C4—1462no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—2921no—
366C22⋊C4—734no—
367C22⋊C4—734no—
368C22⋊C4—734no—
369C22⋊C4—734no—
370C22⋊C4—1462no—
371C22⋊C4—1462no—
372C22⋊C4—1462no—
373C22⋊C4—1462no—
374C22⋊C4—1462no—
375C22⋊C4—1462no—
376C22⋊C4C4×D7314yescomplemented
377C42—22no—
378C42—2921no—
379C42—1462no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—2924no—
387C23—2924no—
388C23—2924no—
389C23—2924no—
390C23—2924no—
391C23—732no—
392C23—732no—
393C23—732no—
394C23—732no—
395C23—732no—
396C23—732no—
397C23—732no—
398C23—1468no—
399C23—1468no—
400C23—1461no—
401C23—1461no—
402C23—1461no—
403C23—1461no—
404C23—1461no—
405C23—1461no—
406C23—1461no—
407C23—1461no—
408C23—1461no—
409C23—1461no—
410C23—1461no—
411C23—1461no—
412C23—1461no—
413C23—1461no—
414C23C2×C4×D7312yes—
415C23C23×D7311yescharacteristic
416D4—2924no—
417D4—1468no—
418D4—1468no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—2924no—
434C2×C4—2924no—
435C2×C4—2924no—
436C2×C4—2924no—
437C2×C4—2924no—
438C2×C4—732no—
439C2×C4—732no—
440C2×C4—732no—
441C2×C4—1461no—
442C2×C4—1461no—
443C2×C4—1461no—
444C2×C4—1461no—
445C2×C4—1461no—
446C2×C4—1461no—
447C2×C4—1461no—
448C2×C4—1461no—
449C2×C4—1461no—
450C2×C4—1461no—
451C2×C4—1461no—
452C2×C4—1461no—
453C2×C4C2×C4×D7312yes—
454C2×C4C2×C4×D7312yes—
455C2×C4D4×D7312yes—
456C2×C4D4×D7312yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—29216no—
465C22—2921no—
466C22—2921no—
467C22—2921no—
468C22—2921no—
469C22—734no—
470C22—734no—
471C22—1462no—
472C22—1462no—
473C22—1462no—
474C22—1462no—
475C22—1462no—
476C22—1462no—
477C22—1462no—
478C22—1462no—
479C22—1462no—
480C22—1462no—
481C22—1462no—
482C22—1462no—
483C22—1462no—
484C22—1462no—
485C22—1462no—
486C22C22×C4×D7311yescharacteristic
487C22C2×D4×D7311yescharacteristic
488C22C2×D4×D7311yescharacteristic
489C22#41×D7311yescharacteristic
490C22#41×D7311yescharacteristic
491C22#1455663711yescharacteristic
492C22#1455663711yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—41no—
499C4—2921no—
500C4—2921no—
501C4—1462no—
502C4—1462no—
503C4—1462no—
504C2—42no—
505C2—2922no—
506C2—1464no—
507C2—1464no—
508C2C4×D4×D7311yescharacteristic
509C2C4×D4×D7311yescharacteristic
510C2#1798906111yescharacteristic
511C2#1798922111yescharacteristic
512C2#1798922911yescharacteristic
513C2#1798923011yescharacteristic
514C2#1798926211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutatorC22×C73C23×C4
Fitting#388×C73C2
socleC23×C73C24
hypercenter#388D73
hypocenterC73#2358
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×D292C2semidirect
3. C2×#14556553C2semidirect
4. C2×C22⋊C4×D73C2semidirect
5. C2×C22⋊C4×D73C2semidirect
6. #17988487C2semidirect
7. #17988480C2semidirect
8. #17988465C2semidirect
9. #17988465C2semidirect
10. #17988463C2semidirect
11. #17988461C2semidirect
12. #17988458C2semidirect
13. C4×#11924005C2semidirect
14. #17988434C2semidirect
15. #388×C73C2semidirect
24. C22×C4×D73C22semidirect
25. #14556561C4semidirect
28. C2×C4⋊Dic73C22semidirect
29. C2×#11924007C22semidirect
38. C2×#11924005C22semidirect
39. C2×#11924005C22semidirect
40. C2×#11924005C22semidirect
43. C2×C4×Dic73C22semidirect
44. C2×C4×Dic73C22semidirect
45. #14556498C22semidirect
46. #14556498C22semidirect
47. #14556498C22semidirect
48. #14556498C22semidirect
49. C2×C4⋊C4×C73C22semidirect
53. C2×C42×C73C22semidirect
54. #95×C73C22semidirect
55. #95×C73C22semidirect
62. C23×D73C2×C4semidirect
70. C2×D292C2×C4semidirect
71. C2×D292C2×C4semidirect
74. C2×C22⋊D73C2×C4semidirect
104. #11924005C2×C4semidirect
105. #11924005C2×C4semidirect
106. #11924005D4semidirect
107. #11924005D4semidirect
120. C22⋊C4×C73C2×C4semidirect
233. C2×D73C4×D4semidirect
234. C2×D73C4×D4semidirect
258. C73#2358semidirect
266. #388D73semidirect
288. C2×C4⋊C4C2×D73semidirect
307. C2×C42C2×D73semidirect
312. #95C2×D73semidirect
313. #95C2×D73semidirect
376. C22⋊C4C4×D73semidirect