Finite Group Databasebeta

← #22614055

Subgroups — #22614055

Order 9344.

786 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556577C211yesmaximal, characteristic, complemented
2C2×#14556571C211yesmaximal, characteristic, complemented
3C2×#14556561C211yesmaximal, characteristic
4C2×C22⋊C4×D73C211yesmaximal, characteristic, complemented
5#17988512C211yesmaximal, characteristic, complemented
6#17988504C211yesmaximal, characteristic, complemented
7#17988503C211yesmaximal, characteristic, complemented
8#17988500C211yesmaximal, characteristic, complemented
9#17988489C211yesmaximal, characteristic, complemented
10#17988479C211yesmaximal, characteristic, complemented
11#17988465C211yesmaximal, characteristic, complemented
12#17988465C211yesmaximal, characteristic, complemented
13#17988442C211yesmaximal, characteristic, complemented
14C4×#11924005C211yesmaximal, characteristic, complemented
15#388×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×Dic146C2211yescharacteristic, complemented
18C22×D292C2211yescharacteristic
19C22×D292C2211yescharacteristic
20C22×C22⋊D73C2211yescharacteristic
21C22×C4×D73C2211yescharacteristic
22C22×C4×D73C2211yescharacteristic
23#14556577—24no—
24#14556571—24no—
25#14556561—24no—
26C2×C4⋊Dic73C2211yescharacteristic, complemented
27C2×C4⋊Dic73C2211yescharacteristic, complemented
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic, complemented
39C2×#11924005C2211yescharacteristic, complemented
40C2×#11924005C2211yescharacteristic, complemented
41C2×#11924005C2211yescharacteristic, complemented
42C22⋊C4×D73—24no—
43C2×C4×Dic73C2211yescharacteristic, complemented
44#14556498C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46#14556498C2211yescharacteristic, complemented
47#14556498C2211yescharacteristic, complemented
48C2×C4⋊C4×C73C2211yescharacteristic, complemented
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C42×C73C2211yescharacteristic, complemented
53#95×C73C2211yescharacteristic, complemented
54#95×C73C2211yescharacteristic, complemented
55C23×D73—22no—
56C23×D73—22no—
57C23×D73—22no—
58C23×D73—22no—
59C23×D73—22no—
60C23×D73—41no—
61C23×D73—41no—
62C23×D73C2311yescharacteristic
63C23×D73C2311yescharacteristic
64C23×D73C2311yescharacteristic
65C2×Dic146—22no—
66C2×Dic146—22no—
67C2×Dic146—41no—
68C2×D292—22no—
69C2×D292—22no—
70C2×D292—22no—
71C2×D292—22no—
72C2×D292—22no—
73C2×D292—41no—
74C2×C22⋊D73—22no—
75C2×C22⋊D73—22no—
76C2×C22⋊D73—41no—
77C22×Dic73C2311yescharacteristic
78C22×Dic73C2311yescharacteristic
79C22×Dic73C2311yescharacteristic
80C22×Dic73C2311yescharacteristic
81C22×Dic73C2311yescharacteristic
82C2×C4×D73—22no—
83C2×C4×D73—22no—
84C2×C4×D73—22no—
85C2×C4×D73—22no—
86C2×C4×D73—41no—
87C2×C4×D73—41no—
88C4⋊Dic73—22no—
89C4⋊Dic73—22no—
90C22⋊Dic73—22no—
91C22⋊Dic73—22no—
92#11924005—22no—
93#11924005—22no—
94#11924005—22no—
95#11924005—22no—
96#11924005—22no—
97#11924005—22no—
98#11924005—22no—
99#11924005—22no—
100#11924005—41no—
101#11924005—41no—
102#11924005—41no—
103#11924005D414yes—
104C4×Dic73—22no—
105C24×C73C2311yescharacteristic
106C22×C4×C73C2311yescharacteristic
107C22×C4×C73C2311yescharacteristic
108C22×C4×C73C2311yescharacteristic
109C22×C4×C73C2311yescharacteristic
110C22×C4×C73C2311yescharacteristic
111C22×C4×C73C2311yescharacteristic
112C4⋊C4×C73—22no—
113C22⋊C4×C73—22no—
114C22⋊C4×C73—41no—
115C22⋊C4×C73D414yescomplemented
116C42×C73—41no—
117C23×C73—21no—
118C23×C73—21no—
119C23×C73—21no—
120C23×C73—21no—
121C23×C73—21no—
122C23×C73—21no—
123C23×C73C2×D412yes—
124C23×C73C2411yescharacteristic
125C22×D73—21no—
126C22×D73—21no—
127C22×D73—21no—
128C22×D73—21no—
129C22×D73—28no—
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—44no—
144C22×D73—44no—
145C22×D73—44no—
146C22×D73—44no—
147C22×D73—44no—
148C22×D73—44no—
149C22×D73C2×D412yes—
150C22×D73#4112yes—
151C22×D73#4112yes—
152C22×D73#4112yes—
153C2×C4×C73—21no—
154C2×C4×C73—21no—
155C2×C4×C73—21no—
156C2×C4×C73—21no—
157C2×C4×C73—21no—
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×C73C2×D412yes—
169C2×C4×C73C2×D412yes—
170C2×C4×C73C2×D412yes—
171C22⋊D73—44no—
172C2×Dic73—21no—
173C2×Dic73—21no—
174C2×Dic73—21no—
175C2×Dic73—21no—
176C2×Dic73—21no—
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×Dic73C2×D412yes—
187D292—44no—
188D292—44no—
189C4×D73—44no—
190C4×D73—44no—
191Dic146—44no—
192C22×C73—22no—
193C22×C73—22no—
194C22×C73—22no—
195C22×C73—41no—
196C22×C73—41no—
197C22×C73—41no—
198C22×C73—41no—
199C22×C73C22×D411yescharacteristic
200C22×C73C22×D411yescharacteristic
201C22×C73C2×#4111yescharacteristic
202C22×C73C2×#4111yescharacteristic
203C22×C73C2×#4111yescharacteristic
204C22×C73H(5,𝔽2)11yescharacteristic
205C22×C73H(5,𝔽2)11yescharacteristic
206C2×D73—22no—
207C2×D73—22no—
208C2×D73—22no—
209C2×D73—22no—
210C2×D73—22no—
211C2×D73—22no—
212C2×D73—22no—
213C2×D73—22no—
214C2×D73—22no—
215C2×D73—416no—
216C2×D73—41no—
217C2×D73—41no—
218C2×D73—41no—
219C2×D73—41no—
220C2×D73—41no—
221C2×D73—41no—
222C2×D73—41no—
223C2×D73—41no—
224C2×D73—41no—
225C2×D73—41no—
226C2×D73—41no—
227C2×D73#12414yescomplemented
228C4×C73—22no—
229C4×C73—22no—
230C4×C73—22no—
231C4×C73—41no—
232C4×C73—41no—
233C4×C73—41no—
234Dic73—22no—
235Dic73—41no—
236Dic73—41no—
237Dic73—41no—
238Dic73—41no—
239C2×C73—42no—
240C2×C73#52511yescharacteristic
241C2×C73C2×#12411yescharacteristic
242C2×C73#53811yescharacteristic
243C2×C73D4211yescharacteristic
244C2×C73#54611yescharacteristic
245C2×C73#54611yescharacteristic
246C2×C73#55111yescharacteristic
247D73—24no—
248D73—42no—
249D73—81no—
250#2472—731nomaximal, Sylow
251C73#247211yescharacteristic, complemented, Sylow
252C2×#124—731no—
253C2×C22⋊Q8—731no—
254C2×#120—731no—
255C22×C22⋊C4—731no—
256#397—731no—
257#394—731no—
258#394—731no—
259#393—731no—
260#390—731no—
261#388—731no—
262#388D7311yescharacteristic, complemented
263#386—731no—
264#386—731no—
265#379—731no—
266C4×C22⋊C4—731no—
267C25—731no—
268C22×Q8—731no—
269C22×D4—731no—
270C22×D4—731no—
271C22×D4—731no—
272C23×C4—731no—
273C23×C4—731no—
274#124—1464no—
275C22⋊Q8—1464no—
276#120—1464no—
277C2×C4⋊C4—731no—
278C2×C4⋊C4—731no—
279C2×C4⋊C4C2×D7311yescharacteristic, complemented
280C2×C22⋊C4—731no—
281C2×C22⋊C4—731no—
282C2×C22⋊C4—731no—
283C2×C22⋊C4—731no—
284C2×C22⋊C4—731no—
285C2×C22⋊C4—731no—
286C2×C22⋊C4—731no—
287C2×C22⋊C4—731no—
288C2×C22⋊C4—731no—
289C2×C22⋊C4—731no—
290C2×C22⋊C4—731no—
291C2×C22⋊C4—731no—
292C2×C22⋊C4—731no—
293C2×C22⋊C4—731no—
294C2×C22⋊C4—1464no—
295C2×C22⋊C4C2×D7311yescharacteristic
296C2×C22⋊C4C2×D7311yescharacteristic
297C2×C22⋊C4C2×D7311yescharacteristic
298C2×C42—731no—
299C2×C42C2×D7311yescharacteristic, complemented
300#95—731no—
301#95—731no—
302#95—731no—
303#95—731no—
304#95C2×D7311yescharacteristic, complemented
305#95C2×D7311yescharacteristic, complemented
306C24—2921no—
307C24—2921no—
308C24—731no—
309C24—731no—
310C24—731no—
311C24—1462no—
312C24—1462no—
313C24—1462no—
314C24—1462no—
315C24—1462no—
316C24C22×D7311yescharacteristic
317C2×Q8—2921no—
318C2×Q8—1462no—
319C2×Q8—1462no—
320C2×D4—2921no—
321C2×D4—2921no—
322C2×D4—1462no—
323C2×D4—1462no—
324C2×D4—1462no—
325C2×D4—1462no—
326C2×D4—1462no—
327C2×D4—1462no—
328C2×D4—1462no—
329C22×C4—2921no—
330C22×C4—2921no—
331C22×C4—731no—
332C22×C4—731no—
333C22×C4—731no—
334C22×C4—731no—
335C22×C4—731no—
336C22×C4—1462no—
337C22×C4—1462no—
338C22×C4—1462no—
339C22×C4—1462no—
340C22×C4C22×D7311yescharacteristic
341C22×C4C22×D7311yescharacteristic
342C22×C4C22×D7311yescharacteristic
343C22×C4C22×D7311yescharacteristic
344C22×C4C22×D7311yescharacteristic
345C22×C4C22×D7311yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—1462no—
348C4⋊C4—1462no—
349C22⋊C4—22no—
350C22⋊C4—41no—
351C22⋊C4—2921no—
352C22⋊C4—2921no—
353C22⋊C4—2921no—
354C22⋊C4—734no—
355C22⋊C4—1462no—
356C22⋊C4—1462no—
357C22⋊C4—1462no—
358C22⋊C4—1462no—
359C22⋊C4—1462no—
360C22⋊C4—1462no—
361C22⋊C4—1462no—
362C22⋊C4—1462no—
363C22⋊C4—1462no—
364C22⋊C4—1462no—
365C22⋊C4D29214yescomplemented
366C42—41no—
367C42—1462no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—2924no—
375C23—2924no—
376C23—2924no—
377C23—2924no—
378C23—2924no—
379C23—2924no—
380C23—732no—
381C23—732no—
382C23—732no—
383C23—732no—
384C23—1468no—
385C23—1461no—
386C23—1461no—
387C23—1461no—
388C23—1461no—
389C23—1461no—
390C23—1461no—
391C23—1461no—
392C23—1461no—
393C23—1461no—
394C23—1461no—
395C23—1461no—
396C23—1461no—
397C23—1461no—
398C23—1461no—
399C23—1461no—
400C23—1461no—
401C23—1461no—
402C23C2×D29212yes—
403C23C23×D7311yescharacteristic
404Q8—2924no—
405D4—2924no—
406D4—2924no—
407D4—2924no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—2924no—
424C2×C4—2924no—
425C2×C4—732no—
426C2×C4—1461no—
427C2×C4—1461no—
428C2×C4—1461no—
429C2×C4—1461no—
430C2×C4—1461no—
431C2×C4—1461no—
432C2×C4—1461no—
433C2×C4—1461no—
434C2×C4—1461no—
435C2×C4—1461no—
436C2×C4—1461no—
437C2×C4—1461no—
438C2×C4—1461no—
439C2×C4—1461no—
440C2×C4D4×D7312yes—
441C2×C4C2×D29212yes—
442C2×C4C2×D29212yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—29216no—
451C22—2921no—
452C22—2921no—
453C22—2921no—
454C22—2921no—
455C22—2921no—
456C22—2921no—
457C22—2921no—
458C22—2921no—
459C22—2921no—
460C22—2921no—
461C22—2921no—
462C22—734no—
463C22—1462no—
464C22—1462no—
465C22—1462no—
466C22—1462no—
467C22—1462no—
468C22—1462no—
469C22—1462no—
470C22—1462no—
471C22—1462no—
472C22C2×D4×D7311yescharacteristic
473C22C22×D29211yescharacteristic
474C22#41×D7311yescharacteristic
475C22#41×D7311yescharacteristic
476C22#41×D7311yescharacteristic
477C22#1455663611yescharacteristic
478C22#1455663711yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—2921no—
486C4—2921no—
487C4—2921no—
488C4—2921no—
489C4—1462no—
490C2—42no—
491C2—2922no—
492C2—5841no—
493C2—1464no—
494C2#1798909911yescharacteristic
495C2#124×D7311yescharacteristic
496C2#1798917311yescharacteristic
497C2D4×D29211yescharacteristic
498C2#1798922611yescharacteristic
499C2#1798923211yescharacteristic
500C2#1798926211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#388×C73C2
hypercenter#388D73
hypocenterC73#2472
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14556577C2semidirect
2. C2×#14556571C2semidirect
4. C2×C22⋊C4×D73C2semidirect
5. #17988512C2semidirect
6. #17988504C2semidirect
7. #17988503C2semidirect
8. #17988500C2semidirect
9. #17988489C2semidirect
10. #17988479C2semidirect
11. #17988465C2semidirect
12. #17988465C2semidirect
13. #17988442C2semidirect
14. C4×#11924005C2semidirect
15. #388×C73C2semidirect
17. C22×Dic146C22semidirect
26. C2×C4⋊Dic73C22semidirect
27. C2×C4⋊Dic73C22semidirect
38. C2×#11924005C22semidirect
39. C2×#11924005C22semidirect
40. C2×#11924005C22semidirect
41. C2×#11924005C22semidirect
43. C2×C4×Dic73C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
46. #14556498C22semidirect
47. #14556498C22semidirect
48. C2×C4⋊C4×C73C22semidirect
52. C2×C42×C73C22semidirect
53. #95×C73C22semidirect
54. #95×C73C22semidirect
115. C22⋊C4×C73D4semidirect
227. C2×D73#124semidirect
251. C73#2472semidirect
262. #388D73semidirect
279. C2×C4⋊C4C2×D73semidirect
299. C2×C42C2×D73semidirect
304. #95C2×D73semidirect
305. #95C2×D73semidirect
365. C22⋊C4D292semidirect