Finite Group Databasebeta

← #22613326

Subgroups — #22613326

Order 9344.

814 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556573C211yesmaximal, characteristic, complemented
2C2×#14556559C211yesmaximal, characteristic
3C22×#11924005C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D73C211yesmaximal, characteristic, complemented
5#17988516C211yesmaximal, characteristic, complemented
6#17988514C211yesmaximal, characteristic, complemented
7#17988503C211yesmaximal, characteristic, complemented
8#17988502C211yesmaximal, characteristic, complemented
9#17988467C211yesmaximal, characteristic, complemented
10#17988463C211yesmaximal, characteristic, complemented
11#17988461C211yesmaximal, characteristic, complemented
12#17988449C211yesmaximal, characteristic, complemented
13#17988447C211yesmaximal, characteristic, complemented
14#17988445C211yesmaximal, characteristic, complemented
15#386×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C23×Dic73C2211yescharacteristic
20C22×C4×D73C2211yescharacteristic
21C22×C4×D73C2211yescharacteristic
22#14556573—24no—
23#14556559—24no—
24C2×C4⋊Dic73C2211yescharacteristic, complemented
25C2×C4⋊Dic73C2211yescharacteristic, complemented
26C2×#11924007C2211yescharacteristic, complemented
27C2×#11924007C2211yescharacteristic, complemented
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic, complemented
31C2×C22⋊Dic73C2211yescharacteristic, complemented
32C2×#11924005—24no—
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic
39C2×#11924005C2211yescharacteristic
40C2×#11924005C2211yescharacteristic
41C22⋊C4×D73—24no—
42#14556498C2211yescharacteristic, complemented
43#14556498C2211yescharacteristic, complemented
44#14556498C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46#14556498C2211yescharacteristic, complemented
47#14556498C2211yescharacteristic, complemented
48C22×D4×C73C2211yescharacteristic
49C23×C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic, complemented
52C2×C22⋊C4×C73C2211yescharacteristic, complemented
53#95×C73C2211yescharacteristic, complemented
54#95×C73C2211yescharacteristic, complemented
55C23×D73—22no—
56C23×D73—22no—
57C23×D73—22no—
58C23×D73—22no—
59C23×D73—41no—
60C23×D73—41no—
61C23×D73D414yes—
62C23×D73C2311yescharacteristic
63C23×D73C2311yescharacteristic
64C2×C22⋊D73—22no—
65C2×C22⋊D73—22no—
66C2×C22⋊D73—22no—
67C2×C22⋊D73—22no—
68C2×C22⋊D73—41no—
69C2×C22⋊D73—41no—
70C22×Dic73—22no—
71C22×Dic73—22no—
72C22×Dic73—41no—
73C22×Dic73C2311yescharacteristic
74C22×Dic73C2311yescharacteristic
75C22×Dic73C2311yescharacteristic
76C22×Dic73C2311yescharacteristic
77C22×Dic73C2311yescharacteristic
78C22×Dic73C2311yescharacteristic
79C2×C4×D73—22no—
80C2×C4×D73—22no—
81C2×C4×D73—22no—
82C2×C4×D73—22no—
83C2×C4×D73—41no—
84C2×C4×D73—41no—
85C4⋊Dic73—22no—
86C4⋊Dic73—41no—
87#11924007—22no—
88#11924007—41no—
89C22⋊Dic73—22no—
90C22⋊Dic73—22no—
91C22⋊Dic73—22no—
92C22⋊Dic73—41no—
93#11924005—22no—
94#11924005—22no—
95#11924005—22no—
96#11924005—22no—
97#11924005—22no—
98#11924005—22no—
99#11924005—22no—
100#11924005D414yescomplemented
101C24×C73C2311yescharacteristic
102C24×C73C2311yescharacteristic
103C2×D4×C73—22no—
104C2×D4×C73—22no—
105C2×D4×C73—22no—
106C22×C4×C73—22no—
107C22×C4×C73—22no—
108C22×C4×C73—41no—
109C22×C4×C73C2311yescharacteristic
110C22×C4×C73C2311yescharacteristic
111C22×C4×C73C2311yescharacteristic
112C22×C4×C73C2311yescharacteristic
113C22×C4×C73C2311yescharacteristic
114C22⋊C4×C73—22no—
115C22⋊C4×C73—22no—
116C22⋊C4×C73—41no—
117C23×C73—21no—
118C23×C73—21no—
119C23×C73—21no—
120C23×C73—21no—
121C23×C73—21no—
122C23×C73—21no—
123C23×C73—21no—
124C23×C73—21no—
125C23×C73—21no—
126C23×C73—21no—
127C23×C73—21no—
128C23×C73C2×D412yes—
129C23×C73#4112yes—
130C23×C73#4112yes—
131C23×C73C2411yescharacteristic
132C22×D73—21no—
133C22×D73—21no—
134C22×D73—21no—
135C22×D73—21no—
136C22×D73—28no—
137C22×D73—21no—
138C22×D73—21no—
139C22×D73—21no—
140C22×D73—21no—
141C22×D73—21no—
142C22×D73—21no—
143C22×D73—28no—
144C22×D73—44no—
145C22×D73—44no—
146C22×D73—44no—
147C22×D73—44no—
148C22×D73—44no—
149C22×D73C2×D412yes—
150C22×D73C2×D412yes—
151C22×D73C2×D412yes—
152C22×D73#4112yes—
153D4×C73—44no—
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×C73—44no—
169C2×C4×C73C2×D412yes—
170C22⋊D73—44no—
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×Dic73—21no—
187C2×Dic73—21no—
188C2×Dic73—21no—
189C2×Dic73—44no—
190C2×Dic73C2×D412yes—
191C4×D73—44no—
192C4×D73—44no—
193C22×C73—22no—
194C22×C73—22no—
195C22×C73—22no—
196C22×C73—22no—
197C22×C73—22no—
198C22×C73—22no—
199C22×C73—41no—
200C22×C73—41no—
201C22×C73—41no—
202C22×C73—41no—
203C22×C73—41no—
204C22×C73—41no—
205C22×C73—41no—
206C22×C73#12314yescomplemented
207C22×C73C22×D411yescharacteristic
208C22×C73C22×D411yescharacteristic
209C22×C73C2×#4111yescharacteristic
210C22×C73C2×#4111yescharacteristic
211C22×C73C2×#4111yescharacteristic
212C22×C73H(5,𝔽2)11yescharacteristic
213C22×C73H(5,𝔽2)11yescharacteristic
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—416no—
224C2×D73—41no—
225C2×D73—41no—
226C2×D73—41no—
227C2×D73—41no—
228C2×D73#12114yes—
229C4×C73—22no—
230C4×C73—41no—
231C4×C73—41no—
232C4×C73—41no—
233C4×C73—41no—
234Dic73—22no—
235Dic73—41no—
236Dic73—41no—
237Dic73—41no—
238Dic73—41no—
239Dic73—41no—
240C2×C73—24no—
241C2×C73—81no—
242C2×C73C2×#12111yescharacteristic
243C2×C73C2×#12311yescharacteristic
244C2×C73#53411yescharacteristic
245C2×C73#54611yescharacteristic
246C2×C73#54611yescharacteristic
247C2×C73#55111yescharacteristic
248C2×C73#55111yescharacteristic
249D73—24no—
250D73—42no—
251#2412—731nomaximal, Sylow
252C73#241211yescharacteristic, complemented, Sylow
253C2×#123—731no—
254C2×#120—731no—
255C22×C22⋊C4—731no—
256C22×C22⋊C4—731no—
257#397—731no—
258#397—731no—
259#394—731no—
260#394—731no—
261#386—731no—
262#386—731no—
263#386D7311yescharacteristic, complemented
264#385—731no—
265#381—731no—
266#380—731no—
267#380—731no—
268C25—731no—
269C22×D4—731no—
270C22×D4—731no—
271C22×D4C2×D7311yescharacteristic
272C23×C4—731no—
273C23×C4—731no—
274C23×C4—731no—
275C23×C4C2×D7311yescharacteristic
276#123—1464no—
277#120—1464no—
278C2×C4⋊C4—731no—
279C2×C4⋊C4—731no—
280C2×C4⋊C4—731no—
281C2×C4⋊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⋊C4—1464no—
296C2×C22⋊C4C2×D7311yescharacteristic
297C2×C22⋊C4C2×D7311yescharacteristic, complemented
298C2×C22⋊C4C2×D7311yescharacteristic, complemented
299#95—731no—
300#95—731no—
301#95—731no—
302#95—731no—
303#95—731no—
304#95—731no—
305#95C2×D7311yescharacteristic, complemented
306#95C2×D7311yescharacteristic, complemented
307C24—2921no—
308C24—2921no—
309C24—734no—
310C24—731no—
311C24—731no—
312C24—1462no—
313C24—1462no—
314C24—1462no—
315C24—1462no—
316C24C22×D7311yescharacteristic
317C24C22×D7311yescharacteristic
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—2921no—
322C2×D4—2921no—
323C2×D4—1462no—
324C2×D4—1462no—
325C2×D4—1462no—
326C2×D4—1462no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—41no—
330C22×C4—2921no—
331C22×C4—2921no—
332C22×C4—2921no—
333C22×C4—731no—
334C22×C4—731no—
335C22×C4—731no—
336C22×C4—731no—
337C22×C4—731no—
338C22×C4—731no—
339C22×C4—1462no—
340C22×C4—1462no—
341C22×C4—1462no—
342C22×C4—1462no—
343C22×C4—1462no—
344C22×C4—1462no—
345C22×C4C22×D7311yescharacteristic
346C22×C4C22×D7311yescharacteristic
347C22×C4C22×D7311yescharacteristic
348C22×C4C22×D7311yescharacteristic
349C22×C4C22×D7311yescharacteristic
350C4⋊C4—2921no—
351C4⋊C4—2921no—
352C4⋊C4—1462no—
353C4⋊C4—1462no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—41no—
357C22⋊C4—2921no—
358C22⋊C4—734no—
359C22⋊C4—1462no—
360C22⋊C4—1462no—
361C22⋊C4—1462no—
362C22⋊C4—1462no—
363C22⋊C4—1462no—
364C22⋊C4—1462no—
365C22⋊C4—1462no—
366C22⋊C4—1462no—
367C22⋊C4—1462no—
368C22⋊C4—1462no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—2924no—
381C23—2924no—
382C23—2924no—
383C23—2924no—
384C23—2924no—
385C23—732no—
386C23—732no—
387C23—732no—
388C23—732no—
389C23—1468no—
390C23—1468no—
391C23—1461no—
392C23—1461no—
393C23—1461no—
394C23—1461no—
395C23—1461no—
396C23—1461no—
397C23—1461no—
398C23—1461no—
399C23—1461no—
400C23—1461no—
401C23D4×D7312yes—
402C23#1192402712yes—
403C23#1192402812yes—
404C23C23×D7311yescharacteristic
405D4—44no—
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—44no—
423C2×C4—2924no—
424C2×C4—2924no—
425C2×C4—2924no—
426C2×C4—732no—
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×C4—1461no—
441C2×C4—1461no—
442C2×C4—1461no—
443C2×C4—1461no—
444C2×C4D4×D7312yes—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—29216no—
459C22—2921no—
460C22—2921no—
461C22—2921no—
462C22—2921no—
463C22—734no—
464C22—1462no—
465C22—1462no—
466C22—1462no—
467C22—1462no—
468C22—1462no—
469C22—1462no—
470C22—1462no—
471C22—1462no—
472C22—1462no—
473C22#1455657314yescomplemented
474C22C2×D4×D7311yescharacteristic
475C22C2×D4×D7311yescharacteristic
476C22#41×D7311yescharacteristic
477C22C2×#1192402711yescharacteristic
478C22C2×#1192402811yescharacteristic
479C22#1455663611yescharacteristic
480C22#1455663711yescharacteristic
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—2921no—
487C4—2921no—
488C4—2921no—
489C4—2921no—
490C4—2921no—
491C4—1462no—
492C2—24no—
493C2—81no—
494C2—2922no—
495C2—1464no—
496C2#121×D7311yescharacteristic
497C2C2×#1455657311yescharacteristic
498C2#1798914511yescharacteristic
499C2#1798922411yescharacteristic
500C2#1798923311yescharacteristic
501C2#1798926011yescharacteristic
502C2#1798926611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#386×C73C2
hypercenter#386D73
hypocenterC73#2412
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#14556573C2semidirect
3. C22×#11924005C2semidirect
4. C2×C22⋊C4×D73C2semidirect
5. #17988516C2semidirect
6. #17988514C2semidirect
7. #17988503C2semidirect
8. #17988502C2semidirect
9. #17988467C2semidirect
10. #17988463C2semidirect
11. #17988461C2semidirect
12. #17988449C2semidirect
13. #17988447C2semidirect
14. #17988445C2semidirect
15. #386×C73C2semidirect
24. C2×C4⋊Dic73C22semidirect
25. C2×C4⋊Dic73C22semidirect
26. C2×#11924007C22semidirect
27. C2×#11924007C22semidirect
30. C2×C22⋊Dic73C22semidirect
31. C2×C22⋊Dic73C22semidirect
42. #14556498C22semidirect
43. #14556498C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
46. #14556498C22semidirect
47. #14556498C22semidirect
51. C2×C22⋊C4×C73C22semidirect
52. C2×C22⋊C4×C73C22semidirect
53. #95×C73C22semidirect
54. #95×C73C22semidirect
100. #11924005D4semidirect
206. C22×C73#123semidirect
252. C73#2412semidirect
263. #386D73semidirect
297. C2×C22⋊C4C2×D73semidirect
298. C2×C22⋊C4C2×D73semidirect
305. #95C2×D73semidirect
306. #95C2×D73semidirect
473. C22#14556573semidirect