Finite Group Databasebeta

← #22620732

Subgroups — #22620732

Order 9344.

462 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D73C211yesmaximal, characteristic, complemented
2#121×D73C211yesmaximal, characteristic
3#17988924C211yesmaximal, characteristic, complemented
4#17988921C211yesmaximal, characteristic, complemented
5#17988902C211yesmaximal, characteristic, complemented
6#17988899C211yesmaximal, characteristic, complemented
7#17988835C211yesmaximal, characteristic, complemented
8#17988833C211yesmaximal, characteristic, complemented
9#17988831C211yesmaximal, characteristic, complemented
10#17988739C211yesmaximal, characteristic, complemented
11#17988736C211yesmaximal, characteristic, complemented
12#17988727C211yesmaximal, characteristic, complemented
13#17988724C211yesmaximal, characteristic, complemented
14#17988550C211yesmaximal, characteristic, complemented
15#468×C73C211yesmaximal, characteristic, complemented
16C2×Q8×D73C2211yescharacteristic, complemented
17C2×D4×D73—21no—
18C2×D4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20C2×#11924017C2211yescharacteristic, complemented
21C2×#11924016C2211yescharacteristic, complemented
22C2×#11924015C2211yescharacteristic, complemented
23C2×#11924012C2211yescharacteristic, complemented
24#14556571C2211yescharacteristic
25#14556570C2211yescharacteristic, complemented
26#14556569—21no—
27#14556568—21no—
28#14556567C2211yescharacteristic
29#14556566C2211yescharacteristic
30#14556565C2211yescharacteristic
31#14556564—21no—
32#14556563—21no—
33#14556562C2211yescharacteristic
34C4⋊C4×D73—21no—
35C4⋊C4×D73C2211yescharacteristic
36C4⋊C4×D73C2211yescharacteristic, complemented
37C22⋊C4×D73—21no—
38C22⋊C4×D73—21no—
39#14556525C2211yescharacteristic, complemented
40#14556524C2211yescharacteristic, complemented
41#14556524C2211yescharacteristic, complemented
42#14556516C2211yescharacteristic, complemented
43#14556515C2211yescharacteristic, complemented
44#14556514C2211yescharacteristic, complemented
45#14556513C2211yescharacteristic, complemented
46#14556512C2211yescharacteristic, complemented
47#14556511C2211yescharacteristic, complemented
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556503C2211yescharacteristic, complemented
51#14556503C2211yescharacteristic, complemented
52C2×SD16×C73C2211yescharacteristic, complemented
53C2×M16×C73C2211yescharacteristic, complemented
54C22⋊Q8×C73C2211yescharacteristic, complemented
55#121×C73C2211yescharacteristic
56#107×C73C2211yescharacteristic, complemented
57#103×C73C2211yescharacteristic, complemented
58#102×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C23×D73D411yescharacteristic
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63Q8×D73—41no—
64Q8×D73—41no—
65C2×D292—21no—
66C2×D292C2311yescharacteristic
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70D4×D73—41no—
71D4×D73—41no—
72D4×D73—44no—
73C22×Dic73D411yescharacteristic
74C2×C4×D73—21no—
75C2×C4×D73—21no—
76C2×C4×D73—21no—
77C2×C4×D73—41no—
78C2×C4×D73—41no—
79C2×C4×D73D411yescharacteristic
80C2×C4×D73D411yescharacteristic
81C2×C4×D73C2311yescharacteristic
82C2×C4×D73C2311yescharacteristic
83#11924017—41no—
84#11924016—41no—
85#11924015—41no—
86#11924012—41no—
87C2×#10596831C2311yescharacteristic
88C2×#10596831C2311yescharacteristic
89C4⋊Dic73—21no—
90C4⋊Dic73C2311yescharacteristic
91C4⋊Dic73C2311yescharacteristic
92#11924007—21no—
93#11924007—21no—
94#11924007—21no—
95#11924007—21no—
96C22⋊Dic73—21no—
97C22⋊Dic73—21no—
98#11924005—21no—
99#11924005—21no—
100#11924005—21no—
101#11924005—21no—
102C2×Q8×C73C2311yescharacteristic
103C2×D4×C73—21no—
104C2×D4×C73C2311yescharacteristic
105C22×C4×C73C2311yescharacteristic
106SD16×C73—41no—
107M16×C73—41no—
108C2×C8×C73C2311yescharacteristic
109C2×C8×C73C2311yescharacteristic
110C4⋊C4×C73—21no—
111C4⋊C4×C73C2311yescharacteristic
112C4⋊C4×C73C2311yescharacteristic
113C22⋊C4×C73—21no—
114C22⋊C4×C73—21no—
115C23×C73—21no—
116C23×C73C2×D411yescharacteristic
117C22×D73—22no—
118C22×D73—22no—
119C22×D73—21no—
120C22×D73—41no—
121C22×D73—42no—
122C22×D73—42no—
123C22×D73—42no—
124C22×D73C2×D411yescharacteristic
125C22×D73C2×D411yescharacteristic
126Q8×C73—21no—
127Q8×C73—21no—
128D4×C73—21no—
129D4×C73—21no—
130D4×C73—42no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73C2×D411yescharacteristic
137C2×C4×C73C2411yescharacteristic
138C22⋊D73—42no—
139C22⋊D73—42no—
140C22⋊D73—42no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—41no—
145C2×Dic73C2×D411yescharacteristic
146C2×Dic73C2×D411yescharacteristic
147D292—21no—
148D292—21no—
149D292—42no—
150C4×D73—21no—
151C4×D73—21no—
152C4×D73—21no—
153C4×D73—21no—
154C4×D73—41no—
155C4×D73—41no—
156C4×D73—42no—
157C4×D73—42no—
158C4×D73—42no—
159Dic146—21no—
160Dic146—21no—
161Dic146—42no—
162C8×C73—21no—
163C8×C73—21no—
164#10596831—21no—
165#10596831—21no—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—41no—
170C22×C73—41no—
171C22×C73—41no—
172C22×C73C22×D411yescharacteristic
173C2×D73—21no—
174C2×D73—21no—
175C2×D73—21no—
176C2×D73—21no—
177C2×D73—44no—
178C2×D73—41no—
179C2×D73—41no—
180C2×D73—41no—
181C2×D73—84no—
182C2×D73AGL(1,ℤ/8)12yes—
183C2×D73#13712yes—
184C4×C73—21no—
185C4×C73—41no—
186C4×C73—41no—
187C4×C73—41no—
188C4×C73H(5,𝔽2)11yescharacteristic
189C4×C73H(5,𝔽2)11yescharacteristic
190Dic73—21no—
191Dic73—21no—
192Dic73—41no—
193Dic73—41no—
194Dic73—41no—
195C2×C73—41no—
196C2×C73—81no—
197C2×C73#53411yescharacteristic
198C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
199C2×C73C2×#13711yescharacteristic
200D73—22no—
201D73—22no—
202D73—81no—
203#3193—731nomaximal, Sylow
204C73#319311yescharacteristic, complemented, Sylow
205C2×C22⋊Q8—731no—
206C2×#121—731no—
207#484—731no—
208#484—731no—
209#480—731no—
210#480—731no—
211#468—731no—
212#468—731no—
213#468—731no—
214#468D7311yescharacteristic, complemented
215#450—731no—
216#450—731no—
217#448—731no—
218#448—731no—
219#407—731no—
220C22×Q8—731no—
221C22×D4—731no—
222C22×D4—1461no—
223C23×C4—731no—
224C2×SD16—731no—
225C2×SD16—731no—
226C2×SD16—731no—
227C2×SD16C2×D7311yescharacteristic, complemented
228C2×M16—731no—
229C2×M16C2×D7311yescharacteristic, complemented
230C22⋊Q8—731no—
231C22⋊Q8—731no—
232C22⋊Q8—731no—
233C22⋊Q8—1461no—
234C22⋊Q8—1461no—
235C22⋊Q8C2×D7311yescharacteristic, complemented
236#121—731no—
237#121—731no—
238#121—731no—
239#121—1461no—
240#121—1461no—
241#121C2×D7311yescharacteristic
242C2×C4⋊C4—731no—
243C2×C4⋊C4—731no—
244C2×C4⋊C4—1461no—
245C2×C22⋊C4—1461no—
246C2×C22⋊C4—1461no—
247#107—731no—
248#107—731no—
249#107—731no—
250#107C2×D7311yescharacteristic, complemented
251#103—731no—
252#103—731no—
253#103—731no—
254#103C2×D7311yescharacteristic, complemented
255#102—731no—
256#102—731no—
257#102—731no—
258#102C2×D7311yescharacteristic, complemented
259C22⋊C8—731no—
260C22⋊C8—731no—
261C22⋊C8—731no—
262C22⋊C8—731no—
263C24—731no—
264C24—1461no—
265C2×Q8—2921no—
266C2×Q8—2921no—
267C2×Q8—731no—
268C2×Q8—1461no—
269C2×Q8C22×D7311yescharacteristic
270C2×D4—21no—
271C2×D4—2924no—
272C2×D4—2921no—
273C2×D4—2921no—
274C2×D4—731no—
275C2×D4—1461no—
276C2×D4—1461no—
277C2×D4—1461no—
278C2×D4—1461no—
279C2×D4C22×D7311yescharacteristic
280C22×C4—2921no—
281C22×C4—2921no—
282C22×C4—731no—
283C22×C4—731no—
284C22×C4—731no—
285C22×C4—731no—
286C22×C4—731no—
287C22×C4—1461no—
288C22×C4—1461no—
289C22×C4—1461no—
290C22×C4C22×D7311yescharacteristic
291SD16—41no—
292SD16—2921no—
293SD16—2921no—
294SD16—2921no—
295M16—41no—
296M16—2921no—
297C2×C8—731no—
298C2×C8—731no—
299C2×C8C22×D7311yescharacteristic
300C2×C8C22×D7311yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—731no—
303C4⋊C4—731no—
304C4⋊C4—1461no—
305C4⋊C4—1461no—
306C4⋊C4—1461no—
307C4⋊C4—1461no—
308C4⋊C4—1461no—
309C4⋊C4C22×D7311yescharacteristic
310C4⋊C4C22×D7311yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—1461no—
314C22⋊C4—1461no—
315C22⋊C4—1461no—
316C22⋊C4—1461no—
317C22⋊C4—1461no—
318C22⋊C4—1461no—
319C23—21no—
320C23—2921no—
321C23—2922no—
322C23—2922no—
323C23—2922no—
324C23—731no—
325C23—731no—
326C23—1462no—
327C23—1462no—
328C23—1461no—
329C23D4×D7311yescharacteristic
330Q8—21no—
331Q8—21no—
332Q8—2922no—
333Q8—1461no—
334Q8—1461no—
335D4—21no—
336D4—21no—
337D4—42no—
338D4—2922no—
339D4—2922no—
340D4—2922no—
341D4—2922no—
342D4—1461no—
343D4—1461no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—2921no—
350C2×C4—2921no—
351C2×C4—2922no—
352C2×C4—2922no—
353C2×C4—2922no—
354C2×C4—2921no—
355C2×C4—731no—
356C2×C4—731no—
357C2×C4—1461no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4—1461no—
362C2×C4—1461no—
363C2×C4—1461no—
364C2×C4D4×D7311yescharacteristic
365C2×C4C23×D7311yescharacteristic
366C8—21no—
367C8—21no—
368C8—1461no—
369C8—1461no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—2924no—
377C22—2921no—
378C22—2921no—
379C22—2921no—
380C22—5844no—
381C22—732no—
382C22—732no—
383C22—1461no—
384C22—1461no—
385C22—1461no—
386C22—1461no—
387C22C2×D4×D7311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—2921no—
393C4—2921no—
394C4—2921no—
395C4—1461no—
396C4—1461no—
397C4#1455663611yescharacteristic
398C4#1455663711yescharacteristic
399C2—41no—
400C2—81no—
401C2—5841no—
402C2—1462no—
403C2—1462no—
404C2#1798914511yescharacteristic
405C2AGL(1,ℤ/8)×D7311yescharacteristic
406C2#137×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#468×C73C2
socleC22×C73C22×D4
hypercenter#468D73
hypocenterC73#3193
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C22⋊Q8×D73C2semidirect
3. #17988924C2semidirect
4. #17988921C2semidirect
5. #17988902C2semidirect
6. #17988899C2semidirect
7. #17988835C2semidirect
8. #17988833C2semidirect
9. #17988831C2semidirect
10. #17988739C2semidirect
11. #17988736C2semidirect
12. #17988727C2semidirect
13. #17988724C2semidirect
14. #17988550C2semidirect
15. #468×C73C2semidirect
16. C2×Q8×D73C22semidirect
20. C2×#11924017C22semidirect
21. C2×#11924016C22semidirect
22. C2×#11924015C22semidirect
23. C2×#11924012C22semidirect
25. #14556570C22semidirect
36. C4⋊C4×D73C22semidirect
39. #14556525C22semidirect
40. #14556524C22semidirect
41. #14556524C22semidirect
42. #14556516C22semidirect
43. #14556515C22semidirect
44. #14556514C22semidirect
45. #14556513C22semidirect
46. #14556512C22semidirect
47. #14556511C22semidirect
50. #14556503C22semidirect
51. #14556503C22semidirect
52. C2×SD16×C73C22semidirect
53. C2×M16×C73C22semidirect
54. C22⋊Q8×C73C22semidirect
56. #107×C73C22semidirect
57. #103×C73C22semidirect
58. #102×C73C22semidirect
204. C73#3193semidirect
214. #468D73semidirect
227. C2×SD16C2×D73semidirect
229. C2×M16C2×D73semidirect
235. C22⋊Q8C2×D73semidirect
250. #107C2×D73semidirect
254. #103C2×D73semidirect
258. #102C2×D73semidirect