Finite Group Databasebeta

← #22621563

Subgroups — #22621563

Order 9344.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556622C211yesmaximal, characteristic, complemented
2C2×#14556616C211yesmaximal, characteristic, complemented
3#17989233C211yesmaximal, characteristic, complemented
4#17988969C211yesmaximal, characteristic, complemented
5#17988843C211yesmaximal, characteristic, complemented
6#17988838C211yesmaximal, characteristic, complemented
7#17988809C211yesmaximal, characteristic, complemented
8#17988799C211yesmaximal, characteristic, complemented
9#17988749C211yesmaximal, characteristic, complemented
10#17988737C211yesmaximal, characteristic, complemented
11#17988730C211yesmaximal, characteristic, complemented
12#17988726C211yesmaximal, characteristic, complemented
13C4×#11924015C211yesmaximal, characteristic, complemented
14#17988665C211yesmaximal, characteristic, complemented
15#548×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×D292C2211yescharacteristic
18#14556622—24no—
19#14556616—24no—
20C2×#11924018C2211yescharacteristic, complemented
21C2×#11924018C2211yescharacteristic, complemented
22C2×#11924016C2211yescharacteristic, complemented
23C2×#11924015C2211yescharacteristic
24C2×#11924015C2211yescharacteristic
25C2×#11924015C2211yescharacteristic
26C2×#11924015C2211yescharacteristic
27C2×#11924013C2211yescharacteristic
28C2×#11924013C2211yescharacteristic
29C2×#11924012C2211yescharacteristic
30C2×#11924012C2211yescharacteristic, complemented
31#14556579C2211yescharacteristic
32#14556576—21no—
33#14556570C2211yescharacteristic
34#14556565C2211yescharacteristic
35#14556564—21no—
36#14556559—21no—
37C4×D292C2211yescharacteristic
38C22⋊C4×D73—21no—
39#14556522C2211yescharacteristic, complemented
40C4⋊#10596831C2211yescharacteristic, complemented
41#14556515C2211yescharacteristic, complemented
42#14556515C2211yescharacteristic, complemented
43#14556514C2211yescharacteristic, complemented
44#14556512C2211yescharacteristic, complemented
45#14556511C2211yescharacteristic
46#14556511C2211yescharacteristic
47C22⋊#10596831C2211yescharacteristic
48C22⋊#10596831C2211yescharacteristic, complemented
49C4×#10596831C2211yescharacteristic, complemented
50C2×#41×C73C2211yescharacteristic
51C22×Q8×C73C2211yescharacteristic, complemented
52#124×C73—21no—
53#124×C73C2211yescharacteristic, complemented
54C22⋊Q8×C73—21no—
55C22⋊Q8×C73C2211yescharacteristic
56#121×C73—21no—
57#121×C73C2211yescharacteristic, complemented
58C4×Q8×C73C2211yescharacteristic, complemented
59C4×D4×C73—21no—
60C4×D4×C73C2211yescharacteristic
61C23×D73—21no—
62#11924028—22no—
63#11924028—41no—
64C2×Dic146C2311yescharacteristic
65C2×D292—22no—
66C2×D292—21no—
67C2×D292—41no—
68C2×D292C2311yescharacteristic
69C2×D292C2311yescharacteristic
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C4×D73—21no—
73C2×C4×D73—21no—
74#11924018—22no—
75#11924018—22no—
76#11924016—41no—
77#11924015—22no—
78#11924015—22no—
79#11924015—41no—
80#11924015D414yescomplemented
81#11924013—22no—
82#11924013—22no—
83#11924012—22no—
84#11924012—22no—
85C2×#10596831C2311yescharacteristic
86C2×#10596831C2311yescharacteristic
87C2×#10596831C2311yescharacteristic
88C2×#10596831C2311yescharacteristic
89C4⋊Dic73C2311yescharacteristic
90#11924007—21no—
91C22⋊Dic73—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#41×C73—22no—
97#41×C73—41no—
98C2×Q8×C73—21no—
99C2×Q8×C73—22no—
100C2×Q8×C73—41no—
101C2×Q8×C73C2311yescharacteristic
102C2×Q8×C73C2311yescharacteristic
103C2×D4×C73—21no—
104C2×D4×C73—21no—
105C2×D4×C73D411yescharacteristic
106C2×D4×C73C2311yescharacteristic
107C22×C4×C73—21no—
108C22×C4×C73—21no—
109C22×C4×C73C2311yescharacteristic
110C22×C4×C73C2311yescharacteristic
111C4⋊C4×C73—21no—
112C4⋊C4×C73—21no—
113C4⋊C4×C73D411yescharacteristic
114C4⋊C4×C73C2311yescharacteristic
115C22⋊C4×C73—21no—
116C22⋊C4×C73—21no—
117C22⋊C4×C73—21no—
118C22⋊C4×C73—21no—
119C22⋊C4×C73D411yescharacteristic
120C22⋊C4×C73D411yescharacteristic
121C42×C73—21no—
122C42×C73C2311yescharacteristic
123C23×C73—21no—
124C23×C73C2×D411yescharacteristic
125C23×C73C2×D411yescharacteristic
126C22×D73—21no—
127C22×D73—21no—
128C22×D73—42no—
129C22×D73—42no—
130C22×D73—81no—
131Q8×C73—21no—
132Q8×C73—21no—
133Q8×C73—21no—
134Q8×C73—42no—
135Q8×C73C2×D412yes—
136D4×C73—21no—
137D4×C73—21no—
138D4×C73—41no—
139D4×C73—42no—
140D4×C73—42no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—42no—
149C2×C4×C73—42no—
150C2×C4×C73C2×D411yescharacteristic
151C2×C4×C73C2×D411yescharacteristic
152C2×C4×C73C2×D411yescharacteristic
153C2×C4×C73C2×D411yescharacteristic
154C2×C4×C73C2411yescharacteristic
155C22⋊D73—42no—
156C22⋊D73—81no—
157C2×Dic73—21no—
158C2×Dic73—21no—
159D292—21no—
160D292—21no—
161D292—21no—
162D292—42no—
163D292C2×D412yes—
164C4×D73—42no—
165C4×D73—81no—
166Dic146—21no—
167Dic146—21no—
168#10596831—21no—
169#10596831—21no—
170#10596831—21no—
171#10596831C2×D412yes—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73—21no—
175C22×C73—21no—
176C22×C73—21no—
177C22×C73—21no—
178C22×C73—41no—
179C22×C73—41no—
180C22×C73—41no—
181C22×C73C22×D411yescharacteristic
182C2×D73—22no—
183C2×D73—41no—
184C2×D73—41no—
185C2×D73—41no—
186C2×D73—41no—
187C2×D73—41no—
188C2×D73—84no—
189C4×C73—21no—
190C4×C73—21no—
191C4×C73—22no—
192C4×C73—21no—
193C4×C73—21no—
194C4×C73—41no—
195C4×C73—41no—
196C4×C73C22×D411yescharacteristic
197C4×C73H(5,𝔽2)11yescharacteristic
198Dic73—41no—
199Dic73—41no—
200C2×C73—41no—
201C2×C73—41no—
202C2×C73—81no—
203C2×C73D4211yescharacteristic
204C2×C73#57511yescharacteristic
205C2×C73#57711yescharacteristic
206D73—42no—
207D73—81no—
208#3275—731nomaximal, Sylow
209C73#327511yescharacteristic, complemented, Sylow
210C2×#137—731no—
211C2×AGL(1,ℤ/8)—731no—
212#548D7311yescharacteristic, complemented
213#546—731no—
214#495—731no—
215#470—731no—
216#469—731no—
217#464—731no—
218#463—731no—
219#452—731no—
220#450—731no—
221#449—731no—
222#448—731no—
223C4×SD16—731no—
224#436—731no—
225C2×#41—731no—
226C2×#41C2×D7311yescharacteristic
227C22×Q8C2×D7311yescharacteristic, complemented
228C22×D4—731no—
229#137—1464no—
230AGL(1,ℤ/8)—1464no—
231C2×Q16—731no—
232C2×Q16—731no—
233C2×SD16—731no—
234C2×SD16—731no—
235C2×SD16—731no—
236C2×SD16—731no—
237C2×SD16—731no—
238C2×D8—731no—
239C2×D8—731no—
240C2×M16—731no—
241C2×M16—731no—
242#124—21no—
243#124—731no—
244#124C2×D7311yescharacteristic, complemented
245#123—1461no—
246C22⋊Q8—21no—
247C22⋊Q8—731no—
248C22⋊Q8C2×D7311yescharacteristic
249#121—21no—
250#121—731no—
251#121—1461no—
252#121C2×D7311yescharacteristic, complemented
253#120—1461no—
254C4×Q8C2×D7311yescharacteristic, complemented
255C4×D4—21no—
256C4×D4—731no—
257C4×D4C2×D7311yescharacteristic
258C2×C22⋊C4—1461no—
259#106—731no—
260C4⋊C8—731no—
261#103—731no—
262#103—731no—
263#103—731no—
264#102—731no—
265#102—731no—
266#102—731no—
267C22⋊C8—731no—
268C22⋊C8—731no—
269C4×C8—731no—
270C24—1461no—
271#41—22no—
272#41—41no—
273#41—2921no—
274#41—1462no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—731no—
279C2×Q8C22×D7311yescharacteristic
280C2×Q8C22×D7311yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—2921no—
284C2×D4—731no—
285C2×D4—731no—
286C2×D4—1462no—
287C2×D4—1461no—
288C2×D4—1461no—
289C2×D4—1461no—
290C2×D4C22⋊D7311yescharacteristic
291C2×D4C22×D7311yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—1461no—
295C22×C4—1461no—
296C22×C4C22×D7311yescharacteristic
297C22×C4C22×D7311yescharacteristic
298Q16—1462no—
299Q16—1462no—
300SD16—2921no—
301SD16—2921no—
302SD16—734no—
303SD16—1462no—
304SD16—1462no—
305D8—1462no—
306D8—1462no—
307M16—1462no—
308M16—1462no—
309C2×C8—731no—
310C2×C8—731no—
311C2×C8—731no—
312C2×C8—731no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—731no—
316C4⋊C4—1461no—
317C4⋊C4C22⋊D7311yescharacteristic
318C4⋊C4C22×D7311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—1461no—
324C22⋊C4—1461no—
325C22⋊C4—1461no—
326C22⋊C4—1461no—
327C22⋊C4—1461no—
328C22⋊C4C22⋊D7311yescharacteristic
329C22⋊C4C22⋊D7311yescharacteristic
330C42—21no—
331C42C22×D7311yescharacteristic
332C23—21no—
333C23—2922no—
334C23—2922no—
335C23—5841no—
336C23—1461no—
337C23—1461no—
338C23C2×C22⋊D7311yescharacteristic
339C23C2×C22⋊D7311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—42no—
344Q8—1461no—
345Q8—1461no—
346Q8D4×D7312yes—
347D4—21no—
348D4—21no—
349D4—41no—
350D4—42no—
351D4—42no—
352D4—2922no—
353D4—2922no—
354D4—5841no—
355D4—732no—
356D4—1461no—
357D4—1461no—
358D4—1461no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—2922no—
369C2×C4—5841no—
370C2×C4—1461no—
371C2×C4—1461no—
372C2×C4C2×C22⋊D7311yescharacteristic
373C2×C4C2×C22⋊D7311yescharacteristic
374C2×C4C2×C22⋊D7311yescharacteristic
375C2×C4C2×C22⋊D7311yescharacteristic
376C2×C4C23×D7311yescharacteristic
377C8—732no—
378C8—1461no—
379C8—1461no—
380C8—1461no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—2921no—
391C22—2921no—
392C22—2921no—
393C22—2921no—
394C22—2921no—
395C22—5844no—
396C22—1462no—
397C22C22×C22⋊D7311yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—22no—
403C4—41no—
404C4—41no—
405C4—2921no—
406C4—2921no—
407C4C2×D4×D7311yescharacteristic
408C4#1455663611yescharacteristic
409C2—41no—
410C2—41no—
411C2—81no—
412C2—2922no—
413C2—5841no—
414C2D4×C22⋊D7311yescharacteristic
415C2#1798938511yescharacteristic
416C2#1798939511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#548×C73C2
socleC22×C73C22×D4
hypercenter#548D73
hypocenterC73#3275
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#14556622C2semidirect
2. C2×#14556616C2semidirect
3. #17989233C2semidirect
4. #17988969C2semidirect
5. #17988843C2semidirect
6. #17988838C2semidirect
7. #17988809C2semidirect
8. #17988799C2semidirect
9. #17988749C2semidirect
10. #17988737C2semidirect
11. #17988730C2semidirect
12. #17988726C2semidirect
13. C4×#11924015C2semidirect
14. #17988665C2semidirect
15. #548×C73C2semidirect
20. C2×#11924018C22semidirect
21. C2×#11924018C22semidirect
22. C2×#11924016C22semidirect
30. C2×#11924012C22semidirect
39. #14556522C22semidirect
40. C4⋊#10596831C22semidirect
41. #14556515C22semidirect
42. #14556515C22semidirect
43. #14556514C22semidirect
44. #14556512C22semidirect
48. C22⋊#10596831C22semidirect
49. C4×#10596831C22semidirect
51. C22×Q8×C73C22semidirect
53. #124×C73C22semidirect
57. #121×C73C22semidirect
58. C4×Q8×C73C22semidirect
80. #11924015D4semidirect
209. C73#3275semidirect
212. #548D73semidirect
227. C22×Q8C2×D73semidirect
244. #124C2×D73semidirect
252. #121C2×D73semidirect
254. C4×Q8C2×D73semidirect