Finite Group Databasebeta

← #22621512

Subgroups — #22621512

Order 9344.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556621C211yesmaximal, characteristic, complemented
2C2×#14556611C211yesmaximal, characteristic, complemented
3#17989246C211yesmaximal, characteristic, complemented
4#17988974C211yesmaximal, characteristic, complemented
5#17988838C211yesmaximal, characteristic, complemented
6#17988814C211yesmaximal, characteristic, complemented
7#17988809C211yesmaximal, characteristic, complemented
8#17988784C211yesmaximal, characteristic, complemented
9#17988749C211yesmaximal, characteristic, complemented
10#17988732C211yesmaximal, characteristic, complemented
11#17988730C211yesmaximal, characteristic, complemented
12#17988725C211yesmaximal, characteristic, complemented
13#17988692C211yesmaximal, characteristic, complemented
14#17988659C211yesmaximal, characteristic, complemented
15#550×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18#14556621—24no—
19#14556611—24no—
20C2×#11924018C2211yescharacteristic
21C2×#11924018C2211yescharacteristic
22C2×#11924016C2211yescharacteristic
23C2×#11924016C2211yescharacteristic
24C2×#11924016C2211yescharacteristic
25C2×#11924016C2211yescharacteristic
26C2×#11924015C2211yescharacteristic
27C2×#11924013C2211yescharacteristic
28C2×#11924013C2211yescharacteristic
29C2×#11924012C2211yescharacteristic
30C22×#10596831C2211yescharacteristic
31#14556579C2211yescharacteristic
32#14556577—21no—
33#14556570C2211yescharacteristic
34#14556569—21no—
35#14556565C2211yescharacteristic
36#14556563—21no—
37C4×Dic146C2211yescharacteristic
38#14556551—21no—
39#14556522C2211yescharacteristic
40C4⋊#10596831C2211yescharacteristic
41#14556515C2211yescharacteristic
42#14556514C2211yescharacteristic
43#14556514C2211yescharacteristic
44#14556512C2211yescharacteristic
45#14556512C2211yescharacteristic
46#14556511C2211yescharacteristic
47C22⋊#10596831C2211yescharacteristic
48C22⋊#10596831C2211yescharacteristic
49#14556502C2211yescharacteristic
50C2×#41×C73C2211yescharacteristic
51C2×#41×C73C2211yescharacteristic
52#127×C73—21no—
53#127×C73C2211yescharacteristic
54#121×C73—21no—
55#121×C73—21no—
56#121×C73C2211yescharacteristic
57#121×C73C2211yescharacteristic
58C4×Q8×C73C2211yescharacteristic
59C4×D4×C73—21no—
60C4×D4×C73C2211yescharacteristic
61#11924028—22no—
62#11924028—41no—
63C2×Dic146—22no—
64C2×Dic146—21no—
65C2×Dic146—41no—
66C2×Dic146C2311yescharacteristic
67C2×Dic146C2311yescharacteristic
68C2×D292C2311yescharacteristic
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C22×Dic73—21no—
72C2×C4×D73—21no—
73#11924018—22no—
74#11924018D414yescomplemented
75#11924016—22no—
76#11924016—22no—
77#11924016—22no—
78#11924016—41no—
79#11924015—22no—
80#11924013—22no—
81#11924013—41no—
82#11924012—22no—
83C2×#10596831—22no—
84C2×#10596831C2311yescharacteristic
85C2×#10596831C2311yescharacteristic
86C2×#10596831C2311yescharacteristic
87C2×#10596831C2311yescharacteristic
88C4⋊Dic73C2311yescharacteristic
89#11924007—21no—
90#11924007—21no—
91C22⋊Dic73—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95C4×Dic73—21no—
96#41×C73—22no—
97#41×C73—22no—
98#41×C73—41no—
99#41×C73—41no—
100C2×Q8×C73C2311yescharacteristic
101C2×D4×C73—21no—
102C2×D4×C73—21no—
103C2×D4×C73—21no—
104C2×D4×C73—21no—
105C2×D4×C73—21no—
106C2×D4×C73—21no—
107C2×D4×C73D411yescharacteristic
108C2×D4×C73C2311yescharacteristic
109C2×D4×C73C2311yescharacteristic
110C22×C4×C73—21no—
111C22×C4×C73—21no—
112C22×C4×C73C2311yescharacteristic
113C22×C4×C73C2311yescharacteristic
114C4⋊C4×C73—21no—
115C4⋊C4×C73D411yescharacteristic
116C4⋊C4×C73C2311yescharacteristic
117C22⋊C4×C73—21no—
118C22⋊C4×C73—21no—
119C22⋊C4×C73D411yescharacteristic
120C22⋊C4×C73D411yescharacteristic
121C42×C73—21no—
122C42×C73C2311yescharacteristic
123C23×C73—21no—
124C23×C73—21no—
125C23×C73C2×D411yescharacteristic
126C23×C73C2×D411yescharacteristic
127C22×D73—21no—
128Q8×C73—21no—
129Q8×C73C2×D412yes—
130D4×C73—21no—
131D4×C73—21no—
132D4×C73—21no—
133D4×C73—21no—
134D4×C73—41no—
135D4×C73—42no—
136D4×C73—42no—
137D4×C73—42no—
138D4×C73—81no—
139D4×C73—81no—
140D4×C73—81no—
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—42no—
148C2×C4×C73—42no—
149C2×C4×C73C2×D411yescharacteristic
150C2×C4×C73C2×D411yescharacteristic
151C2×C4×C73C2×D411yescharacteristic
152C2×C4×C73C2×D411yescharacteristic
153C2×C4×C73C2411yescharacteristic
154C22⋊D73—42no—
155C22⋊D73—42no—
156C2×Dic73—21no—
157C2×Dic73—21no—
158C2×Dic73—21no—
159C2×Dic73—42no—
160D292—21no—
161D292—21no—
162C4×D73—42no—
163Dic146—21no—
164Dic146—21no—
165Dic146—21no—
166Dic146—42no—
167Dic146C2×D412yes—
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×C73—41no—
182C22×C73—41no—
183C22×C73—41no—
184C22×C73C22×D411yescharacteristic
185C2×D73—41no—
186C2×D73—41no—
187C2×D73—41no—
188C4×C73—21no—
189C4×C73—21no—
190C4×C73—22no—
191C4×C73—21no—
192C4×C73—21no—
193C4×C73—41no—
194C4×C73C22×D411yescharacteristic
195C4×C73H(5,𝔽2)11yescharacteristic
196Dic73—22no—
197Dic73—41no—
198Dic73—41no—
199C2×C73—41no—
200C2×C73—41no—
201C2×C73—81no—
202C2×C73—81no—
203C2×C73D4211yescharacteristic
204C2×C73#57511yescharacteristic
205C2×C73#57711yescharacteristic
206D73—81no—
207#3271—731nomaximal, Sylow
208C73#327111yescharacteristic, complemented, Sylow
209C2×#137—731no—
210C2×#135—731no—
211#550D7311yescharacteristic, complemented
212#548—731no—
213#496—731no—
214#469—731no—
215#465—731no—
216#464—731no—
217#460—731no—
218#452—731no—
219#449—731no—
220#449—731no—
221#448—731no—
222#441—731no—
223#435—731no—
224C2×#41—731no—
225C2×#41C2×D7311yescharacteristic
226C2×#41C2×D7311yescharacteristic
227C22×Q8—731no—
228#137—1464no—
229#135—1464no—
230C2×Q16—731no—
231C2×Q16—731no—
232C2×SD16—731no—
233C2×SD16—731no—
234C2×SD16—731no—
235C2×SD16—731no—
236C2×SD16—731no—
237C2×D8—731no—
238C2×D8—731no—
239C2×M16—731no—
240C22×C8—731no—
241#127—21no—
242#127C2×D7311yescharacteristic
243#124—731no—
244#124—1461no—
245C22⋊Q8—731no—
246C22⋊Q8—1461no—
247#121—21no—
248#121—21no—
249#121—731no—
250#121—1461no—
251#121C2×D7311yescharacteristic
252#121C2×D7311yescharacteristic
253C4×Q8—731no—
254C4×Q8C2×D7311yescharacteristic
255C4×D4—21no—
256C4×D4—1461no—
257C4×D4C2×D7311yescharacteristic
258#106—731no—
259C4⋊C8—731no—
260#103—731no—
261#103—731no—
262#103—731no—
263#102—731no—
264#102—731no—
265#102—731no—
266C22⋊C8—731no—
267C22⋊C8—731no—
268#97—731no—
269#41—22no—
270#41—22no—
271#41—41no—
272#41—41no—
273#41—2921no—
274#41—1462no—
275C2×Q8—2921no—
276C2×Q8—731no—
277C2×Q8—731no—
278C2×Q8—1462no—
279C2×Q8—1461no—
280C2×Q8C22×D7311yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—731no—
288C2×D4—1461no—
289C2×D4—1461no—
290C2×D4C22⋊D7311yescharacteristic
291C2×D4C22×D7311yescharacteristic
292C2×D4C22×D7311yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—1461no—
296C22×C4—1461no—
297C22×C4C22×D7311yescharacteristic
298C22×C4C22×D7311yescharacteristic
299Q16—734no—
300Q16—1462no—
301SD16—2921no—
302SD16—1462no—
303SD16—1462no—
304SD16—1462no—
305SD16—1462no—
306D8—2921no—
307D8—1462no—
308M16—1462no—
309C2×C8—731no—
310C2×C8—731no—
311C2×C8—731no—
312C2×C8—731no—
313C2×C8—1462no—
314C4⋊C4—21no—
315C4⋊C4—731no—
316C4⋊C4—1461no—
317C4⋊C4—1461no—
318C4⋊C4C22⋊D7311yescharacteristic
319C4⋊C4C22×D7311yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—1461no—
323C22⋊C4—1461no—
324C22⋊C4—1461no—
325C22⋊C4—1461no—
326C22⋊C4C22⋊D7311yescharacteristic
327C22⋊C4C22⋊D7311yescharacteristic
328C42—21no—
329C42—1461no—
330C42C22×D7311yescharacteristic
331C23—21no—
332C23—21no—
333C23—1461no—
334C23C2×C22⋊D7311yescharacteristic
335C23C2×C22⋊D7311yescharacteristic
336Q8—21no—
337Q8—2922no—
338Q8—732no—
339Q8—1461no—
340Q8—1461no—
341Q8—1461no—
342Q8D4×D7312yes—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—21no—
347D4—41no—
348D4—42no—
349D4—42no—
350D4—42no—
351D4—81no—
352D4—81no—
353D4—81no—
354D4—2922no—
355D4—2922no—
356D4—1461no—
357D4—1461no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—2922no—
367C2×C4—2922no—
368C2×C4—1461no—
369C2×C4—1461no—
370C2×C4—1461no—
371C2×C4C2×C22⋊D7311yescharacteristic
372C2×C4C2×C22⋊D7311yescharacteristic
373C2×C4C2×C22⋊D7311yescharacteristic
374C2×C4C2×C22⋊D7311yescharacteristic
375C2×C4C23×D7311yescharacteristic
376C8—732no—
377C8—1461no—
378C8—1461no—
379C8—1461no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—2921no—
393C22—2921no—
394C22—2921no—
395C22C22×C22⋊D7311yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—22no—
401C4—41no—
402C4—2921no—
403C4—2921no—
404C4—1462no—
405C4C2×D4×D7311yescharacteristic
406C4#1455663611yescharacteristic
407C2—41no—
408C2—41no—
409C2—81no—
410C2—81no—
411C2—5841no—
412C2D4×C22⋊D7311yescharacteristic
413C2#1798938511yescharacteristic
414C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#550×C73C2
socleC22×C73C22×D4
hypercenter#550D73
hypocenterC73#3271
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#14556621C2semidirect
2. C2×#14556611C2semidirect
3. #17989246C2semidirect
4. #17988974C2semidirect
5. #17988838C2semidirect
6. #17988814C2semidirect
7. #17988809C2semidirect
8. #17988784C2semidirect
9. #17988749C2semidirect
10. #17988732C2semidirect
11. #17988730C2semidirect
12. #17988725C2semidirect
13. #17988692C2semidirect
14. #17988659C2semidirect
15. #550×C73C2semidirect
74. #11924018D4semidirect
208. C73#3271semidirect
211. #550D73semidirect