Finite Group Databasebeta

← C2×#20260750 #27150276

Subgroups — C2×#20260750 #27150276

Order 12416.

772 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D97C211yesmaximal, characteristic
2C2×M16×D97C211yesmaximal, characteristic, complemented
3C2×#15690767C211yesmaximal, characteristic, complemented
4#20260750C218yesmaximal, direct product factor
5C2×#15690738C211yesmaximal, characteristic, complemented
6C2×#15690737C211yesmaximal, characteristic, complemented
7C2×#15690736C211yesmaximal, characteristic, complemented
8C2×#104×C97C211yesmaximal, characteristic, complemented
9C2×#13095512C411yescharacteristic, complemented
10C2×#13095511—21no—
11C2×#13095511C2211yescharacteristic
12C2×#13095510—21no—
13C2×#13095510C411yescharacteristic, complemented
14#41×D97—22no—
15#41×D97—22no—
16#41×D97C414yescomplemented
17#41×D97C2214yes—
18C2×Q8×D97C411yescharacteristic, complemented
19C2×D4×D97—21no—
20C2×D4×D97C411yescharacteristic, complemented
21C22×C4×D97—21no—
22C22×C4×D97C2211yescharacteristic
23C2×#13095495C2211yescharacteristic, complemented
24C2×#13095494—21no—
25M16×D97—22no—
26M16×D97C2214yescomplemented
27C2×C8×D97—21no—
28#15690767—22no—
29#15690767C2214yescomplemented
30C2×#13095490—21no—
31C2×#13095488—21no—
32C2×C4×Dic97C2211yescharacteristic, complemented
33#15690738C2214yescomplemented
34#15690737C2214yescomplemented
35#15690736C2214yescomplemented
36C2×#41×C97C2211yescharacteristic
37C2×M16×C97C2211yescharacteristic, complemented
38C2×C42×C97C2211yescharacteristic, complemented
39#104×C97C2214yescomplemented
40C23×D97—21no—
41C23×D97D411yescharacteristic
42#13095512—22no—
43#13095512C2×C414yescomplemented
44#13095511—21no—
45#13095511—21no—
46#13095511—24no—
47#13095511—24no—
48#13095511C2×C412yes—
49#13095511C2312yes—
50#13095510—24no—
51#13095510—24no—
52#13095510—22no—
53#13095510C2×C414yescomplemented
54C2×Dic194—21no—
55C2×Dic194C2×C411yescharacteristic
56Q8×D97—22no—
57Q8×D97C2×C414yescomplemented
58C2×D388—21no—
59C2×D388C2×C411yescharacteristic
60C2×C22⋊D97—21no—
61C2×C22⋊D97—21no—
62C2×C22⋊D97—21no—
63D4×D97—24no—
64D4×D97—24no—
65D4×D97—22no—
66D4×D97C2×C414yescomplemented
67C22×Dic97—21no—
68C22×Dic97—21no—
69C22×Dic97D411yescharacteristic
70C2×C4×D97—21no—
71C2×C4×D97—21no—
72C2×C4×D97—21no—
73C2×C4×D97—24no—
74C2×C4×D97—24no—
75C2×C4×D97C2×C411yescharacteristic
76C2×C4×D97C2×C412yes—
77C2×C4×D97C2×C411yescharacteristic
78C2×C4×D97D412yes—
79C2×C4×D97D411yescharacteristic
80C2×C4×D97D412yes—
81C2×C4×D97D411yescharacteristic
82C2×C4×D97C2312yes—
83#13095495—21no—
84#13095495C2312yescomplemented
85#13095494—24no—
86C2×#11715895—21no—
87C8×D97—24no—
88#13095490—24no—
89#13095488—24no—
90C4×Dic97—21no—
91C4×Dic97C2312yescomplemented
92#41×C97—21no—
93#41×C97—21no—
94#41×C97C2×C412yes—
95#41×C97C2312yes—
96C2×Q8×C97C2×C411yescharacteristic
97C2×D4×C97—21no—
98C2×D4×C97C2×C411yescharacteristic
99C22×C4×C97—21no—
100C22×C4×C97—21no—
101C22×C4×C97C2311yescharacteristic
102M16×C97—21no—
103M16×C97C2312yescomplemented
104C2×C8×C97—21no—
105C42×C97—21no—
106C42×C97C2312yescomplemented
107C23×C97—21no—
108C23×C97C2×D411yescharacteristic
109C22×D97—21no—
110C22×D97—24no—
111C22×D97—42no—
112C22×D97—44no—
113C22×D97C22⋊C411yescharacteristic
114C22×D97C22⋊C411yescharacteristic
115C22×D97C22⋊C412yes—
116C22×D97C2×D412yes—
117Q8×C97—21no—
118Q8×C97C22×C412yes—
119D4×C97—22no—
120D4×C97—22no—
121D4×C97—21no—
122D4×C97C22×C412yes—
123C2×C4×C97—21no—
124C2×C4×C97—22no—
125C2×C4×C97—22no—
126C2×C4×C97—22no—
127C2×C4×C97—42no—
128C2×C4×C97C22×C411yescharacteristic
129C2×C4×C97C22×C411yescharacteristic
130C2×C4×C97C2×D411yescharacteristic
131C2×C4×C97C2×D411yescharacteristic
132C2×C4×C97C2×D411yescharacteristic
133C2×C4×C97C2411yescharacteristic
134C22⋊D97—22no—
135C22⋊D97—22no—
136C22⋊D97—24no—
137C22⋊D97—24no—
138C2×Dic97—21no—
139C2×Dic97—24no—
140C2×Dic97—22no—
141C2×Dic97—42no—
142C2×Dic97C22⋊C411yescharacteristic
143C2×Dic97C22⋊C411yescharacteristic
144C2×Dic97C22⋊C412yes—
145C2×Dic97C2×D412yes—
146D388—24no—
147D388—21no—
148D388C22×C412yes—
149C4×D97—24no—
150C4×D97—22no—
151C4×D97—22no—
152C4×D97—24no—
153C4×D97C22⋊C412yes—
154C4×D97C22⋊C412yes—
155C4×D97C22⋊C412yes—
156C4×D97C22⋊C412yes—
157C4×D97C22×C412yes—
158C4×D97C22×C412yes—
159C4×D97C2×D412yes—
160C4×D97C2×D412yes—
161Dic194—21no—
162Dic194—24no—
163Dic194C22×C412yes—
164C8×C97—22no—
165#11715895—22no—
166C22×C97—22no—
167C22×C97—22no—
168C22×C97—42no—
169C22×C97C2×C22⋊C411yescharacteristic
170C22×C97C2×C22⋊C411yescharacteristic
171C22×C97C22×D411yescharacteristic
172C2×D97—22no—
173C2×D97—22no—
174C2×D97—22no—
175C2×D97—42no—
176C2×D97—42no—
177C2×D97—48no—
178C2×D97—42no—
179C2×D97C2×C22⋊C412yes—
180C2×D97C2×C22⋊C412yes—
181C4×C97—22no—
182C4×C97—42no—
183C4×C97C2×C22⋊C411yescharacteristic
184C4×C97C2×C22⋊C411yescharacteristic
185C4×C97C23×C411yescharacteristic
186C4×C97C22×D411yescharacteristic
187Dic97—22no—
188Dic97—42no—
189Dic97C2×C22⋊C412yes—
190Dic97C2×C22⋊C412yes—
191C2×C97—21no—
192C2×C97—21no—
193C2×C97—42no—
194C2×C97#42112yescomplemented
195C2×C97C22×C22⋊C411yescharacteristic
196D97—22no—
197D97—22no—
198D97—42no—
199C2×#421—971nomaximal, Sylow
200C97C2×#42111yescharacteristic, complemented, Sylow
201C22×#41—971no—
202C22×M16—971no—
203C2×#117—971no—
204#421—978no—
205C2×#104—971no—
206C2×#104—971no—
207C2×#104—971no—
208C2×#104D9711yescharacteristic, complemented
209C2×#41—974no—
210C2×#41—974no—
211C2×#41—971no—
212C2×#41—971no—
213C2×#41—971no—
214C2×#41—1941no—
215C2×#41—1941no—
216C2×#41—1942no—
217C2×#41—1942no—
218C2×#41C2×D9711yescharacteristic
219C22×Q8—971no—
220C22×D4—971no—
221C22×D4—1941no—
222C23×C4—971no—
223C23×C4—1941no—
224C2×M16—971no—
225C2×M16—974no—
226C2×M16—1941no—
227C2×M16—1942no—
228C2×M16C2×D9711yescharacteristic, complemented
229C22×C8—1941no—
230#117—974no—
231#117—1942no—
232C2×C4⋊C4—1941no—
233C2×C22⋊C4—1941no—
234C2×C42—971no—
235C2×C42C2×D9711yescharacteristic, complemented
236#104—974no—
237#104—974no—
238#104—974no—
239#104C2×D9714yescomplemented
240C24—971no—
241C24—1941no—
242#41—21no—
243#41—21no—
244#41—974no—
245#41—974no—
246#41—972no—
247#41—972no—
248#41—1944no—
249#41—1944no—
250#41—1944no—
251#41—1944no—
252#41—1942no—
253#41—1942no—
254#41—1941no—
255#41—1941no—
256#41C4×D9712yes—
257#41C22×D9712yes—
258C2×Q8—974no—
259C2×Q8—971no—
260C2×Q8—1941no—
261C2×Q8—1942no—
262C2×Q8C4×D9711yescharacteristic
263C2×D4—21no—
264C2×D4—974no—
265C2×D4—971no—
266C2×D4—1941no—
267C2×D4—1942no—
268C2×D4—1941no—
269C2×D4—1944no—
270C2×D4—1944no—
271C2×D4—1941no—
272C2×D4—1941no—
273C2×D4C4×D9711yescharacteristic
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—971no—
277C22×C4—971no—
278C22×C4—971no—
279C22×C4—972no—
280C22×C4—972no—
281C22×C4—972no—
282C22×C4—971no—
283C22×C4—971no—
284C22×C4—972no—
285C22×C4—1941no—
286C22×C4—1944no—
287C22×C4—1944no—
288C22×C4—1941no—
289C22×C4—1941no—
290C22×C4—1941no—
291C22×C4—1941no—
292C22×C4C22×D9711yescharacteristic
293M16—21no—
294M16—972no—
295M16—1944no—
296M16—1941no—
297M16C22×D9712yescomplemented
298C2×C8—21no—
299C2×C8—1944no—
300C2×C8—1941no—
301C4⋊C4—1944no—
302C22⋊C4—1944no—
303C42—21no—
304C42—972no—
305C42—1941no—
306C42C22×D9712yescomplemented
307C23—21no—
308C23—972no—
309C23—972no—
310C23—971no—
311C23—971no—
312C23—3882no—
313C23—3884no—
314C23—1944no—
315C23—1941no—
316C23D4×D9711yescharacteristic
317Q8—21no—
318Q8—972no—
319Q8—1944no—
320Q8—1941no—
321Q8C2×C4×D9712yes—
322D4—22no—
323D4—22no—
324D4—21no—
325D4—972no—
326D4—1944no—
327D4—1944no—
328D4—1944no—
329D4—1942no—
330D4—1942no—
331D4—1941no—
332D4C2×C4×D9712yes—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—42no—
338C2×C4—971no—
339C2×C4—971no—
340C2×C4—972no—
341C2×C4—972no—
342C2×C4—972no—
343C2×C4—972no—
344C2×C4—972no—
345C2×C4—972no—
346C2×C4—972no—
347C2×C4—972no—
348C2×C4—972no—
349C2×C4—972no—
350C2×C4—3882no—
351C2×C4—1944no—
352C2×C4—1944no—
353C2×C4—1944no—
354C2×C4—1942no—
355C2×C4—1941no—
356C2×C4—1942no—
357C2×C4—1942no—
358C2×C4C2×C4×D9711yescharacteristic
359C2×C4C2×C4×D9711yescharacteristic
360C2×C4D4×D9711yescharacteristic
361C2×C4D4×D9711yescharacteristic
362C2×C4D4×D9711yescharacteristic
363C2×C4C23×D9711yescharacteristic
364C8—22no—
365C8—1942no—
366C22—22no—
367C22—22no—
368C22—42no—
369C22—972no—
370C22—972no—
371C22—3882no—
372C22—3882no—
373C22—3888no—
374C22—3882no—
375C22—1942no—
376C22—1942no—
377C22—1942no—
378C22C22⋊C4×D9711yescharacteristic
379C22C22⋊C4×D9711yescharacteristic
380C22C2×D4×D9711yescharacteristic
381C4—22no—
382C4—42no—
383C4—972no—
384C4—972no—
385C4—3882no—
386C4—1942no—
387C4C22⋊C4×D9711yescharacteristic
388C4C22⋊C4×D9711yescharacteristic
389C4C22×C4×D9711yescharacteristic
390C4C2×D4×D9711yescharacteristic
391C2—21no—
392C2—21no—
393C2—42no—
394C2—3882no—
395C2—1942no—
396C2—1942no—
397C2#2026075012yesdirect product factor
398C2C2×C22⋊C4×D9711yescharacteristic
subgroupG/H
centerC2×C4D4×D97
commutatorC4×C97C23×C4
FrattiniC2×C4C23×D97
FittingC2×#104×C97C2
socleC22×C97C2×C22⋊C4
prime radicalC2×#41×D97C2
cosocleC2×C4×C97C24
hypercenterC2×#104D97
hypocenterC97C2×#421
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×M16×D97C2semidirect
3. C2×#15690767C2semidirect
4. #20260750C2direct (N × H)
5. C2×#15690738C2semidirect
6. C2×#15690737C2semidirect
7. C2×#15690736C2semidirect
8. C2×#104×C97C2semidirect
9. C2×#13095512C4semidirect
13. C2×#13095510C4semidirect
16. #41×D97C4semidirect
18. C2×Q8×D97C4semidirect
20. C2×D4×D97C4semidirect
23. C2×#13095495C22semidirect
26. M16×D97C22semidirect
29. #15690767C22semidirect
32. C2×C4×Dic97C22semidirect
33. #15690738C22semidirect
34. #15690737C22semidirect
35. #15690736C22semidirect
37. C2×M16×C97C22semidirect
38. C2×C42×C97C22semidirect
39. #104×C97C22semidirect
43. #13095512C2×C4semidirect
53. #13095510C2×C4semidirect
57. Q8×D97C2×C4semidirect
66. D4×D97C2×C4semidirect
84. #13095495C23semidirect
91. C4×Dic97C23semidirect
103. M16×C97C23semidirect
106. C42×C97C23semidirect
194. C2×C97#421semidirect
200. C97C2×#421semidirect
208. C2×#104D97semidirect
228. C2×M16C2×D97semidirect
235. C2×C42C2×D97semidirect
239. #104C2×D97semidirect
297. M16C22×D97semidirect
306. C42C22×D97semidirect
397. C2#20260750direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#41×D972
C2×M16×D972
C2×#156907672
#202607502
C2×#156907382
C2×#156907372
C2×#156907362
C2×#104×C972
C2×#42197