Finite Group Databasebeta

← C2×#31826480 #49129801

Subgroups — C2×#31826480 #49129801

Order 36224.

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×D283C211yesmaximal, characteristic
2C2×M16×D283C211yesmaximal, characteristic, complemented
3C2×#22583567C211yesmaximal, characteristic, complemented
4#31826480C218yesmaximal, direct product factor
5C2×#22583538C211yesmaximal, characteristic, complemented
6C2×#22583537C211yesmaximal, characteristic, complemented
7C2×#22583536C211yesmaximal, characteristic, complemented
8C2×#104×C283C211yesmaximal, characteristic, complemented
9C2×#17985393C411yescharacteristic, complemented
10C2×#17985392—21no—
11C2×#17985392C2211yescharacteristic
12C2×#17985391—21no—
13C2×#17985391C411yescharacteristic, complemented
14#41×D283—22no—
15#41×D283—22no—
16#41×D283C414yescomplemented
17#41×D283C2214yes—
18C2×Q8×D283C411yescharacteristic, complemented
19C2×D4×D283—21no—
20C2×D4×D283C411yescharacteristic, complemented
21C22×C4×D283—21no—
22C22×C4×D283C2211yescharacteristic
23C2×#17985376C2211yescharacteristic, complemented
24C2×#17985375—21no—
25M16×D283—22no—
26M16×D283C2214yescomplemented
27C2×C8×D283—21no—
28#22583567—22no—
29#22583567C2214yescomplemented
30C2×Dic283⋊C4—21no—
31C2×(C2×D283)⋊C4—21no—
32C2×C4×Dic283C2211yescharacteristic, complemented
33#22583538C2214yescomplemented
34#22583537C2214yescomplemented
35#22583536C2214yescomplemented
36C2×#41×C283C2211yescharacteristic
37C2×M16×C283C2211yescharacteristic, complemented
38C2×C42×C283C2211yescharacteristic, complemented
39#104×C283C2214yescomplemented
40C23×D283—21no—
41C23×D283D411yescharacteristic
42#17985393—22no—
43#17985393C2×C414yescomplemented
44#17985392—24no—
45#17985392—24no—
46#17985392—21no—
47#17985392—21no—
48#17985392C2×C412yes—
49#17985392C2312yes—
50#17985391—24no—
51#17985391—24no—
52#17985391—22no—
53#17985391C2×C414yescomplemented
54C2×Dic566—21no—
55C2×Dic566C2×C411yescharacteristic
56Q8×D283—22no—
57Q8×D283C2×C414yescomplemented
58C2×D1132—21no—
59C2×D1132C2×C411yescharacteristic
60C2×C22⋊D283—21no—
61C2×C22⋊D283—21no—
62C2×C22⋊D283—21no—
63D4×D283—24no—
64D4×D283—24no—
65D4×D283—22no—
66D4×D283C2×C414yescomplemented
67C22×Dic283—21no—
68C22×Dic283—21no—
69C22×Dic283D411yescharacteristic
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—24no—
73C2×C4×D283—24no—
74C2×C4×D283—21no—
75C2×C4×D283C2×C411yescharacteristic
76C2×C4×D283C2×C412yes—
77C2×C4×D283C2×C411yescharacteristic
78C2×C4×D283D412yes—
79C2×C4×D283D411yescharacteristic
80C2×C4×D283D412yes—
81C2×C4×D283D411yescharacteristic
82C2×C4×D283C2312yes—
83#17985376—21no—
84#17985376C2312yescomplemented
85#17985375—24no—
86C2×C283⋊C8—21no—
87C8×D283—24no—
88Dic283⋊C4—24no—
89(C2×D283)⋊C4—24no—
90C4×Dic283—21no—
91C4×Dic283C2312yescomplemented
92#41×C283—21no—
93#41×C283—21no—
94#41×C283C2×C412yes—
95#41×C283C2312yes—
96C2×Q8×C283C2×C411yescharacteristic
97C2×D4×C283—21no—
98C2×D4×C283C2×C411yescharacteristic
99C22×C4×C283—21no—
100C22×C4×C283—21no—
101C22×C4×C283C2311yescharacteristic
102M16×C283—21no—
103M16×C283C2312yescomplemented
104C2×C8×C283—21no—
105C42×C283—21no—
106C42×C283C2312yescomplemented
107C22×D283—21no—
108C22×D283—24no—
109C22×D283—42no—
110C22×D283—44no—
111C22×D283C22⋊C411yescharacteristic
112C22×D283C22⋊C411yescharacteristic
113C22×D283C22⋊C412yes—
114C22×D283C2×D412yes—
115Dic566—21no—
116Dic566—24no—
117Dic566C22×C412yes—
118D1132—24no—
119D1132—21no—
120D1132C22×C412yes—
121C22⋊D283—22no—
122C22⋊D283—22no—
123C22⋊D283—24no—
124C22⋊D283—24no—
125C2×Dic283—21no—
126C2×Dic283—24no—
127C2×Dic283—22no—
128C2×Dic283—42no—
129C2×Dic283C22⋊C411yescharacteristic
130C2×Dic283C22⋊C411yescharacteristic
131C2×Dic283C22⋊C412yes—
132C2×Dic283C2×D412yes—
133C4×D283—24no—
134C4×D283—22no—
135C4×D283—22no—
136C4×D283—24no—
137C4×D283C22⋊C412yes—
138C4×D283C22⋊C412yes—
139C4×D283C22⋊C412yes—
140C4×D283C22⋊C412yes—
141C4×D283C22×C412yes—
142C4×D283C22×C412yes—
143C4×D283C2×D412yes—
144C4×D283C2×D412yes—
145C283⋊C8—22no—
146C23×C283—21no—
147C23×C283C2×D411yescharacteristic
148Q8×C283—21no—
149Q8×C283C22×C412yes—
150D4×C283—22no—
151D4×C283—22no—
152D4×C283—21no—
153D4×C283C22×C412yes—
154C2×C4×C283—21no—
155C2×C4×C283—22no—
156C2×C4×C283—22no—
157C2×C4×C283—22no—
158C2×C4×C283—42no—
159C2×C4×C283C22×C411yescharacteristic
160C2×C4×C283C22×C411yescharacteristic
161C2×C4×C283C2×D411yescharacteristic
162C2×C4×C283C2×D411yescharacteristic
163C2×C4×C283C2×D411yescharacteristic
164C2×C4×C283C2411yescharacteristic
165C8×C283—22no—
166C22×C283—22no—
167C22×C283—22no—
168C22×C283—42no—
169C22×C283C2×C22⋊C411yescharacteristic
170C22×C283C2×C22⋊C411yescharacteristic
171C22×C283C22×D411yescharacteristic
172C2×D283—22no—
173C2×D283—22no—
174C2×D283—22no—
175C2×D283—42no—
176C2×D283—42no—
177C2×D283—48no—
178C2×D283—42no—
179C2×D283C2×C22⋊C412yes—
180C2×D283C2×C22⋊C412yes—
181C4×C283—22no—
182C4×C283—42no—
183C4×C283C2×C22⋊C411yescharacteristic
184C4×C283C2×C22⋊C411yescharacteristic
185C4×C283C23×C411yescharacteristic
186C4×C283C22×D411yescharacteristic
187Dic283—22no—
188Dic283—42no—
189Dic283C2×C22⋊C412yes—
190Dic283C2×C22⋊C412yes—
191C2×C283—21no—
192C2×C283—21no—
193C2×C283—42no—
194C2×C283#42112yescomplemented
195C2×C283C22×C22⋊C411yescharacteristic
196D283—22no—
197D283—22no—
198D283—42no—
199C283C2×#42111yescharacteristic, complemented, Sylow
200C2×#421—2831nomaximal, Sylow
201C22×#41—2831no—
202C22×M16—2831no—
203C2×#117—2831no—
204#421—2838no—
205C2×#104—2831no—
206C2×#104—2831no—
207C2×#104—2831no—
208C2×#104D28311yescharacteristic, complemented
209C2×#41—2834no—
210C2×#41—2834no—
211C2×#41—2831no—
212C2×#41—2831no—
213C2×#41—2831no—
214C2×#41—5661no—
215C2×#41—5661no—
216C2×#41—5662no—
217C2×#41—5662no—
218C2×#41C2×D28311yescharacteristic
219C22×Q8—2831no—
220C22×D4—2831no—
221C22×D4—5661no—
222C23×C4—2831no—
223C23×C4—5661no—
224C2×M16—2831no—
225C2×M16—2834no—
226C2×M16—5661no—
227C2×M16—5662no—
228C2×M16C2×D28311yescharacteristic, complemented
229C22×C8—5661no—
230#117—2834no—
231#117—5662no—
232C2×C4⋊C4—5661no—
233C2×C22⋊C4—5661no—
234C2×C42—2831no—
235C2×C42C2×D28311yescharacteristic, complemented
236#104—2834no—
237#104—2834no—
238#104—2834no—
239#104C2×D28314yescomplemented
240C24—2831no—
241C24—5661no—
242#41—21no—
243#41—21no—
244#41—2834no—
245#41—2834no—
246#41—2832no—
247#41—2832no—
248#41—5664no—
249#41—5664no—
250#41—5664no—
251#41—5664no—
252#41—5662no—
253#41—5662no—
254#41—5661no—
255#41—5661no—
256#41C4×D28312yes—
257#41C22×D28312yes—
258C2×Q8—2834no—
259C2×Q8—2831no—
260C2×Q8—5661no—
261C2×Q8—5662no—
262C2×Q8C4×D28311yescharacteristic
263C2×D4—21no—
264C2×D4—2834no—
265C2×D4—2831no—
266C2×D4—5661no—
267C2×D4—5662no—
268C2×D4—5661no—
269C2×D4—5664no—
270C2×D4—5664no—
271C2×D4—5661no—
272C2×D4—5661no—
273C2×D4C4×D28311yescharacteristic
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—2831no—
277C22×C4—2831no—
278C22×C4—2831no—
279C22×C4—2832no—
280C22×C4—2832no—
281C22×C4—2832no—
282C22×C4—2831no—
283C22×C4—2831no—
284C22×C4—2832no—
285C22×C4—5661no—
286C22×C4—5664no—
287C22×C4—5664no—
288C22×C4—5661no—
289C22×C4—5661no—
290C22×C4—5661no—
291C22×C4—5661no—
292C22×C4C22×D28311yescharacteristic
293M16—21no—
294M16—2832no—
295M16—5664no—
296M16—5661no—
297M16C22×D28312yescomplemented
298C2×C8—21no—
299C2×C8—5664no—
300C2×C8—5661no—
301C4⋊C4—5664no—
302C22⋊C4—5664no—
303C42—21no—
304C42—2832no—
305C42—5661no—
306C42C22×D28312yescomplemented
307C23—21no—
308C23—2831no—
309C23—2831no—
310C23—2832no—
311C23—2832no—
312C23—5664no—
313C23—5661no—
314C23—11322no—
315C23—11324no—
316C23D4×D28311yescharacteristic
317Q8—21no—
318Q8—2832no—
319Q8—5664no—
320Q8—5661no—
321Q8C2×C4×D28312yes—
322D4—22no—
323D4—22no—
324D4—21no—
325D4—2832no—
326D4—5664no—
327D4—5664no—
328D4—5664no—
329D4—5662no—
330D4—5662no—
331D4—5661no—
332D4C2×C4×D28312yes—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—42no—
338C2×C4—2831no—
339C2×C4—2831no—
340C2×C4—2832no—
341C2×C4—2832no—
342C2×C4—2832no—
343C2×C4—2832no—
344C2×C4—2832no—
345C2×C4—2832no—
346C2×C4—2832no—
347C2×C4—2832no—
348C2×C4—2832no—
349C2×C4—2832no—
350C2×C4—5664no—
351C2×C4—5664no—
352C2×C4—5664no—
353C2×C4—5661no—
354C2×C4—5662no—
355C2×C4—5662no—
356C2×C4—5662no—
357C2×C4—11322no—
358C2×C4C2×C4×D28311yescharacteristic
359C2×C4C2×C4×D28311yescharacteristic
360C2×C4D4×D28311yescharacteristic
361C2×C4D4×D28311yescharacteristic
362C2×C4D4×D28311yescharacteristic
363C2×C4C23×D28311yescharacteristic
364C8—22no—
365C8—5662no—
366C22—22no—
367C22—22no—
368C22—42no—
369C22—2832no—
370C22—2832no—
371C22—5662no—
372C22—5662no—
373C22—5662no—
374C22—11322no—
375C22—11322no—
376C22—11328no—
377C22—11322no—
378C22C22⋊C4×D28311yescharacteristic
379C22C22⋊C4×D28311yescharacteristic
380C22C2×D4×D28311yescharacteristic
381C4—22no—
382C4—42no—
383C4—2832no—
384C4—2832no—
385C4—5662no—
386C4—11322no—
387C4C22⋊C4×D28311yescharacteristic
388C4C22⋊C4×D28311yescharacteristic
389C4C22×C4×D28311yescharacteristic
390C4C2×D4×D28311yescharacteristic
391C2—21no—
392C2—21no—
393C2—42no—
394C2—5662no—
395C2—5662no—
396C2—11322no—
397C2#3182648012yesdirect product factor
398C2C2×C22⋊C4×D28311yescharacteristic
subgroupG/H
centerC2×C4D4×D283
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
FittingC2×#104×C283C2
socleC22×C283C2×C22⋊C4
prime radicalC2×#41×D283C2
cosocleC2×C4×C283C24
hypercenterC2×#104D283
hypocenterC283C2×#421
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×M16×D283C2semidirect
3. C2×#22583567C2semidirect
4. #31826480C2direct (N × H)
5. C2×#22583538C2semidirect
6. C2×#22583537C2semidirect
7. C2×#22583536C2semidirect
8. C2×#104×C283C2semidirect
9. C2×#17985393C4semidirect
13. C2×#17985391C4semidirect
16. #41×D283C4semidirect
18. C2×Q8×D283C4semidirect
20. C2×D4×D283C4semidirect
23. C2×#17985376C22semidirect
26. M16×D283C22semidirect
29. #22583567C22semidirect
32. C2×C4×Dic283C22semidirect
33. #22583538C22semidirect
34. #22583537C22semidirect
35. #22583536C22semidirect
37. C2×M16×C283C22semidirect
38. C2×C42×C283C22semidirect
39. #104×C283C22semidirect
43. #17985393C2×C4semidirect
53. #17985391C2×C4semidirect
57. Q8×D283C2×C4semidirect
66. D4×D283C2×C4semidirect
84. #17985376C23semidirect
91. C4×Dic283C23semidirect
103. M16×C283C23semidirect
106. C42×C283C23semidirect
194. C2×C283#421semidirect
199. C283C2×#421semidirect
208. C2×#104D283semidirect
228. C2×M16C2×D283semidirect
235. C2×C42C2×D283semidirect
239. #104C2×D283semidirect
297. M16C22×D283semidirect
306. C42C22×D283semidirect
397. C2#31826480direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×D2832
C2×M16×D2832
C2×#225835672
#318264802
C2×#225835382
C2×#225835372
C2×#225835362
C2×#104×C2832
C2×#421283