Finite Group Databasebeta

← C2×#20265192 #27179672

Subgroups — C2×#20265192 #27179672

Order 12928.

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×D101C211yesmaximal, characteristic
2C2×M16×D101C211yesmaximal, characteristic, complemented
3C2×#15692212C211yesmaximal, characteristic, complemented
4#20265192C218yesmaximal, direct product factor
5C2×#15692183C211yesmaximal, characteristic, complemented
6C2×#15692182C211yesmaximal, characteristic, complemented
7C2×#15692181C211yesmaximal, characteristic, complemented
8C2×#104×C101C211yesmaximal, characteristic, complemented
9C2×#13108075C411yescharacteristic, complemented
10C2×#13108074—21no—
11C2×#13108074C2211yescharacteristic
12C2×#13108073—21no—
13C2×#13108073C411yescharacteristic, complemented
14#41×D101—22no—
15#41×D101—22no—
16#41×D101C414yescomplemented
17#41×D101C2214yes—
18C2×Q8×D101C411yescharacteristic, complemented
19C2×D4×D101—21no—
20C2×D4×D101C411yescharacteristic, complemented
21C22×C4×D101—21no—
22C22×C4×D101C2211yescharacteristic
23C2×#13108058C2211yescharacteristic, complemented
24C2×#13108057—21no—
25M16×D101—22no—
26M16×D101C2214yescomplemented
27C2×C8×D101—21no—
28#15692212—22no—
29#15692212C2214yescomplemented
30C2×#13108053—21no—
31C2×#13108051—21no—
32C2×C4×Dic101C2211yescharacteristic, complemented
33#15692183C2214yescomplemented
34#15692182C2214yescomplemented
35#15692181C2214yescomplemented
36C2×#41×C101C2211yescharacteristic
37C2×M16×C101C2211yescharacteristic, complemented
38C2×C42×C101C2211yescharacteristic, complemented
39#104×C101C2214yescomplemented
40C23×D101—21no—
41C23×D101D411yescharacteristic
42#13108075—22no—
43#13108075C2×C414yescomplemented
44#13108074—21no—
45#13108074—21no—
46#13108074—24no—
47#13108074—24no—
48#13108074C2×C412yes—
49#13108074C2312yes—
50#13108073—24no—
51#13108073—24no—
52#13108073—22no—
53#13108073C2×C414yescomplemented
54C2×Dic202—21no—
55C2×Dic202C2×C411yescharacteristic
56Q8×D101—22no—
57Q8×D101C2×C414yescomplemented
58C2×D404—21no—
59C2×D404C2×C411yescharacteristic
60C2×C22⋊D101—21no—
61C2×C22⋊D101—21no—
62C2×C22⋊D101—21no—
63D4×D101—24no—
64D4×D101—24no—
65D4×D101—22no—
66D4×D101C2×C414yescomplemented
67C22×Dic101—21no—
68C22×Dic101—21no—
69C22×Dic101D411yescharacteristic
70C2×C4×D101—21no—
71C2×C4×D101—21no—
72C2×C4×D101—21no—
73C2×C4×D101—24no—
74C2×C4×D101—24no—
75C2×C4×D101C2×C411yescharacteristic
76C2×C4×D101C2×C412yes—
77C2×C4×D101C2×C411yescharacteristic
78C2×C4×D101D412yes—
79C2×C4×D101D411yescharacteristic
80C2×C4×D101D412yes—
81C2×C4×D101D411yescharacteristic
82C2×C4×D101C2312yes—
83#13108058—21no—
84#13108058C2312yescomplemented
85#13108057—24no—
86C2×#11717579—21no—
87C8×D101—24no—
88#13108053—24no—
89#13108051—24no—
90C4×Dic101—21no—
91C4×Dic101C2312yescomplemented
92#41×C101—21no—
93#41×C101—21no—
94#41×C101C2×C412yes—
95#41×C101C2312yes—
96C2×Q8×C101C2×C411yescharacteristic
97C2×D4×C101—21no—
98C2×D4×C101C2×C411yescharacteristic
99C22×C4×C101—21no—
100C22×C4×C101—21no—
101C22×C4×C101C2311yescharacteristic
102M16×C101—21no—
103M16×C101C2312yescomplemented
104C2×C8×C101—21no—
105C42×C101—21no—
106C42×C101C2312yescomplemented
107C23×C101—21no—
108C23×C101C2×D411yescharacteristic
109C22×D101—21no—
110C22×D101—24no—
111C22×D101—42no—
112C22×D101—44no—
113C22×D101C22⋊C411yescharacteristic
114C22×D101C22⋊C411yescharacteristic
115C22×D101C22⋊C412yes—
116C22×D101C2×D412yes—
117Q8×C101—21no—
118Q8×C101C22×C412yes—
119D4×C101—22no—
120D4×C101—22no—
121D4×C101—21no—
122D4×C101C22×C412yes—
123C2×C4×C101—21no—
124C2×C4×C101—22no—
125C2×C4×C101—22no—
126C2×C4×C101—22no—
127C2×C4×C101—42no—
128C2×C4×C101C22×C411yescharacteristic
129C2×C4×C101C22×C411yescharacteristic
130C2×C4×C101C2×D411yescharacteristic
131C2×C4×C101C2×D411yescharacteristic
132C2×C4×C101C2×D411yescharacteristic
133C2×C4×C101C2411yescharacteristic
134C22⋊D101—22no—
135C22⋊D101—22no—
136C22⋊D101—24no—
137C22⋊D101—24no—
138C2×Dic101—21no—
139C2×Dic101—24no—
140C2×Dic101—22no—
141C2×Dic101—42no—
142C2×Dic101C22⋊C411yescharacteristic
143C2×Dic101C22⋊C411yescharacteristic
144C2×Dic101C22⋊C412yes—
145C2×Dic101C2×D412yes—
146D404—24no—
147D404—21no—
148D404C22×C412yes—
149C4×D101—24no—
150C4×D101—22no—
151C4×D101—22no—
152C4×D101—24no—
153C4×D101C22⋊C412yes—
154C4×D101C22⋊C412yes—
155C4×D101C22⋊C412yes—
156C4×D101C22⋊C412yes—
157C4×D101C22×C412yes—
158C4×D101C22×C412yes—
159C4×D101C2×D412yes—
160C4×D101C2×D412yes—
161Dic202—21no—
162Dic202—24no—
163Dic202C22×C412yes—
164C8×C101—22no—
165#11717579—22no—
166C22×C101—22no—
167C22×C101—22no—
168C22×C101—42no—
169C22×C101C2×C22⋊C411yescharacteristic
170C22×C101C2×C22⋊C411yescharacteristic
171C22×C101C22×D411yescharacteristic
172C2×D101—22no—
173C2×D101—22no—
174C2×D101—22no—
175C2×D101—42no—
176C2×D101—42no—
177C2×D101—48no—
178C2×D101—42no—
179C2×D101C2×C22⋊C412yes—
180C2×D101C2×C22⋊C412yes—
181C4×C101—22no—
182C4×C101—42no—
183C4×C101C2×C22⋊C411yescharacteristic
184C4×C101C2×C22⋊C411yescharacteristic
185C4×C101C23×C411yescharacteristic
186C4×C101C22×D411yescharacteristic
187Dic101—22no—
188Dic101—42no—
189Dic101C2×C22⋊C412yes—
190Dic101C2×C22⋊C412yes—
191C2×C101—21no—
192C2×C101—21no—
193C2×C101—42no—
194C2×C101#42112yescomplemented
195C2×C101C22×C22⋊C411yescharacteristic
196D101—22no—
197D101—22no—
198D101—42no—
199C2×#421—1011nomaximal, Sylow
200C101C2×#42111yescharacteristic, complemented, Sylow
201C22×#41—1011no—
202C22×M16—1011no—
203C2×#117—1011no—
204#421—1018no—
205C2×#104—1011no—
206C2×#104—1011no—
207C2×#104—1011no—
208C2×#104D10111yescharacteristic, complemented
209C2×#41—1014no—
210C2×#41—1014no—
211C2×#41—1011no—
212C2×#41—1011no—
213C2×#41—1011no—
214C2×#41—2021no—
215C2×#41—2021no—
216C2×#41—2022no—
217C2×#41—2022no—
218C2×#41C2×D10111yescharacteristic
219C22×Q8—1011no—
220C22×D4—1011no—
221C22×D4—2021no—
222C23×C4—1011no—
223C23×C4—2021no—
224C2×M16—1011no—
225C2×M16—1014no—
226C2×M16—2021no—
227C2×M16—2022no—
228C2×M16C2×D10111yescharacteristic, complemented
229C22×C8—2021no—
230#117—1014no—
231#117—2022no—
232C2×C4⋊C4—2021no—
233C2×C22⋊C4—2021no—
234C2×C42—1011no—
235C2×C42C2×D10111yescharacteristic, complemented
236#104—1014no—
237#104—1014no—
238#104—1014no—
239#104C2×D10114yescomplemented
240C24—1011no—
241C24—2021no—
242#41—21no—
243#41—21no—
244#41—1014no—
245#41—1014no—
246#41—1012no—
247#41—1012no—
248#41—2024no—
249#41—2024no—
250#41—2024no—
251#41—2024no—
252#41—2022no—
253#41—2022no—
254#41—2021no—
255#41—2021no—
256#41C4×D10112yes—
257#41C22×D10112yes—
258C2×Q8—1014no—
259C2×Q8—1011no—
260C2×Q8—2021no—
261C2×Q8—2022no—
262C2×Q8C4×D10111yescharacteristic
263C2×D4—21no—
264C2×D4—1014no—
265C2×D4—1011no—
266C2×D4—2021no—
267C2×D4—2022no—
268C2×D4—2021no—
269C2×D4—2024no—
270C2×D4—2024no—
271C2×D4—2021no—
272C2×D4—2021no—
273C2×D4C4×D10111yescharacteristic
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—1011no—
277C22×C4—1011no—
278C22×C4—1011no—
279C22×C4—1012no—
280C22×C4—1012no—
281C22×C4—1012no—
282C22×C4—1011no—
283C22×C4—1011no—
284C22×C4—1012no—
285C22×C4—2021no—
286C22×C4—2024no—
287C22×C4—2024no—
288C22×C4—2021no—
289C22×C4—2021no—
290C22×C4—2021no—
291C22×C4—2021no—
292C22×C4C22×D10111yescharacteristic
293M16—21no—
294M16—1012no—
295M16—2024no—
296M16—2021no—
297M16C22×D10112yescomplemented
298C2×C8—21no—
299C2×C8—2024no—
300C2×C8—2021no—
301C4⋊C4—2024no—
302C22⋊C4—2024no—
303C42—21no—
304C42—1012no—
305C42—2021no—
306C42C22×D10112yescomplemented
307C23—21no—
308C23—1012no—
309C23—1012no—
310C23—1011no—
311C23—1011no—
312C23—4042no—
313C23—4044no—
314C23—2024no—
315C23—2021no—
316C23D4×D10111yescharacteristic
317Q8—21no—
318Q8—1012no—
319Q8—2024no—
320Q8—2021no—
321Q8C2×C4×D10112yes—
322D4—22no—
323D4—22no—
324D4—21no—
325D4—1012no—
326D4—2024no—
327D4—2024no—
328D4—2024no—
329D4—2022no—
330D4—2022no—
331D4—2021no—
332D4C2×C4×D10112yes—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—42no—
338C2×C4—1012no—
339C2×C4—1011no—
340C2×C4—1011no—
341C2×C4—1012no—
342C2×C4—1012no—
343C2×C4—1012no—
344C2×C4—1012no—
345C2×C4—1012no—
346C2×C4—1012no—
347C2×C4—1012no—
348C2×C4—1012no—
349C2×C4—1012no—
350C2×C4—4042no—
351C2×C4—2024no—
352C2×C4—2024no—
353C2×C4—2024no—
354C2×C4—2022no—
355C2×C4—2021no—
356C2×C4—2022no—
357C2×C4—2022no—
358C2×C4C2×C4×D10111yescharacteristic
359C2×C4C2×C4×D10111yescharacteristic
360C2×C4D4×D10111yescharacteristic
361C2×C4D4×D10111yescharacteristic
362C2×C4D4×D10111yescharacteristic
363C2×C4C23×D10111yescharacteristic
364C8—22no—
365C8—2022no—
366C22—22no—
367C22—22no—
368C22—42no—
369C22—1012no—
370C22—1012no—
371C22—4042no—
372C22—4042no—
373C22—4048no—
374C22—4042no—
375C22—2022no—
376C22—2022no—
377C22—2022no—
378C22C22⋊C4×D10111yescharacteristic
379C22C22⋊C4×D10111yescharacteristic
380C22C2×D4×D10111yescharacteristic
381C4—22no—
382C4—42no—
383C4—1012no—
384C4—1012no—
385C4—4042no—
386C4—2022no—
387C4C22⋊C4×D10111yescharacteristic
388C4C22⋊C4×D10111yescharacteristic
389C4C22×C4×D10111yescharacteristic
390C4C2×D4×D10111yescharacteristic
391C2—21no—
392C2—21no—
393C2—42no—
394C2—4042no—
395C2—2022no—
396C2—2022no—
397C2#2026519212yesdirect product factor
398C2C2×C22⋊C4×D10111yescharacteristic
subgroupG/H
centerC2×C4D4×D101
commutatorC4×C101C23×C4
FrattiniC2×C4C23×D101
FittingC2×#104×C101C2
socleC22×C101C2×C22⋊C4
prime radicalC2×#41×D101C2
cosocleC2×C4×C101C24
hypercenterC2×#104D101
hypocenterC101C2×#421
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×M16×D101C2semidirect
3. C2×#15692212C2semidirect
4. #20265192C2direct (N × H)
5. C2×#15692183C2semidirect
6. C2×#15692182C2semidirect
7. C2×#15692181C2semidirect
8. C2×#104×C101C2semidirect
9. C2×#13108075C4semidirect
13. C2×#13108073C4semidirect
16. #41×D101C4semidirect
18. C2×Q8×D101C4semidirect
20. C2×D4×D101C4semidirect
23. C2×#13108058C22semidirect
26. M16×D101C22semidirect
29. #15692212C22semidirect
32. C2×C4×Dic101C22semidirect
33. #15692183C22semidirect
34. #15692182C22semidirect
35. #15692181C22semidirect
37. C2×M16×C101C22semidirect
38. C2×C42×C101C22semidirect
39. #104×C101C22semidirect
43. #13108075C2×C4semidirect
53. #13108073C2×C4semidirect
57. Q8×D101C2×C4semidirect
66. D4×D101C2×C4semidirect
84. #13108058C23semidirect
91. C4×Dic101C23semidirect
103. M16×C101C23semidirect
106. C42×C101C23semidirect
194. C2×C101#421semidirect
200. C101C2×#421semidirect
208. C2×#104D101semidirect
228. C2×M16C2×D101semidirect
235. C2×C42C2×D101semidirect
239. #104C2×D101semidirect
297. M16C22×D101semidirect
306. C42C22×D101semidirect
397. C2#20265192direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×D1012
C2×M16×D1012
C2×#156922122
#202651922
C2×#156921832
C2×#156921822
C2×#156921812
C2×#104×C1012
C2×#421101