Finite Group Databasebeta

← C2×#104×D101 #27179667

Subgroups — C2×#104×D101 #27179667

Order 12928.

856 conjugacy classes of subgroups.

The subgroup lattice has 404 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×C42×D101C211yesmaximal, characteristic, complemented
4C2×#15692183C211yesmaximal, characteristic, complemented
5C2×#15692182C211yesmaximal, characteristic, complemented
6C2×#15692181C211yesmaximal, characteristic, complemented
7#104×D101C218yesmaximal, direct product factor
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×D101—21no—
23C22×C4×D101C2211yescharacteristic
24C2×#13108058C2211yescharacteristic, complemented
25C2×#13108057—21no—
26M16×D101—22no—
27M16×D101C2214yescomplemented
28C2×C8×D101—21no—
29C2×C4×Dic101—21no—
30C2×C4×Dic101C2211yescharacteristic, complemented
31C42×D101—22no—
32C42×D101C2214yescomplemented
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×C412yescomplemented
49#13108074C2312yes—
50#13108073—24no—
51#13108073—24no—
52#13108073—22no—
53#13108073C2×C414yescomplemented
54C2×Dic202—21no—
55C2×Dic202C2×C411yescharacteristic, complemented
56Q8×D101—22no—
57Q8×D101C2×C414yescomplemented
58C2×D404—21no—
59C2×D404C2×C411yescharacteristic, complemented
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—28no—
71C2×C4×D101—21no—
72C2×C4×D101—24no—
73C2×C4×D101—21no—
74C2×C4×D101—21no—
75C2×C4×D101—24no—
76C2×C4×D101—24no—
77C2×C4×D101C2×C411yescharacteristic
78C2×C4×D101C2×C412yes—
79C2×C4×D101C2×C411yescharacteristic
80C2×C4×D101D412yes—
81C2×C4×D101D411yescharacteristic
82C2×C4×D101D412yes—
83C2×C4×D101D411yescharacteristic
84C2×C4×D101C2312yes—
85#13108058—21no—
86#13108058C2312yescomplemented
87#13108057—24no—
88C2×#11717579—21no—
89C8×D101—24no—
90C4×Dic101—21no—
91C4×Dic101—24no—
92C4×Dic101C2312yescomplemented
93#41×C101—21no—
94#41×C101—21no—
95#41×C101C2×C412yescomplemented
96#41×C101C2312yes—
97C2×Q8×C101C2×C411yescharacteristic, complemented
98C2×D4×C101—21no—
99C2×D4×C101C2×C411yescharacteristic, complemented
100C22×C4×C101—21no—
101C22×C4×C101—21no—
102C22×C4×C101C2311yescharacteristic
103M16×C101—21no—
104M16×C101C2312yescomplemented
105C2×C8×C101—21no—
106C42×C101—21no—
107C42×C101C2312yescomplemented
108C23×C101—21no—
109C23×C101C2×D411yescharacteristic
110C22×D101—24no—
111C22×D101—21no—
112C22×D101—24no—
113C22×D101—44no—
114C22×D101C22⋊C412yes—
115C22×D101C22⋊C411yescharacteristic
116C22×D101C22⋊C411yescharacteristic
117C22×D101C2×D412yes—
118Q8×C101—21no—
119Q8×C101C22×C412yescomplemented
120D4×C101—22no—
121D4×C101—22no—
122D4×C101—21no—
123D4×C101C22×C412yescomplemented
124C2×C4×C101—24no—
125C2×C4×C101—21no—
126C2×C4×C101—22no—
127C2×C4×C101—22no—
128C2×C4×C101—22no—
129C2×C4×C101C22×C411yescharacteristic
130C2×C4×C101C22×C411yescharacteristic
131C2×C4×C101C2×D411yescharacteristic
132C2×C4×C101C2×D411yescharacteristic
133C2×C4×C101C2×D411yescharacteristic
134C2×C4×C101C2411yescharacteristic
135C22⋊D101—22no—
136C22⋊D101—22no—
137C22⋊D101—24no—
138C22⋊D101—24no—
139C2×Dic101—24no—
140C2×Dic101—21no—
141C2×Dic101—22no—
142C2×Dic101—24no—
143C2×Dic101C22⋊C411yescharacteristic
144C2×Dic101C22⋊C411yescharacteristic
145C2×Dic101C22⋊C412yes—
146C2×Dic101C2×D412yes—
147D404—24no—
148D404—21no—
149D404C22×C412yescomplemented
150C4×D101—216no—
151C4×D101—24no—
152C4×D101—22no—
153C4×D101—22no—
154C4×D101—24no—
155C4×D101C22⋊C412yes—
156C4×D101C22⋊C412yes—
157C4×D101C22⋊C412yes—
158C4×D101C22⋊C412yes—
159C4×D101C22×C412yes—
160C4×D101C22×C412yes—
161C4×D101C2×D412yes—
162C4×D101C2×D412yes—
163Dic202—21no—
164Dic202—24no—
165Dic202C22×C412yescomplemented
166C8×C101—22no—
167#11717579—22no—
168C22×C101—22no—
169C22×C101—22no—
170C22×C101—42no—
171C22×C101C2×C22⋊C411yescharacteristic
172C22×C101C2×C22⋊C411yescharacteristic
173C22×C101C22×D411yescharacteristic
174C2×D101—22no—
175C2×D101—24no—
176C2×D101—24no—
177C2×D101—22no—
178C2×D101—42no—
179C2×D101—48no—
180C2×D101#10414yesdirect product factor
181C2×D101C2×C22⋊C412yes—
182C2×D101C2×C22⋊C412yes—
183C4×C101—24no—
184C4×C101—22no—
185C4×C101C2×C22⋊C411yescharacteristic
186C4×C101C2×C22⋊C411yescharacteristic
187C4×C101C23×C411yescharacteristic
188C4×C101C22×D411yescharacteristic
189Dic101—24no—
190Dic101—22no—
191Dic101C2×C22⋊C412yes—
192Dic101C2×C22⋊C412yes—
193C2×C101—21no—
194C2×C101—21no—
195C2×C101—42no—
196C2×C101C2×#10412yescomplemented
197C2×C101C22×C22⋊C411yescharacteristic
198D101—22no—
199D101—42no—
200D101C2×#10414yesdirect product factor
201C22×#104—1011nomaximal, Sylow
202C101C22×#10411yescharacteristic, complemented, Sylow
203C22×#41—1011no—
204C22×M16—1011no—
205C22×C42—1011no—
206C2×#104—1011no—
207C2×#104—1011no—
208C2×#104—1011no—
209C2×#104—1018no—
210C2×#104D10111yescharacteristic, direct product factor
211C2×#41—1014no—
212C2×#41—1014no—
213C2×#41—1011no—
214C2×#41—1011no—
215C2×#41—1011no—
216C2×#41—2021no—
217C2×#41—2021no—
218C2×#41—2022no—
219C2×#41—2022no—
220C2×#41C2×D10111yescharacteristic
221C22×Q8—1011no—
222C22×D4—1011no—
223C22×D4—2021no—
224C23×C4—1011no—
225C23×C4—2021no—
226C23×C4—2021no—
227C2×M16—1011no—
228C2×M16—1014no—
229C2×M16—2021no—
230C2×M16—2022no—
231C2×M16C2×D10111yescharacteristic, complemented
232C22×C8—2021no—
233C2×C42—1011no—
234C2×C42—1014no—
235C2×C42—2022no—
236C2×C42—2021no—
237C2×C42C2×D10111yescharacteristic, complemented
238#104—1014no—
239#104—1014no—
240#104—1014no—
241#104C2×D10114yesdirect product factor
242C24—1011no—
243C24—2021no—
244#41—21no—
245#41—21no—
246#41—1014no—
247#41—1014no—
248#41—1012no—
249#41—1012no—
250#41—2024no—
251#41—2024no—
252#41—2024no—
253#41—2024no—
254#41—2022no—
255#41—2022no—
256#41—2021no—
257#41—2021no—
258#41C4×D10112yescomplemented
259#41C22×D10112yes—
260C2×Q8—1014no—
261C2×Q8—1011no—
262C2×Q8—2021no—
263C2×Q8—2022no—
264C2×Q8C4×D10111yescharacteristic, complemented
265C2×D4—21no—
266C2×D4—1014no—
267C2×D4—1011no—
268C2×D4—2021no—
269C2×D4—2022no—
270C2×D4—2021no—
271C2×D4—2024no—
272C2×D4—2024no—
273C2×D4—2021no—
274C2×D4—2021no—
275C2×D4C4×D10111yescharacteristic, complemented
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—1011no—
279C22×C4—1011no—
280C22×C4—1011no—
281C22×C4—1012no—
282C22×C4—1012no—
283C22×C4—1012no—
284C22×C4—1011no—
285C22×C4—1011no—
286C22×C4—1012no—
287C22×C4—2021no—
288C22×C4—2024no—
289C22×C4—2024no—
290C22×C4—2024no—
291C22×C4—2021no—
292C22×C4—2028no—
293C22×C4—2021no—
294C22×C4—2021no—
295C22×C4—2021no—
296C22×C4C22×D10111yescharacteristic
297M16—21no—
298M16—1012no—
299M16—2024no—
300M16—2021no—
301M16C22×D10112yescomplemented
302C2×C8—21no—
303C2×C8—2024no—
304C2×C8—2021no—
305C42—21no—
306C42—1012no—
307C42—2024no—
308C42—2021no—
309C42C22×D10112yescomplemented
310C23—21no—
311C23—1011no—
312C23—1012no—
313C23—1012no—
314C23—1011no—
315C23—4044no—
316C23—2024no—
317C23—2024no—
318C23—2021no—
319C23D4×D10111yescharacteristic
320Q8—21no—
321Q8—1012no—
322Q8—2024no—
323Q8—2021no—
324Q8C2×C4×D10112yescomplemented
325D4—22no—
326D4—22no—
327D4—21no—
328D4—1012no—
329D4—2024no—
330D4—2024no—
331D4—2024no—
332D4—2022no—
333D4—2022no—
334D4—2021no—
335D4C2×C4×D10112yescomplemented
336C2×C4—24no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—1012no—
342C2×C4—1011no—
343C2×C4—1011no—
344C2×C4—1012no—
345C2×C4—1012no—
346C2×C4—1012no—
347C2×C4—1012no—
348C2×C4—1012no—
349C2×C4—1012no—
350C2×C4—1012no—
351C2×C4—1012no—
352C2×C4—1012no—
353C2×C4—2024no—
354C2×C4—2024no—
355C2×C4—20216no—
356C2×C4—2024no—
357C2×C4—2024no—
358C2×C4—2022no—
359C2×C4—2021no—
360C2×C4—2022no—
361C2×C4—2022no—
362C2×C4C2×C4×D10111yescharacteristic
363C2×C4C2×C4×D10111yescharacteristic
364C2×C4D4×D10111yescharacteristic
365C2×C4D4×D10111yescharacteristic
366C2×C4D4×D10111yescharacteristic
367C2×C4C23×D10111yescharacteristic
368C8—22no—
369C8—2022no—
370C22—22no—
371C22—22no—
372C22—42no—
373C22—1012no—
374C22—1014no—
375C22—1012no—
376C22—4048no—
377C22—4042no—
378C22—2024no—
379C22—2024no—
380C22—2022no—
381C22—2022no—
382C22C22⋊C4×D10111yescharacteristic
383C22C22⋊C4×D10111yescharacteristic
384C22C2×D4×D10111yescharacteristic
385C4—24no—
386C4—22no—
387C4—1012no—
388C4—1012no—
389C4—2024no—
390C4—2022no—
391C4C22⋊C4×D10111yescharacteristic
392C4C22⋊C4×D10111yescharacteristic
393C4C22×C4×D10111yescharacteristic
394C4C2×D4×D10111yescharacteristic
395C2—21no—
396C2—21no—
397C2—42no—
398C2—1014no—
399C2—4042no—
400C2—2022no—
401C2#104×D10112yesdirect product factor
402C2C2×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
hypocenterC101C22×#104
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×C42×D101C2semidirect
4. C2×#15692183C2semidirect
5. C2×#15692182C2semidirect
6. C2×#15692181C2semidirect
7. #104×D101C2direct (N × H)
8. C2×#104×C101C2semidirect
9. C2×#13108075C4semidirect
13. C2×#13108073C4semidirect
16. #41×D101C4semidirect
18. C2×Q8×D101C4semidirect
20. C2×D4×D101C4semidirect
24. C2×#13108058C22semidirect
27. M16×D101C22semidirect
30. C2×C4×Dic101C22semidirect
32. C42×D101C22semidirect
33. #15692183C22semidirect
34. #15692182C22semidirect
35. #15692181C22semidirect
37. C2×M16×C101C22semidirect
38. C2×C42×C101C22semidirect
39. #104×C101C22semidirect
43. #13108075C2×C4semidirect
48. #13108074C2×C4semidirect
53. #13108073C2×C4semidirect
55. C2×Dic202C2×C4semidirect
57. Q8×D101C2×C4semidirect
59. C2×D404C2×C4semidirect
66. D4×D101C2×C4semidirect
86. #13108058C23semidirect
92. C4×Dic101C23semidirect
95. #41×C101C2×C4semidirect
97. C2×Q8×C101C2×C4semidirect
99. C2×D4×C101C2×C4semidirect
104. M16×C101C23semidirect
107. C42×C101C23semidirect
119. Q8×C101C22×C4semidirect
123. D4×C101C22×C4semidirect
149. D404C22×C4semidirect
165. Dic202C22×C4semidirect
180. C2×D101#104direct (N × H)
196. C2×C101C2×#104semidirect
200. D101C2×#104direct (N × H)
202. C101C22×#104semidirect
210. C2×#104D101direct (N × H)
231. C2×M16C2×D101semidirect
237. C2×C42C2×D101semidirect
241. #104C2×D101direct (N × H)
258. #41C4×D101semidirect
264. C2×Q8C4×D101semidirect
275. C2×D4C4×D101semidirect
301. M16C22×D101semidirect
309. C42C22×D101semidirect
324. Q8C2×C4×D101semidirect
335. D4C2×C4×D101semidirect
401. C2#104×D101direct (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×C42×D1012
C2×#156921832
C2×#156921822
C2×#156921812
#104×D1012
C2×#104×C1012
C22×#104101