Finite Group Databasebeta

← C2×D101⋊#104 #27187756

Subgroups — C2×D101⋊#104 #27187756

Order 12928.

856 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D101⋊M16C211yesmaximal, characteristic, complemented
2C22×C4×#87938C211yesmaximal, characteristic, complemented
3C2×#15692320C212yesmaximal, complemented
4D101⋊#104C218yesmaximal, direct product factor
5C2×#15692319C212yesmaximal, complemented
6C2×#41×D101C211yesmaximal, characteristic
7C23×#87938—21no—
8C2×#13108084C2212yescomplemented
9D101⋊M16—22no—
10D101⋊M16C2214yescomplemented
11C2×#13108083—21no—
12C2×D101⋊C8—21no—
13C2×C4×#87938—22no—
14C2×C4×#87938—21no—
15C2×C4×#87938C2212yescomplemented
16C2×C4×#87938C2214yescomplemented
17#15692320C2218yescomplemented
18#15692319C2218yescomplemented
19C2×#13108075C2211yescharacteristic
20C2×#13108074—21no—
21C2×#13108074C411yescharacteristic, complemented
22C2×#13108073—21no—
23C2×#13108073C2211yescharacteristic
24#41×D101—22no—
25#41×D101—22no—
26#41×D101C414yescomplemented
27#41×D101C2214yes—
28C2×Q8×D101C411yescharacteristic, complemented
29C2×D4×D101—21no—
30C2×D4×D101C411yescharacteristic, complemented
31C22×C4×D101—21no—
32C22×C4×D101C2211yescharacteristic
33C2×#41×C101C411yescharacteristic, complemented
34C22×#87938—28no—
35C22×#87938—24no—
36C22×#87938—22no—
37#13108084—22no—
38#13108084C2314yescomplemented
39#13108083—24no—
40D101⋊C8—24no—
41C2×#11717581—22no—
42C4×#87938—22no—
43C4×#87938—24no—
44C4×#87938C2314yescomplemented
45C23×D101—21no—
46C23×D101D411yescharacteristic
47#13108075—21no—
48#13108075—21no—
49#13108075C2×C412yescomplemented
50#13108075C2312yes—
51#13108074—22no—
52#13108074—24no—
53#13108074—24no—
54#13108074C2×C414yescomplemented
55#13108073—24no—
56#13108073—24no—
57#13108073—21no—
58#13108073—21no—
59#13108073C2×C412yescomplemented
60#13108073C2312yes—
61C2×Dic202—21no—
62C2×Dic202C2×C411yescharacteristic, complemented
63Q8×D101—22no—
64Q8×D101C2×C414yescomplemented
65C2×D404—21no—
66C2×D404C2×C411yescharacteristic, complemented
67C2×C22⋊D101—21no—
68C2×C22⋊D101—21no—
69C2×C22⋊D101—21no—
70D4×D101—24no—
71D4×D101—24no—
72D4×D101—22no—
73D4×D101C2×C414yescomplemented
74C22×Dic101—21no—
75C22×Dic101D411yescharacteristic
76C2×C4×D101—21no—
77C2×C4×D101—21no—
78C2×C4×D101—21no—
79C2×C4×D101—24no—
80C2×C4×D101—24no—
81C2×C4×D101C2×C411yescharacteristic
82C2×C4×D101C2×C412yes—
83C2×C4×D101D412yes—
84C2×C4×D101D411yescharacteristic
85C2×C4×D101D411yescharacteristic
86C2×C4×D101D412yes—
87C2×C4×D101C2312yes—
88C2×C4×D101C2311yescharacteristic
89#41×C101—22no—
90#41×C101C2×C414yescomplemented
91C2×Q8×C101C2×C411yescharacteristic, complemented
92C2×D4×C101—21no—
93C2×D4×C101C2×C411yescharacteristic, complemented
94C22×C4×C101—21no—
95C22×C4×C101C2×C411yescharacteristic
96C23×C101—21no—
97C23×C101C22⋊C411yescharacteristic
98C22×D101—24no—
99C22×D101—21no—
100C22×D101—24no—
101C22×D101—44no—
102C22×D101C22⋊C412yes—
103C22×D101C22⋊C411yescharacteristic
104C22×D101C2×D412yes—
105C22×D101C2×D411yescharacteristic
106C2×#87938—28no—
107C2×#87938—216no—
108C2×#87938—24no—
109Q8×C101—21no—
110Q8×C101C22×C412yescomplemented
111D4×C101—24no—
112D4×C101—21no—
113D4×C101C22×C412yescomplemented
114C2×C4×C101—21no—
115C2×C4×C101—24no—
116C2×C4×C101C22⋊C412yes—
117C2×C4×C101C22⋊C411yescharacteristic
118C2×C4×C101C22×C411yescharacteristic
119C2×C4×C101C22×C412yes—
120C22⋊D101—24no—
121C22⋊D101—22no—
122C22⋊D101—22no—
123C22⋊D101—24no—
124C2×Dic101—21no—
125C2×Dic101—22no—
126C2×Dic101—22no—
127C2×Dic101C22⋊C411yescharacteristic
128C2×Dic101C22⋊C412yes—
129C2×Dic101C2×D411yescharacteristic
130C2×Dic101C2×D412yes—
131D404—22no—
132D404—22no—
133D404—21no—
134D404C22×C412yescomplemented
135C4×D101—24no—
136C4×D101—24no—
137C4×D101—22no—
138C4×D101—22no—
139C4×D101C22⋊C412yes—
140C4×D101C22⋊C412yes—
141C4×D101C22⋊C412yes—
142C4×D101C22×C412yes—
143C4×D101C22×C411yescharacteristic
144C4×D101C2×D411yescharacteristic
145C4×D101C2×D412yes—
146C4×D101C2×D412yes—
147C4×D101C2×D411yescharacteristic
148C4×D101C2411yescharacteristic
149Dic202—21no—
150Dic202—24no—
151Dic202C22×C412yescomplemented
152#11717581—24no—
153C22×C101—22no—
154C22×C101—22no—
155C22×C101—42no—
156C22×C101C2×C22⋊C412yes—
157C22×C101C2×C22⋊C411yescharacteristic
158C2×D101—22no—
159C2×D101—24no—
160C2×D101—24no—
161C2×D101—22no—
162C2×D101—42no—
163C2×D101—48no—
164C2×D101#10414yescomplemented
165C2×D101C2×C22⋊C411yescharacteristic
166C2×D101C2×C22⋊C412yes—
167C2×D101C22×D411yescharacteristic
168#87938—28no—
169C4×C101—22no—
170C4×C101C2×C22⋊C411yescharacteristic
171C4×C101C2×C22⋊C412yes—
172C4×C101C23×C411yescharacteristic
173Dic101—22no—
174Dic101C2×C22⋊C412yes—
175Dic101C2×C22⋊C411yescharacteristic
176Dic101C22×D411yescharacteristic
177C2×C101—22no—
178C2×C101—42no—
179C2×C101C2×#10412yescomplemented
180C2×C101C22×C22⋊C411yescharacteristic
181D101—21no—
182D101—21no—
183D101—42no—
184D101C2×#10414yescomplemented
185C22×#104—1011nomaximal, Sylow
186C101C22×#10411yescharacteristic, complemented, Sylow
187C22×#41—1011no—
188C22×M16—1011no—
189C22×C42—1011no—
190C2×#104—1012no—
191C2×#104—1018no—
192C2×#104—1012no—
193C2×#41—1014no—
194C2×#41—1014no—
195C2×#41—1011no—
196C2×#41—1011no—
197C2×#41—1011no—
198C2×#41—2021no—
199C2×#41—2021no—
200C2×#41—2022no—
201C2×#41—2022no—
202C2×#41#8793811yescharacteristic, complemented
203C22×Q8—1011no—
204C22×D4—1011no—
205C22×D4—2021no—
206C23×C4—1011no—
207C23×C4—2021no—
208C23×C4—2021no—
209C2×M16—1014no—
210C2×M16—1012no—
211C2×M16—2021no—
212C2×M16—2022no—
213C22×C8—2021no—
214C2×C42—1012no—
215C2×C42—1014no—
216C2×C42—2022no—
217C2×C42—2021no—
218#104—1018no—
219#104—1018no—
220C24—1011no—
221C24—2021no—
222#41—22no—
223#41—1012no—
224#41—1012no—
225#41—1012no—
226#41—1012no—
227#41—1014no—
228#41—2024no—
229#41—2024no—
230#41—2024no—
231#41—2024no—
232#41—2021no—
233#41—2021no—
234#41—2021no—
235#41—2021no—
236#41—2022no—
237#41C2×#8793814yescomplemented
238C2×Q8—1014no—
239C2×Q8—1011no—
240C2×Q8—2021no—
241C2×Q8—2022no—
242C2×Q8C2×#8793811yescharacteristic, complemented
243C2×D4—21no—
244C2×D4—1014no—
245C2×D4—1011no—
246C2×D4—2021no—
247C2×D4—2022no—
248C2×D4—2021no—
249C2×D4—2024no—
250C2×D4—2024no—
251C2×D4—2021no—
252C2×D4—2021no—
253C2×D4C2×#8793811yescharacteristic, complemented
254C22×C4—21no—
255C22×C4—1011no—
256C22×C4—1012no—
257C22×C4—1012no—
258C22×C4—1011no—
259C22×C4—1011no—
260C22×C4—1011no—
261C22×C4—1012no—
262C22×C4—1011no—
263C22×C4—1012no—
264C22×C4—2021no—
265C22×C4—2024no—
266C22×C4—2024no—
267C22×C4—2021no—
268C22×C4—2021no—
269C22×C4—2024no—
270C22×C4—2022no—
271C22×C4—2028no—
272C22×C4—2021no—
273C22×C4C2×#8793811yescharacteristic
274M16—1014no—
275M16—2024no—
276M16—2022no—
277C2×C8—2022no—
278C2×C8—2024no—
279C42—1014no—
280C42—2022no—
281C42—2024no—
282C23—21no—
283C23—1011no—
284C23—1012no—
285C23—1011no—
286C23—1012no—
287C23—4044no—
288C23—2024no—
289C23—2024no—
290C23—2021no—
291C23C22⋊#8793811yescharacteristic
292Q8—21no—
293Q8—1012no—
294Q8—2024no—
295Q8—2021no—
296Q8C22×#8793812yescomplemented
297D4—24no—
298D4—21no—
299D4—1012no—
300D4—2022no—
301D4—2022no—
302D4—2024no—
303D4—2022no—
304D4—2022no—
305D4—2024no—
306D4—2021no—
307D4C22×#8793812yescomplemented
308C2×C4—21no—
309C2×C4—24no—
310C2×C4—1011no—
311C2×C4—1012no—
312C2×C4—1011no—
313C2×C4—1012no—
314C2×C4—1011no—
315C2×C4—1012no—
316C2×C4—1012no—
317C2×C4—1011no—
318C2×C4—1012no—
319C2×C4—1012no—
320C2×C4—1012no—
321C2×C4—1011no—
322C2×C4—1012no—
323C2×C4—1011no—
324C2×C4—2022no—
325C2×C4—2022no—
326C2×C4—2024no—
327C2×C4—2022no—
328C2×C4—2022no—
329C2×C4—2024no—
330C2×C4—20216no—
331C2×C4—2028no—
332C2×C4—2021no—
333C2×C4—2024no—
334C2×C4C22⋊#8793812yes—
335C2×C4C22⋊#8793811yescharacteristic
336C2×C4C22×#8793811yescharacteristic
337C2×C4C22×#8793812yes—
338C8—2024no—
339C22—22no—
340C22—22no—
341C22—42no—
342C22—1014no—
343C22—1012no—
344C22—1011no—
345C22—1011no—
346C22—4048no—
347C22—4042no—
348C22—2024no—
349C22—2024no—
350C22—2022no—
351C22—2022no—
352C22C2×C22⋊#8793812yes—
353C22C2×C22⋊#8793811yescharacteristic
354C4—22no—
355C4—1011no—
356C4—1011no—
357C4—1012no—
358C4—2028no—
359C4—2022no—
360C4C2×C22⋊#8793812yes—
361C4C2×C22⋊#8793811yescharacteristic
362C4C23×#8793811yescharacteristic
363C2—22no—
364C2—42no—
365C2—1014no—
366C2—4042no—
367C2—2021no—
368C2—2021no—
369C2D101⋊#10412yesdirect product factor
370C2C22×C22⋊#8793811yescharacteristic
subgroupG/H
centerC2×C4C22⋊#87938
commutatorC4×C101C23×C4
FrattiniC4C23×#87938
FittingC2×#41×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC2×#41×D101C2
cosocleC4×D101C24
hypercenterC2×#41#87938
hypocenterC101C22×#104
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×D101⋊M16C2semidirect
2. C22×C4×#87938C2semidirect
3. C2×#15692320C2semidirect
4. D101⋊#104C2direct (N × H)
5. C2×#15692319C2semidirect
8. C2×#13108084C22semidirect
10. D101⋊M16C22semidirect
15. C2×C4×#87938C22semidirect
16. C2×C4×#87938C22semidirect
17. #15692320C22semidirect
18. #15692319C22semidirect
21. C2×#13108074C4semidirect
26. #41×D101C4semidirect
28. C2×Q8×D101C4semidirect
30. C2×D4×D101C4semidirect
33. C2×#41×C101C4semidirect
38. #13108084C23semidirect
44. C4×#87938C23semidirect
49. #13108075C2×C4semidirect
54. #13108074C2×C4semidirect
59. #13108073C2×C4semidirect
62. C2×Dic202C2×C4semidirect
64. Q8×D101C2×C4semidirect
66. C2×D404C2×C4semidirect
73. D4×D101C2×C4semidirect
90. #41×C101C2×C4semidirect
91. C2×Q8×C101C2×C4semidirect
93. C2×D4×C101C2×C4semidirect
110. Q8×C101C22×C4semidirect
113. D4×C101C22×C4semidirect
134. D404C22×C4semidirect
151. Dic202C22×C4semidirect
164. C2×D101#104semidirect
179. C2×C101C2×#104semidirect
184. D101C2×#104semidirect
186. C101C22×#104semidirect
202. C2×#41#87938semidirect
237. #41C2×#87938semidirect
242. C2×Q8C2×#87938semidirect
253. C2×D4C2×#87938semidirect
296. Q8C22×#87938semidirect
307. D4C22×#87938semidirect
369. C2D101⋊#104direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D101⋊M162
C22×C4×#879382
C2×#156923202
D101⋊#1042
C2×#156923192
C2×#41×D1012
C22×#104101