Finite Group Databasebeta

← C2×#20261732 #27158364

Subgroups — C2×#20261732 #27158364

Order 12416.

772 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13095521C211yesmaximal, characteristic, complemented
2C2×#15690889C211yesmaximal, characteristic, complemented
3#20261732C218yesmaximal, direct product factor
4C2×#15690875C212yesmaximal, complemented
5C2×#15690874C212yesmaximal, complemented
6C2×#41×D97C211yesmaximal, characteristic
7C2×#13095521—21no—
8C2×#13095521—22no—
9C2×#13095521C2212yescomplemented
10C2×#13095521C2214yescomplemented
11C22×#11715897—21no—
12#15690889—22no—
13#15690889C2214yescomplemented
14C2×C4⋊#87604—21no—
15C2×C22⋊#87604—21no—
16C2×C4×#87604C2212yescomplemented
17#15690875C2218yescomplemented
18#15690874C2218yescomplemented
19C2×#13095512C2211yescharacteristic
20C2×#13095511—21no—
21C2×#13095511C411yescharacteristic, complemented
22C2×#13095510—21no—
23C2×#13095510C2211yescharacteristic
24#41×D97—22no—
25#41×D97—22no—
26#41×D97C414yescomplemented
27#41×D97C2214yes—
28C2×Q8×D97C411yescharacteristic, complemented
29C2×D4×D97—21no—
30C2×D4×D97C411yescharacteristic, complemented
31C22×C4×D97—21no—
32C22×C4×D97C2211yescharacteristic
33C2×#41×C97C411yescharacteristic, complemented
34C22×#87604—22no—
35#13095521—24no—
36#13095521—22no—
37#13095521C2314yescomplemented
38C2×#11715897—22no—
39C2×#11715897—24no—
40C4⋊#87604—24no—
41C22⋊#87604—24no—
42C4×#87604—22no—
43C4×#87604C2314yescomplemented
44C23×D97—21no—
45C23×D97D411yescharacteristic
46#13095512—21no—
47#13095512—21no—
48#13095512C2×C412yes—
49#13095512C2312yes—
50#13095511—22no—
51#13095511—24no—
52#13095511—24no—
53#13095511C2×C414yescomplemented
54#13095510—24no—
55#13095510—24no—
56#13095510—21no—
57#13095510—21no—
58#13095510C2×C412yes—
59#13095510C2312yes—
60C2×Dic194—21no—
61C2×Dic194C2×C411yescharacteristic
62Q8×D97—22no—
63Q8×D97C2×C414yescomplemented
64C2×D388—21no—
65C2×D388C2×C411yescharacteristic
66C2×C22⋊D97—21no—
67C2×C22⋊D97—21no—
68C2×C22⋊D97—21no—
69D4×D97—24no—
70D4×D97—24no—
71D4×D97—22no—
72D4×D97C2×C414yescomplemented
73C22×Dic97—21no—
74C22×Dic97D411yescharacteristic
75C2×C4×D97—21no—
76C2×C4×D97—21no—
77C2×C4×D97—21no—
78C2×C4×D97—24no—
79C2×C4×D97—24no—
80C2×C4×D97C2×C411yescharacteristic
81C2×C4×D97C2×C412yes—
82C2×C4×D97D412yes—
83C2×C4×D97D411yescharacteristic
84C2×C4×D97D411yescharacteristic
85C2×C4×D97D412yes—
86C2×C4×D97C2312yes—
87C2×C4×D97C2311yescharacteristic
88#41×C97—22no—
89#41×C97C2×C414yescomplemented
90C2×Q8×C97C2×C411yescharacteristic
91C2×D4×C97—21no—
92C2×D4×C97C2×C411yescharacteristic
93C22×C4×C97—21no—
94C22×C4×C97C2×C411yescharacteristic
95C23×C97—21no—
96C23×C97C22⋊C411yescharacteristic
97C22×D97—21no—
98C22×D97—24no—
99C22×D97—42no—
100C22×D97—44no—
101C22×D97C22⋊C411yescharacteristic
102C22×D97C22⋊C412yes—
103C22×D97C2×D411yescharacteristic
104C22×D97C2×D412yes—
105C2×#87604—24no—
106C2×#87604—44no—
107Q8×C97—21no—
108Q8×C97C22×C412yes—
109D4×C97—24no—
110D4×C97—21no—
111D4×C97C22×C412yes—
112C2×C4×C97—21no—
113C2×C4×C97—24no—
114C2×C4×C97C22⋊C411yescharacteristic
115C2×C4×C97C22⋊C412yes—
116C2×C4×C97C22×C411yescharacteristic
117C2×C4×C97C22×C412yes—
118C22⋊D97—24no—
119C22⋊D97—22no—
120C22⋊D97—22no—
121C22⋊D97—24no—
122C2×Dic97—21no—
123C2×Dic97—22no—
124C2×Dic97—22no—
125C2×Dic97C22⋊C411yescharacteristic
126C2×Dic97C22⋊C412yes—
127C2×Dic97C2×D411yescharacteristic
128C2×Dic97C2×D412yes—
129D388—22no—
130D388—22no—
131D388—21no—
132D388C22×C412yes—
133C4×D97—24no—
134C4×D97—24no—
135C4×D97—22no—
136C4×D97—22no—
137C4×D97C22⋊C412yes—
138C4×D97C22⋊C412yes—
139C4×D97C22⋊C412yes—
140C4×D97C22×C412yes—
141C4×D97C22×C411yescharacteristic
142C4×D97C2×D411yescharacteristic
143C4×D97C2×D412yes—
144C4×D97C2×D412yes—
145C4×D97C2×D411yescharacteristic
146C4×D97C2411yescharacteristic
147Dic194—21no—
148Dic194—24no—
149Dic194C22×C412yes—
150#11715897—24no—
151C22×C97—22no—
152C22×C97—22no—
153C22×C97—42no—
154C22×C97C2×C22⋊C412yes—
155C22×C97C2×C22⋊C411yescharacteristic
156C2×D97—22no—
157C2×D97—22no—
158C2×D97—22no—
159C2×D97—42no—
160C2×D97—42no—
161C2×D97—48no—
162C2×D97—42no—
163C2×D97C2×C22⋊C412yes—
164C2×D97C2×C22⋊C411yescharacteristic
165C2×D97C22×D411yescharacteristic
166#87604—44no—
167C4×C97—22no—
168C4×C97C2×C22⋊C411yescharacteristic
169C4×C97C2×C22⋊C412yes—
170C4×C97C23×C411yescharacteristic
171Dic97—22no—
172Dic97C2×C22⋊C412yes—
173Dic97C2×C22⋊C411yescharacteristic
174Dic97C22×D411yescharacteristic
175C2×C97—22no—
176C2×C97—42no—
177C2×C97#42112yescomplemented
178C2×C97C22×C22⋊C411yescharacteristic
179D97—21no—
180D97—22no—
181D97—21no—
182D97—42no—
183C2×#421—971nomaximal, Sylow
184C97C2×#42111yescharacteristic, complemented, Sylow
185C22×#41—971no—
186C22×M16—971no—
187C2×#117—971no—
188#421—978no—
189C2×#104—972no—
190C2×#104—972no—
191C2×#41—974no—
192C2×#41—974no—
193C2×#41—971no—
194C2×#41—971no—
195C2×#41—971no—
196C2×#41—1941no—
197C2×#41—1941no—
198C2×#41—1942no—
199C2×#41—1942no—
200C2×#41#8760411yescharacteristic, complemented
201C22×Q8—971no—
202C22×D4—971no—
203C22×D4—1941no—
204C23×C4—971no—
205C23×C4—1941no—
206C2×M16—972no—
207C2×M16—974no—
208C2×M16—1941no—
209C2×M16—1942no—
210C22×C8—1941no—
211#117—974no—
212#117—1942no—
213C2×C4⋊C4—1941no—
214C2×C22⋊C4—1941no—
215C2×C42—972no—
216#104—978no—
217#104—978no—
218C24—971no—
219C24—1941no—
220#41—22no—
221#41—972no—
222#41—972no—
223#41—972no—
224#41—972no—
225#41—974no—
226#41—1944no—
227#41—1944no—
228#41—1944no—
229#41—1944no—
230#41—1941no—
231#41—1941no—
232#41—1941no—
233#41—1941no—
234#41—1942no—
235#41C2×#8760414yescomplemented
236C2×Q8—974no—
237C2×Q8—971no—
238C2×Q8—1941no—
239C2×Q8—1942no—
240C2×Q8C2×#8760411yescharacteristic
241C2×D4—21no—
242C2×D4—974no—
243C2×D4—971no—
244C2×D4—1941no—
245C2×D4—1942no—
246C2×D4—1941no—
247C2×D4—1944no—
248C2×D4—1944no—
249C2×D4—1941no—
250C2×D4—1941no—
251C2×D4C2×#8760411yescharacteristic
252C22×C4—21no—
253C22×C4—971no—
254C22×C4—971no—
255C22×C4—972no—
256C22×C4—971no—
257C22×C4—972no—
258C22×C4—971no—
259C22×C4—972no—
260C22×C4—971no—
261C22×C4—972no—
262C22×C4—1941no—
263C22×C4—1944no—
264C22×C4—1944no—
265C22×C4—1941no—
266C22×C4—1941no—
267C22×C4—1942no—
268C22×C4—1941no—
269C22×C4C2×#8760411yescharacteristic
270M16—974no—
271M16—1944no—
272M16—1942no—
273C2×C8—1944no—
274C2×C8—1942no—
275C4⋊C4—1944no—
276C22⋊C4—1944no—
277C42—974no—
278C42—1942no—
279C23—21no—
280C23—972no—
281C23—972no—
282C23—971no—
283C23—971no—
284C23—3882no—
285C23—3884no—
286C23—1944no—
287C23—1941no—
288C23C22⋊#8760411yescharacteristic
289Q8—21no—
290Q8—972no—
291Q8—1944no—
292Q8—1941no—
293Q8C22×#8760412yes—
294D4—24no—
295D4—21no—
296D4—972no—
297D4—1942no—
298D4—1942no—
299D4—1944no—
300D4—1942no—
301D4—1942no—
302D4—1944no—
303D4—1941no—
304D4C22×#8760412yes—
305C2×C4—21no—
306C2×C4—24no—
307C2×C4—972no—
308C2×C4—972no—
309C2×C4—971no—
310C2×C4—971no—
311C2×C4—971no—
312C2×C4—972no—
313C2×C4—972no—
314C2×C4—971no—
315C2×C4—972no—
316C2×C4—972no—
317C2×C4—972no—
318C2×C4—971no—
319C2×C4—972no—
320C2×C4—971no—
321C2×C4—3884no—
322C2×C4—1942no—
323C2×C4—1942no—
324C2×C4—1944no—
325C2×C4—1942no—
326C2×C4—1942no—
327C2×C4—1944no—
328C2×C4—1941no—
329C2×C4—1944no—
330C2×C4C22⋊#8760412yes—
331C2×C4C22⋊#8760411yescharacteristic
332C2×C4C22×#8760412yes—
333C2×C4C22×#8760411yescharacteristic
334C8—1944no—
335C22—22no—
336C22—22no—
337C22—42no—
338C22—971no—
339C22—972no—
340C22—971no—
341C22—3882no—
342C22—3882no—
343C22—3888no—
344C22—3882no—
345C22—1942no—
346C22—1942no—
347C22—1942no—
348C22C2×C22⋊#8760412yes—
349C22C2×C22⋊#8760411yescharacteristic
350C4—22no—
351C4—971no—
352C4—971no—
353C4—972no—
354C4—3884no—
355C4—1942no—
356C4C2×C22⋊#8760412yes—
357C4C2×C22⋊#8760411yescharacteristic
358C4C23×#8760411yescharacteristic
359C2—22no—
360C2—42no—
361C2—3882no—
362C2—1941no—
363C2—1942no—
364C2—1941no—
365C2#2026173212yesdirect product factor
366C2C22×C22⋊#8760411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87604
commutatorC4×C97C23×C4
FrattiniC4C23×#87604
FittingC2×#41×C97C4
socleC22×C97C2×C22⋊C4
prime radicalC2×#41×D97C2
cosocleC4×D97C24
hypercenterC2×#41#87604
hypocenterC97C2×#421
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C22×#13095521C2semidirect
2. C2×#15690889C2semidirect
3. #20261732C2direct (N × H)
4. C2×#15690875C2semidirect
5. C2×#15690874C2semidirect
9. C2×#13095521C22semidirect
10. C2×#13095521C22semidirect
13. #15690889C22semidirect
16. C2×C4×#87604C22semidirect
17. #15690875C22semidirect
18. #15690874C22semidirect
21. C2×#13095511C4semidirect
26. #41×D97C4semidirect
28. C2×Q8×D97C4semidirect
30. C2×D4×D97C4semidirect
33. C2×#41×C97C4semidirect
37. #13095521C23semidirect
43. C4×#87604C23semidirect
53. #13095511C2×C4semidirect
63. Q8×D97C2×C4semidirect
72. D4×D97C2×C4semidirect
89. #41×C97C2×C4semidirect
177. C2×C97#421semidirect
184. C97C2×#421semidirect
200. C2×#41#87604semidirect
235. #41C2×#87604semidirect
365. C2#20261732direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130955212
C2×#156908892
#202617322
C2×#156908752
C2×#156908742
C2×#41×D972
C2×#42197