Finite Group Databasebeta

← C2×#10590151 #11783178

Subgroups — C2×#10590151 #11783178

Order 1152.

986 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64286C211yesmaximal, characteristic
2C2×#64283C211yesmaximal, characteristic
3C2×C42×C3⋊D3C211yesmaximal, characteristic
4#10590151C214yesmaximal, direct product factor
5C22×C4×C3⋊D3—21no—
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157—21no—
8C2×#3792—21no—
9#64286—21no—
10#64286—21no—
11#64286C412yescomplemented
12#64286C2212yes—
13C2×C4⋊#157C412yescomplemented
14C2×C4×#157—21no—
15#64283—21no—
16#64283—21no—
17#64283C412yescomplemented
18#64283C2212yes—
19C2×#3788C412yescomplemented
20C2×#3787—21no—
21C2×C32×C42C411yescharacteristic, complemented
22C2×C4×C3⋊Dic3—21no—
23C2×C4×C3⋊Dic3C411yescharacteristic, complemented
24C42×C3⋊D3—21no—
25C42×C3⋊D3—21no—
26C42×C3⋊D3C412yescomplemented
27C42×C3⋊D3C2212yes—
28C2×C42×D3—62no—
29C23×C3⋊D3D411yescharacteristic
30C22×#157—22no—
31C22×C32×C4—21no—
32C22×C32×C4C2×C411yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3D411yescharacteristic
35C2×C4×C3⋊D3—28no—
36C2×C4×C3⋊D3—22no—
37C2×C4×C3⋊D3—22no—
38C2×C4×C3⋊D3C2×C411yescharacteristic
39C2×C4×C3⋊D3C2×C411yescharacteristic
40C2×C4×C3⋊D3C2×C411yescharacteristic
41C2×C4×C3⋊D3C2×C411yescharacteristic
42C2×C4×C3⋊D3C2×C411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3D411yescharacteristic
45C2×C4×C3⋊D3D411yescharacteristic
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C4×C3⋊D3Q811yescharacteristic
48C2×C4×C3⋊D3Q811yescharacteristic
49C2×C4×C3⋊D3C2311yescharacteristic
50C22⋊#157—22no—
51C22⋊#157—22no—
52#3792—22no—
53#3792—22no—
54C2×#622—22no—
55C4⋊#157—22no—
56C4⋊#157C2×C414yescomplemented
57C4×#157—22no—
58C4×#157—22no—
59#3788—22no—
60#3788C2×C414yescomplemented
61#3787—22no—
62#3787—22no—
63C32×C42—21no—
64C32×C42C2×C412yescomplemented
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3—22no—
67C4×C3⋊Dic3—22no—
68C4×C3⋊Dic3C2×C412yescomplemented
69C2×#339—91nomaximal, Sylow
70C22×C4×D3—62no—
71C22×C4×D3—64no—
72C2×C3×C42—22no—
73C2×C4×Dic3—62no—
74C2×C4×Dic3—64no—
75C42×D3—64no—
76C42×D3—64no—
77C42×D3—64no—
78C42×D3—64no—
79C23×C32C22⋊C411yescharacteristic
80C22×C3⋊D3—24no—
81C22×C3⋊D3C22⋊C411yescharacteristic
82C22×C3⋊D3C22⋊C411yescharacteristic
83C22×C3⋊D3C22⋊C411yescharacteristic
84C22×C3⋊D3C4⋊C411yescharacteristic
85C22×C3⋊D3C4⋊C411yescharacteristic
86C22×C3⋊D3C2×D411yescharacteristic
87C2×#157—24no—
88C2×#157—44no—
89C2×C32×C4—24no—
90C2×C32×C4—22no—
91C2×C32×C4C4211yescharacteristic
92C2×C32×C4C4211yescharacteristic
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C4⋊C411yescharacteristic
95C2×C32×C4C4⋊C411yescharacteristic
96C2×C32×C4C22×C411yescharacteristic
97C2×C3⋊Dic3—24no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3C22⋊C411yescharacteristic
100C2×C3⋊Dic3C22⋊C411yescharacteristic
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C2×C3⋊Dic3C4⋊C411yescharacteristic
103C2×C3⋊Dic3C4⋊C411yescharacteristic
104C2×C3⋊Dic3C2×D411yescharacteristic
105C4×C3⋊D3—28no—
106C4×C3⋊D3—28no—
107C4×C3⋊D3C4211yescharacteristic
108C4×C3⋊D3C4211yescharacteristic
109C4×C3⋊D3C22⋊C411yescharacteristic
110C4×C3⋊D3C22⋊C411yescharacteristic
111C4×C3⋊D3C22⋊C411yescharacteristic
112C4×C3⋊D3C22⋊C411yescharacteristic
113C4×C3⋊D3C4⋊C411yescharacteristic
114C4×C3⋊D3C4⋊C411yescharacteristic
115C4×C3⋊D3C4⋊C411yescharacteristic
116C4×C3⋊D3C4⋊C411yescharacteristic
117C4×C3⋊D3C4⋊C411yescharacteristic
118C4×C3⋊D3C4⋊C411yescharacteristic
119C4×C3⋊D3C22×C411yescharacteristic
120C4×C3⋊D3C22×C411yescharacteristic
121C4×C3⋊D3C2×D411yescharacteristic
122C4×C3⋊D3C2×Q811yescharacteristic
123#622—24no—
124C22×M16—91no—
125C2×#117—91no—
126C22×C42—91no—
127#339—94no—
128C23×D3—62no—
129C22×C3×C4—24no—
130C22×C3×C4—22no—
131C22×Dic3—62no—
132C22×Dic3—64no—
133C2×C4×D3—62no—
134C2×C4×D3—62no—
135C2×C4×D3—62no—
136C2×C4×D3—62no—
137C2×C4×D3—62no—
138C2×C4×D3—62no—
139C2×C4×D3—62no—
140C2×C4×D3—62no—
141C2×C4×D3—62no—
142C2×C4×D3—62no—
143C2×C4×D3—62no—
144C2×C4×D3—62no—
145C2×C4×D3—68no—
146C2×C4×D3—68no—
147C2×C4×D3—632no—
148C3×C42—24no—
149C3×C42—24no—
150C4×Dic3—64no—
151C4×Dic3—68no—
152C4×Dic3—68no—
153C4×Dic3—64no—
154C22×C32—22no—
155C22×C32#9511yescharacteristic
156C22×C32#9511yescharacteristic
157C22×C32C2×C22⋊C411yescharacteristic
158C2×C3⋊D3—22no—
159C2×C3⋊D3—22no—
160C2×C3⋊D3—22no—
161C2×C3⋊D3—22no—
162C2×C3⋊D3—22no—
163C2×C3⋊D3#9511yescharacteristic
164C2×C3⋊D3#9511yescharacteristic
165C2×C3⋊D3#10414yes—
166C2×C3⋊D3C2×C22⋊C411yescharacteristic
167C2×C3⋊D3C2×C4⋊C411yescharacteristic
168#157—44no—
169C32×C4—24no—
170C32×C4#9511yescharacteristic
171C32×C4#9511yescharacteristic
172C32×C4C2×C4211yescharacteristic
173C32×C4C2×C4⋊C411yescharacteristic
174C3⋊Dic3—24no—
175C3⋊Dic3#9511yescharacteristic
176C3⋊Dic3#9511yescharacteristic
177C3⋊Dic3C2×C22⋊C411yescharacteristic
178C3⋊Dic3C2×C4⋊C411yescharacteristic
179C23×C4—91no—
180C23×C4—181no—
181C2×M16—92no—
182C2×M16—92no—
183C2×M16—92no—
184C2×M16—181no—
185C2×M16—181no—
186C2×M16—181no—
187C22×C8—181no—
188#117—92no—
189#117—92no—
190#117—181no—
191#117—181no—
192C2×C4⋊C4—92no—
193C2×C22⋊C4—181no—
194C2×C42—91no—
195C2×C42—92no—
196C2×C42—92no—
197C2×C42—181no—
198C2×C42—181no—
199C2×C42—181no—
200C2×C42—181no—
201C2×C42#15711yescharacteristic, complemented
202C23×C3—22no—
203C22×D3—62no—
204C22×D3—62no—
205C22×D3—62no—
206C22×D3—62no—
207C22×D3—62no—
208C22×D3—62no—
209C22×D3—616no—
210C2×C3×C4—28no—
211C2×C3×C4—216no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—22no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C2×Dic3—68no—
225C2×Dic3—616no—
226C4×D3—62no—
227C4×D3—62no—
228C4×D3—62no—
229C4×D3—62no—
230C4×D3—62no—
231C4×D3—62no—
232C4×D3—62no—
233C4×D3—62no—
234C4×D3—62no—
235C4×D3—62no—
236C4×D3—62no—
237C4×D3—62no—
238C4×D3—62no—
239C4×D3—62no—
240C4×D3—62no—
241C4×D3—62no—
242C4×D3—632no—
243C4×D3—632no—
244C2×C32—21no—
245C2×C32—21no—
246C2×C32#33912yescomplemented
247C2×C32C2×#9511yescharacteristic
248C3⋊D3—21no—
249C3⋊D3—21no—
250C3⋊D3#33912yescomplemented
251C3⋊D3C2×#10412yes—
252C24—91no—
253C22×C4—21no—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—91no—
260C22×C4—91no—
261C22×C4—91no—
262C22×C4—91no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—91no—
267C22×C4—182no—
268C22×C4—182no—
269C22×C4—188no—
270C22×C4—181no—
271C22×C4—182no—
272C22×C4C2×#15711yescharacteristic
273M16—94no—
274M16—182no—
275M16—182no—
276M16—182no—
277C2×C8—182no—
278C2×C8—182no—
279C2×C8—182no—
280C4⋊C4—94no—
281C4⋊C4—182no—
282C22⋊C4—182no—
283C22⋊C4—182no—
284C42—21no—
285C42—92no—
286C42—182no—
287C42—182no—
288C42—182no—
289C42—182no—
290C42—181no—
291C42C2×#15712yescomplemented
292C22×C3—28no—
293C22×C3—22no—
294C22×C3—22no—
295C22×C3—22no—
296C2×D3—62no—
297C2×D3—62no—
298C2×D3—62no—
299C2×D3—62no—
300C2×D3—68no—
301C2×D3—68no—
302C2×D3—68no—
303C2×D3—68no—
304C2×D3—68no—
305C2×D3—68no—
306C3×C4—216no—
307C3×C4—22no—
308C3×C4—22no—
309C3×C4—22no—
310C3×C4—22no—
311Dic3—62no—
312Dic3—62no—
313Dic3—62no—
314Dic3—62no—
315Dic3—616no—
316C32C2×#33911yescharacteristic, complemented, Sylow
317C23—91no—
318C23—91no—
319C23—91no—
320C23—91no—
321C23—91no—
322C23—91no—
323C23—184no—
324C23C22⋊#15711yescharacteristic
325C2×C4—24no—
326C2×C4—22no—
327C2×C4—91no—
328C2×C4—91no—
329C2×C4—91no—
330C2×C4—91no—
331C2×C4—91no—
332C2×C4—91no—
333C2×C4—91no—
334C2×C4—91no—
335C2×C4—91no—
336C2×C4—91no—
337C2×C4—91no—
338C2×C4—91no—
339C2×C4—91no—
340C2×C4—91no—
341C2×C4—91no—
342C2×C4—91no—
343C2×C4—91no—
344C2×C4—91no—
345C2×C4—91no—
346C2×C4—91no—
347C2×C4—91no—
348C2×C4—91no—
349C2×C4—188no—
350C2×C4—188no—
351C2×C4—184no—
352C2×C4—182no—
353C2×C4—184no—
354C2×C4—364no—
355C2×C4C4×#15711yescharacteristic
356C2×C4C4×#15711yescharacteristic
357C2×C4C4⋊#15711yescharacteristic
358C2×C4C4⋊#15711yescharacteristic
359C2×C4C22⋊#15711yescharacteristic
360C2×C4C22×#15711yescharacteristic
361C8—184no—
362C2×C3—24no—
363C2×C3—24no—
364C2×C3—22no—
365C2×C3—24no—
366D3—64no—
367D3—64no—
368D3—64no—
369D3—64no—
370C22—22no—
371C22—91no—
372C22—91no—
373C22—94no—
374C22—91no—
375C22—91no—
376C22—182no—
377C22—182no—
378C22—182no—
379C22—182no—
380C22—182no—
381C22#6378111yescharacteristic
382C22#6378111yescharacteristic
383C22C2×C22⋊#15711yescharacteristic
384C4—24no—
385C4—91no—
386C4—91no—
387C4—91no—
388C4—91no—
389C4—184no—
390C4—364no—
391C4#6378111yescharacteristic
392C4#6378111yescharacteristic
393C4C2×C4×#15711yescharacteristic
394C4C2×C4⋊#15711yescharacteristic
395C3—22no—
396C2—21no—
397C2—21no—
398C2—92no—
399C2—92no—
400C2—181no—
401C2—181no—
402C2#1059015112yesdirect product factor
403C2C2×#6378111yescharacteristic
subgroupG/H
centerC2×C4C4⋊#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC2×C32×C42C4
socleC22×C32#95
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C42#157
hypocenterC32C2×#339
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #10590151C2direct (N × H)
11. #64286C4semidirect
13. C2×C4⋊#157C4semidirect
17. #64283C4semidirect
19. C2×#3788C4semidirect
21. C2×C32×C42C4semidirect
23. C2×C4×C3⋊Dic3C4semidirect
26. C42×C3⋊D3C4semidirect
56. C4⋊#157C2×C4semidirect
60. #3788C2×C4semidirect
64. C32×C42C2×C4semidirect
68. C4×C3⋊Dic3C2×C4semidirect
201. C2×C42#157semidirect
246. C2×C32#339semidirect
250. C3⋊D3#339semidirect
291. C42C2×#157semidirect
316. C32C2×#339semidirect
402. C2#10590151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642862
C2×#642832
C2×C42×C3⋊D32
#105901512
C2×#3399