Finite Group Databasebeta

← C2×#10593829 #11857864

Subgroups — C2×#10593829 #11857864

Order 1152.

1602 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic
2C2×#64286C211yesmaximal, characteristic
3C2×#64283C211yesmaximal, characteristic
4#10593829C218yesmaximal, direct product factor
5C2×#63784C214yesmaximal, complemented
6C22×C32×Q8C411yescharacteristic, complemented
7C2×Q8×C3⋊D3—21no—
8C2×Q8×C3⋊D3—22no—
9C2×Q8×C3⋊D3—21no—
10C2×Q8×C3⋊D3—22no—
11C2×Q8×C3⋊D3C412yescomplemented
12C2×Q8×C3⋊D3C414yescomplemented
13C2×Q8×C3⋊D3C2212yes—
14C2×Q8×C3⋊D3C2214yes—
15C22×C4×C3⋊D3—21no—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#634—21no—
18C22×#634C411yescharacteristic, complemented
19C2×C22⋊#157—21no—
20C2×#3792—21no—
21#64286—22no—
22#64286C2214yes—
23C2×C4⋊#157C2212yes—
24C2×C4×#157—21no—
25#64283—22no—
26#64283C2214yes—
27C2×#3788—21no—
28C2×#3787C2212yes—
29#63784C22116yescomplemented
30C22×D3×Q8—62no—
31C23×C3⋊D3D411yescharacteristic
32C22×#157—22no—
33C2×C32×Q8—21no—
34C2×C32×Q8—22no—
35C2×C32×Q8C2×C412yes—
36C2×C32×Q8C2×C414yescomplemented
37C22×C32×C4—21no—
38C22×C32×C4C2×C411yescharacteristic
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3D411yescharacteristic
41Q8×C3⋊D3—24no—
42Q8×C3⋊D3—24no—
43Q8×C3⋊D3—24no—
44Q8×C3⋊D3—22no—
45Q8×C3⋊D3—22no—
46Q8×C3⋊D3—24no—
47Q8×C3⋊D3—24no—
48Q8×C3⋊D3C2×C414yes—
49Q8×C3⋊D3C2×C418yescomplemented
50Q8×C3⋊D3C2314yes—
51C2×C4×C3⋊D3—24no—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3C2×C412yes—
56C2×C4×C3⋊D3C2×C411yescharacteristic
57C2×C4×C3⋊D3D411yescharacteristic
58C2×C4×C3⋊D3D412yes—
59C2×C4×C3⋊D3D411yescharacteristic
60C2×C4×C3⋊D3D412yes—
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×C4×C3⋊D3C2312yes—
63C2×#634—22no—
64C2×#634—21no—
65C2×#634—24no—
66C2×#634—22no—
67C2×#634—22no—
68C2×#634—24no—
69C2×#634C2×C412yes—
70C2×#634C2×C414yescomplemented
71C22⋊#157—24no—
72#3792—24no—
73C2×#622—22no—
74C4⋊#157—22no—
75C4⋊#157C2314yes—
76C4×#157—24no—
77#3788—24no—
78#3787—22no—
79#3787C2314yes—
80C2×#419—91nomaximal, Sylow
81C22×C3×Q8—22no—
82C2×D3×Q8—64no—
83C2×D3×Q8—68no—
84C2×D3×Q8—64no—
85C2×D3×Q8—68no—
86C2×D3×Q8—64no—
87C2×D3×Q8—68no—
88C2×D3×Q8—64no—
89C2×D3×Q8—68no—
90C22×C4×D3—62no—
91C22×C4×D3—64no—
92C22×Dic6—62no—
93C22×Dic6—64no—
94C23×C32C22⋊C411yescharacteristic
95C22×C3⋊D3—24no—
96C22×C3⋊D3C22⋊C411yescharacteristic
97C22×C3⋊D3C22⋊C412yes—
98C22×C3⋊D3C2×D412yes—
99C22×C3⋊D3C2×D411yescharacteristic
100C2×#157—24no—
101C2×#157—44no—
102C32×Q8—22no—
103C32×Q8—24no—
104C32×Q8C22×C414yes—
105C2×C32×C4—22no—
106C2×C32×C4—24no—
107C2×C32×C4C22⋊C412yes—
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22×C411yescharacteristic
110C2×C32×C4C22×C412yes—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—24no—
113C2×C3⋊Dic3C22⋊C412yes—
114C2×C3⋊Dic3C22⋊C411yescharacteristic
115C2×C3⋊Dic3C2×D411yescharacteristic
116C2×C3⋊Dic3C2×D412yes—
117C4×C3⋊D3—24no—
118C4×C3⋊D3—28no—
119C4×C3⋊D3—24no—
120C4×C3⋊D3C22⋊C412yes—
121C4×C3⋊D3C22⋊C412yes—
122C4×C3⋊D3C22⋊C412yes—
123C4×C3⋊D3C22×C411yescharacteristic
124C4×C3⋊D3C22×C412yes—
125C4×C3⋊D3C2×D412yes—
126C4×C3⋊D3C2×D411yescharacteristic
127C4×C3⋊D3C2×D411yescharacteristic
128C4×C3⋊D3C2×D412yes—
129C4×C3⋊D3C2411yescharacteristic
130#634—22no—
131#634—24no—
132#634—24no—
133#634—28no—
134#634—24no—
135#634C22×C414yes—
136#622—24no—
137C23×Q8—91no—
138C22×M16—91no—
139C2×#117—91no—
140#419—98no—
141C2×#103—94no—
142C23×D3—62no—
143C2×C3×Q8—28no—
144C2×C3×Q8—24no—
145C2×C3×Q8—24no—
146C2×C3×Q8—28no—
147C22×C3×C4—24no—
148C22×C3×C4—22no—
149C22×Dic3—62no—
150C22×Dic3—64no—
151D3×Q8—68no—
152D3×Q8—616no—
153D3×Q8—68no—
154D3×Q8—616no—
155D3×Q8—616no—
156D3×Q8—616no—
157D3×Q8—616no—
158D3×Q8—68no—
159D3×Q8—68no—
160D3×Q8—616no—
161C2×C4×D3—64no—
162C2×C4×D3—62no—
163C2×C4×D3—62no—
164C2×C4×D3—64no—
165C2×C4×D3—62no—
166C2×C4×D3—64no—
167C2×C4×D3—62no—
168C2×C4×D3—64no—
169C2×C4×D3—616no—
170C2×C4×D3—68no—
171C2×C4×D3—616no—
172C2×C4×D3—68no—
173C2×Dic6—64no—
174C2×Dic6—68no—
175C2×Dic6—616no—
176C2×Dic6—68no—
177C2×Dic6—616no—
178C2×Dic6—68no—
179C2×Dic6—68no—
180C2×Dic6—64no—
181C22×C32—22no—
182C22×C32C2×C22⋊C412yes—
183C22×C32C2×C22⋊C411yescharacteristic
184C2×C3⋊D3—22no—
185C2×C3⋊D3—24no—
186C2×C3⋊D3—24no—
187C2×C3⋊D3C2×C22⋊C412yes—
188C2×C3⋊D3C2×C22⋊C411yescharacteristic
189C2×C3⋊D3#13714yes—
190C2×C3⋊D3C22×D411yescharacteristic
191#157—44no—
192C32×C4—24no—
193C32×C4C2×C22⋊C411yescharacteristic
194C32×C4C2×C22⋊C412yes—
195C32×C4C23×C411yescharacteristic
196C3⋊Dic3—24no—
197C3⋊Dic3C2×C22⋊C411yescharacteristic
198C3⋊Dic3C2×C22⋊C412yes—
199C3⋊Dic3C22×D411yescharacteristic
200C22×Q8—92no—
201C22×Q8—92no—
202C22×Q8—94no—
203C22×Q8—94no—
204C22×Q8—91no—
205C22×Q8—181no—
206C22×Q8—181no—
207C22×Q8—182no—
208C22×Q8—182no—
209C22×Q8—181no—
210C22×Q8#15711yescharacteristic, complemented
211C23×C4—91no—
212C23×C4—181no—
213C2×M16—94no—
214C2×M16—181no—
215C2×M16—182no—
216C2×M16—181no—
217C22×C8—92no—
218#117—94no—
219#117—182no—
220C2×C4⋊C4—92no—
221C2×C22⋊C4—181no—
222C2×C42—181no—
223#103—916no—
224C23×C3—22no—
225C22×D3—64no—
226C22×D3—62no—
227C22×D3—62no—
228C22×D3—64no—
229C22×D3—616no—
230C3×Q8—28no—
231C3×Q8—216no—
232C3×Q8—28no—
233C2×C3×C4—216no—
234C2×C3×C4—28no—
235C2×C3×C4—24no—
236C2×C3×C4—22no—
237C2×C3×C4—24no—
238C2×C3×C4—22no—
239C2×Dic3—64no—
240C2×Dic3—62no—
241C2×Dic3—64no—
242C2×Dic3—62no—
243C2×Dic3—616no—
244C2×Dic3—68no—
245C4×D3—64no—
246C4×D3—64no—
247C4×D3—64no—
248C4×D3—62no—
249C4×D3—64no—
250C4×D3—64no—
251C4×D3—62no—
252C4×D3—62no—
253C4×D3—64no—
254C4×D3—62no—
255C4×D3—616no—
256C4×D3—632no—
257C4×D3—616no—
258Dic6—68no—
259Dic6—616no—
260Dic6—632no—
261Dic6—616no—
262Dic6—68no—
263Dic6—616no—
264C2×C32—22no—
265C2×C32#41912yescomplemented
266C2×C32C22×C22⋊C411yescharacteristic
267C3⋊D3—22no—
268C3⋊D3#41912yescomplemented
269C3⋊D3C2×#13712yes—
270C24—91no—
271C2×Q8—22no—
272C2×Q8—21no—
273C2×Q8—94no—
274C2×Q8—94no—
275C2×Q8—98no—
276C2×Q8—94no—
277C2×Q8—92no—
278C2×Q8—184no—
279C2×Q8—184no—
280C2×Q8—182no—
281C2×Q8—182no—
282C2×Q8—184no—
283C2×Q8—182no—
284C2×Q8—182no—
285C2×Q8—184no—
286C2×Q8—184no—
287C2×Q8—184no—
288C2×Q8—184no—
289C2×Q8—182no—
290C2×Q8—181no—
291C2×Q8C2×#15712yes—
292C2×Q8C2×#15714yescomplemented
293C22×C4—21no—
294C22×C4—91no—
295C22×C4—91no—
296C22×C4—92no—
297C22×C4—92no—
298C22×C4—91no—
299C22×C4—91no—
300C22×C4—92no—
301C22×C4—92no—
302C22×C4—91no—
303C22×C4—184no—
304C22×C4—184no—
305C22×C4—182no—
306C22×C4—182no—
307C22×C4—181no—
308C22×C4—182no—
309C22×C4C2×#15711yescharacteristic
310M16—184no—
311M16—184no—
312C2×C8—94no—
313C2×C8—182no—
314C2×C8—182no—
315C4⋊C4—94no—
316C4⋊C4—182no—
317C22⋊C4—184no—
318C42—184no—
319C22×C3—28no—
320C22×C3—24no—
321C22×C3—22no—
322C2×D3—62no—
323C2×D3—64no—
324C2×D3—62no—
325C2×D3—68no—
326C2×D3—616no—
327C2×D3—616no—
328C2×D3—68no—
329C3×C4—216no—
330C3×C4—24no—
331C3×C4—22no—
332C3×C4—22no—
333Dic3—64no—
334Dic3—62no—
335Dic3—62no—
336Dic3—616no—
337C32C2×#41911yescharacteristic, complemented, Sylow
338C23—91no—
339C23—92no—
340C23—92no—
341C23—91no—
342C23—184no—
343C23C22⋊#15711yescharacteristic
344Q8—22no—
345Q8—24no—
346Q8—94no—
347Q8—184no—
348Q8—188no—
349Q8—184no—
350Q8—184no—
351Q8—182no—
352Q8C22×#15714yes—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—92no—
356C2×C4—92no—
357C2×C4—91no—
358C2×C4—91no—
359C2×C4—92no—
360C2×C4—91no—
361C2×C4—91no—
362C2×C4—92no—
363C2×C4—92no—
364C2×C4—92no—
365C2×C4—92no—
366C2×C4—91no—
367C2×C4—91no—
368C2×C4—92no—
369C2×C4—184no—
370C2×C4—184no—
371C2×C4—188no—
372C2×C4—184no—
373C2×C4—182no—
374C2×C4—184no—
375C2×C4—364no—
376C2×C4C22⋊#15712yes—
377C2×C4C22⋊#15711yescharacteristic
378C2×C4C22×#15712yes—
379C2×C4C22×#15711yescharacteristic
380C8—184no—
381C2×C3—28no—
382C2×C3—24no—
383C2×C3—22no—
384D3—64no—
385D3—64no—
386D3—68no—
387C22—22no—
388C22—94no—
389C22—91no—
390C22—91no—
391C22—92no—
392C22—184no—
393C22—184no—
394C22—182no—
395C22C2×C22⋊#15712yes—
396C22C2×C22⋊#15711yescharacteristic
397C4—24no—
398C4—91no—
399C4—92no—
400C4—91no—
401C4—184no—
402C4—364no—
403C4C2×C22⋊#15712yes—
404C4C2×C22⋊#15711yescharacteristic
405C4C23×#15711yescharacteristic
406C3—22no—
407C2—22no—
408C2—92no—
409C2—92no—
410C2—182no—
411C2#1059382912yesdirect product factor
412C2C22×C22⋊#15711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC32×C4C23×C4
FrattiniC4C23×#157
FittingC22×C32×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC4×C3⋊D3C24
hypercenterC22×Q8#157
hypocenterC32C2×#419
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. #10593829C2direct (N × H)
5. C2×#63784C2semidirect
6. C22×C32×Q8C4semidirect
11. C2×Q8×C3⋊D3C4semidirect
12. C2×Q8×C3⋊D3C4semidirect
18. C22×#634C4semidirect
29. #63784C22semidirect
36. C2×C32×Q8C2×C4semidirect
49. Q8×C3⋊D3C2×C4semidirect
70. C2×#634C2×C4semidirect
210. C22×Q8#157semidirect
265. C2×C32#419semidirect
268. C3⋊D3#419semidirect
292. C2×Q8C2×#157semidirect
337. C32C2×#419semidirect
411. C2#10593829direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C2×#642862
C2×#642832
#105938292
C2×#637842
C2×#4199