Finite Group Databasebeta

← C2×#10593349 #11857808

Subgroups — C2×#10593349 #11857808

Order 1152.

1402 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 1402 conjugacy classes of subgroups — too many to draw. Only its 207 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×#3798C211yesmaximal, characteristic
2C22×#3787C211yesmaximal, characteristic, complemented
3C2×#63874C211yesmaximal, characteristic, complemented
4C2×#63740C212yesmaximal, complemented
5C2×#63739C212yesmaximal, complemented
6#10593349C218yesmaximal, direct product factor
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×C3×C4×D3—21no—
9C22×#627C2211yescharacteristic
10C22×#626—21no—
11C22×#625C2211yescharacteristic
12C2×#3798—22no—
13C2×#3798—24no—
14C2×#3798C418yescomplemented
15C2×#3798C2214yes—
16C22×#622C2212yes—
17C2×#3787—24no—
18C2×#3787C2214yescomplemented
19C2×C3×C4×Dic3—21no—
20C2×#3724C2212yes—
21C2×#3722—21no—
22#63874—22no—
23#63874C2214yescomplemented
24#63740C2218yescomplemented
25#63739C2218yescomplemented
26C22×#235—61no—
27C2×#872—61no—
28C23×C3⋊D3D411yescharacteristic
29C23×C3×D3—21no—
30C22×C32×C4D411yescharacteristic
31C22×C3⋊Dic3C2311yescharacteristic
32C2×C4×C3⋊D3C2×C414yes—
33C2×C4×C3⋊D3D412yes—
34C2×C4×C3⋊D3D414yes—
35C2×C4×C3⋊D3C2312yes—
36C22×C3×Dic3—21no—
37C22×C3×Dic3—22no—
38C2×C3×C4×D3—28no—
39C2×C3×C4×D3—24no—
40C2×#627—21no—
41C2×#627—22no—
42C2×#627C2×C414yes—
43C2×#627C2312yes—
44C2×#626—28no—
45C2×#626—24no—
46C2×#625—21no—
47C2×#625—22no—
48C2×#625C2×C414yes—
49C2×#625C2312yes—
50#3798—216no—
51#3798—28no—
52#3798C2×C4116yescomplemented
53C2×#622—24no—
54C2×#622C2314yes—
55#3787—28no—
56C3×C4×Dic3—24no—
57#3724—22no—
58#3724C2314yes—
59#3722—24no—
60C2×#416—91nomaximal, Sylow
61C23×C3×C4—61no—
62C22×#67—61no—
63C22×#67—61no—
64C2×#235—68no—
65C2×#235—64no—
66C2×#235—64no—
67C2×#235—68no—
68C22×D12—61no—
69C22×C4×D3—21no—
70C22×C4×D3—61no—
71C22×C4×D3—61no—
72C22×Dic6—61no—
73C2×C3×C42—61no—
74C2×(C2×D3)⋊C4—62no—
75C2×Dic3⋊C4—62no—
76C2×C4×Dic3—21no—
77#872—64no—
78#872—64no—
79C23×C32C2×D411yescharacteristic
80C22×C3⋊D3—24no—
81C22×C3⋊D3C22⋊C414yes—
82C22×C3⋊D3C2×D412yes—
83C22×C3×D3—24no—
84C22×C3×D3—22no—
85C22×C3×D3—44no—
86C2×C32×C4C22⋊C414yes—
87C2×C32×C4C2×D412yes—
88C2×C3⋊Dic3C22×C412yes—
89C2×C3⋊Dic3C2×D411yescharacteristic
90C2×C3⋊Dic3C2×D412yes—
91C2×C3⋊Dic3C2411yescharacteristic
92C4×C3⋊D3C22⋊C418yes—
93C4×C3⋊D3C22×C414yes—
94C4×C3⋊D3C2×D414yes—
95C2×C3×Dic3—24no—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—44no—
99C3×C4×D3—216no—
100#627—24no—
101#627—22no—
102#627C22×C414yes—
103#626—216no—
104#625—24no—
105#625—22no—
106#625C22×C414yes—
107#622—24no—
108C22×#41—91no—
109C23×C8—91no—
110C2×#117—91no—
111#416—98no—
112C2×#103—92no—
113C2×#102—92no—
114C24×C3—61no—
115C23×D3—21no—
116C23×D3—61no—
117C23×D3—61no—
118C22×C3×C4—21no—
119C22×C3×C4—21no—
120C22×C3×C4—64no—
121C22×C3×C4—68no—
122C22×C3×C4—61no—
123C22×C3×C4—62no—
124C2×#67—64no—
125C2×#67—62no—
126C2×#67—68no—
127C2×#67—64no—
128C2×#67—62no—
129C2×#67—64no—
130C22×Dic3—21no—
131C22×Dic3—22no—
132C22×Dic3—61no—
133C22×Dic3—61no—
134#235—616no—
135#235—632no—
136#235—616no—
137C2×D12—68no—
138C2×D12—64no—
139C2×C4×D3—24no—
140C2×C4×D3—28no—
141C2×C4×D3—62no—
142C2×C4×D3—62no—
143C2×C4×D3—64no—
144C2×C4×D3—62no—
145C2×C4×D3—64no—
146C2×C4×D3—62no—
147C2×C4×D3—64no—
148C2×C4×D3—64no—
149C2×Dic6—64no—
150C2×Dic6—62no—
151C2×Dic6—62no—
152C2×Dic6—64no—
153C3×C42—64no—
154(C2×D3)⋊C4—68no—
155Dic3⋊C4—64no—
156Dic3⋊C4—64no—
157C4×Dic3—24no—
158C22×C32C2×C22⋊C412yes—
159C22×C32#13514yes—
160C22×C32C22×D411yescharacteristic
161C2×C3⋊D3—24no—
162C2×C3⋊D3—28no—
163C2×C3⋊D3C2×C22⋊C414yes—
164C2×C3×D3—24no—
165C2×C3×D3—44no—
166C2×C3×D3—48no—
167C32×C4C2×C22⋊C414yes—
168C3⋊Dic3C2×C22⋊C412yes—
169C3⋊Dic3C23×C411yescharacteristic
170C3⋊Dic3C22×D411yescharacteristic
171C3×Dic3—24no—
172C3×Dic3—44no—
173C2×#41—94no—
174C2×#41—98no—
175C2×#41—182no—
176C2×#41—184no—
177C22×Q8—91no—
178C22×D4—91no—
179C22×D4—181no—
180C23×C4—61no—
181C23×C4—91no—
182C22×C8—94no—
183C22×C8—92no—
184C22×C8—184no—
185#117—94no—
186#117—182no—
187C2×C4⋊C4—92no—
188C2×C22⋊C4—181no—
189C2×C42—61no—
190#103—98no—
191#102—98no—
192C23×C3—21no—
193C23×C3—21no—
194C23×C3—62no—
195C23×C3—64no—
196C23×C3—124no—
197C22×D3—22no—
198C22×D3—24no—
199C22×D3—44no—
200C22×D3—64no—
201C22×D3—64no—
202C22×D3—62no—
203C22×D3—62no—
204C22×D3—124no—
205C22×D3—124no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—24no—
209C2×C3×C4—24no—
210C2×C3×C4—616no—
211C2×C3×C4—62no—
212C2×C3×C4—64no—
213C2×C3×C4—64no—
214C2×C3×C4—124no—
215#67—64no—
216#67—616no—
217#67—68no—
218#67—64no—
219C2×Dic3—22no—
220C2×Dic3—24no—
221C2×Dic3—24no—
222C2×Dic3—44no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—61no—
226C2×Dic3—61no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C2×Dic3—61no—
230C2×Dic3—61no—
231D12—616no—
232C4×D3—216no—
233C4×D3—68no—
234C4×D3—68no—
235C4×D3—64no—
236C4×D3—64no—
237C4×D3—64no—
238C4×D3—64no—
239Dic6—64no—
240Dic6—68no—
241Dic6—64no—
242C2×C32#41614yescomplemented
243C2×C32C22×C22⋊C411yescharacteristic
244C2×C32C2×#13512yes—
245C3⋊D3—24no—
246C3×D3—44no—
247C24—61no—
248C24—91no—
249#41—916no—
250#41—188no—
251#41—1816no—
252C2×Q8—92no—
253C2×Q8—94no—
254C2×Q8—181no—
255C2×Q8—182no—
256C2×D4—92no—
257C2×D4—94no—
258C2×D4—184no—
259C2×D4—188no—
260C2×D4—181no—
261C2×D4—182no—
262C22×C4—61no—
263C22×C4—64no—
264C22×C4—68no—
265C22×C4—62no—
266C22×C4—91no—
267C22×C4—92no—
268C22×C4—92no—
269C22×C4—94no—
270C22×C4—94no—
271C22×C4GO+(4,𝔽2)11yescharacteristic
272C2×C8—94no—
273C2×C8—188no—
274C2×C8—184no—
275C4⋊C4—94no—
276C4⋊C4—182no—
277C22⋊C4—184no—
278C42—64no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—24no—
282C22×C3—24no—
283C22×C3—22no—
284C22×C3—22no—
285C22×C3—64no—
286C22×C3—128no—
287C22×C3—124no—
288C2×D3—24no—
289C2×D3—48no—
290C2×D3—44no—
291C2×D3—64no—
292C2×D3—64no—
293C2×D3—128no—
294C2×D3—128no—
295C2×D3—124no—
296C2×D3—124no—
297C3×C4—24no—
298C3×C4—24no—
299C3×C4—64no—
300C3×C4—124no—
301Dic3—24no—
302Dic3—44no—
303Dic3—62no—
304Dic3—61no—
305Dic3—61no—
306Dic3—62no—
307Dic3—61no—
308Dic3—61no—
309C32C2×#41611yescharacteristic, complemented, Sylow
310C23—62no—
311C23—64no—
312C23—92no—
313C23—94no—
314C23—124no—
315C23—184no—
316C23C2×GO+(4,𝔽2)11yescharacteristic
317Q8—94no—
318Q8—182no—
319Q8—184no—
320D4—94no—
321D4—1816no—
322D4—182no—
323D4—184no—
324C2×C4—62no—
325C2×C4—64no—
326C2×C4—616no—
327C2×C4—64no—
328C2×C4—91no—
329C2×C4—91no—
330C2×C4—92no—
331C2×C4—92no—
332C2×C4—94no—
333C2×C4—94no—
334C2×C4—98no—
335C2×C4—124no—
336C2×C4D32⋊C414yes—
337C2×C4C2×GO+(4,𝔽2)12yes—
338C8—184no—
339C2×C3—24no—
340C2×C3—24no—
341C2×C3—22no—
342C2×C3—22no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—124no—
346D3—44no—
347D3—124no—
348D3—124no—
349C22—64no—
350C22—94no—
351C22—128no—
352C22—124no—
353C22—188no—
354C22—184no—
355C22#6422314yes—
356C22C2×D32⋊C412yes—
357C22C22×GO+(4,𝔽2)11yescharacteristic
358C4—64no—
359C4—91no—
360C4—91no—
361C4—92no—
362C4—124no—
363C4C2×D32⋊C414yes—
364C3—21no—
365C3—21no—
366C2—124no—
367C2—184no—
368C2#1059334914yesdirect product factor
369C2C2×#6422312yes—
370C2C22×D32⋊C411yescharacteristic
subgroupG/H
center, hypercenterC22×C4GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#3798C2
cosocleC2×C3⋊Dic3C24
hypocenterC32C2×#416
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3787C2semidirect
3. C2×#63874C2semidirect
4. C2×#63740C2semidirect
5. C2×#63739C2semidirect
6. #10593349C2direct (N × H)
14. C2×#3798C4semidirect
18. C2×#3787C22semidirect
23. #63874C22semidirect
24. #63740C22semidirect
25. #63739C22semidirect
52. #3798C2×C4semidirect
242. C2×C32#416semidirect
309. C32C2×#416semidirect
368. C2#10593349direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37982
C22×#37872
C2×#638742
C2×#637402
C2×#637392
#105933492
C2×#4169