Finite Group Databasebeta

← C2×#10596513 #11901169

Subgroups — C2×#10596513 #11901169

Order 1152.

2530 conjugacy classes of subgroups; only the 455 normal subgroups are shown.

normal subgroups only

This group has 2530 conjugacy classes of subgroups — too many to draw. Only its 455 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
1C2×#64306C212yesmaximal, complemented
2C22×C4⋊#157C211yesmaximal, characteristic, complemented
3C2×#64242C214yesmaximal, complemented
4#10596513C2116yesmaximal, direct product factor
5C2×#64230C214yesmaximal, complemented
6C2×D32⋊Q8C214yesmaximal, complemented
7C23×#157C2212yes—
8C22×GO+(4,𝔽2)C2214yes—
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C3×#235—22no—
11C2×#3811C2214yes—
12C2×#3805—22no—
13#64306—28no—
14#64306C22116yescomplemented
15C2×#3802C2212yes—
16C2×C4×D32C2214yes—
17C2×#3798—22no—
18C2×#3797C2212yes—
19C2×#3796—22no—
20C2×C4⋊#157C2214yes—
21C2×C4⋊#157C2218yescomplemented
22#64242C22132yescomplemented
23C2×#3773C2214yes—
24C2×D32⋊C4C2218yes—
25#64230C22132yescomplemented
26D32⋊Q8C22132yescomplemented
27C2×D3×#41—62no—
28C23×C3⋊D3C2311yescharacteristic
29C22×D32C2314yes—
30C22×#157—44no—
31C22×#157C2314yes—
32C22×#157C2318yes—
33C2×GO+(4,𝔽2)—48no—
34C2×GO+(4,𝔽2)C23116yes—
35C22×C32×C4D411yescharacteristic, complemented
36C22×C3⋊Dic3D411yescharacteristic, complemented
37C2×C4×C3⋊D3D414yescomplemented
38C2×C4×C3⋊D3D412yescomplemented
39C2×C4×C3⋊D3C2312yes—
40C2×C4×C3⋊D3C2314yes—
41C2×C3×#67—24no—
42C3×#235—216no—
43C2×C3×D12—22no—
44C2×C3×C4×D3—24no—
45C2×C3×Dic6—22no—
46#3811—28no—
47#3811C23116yes—
48C2×#627—22no—
49C2×#626—24no—
50C2×#625—22no—
51C2×#624C2314yes—
52#3805—216no—
53C2×D3×Dic3—24no—
54#3802—24no—
55#3802C2318yes—
56C4×D32—28no—
57C4×D32C23116yes—
58#3798—216no—
59#3797—24no—
60#3797C2318yes—
61#3796—216no—
62C4⋊#157C23116yes—
63#3773C23116yes—
64D32⋊C4C23132yes—
65C2×#537—91nomaximal, Sylow
66C2×C3×#41—62no—
67D3×#41—616no—
68D3×#41—616no—
69C2×#239—62no—
70C2×D3×Q8—62no—
71C2×#237—62no—
72C2×#237—64no—
73C2×D3×D4—62no—
74C2×D3×D4—64no—
75C2×#235—22no—
76C2×#235—64no—
77C22×C4×D3—64no—
78C22×C4×D3—62no—
79C23×C32C2×D411yescharacteristic
80C22×C3⋊D3—22no—
81C22×C3⋊D3—22no—
82C22×C3⋊D3C2×D411yescharacteristic
83C22×C3⋊D3C2×D412yes—
84C22×C3⋊D3C2412yes—
85C22×C3⋊D3C2411yescharacteristic
86C22×C3×D3—24no—
87C2×D32—24no—
88C2×D32—28no—
89C2×D32—28no—
90C2×D32C2418yes—
91C2×#157—28no—
92C2×#157—48no—
93C2×#157C2418yes—
94GO+(4,𝔽2)—416no—
95C2×C32×C4C2×D412yes—
96C2×C32×C4C2×D414yescomplemented
97C2×C3⋊Dic3C2×D412yes—
98C2×C3⋊Dic3C2×D414yescomplemented
99C4×C3⋊D3C2×D414yes—
100C4×C3⋊D3C2×D418yescomplemented
101C4×C3⋊D3C2414yes—
102C3×#67—216no—
103C2×C3×Dic3—24no—
104C3×D12—28no—
105C3×C4×D3—216no—
106C3×Dic6—28no—
107#627—28no—
108#626—216no—
109#625—28no—
110#624—24no—
111#624C2418yes—
112D3×Dic3—216no—
113C22×#41—92no—
114#537—916no—
115C2×C22⋊Q8—94no—
116C2×#121—94no—
117C2×#121—94no—
118C22×C4⋊C4—91no—
119C23×D3—64no—
120C23×D3—62no—
121C3×#41—616no—
122C2×C3×Q8—62no—
123C2×C3×D4—62no—
124C2×C3×D4—64no—
125C22×C3×C4—22no—
126C22×C3×C4—64no—
127C2×#67—24no—
128C2×#67—64no—
129C2×#67—64no—
130C22×Dic3—62no—
131C22×Dic3—64no—
132#239—616no—
133D3×Q8—68no—
134D3×Q8—68no—
135#237—616no—
136#237—632no—
137D3×D4—68no—
138D3×D4—616no—
139D3×D4—68no—
140D3×D4—616no—
141#235—216no—
142#235—632no—
143C2×D12—22no—
144C2×D12—64no—
145C2×C4×D3—24no—
146C2×C4×D3—616no—
147C2×C4×D3—64no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×C4×D3—68no—
153C2×C4×D3—68no—
154C2×C4×D3—616no—
155C2×C4×D3—64no—
156C2×Dic6—22no—
157C2×Dic6—64no—
158C22×C32—22no—
159C22×C32C22×D412yes—
160C22×C32C22×D411yescharacteristic
161C2×C3⋊D3—22no—
162C2×C3⋊D3—24no—
163C2×C3⋊D3—22no—
164C2×C3⋊D3—22no—
165C2×C3⋊D3C22×D412yes—
166C2×C3⋊D3C22×D411yescharacteristic
167C2×C3⋊D3H(5,𝔽2)12yes—
168C2×C3⋊D32−1+412yes—
169C2×C3⋊D3C2511yescharacteristic
170C2×C3×D3—28no—
171C2×C3×D3—48no—
172D32—28no—
173D32—28no—
174D32—48no—
175#157—28no—
176C32×C4C22×D414yes—
177C3⋊Dic3C22×D414yes—
178C3×Dic3—28no—
179C2×#41—62no—
180C2×#41—916no—
181C2×#41—182no—
182C2×#41—182no—
183C2×#41—182no—
184C2×#41—188no—
185C22×Q8—92no—
186C22×D4—94no—
187C22×D4—92no—
188C22×D4—94no—
189C23×C4—94no—
190C23×C4—91no—
191C23×C4—92no—
192C22⋊Q8—932no—
193#121—932no—
194#121—932no—
195C2×C4⋊C4—94no—
196C2×C4⋊C4—98no—
197C2×C4⋊C4—94no—
198C2×C22⋊C4—98no—
199C23×C3—22no—
200C23×C3—64no—
201C22×D3—24no—
202C22×D3—68no—
203C22×D3—62no—
204C22×D3—62no—
205C22×D3—64no—
206C22×D3—64no—
207C22×D3—68no—
208C22×D3—128no—
209C22×D3—128no—
210C22×D3—124no—
211C22×D3—124no—
212C3×Q8—68no—
213C3×D4—68no—
214C3×D4—616no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—28no—
218C2×C3×C4—616no—
219C2×C3×C4—64no—
220#67—216no—
221#67—616no—
222#67—616no—
223C2×Dic3—24no—
224C2×Dic3—62no—
225C2×Dic3—62no—
226C2×Dic3—68no—
227C2×Dic3—616no—
228D12—28no—
229D12—616no—
230C4×D3—216no—
231C4×D3—68no—
232C4×D3—64no—
233C4×D3—64no—
234C4×D3—68no—
235C4×D3—68no—
236C4×D3—64no—
237C4×D3—64no—
238C4×D3—68no—
239C4×D3—616no—
240Dic6—28no—
241Dic6—616no—
242C2×C32—22no—
243C2×C32#53712yescomplemented
244C2×C32C23×D411yescharacteristic
245C3⋊D3—22no—
246C3⋊D3#53712yescomplemented
247C3⋊D3C2×H(5,𝔽2)11yescharacteristic
248C3⋊D3C2×2−1+411yescharacteristic
249C3×D3—48no—
250C24—94no—
251C24—91no—
252#41—616no—
253#41—1816no—
254#41—1816no—
255#41—1816no—
256C2×Q8—62no—
257C2×Q8—98no—
258C2×Q8—182no—
259C2×Q8—184no—
260C2×D4—64no—
261C2×D4—62no—
262C2×D4—916no—
263C2×D4—98no—
264C2×D4—916no—
265C2×D4—184no—
266C2×D4—184no—
267C2×D4—182no—
268C2×D4—188no—
269C2×D4—368no—
270C22×C4—64no—
271C22×C4—94no—
272C22×C4—916no—
273C22×C4—91no—
274C22×C4—92no—
275C22×C4—92no—
276C22×C4—94no—
277C22×C4—94no—
278C22×C4—94no—
279C22×C4—98no—
280C22×C4—188no—
281C22×C4—184no—
282C22×C4—364no—
283C22×C4GO+(4,𝔽2)11yescharacteristic, complemented
284C4⋊C4—916no—
285C4⋊C4—916no—
286C22⋊C4—932no—
287C22×C3—24no—
288C22×C3—22no—
289C22×C3—44no—
290C22×C3—68no—
291C22×C3—128no—
292C2×D3—28no—
293C2×D3—48no—
294C2×D3—62no—
295C2×D3—62no—
296C2×D3—64no—
297C2×D3—64no—
298C2×D3—64no—
299C2×D3—128no—
300C2×D3—128no—
301C2×D3—124no—
302C2×D3—128no—
303C2×D3—124no—
304C2×D3—124no—
305C2×D3—1216no—
306C3×C4—24no—
307C3×C4—24no—
308C3×C4—68no—
309Dic3—28no—
310Dic3—64no—
311Dic3—64no—
312C32C2×#53711yescharacteristic, complemented, Sylow
313C23—64no—
314C23—98no—
315C23—91no—
316C23—92no—
317C23—92no—
318C23—91no—
319C23—182no—
320C23—182no—
321C23—184no—
322C23—188no—
323C23—188no—
324C23C2×GO+(4,𝔽2)11yescharacteristic
325Q8—68no—
326Q8—188no—
327D4—616no—
328D4—68no—
329D4—1816no—
330D4—188no—
331D4—3616no—
332C2×C4—64no—
333C2×C4—616no—
334C2×C4—98no—
335C2×C4—94no—
336C2×C4—92no—
337C2×C4—94no—
338C2×C4—94no—
339C2×C4—98no—
340C2×C4—98no—
341C2×C4—184no—
342C2×C4—1816no—
343C2×C4—188no—
344C2×C4—368no—
345C2×C4C2×GO+(4,𝔽2)12yes—
346C2×C4C2×GO+(4,𝔽2)14yescomplemented
347C2×C3—24no—
348C2×C3—22no—
349C2×C3—44no—
350C2×C3—128no—
351D3—48no—
352D3—64no—
353D3—62no—
354D3—62no—
355D3—124no—
356C22—22no—
357C22—68no—
358C22—92no—
359C22—92no—
360C22—91no—
361C22—91no—
362C22—92no—
363C22—128no—
364C22—182no—
365C22—182no—
366C22—184no—
367C22—188no—
368C22—188no—
369C22—182no—
370C22—368no—
371C22C22×GO+(4,𝔽2)12yes—
372C22C22×GO+(4,𝔽2)11yescharacteristic
373C4—68no—
374C4—94no—
375C4—188no—
376C4C22×GO+(4,𝔽2)14yes—
377C3—22no—
378C2—22no—
379C2—91no—
380C2—91no—
381C2—92no—
382C2—128no—
383C2—182no—
384C2#1059651312yesdirect product factor
385C2C23×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊D3C25
FrattiniC2C23×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C22×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#537
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64306C2semidirect
2. C22×C4⋊#157C2semidirect
3. C2×#64242C2semidirect
4. #10596513C2direct (N × H)
5. C2×#64230C2semidirect
6. C2×D32⋊Q8C2semidirect
14. #64306C22semidirect
21. C2×C4⋊#157C22semidirect
22. #64242C22semidirect
25. #64230C22semidirect
26. D32⋊Q8C22semidirect
35. C22×C32×C4D4semidirect
36. C22×C3⋊Dic3D4semidirect
37. C2×C4×C3⋊D3D4semidirect
38. C2×C4×C3⋊D3D4semidirect
96. C2×C32×C4C2×D4semidirect
98. C2×C3⋊Dic3C2×D4semidirect
100. C4×C3⋊D3C2×D4semidirect
243. C2×C32#537semidirect
246. C3⋊D3#537semidirect
283. C22×C4GO+(4,𝔽2)semidirect
312. C32C2×#537semidirect
346. C2×C4C2×GO+(4,𝔽2)semidirect
384. C2#10596513direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643062
C22×C4⋊#1572
C2×#642422
#105965132
C2×#642302
C2×D32⋊Q82
C2×#5379