Finite Group Databasebeta

← C2×#10593498 #11857809

Subgroups — C2×#10593498 #11857809

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×#3805C211yesmaximal, characteristic
2C23×#622C211yesmaximal, characteristic, complemented
3C2×#63957C211yesmaximal, characteristic, complemented
4C2×#63740C212yesmaximal, complemented
5#10593498C218yesmaximal, direct product factor
6C2×#63739C212yesmaximal, complemented
7C23×C3⋊Dic3C2211yescharacteristic
8C22×C3×#67—21no—
9C22×#627C2211yescharacteristic
10C22×#625C2211yescharacteristic
11C2×#3805—24no—
12C2×#3805—22no—
13C2×#3805C418yescomplemented
14C2×#3805C2214yes—
15C22×D3×Dic3—21no—
16C22×#622—24no—
17C22×#622C2212yes—
18C22×#622C2214yescomplemented
19C2×C3×#217—21no—
20C2×#3724C2212yes—
21#63957—22no—
22#63957C2214yescomplemented
23C2×Dic32—21no—
24#63740C2218yescomplemented
25#63739C2218yescomplemented
26C22×#237—61no—
27C2×#877—61no—
28C24×C32D411yescharacteristic
29C23×C3×D3—21no—
30C22×C3⋊Dic3C2×C414yes—
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3⋊Dic3D412yes—
33C22×C3⋊Dic3D414yes—
34C22×C3⋊Dic3C2311yescharacteristic
35C22×C3⋊Dic3C2312yes—
36C2×C3×#67—28no—
37C2×C3×#67—24no—
38C22×C3×Dic3—21no—
39C22×C3×Dic3—22no—
40C2×#627—21no—
41C2×#627—22no—
42C2×#627C2×C414yes—
43C2×#627C2312yes—
44C2×#625—21no—
45C2×#625—22no—
46C2×#625C2×C414yes—
47C2×#625C2312yes—
48#3805—216no—
49#3805—28no—
50#3805C2×C4116yescomplemented
51C2×D3×Dic3—28no—
52C2×D3×Dic3—24no—
53C2×#622—24no—
54C2×#622—28no—
55C2×#622C2314yes—
56C3×#217—24no—
57#3724—22no—
58#3724C2314yes—
59Dic32—24no—
60C2×#416—91nomaximal, Sylow
61C22×C3×D4—61no—
62C22×#67—21no—
63C22×#67—61no—
64C23×Dic3—61no—
65C23×Dic3—61no—
66C23×Dic3—61no—
67C2×#237—68no—
68C2×#237—64no—
69C2×#237—64no—
70C2×#237—68no—
71C22×C4×D3—61no—
72C22×Dic6—61no—
73C2×C3×C22⋊C4—61no—
74C2×#217—21no—
75C2×Dic3⋊C4—62no—
76C2×C4×Dic3—62no—
77#877—64no—
78#877—64no—
79C23×C32—24no—
80C23×C32C22⋊C414yes—
81C23×C32C2×D412yes—
82C23×C32C2×D411yescharacteristic
83C22×C3×D3—24no—
84C22×C3×D3—22no—
85C22×C3×D3—44no—
86C2×C3⋊Dic3C22⋊C414yes—
87C2×C3⋊Dic3C22⋊C418yes—
88C2×C3⋊Dic3C22×C414yes—
89C2×C3⋊Dic3C22×C412yes—
90C2×C3⋊Dic3C2×D412yes—
91C2×C3⋊Dic3C2×D411yescharacteristic
92C2×C3⋊Dic3C2×D414yes—
93C2×C3⋊Dic3C2×D412yes—
94C2×C3⋊Dic3C2411yescharacteristic
95C3×#67—216no—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—44no—
100#627—24no—
101#627—22no—
102#627C22×C414yes—
103#625—24no—
104#625—22no—
105#625C22×C414yes—
106D3×Dic3—216no—
107#622—24no—
108C22×#41—91no—
109C23×C8—91no—
110C2×#117—91no—
111#416—98no—
112C2×#103—92no—
113C2×#102—92no—
114C24×C3—21no—
115C24×C3—21no—
116C24×C3—61no—
117C23×D3—21no—
118C2×C3×D4—64no—
119C2×C3×D4—68no—
120C22×C3×C4—61no—
121C22×C3×C4—62no—
122C2×#67—24no—
123C2×#67—28no—
124C2×#67—64no—
125C2×#67—62no—
126C2×#67—62no—
127C2×#67—64no—
128C22×Dic3—21no—
129C22×Dic3—22no—
130C22×Dic3—62no—
131C22×Dic3—62no—
132C22×Dic3—61no—
133C22×Dic3—61no—
134C22×Dic3—61no—
135C22×Dic3—61no—
136C22×Dic3—64no—
137C22×Dic3—62no—
138C22×Dic3—64no—
139C22×Dic3—62no—
140C22×Dic3—64no—
141C22×Dic3—64no—
142C22×Dic3—68no—
143C22×Dic3—64no—
144#237—616no—
145#237—632no—
146#237—616no—
147C2×C4×D3—68no—
148C2×C4×D3—64no—
149C2×Dic6—64no—
150C2×Dic6—62no—
151C2×Dic6—62no—
152C2×Dic6—64no—
153C3×C22⋊C4—64no—
154#217—24no—
155Dic3⋊C4—64no—
156Dic3⋊C4—64no—
157C4×Dic3—68no—
158C22×C32—24no—
159C22×C32—28no—
160C22×C32C2×C22⋊C414yes—
161C22×C32C2×C22⋊C412yes—
162C22×C32#13514yes—
163C22×C32C22×D411yescharacteristic
164C2×C3×D3—24no—
165C2×C3×D3—44no—
166C2×C3×D3—48no—
167C3⋊Dic3C2×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—61no—
179C22×D4—91no—
180C23×C4—91no—
181C23×C4—181no—
182C22×C8—92no—
183C22×C8—94no—
184C22×C8—184no—
185#117—94no—
186#117—182no—
187C2×C4⋊C4—92no—
188C2×C22⋊C4—61no—
189C2×C42—181no—
190#103—98no—
191#102—98no—
192C23×C3—22no—
193C23×C3—22no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—24no—
197C23×C3—24no—
198C23×C3—44no—
199C23×C3—44no—
200C23×C3—62no—
201C23×C3—64no—
202C23×C3—124no—
203C22×D3—22no—
204C22×D3—24no—
205C22×D3—44no—
206C3×D4—616no—
207C2×C3×C4—62no—
208C2×C3×C4—64no—
209C2×C3×C4—64no—
210C2×C3×C4—124no—
211#67—216no—
212#67—64no—
213#67—68no—
214#67—64no—
215C2×Dic3—22no—
216C2×Dic3—24no—
217C2×Dic3—24no—
218C2×Dic3—44no—
219C2×Dic3—64no—
220C2×Dic3—68no—
221C2×Dic3—64no—
222C2×Dic3—68no—
223C2×Dic3—62no—
224C2×Dic3—64no—
225C2×Dic3—62no—
226C2×Dic3—64no—
227C2×Dic3—62no—
228C2×Dic3—61no—
229C2×Dic3—61no—
230C2×Dic3—62no—
231C2×Dic3—62no—
232C2×Dic3—64no—
233C2×Dic3—62no—
234C2×Dic3—64no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—616no—
238C4×D3—616no—
239Dic6—64no—
240Dic6—68no—
241Dic6—64no—
242C2×C32—24no—
243C2×C32#41614yescomplemented
244C2×C32C22×C22⋊C411yescharacteristic
245C2×C32C2×#13512yes—
246C3×D3—44no—
247C24—61no—
248C24GO+(4,𝔽2)11yescharacteristic
249#41—916no—
250#41—188no—
251#41—1816no—
252C2×Q8—92no—
253C2×Q8—94no—
254C2×Q8—181no—
255C2×Q8—182no—
256C2×D4—64no—
257C2×D4—68no—
258C2×D4—92no—
259C2×D4—94no—
260C2×D4—181no—
261C2×D4—182no—
262C22×C4—61no—
263C22×C4—62no—
264C22×C4—92no—
265C22×C4—92no—
266C22×C4—91no—
267C22×C4—91no—
268C22×C4—94no—
269C22×C4—94no—
270C22×C4—184no—
271C22×C4—188no—
272C2×C8—94no—
273C2×C8—184no—
274C2×C8—188no—
275C4⋊C4—94no—
276C4⋊C4—182no—
277C22⋊C4—64no—
278C42—184no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—22no—
282C22×C3—22no—
283C22×C3—24no—
284C22×C3—24no—
285C22×C3—24no—
286C22×C3—24no—
287C22×C3—44no—
288C22×C3—44no—
289C22×C3—48no—
290C22×C3—48no—
291C22×C3—64no—
292C22×C3—124no—
293C22×C3—128no—
294C2×D3—24no—
295C2×D3—44no—
296C2×D3—48no—
297C3×C4—64no—
298C3×C4—124no—
299Dic3—24no—
300Dic3—44no—
301Dic3—62no—
302Dic3—61no—
303Dic3—61no—
304Dic3—64no—
305Dic3—64no—
306Dic3—62no—
307Dic3—61no—
308Dic3—61no—
309C32C2×#41611yescharacteristic, complemented, Sylow
310C23—24no—
311C23—62no—
312C23—64no—
313C23—124no—
314C23D32⋊C414yes—
315C23C2×GO+(4,𝔽2)12yes—
316C23C2×GO+(4,𝔽2)11yescharacteristic
317Q8—94no—
318Q8—182no—
319Q8—184no—
320D4—616no—
321D4—94no—
322D4—182no—
323D4—184no—
324C2×C4—62no—
325C2×C4—64no—
326C2×C4—64no—
327C2×C4—92no—
328C2×C4—91no—
329C2×C4—91no—
330C2×C4—92no—
331C2×C4—94no—
332C2×C4—94no—
333C2×C4—92no—
334C2×C4—94no—
335C2×C4—98no—
336C2×C4—124no—
337C2×C4—1816no—
338C8—184no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—22no—
342C2×C3—22no—
343C2×C3—24no—
344C2×C3—24no—
345C2×C3—44no—
346C2×C3—44no—
347C2×C3—124no—
348D3—44no—
349C22—24no—
350C22—28no—
351C22—64no—
352C22—124no—
353C22—128no—
354C22C2×D32⋊C414yes—
355C22C2×D32⋊C412yes—
356C22#6423714yes—
357C22C22×GO+(4,𝔽2)11yescharacteristic
358C4—64no—
359C4—91no—
360C4—94no—
361C4—91no—
362C4—92no—
363C4—124no—
364C3—21no—
365C3—21no—
366C2—24no—
367C2—124no—
368C2#1059349814yesdirect product factor
369C2C22×D32⋊C411yescharacteristic
370C2C2×#6423712yes—
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC24×C32D4
socleC23×C32C2×D4
prime radicalC22×#3805C2
cosocleC2×C3⋊Dic3C24
hypercenterC24GO+(4,𝔽2)
hypocenterC32C2×#416
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C23×#622C2semidirect
3. C2×#63957C2semidirect
4. C2×#63740C2semidirect
5. #10593498C2direct (N × H)
6. C2×#63739C2semidirect
13. C2×#3805C4semidirect
18. C22×#622C22semidirect
22. #63957C22semidirect
24. #63740C22semidirect
25. #63739C22semidirect
50. #3805C2×C4semidirect
243. C2×C32#416semidirect
309. C32C2×#416semidirect
368. C2#10593498direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38052
C23×#6222
C2×#639572
C2×#637402
#105934982
C2×#637392
C2×#4169