Finite Group Databasebeta

← C2×#10593365 #11857736

Subgroups — C2×#10593365 #11857736

Order 1152.

1962 conjugacy classes of subgroups; only the 247 normal subgroups are shown.

normal subgroups only

This group has 1962 conjugacy classes of subgroups — too many to draw. Only its 247 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×#3802C211yesmaximal, characteristic
2C22×#3787C211yesmaximal, characteristic, complemented
3C2×#63900C211yesmaximal, characteristic, complemented
4C2×#63739C214yesmaximal, complemented
5#10593365C218yesmaximal, direct product factor
6C23×D32—21no—
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×C3×D12—21no—
9C22×#625C2212yes—
10C22×#624—21no—
11C2×#3802—24no—
12C2×#3802—22no—
13C2×#3802C418yescomplemented
14C2×#3802C2214yes—
15C22×#622C2212yescomplemented
16C2×#3787—24no—
17C2×#3787C2214yescomplemented
18C2×C3×C4⋊Dic3—21no—
19C2×#3724C2212yescomplemented
20#63900—22no—
21#63900C2214yescomplemented
22#63739C22116yescomplemented
23C22×D3×D4—61no—
24C2×D3×C4⋊C4—61no—
25C23×C3⋊D3D411yescharacteristic
26C23×C3×D3—22no—
27C22×D32—28no—
28C22×D32—24no—
29C22×D32—44no—
30C22×D32—44no—
31C22×C32×C4D411yescharacteristic
32C22×C3⋊Dic3C2311yescharacteristic
33C2×C4×C3⋊D3C2×C414yes—
34C2×C4×C3⋊D3D412yes—
35C2×C4×C3⋊D3D414yes—
36C2×C4×C3⋊D3C2312yes—
37C22×C3×Dic3—22no—
38C2×C3×D12—28no—
39C2×C3×D12—24no—
40C2×#625—22no—
41C2×#625—24no—
42C2×#625C2×C418yescomplemented
43C2×#625C2314yes—
44C2×#624—24no—
45C2×#624—44no—
46#3802—216no—
47#3802—28no—
48#3802C2×C4116yescomplemented
49C2×#622—24no—
50C2×#622C2314yescomplemented
51#3787—28no—
52C3×C4⋊Dic3—24no—
53#3724—22no—
54#3724C2314yescomplemented
55C22×#102—91nomaximal, Sylow
56C24×D3—62no—
57C22×C3×D4—61no—
58C22×#67—62no—
59C2×D3×D4—68no—
60C2×D3×D4—64no—
61C2×D3×D4—64no—
62C2×D3×D4—68no—
63C22×D12—21no—
64C22×C4×D3—61no—
65C22×C4×D3—61no—
66C22×C4×D3—62no—
67C2×C3×C4⋊C4—61no—
68C2×C4⋊Dic3—21no—
69C2×Dic3⋊C4—62no—
70D3×C4⋊C4—64no—
71D3×C4⋊C4—64no—
72C23×C32C2×D411yescharacteristic
73C22×C3⋊D3C22⋊C414yes—
74C22×C3⋊D3D814yes—
75C22×C3⋊D3SD1614yes—
76C22×C3⋊D3C2×D412yes—
77C22×C3×D3—28no—
78C22×C3×D3—24no—
79C22×C3×D3—44no—
80C22×C3×D3—44no—
81C2×D32—216no—
82C2×D32—432no—
83C2×D32—48no—
84C2×D32—48no—
85C2×C32×C4C22⋊C414yes—
86C2×C32×C4C2×D412yes—
87C2×C3⋊Dic3C22×C412yes—
88C2×C3⋊Dic3C2×D411yescharacteristic
89C2×C3⋊Dic3C2×D412yes—
90C2×C3⋊Dic3C2411yescharacteristic
91C4×C3⋊D3C22⋊C418yes—
92C4×C3⋊D3C22×C414yes—
93C4×C3⋊D3C2×D414yes—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—44no—
96C3×D12—216no—
97#625—28no—
98#625—24no—
99#625C22×C418yescomplemented
100#624—48no—
101#622—24no—
102C23×D4—91no—
103C23×C8—91no—
104C22×C4⋊C4—91no—
105C2×#102—98no—
106C2×#102—94no—
107C24×C3—62no—
108C23×D3—22no—
109C23×D3—61no—
110C23×D3—61no—
111C23×D3—616no—
112C23×D3—68no—
113C23×D3—128no—
114C23×D3—128no—
115C2×C3×D4—64no—
116C2×C3×D4—68no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4—62no—
120C2×#67—68no—
121C2×#67—64no—
122C2×#67—64no—
123C2×#67—68no—
124C22×Dic3—22no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127D3×D4—616no—
128D3×D4—632no—
129D3×D4—616no—
130C2×D12—24no—
131C2×D12—28no—
132C2×C4×D3—62no—
133C2×C4×D3—62no—
134C2×C4×D3—64no—
135C2×C4×D3—62no—
136C2×C4×D3—64no—
137C2×C4×D3—62no—
138C2×C4×D3—64no—
139C2×C4×D3—64no—
140C2×C4×D3—68no—
141C2×C4×D3—128no—
142C3×C4⋊C4—64no—
143C4⋊Dic3—24no—
144Dic3⋊C4—64no—
145Dic3⋊C4—64no—
146C22×C32C2×C22⋊C412yes—
147C22×C32C2×D812yes—
148C22×C32C2×SD1612yes—
149C22×C32C22×D411yescharacteristic
150C2×C3⋊D3#102116yescomplemented
151C2×C3⋊D3C2×C22⋊C414yes—
152C2×C3⋊D3C2×D814yes—
153C2×C3⋊D3C2×SD1614yes—
154C2×C3×D3—28no—
155C2×C3×D3—44no—
156C2×C3×D3—44no—
157C2×C3×D3—416no—
158D32—432no—
159C32×C4C2×C22⋊C414yes—
160C3⋊Dic3C2×C22⋊C412yes—
161C3⋊Dic3C23×C411yescharacteristic
162C3⋊Dic3C22×D411yescharacteristic
163C3×Dic3—44no—
164C25—181no—
165C22×D4—61no—
166C22×D4—94no—
167C22×D4—98no—
168C22×D4—92no—
169C22×D4—182no—
170C22×D4—184no—
171C23×C4—91no—
172C23×C4—181no—
173C22×C8—94no—
174C22×C8—92no—
175C22×C8—184no—
176C2×C4⋊C4—61no—
177C2×C4⋊C4—94no—
178C2×C4⋊C4—92no—
179C2×C4⋊C4—182no—
180#102—916no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—64no—
184C23×C3—68no—
185C23×C3—124no—
186C23×C3—124no—
187C22×D3—24no—
188C22×D3—28no—
189C22×D3—44no—
190C22×D3—44no—
191C22×D3—64no—
192C22×D3—64no—
193C22×D3—64no—
194C22×D3—64no—
195C22×D3—64no—
196C22×D3—64no—
197C22×D3—62no—
198C22×D3—62no—
199C22×D3—632no—
200C22×D3—1264no—
201C22×D3—1216no—
202C22×D3—1216no—
203C3×D4—616no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—24no—
207C2×C3×C4—24no—
208C2×C3×C4—64no—
209C2×C3×C4—124no—
210#67—68no—
211#67—616no—
212#67—68no—
213C2×Dic3—24no—
214C2×Dic3—44no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—61no—
218C2×Dic3—62no—
219C2×Dic3—61no—
220C2×Dic3—62no—
221C2×Dic3—61no—
222C2×Dic3—61no—
223D12—216no—
224C4×D3—68no—
225C4×D3—68no—
226C4×D3—64no—
227C4×D3—64no—
228C4×D3—64no—
229C4×D3—64no—
230C4×D3—1216no—
231C2×C32C2×#10214yescomplemented
232C2×C32C22×C22⋊C411yescharacteristic
233C2×C32C22×D811yescharacteristic
234C2×C32C22×SD1611yescharacteristic
235C3⋊D3C2×#10218yescomplemented
236C3×D3—48no—
237C24—62no—
238C24—91no—
239C24—184no—
240C24—188no—
241C24—364no—
242C24—364no—
243C2×D4—64no—
244C2×D4—68no—
245C2×D4—916no—
246C2×D4—94no—
247C2×D4—98no—
248C2×D4—188no—
249C2×D4—1816no—
250C2×D4—182no—
251C2×D4—184no—
252C22×C4—62no—
253C22×C4—91no—
254C22×C4—92no—
255C22×C4—92no—
256C22×C4—94no—
257C22×C4—94no—
258C22×C4—184no—
259C22×C4—364no—
260C22×C4GO+(4,𝔽2)11yescharacteristic
261C2×C8—94no—
262C2×C8—188no—
263C2×C8—184no—
264C4⋊C4—64no—
265C4⋊C4—94no—
266C4⋊C4—182no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—22no—
272C22×C3—22no—
273C22×C3—22no—
274C22×C3—22no—
275C22×C3—68no—
276C22×C3—1216no—
277C22×C3—124no—
278C22×C3—124no—
279C2×D3—28no—
280C2×D3—416no—
281C2×D3—44no—
282C2×D3—44no—
283C2×D3—64no—
284C2×D3—64no—
285C2×D3—64no—
286C2×D3—616no—
287C2×D3—64no—
288C2×D3—64no—
289C2×D3—616no—
290C2×D3—64no—
291C2×D3—1264no—
292C3×C4—24no—
293C3×C4—24no—
294C3×C4—124no—
295Dic3—44no—
296Dic3—62no—
297Dic3—61no—
298Dic3—61no—
299Dic3—62no—
300Dic3—61no—
301Dic3—61no—
302C32C22×#10211yescharacteristic, complemented, Sylow
303C23—64no—
304C23—68no—
305C23—92no—
306C23—94no—
307C23—94no—
308C23—94no—
309C23—124no—
310C23—124no—
311C23—1816no—
312C23—3632no—
313C23—368no—
314C23—368no—
315C23C2×GO+(4,𝔽2)11yescharacteristic
316D4—616no—
317D4—98no—
318D4—184no—
319D4—188no—
320C2×C4—64no—
321C2×C4—91no—
322C2×C4—91no—
323C2×C4—92no—
324C2×C4—92no—
325C2×C4—94no—
326C2×C4—94no—
327C2×C4—98no—
328C2×C4—124no—
329C2×C4—368no—
330C2×C4D32⋊C414yes—
331C2×C4C2×GO+(4,𝔽2)12yes—
332C8—184no—
333C2×C3—24no—
334C2×C3—24no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—128no—
342D3—48no—
343D3—68no—
344D3—68no—
345C22—68no—
346C22—916no—
347C22—94no—
348C22—94no—
349C22—94no—
350C22—1216no—
351C22—124no—
352C22—124no—
353C22—3632no—
354C22#6422512yes—
355C22#6422712yes—
356C22C2×D32⋊C412yes—
357C22C22×GO+(4,𝔽2)11yescharacteristic
358C4—91no—
359C4—91no—
360C4—92no—
361C4—124no—
362C4C2×D32⋊C414yes—
363C3—21no—
364C3—21no—
365C2—98no—
366C2—128no—
367C2#1059336514yesdirect product factor
368C2C2×#6422511yescharacteristic
369C2C2×#6422711yescharacteristic
370C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#3802C2
cosocleC2×C3⋊Dic3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C22×#102
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3787C2semidirect
3. C2×#63900C2semidirect
4. C2×#63739C2semidirect
5. #10593365C2direct (N × H)
13. C2×#3802C4semidirect
15. C22×#622C22semidirect
17. C2×#3787C22semidirect
19. C2×#3724C22semidirect
21. #63900C22semidirect
22. #63739C22semidirect
42. C2×#625C2×C4semidirect
48. #3802C2×C4semidirect
50. C2×#622C23semidirect
54. #3724C23semidirect
99. #625C22×C4semidirect
150. C2×C3⋊D3#102semidirect
231. C2×C32C2×#102semidirect
235. C3⋊D3C2×#102semidirect
302. C32C22×#102semidirect
367. C2#10593365direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38022
C22×#37872
C2×#639002
C2×#637392
#105933652
C22×#1029