Finite Group Databasebeta

← C2×#10590552 #11873371

Subgroups — C2×#10590552 #11873371

Order 1152.

1201 conjugacy classes of subgroups; only the 228 normal subgroups are shown.

normal subgroups only

This group has 1201 conjugacy classes of subgroups — too many to draw. Only its 228 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×#64097C211yesmaximal, characteristic, complemented
2C2×#63914C211yesmaximal, characteristic
3C2×C3×#809C212yesmaximal, complemented
4C2×#63563C212yesmaximal, complemented
5C2×#63553C211yesmaximal, characteristic, complemented
6#10590552C218yesmaximal, direct product factor
7C2×#4760—32nomaximal
8C22×#634—21no—
9C22×C3×D12C2212yes—
10C22×#625—21no—
11C22×#625—21no—
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64097—22no—
17#64097C2214yescomplemented
18C22×C3×C3⋊C8C2212yes—
19#63914—22no—
20#63914C2214yes—
21C3×#809C2218yescomplemented
22#63563C2218yescomplemented
23#63553C2214yescomplemented
24C2×#940—32no—
25C2×#888—32no—
26C2×#888—61no—
27C2×C3×#102—32no—
28C2×#832—32no—
29C2×#821—32no—
30C2×C8×Dic3—32no—
31C2×#809D312yescomplemented
32#4760—316no—
33C23×C3×D3—22no—
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C2×#634—24no—
40C2×#634—44no—
41C2×C3×D12—24no—
42C2×C3×D12—24no—
43C2×C3×D12—22no—
44C2×C3×D12C2314yes—
45C2×#625—24no—
46C2×#625—24no—
47C2×#625—44no—
48C2×#625—44no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4C2312yes—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)C2312yes—
53#3750—24no—
54C4×C3⋊Dic3D412yes—
55C4×C3⋊Dic3C2312yes—
56C2×C3×C3⋊C8—24no—
57C2×C3×C3⋊C8C2314yes—
58C2×#486—91noSylow
59C22×C3×D4—32no—
60C22×#67—62no—
61C22×#67—62no—
62C22×D12C2×D312yes—
63C22×Dic6—62no—
64C22×Dic6—62no—
65C22×C3×C8—32no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4C2×D312yes—
68#940—38no—
69#940—64no—
70C2×C4⋊Dic3—32no—
71C2×C4⋊Dic3—61no—
72C2×Dic3⋊C4—62no—
73C2×Dic3⋊C4—62no—
74C2×C4×Dic3—32no—
75C2×C4×Dic3—61no—
76C22×C3⋊C8C2×D312yes—
77#888—38no—
78#888—64no—
79#888—64no—
80#888—64no—
81C3×#102—38no—
82#832—38no—
83#821—38no—
84C8×Dic3—38no—
85#809C2×D318yescomplemented
86C23×C32C2×D411yescharacteristic
87C22×C3×D3—24no—
88C22×C3×D3—44no—
89C22×C3×D3—44no—
90C22×C3×D3—44no—
91C2×C32×C4—22no—
92C2×C32×C4—42no—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4114yes—
95C2×C32×C4C2411yescharacteristic
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—42no—
98C2×C3⋊Dic3D814yes—
99C2×C3⋊Dic3SD1614yes—
100C2×C3⋊Dic3C2×D412yes—
101C2×C3⋊Dic3C2×D412yes—
102#634—48no—
103C3×D12—24no—
104C3×D12—24no—
105C3×D12—44no—
106#625—48no—
107#625—48no—
108C3×C3⋊C8—24no—
109C2×C4⋊Q8—91no—
110C2×#127—91no—
111#486—98no—
112C2×#102—32no—
113C2×#102—92no—
114C2×C4×C8—91no—
115C24×C3—62no—
116C23×D3—22no—
117C2×C3×D4—34no—
118C2×C3×D4—64no—
119C2×C3×D4—62no—
120C2×C3×D4—64no—
121C22×C3×C4—22no—
122C22×C3×C4—22no—
123C22×C3×C4—21no—
124C22×C3×C4C22×D312yes—
125C2×#67—68no—
126C2×#67—68no—
127C2×#67—128no—
128C2×#67—128no—
129C22×Dic3—32no—
130C22×Dic3—32no—
131C22×Dic3—61no—
132C22×Dic3—61no—
133C22×Dic3—62no—
134C22×Dic3—62no—
135C2×D12—24no—
136C2×D12—24no—
137C2×D12—22no—
138C2×D12C22×D314yes—
139C2×Dic6—68no—
140C2×Dic6—68no—
141C2×Dic6—128no—
142C2×Dic6—128no—
143C2×C3×C8—34no—
144C2×C3×C8—64no—
145C3×C4⋊C4—22no—
146C3×C4⋊C4—22no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4C22×D314yes—
149C4⋊Dic3—34no—
150C4⋊Dic3—62no—
151C4⋊Dic3—62no—
152C4⋊Dic3—62no—
153Dic3⋊C4—68no—
154Dic3⋊C4—68no—
155C4×Dic3—34no—
156C4×Dic3—34no—
157C4×Dic3—62no—
158C4×Dic3—62no—
159C2×C3⋊C8—24no—
160C2×C3⋊C8C22×D314yes—
161C22×C32#12412yes—
162C22×C32C2×D812yes—
163C22×C32C2×SD1612yes—
164C22×C32C22×D411yescharacteristic
165C2×C3×D3—44no—
166C2×C3×D3—44no—
167C2×C3×D3—44no—
168C2×C3×D3—88no—
169C32×C4—42no—
170C32×C4#12412yes—
171C32×C4C2×#4112yes—
172C3⋊Dic3—42no—
173C3⋊Dic3C2×D814yes—
174C3⋊Dic3C2×SD1614yes—
175C22×Q8—181no—
176C22×D4—32no—
177C22×D4—181no—
178C22×D4—181no—
179C22×C8—32no—
180C4⋊Q8—94no—
181C4⋊Q8—182no—
182#127—94no—
183#127—182no—
184C2×C4⋊C4—91no—
185C2×C4⋊C4—181no—
186C2×C4⋊C4D3211yescharacteristic
187C2×C42—91no—
188#102—38no—
189#102—98no—
190C4×C8—94no—
191C23×C3—21no—
192C23×C3—64no—
193C23×C3—124no—
194C23×C3—124no—
195C23×C3—124no—
196C23×C3D3×D412yes—
197C22×D3—24no—
198C22×D3—44no—
199C22×D3—44no—
200C22×D3—44no—
201C3×D4—64no—
202C3×D4—64no—
203C3×D4—124no—
204C2×C3×C4—24no—
205C2×C3×C4—24no—
206C2×C3×C4—21no—
207C2×C3×C4—24no—
208C2×C3×C4—21no—
209C2×C3×C4—44no—
210C2×C3×C4—44no—
211C2×C3×C4#23514yes—
212C2×C3×C4D3×D412yes—
213C2×C3×C4#23714yes—
214C2×C3×C4C23×D312yes—
215#67—1216no—
216#67—1216no—
217C2×Dic3—38no—
218C2×Dic3—38no—
219C2×Dic3—34no—
220C2×Dic3—34no—
221C2×Dic3—64no—
222C2×Dic3—64no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—64no—
226C2×Dic3—64no—
227C2×Dic3—124no—
228C2×Dic3—124no—
229D12—24no—
230D12—24no—
231D12—44no—
232Dic6—1216no—
233Dic6—1216no—
234C3×C8—64no—
235C3⋊C8—24no—
236C2×C32#48614yescomplemented
237C2×C32C2×#12411yescharacteristic
238C2×C32C22×D811yescharacteristic
239C2×C32C22×SD1611yescharacteristic
240C3×D3—84no—
241C24—62no—
242C2×Q8—184no—
243C2×Q8—364no—
244C2×D4—34no—
245C2×D4—64no—
246C2×D4—64no—
247C2×D4—62no—
248C2×D4—184no—
249C2×D4—184no—
250C2×D4—364no—
251C2×D4—364no—
252C22×C4—21no—
253C22×C4—91no—
254C22×C4—91no—
255C22×C4—181no—
256C22×C4C2×D3211yescharacteristic
257C2×C8—34no—
258C2×C8—64no—
259C4⋊C4—21no—
260C4⋊C4—92no—
261C4⋊C4—184no—
262C4⋊C4—181no—
263C4⋊C4C2×D3212yes—
264C42—92no—
265C42—92no—
266C22×C3—21no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—124no—
271C22×C3—124no—
272C22×C3—124no—
273C22×C3—248no—
274C22×C3#88514yes—
275C22×C3D3×D814yes—
276C22×C3D3×SD1614yes—
277C22×C3C2×D3×D412yes—
278C2×D3—44no—
279C2×D3—44no—
280C2×D3—44no—
281C2×D3—88no—
282C3×C4—22no—
283C3×C4—22no—
284C3×C4—44no—
285C3×C4—44no—
286C3×C4#88514yes—
287C3×C4C2×#23512yes—
288C3×C4C2×#23712yes—
289Dic3—38no—
290Dic3—38no—
291Dic3—64no—
292Dic3—64no—
293Dic3—124no—
294Dic3—124no—
295C32C2×#48611yescharacteristic, complemented, Sylow
296C23—64no—
297C23—124no—
298C23—124no—
299C23—124no—
300C23#381111yescharacteristic
301Q8—368no—
302D4—64no—
303D4—64no—
304D4—124no—
305D4—368no—
306D4—368no—
307C2×C4—22no—
308C2×C4—42no—
309C2×C4—92no—
310C2×C4—92no—
311C2×C4—94no—
312C2×C4—94no—
313C2×C4—182no—
314C2×C4—362no—
315C2×C4#379514yes—
316C2×C4#381111yescharacteristic
317C2×C4C22×D3211yescharacteristic
318C8—64no—
319C2×C3—21no—
320C2×C3—24no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—244no—
324C2×C3#476018yescomplemented
325C2×C3C2×#88512yes—
326C2×C3C2×D3×D812yes—
327C2×C3C2×D3×SD1612yes—
328D3—84no—
329C22—124no—
330C22—124no—
331C22—124no—
332C22—248no—
333C22#6391312yes—
334C22#6392612yes—
335C22#6394012yes—
336C22C2×#381111yescharacteristic
337C4—42no—
338C4—94no—
339C4—94no—
340C4—362no—
341C4#6391312yes—
342C4C2×#379512yes—
343C3—21no—
344C3C2×#476012yescomplemented
345C2—244no—
346C2#1059055214yesdirect product factor
347C2C2×#6391311yescharacteristic
348C2C2×#6392611yescharacteristic
349C2C2×#6394011yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63914C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#486
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64097C2semidirect
3. C2×C3×#809C2semidirect
4. C2×#63563C2semidirect
5. C2×#63553C2semidirect
6. #10590552C2direct (N × H)
17. #64097C22semidirect
21. C3×#809C22semidirect
22. #63563C22semidirect
23. #63553C22semidirect
31. C2×#809D3semidirect
85. #809C2×D3semidirect
236. C2×C32#486semidirect
295. C32C2×#486semidirect
324. C2×C3#4760semidirect
344. C3C2×#4760semidirect
346. C2#10590552direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640972
C2×#639142
C2×C3×#8092
C2×#635632
C2×#635532
#105905522
C2×#47603