Finite Group Databasebeta

← C2×#10594313 #11903726

Subgroups — C2×#10594313 #11903726

Order 1152.

2373 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic
2C2×C3×#888C212yesmaximal
3C2×#63919C211yesmaximal, characteristic
4C2×C4×#627C211yesmaximal, characteristic
5C2×#63873C212yesmaximal
6C2×#63844C212yesmaximal
7C2×#63839C214yesmaximal
8C2×#63838C212yesmaximal
9#10594313C2116yesmaximal, direct product factor
10C2×#5722—32nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×Dic6C2214yes—
13C22×#627C2212yes—
14C22×#627C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×#3750C2212yes—
17C2×C4×C3⋊Dic3C2212yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19#64096C2218yes—
20C2×C3×C4⋊Dic3C2212yes—
21C2×C3×Dic3⋊C4C2214yes—
22C2×C3×C4×Dic3C2212yes—
23C3×#888C22116yes—
24C2×#3724C2214yes—
25C2×#3724C2211yescharacteristic
26C2×#3724C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic32C2214yes—
29#63919C2218yes—
30C4×#627C2218yes—
31#63873C22116yes—
32#63844C22116yes—
33#63839C22132yes—
34#63838C22116yes—
35C2×C3×C4⋊Q8—32no—
36C2×#944—34no—
37C2×#944—34no—
38#5722—332no—
39C2×#888—34no—
40C2×#888—32no—
41C2×#888D312yes—
42C2×#887—32no—
43C2×#887—34no—
44C2×#887—32no—
45C2×#887—61no—
46C2×C4×Dic6—32no—
47C2×C4×Dic6—32no—
48C22×C32×C4C2312yes—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3C2311yescharacteristic
51C22×C3⋊Dic3C2311yescharacteristic
52C22×C3⋊Dic3C2312yes—
53C2×#634Q818yescomplemented
54C2×#634C2314yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2314yes—
57C22×C3×Dic3C2312yes—
58C2×C3×Dic6—48no—
59C2×C3×Dic6C23116yes—
60C2×#627—44no—
61C2×#627Q818yescomplemented
62C2×#627C2318yes—
63C2×#627C2314yes—
64C32×C4⋊C4C2314yes—
65#3750C2318yes—
66C4×C3⋊Dic3C2318yes—
67C4×C3⋊Dic3C2314yes—
68C3×C4⋊Dic3C2318yes—
69C3×Dic3⋊C4C23116yes—
70C3×C4×Dic3C2318yes—
71#3724C2318yes—
72#3724C23116yes—
73#3724C2314yes—
74Dic3⋊Dic3C2318yes—
75Dic32C23116yes—
76C2×Q82—91noSylow
77C22×C3×Q8—34no—
78C22×Dic6—32no—
79C22×Dic6—32no—
80C22×Dic6—34no—
81C22×Dic6—61no—
82C22×Dic6C2×D314yes—
83C3×C4⋊Q8—316no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—34no—
86C2×C3×C4⋊C4—32no—
87C2×C3×C4⋊C4C2×D312yes—
88C2×C3×C42—32no—
89#944—332no—
90#944—332no—
91C2×C4⋊Dic3—32no—
92C2×C4⋊Dic3C2×D312yes—
93C2×Dic3⋊C4—34no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—34no—
96C2×Dic3⋊C4—32no—
97C2×Dic3⋊C4—34no—
98C2×Dic3⋊C4—34no—
99C2×Dic3⋊C4—62no—
100C2×Dic3⋊C4C2×D314yes—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—34no—
103C2×C4×Dic3—34no—
104C2×C4×Dic3—34no—
105C2×C4×Dic3—62no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3C2×D312yes—
108#888—332no—
109#888—316no—
110#888C2×D3116yes—
111#887—316no—
112#887—332no—
113#887—316no—
114#887—68no—
115C4×Dic6—316no—
116C4×Dic6—316no—
117C23×C32C2411yescharacteristic
118C2×C32×C4—24no—
119C2×C32×C4C2×Q814yes—
120C2×C32×C4C2414yes—
121C2×C32×C4C2412yes—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3C2×Q814yes—
124C2×C3⋊Dic3C2×Q818yes—
125C2×C3⋊Dic3C2412yes—
126C2×C3⋊Dic3C2414yes—
127C2×C3⋊Dic3C2412yes—
128#634C2×Q8116yescomplemented
129C2×C3×Dic3—28no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3C2×Q818yes—
132C2×C3×Dic3C2418yes—
133C2×C3×Dic3C2414yes—
134C2×C3×Dic3C2414yes—
135C3×Dic6—416no—
136#627—48no—
137#627C2×Q8116yescomplemented
138Q82—916no—
139C2×C4⋊Q8—32no—
140C2×C4⋊Q8—91no—
141C2×C4⋊Q8—94no—
142C2×C4⋊Q8—92no—
143C2×C4×Q8—91no—
144C2×C4×Q8—92no—
145C2×C4×Q8—92no—
146C2×C4×Q8—91no—
147C2×C3×Q8—316no—
148C2×C3×Q8—128no—
149C22×C3×C4—21no—
150C22×C3×C4—22no—
151C22×C3×C4—32no—
152C22×C3×C4—34no—
153C22×C3×C4—32no—
154C22×C3×C4C22×D314yes—
155C22×C3×C4C22×D312yes—
156C22×Dic3—32no—
157C22×Dic3—34no—
158C22×Dic3—32no—
159C22×Dic3—61no—
160C22×Dic3—62no—
161C22×Dic3—61no—
162C22×Dic3C22×D314yes—
163C22×Dic3C22×D312yes—
164C22×Dic3C22×D312yes—
165C2×Dic6—316no—
166C2×Dic6—38no—
167C2×Dic6—316no—
168C2×Dic6—38no—
169C2×Dic6—316no—
170C2×Dic6—48no—
171C2×Dic6—64no—
172C2×Dic6—68no—
173C2×Dic6—128no—
174C2×Dic6C22×D3116yes—
175C3×C4⋊C4—24no—
176C3×C4⋊C4—316no—
177C3×C4⋊C4—38no—
178C3×C4⋊C4C22×D318yes—
179C3×C42—38no—
180C4⋊Dic3—38no—
181C4⋊Dic3C22×D318yes—
182Dic3⋊C4—316no—
183Dic3⋊C4—38no—
184Dic3⋊C4—316no—
185Dic3⋊C4—38no—
186Dic3⋊C4—316no—
187Dic3⋊C4—316no—
188Dic3⋊C4—68no—
189Dic3⋊C4C22×D3116yes—
190C4×Dic3—38no—
191C4×Dic3—316no—
192C4×Dic3—316no—
193C4×Dic3—316no—
194C4×Dic3—68no—
195C4×Dic3—64no—
196C4×Dic3C22×D318yes—
197C22×C32C22×Q812yes—
198C22×C32C22×Q812yes—
199C22×C32H(5,𝔽2)12yes—
200C22×C32C2511yescharacteristic
201C32×C4—24no—
202C32×C4C22×Q814yes—
203C3⋊Dic3—22no—
204C3⋊Dic3C22×Q814yes—
205C3⋊Dic3C22×Q818yes—
206C3×Dic3—28no—
207C3×Dic3—24no—
208C3×Dic3C22×Q818yes—
209C22×Q8—34no—
210C22×Q8—91no—
211C22×Q8—92no—
212C22×Q8—91no—
213C4⋊Q8—316no—
214C4⋊Q8—98no—
215C4⋊Q8—932no—
216C4⋊Q8—916no—
217C4×Q8—98no—
218C4×Q8—916no—
219C4×Q8—916no—
220C4×Q8—98no—
221C2×C4⋊C4—34no—
222C2×C4⋊C4—32no—
223C2×C4⋊C4—91no—
224C2×C4⋊C4—94no—
225C2×C4⋊C4—92no—
226C2×C4⋊C4—92no—
227C2×C4⋊C4—92no—
228C2×C4⋊C4D3211yescharacteristic
229C2×C42—32no—
230C2×C42—94no—
231C2×C42—92no—
232C2×C42—91no—
233C23×C3—21no—
234C23×C3C23×D312yes—
235C3×Q8—1216no—
236C2×C3×C4—28no—
237C2×C3×C4—22no—
238C2×C3×C4—24no—
239C2×C3×C4—24no—
240C2×C3×C4—38no—
241C2×C3×C4—34no—
242C2×C3×C4—38no—
243C2×C3×C4—34no—
244C2×C3×C4—44no—
245C2×C3×C4—68no—
246C2×C3×C4—64no—
247C2×C3×C4D3×Q818yes—
248C2×C3×C4C23×D318yes—
249C2×C3×C4C23×D314yes—
250C2×Dic3—24no—
251C2×Dic3—28no—
252C2×Dic3—316no—
253C2×Dic3—38no—
254C2×Dic3—38no—
255C2×Dic3—34no—
256C2×Dic3—34no—
257C2×Dic3—68no—
258C2×Dic3—64no—
259C2×Dic3—62no—
260C2×Dic3—64no—
261C2×Dic3—62no—
262C2×Dic3—64no—
263C2×Dic3—122no—
264C2×Dic3D3×Q818yes—
265C2×Dic3C23×D318yes—
266C2×Dic3C23×D314yes—
267C2×Dic3C23×D314yes—
268Dic6—332no—
269Dic6—332no—
270Dic6—416no—
271Dic6—616no—
272Dic6—1216no—
273C2×C32Q8214yescomplemented
274C2×C32C23×Q811yescharacteristic
275C2×C32C23×Q811yescharacteristic
276C2×C32C2×H(5,𝔽2)11yescharacteristic
277C2×Q8—316no—
278C2×Q8—94no—
279C2×Q8—98no—
280C2×Q8—98no—
281C2×Q8—94no—
282C2×Q8—98no—
283C2×Q8—128no—
284C2×Q8—364no—
285C22×C4—32no—
286C22×C4—32no—
287C22×C4—34no—
288C22×C4—92no—
289C22×C4—91no—
290C22×C4—91no—
291C22×C4C2×D3212yes—
292C22×C4C2×D3211yescharacteristic
293C4⋊C4—316no—
294C4⋊C4—38no—
295C4⋊C4—94no—
296C4⋊C4—916no—
297C4⋊C4—98no—
298C4⋊C4—98no—
299C4⋊C4—98no—
300C4⋊C4C2×D3214yes—
301C42—38no—
302C42—916no—
303C42—98no—
304C42—94no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—21no—
309C22×C3#100414yes—
310C22×C3C2×D3×Q814yes—
311C22×C3C2×D3×Q814yes—
312C22×C3C24×D312yes—
313C3×C4—28no—
314C3×C4—24no—
315C3×C4—38no—
316C3×C4—44no—
317C3×C4—68no—
318C3×C4—64no—
319C3×C4C2×D3×Q818yes—
320Dic3—24no—
321Dic3—28no—
322Dic3—316no—
323Dic3—38no—
324Dic3—68no—
325Dic3—64no—
326Dic3—64no—
327Dic3—122no—
328Dic3C2×D3×Q818yes—
329C32C2×Q8211yescharacteristic, complemented, Sylow
330C23C22×D3211yescharacteristic
331Q8—916no—
332Q8—916no—
333Q8—1216no—
334Q8—368no—
335C2×C4—24no—
336C2×C4—38no—
337C2×C4—34no—
338C2×C4—34no—
339C2×C4—38no—
340C2×C4—64no—
341C2×C4—68no—
342C2×C4—98no—
343C2×C4—94no—
344C2×C4—94no—
345C2×C4—92no—
346C2×C4—92no—
347C2×C4—182no—
348C2×C4#379714yes—
349C2×C4C22×D3214yes—
350C2×C4C22×D3212yes—
351C2×C3—24no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3#572218yescomplemented
356C2×C3C2×#100412yes—
357C2×C3C22×D3×Q812yes—
358C2×C3C22×D3×Q812yes—
359C22C2×#379712yes—
360C22#6431312yes—
361C22D32×Q812yes—
362C22C23×D3211yescharacteristic
363C4—24no—
364C4—38no—
365C4—64no—
366C4—68no—
367C4—98no—
368C4—94no—
369C4—182no—
370C4C2×#379714yes—
371C3—21no—
372C3C2×#572212yescomplemented
373C2#1059431314yesdirect product factor
374C2C22×#379711yescharacteristic
375C2C2×#6431311yescharacteristic
376C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×Q82
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
9. #10594313C2direct (N × H)
53. C2×#634Q8semidirect
61. C2×#627Q8semidirect
128. #634C2×Q8semidirect
137. #627C2×Q8semidirect
273. C2×C32Q82semidirect
329. C32C2×Q82semidirect
355. C2×C3#5722semidirect
372. C3C2×#5722semidirect
373. C2#10594313direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640962
C2×C3×#8882
C2×#639192
C2×C4×#6272
C2×#638732
C2×#638442
C2×#638392
C2×#638382
#105943132
C2×#57223