Finite Group Databasebeta

← C2×#10594595 #11903702

Subgroups — C2×#10594595 #11903702

Order 1152.

2245 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic
2C2×C3×#887C212yesmaximal
3C2×C4×#627C211yesmaximal, characteristic
4C2×C4×#627C212yesmaximal
5C2×#63873C211yesmaximal, characteristic
6C2×#63870C212yesmaximal
7C2×#63867C214yesmaximal
8C2×#63866C212yesmaximal
9#10594595C2116yesmaximal, direct product factor
10C2×#5567—32nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×Dic6C2212yes—
13C22×#627C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3750C2212yes—
16C2×C4×C3⋊Dic3C2212yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18#64096C2218yes—
19C2×C3×Dic3⋊C4C2214yes—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×C4×Dic3C2214yes—
22C3×#887C22116yes—
23C2×#3724C2212yes—
24C2×#3724C2211yescharacteristic
25C2×#3724C2212yes—
26C2×Dic3⋊Dic3C2214yes—
27C2×Dic3⋊Dic3C2214yes—
28C2×Dic3⋊Dic3C2212yes—
29C4×#627C22116yes—
30C4×#627C2218yes—
31#63873C2218yes—
32#63870C22116yes—
33#63867C22132yes—
34#63866C22116yes—
35C2×C3×C4×Q8—32no—
36C2×#944—32no—
37C2×#944—32no—
38#5567—332no—
39C2×#889—34no—
40C2×#889—34no—
41C2×#887—32no—
42C2×#887—61no—
43C2×#887D312yes—
44C2×#870—34no—
45C2×#869—32no—
46C2×C4×Dic6—34no—
47C2×C4×Dic6—32no—
48C22×C32×C4C2312yes—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3C2312yes—
51C22×C3⋊Dic3C2311yescharacteristic
52C22×C3⋊Dic3C2311yescharacteristic
53C2×#634—24no—
54C2×#634C2314yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2314yes—
57C22×C3×Dic3C2312yes—
58C2×C3×Dic6—28no—
59C2×C3×Dic6C2318yes—
60C2×#627Q818yescomplemented
61C2×#627C2314yes—
62C32×C4⋊C4C2314yes—
63#3750C2318yes—
64C4×C3⋊Dic3C2318yes—
65C4×C3⋊Dic3C2314yes—
66C3×Dic3⋊C4C23116yes—
67C3×C4×Dic3C2318yes—
68C3×C4×Dic3C23116yes—
69#3724C2318yes—
70#3724C2314yes—
71#3724C2318yes—
72Dic3⋊Dic3C23116yes—
73Dic3⋊Dic3C23116yes—
74Dic3⋊Dic3C2318yes—
75C2×#557—91noSylow
76C22×C3×Q8—32no—
77C22×Dic6—32no—
78C22×Dic6—32no—
79C22×Dic6—61no—
80C22×Dic6C2×D312yes—
81C3×C4×Q8—316no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4—34no—
84C2×C3×C4⋊C4C2×D312yes—
85C2×C3×C42—32no—
86C2×C3×C42—34no—
87#944—316no—
88#944—316no—
89C2×C4⋊Dic3—34no—
90C2×C4⋊Dic3—32no—
91C2×C4⋊Dic3—34no—
92C2×Dic3⋊C4—34no—
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—34no—
96C2×Dic3⋊C4—34no—
97C2×Dic3⋊C4—34no—
98C2×Dic3⋊C4—34no—
99C2×Dic3⋊C4—62no—
100C2×Dic3⋊C4C2×D314yes—
101C2×C4×Dic3—34no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—62no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3C2×D314yes—
106C2×C4×Dic3C2×D312yes—
107#889—332no—
108#889—332no—
109#887—316no—
110#887—68no—
111#887C2×D3116yes—
112#870—332no—
113#869—316no—
114C4×Dic6—332no—
115C4×Dic6—316no—
116C23×C32C2411yescharacteristic
117C2×C32×C4—24no—
118C2×C32×C4#4114yes—
119C2×C32×C4C2414yes—
120C2×C32×C4C2412yes—
121C2×C3⋊Dic3—24no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3C2×Q814yes—
124C2×C3⋊Dic3C2414yes—
125C2×C3⋊Dic3C2412yes—
126C2×C3⋊Dic3C2412yes—
127#634—28no—
128C2×C3×Dic3—28no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3C2×Q818yes—
131C2×C3×Dic3C2414yes—
132C2×C3×Dic3C2418yes—
133C2×C3×Dic3C2414yes—
134C3×Dic6—216no—
135#627C2×Q8116yescomplemented
136#557—916no—
137C2×C4⋊Q8—92no—
138C2×C4⋊Q8—91no—
139C2×#125—94no—
140C2×#125—92no—
141C2×C4×Q8—32no—
142C2×C4×Q8—92no—
143C2×C4×Q8—91no—
144C2×C4×Q8—91no—
145C2×C3×Q8—38no—
146C2×C3×Q8—68no—
147C22×C3×C4—21no—
148C22×C3×C4—22no—
149C22×C3×C4—32no—
150C22×C3×C4—34no—
151C22×C3×C4—32no—
152C22×C3×C4C22×D314yes—
153C22×C3×C4C22×D312yes—
154C22×Dic3—32no—
155C22×Dic3—32no—
156C22×Dic3—34no—
157C22×Dic3—61no—
158C22×Dic3—62no—
159C22×Dic3—61no—
160C22×Dic3C22×D312yes—
161C22×Dic3C22×D314yes—
162C22×Dic3C22×D312yes—
163C2×Dic6—28no—
164C2×Dic6—316no—
165C2×Dic6—38no—
166C2×Dic6—38no—
167C2×Dic6—64no—
168C2×Dic6—68no—
169C2×Dic6—68no—
170C2×Dic6C22×D318yes—
171C3×C4⋊C4—24no—
172C3×C4⋊C4—316no—
173C3×C4⋊C4C22×D318yes—
174C3×C42—38no—
175C3×C42—316no—
176C4⋊Dic3—316no—
177C4⋊Dic3—38no—
178C4⋊Dic3—316no—
179Dic3⋊C4—316no—
180Dic3⋊C4—38no—
181Dic3⋊C4—38no—
182Dic3⋊C4—316no—
183Dic3⋊C4—316no—
184Dic3⋊C4—316no—
185Dic3⋊C4—316no—
186Dic3⋊C4—68no—
187Dic3⋊C4C22×D3116yes—
188C4×Dic3—316no—
189C4×Dic3—38no—
190C4×Dic3—68no—
191C4×Dic3—64no—
192C4×Dic3C22×D3116yes—
193C4×Dic3C22×D318yes—
194C22×C32C22×Q812yes—
195C22×C32C2×#4112yes—
196C22×C322−1+412yes—
197C22×C32C2511yescharacteristic
198C32×C4—24no—
199C32×C4C2×#4114yes—
200C3⋊Dic3—24no—
201C3⋊Dic3—22no—
202C3⋊Dic3C22×Q814yes—
203C3×Dic3—28no—
204C3×Dic3—24no—
205C3×Dic3C22×Q818yes—
206C22×Q8—32no—
207C22×Q8—91no—
208C22×Q8—91no—
209C4⋊Q8—916no—
210C4⋊Q8—98no—
211#125—932no—
212#125—916no—
213C4×Q8—316no—
214C4×Q8—916no—
215C4×Q8—98no—
216C4×Q8—98no—
217C2×C4⋊C4—34no—
218C2×C4⋊C4—91no—
219C2×C4⋊C4—92no—
220C2×C4⋊C4—92no—
221C2×C4⋊C4—94no—
222C2×C4⋊C4—92no—
223C2×C4⋊C4—94no—
224C2×C4⋊C4—92no—
225C2×C4⋊C4D3211yescharacteristic
226C2×C42—34no—
227C2×C42—32no—
228C2×C42—92no—
229C2×C42—91no—
230C23×C3—21no—
231C23×C3C23×D312yes—
232C3×Q8—616no—
233C2×C3×C4—28no—
234C2×C3×C4—22no—
235C2×C3×C4—24no—
236C2×C3×C4—24no—
237C2×C3×C4—38no—
238C2×C3×C4—34no—
239C2×C3×C4—38no—
240C2×C3×C4—34no—
241C2×C3×C4—44no—
242C2×C3×C4—68no—
243C2×C3×C4—64no—
244C2×C3×C4#23518yes—
245C2×C3×C4C23×D318yes—
246C2×C3×C4C23×D314yes—
247C2×Dic3—28no—
248C2×Dic3—24no—
249C2×Dic3—38no—
250C2×Dic3—34no—
251C2×Dic3—34no—
252C2×Dic3—38no—
253C2×Dic3—64no—
254C2×Dic3—62no—
255C2×Dic3—64no—
256C2×Dic3—62no—
257C2×Dic3—68no—
258C2×Dic3—68no—
259C2×Dic3—64no—
260C2×Dic3—122no—
261C2×Dic3D3×Q818yes—
262C2×Dic3C23×D314yes—
263C2×Dic3C23×D318yes—
264C2×Dic3C23×D314yes—
265Dic6—216no—
266Dic6—332no—
267Dic6—616no—
268Dic6—616no—
269C2×C32#55714yescomplemented
270C2×C32C23×Q811yescharacteristic
271C2×C32C22×#4111yescharacteristic
272C2×C32C2×2−1+411yescharacteristic
273C2×Q8—38no—
274C2×Q8—68no—
275C2×Q8—94no—
276C2×Q8—98no—
277C2×Q8—94no—
278C2×Q8—184no—
279C22×C4—32no—
280C22×C4—32no—
281C22×C4—34no—
282C22×C4—91no—
283C22×C4—91no—
284C22×C4—92no—
285C22×C4C2×D3212yes—
286C22×C4C2×D3211yescharacteristic
287C4⋊C4—316no—
288C4⋊C4—94no—
289C4⋊C4—98no—
290C4⋊C4—98no—
291C4⋊C4—916no—
292C4⋊C4—98no—
293C4⋊C4—916no—
294C4⋊C4—98no—
295C4⋊C4C2×D3214yes—
296C42—316no—
297C42—38no—
298C42—98no—
299C42—94no—
300C22×C3—22no—
301C22×C3—22no—
302C22×C3—22no—
303C22×C3—21no—
304C22×C3C2×#23514yes—
305C22×C3C2×D3×Q814yes—
306C22×C3#101014yes—
307C22×C3C24×D312yes—
308C3×C4—28no—
309C3×C4—24no—
310C3×C4—38no—
311C3×C4—44no—
312C3×C4—68no—
313C3×C4—64no—
314C3×C4C2×#23518yes—
315Dic3—28no—
316Dic3—24no—
317Dic3—38no—
318Dic3—64no—
319Dic3—68no—
320Dic3—68no—
321Dic3—64no—
322Dic3—122no—
323Dic3C2×D3×Q818yes—
324C32C2×#55711yescharacteristic, complemented, Sylow
325C23C22×D3211yescharacteristic
326Q8—616no—
327Q8—916no—
328Q8—188no—
329C2×C4—24no—
330C2×C4—38no—
331C2×C4—34no—
332C2×C4—34no—
333C2×C4—38no—
334C2×C4—68no—
335C2×C4—64no—
336C2×C4—94no—
337C2×C4—92no—
338C2×C4—92no—
339C2×C4—94no—
340C2×C4—184no—
341C2×C4—182no—
342C2×C4#379814yes—
343C2×C4C22×D3214yes—
344C2×C4C22×D3212yes—
345C2×C3—24no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3#556718yescomplemented
350C2×C3C22×#23512yes—
351C2×C3C22×D3×Q812yes—
352C2×C3C2×#101012yes—
353C22C2×#379812yes—
354C22#6430912yes—
355C22D32×Q812yes—
356C22C23×D3211yescharacteristic
357C4—24no—
358C4—38no—
359C4—68no—
360C4—64no—
361C4—94no—
362C4—184no—
363C4—182no—
364C4C2×#379814yes—
365C3—21no—
366C3C2×#556712yescomplemented
367C2#1059459514yesdirect product factor
368C2C22×#379811yescharacteristic
369C2C2×#6430911yescharacteristic
370C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#557
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
9. #10594595C2direct (N × H)
60. C2×#627Q8semidirect
135. #627C2×Q8semidirect
269. C2×C32#557semidirect
324. C32C2×#557semidirect
349. C2×C3#5567semidirect
366. C3C2×#5567semidirect
367. C2#10594595direct (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×#8872
C2×C4×#6272
C2×#638732
C2×#638702
C2×#638672
C2×#638662
#105945952
C2×#55673