Finite Group Databasebeta

← C2×#10594324 #11903706

Subgroups — C2×#10594324 #11903706

Order 1152.

2245 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic
2C2×C3×#890C212yesmaximal
3C2×#63919C211yesmaximal, characteristic
4C2×#63919C212yesmaximal
5C2×C4×#627C211yesmaximal, characteristic
6C2×#63847C214yesmaximal
7C2×#63844C212yesmaximal
8C2×#63838C212yesmaximal
9#10594324C2116yesmaximal, direct product factor
10C2×#5685—32nomaximal
11C22×#634C2211yescharacteristic
12C22×#627C2211yescharacteristic
13C22×#627C2212yes—
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3750C2212yes—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C4×C3⋊Dic3C2212yes—
18#64096C2218yes—
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×C4⋊Dic3C2214yes—
21C2×C3×Dic3⋊C4C2214yes—
22C2×C3×C4×Dic3C2212yes—
23C3×#890C22116yes—
24C2×#3724C2214yes—
25C2×#3724C2212yes—
26C2×#3724C2211yescharacteristic
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic32C2214yes—
29#63919C22116yes—
30#63919C2218yes—
31C4×#627C2218yes—
32#63847C22132yes—
33#63844C22116yes—
34#63838C22116yes—
35C2×C3×#125—32no—
36#5685—332no—
37C2×#890D312yes—
38C2×#889—34no—
39C2×#889—34no—
40C2×#888—32no—
41C2×#888—34no—
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⋊Dic3C2312yes—
52C22×C3⋊Dic3C2311yescharacteristic
53C2×#634Q818yescomplemented
54C2×#634C2314yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2314yes—
58C2×#627—24no—
59C2×#627—28no—
60C2×#627C2318yes—
61C2×#627C2314yes—
62C32×C4⋊C4C2314yes—
63#3750C2318yes—
64C4×C3⋊Dic3C2318yes—
65C4×C3⋊Dic3C2314yes—
66C3×C4⋊Dic3C2318yes—
67C3×C4⋊Dic3C23116yes—
68C3×Dic3⋊C4C23116yes—
69C3×C4×Dic3C2318yes—
70#3724C2314yes—
71#3724C23116yes—
72#3724C2318yes—
73Dic3⋊Dic3C2318yes—
74Dic32C23116yes—
75C2×#557—91noSylow
76C22×Dic6—32no—
77C22×Dic6—32no—
78C22×Dic6—34no—
79C22×Dic6—61no—
80C3×#125—316no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—34no—
83C2×C3×C4⋊C4—32no—
84C2×C3×C4⋊C4—34no—
85C2×C3×C4⋊C4C2×D312yes—
86C2×C3×C42—32no—
87C2×C4⋊Dic3—32no—
88C2×C4⋊Dic3C2×D312yes—
89C2×C4⋊Dic3C2×D314yes—
90C2×Dic3⋊C4—34no—
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4—34no—
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—34no—
95C2×Dic3⋊C4—34no—
96C2×Dic3⋊C4—62no—
97C2×Dic3⋊C4C2×D314yes—
98C2×C4×Dic3—32no—
99C2×C4×Dic3—34no—
100C2×C4×Dic3—34no—
101C2×C4×Dic3—34no—
102C2×C4×Dic3—62no—
103C2×C4×Dic3—61no—
104C2×C4×Dic3C2×D312yes—
105#890C2×D3116yes—
106#889—332no—
107#889—332no—
108#888—316no—
109#888—332no—
110#887—316no—
111#887—332no—
112#887—316no—
113#887—68no—
114C4×Dic6—316no—
115C4×Dic6—316no—
116C23×C32C2411yescharacteristic
117C2×C32×C4—24no—
118C2×C32×C4C2×Q814yes—
119C2×C32×C4C2414yes—
120C2×C32×C4C2412yes—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3C2×Q818yes—
123C2×C3⋊Dic3#4114yes—
124C2×C3⋊Dic3C2412yes—
125C2×C3⋊Dic3C2414yes—
126C2×C3⋊Dic3C2412yes—
127#634C2×Q8116yescomplemented
128C2×C3×Dic3—24no—
129C2×C3×Dic3—28no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3C2414yes—
132C2×C3×Dic3C2418yes—
133C2×C3×Dic3C2414yes—
134#627—216no—
135#627—28no—
136#557—916no—
137C2×C4⋊Q8—91no—
138C2×C4⋊Q8—92no—
139C2×#125—32no—
140C2×#125—94no—
141C2×C4×Q8—91no—
142C2×C4×Q8—92no—
143C2×C4×Q8—92no—
144C2×C4×Q8—91no—
145C22×C3×C4—21no—
146C22×C3×C4—22no—
147C22×C3×C4—32no—
148C22×C3×C4—34no—
149C22×C3×C4—32no—
150C22×C3×C4C22×D314yes—
151C22×C3×C4C22×D312yes—
152C22×Dic3—34no—
153C22×Dic3—32no—
154C22×Dic3—32no—
155C22×Dic3—61no—
156C22×Dic3—62no—
157C22×Dic3—61no—
158C22×Dic3C22×D312yes—
159C22×Dic3C22×D314yes—
160C22×Dic3C22×D312yes—
161C2×Dic6—316no—
162C2×Dic6—38no—
163C2×Dic6—38no—
164C2×Dic6—316no—
165C2×Dic6—64no—
166C2×Dic6—68no—
167C2×Dic6—68no—
168C2×Dic6—616no—
169C3×C4⋊C4—24no—
170C3×C4⋊C4—38no—
171C3×C4⋊C4—316no—
172C3×C4⋊C4—316no—
173C3×C4⋊C4C22×D318yes—
174C3×C42—38no—
175C4⋊Dic3—38no—
176C4⋊Dic3C22×D318yes—
177C4⋊Dic3C22×D3116yes—
178Dic3⋊C4—316no—
179Dic3⋊C4—38no—
180Dic3⋊C4—316no—
181Dic3⋊C4—38no—
182Dic3⋊C4—316no—
183Dic3⋊C4—316no—
184Dic3⋊C4—68no—
185Dic3⋊C4C22×D3116yes—
186C4×Dic3—38no—
187C4×Dic3—316no—
188C4×Dic3—316no—
189C4×Dic3—316no—
190C4×Dic3—68no—
191C4×Dic3—64no—
192C4×Dic3C22×D318yes—
193C22×C32C22×Q812yes—
194C22×C32C2×#4112yes—
195C22×C322−1+412yes—
196C22×C32C2511yescharacteristic
197C32×C4—24no—
198C32×C4C22×Q814yes—
199C3⋊Dic3—22no—
200C3⋊Dic3C22×Q818yes—
201C3⋊Dic3C2×#4114yes—
202C3×Dic3—28no—
203C3×Dic3—24no—
204C3×Dic3—24no—
205C22×Q8—91no—
206C22×Q8—92no—
207C22×Q8—91no—
208C4⋊Q8—98no—
209C4⋊Q8—916no—
210#125—316no—
211#125—932no—
212C4×Q8—98no—
213C4×Q8—916no—
214C4×Q8—916no—
215C4×Q8—98no—
216C2×C4⋊C4—34no—
217C2×C4⋊C4—32no—
218C2×C4⋊C4—34no—
219C2×C4⋊C4—91no—
220C2×C4⋊C4—92no—
221C2×C4⋊C4—94no—
222C2×C4⋊C4—92no—
223C2×C4⋊C4—92no—
224C2×C4⋊C4D3211yescharacteristic
225C2×C42—32no—
226C2×C42—94no—
227C2×C42—92no—
228C2×C42—91no—
229C23×C3—21no—
230C23×C3C23×D312yes—
231C2×C3×C4—28no—
232C2×C3×C4—22no—
233C2×C3×C4—24no—
234C2×C3×C4—24no—
235C2×C3×C4—34no—
236C2×C3×C4—38no—
237C2×C3×C4—34no—
238C2×C3×C4—44no—
239C2×C3×C4—68no—
240C2×C3×C4—64no—
241C2×C3×C4—64no—
242C2×C3×C4D3×Q818yes—
243C2×C3×C4C23×D318yes—
244C2×C3×C4C23×D314yes—
245C2×Dic3—28no—
246C2×Dic3—24no—
247C2×Dic3—24no—
248C2×Dic3—316no—
249C2×Dic3—38no—
250C2×Dic3—38no—
251C2×Dic3—34no—
252C2×Dic3—34no—
253C2×Dic3—68no—
254C2×Dic3—64no—
255C2×Dic3—62no—
256C2×Dic3—64no—
257C2×Dic3—62no—
258C2×Dic3—64no—
259C2×Dic3—122no—
260C2×Dic3C23×D314yes—
261C2×Dic3C23×D318yes—
262C2×Dic3C23×D314yes—
263Dic6—332no—
264Dic6—616no—
265Dic6—616no—
266Dic6—632no—
267C2×C32#55714yescomplemented
268C2×C32C23×Q811yescharacteristic
269C2×C32C22×#4111yescharacteristic
270C2×C32C2×2−1+411yescharacteristic
271C2×Q8—94no—
272C2×Q8—98no—
273C2×Q8—94no—
274C2×Q8—98no—
275C2×Q8—184no—
276C2×Q8—188no—
277C22×C4—32no—
278C22×C4—32no—
279C22×C4—34no—
280C22×C4—92no—
281C22×C4—91no—
282C22×C4—91no—
283C22×C4C2×D3212yes—
284C22×C4C2×D3211yescharacteristic
285C4⋊C4—316no—
286C4⋊C4—38no—
287C4⋊C4—316no—
288C4⋊C4—94no—
289C4⋊C4—98no—
290C4⋊C4—916no—
291C4⋊C4—98no—
292C4⋊C4—98no—
293C4⋊C4C2×D3214yes—
294C42—38no—
295C42—916no—
296C42—98no—
297C42—94no—
298C22×C3—22no—
299C22×C3—22no—
300C22×C3—22no—
301C22×C3—21no—
302C22×C3C2×D3×Q814yes—
303C22×C3D3×#4114yes—
304C22×C3#101014yes—
305C22×C3C24×D312yes—
306C3×C4—28no—
307C3×C4—24no—
308C3×C4—44no—
309C3×C4—68no—
310C3×C4—64no—
311C3×C4—64no—
312C3×C4C2×D3×Q818yes—
313Dic3—28no—
314Dic3—24no—
315Dic3—24no—
316Dic3—316no—
317Dic3—38no—
318Dic3—68no—
319Dic3—64no—
320Dic3—64no—
321Dic3—122no—
322C32C2×#55711yescharacteristic, complemented, Sylow
323C23C22×D3211yescharacteristic
324Q8—916no—
325Q8—188no—
326Q8—1816no—
327C2×C4—24no—
328C2×C4—34no—
329C2×C4—34no—
330C2×C4—38no—
331C2×C4—64no—
332C2×C4—64no—
333C2×C4—68no—
334C2×C4—98no—
335C2×C4—94no—
336C2×C4—94no—
337C2×C4—92no—
338C2×C4—92no—
339C2×C4—182no—
340C2×C4#379714yes—
341C2×C4C22×D3214yes—
342C2×C4C22×D3212yes—
343C2×C3—24no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3#568518yescomplemented
348C2×C3C22×D3×Q812yes—
349C2×C3C2×D3×#4112yes—
350C2×C3C2×#101012yes—
351C22C2×#379712yes—
352C22#6430912yes—
353C22#6431912yes—
354C22C23×D3211yescharacteristic
355C4—24no—
356C4—64no—
357C4—64no—
358C4—68no—
359C4—98no—
360C4—94no—
361C4—182no—
362C4C2×#379714yes—
363C3—21no—
364C3C2×#568512yescomplemented
365C2#1059432414yesdirect product factor
366C2C22×#379711yescharacteristic
367C2C2×#6430911yescharacteristic
368C2C2×#6431911yescharacteristic
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. #10594324C2direct (N × H)
53. C2×#634Q8semidirect
127. #634C2×Q8semidirect
267. C2×C32#557semidirect
322. C32C2×#557semidirect
347. C2×C3#5685semidirect
364. C3C2×#5685semidirect
365. C2#10594324direct (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×#8902
C2×#639192
C2×C4×#6272
C2×#638472
C2×#638442
C2×#638382
#105943242
C2×#56853