Finite Group Databasebeta

← C2×#10595422 #11903703

Subgroups — C2×#10595422 #11903703

Order 1152.

2245 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×Q8×Dic3C211yesmaximal, characteristic
3C2×C3×Q8×Dic3C211yesmaximal, characteristic
4#10595422C2116yesmaximal, direct product factor
5C2×#63918C213yesmaximal
6C2×C4×#627C213yesmaximal
7C2×#63872C213yesmaximal
8C2×#63869C213yesmaximal
9C2×#5569—31nomaximal
10C2×#5570—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×#627C2213yes—
13Q8×C3⋊Dic3C2218yes—
14C2×C4⋊(C3⋊Dic3)C2213yes—
15C2×C4×C3⋊Dic3C2213yes—
16C3×Q8×Dic3C2218yes—
17C3×Q8×Dic3C2218yes—
18C2×C3×C4⋊Dic3C2213yes—
19C2×C3×C4⋊Dic3C2213yes—
20C2×C3×C4×Dic3C2213yes—
21C2×C3×C4×Dic3C2213yes—
22C2×#3724C2213yes—
23C2×Dic3⋊Dic3C2216yes—
24C2×Dic3⋊Dic3C2213yes—
25C2×Dic3⋊Dic3C2211yescharacteristic
26#63918C22124yes—
27C4×#627C22124yes—
28#63872C22124yes—
29#63869C22124yes—
30C2×C3×C4×Q8—31no—
31C2×C3×C4×Q8—31no—
32C2×Q8×Dic3—31no—
33C2×Q8×Dic3—31no—
34C2×Q8×Dic3—61no—
35C2×Q8×Dic3D311yescharacteristic
36C2×Q8×Dic3D311yescharacteristic
37#5570—316no—
38#5569—316no—
39C2×#890—33no—
40C2×#890—33no—
41C2×#890—33no—
42C2×#888—33no—
43C2×#870—33no—
44C2×#869—33no—
45C2×C4×Dic6—33no—
46C2×C4×Dic6—33no—
47C2×C32×Q8Q818yescomplemented
48C2×C32×Q8C2314yes—
49C22×C32×C4C2313yes—
50C22×C3⋊Dic3C2313yes—
51C22×C3⋊Dic3C2311yescharacteristic
52C22×C3×Dic3C2311yescharacteristic
53C22×C3×Dic3C2313yes—
54C22×C3×Dic3C2313yes—
55C22×C3×Dic3C2311yescharacteristic
56C2×#627—212no—
57C2×#627C23112yes—
58C4⋊(C3⋊Dic3)C23112yes—
59C4×C3⋊Dic3C23112yes—
60C3×C4⋊Dic3C23112yes—
61C3×C4⋊Dic3C23112yes—
62C3×C4×Dic3C23112yes—
63C3×C4×Dic3C23112yes—
64#3724C23112yes—
65Dic3⋊Dic3C23124yes—
66Dic3⋊Dic3C23112yes—
67Dic3⋊Dic3C2314yes—
68C2×#557—91noSylow
69C22×C3×Q8—21no—
70C22×C3×Q8C2×D311yescharacteristic
71C22×C3×Q8C2×D311yescharacteristic
72C22×Dic6—33no—
73C22×Dic6—33no—
74C3×C4×Q8—38no—
75C3×C4×Q8—38no—
76C2×C3×C4⋊C4—33no—
77C2×C3×C4⋊C4—33no—
78C2×C3×C42—33no—
79C2×C3×C42—33no—
80Q8×Dic3—38no—
81Q8×Dic3—38no—
82Q8×Dic3—68no—
83Q8×Dic3C2×D318yes—
84Q8×Dic3C2×D318yes—
85C2×C4⋊Dic3—33no—
86C2×C4⋊Dic3—33no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—33no—
89C2×C4⋊Dic3—36no—
90C2×C4⋊Dic3—63no—
91C2×C4⋊Dic3C2×D313yes—
92C2×C4⋊Dic3C2×D313yes—
93C2×Dic3⋊C4—31no—
94C2×Dic3⋊C4—33no—
95C2×Dic3⋊C4—33no—
96C2×Dic3⋊C4—33no—
97C2×Dic3⋊C4—36no—
98C2×C4×Dic3—33no—
99C2×C4×Dic3—33no—
100C2×C4×Dic3—63no—
101C2×C4×Dic3C2×D313yes—
102C2×C4×Dic3C2×D313yes—
103#890—324no—
104#890—324no—
105#890—324no—
106#888—324no—
107#870—324no—
108#869—324no—
109C4×Dic6—324no—
110C4×Dic6—324no—
111C23×C32C2411yescharacteristic
112C32×Q8C2×Q8116yescomplemented
113C2×C32×C4C2×Q8112yes—
114C2×C32×C4C2416yes—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—26no—
117C2×C3⋊Dic3C2412yes—
118C2×C3⋊Dic3C2416yes—
119C2×C3×Dic3—26no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—26no—
122C2×C3×Dic3#4114yes—
123C2×C3×Dic3C2416yes—
124C2×C3×Dic3C2416yes—
125C2×C3×Dic3C2412yes—
126C2×C3×Dic3C2412yes—
127#627—224no—
128#557—916no—
129C2×C4⋊Q8—93no—
130C2×#125—93no—
131C2×#125—93no—
132C2×C4×Q8—31no—
133C2×C4×Q8—31no—
134C2×C4×Q8—93no—
135C2×C4×Q8—91no—
136C2×C3×Q8—28no—
137C2×C3×Q8—24no—
138C2×C3×Q8Dic618yescomplemented
139C2×C3×Q8Dic618yescomplemented
140C2×C3×Q8C22×D314yes—
141C2×C3×Q8C22×D314yes—
142C22×C3×C4—23no—
143C22×C3×C4—31no—
144C22×C3×C4—31no—
145C22×C3×C4—33no—
146C22×C3×C4—33no—
147C22×C3×C4C22×D313yes—
148C22×C3×C4C22×D313yes—
149C22×Dic3—31no—
150C22×Dic3—31no—
151C22×Dic3—33no—
152C22×Dic3—33no—
153C22×Dic3—61no—
154C22×Dic3—63no—
155C22×Dic3C22×D311yescharacteristic
156C22×Dic3C22×D313yes—
157C22×Dic3C22×D313yes—
158C22×Dic3C22×D311yescharacteristic
159C2×Dic6—312no—
160C2×Dic6—312no—
161C2×Dic6—612no—
162C2×Dic6—612no—
163C3×C4⋊C4—312no—
164C3×C4⋊C4—312no—
165C3×C42—312no—
166C3×C42—312no—
167C4⋊Dic3—312no—
168C4⋊Dic3—312no—
169C4⋊Dic3—34no—
170C4⋊Dic3—312no—
171C4⋊Dic3—324no—
172C4⋊Dic3—612no—
173C4⋊Dic3C22×D3112yes—
174C4⋊Dic3C22×D3112yes—
175Dic3⋊C4—34no—
176Dic3⋊C4—312no—
177Dic3⋊C4—312no—
178Dic3⋊C4—312no—
179Dic3⋊C4—324no—
180C4×Dic3—312no—
181C4×Dic3—312no—
182C4×Dic3—612no—
183C4×Dic3C22×D3112yes—
184C4×Dic3C22×D3112yes—
185C22×C32C22×Q812yes—
186C22×C32C2×#4112yes—
187C22×C322−1+412yes—
188C22×C32C2511yescharacteristic
189C32×C4C22×Q8112yes—
190C3⋊Dic3—22no—
191C3⋊Dic3—26no—
192C3×Dic3—26no—
193C3×Dic3—22no—
194C3×Dic3—26no—
195C3×Dic3C2×#4114yes—
196C22×Q8—93no—
197C22×Q8D3211yescharacteristic
198C4⋊Q8—924no—
199#125—924no—
200#125—924no—
201C4×Q8—38no—
202C4×Q8—38no—
203C4×Q8—924no—
204C4×Q8—98no—
205C2×C4⋊C4—33no—
206C2×C4⋊C4—33no—
207C2×C4⋊C4—91no—
208C2×C4⋊C4—93no—
209C2×C4⋊C4—93no—
210C2×C4⋊C4—96no—
211C2×C4⋊C4—93no—
212C2×C42—33no—
213C2×C42—33no—
214C2×C42—93no—
215C23×C3—21no—
216C23×C3C23×D311yescharacteristic
217C23×C3C23×D311yescharacteristic
218C3×Q8—216no—
219C3×Q8C2×Dic6116yescomplemented
220C3×Q8C2×Dic6116yescomplemented
221C2×C3×C4—26no—
222C2×C3×C4—212no—
223C2×C3×C4—34no—
224C2×C3×C4—32no—
225C2×C3×C4—32no—
226C2×C3×C4—36no—
227C2×C3×C4—36no—
228C2×C3×C4—66no—
229C2×C3×C4—66no—
230C2×C3×C4—62no—
231C2×C3×C4C2×Dic6112yes—
232C2×C3×C4C2×Dic6112yes—
233C2×C3×C4C23×D316yes—
234C2×C3×C4C23×D316yes—
235C2×Dic3—22no—
236C2×Dic3—26no—
237C2×Dic3—26no—
238C2×Dic3—32no—
239C2×Dic3—32no—
240C2×Dic3—36no—
241C2×Dic3—36no—
242C2×Dic3—62no—
243C2×Dic3—66no—
244C2×Dic3—64no—
245C2×Dic3—66no—
246C2×Dic3—62no—
247C2×Dic3—66no—
248C2×Dic3—62no—
249C2×Dic3—126no—
250C2×Dic3#23914yes—
251C2×Dic3C23×D312yes—
252C2×Dic3C23×D316yes—
253C2×Dic3C23×D316yes—
254C2×Dic3C23×D312yes—
255Dic6—624no—
256Dic6—624no—
257C2×C32#55714yescomplemented
258C2×C32C23×Q811yescharacteristic
259C2×C32C22×#4111yescharacteristic
260C2×C32C2×2−1+411yescharacteristic
261C2×Q8—912no—
262C2×Q8—1812no—
263C2×Q8#62718yescomplemented
264C2×Q8C2×D3214yes—
265C22×C4—31no—
266C22×C4—31no—
267C22×C4—33no—
268C22×C4—33no—
269C22×C4—91no—
270C22×C4—93no—
271C22×C4C2×D3213yes—
272C4⋊C4—312no—
273C4⋊C4—312no—
274C4⋊C4—94no—
275C4⋊C4—912no—
276C4⋊C4—912no—
277C4⋊C4—924no—
278C4⋊C4—912no—
279C42—312no—
280C42—312no—
281C42—912no—
282C22×C3—22no—
283C22×C3—22no—
284C22×C3—22no—
285C22×C3—21no—
286C22×C3C22×Dic612yes—
287C22×C3C22×Dic612yes—
288C22×C3C2×#23912yes—
289C22×C3#100712yes—
290C22×C3D3×#4112yes—
291C22×C3#101012yes—
292C22×C3C24×D311yescharacteristic
293C22×C3C24×D311yescharacteristic
294C3×C4—212no—
295C3×C4—34no—
296C3×C4—66no—
297C3×C4—66no—
298C3×C4—62no—
299C3×C4C22×Dic6112yes—
300C3×C4C22×Dic6112yes—
301Dic3—22no—
302Dic3—26no—
303Dic3—26no—
304Dic3—64no—
305Dic3—66no—
306Dic3—62no—
307Dic3—66no—
308Dic3—62no—
309Dic3—126no—
310Dic3C2×#23914yes—
311C32C2×#55711yescharacteristic, complemented, Sylow
312C23C22×D3211yescharacteristic
313Q8—1824no—
314Q8C2×#627116yescomplemented
315C2×C4—34no—
316C2×C4—32no—
317C2×C4—32no—
318C2×C4—36no—
319C2×C4—36no—
320C2×C4—62no—
321C2×C4—66no—
322C2×C4—66no—
323C2×C4—92no—
324C2×C4—96no—
325C2×C4—182no—
326C2×C4—186no—
327C2×C4C2×#627112yes—
328C2×C4C22×D3216yes—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—24no—
332C2×C3—21no—
333C2×C3#556914yescomplemented
334C2×C3#557014yescomplemented
335C2×C3C23×Dic611yescharacteristic
336C2×C3C23×Dic611yescharacteristic
337C2×C3C22×#23911yescharacteristic
338C2×C3C2×#100711yescharacteristic
339C2×C3C2×D3×#4111yescharacteristic
340C2×C3C2×#101011yescharacteristic
341C22#6431512yes—
342C22D3×#23912yes—
343C22C22×#62712yes—
344C22C23×D3211yescharacteristic
345C4—34no—
346C4—62no—
347C4—66no—
348C4—66no—
349C4—182no—
350C4—186no—
351C4C22×#627112yes—
352C3—21no—
353C3C2×#557011yescharacteristic, complemented
354C3C2×#556911yescharacteristic, complemented
355C2#1059542214yesdirect product factor
356C2C2×#6431511yescharacteristic
357C2C2×D3×#23911yescharacteristic
358C2C23×#62711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socle, prime radicalC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#557
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. #10595422C2direct (N × H)
47. C2×C32×Q8Q8semidirect
112. C32×Q8C2×Q8semidirect
138. C2×C3×Q8Dic6semidirect
139. C2×C3×Q8Dic6semidirect
219. C3×Q8C2×Dic6semidirect
220. C3×Q8C2×Dic6semidirect
257. C2×C32#557semidirect
263. C2×Q8#627semidirect
311. C32C2×#557semidirect
314. Q8C2×#627semidirect
333. C2×C3#5569semidirect
334. C2×C3#5570semidirect
353. C3C2×#5570semidirect
354. C3C2×#5569semidirect
355. C2#10595422direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C2×C3×Q8×Dic32
#105954222
C2×#639182
C2×C4×#6272
C2×#638722
C2×#638692
C2×#55693
C2×#55703