Finite Group Databasebeta

← C2×#10593327 #11858296

Subgroups — C2×#10593327 #11858296

Order 1152.

830 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 199 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×#64286C211yesmaximal, characteristic
2C2×#63818C211yesmaximal, characteristic
3C22×#3710C211yesmaximal, characteristic
4#10593327C218yesmaximal, direct product factor
5C2×#63732C214yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157C412yes—
8#64286C414yes—
9#64286C2214yes—
10C2×C4⋊#157C412yes—
11C2×C4×#157C2212yes—
12C2×C3×#208—21no—
13C22×C3×C3⋊C8—21no—
14C2×#3712—21no—
15#63818—22no—
16#63818C2214yes—
17C2×#3710—22no—
18C2×#3710—21no—
19C2×#3710C2212yes—
20C2×#3710C2212yes—
21C2×#3710C2214yes—
22#63732C22116yescomplemented
23C2×D3×M16—61no—
24C22×D3×C8—61no—
25C23×C3⋊D3C2×C411yescharacteristic
26C22×#157C2×C414yes—
27C22×C32×C4D411yescharacteristic
28C22×C3⋊Dic3Q811yescharacteristic
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3C2×C412yes—
31C2×C4×C3⋊D3D412yes—
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3Q811yescharacteristic
34C2×C4×C3⋊D3Q812yes—
35C2×C4×C3⋊D3C2311yescharacteristic
36C2×C4×C3⋊D3C2312yes—
37C22⋊#157C2×C418yes—
38C4⋊#157C2×C418yes—
39C4×#157C2×C414yes—
40C4×#157C2314yes—
41C3×#208—24no—
42C2×C3×C3⋊C8—22no—
43C2×C3×C3⋊C8—24no—
44C2×C3×C3⋊C8—22no—
45#3712—24no—
46#3710—22no—
47#3710—24no—
48#3710—22no—
49#3710C2314yes—
50#3710C2314yes—
51C2×#424—91nomaximal, Sylow
52C22×C4×D3—61no—
53C22×C4×D3—61no—
54C2×C3×M16—61no—
55C22×C3×C8—61no—
56C2×#208—21no—
57C22×C3⋊C8—21no—
58D3×M16—64no—
59D3×M16—64no—
60C2×ΓL(1,𝔽25)—62no—
61C2×D3×C8—62no—
62C2×D3×C8—64no—
63C2×D3×C8—62no—
64C2×D3×C8—64no—
65C2×D3×C8—62no—
66C23×C32C4⋊C411yescharacteristic
67C22×C3⋊D3—24no—
68C22×C3⋊D3C4⋊C411yescharacteristic
69C22×C3⋊D3C4⋊C412yes—
70C22×C3⋊D3C22×C412yes—
71C22×C3⋊D3C22×C411yescharacteristic
72C2×#157—28no—
73C2×#157C22×C418yes—
74C2×C32×C4C4⋊C412yes—
75C2×C32×C4C4⋊C411yescharacteristic
76C2×C32×C4C2×D411yescharacteristic
77C2×C32×C4C2×D412yes—
78C2×C3⋊Dic3C4⋊C412yes—
79C2×C3⋊Dic3C4⋊C411yescharacteristic
80C2×C3⋊Dic3C2×Q812yes—
81C2×C3⋊Dic3C2×Q811yescharacteristic
82C4×C3⋊D3C4⋊C412yes—
83C4×C3⋊D3C4⋊C412yes—
84C4×C3⋊D3C4⋊C412yes—
85C4×C3⋊D3C22×C411yescharacteristic
86C4×C3⋊D3C22×C412yes—
87C4×C3⋊D3C2×D411yescharacteristic
88C4×C3⋊D3C2×D412yes—
89C4×C3⋊D3C2×Q812yes—
90C4×C3⋊D3C2×Q811yescharacteristic
91C4×C3⋊D3C2411yescharacteristic
92C3×C3⋊C8—24no—
93C3×C3⋊C8—24no—
94C22×M16—91no—
95C23×C8—91no—
96C2×#117—91no—
97#424—98no—
98C2×C4⋊C8—94no—
99C23×D3—61no—
100C23×D3—61no—
101C22×C3×C4—21no—
102C22×C3×C4—21no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C2×C4×D3—62no—
106C2×C4×D3—61no—
107C2×C4×D3—62no—
108C2×C4×D3—61no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C2×C4×D3—62no—
112C2×C4×D3—62no—
113C2×C4×D3—61no—
114C2×C4×D3—61no—
115C2×C4×D3—62no—
116C2×C4×D3—62no—
117C2×C4×D3—62no—
118C2×C4×D3—61no—
119C2×C4×D3—62no—
120C2×C4×D3—61no—
121C3×M16—64no—
122C2×C3×C8—64no—
123C2×C3×C8—62no—
124C2×C3×C8—62no—
125#208—24no—
126C2×C3⋊C8—24no—
127C2×C3⋊C8—22no—
128C2×C3⋊C8—22no—
129ΓL(1,𝔽25)—68no—
130D3×C8—64no—
131D3×C8—64no—
132D3×C8—64no—
133D3×C8—68no—
134D3×C8—64no—
135C22×C32—22no—
136C22×C32C2×C4⋊C412yes—
137C22×C32C2×C4⋊C411yescharacteristic
138C2×C3⋊D3—22no—
139C2×C3⋊D3—24no—
140C2×C3⋊D3—24no—
141C2×C3⋊D3C2×C4⋊C412yes—
142C2×C3⋊D3C2×C4⋊C411yescharacteristic
143C2×C3⋊D3#13114yes—
144C2×C3⋊D3C23×C411yescharacteristic
145#157—28no—
146C32×C4C2×C4⋊C411yescharacteristic
147C32×C4C2×C4⋊C412yes—
148C32×C4C22×D411yescharacteristic
149C3⋊Dic3C2×C4⋊C411yescharacteristic
150C3⋊Dic3C2×C4⋊C412yes—
151C3⋊Dic3C22×Q811yescharacteristic
152C23×C4—91no—
153C2×M16—61no—
154C2×M16—94no—
155C2×M16—181no—
156C2×M16—182no—
157C22×C8—61no—
158C22×C8—92no—
159C22×C8—94no—
160C22×C8—92no—
161C22×C8—182no—
162C22×C8—181no—
163#117—94no—
164#117—94no—
165C2×C4⋊C4—92no—
166C2×C22⋊C4—92no—
167C2×C42—92no—
168C4⋊C8—916no—
169C23×C3—21no—
170C23×C3—21no—
171C22×D3—62no—
172C22×D3—61no—
173C22×D3—61no—
174C22×D3—61no—
175C22×D3—62no—
176C22×D3—62no—
177C22×D3—61no—
178C22×D3—62no—
179C22×D3—68no—
180C22×D3—124no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—22no—
187C2×C3×C4—21no—
188C2×C3×C4—22no—
189C2×Dic3—62no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—62no—
193C2×Dic3—62no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—62no—
197C4×D3—62no—
198C4×D3—62no—
199C4×D3—62no—
200C4×D3—62no—
201C4×D3—62no—
202C4×D3—62no—
203C4×D3—61no—
204C4×D3—61no—
205C4×D3—62no—
206C4×D3—62no—
207C4×D3—61no—
208C4×D3—61no—
209C4×D3—62no—
210C4×D3—62no—
211C4×D3—62no—
212C4×D3—61no—
213C4×D3—61no—
214C4×D3—62no—
215C4×D3—61no—
216C4×D3—61no—
217C3×C8—64no—
218C3×C8—64no—
219C3⋊C8—24no—
220C3⋊C8—24no—
221C2×C32—22no—
222C2×C32#42412yescomplemented
223C2×C32C22×C4⋊C411yescharacteristic
224C3⋊D3—22no—
225C3⋊D3#42412yescomplemented
226C3⋊D3C2×#13112yes—
227C24—91no—
228C22×C4—91no—
229C22×C4—92no—
230C22×C4—92no—
231C22×C4—91no—
232C22×C4—91no—
233C22×C4—91no—
234C22×C4—92no—
235C22×C4—92no—
236C22×C4—91no—
237C22×C4—94no—
238C22×C4GO+(4,𝔽2)11yescharacteristic
239M16—64no—
240M16—184no—
241C2×C8—64no—
242C2×C8—62no—
243C2×C8—62no—
244C2×C8—94no—
245C2×C8—94no—
246C2×C8—182no—
247C2×C8—184no—
248C2×C8—182no—
249C4⋊C4—98no—
250C22⋊C4—98no—
251C42—94no—
252C42—94no—
253C22×C3—24no—
254C22×C3—22no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—22no—
258C22×C3—42no—
259C2×D3—61no—
260C2×D3—61no—
261C2×D3—62no—
262C2×D3—61no—
263C2×D3—61no—
264C2×D3—64no—
265C2×D3—64no—
266C2×D3—62no—
267C2×D3—68no—
268C2×D3—68no—
269C2×D3—64no—
270C2×D3—124no—
271C2×D3—124no—
272C2×D3—122no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—21no—
278C3×C4—21no—
279Dic3—61no—
280Dic3—61no—
281Dic3—62no—
282Dic3—62no—
283Dic3—61no—
284Dic3—61no—
285C32C2×#42411yescharacteristic, complemented, Sylow
286C23—91no—
287C23—92no—
288C23—92no—
289C23—91no—
290C23—184no—
291C23#377311yescharacteristic
292C2×C4—92no—
293C2×C4—92no—
294C2×C4—91no—
295C2×C4—91no—
296C2×C4—91no—
297C2×C4—91no—
298C2×C4—92no—
299C2×C4—91no—
300C2×C4—92no—
301C2×C4—92no—
302C2×C4—92no—
303C2×C4—92no—
304C2×C4—91no—
305C2×C4—92no—
306C2×C4—98no—
307C2×C4—188no—
308C2×C4#377311yescharacteristic
309C2×C4#377312yes—
310C2×C4C2×GO+(4,𝔽2)12yes—
311C2×C4C2×GO+(4,𝔽2)11yescharacteristic
312C8—64no—
313C8—64no—
314C2×C3—24no—
315C2×C3—22no—
316C2×C3—22no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—42no—
320D3—62no—
321D3—62no—
322D3—62no—
323D3—62no—
324D3—64no—
325D3—122no—
326C22—22no—
327C22—94no—
328C22—91no—
329C22—91no—
330C22—92no—
331C22—184no—
332C22—184no—
333C22—182no—
334C22C2×#377312yes—
335C22C2×#377311yescharacteristic
336C4—91no—
337C4—91no—
338C4—92no—
339C4—188no—
340C4C2×#377312yes—
341C4C2×#377311yescharacteristic
342C4C22×GO+(4,𝔽2)11yescharacteristic
343C3—21no—
344C3—21no—
345C2—22no—
346C2—92no—
347C2—92no—
348C2—182no—
349C2#1059332712yesdirect product factor
350C2C22×#377311yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FrattiniC4C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC4×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#424
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10593327C2direct (N × H)
5. C2×#63732C2semidirect
22. #63732C22semidirect
222. C2×C32#424semidirect
225. C3⋊D3#424semidirect
285. C32C2×#424semidirect
349. C2#10593327direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642862
C2×#638182
C22×#37102
#105933272
C2×#637322
C2×#4249