Finite Group Databasebeta

← C2×#10593330 #11858654

Subgroups — C2×#10593330 #11858654

Order 1152.

758 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 191 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×#64283C211yesmaximal, characteristic
2C22×#3712C211yesmaximal, characteristic
3C2×#63818C211yesmaximal, characteristic
4#10593330C218yesmaximal, direct product factor
5C2×#63733C214yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×#3792C412yes—
8#64283C414yes—
9#64283C2214yes—
10C2×#3788C412yes—
11C2×#3787C2212yes—
12C2×C3×#208—21no—
13C22×C3×C3⋊C8—21no—
14C2×#3712—21no—
15C2×#3712—22no—
16C2×#3712C2212yes—
17C2×#3712C2212yes—
18C2×#3712C2214yes—
19#63818—22no—
20#63818C2214yes—
21C2×#3710—21no—
22#63733C22116yescomplemented
23C2×D3×M16—61no—
24C22×ΓL(1,𝔽25)—61no—
25C23×C3⋊D3Q811yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3C2×C412yes—
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3D412yes—
32C2×C4×C3⋊D3Q811yescharacteristic
33C2×C4×C3⋊D3Q812yes—
34C2×C4×C3⋊D3C2311yescharacteristic
35C2×C4×C3⋊D3C2312yes—
36#3792C2×C418yes—
37C2×#622C2×C414yes—
38#3788C2×C418yes—
39#3787C2×C414yes—
40#3787C2314yes—
41C3×#208—24no—
42C2×C3×C3⋊C8—22no—
43C2×C3×C3⋊C8—24no—
44C2×C3×C3⋊C8—22no—
45#3712—22no—
46#3712—24no—
47#3712—22no—
48#3712C2314yes—
49#3712C2314yes—
50#3710—24no—
51C2×#430—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×ΓL(1,𝔽25)—64no—
62C2×ΓL(1,𝔽25)—62no—
63C2×ΓL(1,𝔽25)—64no—
64C2×ΓL(1,𝔽25)—62no—
65C2×D3×C8—62no—
66C23×C32C4⋊C411yescharacteristic
67C22×C3⋊D3—42no—
68C22×C3⋊D3C4⋊C411yescharacteristic
69C22×C3⋊D3C4⋊C412yes—
70C22×C3⋊D3C2×Q811yescharacteristic
71C22×C3⋊D3C2×Q812yes—
72C2×C32×C4C4⋊C412yes—
73C2×C32×C4C4⋊C411yescharacteristic
74C2×C32×C4C2×D411yescharacteristic
75C2×C32×C4C2×D412yes—
76C2×C3⋊Dic3C4⋊C412yes—
77C2×C3⋊Dic3C4⋊C411yescharacteristic
78C2×C3⋊Dic3C22×C411yescharacteristic
79C2×C3⋊Dic3C22×C412yes—
80C4×C3⋊D3C4⋊C412yes—
81C4×C3⋊D3C4⋊C412yes—
82C4×C3⋊D3C4⋊C412yes—
83C4×C3⋊D3C22×C411yescharacteristic
84C4×C3⋊D3C22×C412yes—
85C4×C3⋊D3C2×D412yes—
86C4×C3⋊D3C2×D411yescharacteristic
87C4×C3⋊D3C2×Q811yescharacteristic
88C4×C3⋊D3C2×Q812yes—
89C4×C3⋊D3C2411yescharacteristic
90#622C22×C418yes—
91C3×C3⋊C8—24no—
92C3×C3⋊C8—24no—
93C22×M16—91no—
94C22×M16—91no—
95C22×M16—91no—
96#430—98no—
97C2×#108—94no—
98C23×D3—61no—
99C23×D3—61no—
100C22×C3×C4—21no—
101C22×C3×C4—21no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—62no—
106C2×C4×D3—61no—
107C2×C4×D3—62no—
108C2×C4×D3—61no—
109C2×C4×D3—61no—
110C2×C4×D3—62no—
111C2×C4×D3—62no—
112C2×C4×D3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—62no—
115C2×C4×D3—62no—
116C2×C4×D3—61no—
117C2×C4×D3—62no—
118C2×C4×D3—61no—
119C2×C4×D3—62no—
120C3×M16—64no—
121C2×C3×C8—62no—
122C2×C3×C8—64no—
123C2×C3×C8—62no—
124#208—24no—
125C2×C3⋊C8—22no—
126C2×C3⋊C8—24no—
127C2×C3⋊C8—22no—
128ΓL(1,𝔽25)—64no—
129ΓL(1,𝔽25)—64no—
130ΓL(1,𝔽25)—68no—
131ΓL(1,𝔽25)—64no—
132ΓL(1,𝔽25)—64no—
133D3×C8—68no—
134C22×C32—22no—
135C22×C32C2×C4⋊C412yes—
136C22×C32C2×C4⋊C411yescharacteristic
137C2×C3⋊D3—22no—
138C2×C3⋊D3—22no—
139C2×C3⋊D3—42no—
140C2×C3⋊D3—42no—
141C2×C3⋊D3C2×C4⋊C412yes—
142C2×C3⋊D3C2×C4⋊C411yescharacteristic
143C2×C3⋊D3C22×Q811yescharacteristic
144C32×C4C2×C4⋊C411yescharacteristic
145C32×C4C2×C4⋊C412yes—
146C32×C4C22×D411yescharacteristic
147C3⋊Dic3C2×C4⋊C412yes—
148C3⋊Dic3C2×C4⋊C411yescharacteristic
149C3⋊Dic3C23×C411yescharacteristic
150C23×C4—91no—
151C2×M16—61no—
152C2×M16—92no—
153C2×M16—92no—
154C2×M16—94no—
155C2×M16—92no—
156C2×M16—94no—
157C2×M16—94no—
158C2×M16—92no—
159C2×M16—94no—
160C2×M16—182no—
161C2×M16—181no—
162C2×M16—182no—
163C22×C8—61no—
164C22×C8—92no—
165C22×C8—181no—
166#108—916no—
167C23×C3—21no—
168C23×C3—21no—
169C22×D3—61no—
170C22×D3—61no—
171C22×D3—62no—
172C22×D3—62no—
173C22×D3—61no—
174C22×D3—61no—
175C22×D3—62no—
176C22×D3—62no—
177C22×D3—124no—
178C22×D3—124no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—22no—
185C2×C3×C4—21no—
186C2×C3×C4—22no—
187C2×Dic3—61no—
188C2×Dic3—62no—
189C2×Dic3—61no—
190C2×Dic3—62no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C4×D3—62no—
196C4×D3—62no—
197C4×D3—62no—
198C4×D3—62no—
199C4×D3—62no—
200C4×D3—62no—
201C4×D3—61no—
202C4×D3—61no—
203C4×D3—62no—
204C4×D3—62no—
205C4×D3—62no—
206C4×D3—62no—
207C4×D3—61no—
208C4×D3—61no—
209C4×D3—62no—
210C4×D3—61no—
211C4×D3—61no—
212C4×D3—62no—
213C4×D3—61no—
214C4×D3—61no—
215C3×C8—64no—
216C3×C8—64no—
217C3⋊C8—24no—
218C3⋊C8—24no—
219C2×C32—22no—
220C2×C32#43012yescomplemented
221C2×C32C22×C4⋊C411yescharacteristic
222C3⋊D3—22no—
223C3⋊D3—21no—
224C3⋊D3—21no—
225C24—91no—
226C22×C4—91no—
227C22×C4—92no—
228C22×C4—92no—
229C22×C4—91no—
230C22×C4—91no—
231C22×C4—91no—
232C22×C4—92no—
233C22×C4—91no—
234C22×C4—92no—
235C22×C4GO+(4,𝔽2)11yescharacteristic
236M16—64no—
237M16—94no—
238M16—94no—
239M16—98no—
240M16—98no—
241M16—184no—
242M16—182no—
243M16—182no—
244C2×C8—64no—
245C2×C8—62no—
246C2×C8—62no—
247C2×C8—94no—
248C2×C8—94no—
249C2×C8—94no—
250C2×C8—184no—
251C22×C3—24no—
252C22×C3—22no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—22no—
256C22×C3—42no—
257C2×D3—62no—
258C2×D3—62no—
259C2×D3—61no—
260C2×D3—61no—
261C2×D3—61no—
262C2×D3—61no—
263C2×D3—64no—
264C2×D3—122no—
265C2×D3—122no—
266C2×D3—122no—
267C2×D3—124no—
268C2×D3—124no—
269C2×D3—124no—
270C2×D3—124no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—22no—
274C3×C4—22no—
275C3×C4—21no—
276C3×C4—21no—
277Dic3—62no—
278Dic3—61no—
279Dic3—61no—
280Dic3—62no—
281Dic3—61no—
282Dic3—61no—
283C32C2×#43011yescharacteristic, complemented, Sylow
284C23—91no—
285C23—91no—
286C23—92no—
287C23—92no—
288C23—362no—
289C23#377311yescharacteristic
290C2×C4—91no—
291C2×C4—92no—
292C2×C4—92no—
293C2×C4—91no—
294C2×C4—91no—
295C2×C4—92no—
296C2×C4—91no—
297C2×C4—91no—
298C2×C4—92no—
299C2×C4—92no—
300C2×C4—92no—
301C2×C4—92no—
302C2×C4—91no—
303C2×C4—92no—
304C2×C4#377311yescharacteristic
305C2×C4#377312yes—
306C2×C4C2×GO+(4,𝔽2)12yes—
307C2×C4C2×GO+(4,𝔽2)11yescharacteristic
308C8—64no—
309C8—64no—
310C8—98no—
311C2×C3—24no—
312C2×C3—22no—
313C2×C3—22no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—42no—
317D3—64no—
318D3—122no—
319D3—121no—
320D3—121no—
321D3—121no—
322D3—121no—
323C22—22no—
324C22—92no—
325C22—91no—
326C22—91no—
327C22—182no—
328C22—182no—
329C22—362no—
330C22—362no—
331C22C2×#377312yes—
332C22C2×#377311yescharacteristic
333C4—91no—
334C4—91no—
335C4—92no—
336C4C2×#377312yes—
337C4C2×#377311yescharacteristic
338C4C22×GO+(4,𝔽2)11yescharacteristic
339C3—21no—
340C3—21no—
341C2—22no—
342C2—182no—
343C2—181no—
344C2—181no—
345C2#1059333012yesdirect product factor
346C2C22×#377311yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC4C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3Q8
cosocleC4×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#430
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10593330C2direct (N × H)
5. C2×#63733C2semidirect
22. #63733C22semidirect
220. C2×C32#430semidirect
283. C32C2×#430semidirect
345. C2#10593330direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642832
C22×#37122
C2×#638182
#105933302
C2×#637332
C2×#4309