Finite Group Databasebeta

← C2×#10593364 #11868375

Subgroups — C2×#10593364 #11868375

Order 1152.

774 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 774 conjugacy classes of subgroups — too many to draw. Only its 127 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×#63902C211yesmaximal, characteristic
2C2×#63870C211yesmaximal, characteristic, complemented
3C2×C4⋊#622C211yesmaximal, characteristic, complemented
4C2×#63743C211yesmaximal, characteristic, complemented
5C2×#63742C211yesmaximal, characteristic, complemented
6C2×#63739C211yesmaximal, characteristic
7C2×#63739C211yesmaximal, characteristic
8#10593364C218yesmaximal, direct product factor
9C22×#625C2211yescharacteristic
10C22×D3×Dic3—21no—
11C22×#622C2211yescharacteristic
12C22×#622C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×Dic3⋊C4—21no—
16C2×#3724C2211yescharacteristic
17C2×#3724C2211yescharacteristic
18C2×#3724C2211yescharacteristic
19C2×Dic3⋊Dic3—21no—
20#63902—22no—
21#63902C2214yes—
22#63870—22no—
23#63870C2214yescomplemented
24C4⋊#622C2214yescomplemented
25#63743C2214yescomplemented
26#63742C2214yescomplemented
27#63739C2214yes—
28#63739C2214yes—
29C2×#889—61no—
30C2×#67⋊C4—61no—
31C23×C3×D3—21no—
32C22×C32×C4D411yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C22×C3⋊Dic3C2311yescharacteristic
35C22×C3×Dic3—21no—
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C2×#625—21no—
39C2×#625—22no—
40C2×#625Q814yes—
41C2×#625C2312yes—
42C2×D3×Dic3—24no—
43C2×D3×Dic3—44no—
44C2×#622—22no—
45C2×#622—22no—
46C2×#622C2312yes—
47C2×#622C2312yes—
48C4×C3⋊Dic3D412yes—
49C4×C3⋊Dic3C2312yes—
50C3×(C2×D3)⋊C4—24no—
51C3×Dic3⋊C4—24no—
52#3724—21no—
53#3724—21no—
54#3724—21no—
55#3724C2312yes—
56#3724C2312yes—
57#3724C2312yes—
58Dic3⋊Dic3—24no—
59C2×#478—91nomaximal, Sylow
60C22×#67—61no—
61C23×Dic3—61no—
62C22×C4×D3—61no—
63C2×C3×C4⋊C4—61no—
64C2×C3×C22⋊C4—61no—
65C2×(C2×D3)⋊C4—21no—
66C2×C4⋊Dic3—61no—
67C2×Dic3⋊C4—21no—
68C2×Dic3⋊C4—61no—
69C2×Dic3⋊C4—61no—
70C2×Dic3⋊C4—61no—
71C2×Dic3⋊C4—61no—
72C2×C4×Dic3—61no—
73C2×C4×Dic3—61no—
74#889—64no—
75#889—64no—
76#67⋊C4—64no—
77#67⋊C4—64no—
78C23×C32C2×D411yescharacteristic
79C22×C3×D3—24no—
80C22×C3×D3—22no—
81C22×C3×D3—42no—
82C22×C3×D3—42no—
83C2×C32×C4—22no—
84C2×C32×C4C2×D412yes—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3C2×D412yes—
87C2×C3⋊Dic3C2×D411yescharacteristic
88C2×C3⋊Dic3C2×Q812yes—
89C2×C3⋊Dic3#4112yes—
90C2×C3⋊Dic3C2411yescharacteristic
91C2×C3×Dic3—22no—
92C2×C3×Dic3—22no—
93C2×C3×Dic3—22no—
94C2×C3×Dic3—42no—
95C2×C3×Dic3—42no—
96C2×C3×Dic3—42no—
97#625—24no—
98#625—22no—
99#625C2×Q814yes—
100D3×Dic3—48no—
101#622—22no—
102#622—22no—
103C2×#125—91no—
104C2×C4×D4—91no—
105#478—98no—
106C2×#107—91no—
107C2×#106—91no—
108C2×C4⋊C8—91no—
109C2×#102—91no—
110C2×#102—91no—
111C24×C3—61no—
112C23×D3—21no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—61no—
116C22×C3×C4—61no—
117C22×C3×C4—61no—
118C2×#67—62no—
119C2×#67—64no—
120C2×#67—62no—
121C2×#67—64no—
122C22×Dic3—21no—
123C22×Dic3—21no—
124C22×Dic3—21no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C22×Dic3—61no—
129C22×Dic3—64no—
130C22×Dic3—124no—
131C2×C4×D3—64no—
132C2×C4×D3—124no—
133C3×C4⋊C4—64no—
134C3×C22⋊C4—64no—
135(C2×D3)⋊C4—24no—
136C4⋊Dic3—64no—
137Dic3⋊C4—24no—
138Dic3⋊C4—62no—
139Dic3⋊C4—62no—
140Dic3⋊C4—62no—
141Dic3⋊C4—62no—
142Dic3⋊C4—64no—
143Dic3⋊C4—62no—
144Dic3⋊C4—62no—
145C4×Dic3—62no—
146C4×Dic3—62no—
147C4×Dic3—62no—
148C4×Dic3—62no—
149C22×C32C22⋊Q812yes—
150C22×C32#13512yes—
151C22×C32AGL(1,ℤ/8)12yes—
152C22×C32C22×D411yescharacteristic
153C2×C3×D3—24no—
154C2×C3×D3—42no—
155C2×C3×D3—42no—
156C2×C3×D3—48no—
157C32×C4—22no—
158C3⋊Dic3—22no—
159C3⋊Dic3C22⋊Q812yes—
160C3⋊Dic3C22×Q811yescharacteristic
161C3⋊Dic3C2×#4111yescharacteristic
162C3×Dic3—42no—
163C3×Dic3—42no—
164C3×Dic3—42no—
165C22×D4—91no—
166C23×C4—181no—
167C22×C8—91no—
168C22×C8—91no—
169#125—94no—
170#125—182no—
171C4×D4—94no—
172C4×D4—182no—
173C2×C4⋊C4—61no—
174C2×C4⋊C4—91no—
175C2×C4⋊C4—91no—
176C2×C4⋊C4—91no—
177C2×C4⋊C4—181no—
178C2×C22⋊C4—61no—
179C2×C42—91no—
180#107—94no—
181#106—94no—
182C4⋊C8—94no—
183#102—94no—
184#102—94no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3—62no—
188C23×C3—64no—
189C23×C3—122no—
190C23×C3—122no—
191C22×D3—22no—
192C22×D3—24no—
193C22×D3—42no—
194C22×D3—42no—
195C2×C3×C4—22no—
196C2×C3×C4—22no—
197C2×C3×C4—42no—
198C2×C3×C4—42no—
199C2×C3×C4—62no—
200C2×C3×C4—62no—
201C2×C3×C4—62no—
202C2×C3×C4—122no—
203C2×C3×C4—122no—
204C2×C3×C4—122no—
205#67—64no—
206#67—68no—
207#67—64no—
208C2×Dic3—22no—
209C2×Dic3—22no—
210C2×Dic3—22no—
211C2×Dic3—42no—
212C2×Dic3—42no—
213C2×Dic3—42no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—61no—
222C2×Dic3—61no—
223C2×Dic3—62no—
224C2×Dic3—64no—
225C2×Dic3—122no—
226C2×Dic3—128no—
227C4×D3—128no—
228C2×C32#47814yescomplemented
229C2×C32C2×C22⋊Q811yescharacteristic
230C2×C32C2×#13511yescharacteristic
231C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
232C3×D3—44no—
233C24—61no—
234C2×D4—92no—
235C2×D4—94no—
236C2×D4—181no—
237C2×D4—182no—
238C22×C4—61no—
239C22×C4—61no—
240C22×C4—61no—
241C22×C4—91no—
242C22×C4—91no—
243C22×C4—184no—
244C22×C4—364no—
245C22×C4GO+(4,𝔽2)11yescharacteristic
246C2×C8—92no—
247C2×C8—92no—
248C2×C8—182no—
249C2×C8—182no—
250C4⋊C4—64no—
251C4⋊C4—92no—
252C4⋊C4—92no—
253C4⋊C4—92no—
254C4⋊C4—181no—
255C4⋊C4—181no—
256C4⋊C4—181no—
257C4⋊C4—184no—
258C22⋊C4—64no—
259C42—92no—
260C42—92no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—64no—
270C22×C3—122no—
271C22×C3—128no—
272C22×C3—122no—
273C2×D3—24no—
274C2×D3—42no—
275C2×D3—48no—
276C2×D3—42no—
277C3×C4—42no—
278C3×C4—42no—
279C3×C4—122no—
280C3×C4—122no—
281C3×C4—122no—
282Dic3—42no—
283Dic3—42no—
284Dic3—42no—
285Dic3—62no—
286Dic3—61no—
287Dic3—61no—
288Dic3—62no—
289Dic3—61no—
290Dic3—61no—
291Dic3—64no—
292Dic3—122no—
293C32C2×#47811yescharacteristic, complemented, Sylow
294C23—62no—
295C23—64no—
296C23—122no—
297C23—122no—
298C23C2×GO+(4,𝔽2)11yescharacteristic
299D4—94no—
300D4—182no—
301D4—184no—
302C2×C4—22no—
303C2×C4—62no—
304C2×C4—62no—
305C2×C4—62no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—92no—
309C2×C4—92no—
310C2×C4—92no—
311C2×C4—122no—
312C2×C4—122no—
313C2×C4—122no—
314C2×C4—182no—
315C2×C4—368no—
316C2×C4C2×GO+(4,𝔽2)12yes—
317C8—182no—
318C8—182no—
319C2×C3—24no—
320C2×C3—24no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—124no—
328D3—44no—
329C22—64no—
330C22—128no—
331C22—122no—
332C22—122no—
333C22D32⋊Q812yes—
334C22#6422412yes—
335C22#6423712yes—
336C22C22×GO+(4,𝔽2)11yescharacteristic
337C4—22no—
338C4—91no—
339C4—91no—
340C4—92no—
341C4—122no—
342C4—122no—
343C4—122no—
344C4—182no—
345C3—21no—
346C3—21no—
347C2—124no—
348C2#1059336414yesdirect product factor
349C2C2×D32⋊Q811yescharacteristic
350C2C2×#6422411yescharacteristic
351C2C2×#6423711yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#625C22
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#478
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63870C2semidirect
3. C2×C4⋊#622C2semidirect
4. C2×#63743C2semidirect
5. C2×#63742C2semidirect
8. #10593364C2direct (N × H)
23. #63870C22semidirect
24. C4⋊#622C22semidirect
25. #63743C22semidirect
26. #63742C22semidirect
228. C2×C32#478semidirect
293. C32C2×#478semidirect
348. C2#10593364direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639022
C2×#638702
C2×C4⋊#6222
C2×#637432
C2×#637422
C2×#637392
#105933642
C2×#4789