Finite Group Databasebeta

← C2×#10590030 #11774189

Subgroups — C2×#10590030 #11774189

Order 1152.

638 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 95 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×#63779C211yesmaximal, characteristic, complemented
3C2×#63553C211yesmaximal, characteristic, complemented
4#10590030C214yesmaximal, direct product factor
5C22×#625C411yescharacteristic
6C22×D3×Dic3—21no—
7C22×#622—21no—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C2×C3×(C2×D3)⋊C4—21no—
10C22×C3×C3⋊C8—21no—
11C2×#3724C411yescharacteristic
12#63902—21no—
13#63902—21no—
14#63902C412yes—
15#63902C2212yes—
16#63779—21no—
17#63779C2212yescomplemented
18#63553—21no—
19#63553C2212yescomplemented
20C2×#67⋊C4—61no—
21C2×C8×Dic3—61no—
22C23×C3×D3—21no—
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C22×C3×Dic3—21no—
27C2×#625—21no—
28C2×#625—22no—
29C2×#625C814yescomplemented
30C2×#625C2×C412yes—
31C2×D3×Dic3—22no—
32C2×D3×Dic3—22no—
33C2×D3×Dic3—42no—
34C2×D3×Dic3—42no—
35C2×#622—22no—
36C2×#622—42no—
37C4×C3⋊Dic3C2×C411yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3C2311yescharacteristic
41C3×(C2×D3)⋊C4—22no—
42C3×(C2×D3)⋊C4—22no—
43C2×C3×C3⋊C8—24no—
44C2×C3×C3⋊C8—22no—
45#3724—21no—
46#3724C2×C412yes—
47C2×D4⋊C8—91nomaximal, Sylow
48C22×#67—61no—
49C23×Dic3—61no—
50C22×C4×D3—61no—
51C22×C3×C8—61no—
52C2×C3×C22⋊C4—61no—
53C2×(C2×D3)⋊C4—21no—
54C2×Dic3⋊C4—61no—
55C2×C4×Dic3—61no—
56C2×C4×Dic3—61no—
57C22×C3⋊C8—21no—
58#67⋊C4—62no—
59#67⋊C4—62no—
60#67⋊C4—62no—
61#67⋊C4—62no—
62C8×Dic3—62no—
63C8×Dic3—62no—
64C23×C32C22⋊C411yescharacteristic
65C22×C3×D3—24no—
66C22×C3×D3—22no—
67C22×C3×D3—42no—
68C22×C3×D3—42no—
69C2×C32×C4—22no—
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C32×C4C2×D411yescharacteristic
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C2×C812yes—
75C2×C3⋊Dic3M1612yes—
76C2×C3⋊Dic3D812yes—
77C2×C3⋊Dic3SD1612yes—
78C2×C3⋊Dic3C22×C411yescharacteristic
79C2×C3⋊Dic3C2×D411yescharacteristic
80C2×C3×Dic3—22no—
81C2×C3×Dic3—42no—
82#625—24no—
83#625—22no—
84#625C2×C814yescomplemented
85D3×Dic3—44no—
86D3×Dic3—42no—
87D3×Dic3—42no—
88#622—42no—
89C3×C3⋊C8—24no—
90C2×C4×D4—91no—
91C2×C4⋊C8—91no—
92C2×C4×C8—91no—
93D4⋊C8—94no—
94C24×C3—61no—
95C23×D3—21no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×C3×C4—61no—
99C2×#67—62no—
100C2×#67—64no—
101C2×#67—62no—
102C2×#67—64no—
103C22×Dic3—21no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107C22×Dic3—61no—
108C22×Dic3—62no—
109C22×Dic3—62no—
110C22×Dic3—122no—
111C22×Dic3—122no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—122no—
115C2×C4×D3—122no—
116C2×C3×C8—62no—
117C2×C3×C8—64no—
118C3×C22⋊C4—62no—
119C3×C22⋊C4—62no—
120(C2×D3)⋊C4—22no—
121(C2×D3)⋊C4—22no—
122Dic3⋊C4—62no—
123Dic3⋊C4—62no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C4×Dic3—61no—
127C4×Dic3—61no—
128C4×Dic3—61no—
129C4×Dic3—61no—
130C4×Dic3—61no—
131C4×Dic3—61no—
132C2×C3⋊C8—22no—
133C2×C3⋊C8—24no—
134C22×C32C22⋊C812yes—
135C22×C32#10212yes—
136C22×C32#10412yes—
137C22×C32C2×C22⋊C411yescharacteristic
138C2×C3×D3—24no—
139C2×C3×D3—48no—
140C2×C3×D3—42no—
141C2×C3×D3—42no—
142C32×C4—21no—
143C32×C4—21no—
144C3⋊Dic3C22⋊C812yes—
145C3⋊Dic3#10212yes—
146C3⋊Dic3C22×C811yescharacteristic
147C3⋊Dic3C2×M1611yescharacteristic
148C3⋊Dic3C2×D811yescharacteristic
149C3⋊Dic3C2×SD1611yescharacteristic
150C3×Dic3—42no—
151C22×D4—91no—
152C23×C4—181no—
153C22×C8—61no—
154C22×C8—181no—
155C4×D4—92no—
156C4×D4—92no—
157C4×D4—181no—
158C4×D4—181no—
159C2×C4⋊C4—91no—
160C2×C22⋊C4—61no—
161C2×C42—91no—
162C4⋊C8—92no—
163C4⋊C8—181no—
164C4×C8—92no—
165C4×C8—181no—
166C23×C3—21no—
167C23×C3—21no—
168C23×C3—62no—
169C23×C3—64no—
170C23×C3—122no—
171C23×C3—122no—
172C22×D3—22no—
173C22×D3—24no—
174C22×D3—42no—
175C22×D3—42no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—42no—
183C2×C3×C4—62no—
184C2×C3×C4—122no—
185#67—64no—
186#67—68no—
187#67—64no—
188C2×Dic3—22no—
189C2×Dic3—42no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—62no—
195C2×Dic3—62no—
196C2×Dic3—62no—
197C2×Dic3—62no—
198C2×Dic3—62no—
199C2×Dic3—62no—
200C2×Dic3—62no—
201C2×Dic3—62no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—124no—
207C2×Dic3—122no—
208C2×Dic3—122no—
209C4×D3—124no—
210C4×D3—122no—
211C4×D3—122no—
212C3×C8—64no—
213C3⋊C8—24no—
214C2×C32D4⋊C814yescomplemented
215C2×C32C2×C22⋊C811yescharacteristic
216C2×C32C2×#10211yescharacteristic
217C2×C32C2×#10411yescharacteristic
218C3×D3—44no—
219C24—61no—
220C2×D4—92no—
221C2×D4—94no—
222C2×D4—181no—
223C2×D4—182no—
224C22×C4—61no—
225C22×C4—91no—
226C22×C4—91no—
227C22×C4—182no—
228C22×C4—182no—
229C22×C4—362no—
230C22×C4—362no—
231C22×C4GO+(4,𝔽2)11yescharacteristic
232C2×C8—64no—
233C2×C8—62no—
234C2×C8—182no—
235C2×C8—362no—
236C4⋊C4—92no—
237C4⋊C4—181no—
238C22⋊C4—62no—
239C22⋊C4—62no—
240C42—91no—
241C42—91no—
242C42—91no—
243C42—91no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—22no—
251C22×C3—22no—
252C22×C3—64no—
253C22×C3—122no—
254C22×C3—128no—
255C22×C3—122no—
256C2×D3—24no—
257C2×D3—42no—
258C2×D3—48no—
259C2×D3—42no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—22no—
263C3×C4—41no—
264C3×C4—41no—
265C3×C4—122no—
266Dic3—42no—
267Dic3—62no—
268Dic3—61no—
269Dic3—61no—
270Dic3—62no—
271Dic3—61no—
272Dic3—61no—
273Dic3—62no—
274Dic3—62no—
275Dic3—61no—
276Dic3—61no—
277Dic3—61no—
278Dic3—61no—
279C32C2×D4⋊C811yescharacteristic, complemented, Sylow
280C23—62no—
281C23—64no—
282C23—122no—
283C23—122no—
284C23D32⋊C411yescharacteristic
285D4—94no—
286D4—182no—
287D4—184no—
288C2×C4—22no—
289C2×C4—62no—
290C2×C4—91no—
291C2×C4—91no—
292C2×C4—91no—
293C2×C4—91no—
294C2×C4—92no—
295C2×C4—92no—
296C2×C4—92no—
297C2×C4—92no—
298C2×C4—122no—
299C2×C4—362no—
300C2×C4—362no—
301C2×C4—364no—
302C2×C4D32⋊C411yescharacteristic
303C2×C4C2×GO+(4,𝔽2)11yescharacteristic
304C8—64no—
305C8—362no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—24no—
311C2×C3—24no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—124no—
315D3—44no—
316C22—64no—
317C22—122no—
318C22—128no—
319C22—122no—
320C22D32⋊C812yes—
321C22#6372912yes—
322C22#6374112yes—
323C22C2×D32⋊C411yescharacteristic
324C4—21no—
325C4—21no—
326C4—91no—
327C4—91no—
328C4—92no—
329C4—91no—
330C4—91no—
331C4—92no—
332C4—122no—
333C3—21no—
334C3—21no—
335C2—124no—
336C2#1059003014yesdirect product factor
337C2C2×D32⋊C811yescharacteristic
338C2C2×#6372911yescharacteristic
339C2C2×#6374111yescharacteristic
subgroupG/H
centerC23D32⋊C4
commutatorC3⋊Dic3C22×C8
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C22⋊C4
prime radicalC22×#625C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×D4⋊C8
LCSG ▷ 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×#63779C2semidirect
3. C2×#63553C2semidirect
4. #10590030C2direct (N × H)
17. #63779C22semidirect
19. #63553C22semidirect
29. C2×#625C8semidirect
84. #625C2×C8semidirect
214. C2×C32D4⋊C8semidirect
279. C32C2×D4⋊C8semidirect
336. C2#10590030direct (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×#637792
C2×#635532
#105900302
C2×D4⋊C89