Finite Group Databasebeta

← C2×#10593347 #11868265

Subgroups — C2×#10593347 #11868265

Order 1152.

838 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 838 conjugacy classes of subgroups — too many to draw. Only its 143 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×C4×#625C211yesmaximal, characteristic
2C2×#63873C211yesmaximal, characteristic, complemented
3C2×C4⋊#622C211yesmaximal, characteristic, complemented
4C2×#63743C212yesmaximal, complemented
5C2×#63739C212yesmaximal
6#10593347C218yesmaximal, direct product factor
7C22×C3×C4×D3—21no—
8C22×C3×Dic6—21no—
9C22×#625C2211yescharacteristic
10C22×#622C2212yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×#3724—21no—
13C2×#3724C2212yes—
14C2×#3724C2211yescharacteristic
15C2×(C2×D3)⋊Dic3—21no—
16C4×#625—22no—
17C4×#625C2214yes—
18#63873—22no—
19#63873C2214yescomplemented
20C4⋊#622C2214yescomplemented
21#63743C2218yescomplemented
22#63739C2218yes—
23C2×#944—61no—
24C2×C4×#67—61no—
25C23×C3×D3—21no—
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C22×C3×Dic3—22no—
30C22×C3×Dic3—21no—
31C2×C3×C4×D3—24no—
32C2×C3×C4×D3—44no—
33C2×C3×Dic6—24no—
34C2×C3×Dic6—44no—
35C2×#625—21no—
36C2×#625—22no—
37C2×#625Q814yescomplemented
38C2×#625C2312yes—
39C2×#622—24no—
40C2×#622C2314yes—
41C4×C3⋊Dic3D412yes—
42C4×C3⋊Dic3C2312yes—
43#3724—22no—
44#3724—24no—
45#3724—21no—
46#3724C2314yes—
47#3724C2312yes—
48(C2×D3)⋊Dic3—24no—
49C2×#474—91nomaximal, Sylow
50C22×C3×Q8—61no—
51C23×C3×C4—61no—
52C22×#67—61no—
53C22×C4×D3—21no—
54C22×Dic6—21no—
55C2×#217—61no—
56#944—64no—
57#944—64no—
58C4×#67—64no—
59C4×#67—64no—
60C2×(C2×D3)⋊C4—61no—
61C2×Dic3⋊C4—61no—
62C2×Dic3⋊C4—62no—
63C2×Dic3⋊C4—62no—
64C2×C4×Dic3—61no—
65C2×C4×Dic3—61no—
66C23×C32C2×D411yescharacteristic
67C22×C3×D3—24no—
68C22×C3×D3—22no—
69C22×C3×D3—42no—
70C22×C3×D3—42no—
71C2×C32×C4D814yes—
72C2×C32×C4C2×D412yes—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3C2×D412yes—
75C2×C3⋊Dic3C2×D411yescharacteristic
76C2×C3⋊Dic3C2×Q812yes—
77C2×C3⋊Dic3#4112yes—
78C2×C3⋊Dic3C2411yescharacteristic
79C2×C3×Dic3—22no—
80C2×C3×Dic3—24no—
81C2×C3×Dic3—44no—
82C2×C3×Dic3—42no—
83C3×C4×D3—48no—
84C3×Dic6—48no—
85#625—24no—
86#625—22no—
87#625C2×Q814yescomplemented
88#622—24no—
89C2×C4⋊Q8—91no—
90C2×C4×D4—91no—
91#474—98no—
92C2×#107—92no—
93C2×C4⋊C8—91no—
94C2×#102—92no—
95C24×C3—61no—
96C23×D3—21no—
97C2×C3×Q8—64no—
98C2×C3×Q8—124no—
99C22×C3×C4—21no—
100C22×C3×C4—21no—
101C22×C3×C4—64no—
102C22×C3×C4—62no—
103C22×C3×C4—61no—
104C22×C3×C4—124no—
105C2×#67—62no—
106C2×#67—64no—
107C2×#67—62no—
108C2×#67—64no—
109C22×Dic3—22no—
110C22×Dic3—21no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C22×Dic3—61no—
114C22×Dic3—61no—
115C2×C4×D3—24no—
116C2×C4×D3—44no—
117C2×Dic6—24no—
118C2×Dic6—44no—
119#217—64no—
120(C2×D3)⋊C4—64no—
121Dic3⋊C4—62no—
122Dic3⋊C4—64no—
123Dic3⋊C4—62no—
124Dic3⋊C4—64no—
125Dic3⋊C4—68no—
126C4×Dic3—62no—
127C4×Dic3—62no—
128C4×Dic3—62no—
129C4×Dic3—62no—
130C22×C32C22⋊Q812yes—
131C22×C32C2×D812yes—
132C22×C32#13712yes—
133C22×C32C22×D411yescharacteristic
134C2×C3×D3—24no—
135C2×C3×D3—42no—
136C2×C3×D3—42no—
137C2×C3×D3—48no—
138C32×C4C2×D814yes—
139C3⋊Dic3—22no—
140C3⋊Dic3C22⋊Q812yes—
141C3⋊Dic3C22×Q811yescharacteristic
142C3⋊Dic3C2×#4111yescharacteristic
143C3×Dic3—44no—
144C3×Dic3—42no—
145C22×Q8—61no—
146C22×D4—91no—
147C23×C4—61no—
148C22×C8—92no—
149C4⋊Q8—94no—
150C4⋊Q8—182no—
151C4×D4—94no—
152C4×D4—182no—
153C2×C4⋊C4—91no—
154C2×C4⋊C4—92no—
155C2×C4⋊C4—181no—
156C2×C22⋊C4—181no—
157C2×C42—91no—
158#107—98no—
159C4⋊C8—94no—
160#102—98no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—62no—
164C23×C3—64no—
165C23×C3—122no—
166C23×C3—122no—
167C22×D3—22no—
168C22×D3—24no—
169C22×D3—42no—
170C22×D3—42no—
171C3×Q8—128no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—24no—
175C2×C3×C4—24no—
176C2×C3×C4—64no—
177C2×C3×C4—62no—
178C2×C3×C4—128no—
179C2×C3×C4—122no—
180C2×C3×C4—124no—
181#67—64no—
182#67—68no—
183#67—64no—
184C2×Dic3—24no—
185C2×Dic3—22no—
186C2×Dic3—44no—
187C2×Dic3—42no—
188C2×Dic3—61no—
189C2×Dic3—62no—
190C2×Dic3—61no—
191C2×Dic3—62no—
192C2×Dic3—62no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—62no—
198C2×Dic3—64no—
199C2×Dic3—122no—
200C4×D3—48no—
201Dic6—48no—
202C2×C32#47414yescomplemented
203C2×C32C2×C22⋊Q811yescharacteristic
204C2×C32C22×D811yescharacteristic
205C2×C32C2×#13711yescharacteristic
206C3×D3—44no—
207C24—61no—
208C2×Q8—64no—
209C2×Q8—124no—
210C2×D4—92no—
211C2×D4—94no—
212C2×D4—181no—
213C2×D4—182no—
214C22×C4—61no—
215C22×C4—62no—
216C22×C4—64no—
217C22×C4—91no—
218C22×C4—91no—
219C22×C4—124no—
220C22×C4GO+(4,𝔽2)11yescharacteristic
221C2×C8—94no—
222C2×C8—184no—
223C4⋊C4—94no—
224C4⋊C4—92no—
225C4⋊C4—181no—
226C4⋊C4—182no—
227C4⋊C4—184no—
228C22⋊C4—184no—
229C42—92no—
230C42—92no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—22no—
234C22×C3—22no—
235C22×C3—22no—
236C22×C3—22no—
237C22×C3—22no—
238C22×C3—22no—
239C22×C3—64no—
240C22×C3—122no—
241C22×C3—128no—
242C22×C3—122no—
243C2×D3—24no—
244C2×D3—42no—
245C2×D3—48no—
246C2×D3—42no—
247C3×C4—24no—
248C3×C4—24no—
249C3×C4—122no—
250C3×C4—124no—
251Dic3—44no—
252Dic3—42no—
253Dic3—62no—
254Dic3—61no—
255Dic3—61no—
256Dic3—62no—
257Dic3—61no—
258Dic3—61no—
259Dic3—64no—
260Dic3—122no—
261C32C2×#47411yescharacteristic, complemented, Sylow
262C23—62no—
263C23—64no—
264C23—122no—
265C23—122no—
266C23C2×GO+(4,𝔽2)11yescharacteristic
267Q8—128no—
268D4—94no—
269D4—182no—
270D4—184no—
271C2×C4—62no—
272C2×C4—64no—
273C2×C4—91no—
274C2×C4—91no—
275C2×C4—92no—
276C2×C4—92no—
277C2×C4—92no—
278C2×C4—122no—
279C2×C4—124no—
280C2×C4—128no—
281C2×C4—182no—
282C2×C4#377414yes—
283C2×C4C2×GO+(4,𝔽2)12yes—
284C8—184no—
285C2×C3—24no—
286C2×C3—24no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—124no—
294D3—44no—
295C22—64no—
296C22—128no—
297C22—122no—
298C22—122no—
299C22D32⋊Q812yes—
300C22#6422612yes—
301C22C2×#377412yes—
302C22C22×GO+(4,𝔽2)11yescharacteristic
303C4—91no—
304C4—91no—
305C4—92no—
306C4—122no—
307C4—124no—
308C4—182no—
309C4C2×#377414yes—
310C3—21no—
311C3—21no—
312C2—124no—
313C2#1059334714yesdirect product factor
314C2C2×D32⋊Q811yescharacteristic
315C2C2×#6422611yescharacteristic
316C2C22×#377411yescharacteristic
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×#474
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×#63873C2semidirect
3. C2×C4⋊#622C2semidirect
4. C2×#63743C2semidirect
6. #10593347C2direct (N × H)
19. #63873C22semidirect
20. C4⋊#622C22semidirect
21. #63743C22semidirect
37. C2×#625Q8semidirect
87. #625C2×Q8semidirect
202. C2×C32#474semidirect
261. C32C2×#474semidirect
313. C2#10593347direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6252
C2×#638732
C2×C4⋊#6222
C2×#637432
C2×#637392
#105933472
C2×#4749