Finite Group Databasebeta

← C2×#10593499 #11863679

Subgroups — C2×#10593499 #11863679

Order 1152.

1326 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 1326 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C23×#627C211yesmaximal, characteristic
2C22×#3776C212yesmaximal, complemented
3C2×#63982C211yesmaximal, characteristic
4C2×C22⋊#622C211yesmaximal, characteristic
5C2×#63740C212yesmaximal, complemented
6#10593499C218yesmaximal, direct product factor
7C23×C3⋊Dic3C2211yescharacteristic
8C23×C3×Dic3—21no—
9C22×#627—21no—
10C22×#627—22no—
11C22×#627—28no—
12C22×#627C2214yes—
13C22×#627C2211yescharacteristic
14C22×#627C2212yes—
15C22×#622C2212yes—
16C2×#3776—28no—
17C2×#3776C2218yescomplemented
18C2×C3×#217—21no—
19#63982—22no—
20#63982C2214yes—
21C2×#3724C2211yescharacteristic
22C2×Dic3⋊Dic3—21no—
23C22⋊#622C2214yes—
24#63740C2218yescomplemented
25C23×Dic6—61no—
26C2×#878—61no—
27C24×C32D411yescharacteristic
28C22×C3⋊Dic3—24no—
29C22×C3⋊Dic3D411yescharacteristic
30C22×C3⋊Dic3D412yes—
31C22×C3⋊Dic3C2312yes—
32C22×C3⋊Dic3C2311yescharacteristic
33C22×C3×Dic3—28no—
34C22×C3×Dic3—24no—
35C22×C3×Dic3—22no—
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C2×#627—28no—
39C2×#627—216no—
40C2×#627—24no—
41C2×#627—22no—
42C2×#627—24no—
43C2×#627—216no—
44C2×#627—24no—
45C2×#627—21no—
46C2×#627D418yes—
47C2×#627C2312yes—
48C2×#627C2314yes—
49C2×#622—24no—
50C2×#622C2314yes—
51#3776—216no—
52C3×#217—24no—
53#3724—21no—
54#3724C2312yes—
55Dic3⋊Dic3—24no—
56C2×#451—91nomaximal, Sylow
57C23×C3×C4—61no—
58C23×Dic3—21no—
59C23×Dic3—61no—
60C23×Dic3—61no—
61C22×Dic6—62no—
62C22×Dic6—64no—
63C22×Dic6—61no—
64C22×Dic6—64no—
65C22×Dic6—62no—
66C22×Dic6—616no—
67C2×C3×C22⋊C4—61no—
68C2×#217—21no—
69C2×C4⋊Dic3—61no—
70C2×Dic3⋊C4—61no—
71C2×Dic3⋊C4—61no—
72#878—64no—
73#878—64no—
74C23×C32—22no—
75C23×C32—22no—
76C23×C32Q1614yescomplemented
77C23×C32C2×D412yes—
78C23×C32C2×D411yescharacteristic
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3—24no—
81C2×C3⋊Dic3—24no—
82C2×C3⋊Dic3C2×D412yes—
83C2×C3⋊Dic3C2×D411yescharacteristic
84C2×C3⋊Dic3C2×D414yes—
85C2×C3⋊Dic3C2411yescharacteristic
86C2×C3×Dic3—216no—
87C2×C3×Dic3—28no—
88C2×C3×Dic3—24no—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—42no—
92C2×C3×Dic3—42no—
93#627—216no—
94#627—28no—
95#627—24no—
96#627—24no—
97#627—42no—
98#627C2×D418yes—
99#622—24no—
100C23×Q8—91no—
101C22×Q16—92no—
102C2×C22⋊Q8—91no—
103#451—98no—
104C2×#103—92no—
105C2×C22⋊C8—91no—
106C24×C3—21no—
107C24×C3—21no—
108C22×C3×C4—68no—
109C22×C3×C4—64no—
110C22×C3×C4—62no—
111C22×C3×C4—61no—
112C22×C3×C4—61no—
113C22×Dic3—28no—
114C22×Dic3—24no—
115C22×Dic3—22no—
116C22×Dic3—21no—
117C22×Dic3—21no—
118C22×Dic3—61no—
119C22×Dic3—62no—
120C22×Dic3—61no—
121C22×Dic3—61no—
122C22×Dic3—62no—
123C22×Dic3—62no—
124C22×Dic3—62no—
125C22×Dic3—61no—
126C22×Dic3—68no—
127C22×Dic3—124no—
128C2×Dic6—68no—
129C2×Dic6—64no—
130C2×Dic6—62no—
131C2×Dic6—64no—
132C2×Dic6—68no—
133C2×Dic6—68no—
134C2×Dic6—632no—
135C2×Dic6—632no—
136C2×Dic6—616no—
137C2×Dic6—62no—
138C2×Dic6—124no—
139C3×C22⋊C4—64no—
140#217—24no—
141C4⋊Dic3—64no—
142Dic3⋊C4—62no—
143Dic3⋊C4—64no—
144Dic3⋊C4—62no—
145C22×C32—22no—
146C22×C32—22no—
147C22×C32—28no—
148C22×C32#12012yes—
149C22×C32C2×Q1612yes—
150C22×C32C2×Q1614yescomplemented
151C22×C32#13712yes—
152C22×C32C22×D411yescharacteristic
153C3⋊Dic3—22no—
154C3⋊Dic3#12012yes—
155C3⋊Dic3C22×D412yes—
156C3×Dic3—28no—
157C3×Dic3—42no—
158C3×Dic3—42no—
159C22×Q8—92no—
160C22×Q8—91no—
161C22×Q8—94no—
162C22×Q8—182no—
163C22×Q8—181no—
164C22×Q8—188no—
165C23×C4—61no—
166C23×C4—91no—
167C2×Q16—98no—
168C2×Q16—188no—
169C22×C8—92no—
170C22⋊Q8—94no—
171C22⋊Q8—182no—
172C2×C4⋊C4—91no—
173C2×C4⋊C4—181no—
174C2×C22⋊C4—61no—
175#103—98no—
176C22⋊C8—94no—
177C23×C3—24no—
178C23×C3—24no—
179C23×C3—22no—
180C23×C3—22no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—24no—
184C23×C3—24no—
185C23×C3—42no—
186C23×C3—42no—
187C2×C3×C4—616no—
188C2×C3×C4—64no—
189C2×C3×C4—68no—
190C2×C3×C4—62no—
191C2×C3×C4—62no—
192C2×C3×C4—122no—
193C2×C3×C4—122no—
194C2×Dic3—216no—
195C2×Dic3—24no—
196C2×Dic3—28no—
197C2×Dic3—22no—
198C2×Dic3—22no—
199C2×Dic3—42no—
200C2×Dic3—42no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—64no—
204C2×Dic3—62no—
205C2×Dic3—64no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—62no—
209C2×Dic3—68no—
210C2×Dic3—68no—
211C2×Dic3—64no—
212C2×Dic3—124no—
213C2×Dic3—124no—
214C2×Dic3—122no—
215Dic6—68no—
216Dic6—616no—
217Dic6—68no—
218Dic6—632no—
219Dic6—124no—
220Dic6—124no—
221C2×C32—24no—
222C2×C32#45114yescomplemented
223C2×C32C2×#12011yescharacteristic
224C2×C32C22×Q1611yescharacteristic
225C2×C32C2×#13711yescharacteristic
226C24GO+(4,𝔽2)11yescharacteristic
227C2×Q8—94no—
228C2×Q8—98no—
229C2×Q8—92no—
230C2×Q8—182no—
231C2×Q8—184no—
232C2×Q8—184no—
233C2×Q8—181no—
234C2×Q8—1816no—
235C2×Q8—1816no—
236C2×Q8—188no—
237C2×Q8—184no—
238C22×C4—68no—
239C22×C4—64no—
240C22×C4—62no—
241C22×C4—61no—
242C22×C4—61no—
243C22×C4—91no—
244C22×C4—92no—
245C22×C4—92no—
246C22×C4—91no—
247C22×C4—184no—
248Q16—1816no—
249C2×C8—94no—
250C2×C8—184no—
251C4⋊C4—92no—
252C4⋊C4—181no—
253C4⋊C4—184no—
254C22⋊C4—64no—
255C22×C3—24no—
256C22×C3—24no—
257C22×C3—216no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—22no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—24no—
265C22×C3—24no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—42no—
269C22×C3—42no—
270C22×C3—48no—
271C3×C4—68no—
272C3×C4—122no—
273C3×C4—122no—
274Dic3—28no—
275Dic3—42no—
276Dic3—42no—
277Dic3—62no—
278Dic3—62no—
279Dic3—62no—
280Dic3—62no—
281Dic3—64no—
282Dic3—122no—
283C32C2×#45111yescharacteristic, complemented, Sylow
284C23—22no—
285C23—22no—
286C23#377614yescomplemented
287C23C2×GO+(4,𝔽2)12yes—
288C23C2×GO+(4,𝔽2)11yescharacteristic
289Q8—98no—
290Q8—184no—
291Q8—188no—
292Q8—1816no—
293Q8—184no—
294Q8—362no—
295C2×C4—616no—
296C2×C4—64no—
297C2×C4—68no—
298C2×C4—62no—
299C2×C4—62no—
300C2×C4—91no—
301C2×C4—91no—
302C2×C4—94no—
303C2×C4—92no—
304C2×C4—122no—
305C2×C4—122no—
306C2×C4—184no—
307C2×C4—184no—
308C2×C4—182no—
309C8—184no—
310C2×C3—28no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—24no—
318C2×C3—24no—
319C2×C3—44no—
320C22—22no—
321C22—22no—
322C22—28no—
323C22#6423912yes—
324C22C2×#377612yes—
325C22C2×#377614yescomplemented
326C22#6424112yes—
327C22C22×GO+(4,𝔽2)11yescharacteristic
328C4—68no—
329C4—92no—
330C4—92no—
331C4—122no—
332C4—122no—
333C4—182no—
334C3—21no—
335C3—21no—
336C2—24no—
337C2#1059349914yesdirect product factor
338C2C2×#6423911yescharacteristic
339C2C22×#377611yescharacteristic
340C2C2×#6424111yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
Fitting, prime radicalC24×C32D4
socleC23×C32C2×D4
hypercenterC24GO+(4,𝔽2)
hypocenterC32C2×#451
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C22×#3776C2semidirect
5. C2×#63740C2semidirect
6. #10593499C2direct (N × H)
17. C2×#3776C22semidirect
24. #63740C22semidirect
76. C23×C32Q16semidirect
150. C22×C32C2×Q16semidirect
222. C2×C32#451semidirect
283. C32C2×#451semidirect
286. C23#3776semidirect
325. C22C2×#3776semidirect
337. C2#10593499direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6272
C22×#37762
C2×#639822
C2×C22⋊#6222
C2×#637402
#105934992
C2×#4519