Finite Group Databasebeta

← C2×#10593371 #11863680

Subgroups — C2×#10593371 #11863680

Order 1152.

1326 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 1326 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
1C22×#3797C211yesmaximal, characteristic
2C22×#3776C212yesmaximal, complemented
3C2×#63865C211yesmaximal, characteristic
4C2×#63778C211yesmaximal, characteristic
5C2×#63740C212yesmaximal, complemented
6#10593371C218yesmaximal, direct product factor
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×C3×Dic6—21no—
9C22×#627C2211yescharacteristic
10C22×#627C2212yes—
11C22×#624—21no—
12C2×#3797—22no—
13C2×#3797—28no—
14C2×#3797C2214yes—
15C22×#622C2212yes—
16C2×#3776—28no—
17C2×#3776C2218yescomplemented
18C2×C3×Dic3⋊C4—21no—
19C2×#3724C2211yescharacteristic
20C2×#3722—21no—
21#63865—22no—
22#63865C2214yes—
23#63778C2214yes—
24#63740C2218yescomplemented
25C22×D3×Q8—61no—
26C2×#896—61no—
27C23×C3⋊D3D411yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C3⋊Dic3C2311yescharacteristic
30C2×C4×C3⋊D3—24no—
31C2×C4×C3⋊D3D412yes—
32C2×C4×C3⋊D3C2312yes—
33C22×C3×Dic3—22no—
34C22×C3×Dic3—21no—
35C22×C3×Dic3—21no—
36C2×C3×Dic6—28no—
37C2×C3×Dic6—24no—
38C2×#627—22no—
39C2×#627—24no—
40C2×#627—24no—
41C2×#627—21no—
42C2×#627D418yes—
43C2×#627C2312yes—
44C2×#627C2314yes—
45C2×#624—28no—
46C2×#624—24no—
47#3797—216no—
48#3797—216no—
49C2×#622—24no—
50C2×#622C2314yes—
51#3776—216no—
52C3×Dic3⋊C4—24no—
53#3724—21no—
54#3724C2312yes—
55#3722—24no—
56C2×#451—91nomaximal, Sylow
57C22×C3×Q8—61no—
58C2×D3×Q8—64no—
59C2×D3×Q8—64no—
60C2×D3×Q8—616no—
61C22×C4×D3—61no—
62C22×C4×D3—61no—
63C22×C4×D3—62no—
64C22×Dic6—21no—
65C22×Dic6—62no—
66C22×Dic6—61no—
67C2×C3×C4⋊C4—61no—
68C2×(C2×D3)⋊C4—61no—
69C2×(C2×D3)⋊C4—61no—
70C2×Dic3⋊C4—21no—
71C2×Dic3⋊C4—61no—
72#896—64no—
73#896—64no—
74C23×C32C2×D411yescharacteristic
75C22×C3⋊D3—22no—
76C22×C3⋊D3—22no—
77C22×C3⋊D3Q1614yescomplemented
78C22×C3⋊D3C2×D412yes—
79C2×C32×C4—22no—
80C2×C32×C4C2×D412yes—
81C2×C3⋊Dic3C2×D411yescharacteristic
82C2×C3⋊Dic3C2×D414yes—
83C2×C3⋊Dic3C2411yescharacteristic
84C4×C3⋊D3—24no—
85C4×C3⋊D3—24no—
86C2×C3×Dic3—28no—
87C2×C3×Dic3—24no—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3—42no—
92C3×Dic6—216no—
93#627—28no—
94#627—24no—
95#627—24no—
96#627—42no—
97#627C2×D418yes—
98#624—216no—
99#622—24no—
100C23×Q8—91no—
101C22×Q16—92no—
102C2×C22⋊Q8—91no—
103#451—98no—
104C2×#103—92no—
105C2×C22⋊C8—91no—
106C23×D3—61no—
107C23×D3—61no—
108C2×C3×Q8—68no—
109C2×C3×Q8—64no—
110C22×C3×C4—21no—
111C22×C3×C4—21no—
112C22×C3×C4—62no—
113C22×C3×C4—61no—
114C22×C3×C4—61no—
115C22×Dic3—22no—
116C22×Dic3—21no—
117C22×Dic3—21no—
118C22×Dic3—61no—
119C22×Dic3—61no—
120D3×Q8—632no—
121D3×Q8—632no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—62no—
126C2×C4×D3—68no—
127C2×C4×D3—616no—
128C2×C4×D3—68no—
129C2×C4×D3—124no—
130C2×Dic6—28no—
131C2×Dic6—24no—
132C2×Dic6—68no—
133C2×Dic6—64no—
134C2×Dic6—62no—
135C2×Dic6—64no—
136C2×Dic6—68no—
137C2×Dic6—62no—
138C2×Dic6—124no—
139C3×C4⋊C4—64no—
140(C2×D3)⋊C4—64no—
141(C2×D3)⋊C4—64no—
142Dic3⋊C4—24no—
143Dic3⋊C4—62no—
144Dic3⋊C4—62no—
145C22×C32#12012yes—
146C22×C32C2×Q1612yes—
147C22×C32#13712yes—
148C22×C32C22×D411yescharacteristic
149C2×C3⋊D3—22no—
150C2×C3⋊D3—22no—
151C2×C3⋊D3—28no—
152C2×C3⋊D3C2×Q1614yescomplemented
153C32×C4—22no—
154C3⋊Dic3#12012yes—
155C3⋊Dic3C22×D412yes—
156C3×Dic3—28no—
157C3×Dic3—42no—
158C3×Dic3—42no—
159C22×Q8—61no—
160C22×Q8—92no—
161C22×Q8—91no—
162C22×Q8—94no—
163C22×Q8—182no—
164C22×Q8—188no—
165C23×C4—91no—
166C23×C4—181no—
167C2×Q16—98no—
168C2×Q16—188no—
169C22×C8—92no—
170C22⋊Q8—94no—
171C22⋊Q8—182no—
172C2×C4⋊C4—61no—
173C2×C4⋊C4—91no—
174C2×C22⋊C4—181no—
175#103—98no—
176C22⋊C8—94no—
177C23×C3—21no—
178C23×C3—21no—
179C22×D3—64no—
180C22×D3—62no—
181C22×D3—64no—
182C22×D3—62no—
183C22×D3—64no—
184C22×D3—64no—
185C22×D3—122no—
186C22×D3—122no—
187C3×Q8—616no—
188C2×C3×C4—24no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—42no—
192C2×C3×C4—64no—
193C2×C3×C4—68no—
194C2×C3×C4—62no—
195C2×C3×C4—62no—
196C2×C3×C4—122no—
197C2×C3×C4—122no—
198C2×Dic3—24no—
199C2×Dic3—28no—
200C2×Dic3—22no—
201C2×Dic3—22no—
202C2×Dic3—42no—
203C2×Dic3—42no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—64no—
207C2×Dic3—64no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C4×D3—632no—
211C4×D3—68no—
212C4×D3—68no—
213C4×D3—124no—
214C4×D3—124no—
215Dic6—216no—
216Dic6—68no—
217Dic6—616no—
218Dic6—68no—
219Dic6—124no—
220Dic6—124no—
221C2×C32#45114yescomplemented
222C2×C32C2×#12011yescharacteristic
223C2×C32C22×Q1611yescharacteristic
224C2×C32C2×#13711yescharacteristic
225C3⋊D3—24no—
226C24—91no—
227C2×Q8—68no—
228C2×Q8—64no—
229C2×Q8—94no—
230C2×Q8—98no—
231C2×Q8—92no—
232C2×Q8—182no—
233C2×Q8—184no—
234C2×Q8—181no—
235C2×Q8—184no—
236C2×Q8—1816no—
237C2×Q8—1816no—
238C22×C4—62no—
239C22×C4—61no—
240C22×C4—61no—
241C22×C4—91no—
242C22×C4—92no—
243C22×C4—92no—
244C22×C4—184no—
245C22×C4—184no—
246C22×C4—188no—
247C22×C4GO+(4,𝔽2)11yescharacteristic
248Q16—1816no—
249C2×C8—94no—
250C2×C8—184no—
251C4⋊C4—64no—
252C4⋊C4—92no—
253C4⋊C4—181no—
254C22⋊C4—184no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—22no—
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—22no—
262C22×C3—22no—
263C2×D3—64no—
264C2×D3—64no—
265C2×D3—64no—
266C2×D3—616no—
267C2×D3—64no—
268C2×D3—122no—
269C2×D3—128no—
270C2×D3—122no—
271C3×C4—24no—
272C3×C4—42no—
273C3×C4—68no—
274C3×C4—122no—
275C3×C4—122no—
276Dic3—28no—
277Dic3—42no—
278Dic3—42no—
279Dic3—62no—
280Dic3—62no—
281Dic3—62no—
282Dic3—62no—
283C32C2×#45111yescharacteristic, complemented, Sylow
284C23—92no—
285C23—94no—
286C23—182no—
287C23—182no—
288C23C2×GO+(4,𝔽2)11yescharacteristic
289Q8—616no—
290Q8—98no—
291Q8—184no—
292Q8—188no—
293Q8—184no—
294Q8—362no—
295C2×C4—22no—
296C2×C4—64no—
297C2×C4—68no—
298C2×C4—62no—
299C2×C4—62no—
300C2×C4—91no—
301C2×C4—91no—
302C2×C4—94no—
303C2×C4—122no—
304C2×C4—122no—
305C2×C4—184no—
306C2×C4—184no—
307C2×C4—1816no—
308C2×C4C2×GO+(4,𝔽2)12yes—
309C8—184no—
310C2×C3—24no—
311C2×C3—24no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318D3—68no—
319D3—124no—
320C22—94no—
321C22—188no—
322C22—182no—
323C22—182no—
324C22#6422612yes—
325C22#6422812yes—
326C22#6424112yes—
327C22C22×GO+(4,𝔽2)11yescharacteristic
328C4—22no—
329C4—68no—
330C4—92no—
331C4—92no—
332C4—122no—
333C4—122no—
334C3—21no—
335C3—21no—
336C2—184no—
337C2#1059337114yesdirect product factor
338C2C2×#6422611yescharacteristic
339C2C2×#6422811yescharacteristic
340C2C2×#6424111yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#451
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. C22×#3776C2semidirect
5. C2×#63740C2semidirect
6. #10593371C2direct (N × H)
17. C2×#3776C22semidirect
24. #63740C22semidirect
77. C22×C3⋊D3Q16semidirect
152. C2×C3⋊D3C2×Q16semidirect
221. C2×C32#451semidirect
283. C32C2×#451semidirect
337. C2#10593371direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C22×#37762
C2×#638652
C2×#637782
C2×#637402
#105933712
C2×#4519