Finite Group Databasebeta

← #11868421

Subgroups — #11868421

Order 1152.

710 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#10593909C211yesmaximal, characteristic
2C4×#3797C211yesmaximal, characteristic
3#10593726C211yesmaximal, characteristic
4#10593387C212yesmaximal
5#10593385C214yesmaximal, complemented
6#10593376C214yesmaximal, complemented
7#10593375C212yesmaximal
8C2×#3797—21no—
9C2×#3797C2211yescharacteristic
10C2×#3787C2212yes—
11C42×C3⋊D3C2211yescharacteristic
12C3×#869—21no—
13C3×C4×Dic6—21no—
14#63919—21no—
15#63919C2212yes—
16C4×#627C2212yes—
17#63900—21no—
18#63900C2212yes—
19#63900C2211yescharacteristic
20#63883—21no—
21C4×#624—21no—
22#63873C2212yes—
23#63843—21no—
24#63838C2212yes—
25#63779C2212yes—
26C4⋊#622C2212yes—
27#63742C2218yes—
28#63740C2218yes—
29D3×C4⋊Q8—61no—
30C4×D3×Q8—61no—
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3C2311yescharacteristic
34C2×C3×Dic6—21no—
35C2×C3×Dic6—22no—
36C2×#627—22no—
37C2×#627C2312yes—
38C2×#624—21no—
39C2×#624—22no—
40C2×#624—21no—
41#3797—22no—
42#3797—44no—
43#3797Q814yescomplemented
44C2×#622C2314yes—
45#3787—24no—
46C32×C42D411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C4×C3⋊Dic3C2311yescharacteristic
49C4×C3⋊Dic3C2311yescharacteristic
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—22no—
52C3×C4⋊Dic3—22no—
53C3×Dic3⋊C4—22no—
54C3×C4×Dic3—22no—
55#3724—22no—
56#3724C2312yes—
57#3724C2314yes—
58Dic3⋊Dic3—22no—
59Dic32—22no—
60C2×#475—91nomaximal, Sylow
61C2×D3×Q8—61no—
62C2×D3×Q8—62no—
63C3×C4⋊Q8—61no—
64C3×C4×Q8—61no—
65Q8×Dic3—61no—
66#944—62no—
67D3×C4⋊C4—62no—
68D3×C4⋊C4—61no—
69D3×C4⋊C4—62no—
70D3×C4⋊C4—62no—
71#888—62no—
72#888—62no—
73#887—62no—
74#887—61no—
75C42×D3—61no—
76C42×D3—61no—
77C42×D3—62no—
78#869—21no—
79C4×Dic6—21no—
80C4×Dic6—62no—
81C22×C3⋊D3C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C3⋊Dic3C2×D411yescharacteristic
86C2×C3⋊Dic3C2×D411yescharacteristic
87C2×C3⋊Dic3C2411yescharacteristic
88C4×C3⋊D3—22no—
89C4×C3⋊D3SD1614yes—
90C4×C3⋊D3C2×Q812yes—
91C4×C3⋊D3#4112yes—
92C2×C3×Dic3—22no—
93C2×C3×Dic3—22no—
94C2×C3×Dic3—24no—
95C3×Dic6—24no—
96C3×Dic6—44no—
97#627—22no—
98#627—44no—
99#627C2×Q814yescomplemented
100#624—24no—
101#624—44no—
102#624—42no—
103#622—24no—
104C2×C4⋊Q8—91no—
105C2×C4×Q8—91no—
106#475—94no—
107#475—94no—
108C2×#106—92no—
109C2×C4⋊C8—91no—
110C2×#103—92no—
111C2×C3×Q8—61no—
112C2×C3×Q8—62no—
113D3×Q8—64no—
114D3×Q8—64no—
115D3×Q8—128no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—64no—
125C2×Dic6—21no—
126C2×Dic6—22no—
127C2×Dic6—62no—
128C2×Dic6—64no—
129C3×C4⋊C4—62no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—62no—
132C3×C4⋊C4—62no—
133C3×C42—21no—
134C3×C42—21no—
135C3×C42—62no—
136C4⋊Dic3—21no—
137C4⋊Dic3—22no—
138C4⋊Dic3—22no—
139C4⋊Dic3—62no—
140Dic3⋊C4—22no—
141Dic3⋊C4—62no—
142Dic3⋊C4—64no—
143Dic3⋊C4—62no—
144Dic3⋊C4—64no—
145C4×Dic3—22no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C4×Dic3—61no—
152C4×Dic3—62no—
153C4×Dic3—62no—
154C22×C32C22×D411yescharacteristic
155C2×C3⋊D3C22⋊Q812yes—
156C2×C3⋊D3C2×SD1612yes—
157C2×C3⋊D3#13712yes—
158C32×C4—21no—
159C32×C4C22⋊Q812yes—
160C32×C4C2×SD1612yes—
161C3⋊Dic3—21no—
162C3⋊Dic3C2×SD1612yes—
163C3⋊Dic3C22×Q811yescharacteristic
164C3⋊Dic3C2×#4111yescharacteristic
165C3×Dic3—24no—
166C3×Dic3—44no—
167C3×Dic3—42no—
168C22×Q8—91no—
169C22×Q8—181no—
170C22×C8—92no—
171C4⋊Q8—61no—
172C4⋊Q8—92no—
173C4⋊Q8—92no—
174C4⋊Q8—181no—
175C4×Q8—61no—
176C4×Q8—92no—
177C4×Q8—92no—
178C4×Q8—181no—
179C2×C4⋊C4—91no—
180C2×C4⋊C4—92no—
181C2×C4⋊C4—181no—
182C2×C4⋊C4—181no—
183C2×C42—91no—
184C2×C42—181no—
185#106—98no—
186C4⋊C8—92no—
187C4⋊C8—92no—
188#103—98no—
189C22×D3—61no—
190C22×D3—61no—
191C3×Q8—64no—
192C3×Q8—124no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—62no—
200C2×C3×C4—62no—
201C2×C3×C4—64no—
202C2×Dic3—22no—
203C2×Dic3—22no—
204C2×Dic3—24no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C4×D3—64no—
212C4×D3—64no—
213C4×D3—62no—
214C4×D3—62no—
215C4×D3—62no—
216C4×D3—62no—
217C4×D3—68no—
218C4×D3—64no—
219C4×D3—122no—
220C4×D3—124no—
221C4×D3—128no—
222Dic6—24no—
223Dic6—44no—
224Dic6—64no—
225Dic6—64no—
226Dic6—128no—
227C2×C32C2×C22⋊Q811yescharacteristic
228C2×C32C22×SD1611yescharacteristic
229C2×C32C2×#13711yescharacteristic
230C3⋊D3#47514yescomplemented
231C2×Q8—61no—
232C2×Q8—62no—
233C2×Q8—92no—
234C2×Q8—94no—
235C2×Q8—182no—
236C2×Q8—182no—
237C2×Q8—364no—
238C22×C4—91no—
239C22×C4—91no—
240C22×C4—91no—
241C22×C4—181no—
242C22×C4—181no—
243C22×C4—182no—
244C2×C8—94no—
245C2×C8—184no—
246C4⋊C4—61no—
247C4⋊C4—62no—
248C4⋊C4—62no—
249C4⋊C4—62no—
250C4⋊C4—94no—
251C4⋊C4—92no—
252C4⋊C4—182no—
253C4⋊C4—182no—
254C42—62no—
255C42—91no—
256C42—91no—
257C42—91no—
258C42—182no—
259C42GO+(4,𝔽2)11yescharacteristic
260C22×C3—21no—
261C22×C3—21no—
262C2×D3—62no—
263C2×D3—62no—
264C2×D3—62no—
265C2×D3—62no—
266C2×D3—62no—
267C2×D3—62no—
268C3×C4—22no—
269C3×C4—22no—
270C3×C4—22no—
271C3×C4—22no—
272C3×C4—22no—
273C3×C4—41no—
274C3×C4—64no—
275C3×C4—124no—
276C3×C4—122no—
277Dic3—24no—
278Dic3—44no—
279Dic3—42no—
280Dic3—61no—
281Dic3—61no—
282Dic3—62no—
283Dic3—62no—
284Dic3—61no—
285Dic3—61no—
286Dic3—62no—
287Dic3—121no—
288C32C2×#47511yescharacteristic, complemented, Sylow
289C23—91no—
290Q8—64no—
291Q8—94no—
292Q8—124no—
293Q8—182no—
294Q8—364no—
295C2×C4—62no—
296C2×C4—62no—
297C2×C4—64no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—92no—
301C2×C4—92no—
302C2×C4—94no—
303C2×C4—91no—
304C2×C4—182no—
305C2×C4—184no—
306C2×C4—364no—
307C2×C4—362no—
308C2×C4C2×GO+(4,𝔽2)11yescharacteristic
309C2×C4C2×GO+(4,𝔽2)11yescharacteristic
310C2×C4C2×GO+(4,𝔽2)11yescharacteristic
311C8—184no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318D3—64no—
319D3—64no—
320C22—92no—
321C22—92no—
322C22—92no—
323C22C22×GO+(4,𝔽2)11yescharacteristic
324C4—21no—
325C4—64no—
326C4—91no—
327C4—91no—
328C4—92no—
329C4—124no—
330C4—122no—
331C4—181no—
332C4D32⋊Q812yes—
333C4#6422712yes—
334C3—21no—
335C3—21no—
336C2—94no—
337C2C2×D32⋊Q811yescharacteristic
338C2C2×#6422711yescharacteristic
339C2#1059650511yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#475
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
5. #10593385C2semidirect
6. #10593376C2semidirect
43. #3797Q8semidirect
99. #627C2×Q8semidirect
230. C3⋊D3#475semidirect
288. C32C2×#475semidirect

Maximal subgroups

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

subgroupindex
#105939092
C4×#37972
#105937262
#105933872
#105933852
#105933762
#105933752
C2×#4759