Finite Group Databasebeta

← #11783428

Subgroups — #11783428

Order 1152.

702 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 127 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×#3788C211yesmaximal, characteristic
2#10594969C211yesmaximal, characteristic
3C2×#63818C211yesmaximal, characteristic
4#10590052C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#622—21no—
7C2×#3788—21no—
8C2×#3788—22no—
9C2×#3788C414yescomplemented
10C2×#3788C2212yes—
11C3×#926—21no—
12C2×C3×#208—21no—
13#63974C412yes—
14#63957—21no—
15#63900C2212yes—
16C4×#624C412yes—
17#63874—21no—
18#63849—21no—
19C2×#3712C2212yes—
20#63818—22no—
21#63818C414yescomplemented
22C2×#3710—21no—
23C2×D3×M16—61no—
24D3×#117—61no—
25C23×C3⋊D3C2×C411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3C2×C412yes—
30C2×C4×C3⋊D3C2×C412yes—
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D412yes—
34C2×C4×C3⋊D3Q812yes—
35C2×C4×C3⋊D3C2311yescharacteristic
36C2×#624C2×C414yes—
37C2×#622—24no—
38C2×#622—22no—
39#3788—24no—
40#3788—22no—
41#3788C2×C414yes—
42C3×#217—22no—
43C3×C4⋊Dic3—22no—
44C3×C4×Dic3—22no—
45C3×#208—24no—
46C2×C3×C3⋊C8—22no—
47#3724—22no—
48#3722—22no—
49Dic32—22no—
50#3712—22no—
51#3712C2×C414yes—
52#3710—24no—
53#1742—91nomaximal, Sylow
54C22×C4×D3—61no—
55C22×C4×D3—61no—
56C2×C3×M16—61no—
57C3×#117—61no—
58#926—21no—
59C2×#208—21no—
60D3×M16—64no—
61D3×M16—64no—
62C2×ΓL(1,𝔽25)—62no—
63C2×D3×C8—62no—
64#892—62no—
65D3×C4⋊C4—62no—
66D3×C22⋊C4—62no—
67#877—62no—
68#872—62no—
69C42×D3—62no—
70C23×C32C22⋊C411yescharacteristic
71C22×C3⋊D3—42no—
72C22×C3⋊D3C4212yes—
73C22×C3⋊D3C22⋊C411yescharacteristic
74C22×C3⋊D3C4⋊C412yes—
75C22×C3⋊D3C22×C411yescharacteristic
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C22⋊C412yes—
78C2×C32×C4C4⋊C412yes—
79C2×C32×C4C2×D411yescharacteristic
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22⋊C412yes—
82C2×C3⋊Dic3C4⋊C412yes—
83C2×C3⋊Dic3C2×D411yescharacteristic
84C4×C3⋊D3C4212yes—
85C4×C3⋊D3C22⋊C412yes—
86C4×C3⋊D3C22⋊C412yes—
87C4×C3⋊D3C4⋊C412yes—
88C4×C3⋊D3C4⋊C412yes—
89C4×C3⋊D3C4⋊C412yes—
90C4×C3⋊D3C22×C411yescharacteristic
91C4×C3⋊D3C22×C411yescharacteristic
92C4×C3⋊D3C2×D411yescharacteristic
93C4×C3⋊D3C2×Q811yescharacteristic
94C2×C3×Dic3—24no—
95#624—44no—
96#622—24no—
97C3×C3⋊C8—24no—
98C22×M16—91no—
99C22×M16—91no—
100C2×#117—91no—
101#343—94no—
102C23×D3—61no—
103C23×D3—61no—
104C22×C3×C4—21no—
105C22×C3×C4—21no—
106C22×Dic3—61no—
107C22×Dic3—61no—
108C2×C4×D3—61no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C2×C4×D3—61no—
112C2×C4×D3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—62no—
115C2×C4×D3—62no—
116C2×C4×D3—61no—
117C2×C4×D3—62no—
118C2×C4×D3—62no—
119C2×C4×D3—62no—
120C2×C4×D3—61no—
121C2×C4×D3—62no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—64no—
125C3×M16—64no—
126C2×C3×C8—62no—
127C3×C4⋊C4—62no—
128C3×C22⋊C4—62no—
129C3×C42—62no—
130#217—22no—
131(C2×D3)⋊C4—64no—
132C4⋊Dic3—22no—
133Dic3⋊C4—64no—
134C4×Dic3—22no—
135C4×Dic3—64no—
136#208—24no—
137C2×C3⋊C8—22no—
138ΓL(1,𝔽25)—64no—
139ΓL(1,𝔽25)—64no—
140D3×C8—68no—
141C22×C32—22no—
142C22×C32#9512yes—
143C22×C32C2×C22⋊C411yescharacteristic
144C2×C3⋊D3—22no—
145C2×C3⋊D3—22no—
146C2×C3⋊D3—42no—
147C2×C3⋊D3—42no—
148C2×C3⋊D3#9512yes—
149C2×C3⋊D3C2×C4211yescharacteristic
150C2×C3⋊D3C2×C4⋊C411yescharacteristic
151C32×C4#9512yes—
152C32×C4C2×C22⋊C411yescharacteristic
153C32×C4C2×C4⋊C411yescharacteristic
154C3⋊Dic3#9512yes—
155C3⋊Dic3C2×C22⋊C411yescharacteristic
156C3⋊Dic3C2×C4⋊C411yescharacteristic
157C3×Dic3—44no—
158C23×C4—91no—
159C2×M16—61no—
160C2×M16—92no—
161C2×M16—94no—
162C2×M16—94no—
163C2×M16—92no—
164C2×M16—182no—
165C2×M16—181no—
166C2×M16—182no—
167C22×C8—181no—
168C22×C8—181no—
169#117—61no—
170#117—181no—
171#117—181no—
172#117—181no—
173C2×C4⋊C4—92no—
174C2×C22⋊C4—92no—
175C2×C42—92no—
176C23×C3—21no—
177C23×C3—21no—
178C22×D3—61no—
179C22×D3—61no—
180C22×D3—62no—
181C22×D3—62no—
182C22×D3—61no—
183C22×D3—62no—
184C22×D3—62no—
185C22×D3—61no—
186C22×D3—124no—
187C22×D3—124no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—22no—
191C2×C3×C4—21no—
192C2×C3×C4—22no—
193C2×C3×C4—21no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—64no—
197C2×Dic3—24no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—62no—
201C2×Dic3—62no—
202C2×Dic3—62no—
203C2×Dic3—62no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C4×D3—62no—
207C4×D3—62no—
208C4×D3—62no—
209C4×D3—62no—
210C4×D3—62no—
211C4×D3—62no—
212C4×D3—62no—
213C4×D3—62no—
214C4×D3—62no—
215C4×D3—62no—
216C4×D3—62no—
217C4×D3—62no—
218C4×D3—61no—
219C4×D3—61no—
220C4×D3—61no—
221C4×D3—61no—
222C4×D3—61no—
223C4×D3—61no—
224C4×D3—61no—
225C4×D3—61no—
226C4×D3—128no—
227C3×C8—64no—
228C3⋊C8—24no—
229C2×C32—22no—
230C2×C32C2×#9511yescharacteristic
231C2×C32#41312yes—
232C3⋊D3—22no—
233C3⋊D3—21no—
234C3⋊D3—21no—
235C24—91no—
236C22×C4—94no—
237C22×C4—91no—
238C22×C4—91no—
239C22×C4—91no—
240C22×C4—91no—
241C22×C4—91no—
242C22×C4—92no—
243C22×C4—92no—
244C22×C4—92no—
245C22×C4—92no—
246C22×C4GO+(4,𝔽2)11yescharacteristic
247M16—64no—
248M16—94no—
249M16—94no—
250M16—182no—
251M16—182no—
252M16—184no—
253C2×C8—62no—
254C2×C8—184no—
255C2×C8—182no—
256C2×C8—184no—
257C4⋊C4—62no—
258C4⋊C4—182no—
259C22⋊C4—62no—
260C22⋊C4—182no—
261C42—62no—
262C42—182no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—42no—
268C22×C3—42no—
269C2×D3—62no—
270C2×D3—61no—
271C2×D3—61no—
272C2×D3—62no—
273C2×D3—61no—
274C2×D3—61no—
275C2×D3—64no—
276C2×D3—64no—
277C2×D3—122no—
278C2×D3—122no—
279C2×D3—124no—
280C2×D3—124no—
281C2×D3—124no—
282C2×D3—124no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—22no—
288C3×C4—22no—
289C3×C4—124no—
290Dic3—44no—
291Dic3—62no—
292Dic3—62no—
293Dic3—61no—
294Dic3—61no—
295Dic3—61no—
296Dic3—61no—
297C32#174211yescharacteristic, complemented, Sylow
298C23—91no—
299C23—91no—
300C23—92no—
301C23—92no—
302C23—362no—
303C23D32⋊C411yescharacteristic
304C2×C4—64no—
305C2×C4—91no—
306C2×C4—91no—
307C2×C4—92no—
308C2×C4—92no—
309C2×C4—92no—
310C2×C4—91no—
311C2×C4—91no—
312C2×C4—91no—
313C2×C4—91no—
314C2×C4—92no—
315C2×C4—92no—
316C2×C4—92no—
317C2×C4—92no—
318C2×C4—92no—
319C2×C4—364no—
320C2×C4D32⋊C412yes—
321C2×C4D32⋊C411yescharacteristic
322C2×C4#377312yes—
323C2×C4C2×GO+(4,𝔽2)11yescharacteristic
324C8—64no—
325C8—184no—
326C2×C3—22no—
327C2×C3—22no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—42no—
331C2×C3—42no—
332D3—64no—
333D3—62no—
334D3—62no—
335D3—122no—
336D3—121no—
337D3—121no—
338C22—22no—
339C22—92no—
340C22—91no—
341C22—91no—
342C22—182no—
343C22—182no—
344C22—362no—
345C22—362no—
346C22#6373712yes—
347C22C2×D32⋊C411yescharacteristic
348C4—91no—
349C4—92no—
350C4—91no—
351C4—124no—
352C4#6373712yes—
353C4C2×D32⋊C411yescharacteristic
354C4C2×#377311yescharacteristic
355C3—21no—
356C3—21no—
357C2—22no—
358C2—181no—
359C2—181no—
360C2—182no—
361C2#1059331312yes—
362C2C2×#6373711yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊D3C2×C42
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1742
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590052C2semidirect
9. C2×#3788C4semidirect
21. #63818C4semidirect
297. C32#1742semidirect

Maximal subgroups

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

subgroupindex
C22×#37882
#105949692
C2×#638182
#105900522
#17429