Finite Group Databasebeta

← #11783296

Subgroups — #11783296

Order 1152.

762 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 135 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×C4⋊#157C211yesmaximal, characteristic
2#10594969C211yesmaximal, characteristic
3C2×#63818C211yesmaximal, characteristic
4#10590049C214yesmaximal, complemented
5C23×#157—21no—
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C4⋊#157—22no—
8C2×C4⋊#157—21no—
9C2×C4⋊#157C414yescomplemented
10C2×C4⋊#157C2212yes—
11C3×#926—21no—
12C2×C3×#208—21no—
13#63974—21no—
14#63957C412yescomplemented
15#63900C2212yes—
16C4×#624—21no—
17#63874C412yescomplemented
18#63849—21no—
19C2×#3712—21no—
20#63818—22no—
21#63818C414yescomplemented
22C2×#3710C2212yes—
23C2×D3×M16—61no—
24D3×#117—61no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—24no—
27C22×#157—22no—
28C22×#157—44no—
29C22×C32×C4D411yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3C2×C412yes—
33C2×C4×C3⋊D3C2×C412yes—
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3D412yes—
37C2×C4×C3⋊D3Q812yes—
38C2×C4×C3⋊D3C2311yescharacteristic
39C2×#624—22no—
40C4⋊#157—24no—
41C4⋊#157—22no—
42C4⋊#157C2×C414yes—
43C3×#217—22no—
44C3×C4⋊Dic3—22no—
45C3×C4×Dic3—22no—
46C3×#208—24no—
47C2×C3×C3⋊C8—22no—
48#3724C2×C414yescomplemented
49#3722—22no—
50Dic32—22no—
51#3712—24no—
52#3710—22no—
53#3710C2×C414yescomplemented
54#1736—91nomaximal, Sylow
55C22×C4×D3—61no—
56C22×C4×D3—61no—
57C2×C3×M16—61no—
58C3×#117—61no—
59#926—21no—
60C2×#208—21no—
61D3×M16—64no—
62D3×M16—64no—
63C2×ΓL(1,𝔽25)—62no—
64C2×D3×C8—62no—
65#892—62no—
66D3×C4⋊C4—62no—
67D3×C22⋊C4—62no—
68#877—62no—
69#872—62no—
70C42×D3—62no—
71C23×C32C22⋊C411yescharacteristic
72C22×C3⋊D3—22no—
73C22×C3⋊D3—22no—
74C22×C3⋊D3C22⋊C411yescharacteristic
75C22×C3⋊D3C22⋊C412yes—
76C22×C3⋊D3C4⋊C412yes—
77C22×C3⋊D3C2×D411yescharacteristic
78C2×#157—24no—
79C2×#157—48no—
80C2×#157—44no—
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C32×C4C22⋊C412yes—
83C2×C32×C4C4⋊C412yes—
84C2×C32×C4C2×D411yescharacteristic
85C2×C3⋊Dic3C4212yes—
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C4⋊C412yes—
88C2×C3⋊Dic3C22×C411yescharacteristic
89C4×C3⋊D3C4212yes—
90C4×C3⋊D3C22⋊C412yes—
91C4×C3⋊D3C22⋊C412yes—
92C4×C3⋊D3C4⋊C412yes—
93C4×C3⋊D3C4⋊C412yes—
94C4×C3⋊D3C4⋊C412yes—
95C4×C3⋊D3C22×C411yescharacteristic
96C4×C3⋊D3C22×C411yescharacteristic
97C4×C3⋊D3C2×D411yescharacteristic
98C4×C3⋊D3C2×Q811yescharacteristic
99C2×C3×Dic3—24no—
100#624—42no—
101#624—42no—
102C3×C3⋊C8—24no—
103C22×M16—91no—
104C2×#117—91no—
105C22×C4⋊C4—91no—
106#340—94no—
107C23×D3—61no—
108C23×D3—61no—
109C22×C3×C4—21no—
110C22×C3×C4—21no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—62no—
120C2×C4×D3—62no—
121C2×C4×D3—61no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—61no—
126C2×C4×D3—62no—
127C2×C4×D3—62no—
128C2×C4×D3—62no—
129C2×C4×D3—64no—
130C3×M16—64no—
131C2×C3×C8—62no—
132C3×C4⋊C4—62no—
133C3×C22⋊C4—62no—
134C3×C42—62no—
135#217—22no—
136(C2×D3)⋊C4—64no—
137C4⋊Dic3—22no—
138Dic3⋊C4—64no—
139C4×Dic3—22no—
140C4×Dic3—64no—
141#208—24no—
142C2×C3⋊C8—22no—
143ΓL(1,𝔽25)—68no—
144D3×C8—64no—
145D3×C8—64no—
146C22×C32—22no—
147C22×C32#9512yes—
148C22×C32C2×C22⋊C411yescharacteristic
149C2×C3⋊D3—22no—
150C2×C3⋊D3—22no—
151C2×C3⋊D3—22no—
152C2×C3⋊D3—24no—
153C2×C3⋊D3#9512yes—
154C2×C3⋊D3C2×C22⋊C411yescharacteristic
155C2×C3⋊D3C2×C4⋊C411yescharacteristic
156C2×C3⋊D3AGL(1,ℤ/8)12yes—
157C2×C3⋊D3#13712yes—
158#157—44no—
159C32×C4#9512yes—
160C32×C4C2×C22⋊C411yescharacteristic
161C32×C4C2×C4⋊C411yescharacteristic
162C3⋊Dic3#9512yes—
163C3⋊Dic3C2×C4211yescharacteristic
164C3⋊Dic3C2×C4⋊C411yescharacteristic
165C3×Dic3—44no—
166C23×C4—91no—
167C23×C4—181no—
168C2×M16—61no—
169C2×M16—94no—
170C2×M16—181no—
171C2×M16—182no—
172C22×C8—92no—
173#117—61no—
174#117—92no—
175#117—92no—
176#117—181no—
177C2×C4⋊C4—92no—
178C2×C4⋊C4—94no—
179C2×C4⋊C4—92no—
180C2×C4⋊C4—181no—
181C2×C4⋊C4—182no—
182C2×C22⋊C4—181no—
183C2×C42—181no—
184C23×C3—21no—
185C23×C3—21no—
186C22×D3—61no—
187C22×D3—61no—
188C22×D3—61no—
189C22×D3—61no—
190C22×D3—62no—
191C22×D3—62no—
192C22×D3—62no—
193C22×D3—62no—
194C22×D3—122no—
195C22×D3—122no—
196C22×D3—122no—
197C22×D3—122no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—22no—
201C2×C3×C4—21no—
202C2×C3×C4—22no—
203C2×C3×C4—21no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—64no—
207C2×Dic3—24no—
208C2×Dic3—62no—
209C2×Dic3—62no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C4×D3—62no—
217C4×D3—62no—
218C4×D3—62no—
219C4×D3—62no—
220C4×D3—62no—
221C4×D3—62no—
222C4×D3—62no—
223C4×D3—62no—
224C4×D3—62no—
225C4×D3—62no—
226C4×D3—62no—
227C4×D3—62no—
228C4×D3—61no—
229C4×D3—61no—
230C4×D3—61no—
231C4×D3—61no—
232C4×D3—61no—
233C4×D3—61no—
234C4×D3—61no—
235C4×D3—61no—
236C4×D3—124no—
237C4×D3—124no—
238C3×C8—64no—
239C3⋊C8—24no—
240C2×C32—22no—
241C2×C32C2×#9511yescharacteristic
242C2×C32#41712yes—
243C3⋊D3—22no—
244C3⋊D3#41811yescharacteristic
245C3⋊D3#41911yescharacteristic
246C3⋊D3#42812yes—
247C24—91no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—92no—
253C22×C4—91no—
254C22×C4—92no—
255C22×C4—92no—
256C22×C4—92no—
257C22×C4—182no—
258C22×C4—182no—
259C22×C4—184no—
260C22×C4—364no—
261C22×C4GO+(4,𝔽2)11yescharacteristic
262M16—64no—
263M16—184no—
264C2×C8—62no—
265C2×C8—94no—
266C2×C8—182no—
267C4⋊C4—62no—
268C4⋊C4—94no—
269C4⋊C4—94no—
270C4⋊C4—182no—
271C4⋊C4—184no—
272C22⋊C4—62no—
273C22⋊C4—182no—
274C42—62no—
275C42—182no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—22no—
279C22×C3—22no—
280C22×C3—42no—
281C22×C3—42no—
282C2×D3—61no—
283C2×D3—61no—
284C2×D3—61no—
285C2×D3—61no—
286C2×D3—62no—
287C2×D3—62no—
288C2×D3—62no—
289C2×D3—62no—
290C2×D3—62no—
291C2×D3—62no—
292C2×D3—122no—
293C2×D3—122no—
294C2×D3—122no—
295C2×D3—122no—
296C2×D3—124no—
297C2×D3—124no—
298C2×D3—122no—
299C2×D3—122no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—22no—
305C3×C4—22no—
306C3×C4—124no—
307Dic3—44no—
308Dic3—62no—
309Dic3—62no—
310Dic3—61no—
311Dic3—61no—
312Dic3—61no—
313Dic3—61no—
314C32#173611yescharacteristic, complemented, Sylow
315C23—91no—
316C23—91no—
317C23—92no—
318C23—92no—
319C23—182no—
320C23—182no—
321C23D32⋊C411yescharacteristic
322C2×C4—64no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—92no—
326C2×C4—92no—
327C2×C4—91no—
328C2×C4—91no—
329C2×C4—92no—
330C2×C4—91no—
331C2×C4—91no—
332C2×C4—92no—
333C2×C4—92no—
334C2×C4—92no—
335C2×C4—92no—
336C2×C4—92no—
337C2×C4—184no—
338C2×C4—362no—
339C2×C4—362no—
340C2×C4—364no—
341C2×C4—368no—
342C2×C4D32⋊C412yes—
343C2×C4D32⋊C411yescharacteristic
344C2×C4#377312yes—
345C2×C4C2×GO+(4,𝔽2)11yescharacteristic
346C8—64no—
347C2×C3—22no—
348C2×C3—22no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—42no—
352C2×C3—42no—
353D3—61no—
354D3—61no—
355D3—61no—
356D3—61no—
357D3—62no—
358D3—62no—
359D3—122no—
360D3—122no—
361C22—22no—
362C22—92no—
363C22—92no—
364C22—91no—
365C22—91no—
366C22—92no—
367C22—182no—
368C22—182no—
369C22—184no—
370C22—182no—
371C22#6373712yes—
372C22C2×D32⋊C411yescharacteristic
373C4—92no—
374C4—91no—
375C4—91no—
376C4—124no—
377C4—364no—
378C4#6373712yes—
379C4C2×D32⋊C411yescharacteristic
380C4C2×#377311yescharacteristic
381C3—21no—
382C3—21no—
383C2—22no—
384C2—91no—
385C2—92no—
386C2—91no—
387C2—182no—
388C2#1059331912yes—
389C2C2×#6373711yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC3⋊Dic3C2×C42
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1736
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590049C2semidirect
9. C2×C4⋊#157C4semidirect
14. #63957C4semidirect
17. #63874C4semidirect
21. #63818C4semidirect
48. #3724C2×C4semidirect
53. #3710C2×C4semidirect
314. C32#1736semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#1572
#105949692
C2×#638182
#105900492
#17369