Finite Group Databasebeta

← #11791855

Subgroups — #11791855

Order 1152.

614 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 71 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#10594925C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic
3C4×#3722C211yesmaximal, characteristic
4#10590076C214yesmaximal
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3797C411yescharacteristic, complemented
7C2×C22⋊#157C2212yes—
8C2×C4⋊#157—21no—
9C3×#924—21no—
10C2×C3×C4×Dic3—21no—
11#63982—21no—
12#63974C2212yes—
13C2×#3722C2212yes—
14#63900C411yescharacteristic, complemented
15#63883C412yescomplemented
16#63871—21no—
17#63865—21no—
18#63781—21no—
19#63579—21no—
20D3×C22⋊Q8—61no—
21C4×(C2×D3)⋊C4—61no—
22C23×C3⋊D3C2311yescharacteristic
23C22×#157—22no—
24C22×C32×C4D411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C2×C4×C3⋊D3—42no—
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C22×C3×Dic3—22no—
32C2×C3×Dic6—21no—
33C2×#627—21no—
34C2×#624C2×C412yes—
35C2×#624C2×C412yes—
36#3797—42no—
37C22⋊#157—24no—
38C4⋊#157—42no—
39C3×#217—22no—
40C3×C4⋊Dic3—21no—
41C3×Dic3⋊C4—22no—
42C3×C4×Dic3—42no—
43#3724—21no—
44Dic3⋊Dic3—22no—
45#3722—22no—
46#3722—22no—
47#3722Q814yescomplemented
48#1996—91nomaximal, Sylow
49C2×D3×Q8—61no—
50C22×C4×D3—61no—
51C22×C4×D3—61no—
52C3×C22⋊Q8—61no—
53C2×C3×C42—61no—
54#946—61no—
55C2×(C2×D3)⋊C4—62no—
56#924—21no—
57C2×C4×Dic3—21no—
58#897—61no—
59#896—62no—
60D3×C4⋊C4—62no—
61D3×C4⋊C4—61no—
62D3×C22⋊C4—62no—
63#878—62no—
64C3⋊#95—62no—
65C23×C32C2×D411yescharacteristic
66C22×C3⋊D3—41no—
67C22×C3⋊D3—41no—
68C22×C3⋊D3C22×C411yescharacteristic
69C22×C3⋊D3C2×D411yescharacteristic
70C22×C3⋊D3C2×Q812yes—
71C22×C3⋊D3#4112yes—
72C2×#157—42no—
73C2×#157—42no—
74C2×#157—42no—
75C2×C32×C4—22no—
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C3⋊Dic3—41no—
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C4×C3⋊D3—22no—
82C4×C3⋊D3—22no—
83C4×C3⋊D3—41no—
84C4×C3⋊D3—41no—
85C2×C3×Dic3—22no—
86C2×C3×Dic3—22no—
87C2×C3×Dic3—24no—
88C2×C3×Dic3—42no—
89C2×C3×Dic3—42no—
90C3×Dic6—42no—
91#627—42no—
92#624—42no—
93#624—42no—
94C2×C22⋊Q8—91no—
95#380—91no—
96C4×C22⋊C4—91no—
97#342—94no—
98C23×D3—61no—
99C23×D3—61no—
100C2×C3×Q8—61no—
101C22×C3×C4—21no—
102C22×C3×C4—21no—
103C22×C3×C4—62no—
104C22×Dic3—22no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107D3×Q8—124no—
108C2×C4×D3—61no—
109C2×C4×D3—62no—
110C2×C4×D3—62no—
111C2×C4×D3—61no—
112C2×C4×D3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—124no—
119C2×C4×D3—122no—
120C2×C4×D3—122no—
121C2×Dic6—21no—
122C2×Dic6—62no—
123C3×C4⋊C4—62no—
124C3×C4⋊C4—61no—
125C3×C22⋊C4—62no—
126C3×C42—122no—
127#217—22no—
128(C2×D3)⋊C4—64no—
129(C2×D3)⋊C4—62no—
130(C2×D3)⋊C4—62no—
131(C2×D3)⋊C4—64no—
132C4⋊Dic3—21no—
133C4⋊Dic3—62no—
134Dic3⋊C4—22no—
135Dic3⋊C4—62no—
136Dic3⋊C4—62no—
137C4×Dic3—42no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32C2×C22⋊C411yescharacteristic
141C22×C32C22⋊Q812yes—
142C2×C3⋊D3—21no—
143C2×C3⋊D3—21no—
144C2×C3⋊D3—21no—
145C2×C3⋊D3—21no—
146C2×C3⋊D3—42no—
147C2×C3⋊D3—42no—
148C2×C3⋊D3C4×Q812yes—
149C2×C3⋊D3#12411yescharacteristic
150C2×C3⋊D3C4⋊Q811yescharacteristic
151#157—82no—
152C32×C4—21no—
153C32×C4#9912yes—
154C3⋊Dic3—21no—
155C3⋊Dic3—21no—
156C3×Dic3—44no—
157C3×Dic3—42no—
158C3×Dic3—42no—
159C22×Q8—91no—
160C23×C4—91no—
161C22⋊Q8—61no—
162C22⋊Q8—181no—
163C22⋊Q8—181no—
164C22⋊Q8—181no—
165C2×C4⋊C4—92no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—181no—
168C2×C22⋊C4—92no—
169C2×C22⋊C4—92no—
170C2×C22⋊C4—92no—
171C2×C42—61no—
172#95—181no—
173#95—181no—
174C23×C3—21no—
175C23×C3—21no—
176C22×D3—61no—
177C22×D3—61no—
178C22×D3—61no—
179C22×D3—61no—
180C22×D3—62no—
181C22×D3—62no—
182C22×D3—62no—
183C22×D3—62no—
184C22×D3—122no—
185C22×D3—122no—
186C22×D3—121no—
187C22×D3—121no—
188C22×D3—122no—
189C3×Q8—122no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—42no—
197C2×C3×C4—62no—
198C2×C3×C4—62no—
199C2×C3×C4—64no—
200C2×C3×C4—122no—
201C2×C3×C4—122no—
202C2×Dic3—22no—
203C2×Dic3—22no—
204C2×Dic3—24no—
205C2×Dic3—42no—
206C2×Dic3—42no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—122no—
212C2×Dic3—121no—
213C2×Dic3—121no—
214C4×D3—64no—
215C4×D3—122no—
216C4×D3—122no—
217C4×D3—122no—
218C4×D3—124no—
219C4×D3—124no—
220C4×D3—122no—
221C4×D3—122no—
222C4×D3—122no—
223C4×D3—122no—
224Dic6—42no—
225Dic6—124no—
226C2×C32—22no—
227C2×C32#39111yescharacteristic
228C2×C32C2×#9911yescharacteristic
229C2×C32#41011yescharacteristic
230C3⋊D3—22no—
231C3⋊D3—21no—
232C3⋊D3—21no—
233C24—91no—
234C2×Q8—61no—
235C2×Q8—181no—
236C2×Q8—362no—
237C22×C4—62no—
238C22×C4—92no—
239C22×C4—92no—
240C22×C4—91no—
241C22×C4—91no—
242C22×C4—91no—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4—182no—
246C22×C4—362no—
247C22×C4GO+(4,𝔽2)11yescharacteristic
248C4⋊C4—62no—
249C4⋊C4—61no—
250C4⋊C4—181no—
251C4⋊C4—182no—
252C4⋊C4—362no—
253C22⋊C4—62no—
254C22⋊C4—94no—
255C22⋊C4—182no—
256C22⋊C4—182no—
257C22⋊C4—184no—
258C42—122no—
259C22×C3—21no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—41no—
267C22×C3—41no—
268C2×D3—62no—
269C2×D3—62no—
270C2×D3—61no—
271C2×D3—61no—
272C2×D3—61no—
273C2×D3—61no—
274C2×D3—62no—
275C2×D3—62no—
276C2×D3—121no—
277C2×D3—121no—
278C2×D3—121no—
279C2×D3—121no—
280C2×D3—121no—
281C2×D3—121no—
282C2×D3—124no—
283C2×D3—124no—
284C2×D3—122no—
285C2×D3—122no—
286C2×D3—122no—
287C2×D3—122no—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—41no—
292C3×C4—122no—
293C3×C4—122no—
294C3×C4—124no—
295Dic3—42no—
296Dic3—42no—
297Dic3—44no—
298Dic3—62no—
299Dic3—121no—
300Dic3—121no—
301Dic3—121no—
302C32#199611yescharacteristic, complemented, Sylow
303C23—91no—
304C23—91no—
305C23—92no—
306C23—92no—
307C23—361no—
308C23—361no—
309C23C2×GO+(4,𝔽2)11yescharacteristic
310Q8—122no—
311Q8—362no—
312C2×C4—22no—
313C2×C4—64no—
314C2×C4—62no—
315C2×C4—62no—
316C2×C4—91no—
317C2×C4—91no—
318C2×C4—122no—
319C2×C4—122no—
320C2×C4—182no—
321C2×C4—182no—
322C2×C4—361no—
323C2×C4—361no—
324C2×C4—362no—
325C2×C4—362no—
326C2×C4—361no—
327C2×C4—362no—
328C2×C4—362no—
329C2×C4—362no—
330C2×C4D32⋊C411yescharacteristic
331C2×C4D32⋊C411yescharacteristic
332C2×C3—22no—
333C2×C3—22no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—42no—
341D3—64no—
342D3—121no—
343D3—121no—
344D3—122no—
345D3—121no—
346D3—121no—
347C22—21no—
348C22—21no—
349C22—91no—
350C22—92no—
351C22—91no—
352C22—181no—
353C22—181no—
354C22—181no—
355C22—181no—
356C22—362no—
357C22—362no—
358C22D32⋊Q812yes—
359C22C2×D32⋊C411yescharacteristic
360C4—21no—
361C4—124no—
362C4—122no—
363C4—122no—
364C4—181no—
365C4—181no—
366C4—722no—
367C4#6373812yes—
368C3—21no—
369C3—21no—
370C2—22no—
371C2—181no—
372C2—182no—
373C2—181no—
374C2#1059334111yescharacteristic
375C2#1059334511yescharacteristic
376C2C2×#6373811yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC22×C3⋊D3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1996
LCSG ▷ C22×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. C2×#3797C4semidirect
14. #63900C4semidirect
15. #63883C4semidirect
47. #3722Q8semidirect
302. C32#1996semidirect

Maximal subgroups

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

subgroupindex
#105949252
#105938122
C4×#37222
#105900762
#19969