Finite Group Databasebeta

← #11783190

Subgroups — #11783190

Order 1152.

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

normal subgroups only

This group has 802 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#10590047C214yesmaximal, 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#63900C412yescomplemented
16C4×#624—21no—
17#63874C2212yes—
18#63849—21no—
19C2×#3712C2212yes—
20#63818—22no—
21#63818C414yescomplemented
22C2×#3710—21no—
23C2×D3×M16—61no—
24D3×#117—61no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—28no—
27C22×#157—24no—
28C22×#157—22no—
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×C414yescomplemented
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—22no—
52#3712C2×C414yescomplemented
53#3710—24no—
54C2×#339—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—24no—
73C22×C3⋊D3C22⋊C412yes—
74C22×C3⋊D3C22⋊C411yescharacteristic
75C22×C3⋊D3C4⋊C412yes—
76C22×C3⋊D3C2×D411yescharacteristic
77C2×#157—28no—
78C2×#157—216no—
79C2×#157—24no—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22⋊C412yes—
82C2×C32×C4C4⋊C412yes—
83C2×C32×C4C2×D411yescharacteristic
84C2×C3⋊Dic3C4212yes—
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C4⋊C412yes—
87C2×C3⋊Dic3C22×C411yescharacteristic
88C4×C3⋊D3C4212yes—
89C4×C3⋊D3C22⋊C412yes—
90C4×C3⋊D3C22⋊C412yes—
91C4×C3⋊D3C4⋊C412yes—
92C4×C3⋊D3C4⋊C412yes—
93C4×C3⋊D3C4⋊C412yes—
94C4×C3⋊D3C22×C411yescharacteristic
95C4×C3⋊D3C22×C411yescharacteristic
96C4×C3⋊D3C2×D411yescharacteristic
97C4×C3⋊D3C2×Q811yescharacteristic
98C2×C3×Dic3—24no—
99#624—44no—
100C3×C3⋊C8—24no—
101C22×M16—91no—
102C2×#117—91no—
103C22×C42—91no—
104#339—94no—
105C23×D3—61no—
106C23×D3—61no—
107C22×C3×C4—21no—
108C22×C3×C4—21no—
109C22×Dic3—61no—
110C22×Dic3—61no—
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—62no—
118C2×C4×D3—62no—
119C2×C4×D3—61no—
120C2×C4×D3—62no—
121C2×C4×D3—62no—
122C2×C4×D3—62no—
123C2×C4×D3—61no—
124C2×C4×D3—62no—
125C2×C4×D3—62no—
126C2×C4×D3—62no—
127C2×C4×D3—64no—
128C3×M16—64no—
129C2×C3×C8—62no—
130C3×C4⋊C4—62no—
131C3×C22⋊C4—62no—
132C3×C42—62no—
133#217—22no—
134(C2×D3)⋊C4—64no—
135C4⋊Dic3—22no—
136Dic3⋊C4—64no—
137C4×Dic3—22no—
138C4×Dic3—64no—
139#208—24no—
140C2×C3⋊C8—22no—
141ΓL(1,𝔽25)—64no—
142ΓL(1,𝔽25)—64no—
143D3×C8—68no—
144C22×C32—22no—
145C22×C32#9512yes—
146C22×C32C2×C22⋊C411yescharacteristic
147C2×C3⋊D3—22no—
148C2×C3⋊D3—24no—
149C2×C3⋊D3—24no—
150C2×C3⋊D3#9512yes—
151C2×C3⋊D3#10414yes—
152C2×C3⋊D3C2×C22⋊C411yescharacteristic
153C2×C3⋊D3C2×C4⋊C411yescharacteristic
154#157—28no—
155C32×C4#9512yes—
156C32×C4C2×C22⋊C411yescharacteristic
157C32×C4C2×C4⋊C411yescharacteristic
158C3⋊Dic3#9512yes—
159C3⋊Dic3C2×C4211yescharacteristic
160C3⋊Dic3C2×C4⋊C411yescharacteristic
161C3×Dic3—44no—
162C23×C4—91no—
163C23×C4—181no—
164C2×M16—61no—
165C2×M16—92no—
166C2×M16—94no—
167C2×M16—182no—
168C22×C8—181no—
169#117—61no—
170#117—92no—
171#117—92no—
172#117—181no—
173C2×C4⋊C4—92no—
174C2×C22⋊C4—181no—
175C2×C42—94no—
176C2×C42—92no—
177C2×C42—181no—
178C2×C42—181no—
179C2×C42—182no—
180C23×C3—21no—
181C23×C3—21no—
182C22×D3—61no—
183C22×D3—61no—
184C22×D3—62no—
185C22×D3—62no—
186C22×D3—62no—
187C22×D3—62no—
188C22×D3—61no—
189C22×D3—61no—
190C22×D3—124no—
191C22×D3—124no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—22no—
195C2×C3×C4—21no—
196C2×C3×C4—22no—
197C2×C3×C4—21no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—64no—
201C2×Dic3—24no—
202C2×Dic3—62no—
203C2×Dic3—62no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—62no—
207C2×Dic3—62no—
208C2×Dic3—61no—
209C2×Dic3—61no—
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—62no—
219C4×D3—62no—
220C4×D3—62no—
221C4×D3—62no—
222C4×D3—61no—
223C4×D3—61no—
224C4×D3—61no—
225C4×D3—61no—
226C4×D3—61no—
227C4×D3—61no—
228C4×D3—61no—
229C4×D3—61no—
230C4×D3—128no—
231C3×C8—64no—
232C3⋊C8—24no—
233C2×C32—22no—
234C2×C32C2×#9511yescharacteristic
235C2×C32C2×#10412yes—
236C3⋊D3—21no—
237C3⋊D3—21no—
238C3⋊D3#33914yescomplemented
239C24—91no—
240C22×C4—91no—
241C22×C4—91no—
242C22×C4—91no—
243C22×C4—91no—
244C22×C4—92no—
245C22×C4—91no—
246C22×C4—92no—
247C22×C4—92no—
248C22×C4—92no—
249C22×C4—182no—
250C22×C4—182no—
251C22×C4—184no—
252C22×C4—188no—
253C22×C4GO+(4,𝔽2)11yescharacteristic
254M16—64no—
255M16—94no—
256M16—182no—
257C2×C8—62no—
258C2×C8—184no—
259C4⋊C4—62no—
260C4⋊C4—94no—
261C22⋊C4—62no—
262C22⋊C4—182no—
263C42—62no—
264C42—94no—
265C42—182no—
266C42—182no—
267C42—184no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—22no—
271C22×C3—22no—
272C22×C3—42no—
273C22×C3—42no—
274C2×D3—62no—
275C2×D3—62no—
276C2×D3—64no—
277C2×D3—64no—
278C2×D3—61no—
279C2×D3—61no—
280C2×D3—61no—
281C2×D3—61no—
282C2×D3—124no—
283C2×D3—124no—
284C2×D3—124no—
285C2×D3—124no—
286C2×D3—122no—
287C2×D3—122no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—22no—
293C3×C4—22no—
294C3×C4—124no—
295Dic3—44no—
296Dic3—62no—
297Dic3—62no—
298Dic3—61no—
299Dic3—61no—
300Dic3—61no—
301Dic3—61no—
302C32C2×#33911yescharacteristic, complemented, Sylow
303C23—91no—
304C23—91no—
305C23—92no—
306C23—92no—
307C23—184no—
308C23D32⋊C411yescharacteristic
309C2×C4—64no—
310C2×C4—91no—
311C2×C4—91no—
312C2×C4—92no—
313C2×C4—92no—
314C2×C4—91no—
315C2×C4—92no—
316C2×C4—91no—
317C2×C4—91no—
318C2×C4—92no—
319C2×C4—91no—
320C2×C4—92no—
321C2×C4—92no—
322C2×C4—92no—
323C2×C4—92no—
324C2×C4—184no—
325C2×C4—1816no—
326C2×C4—188no—
327C2×C4—364no—
328C2×C4D32⋊C412yes—
329C2×C4D32⋊C411yescharacteristic
330C2×C4#377312yes—
331C2×C4C2×GO+(4,𝔽2)11yescharacteristic
332C8—64no—
333C2×C3—22no—
334C2×C3—22no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—42no—
338C2×C3—42no—
339D3—64no—
340D3—64no—
341D3—121no—
342D3—121no—
343D3—121no—
344D3—121no—
345C22—22no—
346C22—94no—
347C22—92no—
348C22—91no—
349C22—91no—
350C22—184no—
351C22—184no—
352C22—182no—
353C22#6373712yes—
354C22C2×D32⋊C411yescharacteristic
355C4—92no—
356C4—91no—
357C4—91no—
358C4—124no—
359C4—188no—
360C4#6373712yes—
361C4C2×D32⋊C411yescharacteristic
362C4C2×#377311yescharacteristic
363C3—21no—
364C3—21no—
365C2—22no—
366C2—94no—
367C2—181no—
368C2—181no—
369C2#1059332512yes—
370C2C2×#6373711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C2×C42
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#339
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590047C2semidirect
9. C2×C4×#157C4semidirect
14. #63957C4semidirect
15. #63900C4semidirect
21. #63818C4semidirect
42. C4×#157C2×C4semidirect
48. #3724C2×C4semidirect
52. #3712C2×C4semidirect
238. C3⋊D3#339semidirect
302. C32C2×#339semidirect

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
#105900472
C2×#3399