Finite Group Databasebeta

← #11783923

Subgroups — #11783923

Order 1152.

564 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C4×#3805C211yesmaximal, characteristic
2C4×#3792C211yesmaximal, characteristic, complemented
3C2×#63741C212yesmaximal
4#10591252C211yesmaximal, characteristic, complemented
5#10590074C212yesmaximal, complemented
6C2×#3805C2211yescharacteristic
7C2×#3792C2212yes—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C3×C4×#67—21no—
10#67⋊Dic3—21no—
11#63957C2211yescharacteristic
12C2×Dic32C2212yes—
13C4×#627C411yescharacteristic, complemented
14#63902C411yescharacteristic, complemented
15C4×#625C411yescharacteristic, complemented
16#63878—21no—
17C4×D3×Dic3—21no—
18#63838C411yescharacteristic, complemented
19#63777—21no—
20C4×#622—21no—
21#63741C418yescomplemented
22C3×C3⋊#95—21no—
23#63579—21no—
24C4×#237—61no—
25#4648—61no—
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C2×C3×#67—21no—
30C22×C3×Dic3—22no—
31C2×C3×C4×D3—21no—
32C2×#627C2×C411yescharacteristic
33C2×#625C2×C411yescharacteristic
34#3805—22no—
35#3805C2×C414yes—
36C2×D3×Dic3—21no—
37C2×D3×Dic3—21no—
38#3792—22no—
39#3792C2×C414yescomplemented
40C2×#622—22no—
41C4×C3⋊Dic3C2×C411yescharacteristic
42C4×C3⋊Dic3C2×C411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44C4×C3⋊Dic3D411yescharacteristic
45C3×#217—21no—
46C3×(C2×D3)⋊C4—21no—
47C3×Dic3⋊C4—21no—
48C3×C4×Dic3—21no—
49#3724C2×C411yescharacteristic
50#3724C2×C411yescharacteristic
51Dic3⋊Dic3—21no—
52(C2×D3)⋊Dic3—21no—
53Dic32—21no—
54Dic32—21no—
55Dic32—22no—
56Dic32C2×C414yescomplemented
57#1759—91nomaximal, Sylow
58C2×#237—61no—
59C3×C4×D4—61no—
60D4×Dic3—61no—
61C4×#67—21no—
62C4×#67—61no—
63C2×C4×Dic3—62no—
64C2×C4×Dic3—61no—
65C2×C4×Dic3—61no—
66C2×C4×Dic3—61no—
67#892—61no—
68#887—61no—
69#67⋊C4—61no—
70#67⋊C4—61no—
71#877—61no—
72#877—61no—
73C42×D3—61no—
74C4×Dic6—61no—
75C3×#95—61no—
76C3⋊#95—21no—
77C3⋊#95—62no—
78C23×C32C2×D411yescharacteristic
79C22×C3×D3—21no—
80C2×C32×C4—41no—
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C32×C4C22⋊C411yescharacteristic
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22×C411yescharacteristic
87C2×C3⋊Dic3C22×C412yes—
88C2×C3⋊Dic3C2×D411yescharacteristic
89C2×C3⋊Dic3#4112yes—
90C3×#67—24no—
91C2×C3×Dic3—21no—
92C2×C3×Dic3—21no—
93C2×C3×Dic3—21no—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—42no—
96C2×C3×Dic3—42no—
97C3×C4×D3—42no—
98#627—21no—
99#627C4212yes—
100#625—21no—
101#625C4212yes—
102D3×Dic3—24no—
103D3×Dic3—42no—
104#622—24no—
105C4×#41—91no—
106C2×#104—92no—
107C4×M16—91no—
108#376—91no—
109#339—92no—
110C2×C3×D4—61no—
111C22×C3×C4—21no—
112C22×C3×C4—21no—
113C22×C3×C4—61no—
114C22×C3×C4—62no—
115C2×#67—21no—
116C2×#67—61no—
117C22×Dic3—22no—
118C22×Dic3—61no—
119C22×Dic3—61no—
120C22×Dic3—61no—
121C22×Dic3—61no—
122C22×Dic3—61no—
123C22×Dic3—61no—
124#237—64no—
125#237—64no—
126C2×C4×D3—21no—
127C2×C4×D3—61no—
128C2×C4×D3—61no—
129C2×Dic6—61no—
130C3×C4⋊C4—61no—
131C3×C22⋊C4—61no—
132C3×C22⋊C4—61no—
133C3×C42—61no—
134#217—21no—
135#217—61no—
136(C2×D3)⋊C4—21no—
137(C2×D3)⋊C4—61no—
138C4⋊Dic3—61no—
139Dic3⋊C4—21no—
140Dic3⋊C4—61no—
141Dic3⋊C4—61no—
142Dic3⋊C4—61no—
143C4×Dic3—21no—
144C4×Dic3—64no—
145C4×Dic3—61no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C4×Dic3—61no—
152C4×Dic3—61no—
153C4×Dic3—61no—
154C4×Dic3—61no—
155C4×Dic3—61no—
156C4×Dic3—61no—
157C4×Dic3—64no—
158C22×C32—21no—
159C22×C32—21no—
160C22×C32C2×C22⋊C411yescharacteristic
161C22×C32C4×D412yes—
162C2×C3×D3—22no—
163C2×C3×D3—41no—
164C2×C3×D3—41no—
165C32×C4—21no—
166C32×C4—21no—
167C3⋊Dic3—21no—
168C3⋊Dic3—21no—
169C3⋊Dic3C2×C4211yescharacteristic
170C3⋊Dic3#11711yescharacteristic
171C3⋊Dic3C4×D412yes—
172C3×Dic3—22no—
173C3×Dic3—44no—
174C3×Dic3—41no—
175C3×Dic3—41no—
176C2×#41—91no—
177C2×M16—92no—
178C4×Q8—91no—
179C4×Q8—91no—
180C4×D4—61no—
181C4×D4—91no—
182C4×D4—91no—
183C4×D4—181no—
184#117—91no—
185#117—181no—
186C2×C42—91no—
187C2×C42—92no—
188C2×C42—181no—
189#104—98no—
190#97—181no—
191C4×C8—181no—
192#95—61no—
193#95—181no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—61no—
197C22×D3—21no—
198C3×D4—64no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—42no—
204C2×C3×C4—42no—
205C2×C3×C4—61no—
206C2×C3×C4—61no—
207C2×C3×C4—64no—
208C2×C3×C4—61no—
209C2×C3×C4—122no—
210C2×C3×C4—122no—
211C2×C3×C4—122no—
212#67—24no—
213#67—62no—
214#67—62no—
215C2×Dic3—21no—
216C2×Dic3—21no—
217C2×Dic3—21no—
218C2×Dic3—24no—
219C2×Dic3—42no—
220C2×Dic3—42no—
221C2×Dic3—61no—
222C2×Dic3—61no—
223C2×Dic3—62no—
224C2×Dic3—61no—
225C2×Dic3—62no—
226C2×Dic3—61no—
227C2×Dic3—61no—
228C2×Dic3—62no—
229C2×Dic3—62no—
230C2×Dic3—61no—
231C2×Dic3—61no—
232C2×Dic3—61no—
233C2×Dic3—64no—
234C2×Dic3—122no—
235C2×Dic3—122no—
236C2×Dic3—121no—
237C2×Dic3—121no—
238C4×D3—42no—
239C4×D3—64no—
240C4×D3—122no—
241Dic6—62no—
242Dic6—62no—
243C2×C32—22no—
244C2×C32C4×C22⋊C411yescharacteristic
245C2×C32#42111yescharacteristic
246C2×C32#42111yescharacteristic
247C3×D3—42no—
248#41—94no—
249#41—182no—
250C2×Q8—91no—
251C2×D4—61no—
252C2×D4—91no—
253C22×C4—62no—
254C22×C4—61no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—181no—
258C22×C4—181no—
259C22×C4GO+(4,𝔽2)11yescharacteristic
260M16—94no—
261M16—182no—
262C2×C8—182no—
263C4⋊C4—61no—
264C4⋊C4—91no—
265C4⋊C4—91no—
266C4⋊C4—181no—
267C22⋊C4—61no—
268C22⋊C4—61no—
269C22⋊C4—181no—
270C42—61no—
271C42—94no—
272C42—91no—
273C42—91no—
274C42—91no—
275C42—91no—
276C42—182no—
277C42—181no—
278C42—181no—
279C22×C3—21no—
280C22×C3—22no—
281C22×C3—21no—
282C22×C3—22no—
283C22×C3—22no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—41no—
287C22×C3—41no—
288C22×C3—62no—
289C22×C3—121no—
290C22×C3—121no—
291C2×D3—22no—
292C2×D3—41no—
293C2×D3—41no—
294C3×C4—22no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—41no—
298C3×C4—62no—
299C3×C4—121no—
300C3×C4—124no—
301C3×C4—121no—
302Dic3—22no—
303Dic3—41no—
304Dic3—44no—
305Dic3—41no—
306Dic3—61no—
307Dic3—61no—
308Dic3—62no—
309Dic3—61no—
310Dic3—61no—
311Dic3—62no—
312Dic3—62no—
313Dic3—121no—
314Dic3—121no—
315Dic3—121no—
316C32#175911yescharacteristic, complemented, Sylow
317C23—61no—
318C23C2×GO+(4,𝔽2)11yescharacteristic
319Q8—92no—
320Q8—181no—
321D4—64no—
322D4—92no—
323D4—181no—
324C2×C4—41no—
325C2×C4—61no—
326C2×C4—64no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—92no—
330C2×C4—92no—
331C2×C4—91no—
332C2×C4—91no—
333C2×C4—91no—
334C2×C4—91no—
335C2×C4—122no—
336C2×C4—122no—
337C2×C4—122no—
338C2×C4—184no—
339C2×C4—362no—
340C2×C4—361no—
341C2×C4D32⋊C411yescharacteristic
342C2×C4D32⋊C411yescharacteristic
343C8—184no—
344C2×C3—22no—
345C2×C3—22no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—42no—
353C2×C3—122no—
354D3—42no—
355C22—21no—
356C22—21no—
357C22—62no—
358C22—121no—
359C22—121no—
360C22C4×GO+(4,𝔽2)12yes—
361C22C2×D32⋊C411yescharacteristic
362C4—21no—
363C4—21no—
364C4—62no—
365C4—92no—
366C4—91no—
367C4—91no—
368C4—124no—
369C4—121no—
370C4—121no—
371C4—181no—
372C4—181no—
373C3—21no—
374C3—21no—
375C2—22no—
376C2—122no—
377C2#1059338111yescharacteristic
378C2C4×D32⋊C411yescharacteristic
379C2#1059350611yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC3⋊Dic3C2×C42
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3805C22
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1759
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×#3792C2semidirect
4. #10591252C2semidirect
5. #10590074C2semidirect
13. C4×#627C4semidirect
14. #63902C4semidirect
15. C4×#625C4semidirect
18. #63838C4semidirect
21. #63741C4semidirect
39. #3792C2×C4semidirect
56. Dic32C2×C4semidirect
316. C32#1759semidirect

Maximal subgroups

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

subgroupindex
C4×#38052
C4×#37922
C2×#637412
#105912522
#105900742
#17599