Finite Group Databasebeta

← #11868850

Subgroups — #11868850

Order 1152.

716 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×#63919C211yesmaximal, characteristic, complemented
2C4×#3805C211yesmaximal, characteristic
3#10593805C211yesmaximal, characteristic, complemented
4#10593507C212yesmaximal, complemented
5#10593496C212yesmaximal
6#10593393C212yesmaximal, complemented
7#10593385C212yesmaximal, complemented
8#10593367C212yesmaximal, complemented
9#10593359C212yesmaximal, complemented
10C22×#627—21no—
11C2×#3805C2211yescharacteristic
12C2×#3792C2212yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C3×C4×#67—21no—
15C2×C3×C4⋊Dic3—21no—
16#67⋊Dic3—21no—
17C2×#3724C2212yes—
18#63957C2211yescharacteristic
19#63919—21no—
20#63919—21no—
21#63919C2212yes—
22#63919C2212yes—
23C4×#627C2211yescharacteristic
24#63902C2211yescharacteristic
25C4×#625C2211yescharacteristic
26#63878—21no—
27C4×D3×Dic3—21no—
28#63838C2211yescharacteristic
29#63779C2212yes—
30C4⋊#622C2212yes—
31#63743C2214yes—
32#63742C2214yes—
33#63740C2214yes—
34#63739C2214yes—
35C4×#237—61no—
36C2×#888—61no—
37C22×C32×C4D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C22×C3⋊Dic3C2311yescharacteristic
40C2×C3×#67—21no—
41C22×C3×Dic3—22no—
42C2×C3×C4×D3—21no—
43C2×#627—22no—
44C2×#627—22no—
45C2×#627—44no—
46C2×#627C2311yescharacteristic
47C2×#625C2311yescharacteristic
48#3805—22no—
49#3805Q814yescomplemented
50C2×D3×Dic3—21no—
51C2×D3×Dic3—21no—
52#3792—24no—
53C2×#622C2314yes—
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3C2311yescharacteristic
57C4×C3⋊Dic3C2311yescharacteristic
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—22no—
61C3×C4⋊Dic3—22no—
62C3×Dic3⋊C4—21no—
63C3×C4×Dic3—21no—
64#3724—22no—
65#3724C2311yescharacteristic
66#3724C2311yescharacteristic
67#3724C2314yes—
68Dic3⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70Dic32—21no—
71Dic32—21no—
72#3079—91nomaximal, Sylow
73C2×#237—61no—
74C22×Dic6—62no—
75C3×C4×D4—61no—
76C2×C3×C4⋊C4—61no—
77D4×Dic3—61no—
78C4×#67—21no—
79C4×#67—61no—
80C2×C4⋊Dic3—21no—
81C2×Dic3⋊C4—62no—
82C2×C4×Dic3—61no—
83C2×C4×Dic3—61no—
84C2×C4×Dic3—61no—
85#892—61no—
86#888—62no—
87#888—62no—
88#888—62no—
89#888—62no—
90#887—61no—
91#67⋊C4—61no—
92#67⋊C4—61no—
93#877—61no—
94#877—61no—
95C42×D3—61no—
96C4×Dic6—61no—
97C23×C32C2×D411yescharacteristic
98C22×C3×D3—21no—
99C2×C32×C4—22no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3C2×D411yescharacteristic
104C2×C3⋊Dic3C2×D411yescharacteristic
105C2×C3⋊Dic3C2×D411yescharacteristic
106C2×C3⋊Dic3C2×Q812yes—
107C2×C3⋊Dic3#4112yes—
108C2×C3⋊Dic3C2411yescharacteristic
109C3×#67—24no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—44no—
115C3×C4×D3—42no—
116#627—21no—
117#627—44no—
118#627—44no—
119#627C2×Q812yescomplemented
120#625—21no—
121#625C2×Q812yescomplemented
122D3×Dic3—24no—
123D3×Dic3—42no—
124#622—24no—
125C2×C4⋊Q8—91no—
126C4×#41—91no—
127#477—92no—
128#476—92no—
129#475—92no—
130#474—92no—
131#428—92no—
132#423—91no—
133#417—92no—
134C2×C3×D4—61no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—61no—
138C22×C3×C4—62no—
139C2×#67—21no—
140C2×#67—61no—
141C22×Dic3—22no—
142C22×Dic3—61no—
143C22×Dic3—61no—
144C22×Dic3—61no—
145C22×Dic3—61no—
146C22×Dic3—61no—
147C22×Dic3—61no—
148#237—64no—
149#237—64no—
150C2×C4×D3—21no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×Dic6—61no—
154C2×Dic6—64no—
155C2×Dic6—64no—
156C2×Dic6—128no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—62no—
159C3×C4⋊C4—62no—
160C3×C22⋊C4—61no—
161C3×C22⋊C4—61no—
162C3×C42—61no—
163#217—21no—
164#217—61no—
165(C2×D3)⋊C4—21no—
166(C2×D3)⋊C4—61no—
167C4⋊Dic3—22no—
168C4⋊Dic3—22no—
169C4⋊Dic3—61no—
170Dic3⋊C4—21no—
171Dic3⋊C4—61no—
172Dic3⋊C4—61no—
173Dic3⋊C4—64no—
174Dic3⋊C4—61no—
175Dic3⋊C4—64no—
176C4×Dic3—21no—
177C4×Dic3—61no—
178C4×Dic3—61no—
179C4×Dic3—61no—
180C4×Dic3—61no—
181C4×Dic3—61no—
182C4×Dic3—61no—
183C4×Dic3—61no—
184C4×Dic3—61no—
185C4×Dic3—61no—
186C4×Dic3—61no—
187C4×Dic3—61no—
188C4×Dic3—61no—
189C22×C32—21no—
190C22×C32—21no—
191C22×C32C22⋊Q812yes—
192C22×C32C22×D411yescharacteristic
193C2×C3×D3—22no—
194C2×C3×D3—41no—
195C2×C3×D3—41no—
196C32×C4—21no—
197C32×C4#13712yes—
198C3⋊Dic3—21no—
199C3⋊Dic3C22⋊Q812yes—
200C3⋊Dic3AGL(1,ℤ/8)12yes—
201C3⋊Dic3C22×Q811yescharacteristic
202C3⋊Dic3C2×#4111yescharacteristic
203C3×Dic3—22no—
204C3×Dic3—41no—
205C3×Dic3—44no—
206C3×Dic3—41no—
207C2×#41—91no—
208C22×Q8—181no—
209C2×M16—92no—
210C4⋊Q8—92no—
211C4⋊Q8—92no—
212C4⋊Q8—181no—
213C4⋊Q8—181no—
214C4×Q8—91no—
215C4×Q8—91no—
216C4×D4—61no—
217C4×D4—91no—
218C4×D4—91no—
219C4×D4—181no—
220#117—91no—
221#117—181no—
222C2×C4⋊C4—61no—
223C2×C4⋊C4—92no—
224C2×C42—91no—
225C2×C42—181no—
226#107—94no—
227#106—94no—
228C4⋊C8—92no—
229C4⋊C8—92no—
230#103—94no—
231#102—94no—
232C23×C3—21no—
233C23×C3—21no—
234C23×C3—61no—
235C22×D3—21no—
236C3×D4—64no—
237C2×C3×C4—24no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—42no—
243C2×C3×C4—61no—
244C2×C3×C4—61no—
245C2×C3×C4—61no—
246C2×C3×C4—64no—
247C2×C3×C4—122no—
248C2×C3×C4—124no—
249#67—24no—
250#67—62no—
251#67—62no—
252C2×Dic3—21no—
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—24no—
256C2×Dic3—44no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—62no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—61no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—64no—
270C2×Dic3—64no—
271C2×Dic3—122no—
272C2×Dic3—122no—
273C4×D3—42no—
274C4×D3—64no—
275C4×D3—122no—
276Dic6—62no—
277Dic6—62no—
278Dic6—128no—
279Dic6—128no—
280C2×C32—22no—
281C2×C32C2×C22⋊Q811yescharacteristic
282C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
283C2×C32C2×#13711yescharacteristic
284C3×D3—42no—
285#41—94no—
286#41—182no—
287C2×Q8—91no—
288C2×Q8—182no—
289C2×Q8—182no—
290C2×Q8—364no—
291C2×D4—61no—
292C2×D4—91no—
293C22×C4—62no—
294C22×C4—61no—
295C22×C4—91no—
296C22×C4—91no—
297C22×C4—181no—
298C22×C4—181no—
299C22×C4GO+(4,𝔽2)11yescharacteristic
300M16—184no—
301C2×C8—94no—
302C4⋊C4—62no—
303C4⋊C4—62no—
304C4⋊C4—61no—
305C4⋊C4—94no—
306C4⋊C4—91no—
307C4⋊C4—91no—
308C4⋊C4—182no—
309C4⋊C4—181no—
310C22⋊C4—61no—
311C22⋊C4—61no—
312C22⋊C4—181no—
313C42—61no—
314C42—91no—
315C42—91no—
316C42—91no—
317C42—91no—
318C42—181no—
319C42—181no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—22no—
325C22×C3—22no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—62no—
329C22×C3—121no—
330C22×C3—121no—
331C2×D3—22no—
332C2×D3—41no—
333C2×D3—41no—
334C3×C4—22no—
335C3×C4—22no—
336C3×C4—22no—
337C3×C4—41no—
338C3×C4—62no—
339C3×C4—124no—
340C3×C4—121no—
341C3×C4—121no—
342Dic3—22no—
343Dic3—44no—
344Dic3—41no—
345Dic3—41no—
346Dic3—61no—
347Dic3—61no—
348Dic3—62no—
349Dic3—62no—
350Dic3—62no—
351Dic3—62no—
352Dic3—61no—
353Dic3—61no—
354Dic3—62no—
355Dic3—121no—
356C32#307911yescharacteristic, complemented, Sylow
357C23—61no—
358C23C2×GO+(4,𝔽2)11yescharacteristic
359Q8—92no—
360Q8—181no—
361Q8—364no—
362Q8—364no—
363D4—64no—
364D4—92no—
365D4—181no—
366C2×C4—22no—
367C2×C4—61no—
368C2×C4—61no—
369C2×C4—61no—
370C2×C4—64no—
371C2×C4—91no—
372C2×C4—91no—
373C2×C4—91no—
374C2×C4—92no—
375C2×C4—92no—
376C2×C4—91no—
377C2×C4—124no—
378C2×C4—122no—
379C2×C4—184no—
380C2×C4—182no—
381C2×C4—362no—
382C2×C4C2×GO+(4,𝔽2)11yescharacteristic
383C2×C4C2×GO+(4,𝔽2)11yescharacteristic
384C8—184no—
385C2×C3—24no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—42no—
393C2×C3—122no—
394D3—42no—
395C22—21no—
396C22—21no—
397C22—62no—
398C22—121no—
399C22—121no—
400C22D32⋊Q812yes—
401C22C22×GO+(4,𝔽2)11yescharacteristic
402C4—21no—
403C4—62no—
404C4—91no—
405C4—92no—
406C4—91no—
407C4—92no—
408C4—124no—
409C4—121no—
410C4—121no—
411C4—181no—
412C4#6423912yes—
413C3—21no—
414C3—21no—
415C2—22no—
416C2—122no—
417C2C2×D32⋊Q811yescharacteristic
418C2#1059650111yescharacteristic
419C2C2×#6423911yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC2×#3805C22
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3079
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#63919C2semidirect
3. #10593805C2semidirect
4. #10593507C2semidirect
6. #10593393C2semidirect
7. #10593385C2semidirect
8. #10593367C2semidirect
9. #10593359C2semidirect
49. #3805Q8semidirect
119. #627C2×Q8semidirect
121. #625C2×Q8semidirect
356. C32#3079semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
C4×#38052
#105938052
#105935072
#105934962
#105933932
#105933852
#105933672
#105933592
#30799