Finite Group Databasebeta

← #11868443

Subgroups — #11868443

Order 1152.

977 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2C4×#3797C211yesmaximal, characteristic
3C3×#5091C212yesmaximal, complemented
4#10590601C212yesmaximal
5#10590573C212yesmaximal
6#10590496C214yesmaximal, complemented
7#10590331C211yesmaximal, characteristic
8#10590283C212yesmaximal, complemented
9D3×#477—32nomaximal
10C2×Q8×C3⋊D3—21no—
11C2×#3797C2211yescharacteristic
12C32×C4⋊Q8C2211yescharacteristic
13#64153—21no—
14C4⋊C4×C3⋊D3—21no—
15C4⋊C4×C3⋊D3C2212yes—
16#64097—21no—
17#64097C2212yes—
18C42×C3⋊D3C2211yescharacteristic
19#64078C2211yescharacteristic
20C3×C4×Dic6C2212yes—
21C4×#627—21no—
22#63900C2211yescharacteristic
23#63883—21no—
24C4×#624—21no—
25#63843C2212yes—
26#63838—21no—
27C2×#3710C2212yes—
28C3×#810C2214yes—
29C3×#807C2214yes—
30C3×C4⋊(C3⋊C8)C2212yes—
31#63575C2214yes—
32#63572C2212yes—
33#63566C2214yes—
34D3×C4⋊Q8—32no—
35D3×C4⋊Q8—61no—
36C4×D3×Q8—32no—
37C3×#477—32no—
38#5091D312yescomplemented
39#5021—32no—
40D3×#107—34no—
41#4875—34no—
42#4850—32no—
43D3×C4⋊C8—32no—
44D3×#103—34no—
45#4793—34no—
46C2×C32×Q8—21no—
47Q8×C3⋊D3—44no—
48C2×C4×C3⋊D3—22no—
49C2×C4×C3⋊D3D411yescharacteristic
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C4×C3⋊D3C2311yescharacteristic
52C2×#634—21no—
53C2×#634—22no—
54C2×C3×Dic6C2312yes—
55C2×#627—21no—
56C2×#624—21no—
57C2×#624—21no—
58#3797—22no—
59#3797Q814yescomplemented
60C32×C4⋊C4—21no—
61C32×C4⋊C4C2312yes—
62C32×C42C2311yescharacteristic
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)C2312yes—
65#3750—22no—
66#3750—22no—
67C4×C3⋊Dic3D411yescharacteristic
68C4×C3⋊Dic3D411yescharacteristic
69C4×C3⋊Dic3C2311yescharacteristic
70C3×C4⋊Dic3C2312yes—
71C3×Dic3⋊C4—22no—
72C3×C4×Dic3—22no—
73C2×C3×C3⋊C8C2314yes—
74#3724—21no—
75Dic3⋊Dic3—22no—
76Dic32—22no—
77#3710—24no—
78C2×#477—91noSylow
79C2×D3×Q8—32no—
80C2×D3×Q8—62no—
81C2×D3×Q8—62no—
82C3×C4⋊Q8—21no—
83C3×C4⋊Q8C2×D312yes—
84C3×C4×Q8—32no—
85Q8×Dic3—32no—
86#944—62no—
87#944—62no—
88C2×D3×C8—34no—
89D3×C4⋊C4—34no—
90D3×C4⋊C4—32no—
91D3×C4⋊C4—62no—
92D3×C4⋊C4—62no—
93D3×C4⋊C4—62no—
94D3×C4⋊C4—62no—
95#888—34no—
96#888—62no—
97#888—62no—
98#888—62no—
99#887—32no—
100#887—62no—
101C42×D3—32no—
102C42×D3—61no—
103C42×D3—62no—
104#869—32no—
105#869—61no—
106C4×Dic6—62no—
107C4×Dic6C2×D312yes—
108C3×#107—34no—
109C3×C4⋊C8—32no—
110C3×#103—34no—
111#835—34no—
112#818—34no—
113#816—34no—
114Dic3⋊C8—34no—
115#810C2×D314yes—
116#807—34no—
117#807C2×D314yes—
118C4⋊(C3⋊C8)C2×D312yes—
119C22×C3⋊D3C2×D411yescharacteristic
120C32×Q8—42no—
121C2×C32×C4—22no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2411yescharacteristic
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3C2×D411yescharacteristic
127C2×C3⋊Dic3C2×D411yescharacteristic
128C2×C3⋊Dic3C2×D411yescharacteristic
129C4×C3⋊D3—22no—
130C4×C3⋊D3—44no—
131C4×C3⋊D3Q1614yes—
132C4×C3⋊D3C2×Q812yes—
133C4×C3⋊D3#4112yes—
134#634—44no—
135#634—42no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C3×Dic6—22no—
139C3×Dic6C2×Q814yescomplemented
140#627—24no—
141#624—24no—
142#624—42no—
143C3×C3⋊C8—24no—
144C2×C4⋊Q8—91no—
145C2×C4×Q8—91no—
146#477—32no—
147#477—94no—
148#477—92no—
149C2×#107—92no—
150C2×C4⋊C8—91no—
151C2×#103—92no—
152C2×C3×Q8—22no—
153C2×C3×Q8—22no—
154C2×C3×Q8—32no—
155D3×Q8—38no—
156D3×Q8—64no—
157D3×Q8—128no—
158D3×Q8—128no—
159C2×C4×D3—32no—
160C2×C4×D3—32no—
161C2×C4×D3—32no—
162C2×C4×D3—61no—
163C2×C4×D3—61no—
164C2×C4×D3—61no—
165C2×C4×D3—62no—
166C2×C4×D3—62no—
167C2×C4×D3—64no—
168C2×C4×D3—64no—
169C2×Dic6—62no—
170C2×Dic6—64no—
171C2×Dic6—62no—
172C2×Dic6—64no—
173C2×Dic6—62no—
174C2×Dic6C22×D312yes—
175C2×C3×C8—34no—
176C3×C4⋊C4—22no—
177C3×C4⋊C4—22no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—32no—
180C3×C4⋊C4—62no—
181C3×C4⋊C4C22×D314yes—
182C3×C42—21no—
183C3×C42—62no—
184C3×C42C22×D312yes—
185C4⋊Dic3—34no—
186C4⋊Dic3—62no—
187C4⋊Dic3—62no—
188C4⋊Dic3—62no—
189C4⋊Dic3—62no—
190C4⋊Dic3C22×D312yes—
191Dic3⋊C4—22no—
192Dic3⋊C4—62no—
193Dic3⋊C4—62no—
194Dic3⋊C4—64no—
195Dic3⋊C4—64no—
196Dic3⋊C4—64no—
197Dic3⋊C4—64no—
198C4×Dic3—22no—
199C4×Dic3—32no—
200C4×Dic3—32no—
201C4×Dic3—32no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—62no—
206C4×Dic3—62no—
207C2×C3⋊C8C22×D314yes—
208D3×C8—68no—
209C22×C32C22×D411yescharacteristic
210C2×C3⋊D3C22⋊Q812yes—
211C2×C3⋊D3C2×Q1612yes—
212C2×C3⋊D3AGL(1,ℤ/8)12yes—
213C32×C4—21no—
214C32×C4—42no—
215C32×C4C2×Q1612yes—
216C32×C4C22×Q811yescharacteristic
217C32×C4C2×#4111yescharacteristic
218C3⋊Dic3—21no—
219C3⋊Dic3—42no—
220C3⋊Dic3C22⋊Q812yes—
221C3⋊Dic3C2×Q1612yes—
222C3×Dic3—24no—
223C3×Dic3—42no—
224C22×Q8—91no—
225C22×Q8—181no—
226C22×C8—92no—
227C4⋊Q8—92no—
228C4⋊Q8—91no—
229C4⋊Q8—181no—
230C4⋊Q8—181no—
231C4⋊Q8D3211yescharacteristic
232C4×Q8—32no—
233C4×Q8—92no—
234C4×Q8—181no—
235C4×Q8—181no—
236C2×C4⋊C4—91no—
237C2×C4⋊C4—92no—
238C2×C4⋊C4—181no—
239C2×C4⋊C4—181no—
240C2×C42—91no—
241C2×C42—181no—
242#107—34no—
243#107—94no—
244C4⋊C8—32no—
245C4⋊C8—92no—
246#103—34no—
247#103—94no—
248C22×D3—32no—
249C22×D3—61no—
250C3×Q8—34no—
251C3×Q8—44no—
252C3×Q8—44no—
253C3×Q8—62no—
254C2×C3×C4—24no—
255C2×C3×C4—24no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—62no—
260C2×C3×C4—62no—
261C2×C3×C4D3×D412yes—
262C2×C3×C4D3×D412yes—
263C2×C3×C4C23×D312yes—
264C2×Dic3—22no—
265C2×Dic3—22no—
266C2×Dic3—32no—
267C2×Dic3—32no—
268C2×Dic3—32no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—64no—
273C2×Dic3—64no—
274C4×D3—38no—
275C4×D3—34no—
276C4×D3—34no—
277C4×D3—64no—
278C4×D3—62no—
279C4×D3—62no—
280C4×D3—68no—
281C4×D3—64no—
282C4×D3—64no—
283C4×D3—124no—
284C4×D3—128no—
285C4×D3—128no—
286Dic6—22no—
287Dic6—68no—
288Dic6—128no—
289Dic6—128no—
290Dic6—124no—
291Dic6—124no—
292Dic6D3×Q814yescomplemented
293C3×C8—64no—
294C3⋊C8—24no—
295C2×C32C2×C22⋊Q811yescharacteristic
296C2×C32C22×Q1611yescharacteristic
297C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
298C3⋊D3#47714yescomplemented
299C2×Q8—21no—
300C2×Q8—32no—
301C2×Q8—94no—
302C2×Q8—182no—
303C2×Q8—181no—
304C2×Q8—182no—
305C2×Q8—181no—
306C2×Q8—364no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—182no—
311C22×C4—181no—
312C22×C4—181no—
313C2×C8—34no—
314C2×C8—184no—
315C4⋊C4—21no—
316C4⋊C4—32no—
317C4⋊C4—62no—
318C4⋊C4—92no—
319C4⋊C4—182no—
320C4⋊C4—182no—
321C4⋊C4—181no—
322C4⋊C4—182no—
323C4⋊C4—181no—
324C4⋊C4C2×D3212yes—
325C42—62no—
326C42—91no—
327C42—91no—
328C42—91no—
329C42—182no—
330C42C2×D3211yescharacteristic
331C22×C3—21no—
332C22×C3C2×D3×D412yes—
333C2×D3—34no—
334C2×D3—34no—
335C2×D3—34no—
336C2×D3—62no—
337C2×D3—62no—
338C2×D3—62no—
339C3×C4—22no—
340C3×C4—22no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—22no—
344C3×C4—44no—
345C3×C4—44no—
346C3×C4—64no—
347C3×C4—122no—
348C3×C4D3×Q1614yes—
349C3×C4C2×D3×Q812yes—
350C3×C4D3×#4112yes—
351Dic3—24no—
352Dic3—34no—
353Dic3—34no—
354Dic3—42no—
355Dic3—62no—
356Dic3—62no—
357Dic3—62no—
358Dic3—62no—
359Dic3—124no—
360Dic3—124no—
361C32C2×#47711yescharacteristic, complemented, Sylow
362C23—91no—
363Q8—34no—
364Q8—42no—
365Q8—62no—
366Q8—184no—
367Q8—362no—
368Q8—364no—
369C2×C4—22no—
370C2×C4—62no—
371C2×C4—62no—
372C2×C4—91no—
373C2×C4—91no—
374C2×C4—92no—
375C2×C4—92no—
376C2×C4—94no—
377C2×C4—91no—
378C2×C4—182no—
379C2×C4—184no—
380C2×C4—182no—
381C2×C4—364no—
382C2×C4—362no—
383C2×C4#381111yescharacteristic
384C2×C4#381111yescharacteristic
385C2×C4C22×D3211yescharacteristic
386C8—64no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3D3×C22⋊Q812yes—
391C2×C3C2×D3×Q1612yes—
392C2×C3D3×AGL(1,ℤ/8)12yes—
393D3—38no—
394D3—64no—
395C22—92no—
396C22—92no—
397C22—92no—
398C22C2×#381111yescharacteristic
399C4—21no—
400C4—42no—
401C4—64no—
402C4—92no—
403C4—92no—
404C4—122no—
405C4—181no—
406C4—362no—
407C4#6394412yes—
408C4D32×Q811yescharacteristic
409C4#6431911yescharacteristic
410C3—21no—
411C3D3×#47712yescomplemented
412C2—94no—
413C2#1059510011yescharacteristic
414C2C2×#6394411yescharacteristic
415C2#1059542911yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32C2×#477
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5091C2semidirect
6. #10590496C2semidirect
8. #10590283C2semidirect
38. #5091D3semidirect
59. #3797Q8semidirect
139. C3×Dic6C2×Q8semidirect
292. Dic6D3×Q8semidirect
298. C3⋊D3#477semidirect
361. C32C2×#477semidirect
411. C3D3×#477semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C4×#37972
C3×#50912
#105906012
#105905732
#105904962
#105903312
#105902832
D3×#4773