Finite Group Databasebeta

← #11868533

Subgroups — #11868533

Order 1152.

1164 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic, complemented
2C4×#3830C211yesmaximal, characteristic
3C32×#474C211yesmaximal, characteristic, complemented
4#10592793C211yesmaximal, characteristic, complemented
5#10592707C211yesmaximal, characteristic, complemented
6#10592579C212yesmaximal, complemented
7#10592576C212yesmaximal, complemented
8#10592549C211yesmaximal, characteristic, complemented
9C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
10#10592471C212yesmaximal
11#10592465C212yesmaximal, complemented
12#80964—34nomaximal
13C2×#3830C2211yescharacteristic
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×D4C2211yescharacteristic
16#64155—21no—
17Q8×C3⋊Dic3—21no—
18D4×C3⋊Dic3C2211yescharacteristic
19C4×#638—21no—
20C2×C4×C3⋊Dic3—21no—
21C2×C8×C3⋊D3C2212yes—
22#64106—21no—
23#64101C2211yescharacteristic
24#64101C2212yes—
25#64099C2212yes—
26#64096—21no—
27#64096C2211yescharacteristic
28#64090—21no—
29#64086—21no—
30C42×C3⋊D3C2211yescharacteristic
31#64078C2211yescharacteristic
32C4×#634C2211yescharacteristic
33C32×#107C2212yes—
34C32×C4⋊C8C2211yescharacteristic
35C32×#102C2212yes—
36#63659C2212yes—
37#63645C2212yes—
38#63643C2212yes—
39#63641C2212yes—
40#63637C2212yes—
41#63635C2212yes—
42#63635C2212yes—
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
44#5728—34no—
45C4×#237—34no—
46C3×#474D314yescomplemented
47#5094—34no—
48#5008—34no—
49#4880—38no—
50#4877—38no—
51#4850—34no—
52D3×C4⋊C8—34no—
53#4772—38no—
54#4766—38no—
55C2×C32×Q8—21no—
56C2×C32×D4C2311yescharacteristic
57C22×C32×C4—21no—
58C2×#638—21no—
59C22×C3⋊Dic3—21no—
60C22×C3⋊Dic3—21no—
61#3830—22no—
62#3830Q814yescomplemented
63C2×C4×C3⋊D3D411yescharacteristic
64C2×C4×C3⋊D3D411yescharacteristic
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×#634—21no—
67C2×#634C2311yescharacteristic
68C2×C32×C8C2312yes—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2311yescharacteristic
71C32×C4⋊C4C2312yes—
72C32×C22⋊C4—21no—
73C32×C42C2311yescharacteristic
74#3757—21no—
75#3752—21no—
76#3752—22no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)—22no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2312yes—
81#3750—21no—
82#3750—21no—
83#3750—22no—
84C4×C3⋊Dic3—21no—
85C4×C3⋊Dic3—21no—
86C4×C3⋊Dic3—21no—
87C4×C3⋊Dic3—22no—
88C4×C3⋊Dic3D411yescharacteristic
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊(C3⋊C8)C2312yes—
92C8×C3⋊D3—24no—
93#3076—91noSylow
94C2×#237—34no—
95C3×C4⋊Q8C2×D314yes—
96C3×C4×D4C2×D314yes—
97#946—64no—
98Q8×Dic3—64no—
99D4×Dic3—34no—
100C4×#67—64no—
101C2×C4×Dic3—64no—
102C2×D3×C8—38no—
103#897—64no—
104#892—34no—
105#892—38no—
106#890—38no—
107#887—34no—
108#887—64no—
109#67⋊C4—64no—
110#877—64no—
111C42×D3—34no—
112#869—34no—
113C4×Dic6—34no—
114C3×#107C2×D318yes—
115C3×C4⋊C8C2×D314yes—
116C3×#102C2×D318yes—
117#832—38no—
118#818—38no—
119#816—38no—
120Dic3⋊C8—38no—
121#810—38no—
122#808—38no—
123#808—38no—
124C4⋊(C3⋊C8)—34no—
125C23×C32—21no—
126C22×C3⋊D3C2×D411yescharacteristic
127C32×Q8—42no—
128C32×D4—21no—
129C32×D4C2×Q812yes—
130C2×C32×C4—21no—
131C2×C32×C4—22no—
132C2×C32×C4—42no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2411yescharacteristic
136#638—24no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—24no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—42no—
142C2×C3⋊Dic3C2×D411yescharacteristic
143C2×C3⋊Dic3C2×D411yescharacteristic
144C2×C3⋊Dic3C2×D411yescharacteristic
145C4×C3⋊D3—22no—
146C4×C3⋊D3—41no—
147C4×C3⋊D3C2×Q812yes—
148C4×C3⋊D3#4112yes—
149#634—21no—
150#634—42no—
151#634C2×Q812yes—
152C32×C8—22no—
153C3⋊(C3⋊C8)—22no—
154#533—91no—
155C4×#41—91no—
156#479—92no—
157#478—92no—
158#477—91no—
159#476—91no—
160#475—91no—
161#474C3⋊D311yescharacteristic, complemented
162#427—92no—
163C2×C4⋊C8—91no—
164#416—92no—
165C2×C3×Q8—24no—
166C2×C3×D4C22×D314yes—
167C22×C3×C4—24no—
168C2×#67—64no—
169C22×Dic3—64no—
170C22×Dic3—64no—
171#237—316no—
172#237—68no—
173C2×C4×D3—34no—
174C2×C4×D3—34no—
175C2×C4×D3—34no—
176C2×Dic6—34no—
177C2×Dic6—64no—
178C2×C3×C8C22×D318yes—
179C3×C4⋊C4—24no—
180C3×C4⋊C4C22×D314yes—
181C3×C4⋊C4C22×D318yes—
182C3×C22⋊C4—24no—
183C3×C42C22×D314yes—
184#217—64no—
185(C2×D3)⋊C4—64no—
186(C2×D3)⋊C4—68no—
187C4⋊Dic3—34no—
188C4⋊Dic3—38no—
189C4⋊Dic3—68no—
190C4⋊Dic3—64no—
191Dic3⋊C4—64no—
192Dic3⋊C4—68no—
193Dic3⋊C4—64no—
194C4×Dic3—34no—
195C4×Dic3—34no—
196C4×Dic3—34no—
197C4×Dic3—64no—
198C4×Dic3—64no—
199C4×Dic3—68no—
200C4×Dic3—64no—
201C2×C3⋊C8—38no—
202D3×C8—616no—
203C22×C32—22no—
204C22×C32—41no—
205C22×C32—41no—
206C22×C32C22×D411yescharacteristic
207C2×C3⋊D3—21no—
208C2×C3⋊D3—21no—
209C2×C3⋊D3C22⋊Q812yes—
210C32×C4—21no—
211C32×C4—41no—
212C32×C4—42no—
213C32×C4#13512yes—
214C32×C4C22×Q811yescharacteristic
215C32×C4C2×#4111yescharacteristic
216C3⋊Dic3—22no—
217C3⋊Dic3—21no—
218C3⋊Dic3—21no—
219C3⋊Dic3—42no—
220C3⋊Dic3—41no—
221C3⋊Dic3C22⋊Q812yes—
222C2×#41—91no—
223C22×C8—92no—
224C4⋊Q8—91no—
225C4⋊Q8C2×C3⋊D311yescharacteristic
226#125—92no—
227C22⋊Q8—181no—
228C22⋊Q8—181no—
229C4×Q8—91no—
230C4×Q8—91no—
231C4×Q8—181no—
232C4×Q8—181no—
233C4×D4—91no—
234C4×D4—181no—
235C4×D4—181no—
236C4×D4C2×C3⋊D311yescharacteristic
237#117—91no—
238#117—92no—
239#117—181no—
240C2×C42—91no—
241C2×C42—181no—
242#107—92no—
243#107C2×C3⋊D312yes—
244#106—92no—
245#106—92no—
246C4⋊C8—92no—
247C4⋊C8—91no—
248C4⋊C8C2×C3⋊D311yescharacteristic
249#103—92no—
250#103—92no—
251#102—92no—
252#102C2×C3⋊D312yes—
253C23×C3—24no—
254C22×D3—34no—
255C3×Q8—48no—
256C3×D4—24no—
257C3×D4D3×Q818yes—
258C2×C3×C4—24no—
259C2×C3×C4—28no—
260C2×C3×C4—48no—
261C2×C3×C4D3×D414yes—
262C2×C3×C4D3×D414yes—
263C2×C3×C4C23×D314yes—
264#67—616no—
265C2×Dic3—34no—
266C2×Dic3—34no—
267C2×Dic3—34no—
268C2×Dic3—616no—
269C2×Dic3—64no—
270C2×Dic3—64no—
271C2×Dic3—68no—
272C2×Dic3—128no—
273C4×D3—38no—
274C4×D3—38no—
275C4×D3—68no—
276C4×D3—124no—
277Dic6—38no—
278Dic6—64no—
279Dic6—128no—
280C3×C8—28no—
281C3⋊C8—68no—
282C2×C32—42no—
283C2×C32C2×C22⋊Q811yescharacteristic
284C2×C32C2×#13511yescharacteristic
285C2×C32#57511yescharacteristic
286C3⋊D3—22no—
287#41—94no—
288#41—182no—
289C2×Q8—21no—
290C2×Q8—91no—
291C2×Q8—181no—
292C2×D4—181no—
293C2×D4C22×C3⋊D311yescharacteristic
294C22×C4—21no—
295C22×C4—91no—
296C22×C4—91no—
297C22×C4—91no—
298C22×C4—181no—
299C22×C4—181no—
300C2×C8—92no—
301C2×C8—184no—
302C2×C8C22×C3⋊D312yes—
303C4⋊C4—21no—
304C4⋊C4—92no—
305C4⋊C4—91no—
306C4⋊C4—181no—
307C4⋊C4—182no—
308C4⋊C4—182no—
309C4⋊C4—181no—
310C4⋊C4—181no—
311C4⋊C4C22×C3⋊D312yes—
312C4⋊C4C22×C3⋊D311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—181no—
315C22⋊C4—182no—
316C22⋊C4—181no—
317C42—91no—
318C42—91no—
319C42—91no—
320C42—181no—
321C42—181no—
322C42—182no—
323C42—181no—
324C42C22×C3⋊D311yescharacteristic
325C22×C3—28no—
326C22×C3—44no—
327C22×C3—44no—
328C22×C3C2×D3×D414yes—
329C2×D3—38no—
330C2×D3—64no—
331C2×D3—64no—
332C3×C4—24no—
333C3×C4—44no—
334C3×C4—48no—
335C3×C4#91218yes—
336C3×C4C2×D3×Q814yes—
337C3×C4D3×#4114yes—
338Dic3—38no—
339Dic3—64no—
340Dic3—64no—
341Dic3—68no—
342Dic3—128no—
343Dic3—124no—
344C32#307611yescharacteristic, complemented, Sylow
345C23—21no—
346C23—91no—
347Q8—42no—
348Q8—92no—
349Q8—181no—
350Q8—362no—
351D4—21no—
352D4—184no—
353D4Q8×C3⋊D312yes—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—42no—
357C2×C4—91no—
358C2×C4—92no—
359C2×C4—92no—
360C2×C4—91no—
361C2×C4—91no—
362C2×C4—184no—
363C2×C4—181no—
364C2×C4—182no—
365C2×C4—181no—
366C2×C4—182no—
367C2×C4—361no—
368C2×C4—362no—
369C2×C4D4×C3⋊D311yescharacteristic
370C2×C4D4×C3⋊D311yescharacteristic
371C2×C4C23×C3⋊D311yescharacteristic
372C8—22no—
373C8—182no—
374C2×C3—48no—
375C2×C3D3×C22⋊Q814yes—
376C2×C3C2×#91214yes—
377C2×C3#577714yes—
378D3—68no—
379C22—22no—
380C22—41no—
381C22—41no—
382C22—92no—
383C22—181no—
384C22—181no—
385C22C2×D4×C3⋊D311yescharacteristic
386C4—21no—
387C4—41no—
388C4—42no—
389C4—92no—
390C4—182no—
391C4—181no—
392C4—181no—
393C4—361no—
394C4—362no—
395C4#6412112yes—
396C4C2×Q8×C3⋊D311yescharacteristic
397C4#41×C3⋊D311yescharacteristic
398C3#8096414yescomplemented
399C2—42no—
400C2—182no—
401C2C3⋊D3×C22⋊Q811yescharacteristic
402C2C2×#6412111yescharacteristic
403C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radicalC2×#3830C22
hypercenter#474C3⋊D3
hypocenterC32#3076
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
3. C32×#474C2semidirect
4. #10592793C2semidirect
5. #10592707C2semidirect
6. #10592579C2semidirect
7. #10592576C2semidirect
8. #10592549C2semidirect
9. C3⋊D3×C4⋊C8C2semidirect
11. #10592465C2semidirect
46. C3×#474D3semidirect
62. #3830Q8semidirect
161. #474C3⋊D3semidirect
344. C32#3076semidirect
398. C3#80964semidirect

Maximal subgroups

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

subgroupindex
#105961992
C4×#38302
C32×#4742
#105927932
#105927072
#105925792
#105925762
#105925492
C3⋊D3×C4⋊C82
#105924712
#105924652
#809643