Finite Group Databasebeta

← #11878919

Subgroups — #11878919

Order 1152.

913 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 913 conjugacy classes of subgroups — too many to draw. Only its 166 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×#64153C211yesmaximal, characteristic
2#10594810C211yesmaximal, characteristic
3C3×#5228C212yesmaximal
4#10591628C212yesmaximal, complemented
5#10591580C214yesmaximal, complemented
6#10591538C212yesmaximal, complemented
7#10591190C212yesmaximal
8#10591061C211yesmaximal, characteristic
9#80178—32nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×#634C2211yescharacteristic
12#64153—21no—
13#64153—21no—
14#64153C2212yes—
15#64153C2212yes—
16C2×#3750—21no—
17C2×#3750—21no—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×#216C2214yes—
20C3×#924C2212yes—
21#63982—21no—
22#63957—21no—
23#63919C2211yescharacteristic
24#63873C2211yescharacteristic
25#63870—21no—
26#63843C2212yes—
27#63838—21no—
28C2×#3719C2214yes—
29C3×#835C2214yes—
30C3×#830C2212yes—
31#63572C2212yes—
32#63567C2214yes—
33#63553C2212yes—
34C2×#944—32no—
35C2×#944—61no—
36#5622—32no—
37C3×#451—32no—
38#5228D312yes—
39#5183—34no—
40#5182—34no—
41#5050—32no—
42#4795—34no—
43#4792—34no—
44#4739—32no—
45#4718—32no—
46C2×C32×Q8—21no—
47C2×C32×Q8—42no—
48C2×C32×Q8C2312yes—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3D411yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C2×#634—21no—
55C2×#634—42no—
56C2×#634C2312yes—
57C2×C3×Dic6C2312yes—
58C2×#627—21no—
59#3750—22no—
60#3750—22no—
61#3750—22no—
62#3750—22no—
63C4×C3⋊Dic3D411yescharacteristic
64C4×C3⋊Dic3D411yescharacteristic
65C4×C3⋊Dic3C2311yescharacteristic
66C4×C3⋊Dic3C2311yescharacteristic
67C3×#217—22no—
68C3×#216—44no—
69C3×C4⋊Dic3C2312yes—
70C3×Dic3⋊C4—22no—
71C2×C3×C3⋊C8C2314yes—
72#3724—21no—
73#3724—21no—
74#3724—21no—
75Dic3⋊Dic3—22no—
76Dic32—22no—
77#3719—44no—
78#3209—91noSylow
79C22×C3×Q8—21no—
80C22×C3×Q8C2×D312yes—
81C22×Dic6—32no—
82C22×Dic6—61no—
83C2×C3×Q16—34no—
84C3×C22⋊Q8—32no—
85Q8×Dic3—32no—
86#944—34no—
87#944—34no—
88#944—32no—
89#944—62no—
90#944—62no—
91#944—62no—
92#944—62no—
93#944—62no—
94#944—62no—
95C2×#216—34no—
96C2×#216C2×D314yes—
97#924C2×D312yes—
98C2×Dic3⋊C4—62no—
99C2×Dic3⋊C4—62no—
100C2×Dic3⋊C4—62no—
101C2×Dic3⋊C4—62no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—61no—
104C2×Dic12—34no—
105#889—62no—
106#888—32no—
107#887—32no—
108#887—62no—
109#878—62no—
110#877—62no—
111C3×#103—34no—
112C3×C22⋊C8—32no—
113#835C2×D314yes—
114#830C2×D312yes—
115#816—34no—
116Dic3⋊C8—34no—
117C8×Dic3—34no—
118#810—34no—
119C23×C32C2×D411yescharacteristic
120C32×Q8—24no—
121C32×Q8—42no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—42no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2411yescharacteristic
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—42no—
130C2×C3⋊Dic3Q1614yescomplemented
131C2×C3⋊Dic3C2×D411yescharacteristic
132C2×C3⋊Dic3C2×D411yescharacteristic
133C2×C3⋊Dic3C2×D411yescharacteristic
134C2×C3⋊Dic3C2×D411yescharacteristic
135#634—24no—
136#634—42no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C3×Dic6—24no—
140#627—42no—
141C3×C3⋊C8—24no—
142#533—91no—
143C2×C4⋊Q8—91no—
144#494—92no—
145#487—92no—
146#462—94no—
147#451—32no—
148#451—92no—
149#431—91no—
150C2×C3×Q8—22no—
151C2×C3×Q8—22no—
152C2×C3×Q8—22no—
153C2×C3×Q8—32no—
154C2×C3×Q8—44no—
155C2×C3×Q8—44no—
156C2×C3×Q8C22×D314yes—
157C22×C3×C4—22no—
158C22×C3×C4—22no—
159C22×C3×C4—21no—
160C22×C3×C4C22×D312yes—
161C22×Dic3—32no—
162C22×Dic3—32no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—62no—
166C22×Dic3—62no—
167C2×Dic6—34no—
168C2×Dic6—62no—
169C2×Dic6—62no—
170C2×Dic6—62no—
171C2×Dic6—62no—
172C2×Dic6—124no—
173C2×Dic6—124no—
174C2×Dic6C22×D312yes—
175C3×Q16—124no—
176C2×C3×C8—34no—
177C3×C4⋊C4—32no—
178C3×C4⋊C4—62no—
179C3×C22⋊C4—62no—
180#217—22no—
181#216—44no—
182#216—124no—
183C4⋊Dic3—62no—
184C4⋊Dic3C22×D312yes—
185Dic3⋊C4—22no—
186Dic3⋊C4—62no—
187Dic3⋊C4—62no—
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190Dic3⋊C4—64no—
191Dic3⋊C4—64no—
192Dic3⋊C4—64no—
193Dic3⋊C4—64no—
194Dic3⋊C4—64no—
195Dic3⋊C4—64no—
196Dic3⋊C4—64no—
197Dic3⋊C4—64no—
198C4×Dic3—32no—
199C4×Dic3—32no—
200C4×Dic3—32no—
201C4×Dic3—32no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—62no—
207C4×Dic3—62no—
208C2×C3⋊C8C22×D314yes—
209Dic12—124no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32C2×Q1612yes—
213C22×C32C22×D411yescharacteristic
214C32×C4—21no—
215C32×C4—42no—
216C32×C4H(5,𝔽2)12yes—
217C3⋊Dic3—21no—
218C3⋊Dic3—42no—
219C3⋊Dic3C2×Q1612yes—
220C3⋊Dic3C2×Q1612yes—
221C3⋊Dic3#13712yes—
222C3×Dic3—42no—
223C3×Dic3—42no—
224C22×Q8—91no—
225C22×Q8D3211yescharacteristic
226C2×Q16—34no—
227C2×Q16—94no—
228C4⋊Q8—91no—
229C4⋊Q8—91no—
230C4⋊Q8—92no—
231C4⋊Q8—92no—
232C4⋊Q8—181no—
233C4⋊Q8—181no—
234#125—181no—
235C22⋊Q8—32no—
236C22⋊Q8—181no—
237C4×Q8—92no—
238C4×Q8—181no—
239#117—181no—
240C2×C4⋊C4—181no—
241C2×C4⋊C4—181no—
242C2×C42—91no—
243C4⋊C8—92no—
244#103—34no—
245#103—94no—
246C22⋊C8—32no—
247C4×C8—92no—
248C23×C3—21no—
249C23×C3D3×D412yes—
250C3×Q8—24no—
251C3×Q8—24no—
252C3×Q8—44no—
253C3×Q8—44no—
254C3×Q8—44no—
255C3×Q8—64no—
256C2×C3×C4—24no—
257C2×C3×C4—24no—
258C2×C3×C4—24no—
259C2×C3×C4—24no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—44no—
263C2×C3×C4—44no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4D3×D412yes—
267C2×C3×C4C23×D312yes—
268C2×Dic3—22no—
269C2×Dic3—22no—
270C2×Dic3—38no—
271C2×Dic3—32no—
272C2×Dic3—32no—
273C2×Dic3—32no—
274C2×Dic3—32no—
275C2×Dic3—64no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—64no—
281C2×Dic3—64no—
282C2×Dic3—64no—
283C2×Dic3—64no—
284C2×Dic3—124no—
285C2×Dic3—124no—
286Dic6—24no—
287Dic6—64no—
288Dic6—64no—
289Dic6—124no—
290Dic6—124no—
291Dic6—124no—
292Dic6—124no—
293C3×C8—64no—
294C3⋊C8—24no—
295C2×C32—22no—
296C2×C32#53511yescharacteristic
297C2×C32C22×Q1611yescharacteristic
298C2×C32C2×#13711yescharacteristic
299C2×Q8—21no—
300C2×Q8—32no—
301C2×Q8—42no—
302C2×Q8—92no—
303C2×Q8—181no—
304C2×Q8—181no—
305C2×Q8—362no—
306C2×Q8C2×D3212yes—
307C22×C4—21no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—181no—
311C22×C4C2×D3211yescharacteristic
312Q16—124no—
313Q16—364no—
314C2×C8—34no—
315C4⋊C4—32no—
316C4⋊C4—62no—
317C4⋊C4—182no—
318C4⋊C4—182no—
319C4⋊C4—182no—
320C4⋊C4—182no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4—182no—
324C4⋊C4—181no—
325C22⋊C4—62no—
326C42—91no—
327C42—91no—
328C42—91no—
329C42—91no—
330C42—182no—
331C22×C3—22no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—22no—
337C22×C3D3×Q1614yes—
338C22×C3C2×D3×D412yes—
339C3×C4—22no—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—44no—
343C3×C4—44no—
344C3×C4—122no—
345C3×C4—122no—
346C3×C4#100414yes—
347Dic3—34no—
348Dic3—34no—
349Dic3—34no—
350Dic3—42no—
351Dic3—42no—
352Dic3—62no—
353Dic3—62no—
354Dic3—62no—
355Dic3—62no—
356Dic3—62no—
357Dic3—124no—
358Dic3—124no—
359C32#320911yescharacteristic, complemented, Sylow
360C23#381111yescharacteristic
361Q8—24no—
362Q8—42no—
363Q8—64no—
364Q8—184no—
365Q8—362no—
366Q8—362no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—42no—
370C2×C4—62no—
371C2×C4—62no—
372C2×C4—91no—
373C2×C4—91no—
374C2×C4—91no—
375C2×C4—94no—
376C2×C4—91no—
377C2×C4—182no—
378C2×C4—182no—
379C2×C4—362no—
380C2×C4#381111yescharacteristic
381C2×C4C22×D3211yescharacteristic
382C8—64no—
383C2×C3—24no—
384C2×C3—24no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3#559212yes—
389C2×C3C2×D3×Q1612yes—
390C2×C3D3×#13712yes—
391C22—21no—
392C22—21no—
393C22#6394412yes—
394C22C2×#381111yescharacteristic
395C4—21no—
396C4—42no—
397C4—92no—
398C4—92no—
399C4—92no—
400C4—122no—
401C4—122no—
402C4—181no—
403C4—362no—
404C4#6433012yes—
405C3—21no—
406C3#8017812yescomplemented
407C2—22no—
408C2#1059532211yescharacteristic
409C2C2×#6394411yescharacteristic
410C2#1059550211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22×Q8D32
hypocenterC32#3209
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. #10591628C2semidirect
5. #10591580C2semidirect
6. #10591538C2semidirect
130. C2×C3⋊Dic3Q16semidirect
359. C32#3209semidirect
406. C3#80178semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
#105948102
C3×#52282
#105916282
#105915802
#105915382
#105911902
#105910612
#801783