Finite Group Databasebeta

← #11775855

Subgroups — #11775855

Order 1152.

462 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 94 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
1#10593921C211yesmaximal, characteristic
2C3×#4705C211yesmaximal, characteristic, complemented
3#10590334C211yesmaximal, characteristic, complemented
4#10589331C211yesmaximal, characteristic, complemented
5C3×#4464C211yesmaximal, characteristic, complemented
6#10589089C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#70805—31nomaximal
9#68344—31nomaximal
10#64079C2211yescharacteristic
11C3×#875C2211yescharacteristic
12C3×C42×D3C2211yescharacteristic
13#63908C411yescharacteristic
14#63905—21no—
15Dic3×D12C411yescharacteristic
16#63879—21no—
17#63877—21no—
18#63859—21no—
19#63856C411yescharacteristic
20Dic3×Dic6C411yescharacteristic
21C2×#3711—21no—
22C32×#97C2211yescharacteristic
23#63630C2211yescharacteristic
24C3×(C2×D3)⋊C8—21no—
25C3×Dic3⋊C8—21no—
26C3×#803C2211yescharacteristic
27C3×#803C2211yescharacteristic
28Dic3×C3⋊C8—21no—
29#5680—31no—
30#5479—31no—
31C3×#432—31no—
32C4×#208—31no—
33#4707—31no—
34#4705D311yescharacteristic, complemented
35C3×#329—31no—
36#4540—31no—
37#4465—31no—
38#4465—31no—
39#4465—31no—
40#4465—31no—
41#4465—61no—
42#4464—31no—
43#4464D311yescharacteristic, complemented
44C2×C3×D12C2×C411yescharacteristic
45C2×C3×C4×D3C2×C411yescharacteristic
46C2×C3×C4×D3D411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×Dic6C2×C411yescharacteristic
49C2×#625—21no—
50C2×D3×Dic3—21no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55#3750—21no—
56#3750—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4×Dic3C2×C411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#3724—21no—
66Dic3⋊Dic3—21no—
67(C2×D3)⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70Dic32—21no—
71#3711—24no—
72#1529—91noSylow
73C3×#124—31no—
74C2×C3×C42—31no—
75#946—31no—
76Q8×Dic3—31no—
77#938—31no—
78D4×Dic3—31no—
79#930—31no—
80#929—61no—
81C4×#67—61no—
82#924—31no—
83C2×#208—61no—
84C2×ΓL(1,𝔽25)—61no—
85#883—61no—
86#67⋊C4—61no—
87#879—61no—
88#877—61no—
89#876—61no—
90#875C2×D311yescharacteristic
91C4×D12—31no—
92#872—61no—
93C42×D3C2×D311yescharacteristic
94#870—31no—
95#870—31no—
96#870—61no—
97C4×Dic6—31no—
98C3×C4⋊C8—61no—
99C3×C22⋊C8—61no—
100C3×#97—21no—
101C3×#97—31no—
102C3×#97—31no—
103C3×#97C2×D311yescharacteristic
104C3×#97C2×D311yescharacteristic
105(C2×D3)⋊C8—21no—
106Dic3⋊C8—21no—
107C8×Dic3—61no—
108#803—31no—
109#803—31no—
110#803—61no—
111#803C2×D311yescharacteristic
112#803C2×D311yescharacteristic
113C4×C3⋊C8—61no—
114C22×C3×D3—21no—
115C22×C3×D3C22⋊C411yescharacteristic
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3C22⋊C411yescharacteristic
123C2×C3×Dic3C22⋊C411yescharacteristic
124C2×C3×Dic3C22⋊C411yescharacteristic
125C3×D12—41no—
126C3×C4×D3—22no—
127C3×C4×D3—41no—
128C3×C4×D3—41no—
129C3×Dic6—41no—
130#625—42no—
131D3×Dic3—42no—
132C32×C8—41no—
133C3⋊(C3⋊C8)—22no—
134C3×C3⋊C8—22no—
135C3×C3⋊C8—41no—
136#529—91no—
137#432—31no—
138C4×M16—91no—
139#330—91no—
140#330—91no—
141#329—31no—
142#329—91no—
143C2×C3×Q8—31no—
144C2×C3×D4—31no—
145C22×C3×C4—31no—
146C22×C3×C4—31no—
147C22×C3×C4—31no—
148C2×#67—61no—
149C2×#67—61no—
150C22×Dic3—61no—
151C2×D12C4×D311yescharacteristic
152C2×C4×D3—61no—
153C2×C4×D3C4×D311yescharacteristic
154C2×C4×D3D1211yescharacteristic
155C2×C4×D3#6711yescharacteristic
156C2×Dic6C4×D311yescharacteristic
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—41no—
160C2×C3×C8—61no—
161C2×C3×C8—61no—
162C3×C22⋊C4—61no—
163C3×C22⋊C4—61no—
164C3×C42—21no—
165C3×C42—31no—
166C3×C42—31no—
167C3×C42—31no—
168C3×C42C22×D311yescharacteristic
169C3×C42C22×D311yescharacteristic
170#217—61no—
171#217—61no—
172#217—61no—
173(C2×D3)⋊C4—21no—
174(C2×D3)⋊C4—21no—
175(C2×D3)⋊C4—61no—
176(C2×D3)⋊C4—61no—
177(C2×D3)⋊C4—61no—
178C4⋊Dic3—31no—
179C4⋊Dic3—31no—
180C4⋊Dic3—31no—
181C4⋊Dic3—31no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185Dic3⋊C4—61no—
186Dic3⋊C4—61no—
187Dic3⋊C4—61no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—121no—
193Dic3⋊C4—121no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C4×Dic3C4×D311yescharacteristic
197C4×Dic3D1211yescharacteristic
198C4×Dic3#6711yescharacteristic
199#208—64no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—121no—
205ΓL(1,𝔽25)—64no—
206C22×C32C2×C22⋊C411yescharacteristic
207C2×C3×D3—21no—
208C2×C3×D3—21no—
209C2×C3×D3—21no—
210C2×C3×D3—41no—
211C2×C3×D3—41no—
212C2×C3×D3—41no—
213C32×C4—21no—
214C32×C4—21no—
215C32×C4—21no—
216C3⋊Dic3—41no—
217C3⋊Dic3—41no—
218C3×Dic3—21no—
219C3×Dic3—21no—
220C3×Dic3—41no—
221C3×Dic3#10412yes—
222C2×M16—181no—
223#126—181no—
224#125—91no—
225#124—31no—
226#123—181no—
227C22⋊Q8—91no—
228#121—91no—
229C4×Q8—91no—
230C4×D4—91no—
231C4×D4—181no—
232#117—181no—
233C2×C42—31no—
234C4⋊C8—61no—
235C22⋊C8—61no—
236#97—31no—
237#97—31no—
238#97—91no—
239#97D3211yescharacteristic
240C4×C8—181no—
241C23×C3—31no—
242C23×C3—61no—
243C22×D3—21no—
244C22×D3(C2×D3)⋊C411yescharacteristic
245C3×Q8—121no—
246C3×D4—121no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—31no—
251C2×C3×C4—31no—
252C2×C3×C4—31no—
253C2×C3×C4—62no—
254C2×C3×C4—61no—
255C2×C3×C4—121no—
256C2×C3×C4—121no—
257C2×C3×C4C2×C4×D311yescharacteristic
258C2×C3×C4C2×C4×D311yescharacteristic
259C2×C3×C4C2×D1211yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4C2×#6711yescharacteristic
263#67—122no—
264#67—122no—
265C2×Dic3—21no—
266C2×Dic3—61no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—121no—
271C2×Dic3—121no—
272C2×Dic3—122no—
273C2×Dic3(C2×D3)⋊C411yescharacteristic
274C2×Dic3(C2×D3)⋊C411yescharacteristic
275C2×Dic3(C2×D3)⋊C411yescharacteristic
276D12—41no—
277C4×D3—22no—
278C4×D3—41no—
279C4×D3—41no—
280C4×D3—122no—
281Dic6—41no—
282C3×C8—41no—
283C3×C8—41no—
284C3×C8—42no—
285C3×C8—62no—
286C3×C8—121no—
287C3⋊C8—22no—
288C3⋊C8—41no—
289C3⋊C8—62no—
290C3⋊C8—62no—
291C3⋊C8—122no—
292C2×C32#41311yescharacteristic
293C2×C32C2×#10411yescharacteristic
294C2×C32#42111yescharacteristic
295C3×D3—41no—
296C3×D3—81no—
297C2×Q8—31no—
298C2×D4—31no—
299C2×D4—181no—
300C22×C4—31no—
301C22×C4—31no—
302C22×C4—31no—
303C22×C4—181no—
304M16—184no—
305C2×C8—21no—
306C2×C8—61no—
307C2×C8—61no—
308C2×C8—181no—
309C4⋊C4—91no—
310C4⋊C4—91no—
311C4⋊C4—181no—
312C4⋊C4—181no—
313C4⋊C4—181no—
314C4⋊C4—181no—
315C22⋊C4—61no—
316C22⋊C4—61no—
317C22⋊C4—181no—
318C22⋊C4—181no—
319C22⋊C4—181no—
320C42—31no—
321C42—31no—
322C42—31no—
323C42—181no—
324C42C2×D3211yescharacteristic
325C22×C3—21no—
326C22×C3—61no—
327C22×C3—61no—
328C22×C3—61no—
329C22×C3—121no—
330C22×C3—121no—
331C22×C3—121no—
332C22×C3D3×C22⋊C411yescharacteristic
333C22×C3C2×(C2×D3)⋊C411yescharacteristic
334C2×D3—21no—
335C2×D3—21no—
336C2×D3—21no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—32no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—61no—
351C3×C4—61no—
352C3×C4—121no—
353Dic3—21no—
354Dic3—21no—
355Dic3—41no—
356Dic3—121no—
357Dic3—121no—
358Dic3—121no—
359Dic3—121no—
360Dic3—241no—
361Dic3—241no—
362Dic3#82512yes—
363C32#152911yescharacteristic, complemented, Sylow
364C23—31no—
365C23—61no—
366Q8—121no—
367D4—121no—
368D4—362no—
369C2×C4—31no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—62no—
373C2×C4—61no—
374C2×C4—121no—
375C2×C4—121no—
376C2×C4—181no—
377C2×C4—181no—
378C2×C4—362no—
379C2×C4C4×D3211yescharacteristic
380C2×C4D3×D1211yescharacteristic
381C2×C4D3×#6711yescharacteristic
382C8—41no—
383C8—62no—
384C8—121no—
385C8—182no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—121no—
390C2×C3—241no—
391C2×C3#474511yescharacteristic
392C2×C3D3×#10411yescharacteristic
393C2×C3#482111yescharacteristic
394C2×C3#500511yescharacteristic
395C2×C3#513211yescharacteristic
396C2×C3C2×#82511yescharacteristic
397D3—41no—
398D3—81no—
399C22—61no—
400C22—61no—
401C22—61no—
402C22—121no—
403C22—121no—
404C22—121no—
405C22D3×(C2×D3)⋊C411yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—32no—
410C4—61no—
411C4—61no—
412C4—121no—
413C4—361no—
414C4—361no—
415C3—21no—
416C3#6834411yescharacteristic, complemented
417C3#7080511yescharacteristic, complemented
418C2—121no—
419C2—241no—
420C2#1059039211yescharacteristic
421C2D3×#82511yescharacteristic
422C2#1059100611yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32C2×C22⋊C4
prime radical#63908C4
cosocleC32×C42C23
hypercenter#97D32
hypocenterC32#1529
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. C3×#4705C2semidirect
3. #10590334C2semidirect
4. #10589331C2semidirect
5. C3×#4464C2semidirect
6. #10589089C2semidirect
7. #10589086C2semidirect
34. #4705D3semidirect
43. #4464D3semidirect
363. C32#1529semidirect
416. C3#68344semidirect
417. C3#70805semidirect

Maximal subgroups

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

subgroupindex
#105939212
C3×#47052
#105903342
#105893312
C3×#44642
#105890892
#105890862
#708053
#683443