Finite Group Databasebeta

← #11775853

Subgroups — #11775853

Order 1152.

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

normal subgroups only

This group has 467 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#10593976C211yesmaximal, characteristic
2C3×#4705C211yesmaximal, characteristic, complemented
3#10590334C211yesmaximal, characteristic, complemented
4#10589330C211yesmaximal, characteristic, complemented
5C3×#4465C211yesmaximal, characteristic, complemented
6#10589088C211yesmaximal, characteristic, complemented
7#10589087C211yesmaximal, characteristic, complemented
8#70805—31nomaximal
9#68364—31nomaximal
10#64084C2211yescharacteristic
11C3×C42×D3C2211yescharacteristic
12C3×#870C2211yescharacteristic
13#63909C411yescharacteristic
14#63904—21no—
15#63894C411yescharacteristic
16#63868—21no—
17#63857C411yescharacteristic
18#63850—21no—
19#63844C411yescharacteristic
20#63836—21no—
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#5691—31no—
30#5479—31no—
31C3×#432—31no—
32C4×#208—31no—
33#4707—31no—
34#4705D311yescharacteristic, complemented
35C3×#330—31no—
36#4543—31no—
37#4465—31no—
38#4465D311yescharacteristic, complemented
39#4464—31no—
40#4464—31no—
41#4464—31no—
42#4464—31no—
43#4464—61no—
44C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
45C2×#634C2×C411yescharacteristic
46C2×C3×C4×D3C2×C411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×#626—21no—
50C2×#624—21no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53#3752—21no—
54#3752—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4⋊Dic3C2×C411yescharacteristic
57C3×C4⋊Dic3C2×C411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊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#3722—21no—
68#3722—21no—
69(C2×D3)⋊Dic3—21no—
70Dic32—21no—
71#3711—24no—
72#1529—91noSylow
73C3×#125—31no—
74C2×C3×C42—31no—
75#930—31no—
76#929—61no—
77C4×#67—61no—
78#924—31no—
79C2×#208—61no—
80C2×ΓL(1,𝔽25)—61no—
81#898—61no—
82#897—31no—
83#895—31no—
84#894—61no—
85#893—31no—
86#893—61no—
87#892—61no—
88#887—31no—
89#876—61no—
90#875—31no—
91#875—31no—
92#875—61no—
93C4×D12—31no—
94#872—61no—
95C42×D3C2×D311yescharacteristic
96#870C2×D311yescharacteristic
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—
120C4⋊(C3⋊D3)—41no—
121#634—41no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3C22⋊C411yescharacteristic
125C2×C3×Dic3C22⋊C411yescharacteristic
126C2×C3×Dic3C22⋊C411yescharacteristic
127C3×C4×D3—22no—
128C3×C4×D3—41no—
129C3×C4×D3—41no—
130#626—42no—
131#624—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—31no—
140#330—91no—
141#329—91no—
142#329—91no—
143C22×C3×C4—31no—
144C22×C3×C4—31no—
145C22×C3×C4—31no—
146C2×#67—61no—
147C2×D12—31no—
148C2×D12—31no—
149C2×D12—61no—
150C2×D12—61no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3C4×D311yescharacteristic
154C2×C4×D3D1211yescharacteristic
155C2×C4×D3#6711yescharacteristic
156C2×Dic6—31no—
157C2×Dic6—31no—
158C2×Dic6—61no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—41no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C42—21no—
169C3×C42—31no—
170C3×C42—31no—
171C3×C42—31no—
172C3×C42C22×D311yescharacteristic
173C3×C42C22×D311yescharacteristic
174#217—61no—
175(C2×D3)⋊C4—61no—
176(C2×D3)⋊C4—61no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4—61no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—121no—
185(C2×D3)⋊C4—121no—
186C4⋊Dic3—61no—
187C4⋊Dic3C4×D311yescharacteristic
188C4⋊Dic3C4×D311yescharacteristic
189Dic3⋊C4—21no—
190Dic3⋊C4—21no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
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—41no—
208C2×C3⋊D3—41no—
209C2×C3⋊D3—41no—
210C2×C3×D3—21no—
211C2×C3×D3—21no—
212C2×C3×D3—21no—
213C32×C4—21no—
214C32×C4—21no—
215C32×C4—21no—
216C3⋊Dic3—41no—
217C3×Dic3—21no—
218C3×Dic3—21no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3#10412yes—
222C2×M16—181no—
223#126—181no—
224#125—31no—
225#124—91no—
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—
242C22×D3—61no—
243C22×D3—61no—
244C22×D3—121no—
245C22×D3(C2×D3)⋊C411yescharacteristic
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—31no—
250C2×C3×C4—31no—
251C2×C3×C4—31no—
252C2×C3×C4—62no—
253C2×C3×C4—61no—
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—
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3—61no—
267C2×Dic3—61no—
268C2×Dic3—121no—
269C2×Dic3(C2×D3)⋊C411yescharacteristic
270C2×Dic3(C2×D3)⋊C411yescharacteristic
271C2×Dic3(C2×D3)⋊C411yescharacteristic
272D12—121no—
273D12—121no—
274D12—122no—
275D12—241no—
276C4×D3—22no—
277C4×D3—41no—
278C4×D3—41no—
279C4×D3—122no—
280C4×D3—122no—
281Dic6—121no—
282Dic6—121no—
283Dic6—241no—
284C3×C8—41no—
285C3×C8—41no—
286C3×C8—42no—
287C3×C8—62no—
288C3×C8—121no—
289C3⋊C8—22no—
290C3⋊C8—41no—
291C3⋊C8—62no—
292C3⋊C8—62no—
293C3⋊C8—122no—
294C2×C32#41311yescharacteristic
295C2×C32C2×#10411yescharacteristic
296C2×C32#42111yescharacteristic
297C3⋊D3—81no—
298C3×D3—41no—
299C2×Q8—91no—
300C2×D4—91no—
301C2×D4—181no—
302C22×C4—31no—
303C22×C4—31no—
304C22×C4—31no—
305C22×C4—181no—
306M16—184no—
307C2×C8—21no—
308C2×C8—61no—
309C2×C8—61no—
310C2×C8—181no—
311C4⋊C4—31no—
312C4⋊C4—31no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4—181no—
316C4⋊C4—181no—
317C22⋊C4—181no—
318C22⋊C4—181no—
319C22⋊C4—181no—
320C22⋊C4—181no—
321C22⋊C4—181no—
322C42—31no—
323C42—31no—
324C42—31no—
325C42—181no—
326C42C2×D3211yescharacteristic
327C22×C3—21no—
328C22×C3—61no—
329C22×C3—61no—
330C22×C3—61no—
331C22×C3D3×C22⋊C411yescharacteristic
332C22×C3C2×(C2×D3)⋊C411yescharacteristic
333C2×D3—21no—
334C2×D3—21no—
335C2×D3—21no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3—121no—
339C2×D3—121no—
340C2×D3—121no—
341C2×D3—121no—
342C2×D3—241no—
343C2×D3—241no—
344C2×D3—241no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—32no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—61no—
356C3×C4—61no—
357C3×C4—121no—
358C3×C4—121no—
359Dic3—21no—
360Dic3—21no—
361Dic3—41no—
362Dic3—41no—
363Dic3—121no—
364Dic3—121no—
365Dic3—241no—
366Dic3#82512yes—
367C32#152911yescharacteristic, complemented, Sylow
368C23—31no—
369C23—181no—
370Q8—361no—
371D4—361no—
372D4—362no—
373C2×C4—31no—
374C2×C4—31no—
375C2×C4—31no—
376C2×C4—62no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—121no—
380C2×C4—121no—
381C2×C4—181no—
382C2×C4—362no—
383C2×C4C4×D3211yescharacteristic
384C2×C4D3×D1211yescharacteristic
385C2×C4D3×#6711yescharacteristic
386C8—41no—
387C8—62no—
388C8—121no—
389C8—182no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—121no—
394C2×C3#475111yescharacteristic
395C2×C3D3×#10411yescharacteristic
396C2×C3#482111yescharacteristic
397C2×C3#500511yescharacteristic
398C2×C3#513211yescharacteristic
399C2×C3C2×#82511yescharacteristic
400D3—41no—
401D3—241no—
402D3—241no—
403D3—481no—
404C22—61no—
405C22—61no—
406C22—61no—
407C22—361no—
408C22—361no—
409C22—361no—
410C22D3×(C2×D3)⋊C411yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—32no—
415C4—61no—
416C4—61no—
417C4—121no—
418C4—121no—
419C4—361no—
420C3—21no—
421C3#6836411yescharacteristic, complemented
422C3#7080511yescharacteristic, complemented
423C2—121no—
424C2—721no—
425C2#1059039211yescharacteristic
426C2D3×#82511yescharacteristic
427C2#1059100711yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32C2×C22⋊C4
prime radical#63909C4
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. #10589330C2semidirect
5. C3×#4465C2semidirect
6. #10589088C2semidirect
7. #10589087C2semidirect
34. #4705D3semidirect
38. #4465D3semidirect
367. C32#1529semidirect
421. C3#68364semidirect
422. C3#70805semidirect

Maximal subgroups

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

subgroupindex
#105939762
C3×#47052
#105903342
#105893302
C3×#44652
#105890882
#105890872
#708053
#683643