Finite Group Databasebeta

← #11780767

Subgroups — #11780767

Order 1152.

466 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 72 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#10596143C211yesmaximal, characteristic
2C3×#5055C211yesmaximal, characteristic
3#10590305C211yesmaximal, characteristic, complemented
4#10590289C211yesmaximal, characteristic, complemented
5C3×#4540C211yesmaximal, characteristic
6#10589089C211yesmaximal, characteristic, complemented
7#10589089C211yesmaximal, characteristic, complemented
8#71247—31nomaximal
9#68359—31nomaximal
10C32×#124C2211yescharacteristic
11#64153—21no—
12#64144—21no—
13#64088—21no—
14#64088—21no—
15#64087—21no—
16#64087—21no—
17#64079C2211yescharacteristic
18#64079C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×#835—21no—
21C3×#832—21no—
22C3×#803C2211yescharacteristic
23C3×#803C2211yescharacteristic
24C3×#803C2211yescharacteristic
25#63575—21no—
26#63573—21no—
27#63566—21no—
28#63566—21no—
29#5672—31no—
30#5672—31no—
31#5672—61no—
32C3×#489—31no—
33#5082—31no—
34#5081—31no—
35#5055D311yescharacteristic
36#4703—31no—
37#4702—31no—
38C3×#329—31no—
39#4540D311yescharacteristic
40#4465—31no—
41#4465—31no—
42#4465—31no—
43#4465—31no—
44C2×C32×Q8D411yescharacteristic
45C2×C32×D4D411yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×#634—21no—
48C2×C3×Dic6—21no—
49C32×C22⋊C4—21no—
50C32×C22⋊C4—21no—
51C32×C42C2311yescharacteristic
52#3757—21no—
53#3757—21no—
54#3757—21no—
55C4⋊(C3⋊Dic3)D411yescharacteristic
56C4⋊(C3⋊Dic3)D411yescharacteristic
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C4⋊(C3⋊Dic3)D411yescharacteristic
59#3750—21no—
60#3750—21no—
61#3750—21no—
62#3750—21no—
63#3750—21no—
64#3750—21no—
65C4×C3⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#1664—91noSylow
72C3×C4⋊Q8—31no—
73C3×#124—21no—
74C3×#124C2×D311yescharacteristic
75C3×#124C2×D311yescharacteristic
76#944—62no—
77#944—61no—
78#944—61no—
79#935—62no—
80#935—61no—
81#935—61no—
82#879—61no—
83#879—61no—
84#879—61no—
85#879—61no—
86#879—62no—
87#879—62no—
88#878—61no—
89#878—61no—
90#878—61no—
91#878—61no—
92#878—62no—
93#878—62no—
94#870—31no—
95#870—31no—
96#870—31no—
97#870—31no—
98#870—61no—
99#870—61no—
100#869C2×D311yescharacteristic
101C3×#103—61no—
102C3×#102—61no—
103C3×#97—31no—
104C3×#97—31no—
105C3×#97—31no—
106#835—21no—
107#835—61no—
108#835—61no—
109#832—21no—
110#818—61no—
111#817—61no—
112#816—61no—
113#816—61no—
114#808—61no—
115#807—61no—
116#803C2×D311yescharacteristic
117#803C2×D311yescharacteristic
118#803C2×D311yescharacteristic
119C23×C32—21no—
120C32×Q8—41no—
121C32×D4—41no—
122C2×C32×C4—21no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—81no—
131#634—81no—
132C2×C3×Dic3—41no—
133C3×Dic6—42no—
134C3×C3⋊C8—22no—
135C3×C3⋊C8—41no—
136C3×C3⋊C8—41no—
137#563—91no—
138#501—91no—
139#491—91no—
140#489—31no—
141#330—91no—
142#330—91no—
143#329—31no—
144C2×C3×Q8—21no—
145C2×C3×Q8—61no—
146C2×C3×Q8D1211yescharacteristic
147C2×C3×Q8#6711yescharacteristic
148C2×C3×D4—21no—
149C2×C3×D4D1211yescharacteristic
150C2×C3×D4#6711yescharacteristic
151C22×Dic3—62no—
152C22×Dic3—61no—
153C22×Dic3—61no—
154C2×Dic6—21no—
155C2×Dic6—62no—
156C2×Dic6—61no—
157C2×Dic6—61no—
158C2×C3×C8—61no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C22⋊C4—22no—
164C3×C22⋊C4—22no—
165C3×C22⋊C4—21no—
166C3×C22⋊C4—21no—
167C3×C22⋊C4—21no—
168C3×C22⋊C4—21no—
169C3×C42—21no—
170C3×C42C22×D311yescharacteristic
171C3×C42C22×D311yescharacteristic
172#217—62no—
173#217—62no—
174#217—61no—
175#217—61no—
176#217—61no—
177#217—61no—
178#217—62no—
179#217—61no—
180#217—61no—
181C4⋊Dic3—21no—
182C4⋊Dic3—21no—
183C4⋊Dic3—31no—
184C4⋊Dic3—31no—
185C4⋊Dic3—31no—
186C4⋊Dic3—31no—
187C4⋊Dic3—31no—
188C4⋊Dic3—31no—
189C4⋊Dic3—31no—
190C4⋊Dic3—31no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195Dic3⋊C4—62no—
196Dic3⋊C4—62no—
197Dic3⋊C4—62no—
198Dic3⋊C4—62no—
199Dic3⋊C4—62no—
200Dic3⋊C4—62no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213C4×Dic3—62no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32—41no—
222C22×C32#12011yescharacteristic
223C32×C4—21no—
224C32×C4—21no—
225C32×C4—21no—
226C32×C4—41no—
227C3⋊Dic3—41no—
228C3⋊Dic3—41no—
229C3⋊Dic3—41no—
230C3⋊Dic3—41no—
231C3×Dic3—81no—
232C4⋊Q8—31no—
233C4⋊Q8—181no—
234#126—181no—
235#126—181no—
236#125—91no—
237#125—91no—
238#124D3211yescharacteristic
239#123—181no—
240C22⋊Q8—181no—
241C22⋊Q8—181no—
242#107—181no—
243#106—181no—
244#103—61no—
245#103—181no—
246#103—181no—
247#102—61no—
248#97—31no—
249#97—31no—
250#97—31no—
251C23×C3—22no—
252C23×C3—21no—
253C23×C3—21no—
254C3×Q8—41no—
255C3×Q8—41no—
256C3×Q8—81no—
257C3×Q8—122no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—81no—
261C2×C3×C4—22no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—121no—
268C2×C3×C4C2×D1211yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274C2×Dic3—41no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—242no—
288C2×Dic3—241no—
289C2×Dic3—241no—
290Dic6—42no—
291Dic6—242no—
292Dic6—241no—
293Dic6—241no—
294C3×C8—62no—
295C3×C8—121no—
296C3×C8—121no—
297C3⋊C8—22no—
298C3⋊C8—41no—
299C3⋊C8—41no—
300C2×C32—81no—
301C2×C32#45411yescharacteristic
302C2×C32#45511yescharacteristic
303C2×C32#45611yescharacteristic
304C2×Q8—61no—
305C2×Q8—181no—
306C2×Q8#62611yescharacteristic
307C2×D4#62611yescharacteristic
308C22×C4—181no—
309C2×C8—61no—
310C2×C8—61no—
311C2×C8—61no—
312C4⋊C4—61no—
313C4⋊C4—61no—
314C4⋊C4—91no—
315C4⋊C4—91no—
316C4⋊C4—91no—
317C4⋊C4—91no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—181no—
327C22⋊C4—181no—
328C22⋊C4—181no—
329C42—181no—
330C42C2×D3211yescharacteristic
331C22×C3—21no—
332C22×C3—42no—
333C22×C3—42no—
334C22×C3—42no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3#88211yescharacteristic
342C22×C3#93711yescharacteristic
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—41no—
352C3×C4—42no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—241no—
356Dic3—81no—
357Dic3—122no—
358Dic3—122no—
359Dic3—122no—
360Dic3—122no—
361Dic3—121no—
362Dic3—121no—
363Dic3—121no—
364Dic3—121no—
365Dic3—121no—
366Dic3—121no—
367Dic3—121no—
368Dic3—121no—
369C32#166411yescharacteristic, complemented, Sylow
370C23—21no—
371Q8—41no—
372Q8—122no—
373Q8—721no—
374D4—41no—
375C2×C4—21no—
376C2×C4—121no—
377C2×C4—181no—
378C2×C4—181no—
379C2×C4—181no—
380C2×C4—181no—
381C2×C4—721no—
382C2×C4C2×#62611yescharacteristic
383C2×C4#381111yescharacteristic
384C2×C4#381111yescharacteristic
385C8—62no—
386C8—121no—
387C8—121no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—82no—
392C2×C3—81no—
393C2×C3—81no—
394C2×C3#474611yescharacteristic
395C2×C3#482611yescharacteristic
396C2×C3#482711yescharacteristic
397C2×C3#506111yescharacteristic
398C2×C3#520111yescharacteristic
399C2×C3#520511yescharacteristic
400C22—41no—
401C22—41no—
402C22—41no—
403C22#6398111yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—241no—
409C4—361no—
410C4—361no—
411C4—361no—
412C4—361no—
413C3—21no—
414C3#6835911yescharacteristic, complemented
415C3#7124711yescharacteristic, complemented
416C2—81no—
417C2#1059151411yescharacteristic
418C2#1059166811yescharacteristic
419C2#1059168611yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#124C22
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenter#124D32
hypocenterC32#1664
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
3. #10590305C2semidirect
4. #10590289C2semidirect
6. #10589089C2semidirect
7. #10589089C2semidirect
369. C32#1664semidirect
414. C3#68359semidirect
415. C3#71247semidirect

Maximal subgroups

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

subgroupindex
#105961432
C3×#50552
#105903052
#105902892
C3×#45402
#105890892
#712473
#683593