Finite Group Databasebeta

← #11780614

Subgroups — #11780614

Order 1152.

437 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 437 conjugacy classes of subgroups — too many to draw. Only its 70 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#10593952C211yesmaximal, characteristic
2#10592401C211yesmaximal, characteristic, complemented
3#10590372C211yesmaximal, characteristic
4#10590306C211yesmaximal, characteristic, complemented
5C3×#4465C211yesmaximal, characteristic, complemented
6C3×#4464C211yesmaximal, characteristic
7#10589089C211yesmaximal, characteristic, complemented
8#68372—31nomaximal
9#68355—31nomaximal
10#64079C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#875C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63899—21no—
15#63893—21no—
16#63884—21no—
17#63861—21no—
18#63858—21no—
19#63839—21no—
20C2×#3719—21no—
21C2×#3716—21no—
22C32×#97C2211yescharacteristic
23#63645—21no—
24#63644—21no—
25C3×#803C2211yescharacteristic
26C3×#803C2211yescharacteristic
27#63575—21no—
28#63573—21no—
29#5699—31no—
30#5672—31no—
31#5064—31no—
32#5060—31no—
33#4715—31no—
34#4702—31no—
35#4702—31no—
36#4702—31no—
37#4702—61no—
38C3×#330—31no—
39C3×#329—31no—
40#4465—31no—
41#4465—31no—
42#4465D311yescharacteristic, complemented
43#4464D311yescharacteristic
44C2×#634—21no—
45C2×C3×D12D411yescharacteristic
46C2×C3×Dic6D411yescharacteristic
47C2×#627—21no—
48C2×D3×Dic3—21no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)D411yescharacteristic
54C4⋊(C3⋊Dic3)D411yescharacteristic
55#3750—21no—
56#3750—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
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#3719—42no—
72#3716—42no—
73#1660—91noSylow
74C3×#125—31no—
75C3×#124—31no—
76#944—61no—
77C2×#216—61no—
78#935—61no—
79C2×#214—61no—
80C2×Dic12—61no—
81C2×#204—61no—
82#898—61no—
83#898—61no—
84#897—61no—
85#896—61no—
86#894—61no—
87#888—61no—
88#879—61no—
89#879—61no—
90#878—61no—
91#878—61no—
92#875C2×D311yescharacteristic
93#870—31no—
94#870—31no—
95#870—61no—
96#870C2×D311yescharacteristic
97#869—31no—
98#869—31no—
99#869—61no—
100C3×#97—21no—
101C3×#97—31no—
102C3×#97—31no—
103C3×#97C2×D311yescharacteristic
104C3×#97C2×D311yescharacteristic
105#818—61no—
106#818—61no—
107#818—62no—
108#818—61no—
109#817—61no—
110#817—61no—
111#817—62no—
112#817—61no—
113#808—61no—
114#807—61no—
115#803C2×D311yescharacteristic
116#803C2×D311yescharacteristic
117C22×C3×D3—21no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—41no—
124#634—41no—
125#634—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C3×D12—41no—
130C3×Dic6—41no—
131#627—81no—
132D3×Dic3—81no—
133C32×C8—22no—
134C3×C3⋊C8—22no—
135C3×C3⋊C8—22no—
136#563—91no—
137#501—91no—
138#501—91no—
139#497—91no—
140#330—31no—
141#330—91no—
142#329—31no—
143C2×C3×Q8—31no—
144C2×C3×D4—31no—
145C22×Dic3—61no—
146C2×D12D1211yescharacteristic
147C2×C4×D3—61no—
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×Dic6—61no—
151C2×Dic6—61no—
152C2×Dic6—121no—
153C2×Dic6D1211yescharacteristic
154C2×C3×C8—22no—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8—61no—
158C2×C3×C8—61no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C22⋊C4—61no—
164C3×C22⋊C4—61no—
165C3×C42—21no—
166C3×C42C22×D311yescharacteristic
167C3×C42C22×D311yescharacteristic
168#217—61no—
169#217—61no—
170#217—61no—
171#216—122no—
172#214—122no—
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—
185C4⋊Dic3—62no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—121no—
191C4⋊Dic3D1211yescharacteristic
192C4⋊Dic3D1211yescharacteristic
193Dic3⋊C4—21no—
194Dic3⋊C4—21no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—121no—
203Dic3⋊C4—121no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—21no—
208Dic12—122no—
209#204—122no—
210C22×C32#12011yescharacteristic
211C2×C3×D3—41no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C32×C4—21no—
215C32×C4—21no—
216C32×C4—21no—
217C3⋊Dic3—41no—
218C3⋊Dic3—41no—
219C3⋊Dic3—81no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—41no—
223C2×Q16—181no—
224C2×SD16—181no—
225C4⋊Q8—91no—
226C4⋊Q8—181no—
227#126—181no—
228#126—181no—
229#125—31no—
230#125—91no—
231#124—31no—
232#123—181no—
233C22⋊Q8—181no—
234C22⋊Q8—181no—
235#107—181no—
236#107—181no—
237#106—181no—
238#106—181no—
239#97—31no—
240#97—31no—
241#97D3211yescharacteristic
242C23×C3—61no—
243C22×D3—21no—
244C3×Q8—121no—
245C3×D4—121no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—61no—
250C2×C3×C4—61no—
251C2×C3×C4—61no—
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4C2×D1211yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—21no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—121no—
266C2×Dic3—121no—
267C2×Dic3—122no—
268C2×Dic3—121no—
269C2×Dic3—121no—
270C2×Dic3—241no—
271D12—41no—
272C4×D3—241no—
273Dic6—41no—
274Dic6—121no—
275Dic6—121no—
276Dic6—121no—
277Dic6—121no—
278Dic6—241no—
279Dic6—241no—
280Dic6—241no—
281Dic6—241no—
282C3×C8—24no—
283C3×C8—22no—
284C3×C8—22no—
285C3×C8—62no—
286C3×C8—62no—
287C3⋊C8—22no—
288C3⋊C8—22no—
289C2×C32#45311yescharacteristic
290C2×C32#45611yescharacteristic
291C2×C32#45611yescharacteristic
292C3×D3—81no—
293C2×Q8—31no—
294C2×Q8—181no—
295C2×Q8—181no—
296C2×D4—31no—
297C22×C4—181no—
298Q16—362no—
299SD16—362no—
300C2×C8—21no—
301C2×C8—61no—
302C2×C8—61no—
303C4⋊C4—31no—
304C4⋊C4—31no—
305C4⋊C4—61no—
306C4⋊C4—61no—
307C4⋊C4—91no—
308C4⋊C4—91no—
309C4⋊C4—181no—
310C4⋊C4—181no—
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—181no—
321C42C2×D3211yescharacteristic
322C22×C3—21no—
323C22×C3—121no—
324C22×C3—121no—
325C22×C3—121no—
326C22×C3#88211yescharacteristic
327C22×C3#88211yescharacteristic
328C2×D3—41no—
329C2×D3—41no—
330C2×D3—41no—
331C3×C4—22no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—41no—
339C3×C4—41no—
340C3×C4—121no—
341C3×C4—121no—
342C3×C4—121no—
343Dic3—41no—
344Dic3—41no—
345Dic3—41no—
346Dic3—121no—
347Dic3—121no—
348Dic3—121no—
349Dic3—121no—
350Dic3—241no—
351Dic3—241no—
352Dic3—242no—
353Dic3—241no—
354Dic3—241no—
355C32#166011yescharacteristic, complemented, Sylow
356C23—61no—
357Q8—121no—
358Q8—361no—
359Q8—361no—
360Q8—721no—
361D4—121no—
362C2×C4—61no—
363C2×C4—61no—
364C2×C4—61no—
365C2×C4—181no—
366C2×C4—181no—
367C2×C4—361no—
368C2×C4—721no—
369C2×C4D3×D1211yescharacteristic
370C2×C4D3×D1211yescharacteristic
371C2×C4#381111yescharacteristic
372C8—22no—
373C8—62no—
374C8—62no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—241no—
379C2×C3#474711yescharacteristic
380C2×C3#475211yescharacteristic
381C2×C3#482211yescharacteristic
382C2×C3#482611yescharacteristic
383C2×C3#482611yescharacteristic
384C2×C3#482611yescharacteristic
385D3—81no—
386C22—121no—
387C22—121no—
388C22—121no—
389C22#6392311yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—121no—
394C4—121no—
395C4—121no—
396C4—361no—
397C4—361no—
398C4—721no—
399C3—21no—
400C3#6835511yescharacteristic, complemented
401C3#6837211yescharacteristic, complemented
402C2—241no—
403C2#1059040111yescharacteristic
404C2#1059101511yescharacteristic
405C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenter#97D32
hypocenterC32#1660
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10592401C2semidirect
4. #10590306C2semidirect
5. C3×#4465C2semidirect
7. #10589089C2semidirect
42. #4465D3semidirect
355. C32#1660semidirect
400. C3#68355semidirect
401. C3#68372semidirect

Maximal subgroups

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

subgroupindex
#105939522
#105924012
#105903722
#105903062
C3×#44652
C3×#44642
#105890892
#683723
#683553