Finite Group Databasebeta

← #11780604

Subgroups — #11780604

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#10592780C211yesmaximal, characteristic, complemented
3C3×#5086C211yesmaximal, characteristic
4C3×#5081C211yesmaximal, characteristic, complemented
5#10589089C211yesmaximal, characteristic, complemented
6#10589088C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic
8#71391—31nomaximal
9#71330—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64079C2211yescharacteristic
12C2×C3×#216—21no—
13C2×C3×#215—21no—
14C3×#875C2211yescharacteristic
15C3×#870C2211yescharacteristic
16#63899—21no—
17#63893—21no—
18#63884—21no—
19#63861—21no—
20#63858—21no—
21#63839—21no—
22#63635—21no—
23#63634—21no—
24#63630C2211yescharacteristic
25C3×#808—21no—
26C3×#807—21no—
27C3×#803C2211yescharacteristic
28C3×#803C2211yescharacteristic
29#5699—31no—
30#5672—31no—
31C3×#501—31no—
32C3×#497—31no—
33#5086D311yescharacteristic
34#5081—31no—
35#5081—31no—
36#5081—61no—
37#5081D311yescharacteristic, complemented
38#4543—31no—
39#4540—31no—
40#4465—31no—
41#4465—31no—
42#4465—31no—
43#4464—31no—
44C2×C32×Q8—21no—
45C2×C3×D12D411yescharacteristic
46C2×C3×Dic6D411yescharacteristic
47C2×#627—21no—
48C2×D3×Dic3—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C42C2311yescharacteristic
52C4⋊(C3⋊Dic3)D411yescharacteristic
53C4⋊(C3⋊Dic3)D411yescharacteristic
54#3750—21no—
55#3750—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×#216—42no—
58C3×#215—42no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#3724—21no—
68Dic3⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72Dic32—21no—
73#1660—91noSylow
74C2×C3×Q16—61no—
75C2×C3×SD16—61no—
76C3×C4⋊Q8—21no—
77C3×C4⋊Q8C2×D311yescharacteristic
78C3×C4⋊Q8C2×D311yescharacteristic
79C3×#125—31no—
80C3×#124—31no—
81#944—61no—
82C2×#216—21no—
83C2×#215—21no—
84#935—61no—
85#898—61no—
86#898—61no—
87#897—61no—
88#896—61no—
89#894—61no—
90#888—61no—
91#879—61no—
92#879—61no—
93#878—61no—
94#878—61no—
95#875C2×D311yescharacteristic
96#870—31no—
97#870—31no—
98#870—61no—
99#870C2×D311yescharacteristic
100C3×#107—61no—
101C3×#106—61no—
102C3×#97—31no—
103C3×#97—31no—
104#808—21no—
105#808—61no—
106#808—61no—
107#808—62no—
108#807—21no—
109#807—61no—
110#807—61no—
111#807—62no—
112#803—31no—
113#803—31no—
114#803—61no—
115#803C2×D311yescharacteristic
116#803C2×D311yescharacteristic
117C22×C3×D3—21no—
118C32×Q8—41no—
119C32×Q8—41no—
120C2×C32×C4—41no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C3×D12—41no—
130C3×Dic6—41no—
131#627—81no—
132D3×Dic3—81no—
133C3⋊(C3⋊C8)—22no—
134C3×C3⋊C8—22no—
135C3×C3⋊C8—22no—
136#563—91no—
137#501—31no—
138#501—91no—
139#497—31no—
140#330—91no—
141#330—91no—
142#329—91no—
143C2×C3×Q8—21no—
144C2×C3×Q8—21no—
145C2×C3×Q8—31no—
146C2×C3×Q8—41no—
147C2×C3×D4—31no—
148C22×Dic3—61no—
149C2×D12#6711yescharacteristic
150C2×C4×D3—61no—
151C2×Dic6—61no—
152C2×Dic6—61no—
153C2×Dic6#6711yescharacteristic
154C3×Q16—122no—
155C3×SD16—122no—
156C2×C3×C8—61no—
157C2×C3×C8—61no—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—41no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C22⋊C4—61no—
169C3×C22⋊C4—61no—
170C3×C42—21no—
171C3×C42C22×D311yescharacteristic
172C3×C42C22×D311yescharacteristic
173#217—61no—
174#217—61no—
175#217—61no—
176#216—42no—
177#215—42no—
178(C2×D3)⋊C4—21no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183C4⋊Dic3—31no—
184C4⋊Dic3—31no—
185C4⋊Dic3—31no—
186C4⋊Dic3—31no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3#6711yescharacteristic
191C4⋊Dic3#6711yescharacteristic
192Dic3⋊C4—21no—
193Dic3⋊C4—21no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—121no—
202Dic3⋊C4—121no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—62no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C22×C32#12011yescharacteristic
211C2×C3×D3—41no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C32×C4—21no—
215C32×C4—21no—
216C32×C4—21no—
217C32×C4—81no—
218C3⋊Dic3—41no—
219C3⋊Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—41no—
223C2×Q16—61no—
224C2×SD16—61no—
225C4⋊Q8—181no—
226C4⋊Q8D3211yescharacteristic
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—61no—
236#107—181no—
237#106—61no—
238#106—181no—
239#97—31no—
240#97—31no—
241#97—91no—
242C23×C3—61no—
243C22×D3—21no—
244C3×Q8—41no—
245C3×Q8—41no—
246C3×Q8—41no—
247C3×Q8—41no—
248C3×Q8—81no—
249C3×Q8—81no—
250C3×Q8—121no—
251C3×D4—121no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—42no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266C2×C3×C4C2×#6711yescharacteristic
267C2×Dic3—21no—
268C2×Dic3—21no—
269C2×Dic3—21no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—121no—
275C2×Dic3—121no—
276C2×Dic3—241no—
277D12—41no—
278C4×D3—241no—
279Dic6—41no—
280Dic6—241no—
281Dic6—241no—
282C3×C8—62no—
283C3×C8—62no—
284C3⋊C8—22no—
285C3⋊C8—22no—
286C3⋊C8—64no—
287C3⋊C8—62no—
288C3⋊C8—62no—
289C2×C32#45311yescharacteristic
290C2×C32#45611yescharacteristic
291C2×C32#45611yescharacteristic
292C3×D3—81no—
293C2×Q8—21no—
294C2×Q8—31no—
295C2×Q8—181no—
296C2×D4—31no—
297C22×C4—181no—
298Q16—122no—
299SD16—122no—
300C2×C8—61no—
301C2×C8—61no—
302C2×C8—181no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—31no—
306C4⋊C4—31no—
307C4⋊C4—61no—
308C4⋊C4—61no—
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—181no—
321C42C2×D3211yescharacteristic
322C22×C3—21no—
323C22×C3—121no—
324C22×C3—121no—
325C22×C3—121no—
326C22×C3#93711yescharacteristic
327C22×C3#93711yescharacteristic
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—82no—
341C3×C4—81no—
342C3×C4—81no—
343C3×C4—121no—
344C3×C4—121no—
345C3×C4—121no—
346Dic3—41no—
347Dic3—41no—
348Dic3—41no—
349Dic3—121no—
350Dic3—121no—
351Dic3—121no—
352Dic3—121no—
353Dic3—241no—
354Dic3—241no—
355C32#166011yescharacteristic, complemented, Sylow
356C23—61no—
357Q8—41no—
358Q8—41no—
359Q8—121no—
360Q8—721no—
361D4—121no—
362C2×C4—41no—
363C2×C4—61no—
364C2×C4—61no—
365C2×C4—61no—
366C2×C4—181no—
367C2×C4—181no—
368C2×C4—721no—
369C2×C4D3×#6711yescharacteristic
370C2×C4D3×#6711yescharacteristic
371C2×C4#381111yescharacteristic
372C8—62no—
373C8—62no—
374C8—182no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—241no—
379C2×C3#507711yescharacteristic
380C2×C3#509511yescharacteristic
381C2×C3#519811yescharacteristic
382C2×C3#520511yescharacteristic
383C2×C3#520511yescharacteristic
384C2×C3#520511yescharacteristic
385D3—81no—
386C22—121no—
387C22—121no—
388C22—121no—
389C22#6398311yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—81no—
394C4—121no—
395C4—121no—
396C4—121no—
397C4—361no—
398C4—361no—
399C3—21no—
400C3#7133011yescharacteristic, complemented
401C3#7139111yescharacteristic, complemented
402C2—241no—
403C2#1059152311yescharacteristic
404C2#1059166011yescharacteristic
405C2#1059166111yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4⋊Q8D32
hypocenterC32#1660
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10592780C2semidirect
4. C3×#5081C2semidirect
5. #10589089C2semidirect
6. #10589088C2semidirect
37. #5081D3semidirect
355. C32#1660semidirect
400. C3#71330semidirect
401. C3#71391semidirect

Maximal subgroups

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

subgroupindex
#105939522
#105927802
C3×#50862
C3×#50812
#105890892
#105890882
#105890862
#713913
#713303