Finite Group Databasebeta

← #11780751

Subgroups — #11780751

Order 1152.

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

normal subgroups only

This group has 413 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#10592781C211yesmaximal, characteristic, complemented
3C3×#5089C211yesmaximal, characteristic
4C3×#5081C211yesmaximal, characteristic, complemented
5#10589089C211yesmaximal, characteristic, complemented
6#10589088C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic
8#71394—31nomaximal
9#71247—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64079C2211yescharacteristic
12C3×#875C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63899—21no—
15#63893—21no—
16#63884—21no—
17#63861—21no—
18#63858—21no—
19#63839—21no—
20#63662—21no—
21#63662—21no—
22#63630C2211yescharacteristic
23C3×#810—21no—
24C3×#809—21no—
25C3×#808—21no—
26C3×#807—21no—
27C3×#803C2211yescharacteristic
28C3×#803C2211yescharacteristic
29#5699—31no—
30#5672—31no—
31C3×#501—31no—
32C3×#489—31no—
33#5089D311yescharacteristic
34#5082—31no—
35#5082—31no—
36#5082—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×(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#1664—91noSylow
72C3×C4⋊Q8—21no—
73C3×C4⋊Q8C2×D311yescharacteristic
74C3×C4⋊Q8C2×D311yescharacteristic
75C3×#125—31no—
76C3×#124—31no—
77#944—61no—
78#935—61no—
79#898—61no—
80#898—61no—
81#897—61no—
82#896—61no—
83#894—61no—
84#888—61no—
85#879—61no—
86#879—61no—
87#878—61no—
88#878—61no—
89#875C2×D311yescharacteristic
90#870—31no—
91#870—31no—
92#870—61no—
93#870C2×D311yescharacteristic
94C3×#107—61no—
95C3×#106—61no—
96C3×#103—61no—
97C3×#102—61no—
98C3×#97—31no—
99C3×#97—31no—
100#835—61no—
101#835—61no—
102#835—61no—
103#835—61no—
104#835—62no—
105#835—62no—
106#810—21no—
107#809—21no—
108#808—21no—
109#807—21no—
110#803—31no—
111#803—31no—
112#803—61no—
113#803C2×D311yescharacteristic
114#803C2×D311yescharacteristic
115C22×C3×D3—21no—
116C32×Q8—42no—
117C2×C32×C4—41no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C3×D12—41no—
127C3×Dic6—41no—
128#627—81no—
129D3×Dic3—81no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—41no—
133#563—91no—
134#501—31no—
135#491—91no—
136#489—31no—
137#330—91no—
138#330—91no—
139#329—91no—
140C2×C3×Q8—22no—
141C2×C3×Q8—21no—
142C2×C3×Q8—21no—
143C2×C3×Q8—31no—
144C2×C3×D4—31no—
145C22×Dic3—61no—
146C2×D12#6711yescharacteristic
147C2×C4×D3—61no—
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×Dic6#6711yescharacteristic
151C2×C3×C8—61no—
152C2×C3×C8—61no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—41no—
160C3×C4⋊C4—41no—
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(C2×D3)⋊C4—21no—
172(C2×D3)⋊C4—21no—
173(C2×D3)⋊C4—61no—
174(C2×D3)⋊C4—61no—
175(C2×D3)⋊C4—61no—
176C4⋊Dic3—31no—
177C4⋊Dic3—31no—
178C4⋊Dic3—31no—
179C4⋊Dic3—31no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3#6711yescharacteristic
184C4⋊Dic3#6711yescharacteristic
185Dic3⋊C4—21no—
186Dic3⋊C4—21no—
187Dic3⋊C4—61no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—121no—
195Dic3⋊C4—121no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—62no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C22×C32#12011yescharacteristic
204C2×C3×D3—41no—
205C2×C3×D3—41no—
206C2×C3×D3—41no—
207C32×C4—21no—
208C32×C4—21no—
209C32×C4—21no—
210C32×C4—81no—
211C3⋊Dic3—41no—
212C3⋊Dic3—41no—
213C3×Dic3—41no—
214C3×Dic3—41no—
215C3×Dic3—41no—
216C4⋊Q8—181no—
217C4⋊Q8D3211yescharacteristic
218#126—181no—
219#126—181no—
220#125—31no—
221#125—91no—
222#124—31no—
223#123—181no—
224C22⋊Q8—181no—
225C22⋊Q8—181no—
226#107—61no—
227#106—61no—
228#103—61no—
229#103—181no—
230#103—181no—
231#102—61no—
232#97—31no—
233#97—31no—
234#97—91no—
235C23×C3—61no—
236C22×D3—21no—
237C3×Q8—44no—
238C3×Q8—42no—
239C3×Q8—42no—
240C3×Q8—121no—
241C3×D4—121no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—42no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—61no—
249C2×C3×C4—61no—
250C2×C3×C4—61no—
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—121no—
265C2×Dic3—121no—
266C2×Dic3—241no—
267D12—41no—
268C4×D3—241no—
269Dic6—41no—
270Dic6—241no—
271Dic6—241no—
272C3×C8—62no—
273C3×C8—121no—
274C3⋊C8—22no—
275C3⋊C8—41no—
276C3⋊C8—122no—
277C3⋊C8—121no—
278C3⋊C8—121no—
279C2×C32#45411yescharacteristic
280C2×C32#45511yescharacteristic
281C2×C32#45611yescharacteristic
282C3×D3—81no—
283C2×Q8—21no—
284C2×Q8—31no—
285C2×Q8—181no—
286C2×D4—31no—
287C22×C4—181no—
288C2×C8—61no—
289C2×C8—61no—
290C2×C8—181no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—31no—
294C4⋊C4—31no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C4⋊C4—91no—
298C4⋊C4—91no—
299C4⋊C4—181no—
300C4⋊C4—181no—
301C4⋊C4—181no—
302C4⋊C4—181no—
303C22⋊C4—61no—
304C22⋊C4—61no—
305C22⋊C4—181no—
306C22⋊C4—181no—
307C22⋊C4—181no—
308C42—181no—
309C42C2×D3211yescharacteristic
310C22×C3—21no—
311C22×C3—121no—
312C22×C3—121no—
313C22×C3—121no—
314C22×C3#93711yescharacteristic
315C22×C3#93711yescharacteristic
316C2×D3—41no—
317C2×D3—41no—
318C2×D3—41no—
319C3×C4—22no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—41no—
327C3×C4—41no—
328C3×C4—82no—
329C3×C4—81no—
330C3×C4—81no—
331C3×C4—121no—
332C3×C4—121no—
333C3×C4—121no—
334Dic3—41no—
335Dic3—41no—
336Dic3—41no—
337Dic3—121no—
338Dic3—121no—
339Dic3—121no—
340Dic3—121no—
341Dic3—241no—
342Dic3—241no—
343C32#166411yescharacteristic, complemented, Sylow
344C23—61no—
345Q8—42no—
346Q8—121no—
347Q8—721no—
348D4—121no—
349C2×C4—41no—
350C2×C4—61no—
351C2×C4—61no—
352C2×C4—61no—
353C2×C4—181no—
354C2×C4—181no—
355C2×C4—721no—
356C2×C4D3×#6711yescharacteristic
357C2×C4D3×#6711yescharacteristic
358C2×C4#381111yescharacteristic
359C8—62no—
360C8—121no—
361C8—361no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—241no—
366C2×C3#506111yescharacteristic
367C2×C3#509511yescharacteristic
368C2×C3#520111yescharacteristic
369C2×C3#520111yescharacteristic
370C2×C3#520211yescharacteristic
371C2×C3#520511yescharacteristic
372D3—81no—
373C22—121no—
374C22—121no—
375C22—121no—
376C22#6398311yescharacteristic
377C4—21no—
378C4—21no—
379C4—21no—
380C4—81no—
381C4—121no—
382C4—121no—
383C4—121no—
384C4—361no—
385C4—361no—
386C3—21no—
387C3#7124711yescharacteristic, complemented
388C3#7139411yescharacteristic, complemented
389C2—241no—
390C2#1059152411yescharacteristic
391C2#1059165911yescharacteristic
392C2#1059166111yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4⋊Q8D32
hypocenterC32#1664
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. #10592781C2semidirect
4. C3×#5081C2semidirect
5. #10589089C2semidirect
6. #10589088C2semidirect
37. #5081D3semidirect
343. C32#1664semidirect
387. C3#71247semidirect
388. C3#71394semidirect

Maximal subgroups

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

subgroupindex
#105939522
#105927812
C3×#50892
C3×#50812
#105890892
#105890882
#105890862
#713943
#712473