Finite Group Databasebeta

← #11780684

Subgroups — #11780684

Order 1152.

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

normal subgroups only

This group has 442 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#10593953C211yesmaximal, characteristic
2#10592788C211yesmaximal, characteristic, complemented
3C3×#5089C211yesmaximal, characteristic, complemented
4C3×#5082C211yesmaximal, characteristic, complemented
5#10589088C211yesmaximal, characteristic, complemented
6#10589087C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#71251—31nomaximal
9#71246—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64084C2211yescharacteristic
12C3×#875C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63910—21no—
15#63896—21no—
16#63890—21no—
17#63888—21no—
18#63886—21no—
19#63854—21no—
20#63637—21no—
21#63636—21no—
22#63630C2211yescharacteristic
23C3×#835—21no—
24C3×#835—21no—
25C3×#810—21no—
26C3×#809—21no—
27C3×#803C2211yescharacteristic
28C3×#803C2211yescharacteristic
29#5700—31no—
30#5684—31no—
31C3×#491—31no—
32C3×#489—31no—
33#5089—31no—
34#5089—31no—
35#5089—61no—
36#5089D311yescharacteristic, complemented
37#5082D311yescharacteristic, complemented
38#4543—31no—
39#4540—31no—
40#4465—31no—
41#4464—31no—
42#4464—31no—
43#4464—31no—
44C2×C32×Q8—21no—
45C2×C4⋊(C3⋊D3)D411yescharacteristic
46C2×#634D411yescharacteristic
47C2×C3×D12D411yescharacteristic
48C2×C3×Dic6D411yescharacteristic
49C2×#626—21no—
50C2×#626—21no—
51C2×#624—21no—
52C2×D3×Dic3—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C42C2311yescharacteristic
56#3752—21no—
57#3752—21no—
58C2×C3⋊(C3⋊C8)—21no—
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#3722—21no—
70(C2×D3)⋊Dic3—21no—
71#1662—91noSylow
72C3×C4⋊Q8—21no—
73C3×C4⋊Q8C2×D311yescharacteristic
74C3×C4⋊Q8C2×D311yescharacteristic
75C3×#125—31no—
76C3×#124—31no—
77#946—61no—
78#939—61no—
79#896—61no—
80#896—61no—
81#895—61no—
82#895—61no—
83#894—61no—
84#894—61no—
85#886—61no—
86#884—61no—
87#883—61no—
88#878—61no—
89#875—31no—
90#875—31no—
91#875—61no—
92#875C2×D311yescharacteristic
93#870C2×D311yescharacteristic
94C3×#103—61no—
95C3×#103—61no—
96C3×#103—61no—
97C3×#102—61no—
98C3×#97—31no—
99C3×#97—31no—
100#835—21no—
101#835—21no—
102#810—21no—
103#810—61no—
104#810—61no—
105#810—62no—
106#809—21no—
107#809—61no—
108#809—61no—
109#809—62no—
110#803—31no—
111#803—31no—
112#803—61no—
113#803C2×D311yescharacteristic
114#803C2×D311yescharacteristic
115C22×C3⋊D3—21no—
116C22×C3×D3—21no—
117C32×Q8—42no—
118C2×C32×C4—41no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3⋊Dic3—21no—
123C4⋊(C3⋊D3)—41no—
124#634—41no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C3×D12—41no—
129C3×Dic6—41no—
130#626—81no—
131#626—81no—
132#624—81no—
133D3×Dic3—81no—
134C3⋊(C3⋊C8)—41no—
135C3×C3⋊C8—41no—
136C3×C3⋊C8—41no—
137#562—91no—
138#491—31no—
139#489—31no—
140#489—91no—
141#330—91no—
142#329—91no—
143#329—91no—
144C2×C3×Q8—21no—
145C2×C3×Q8—21no—
146C2×C3×Q8—31no—
147C2×C3×Q8—41no—
148C2×C3×D4—31no—
149C2×#67—61no—
150C2×#67—61no—
151C22×Dic3—61no—
152C2×D12—31no—
153C2×D12—31no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12#6711yescharacteristic
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×C4×D3—61no—
161C2×Dic6—31no—
162C2×Dic6—31no—
163C2×Dic6—61no—
164C2×Dic6#6711yescharacteristic
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—41no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C22⋊C4—61no—
178C3×C22⋊C4—61no—
179C3×C42—21no—
180C3×C42C22×D311yescharacteristic
181C3×C42C22×D311yescharacteristic
182#217—61no—
183(C2×D3)⋊C4—21no—
184(C2×D3)⋊C4—21no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—61no—
190(C2×D3)⋊C4—61no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—121no—
193(C2×D3)⋊C4—121no—
194C4⋊Dic3—61no—
195C4⋊Dic3#6711yescharacteristic
196C4⋊Dic3#6711yescharacteristic
197Dic3⋊C4—21no—
198Dic3⋊C4—21no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—62no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C22×C32#12011yescharacteristic
208C2×C3⋊D3—41no—
209C2×C3⋊D3—41no—
210C2×C3⋊D3—41no—
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—
222C4⋊Q8D3211yescharacteristic
223#125—31no—
224#124—31no—
225#124—91no—
226#123—181no—
227#123—181no—
228C22⋊Q8—181no—
229C22⋊Q8—181no—
230#121—181no—
231#121—181no—
232#103—61no—
233#103—61no—
234#103—61no—
235#103—181no—
236#102—61no—
237#102—181no—
238#97—31no—
239#97—31no—
240#97—91no—
241C23×C3—61no—
242C22×D3—21no—
243C22×D3—61no—
244C22×D3—61no—
245C22×D3—121no—
246C3×Q8—42no—
247C3×Q8—42no—
248C3×Q8—82no—
249C3×Q8—121no—
250C3×D4—121no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—42no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266#67—241no—
267#67—241no—
268C2×Dic3—21no—
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—61no—
272C2×Dic3—61no—
273C2×Dic3—121no—
274C2×Dic3—241no—
275D12—41no—
276D12—121no—
277D12—121no—
278D12—122no—
279D12—241no—
280D12—241no—
281C4×D3—241no—
282C4×D3—241no—
283C4×D3—241no—
284Dic6—41no—
285Dic6—121no—
286Dic6—121no—
287Dic6—122no—
288C3×C8—121no—
289C3×C8—121no—
290C3⋊C8—41no—
291C3⋊C8—41no—
292C3⋊C8—122no—
293C3⋊C8—121no—
294C3⋊C8—121no—
295C2×C32#45411yescharacteristic
296C2×C32#45511yescharacteristic
297C2×C32#45511yescharacteristic
298C3⋊D3—81no—
299C3×D3—81no—
300C2×Q8—21no—
301C2×Q8—31no—
302C2×Q8—91no—
303C2×D4—31no—
304C2×D4—91no—
305C2×D4—181no—
306C2×D4—181no—
307C22×C4—181no—
308C22×C4—181no—
309C2×C8—61no—
310C2×C8—61no—
311C2×C8—181no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—31no—
315C4⋊C4—31no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C22⋊C4—61no—
321C22⋊C4—61no—
322C22⋊C4—181no—
323C22⋊C4—181no—
324C22⋊C4—181no—
325C22⋊C4—181no—
326C42C2×D3211yescharacteristic
327C22×C3—21no—
328C22×C3—121no—
329C22×C3—121no—
330C22×C3—121no—
331C22×C3#93711yescharacteristic
332C22×C3#93711yescharacteristic
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—41no—
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—22no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—82no—
355C3×C4—81no—
356C3×C4—81no—
357C3×C4—121no—
358C3×C4—121no—
359C3×C4—121no—
360Dic3—41no—
361Dic3—41no—
362Dic3—41no—
363Dic3—121no—
364Dic3—121no—
365Dic3—241no—
366C32#166211yescharacteristic, complemented, Sylow
367C23—61no—
368C23—181no—
369Q8—42no—
370Q8—121no—
371Q8—361no—
372D4—121no—
373D4—361no—
374D4—721no—
375D4—721no—
376C2×C4—41no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—181no—
381C2×C4—721no—
382C2×C4—721no—
383C2×C4D3×#6711yescharacteristic
384C2×C4D3×#6711yescharacteristic
385C2×C4#381111yescharacteristic
386C8—121no—
387C8—121no—
388C8—361no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—241no—
393C2×C3#506111yescharacteristic
394C2×C3#506211yescharacteristic
395C2×C3#520111yescharacteristic
396C2×C3#520211yescharacteristic
397C2×C3#520211yescharacteristic
398C2×C3#520211yescharacteristic
399D3—81no—
400D3—241no—
401D3—241no—
402D3—481no—
403C22—121no—
404C22—121no—
405C22—121no—
406C22—361no—
407C22—361no—
408C22—361no—
409C22#6398311yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—81no—
414C4—121no—
415C4—121no—
416C4—121no—
417C4—361no—
418C3—21no—
419C3#7124611yescharacteristic, complemented
420C3#7125111yescharacteristic, complemented
421C2—241no—
422C2—721no—
423C2#1059152511yescharacteristic
424C2#1059165811yescharacteristic
425C2#1059165911yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radical#10593953C2
hypercenterC4⋊Q8D32
hypocenterC32#1662
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. #10592788C2semidirect
3. C3×#5089C2semidirect
4. C3×#5082C2semidirect
5. #10589088C2semidirect
6. #10589087C2semidirect
7. #10589086C2semidirect
36. #5089D3semidirect
37. #5082D3semidirect
366. C32#1662semidirect
419. C3#71246semidirect
420. C3#71251semidirect

Maximal subgroups

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

subgroupindex
#105939532
#105927882
C3×#50892
C3×#50822
#105890882
#105890872
#105890862
#712513
#712463