Finite Group Databasebeta

← #11780643

Subgroups — #11780643

Order 1152.

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

normal subgroups only

This group has 466 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×#5086C211yesmaximal, characteristic, complemented
4C3×#5081C211yesmaximal, characteristic, complemented
5#10589088C211yesmaximal, characteristic, complemented
6#10589087C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#71392—31nomaximal
9#71331—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64084C2211yescharacteristic
12C2×C3×#216—21no—
13C2×C3×#215—21no—
14C3×#875C2211yescharacteristic
15C3×#870C2211yescharacteristic
16#63910—21no—
17#63896—21no—
18#63890—21no—
19#63888—21no—
20#63886—21no—
21#63854—21no—
22#63637—21no—
23#63636—21no—
24#63630C2211yescharacteristic
25C3×#808—21no—
26C3×#807—21no—
27C3×#803C2211yescharacteristic
28C3×#803C2211yescharacteristic
29#5700—31no—
30#5684—31no—
31C3×#501—31no—
32C3×#497—31no—
33#5089—31no—
34#5089—31no—
35#5089—61no—
36#5086D311yescharacteristic, complemented
37#5081D311yescharacteristic, 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×#216—42no—
60C3×#215—42no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×C4⋊Dic3D411yescharacteristic
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69#3724—21no—
70Dic3⋊Dic3—21no—
71#3722—21no—
72(C2×D3)⋊Dic3—21no—
73#1661—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#946—61no—
82C2×#216—21no—
83C2×#215—21no—
84#939—61no—
85#896—61no—
86#896—61no—
87#895—61no—
88#895—61no—
89#894—61no—
90#894—61no—
91#886—61no—
92#884—61no—
93#883—61no—
94#878—61no—
95#875—31no—
96#875—31no—
97#875—61no—
98#875C2×D311yescharacteristic
99#870C2×D311yescharacteristic
100C3×#107—61no—
101C3×#106—61no—
102C3×#97—31no—
103C3×#97—31no—
104#810—61no—
105#810—61no—
106#810—62no—
107#809—61no—
108#809—61no—
109#809—62no—
110#808—21no—
111#807—21no—
112#803—31no—
113#803—31no—
114#803—61no—
115#803C2×D311yescharacteristic
116#803C2×D311yescharacteristic
117C22×C3⋊D3—21no—
118C22×C3×D3—21no—
119C32×Q8—41no—
120C32×Q8—41no—
121C2×C32×C4—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C3⋊Dic3—21no—
126C4⋊(C3⋊D3)—41no—
127#634—41no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C3×D12—41no—
132C3×Dic6—41no—
133#626—81no—
134#626—81no—
135#624—81no—
136D3×Dic3—81no—
137C3⋊(C3⋊C8)—41no—
138C3×C3⋊C8—22no—
139C3×C3⋊C8—22no—
140#562—91no—
141#501—31no—
142#497—31no—
143#489—91no—
144#330—91no—
145#329—91no—
146#329—91no—
147C2×C3×Q8—21no—
148C2×C3×Q8—21no—
149C2×C3×Q8—31no—
150C2×C3×Q8—41no—
151C2×C3×D4—31no—
152C2×#67—61no—
153C2×#67—61no—
154C22×Dic3—61no—
155C2×D12—31no—
156C2×D12—31no—
157C2×D12—61no—
158C2×D12—61no—
159C2×D12—61no—
160C2×D12#6711yescharacteristic
161C2×C4×D3—61no—
162C2×C4×D3—61no—
163C2×C4×D3—61no—
164C2×Dic6—31no—
165C2×Dic6—31no—
166C2×Dic6—61no—
167C2×Dic6#6711yescharacteristic
168C3×Q16—122no—
169C3×SD16—122no—
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C3×C4⋊C4—22no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—31no—
178C3×C4⋊C4—31no—
179C3×C4⋊C4—41no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C22⋊C4—61no—
183C3×C22⋊C4—61no—
184C3×C42—21no—
185C3×C42C22×D311yescharacteristic
186C3×C42C22×D311yescharacteristic
187#217—61no—
188#216—42no—
189#215—42no—
190(C2×D3)⋊C4—21no—
191(C2×D3)⋊C4—21no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—61no—
198(C2×D3)⋊C4—61no—
199(C2×D3)⋊C4—121no—
200(C2×D3)⋊C4—121no—
201C4⋊Dic3—61no—
202C4⋊Dic3#6711yescharacteristic
203C4⋊Dic3#6711yescharacteristic
204Dic3⋊C4—21no—
205Dic3⋊C4—21no—
206Dic3⋊C4—61no—
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—62no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C22×C32#12011yescharacteristic
215C2×C3⋊D3—41no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3—41no—
218C2×C3×D3—41no—
219C2×C3×D3—41no—
220C2×C3×D3—41no—
221C32×C4—21no—
222C32×C4—21no—
223C32×C4—21no—
224C32×C4—81no—
225C3⋊Dic3—41no—
226C3×Dic3—41no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C2×Q16—61no—
230C2×SD16—61no—
231C4⋊Q8D3211yescharacteristic
232#125—31no—
233#124—31no—
234#124—91no—
235#123—181no—
236#123—181no—
237C22⋊Q8—181no—
238C22⋊Q8—181no—
239#121—181no—
240#121—181no—
241#107—61no—
242#106—61no—
243#103—181no—
244#102—181no—
245#97—31no—
246#97—31no—
247#97—91no—
248C23×C3—61no—
249C22×D3—21no—
250C22×D3—61no—
251C22×D3—61no—
252C22×D3—121no—
253C3×Q8—41no—
254C3×Q8—41no—
255C3×Q8—41no—
256C3×Q8—41no—
257C3×Q8—81no—
258C3×Q8—81no—
259C3×Q8—121no—
260C3×D4—121no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—42no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×C3×C4C2×#6711yescharacteristic
276#67—241no—
277#67—241no—
278C2×Dic3—21no—
279C2×Dic3—21no—
280C2×Dic3—21no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C2×Dic3—121no—
284C2×Dic3—241no—
285D12—41no—
286D12—121no—
287D12—121no—
288D12—122no—
289D12—241no—
290D12—241no—
291C4×D3—241no—
292C4×D3—241no—
293C4×D3—241no—
294Dic6—41no—
295Dic6—121no—
296Dic6—121no—
297Dic6—122no—
298C3×C8—62no—
299C3×C8—62no—
300C3⋊C8—22no—
301C3⋊C8—22no—
302C3⋊C8—122no—
303C3⋊C8—121no—
304C3⋊C8—121no—
305C2×C32#45311yescharacteristic
306C2×C32#45511yescharacteristic
307C2×C32#45611yescharacteristic
308C3⋊D3—81no—
309C3×D3—81no—
310C2×Q8—21no—
311C2×Q8—31no—
312C2×Q8—91no—
313C2×D4—31no—
314C2×D4—91no—
315C2×D4—181no—
316C2×D4—181no—
317C22×C4—181no—
318C22×C4—181no—
319Q16—122no—
320SD16—122no—
321C2×C8—61no—
322C2×C8—61no—
323C2×C8—181no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—31no—
327C4⋊C4—31no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C22⋊C4—61no—
333C22⋊C4—61no—
334C22⋊C4—181no—
335C22⋊C4—181no—
336C22⋊C4—181no—
337C22⋊C4—181no—
338C42C2×D3211yescharacteristic
339C22×C3—21no—
340C22×C3—121no—
341C22×C3—121no—
342C22×C3—121no—
343C22×C3#93711yescharacteristic
344C22×C3#93711yescharacteristic
345C2×D3—41no—
346C2×D3—41no—
347C2×D3—41no—
348C2×D3—121no—
349C2×D3—121no—
350C2×D3—121no—
351C2×D3—121no—
352C2×D3—121no—
353C2×D3—121no—
354C2×D3—241no—
355C2×D3—241no—
356C2×D3—241no—
357C3×C4—22no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—82no—
367C3×C4—81no—
368C3×C4—81no—
369C3×C4—121no—
370C3×C4—121no—
371C3×C4—121no—
372Dic3—41no—
373Dic3—41no—
374Dic3—41no—
375Dic3—121no—
376Dic3—121no—
377Dic3—241no—
378C32#166111yescharacteristic, complemented, Sylow
379C23—61no—
380C23—181no—
381Q8—41no—
382Q8—41no—
383Q8—121no—
384Q8—361no—
385D4—121no—
386D4—361no—
387D4—721no—
388D4—721no—
389C2×C4—41no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—181no—
394C2×C4—721no—
395C2×C4—721no—
396C2×C4D3×#6711yescharacteristic
397C2×C4D3×#6711yescharacteristic
398C2×C4#381111yescharacteristic
399C8—62no—
400C8—62no—
401C8—361no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—241no—
406C2×C3#507711yescharacteristic
407C2×C3#509511yescharacteristic
408C2×C3#519811yescharacteristic
409C2×C3#520211yescharacteristic
410C2×C3#520211yescharacteristic
411C2×C3#520511yescharacteristic
412D3—81no—
413D3—241no—
414D3—241no—
415D3—481no—
416C22—121no—
417C22—121no—
418C22—121no—
419C22—361no—
420C22—361no—
421C22—361no—
422C22#6398311yescharacteristic
423C4—21no—
424C4—21no—
425C4—21no—
426C4—81no—
427C4—121no—
428C4—121no—
429C4—121no—
430C4—361no—
431C3—21no—
432C3#7133111yescharacteristic, complemented
433C3#7139211yescharacteristic, complemented
434C2—241no—
435C2—721no—
436C2#1059152311yescharacteristic
437C2#1059165811yescharacteristic
438C2#1059166111yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radical#10593953C2
hypercenterC4⋊Q8D32
hypocenterC32#1661
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×#5086C2semidirect
4. C3×#5081C2semidirect
5. #10589088C2semidirect
6. #10589087C2semidirect
7. #10589086C2semidirect
36. #5086D3semidirect
37. #5081D3semidirect
378. C32#1661semidirect
432. C3#71331semidirect
433. C3#71392semidirect

Maximal subgroups

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

subgroupindex
#105939532
#105927882
C3×#50862
C3×#50812
#105890882
#105890872
#105890862
#713923
#713313