Finite Group Databasebeta

← #11780641

Subgroups — #11780641

Order 1152.

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

normal subgroups only

This group has 478 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#10592785C211yesmaximal, characteristic, complemented
3C3×#5089C211yesmaximal, characteristic, complemented
4C3×#5081C211yesmaximal, characteristic, complemented
5#10589088C211yesmaximal, characteristic, complemented
6#10589087C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#71392—31nomaximal
9#71245—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3756—21no—
12C2×#3755—21no—
13#64084C2211yescharacteristic
14C3×#875C2211yescharacteristic
15C3×#870C2211yescharacteristic
16#63910—21no—
17#63896—21no—
18#63890—21no—
19#63888—21no—
20#63886—21no—
21#63854—21no—
22#63630C2211yescharacteristic
23C3×#810—21no—
24C3×#809—21no—
25C3×#808—21no—
26C3×#807—21no—
27C3×#803C2211yescharacteristic
28C3×#803C2211yescharacteristic
29#5700—31no—
30#5684—31no—
31C3×#501—31no—
32C3×#489—31no—
33#5089D311yescharacteristic, complemented
34#5086—31no—
35#5086—31no—
36#5086—61no—
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#3756—42no—
57#3755—42no—
58#3752—21no—
59#3752—21no—
60C2×C3⋊(C3⋊C8)—21no—
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
74C3×C4⋊Q8—21no—
75C3×C4⋊Q8C2×D311yescharacteristic
76C3×C4⋊Q8C2×D311yescharacteristic
77C3×#125—31no—
78C3×#124—31no—
79#946—61no—
80C2×#216—61no—
81C2×#216—61no—
82C2×#216—62no—
83C2×#215—61no—
84C2×#215—61no—
85C2×#215—62no—
86#939—61no—
87#896—61no—
88#896—61no—
89#895—61no—
90#895—61no—
91#894—61no—
92#894—61no—
93#886—61no—
94#884—61no—
95#883—61no—
96#878—61no—
97#875—31no—
98#875—31no—
99#875—61no—
100#875C2×D311yescharacteristic
101#870C2×D311yescharacteristic
102C3×#107—61no—
103C3×#106—61no—
104C3×#103—61no—
105C3×#102—61no—
106C3×#97—31no—
107C3×#97—31no—
108#810—21no—
109#809—21no—
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)—22no—
138C3×C3⋊C8—22no—
139C3×C3⋊C8—41no—
140#562—91no—
141#501—31no—
142#497—91no—
143#489—31no—
144#330—91no—
145#329—91no—
146#329—91no—
147C2×C3×Q8—22no—
148C2×C3×Q8—21no—
149C2×C3×Q8—21no—
150C2×C3×Q8—31no—
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
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—41no—
177C3×C4⋊C4—41no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C22⋊C4—61no—
181C3×C22⋊C4—61no—
182C3×C42—21no—
183C3×C42C22×D311yescharacteristic
184C3×C42C22×D311yescharacteristic
185#217—61no—
186#216—122no—
187#216—122no—
188#216—124no—
189#215—122no—
190#215—122no—
191#215—124no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—21no—
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—61no—
200(C2×D3)⋊C4—61no—
201(C2×D3)⋊C4—121no—
202(C2×D3)⋊C4—121no—
203C4⋊Dic3—61no—
204C4⋊Dic3#6711yescharacteristic
205C4⋊Dic3#6711yescharacteristic
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—62no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—61no—
216C22×C32#12011yescharacteristic
217C2×C3⋊D3—41no—
218C2×C3⋊D3—41no—
219C2×C3⋊D3—41no—
220C2×C3×D3—41no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C32×C4—21no—
224C32×C4—21no—
225C32×C4—21no—
226C32×C4—81no—
227C3⋊Dic3—41no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3—41no—
231C2×Q16—181no—
232C2×SD16—181no—
233C4⋊Q8D3211yescharacteristic
234#125—31no—
235#124—31no—
236#124—91no—
237#123—181no—
238#123—181no—
239C22⋊Q8—181no—
240C22⋊Q8—181no—
241#121—181no—
242#121—181no—
243#107—61no—
244#106—61no—
245#103—61no—
246#102—61no—
247#97—31no—
248#97—31no—
249#97—91no—
250C23×C3—61no—
251C22×D3—21no—
252C22×D3—61no—
253C22×D3—61no—
254C22×D3—121no—
255C3×Q8—42no—
256C3×Q8—41no—
257C3×Q8—41no—
258C3×Q8—42no—
259C3×Q8—41no—
260C3×Q8—41no—
261C3×Q8—121no—
262C3×D4—121no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—42no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278#67—241no—
279#67—241no—
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285C2×Dic3—121no—
286C2×Dic3—241no—
287D12—41no—
288D12—121no—
289D12—121no—
290D12—122no—
291D12—241no—
292D12—241no—
293C4×D3—241no—
294C4×D3—241no—
295C4×D3—241no—
296Dic6—41no—
297Dic6—121no—
298Dic6—121no—
299Dic6—122no—
300C3×C8—62no—
301C3×C8—121no—
302C3⋊C8—22no—
303C3⋊C8—41no—
304C3⋊C8—64no—
305C3⋊C8—62no—
306C3⋊C8—62no—
307C2×C32#45311yescharacteristic
308C2×C32#45511yescharacteristic
309C2×C32#45611yescharacteristic
310C3⋊D3—81no—
311C3×D3—81no—
312C2×Q8—21no—
313C2×Q8—31no—
314C2×Q8—91no—
315C2×D4—31no—
316C2×D4—91no—
317C2×D4—181no—
318C2×D4—181no—
319C22×C4—181no—
320C22×C4—181no—
321Q16—362no—
322SD16—362no—
323C2×C8—61no—
324C2×C8—61no—
325C2×C8—181no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—31no—
329C4⋊C4—31no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—181no—
333C4⋊C4—181no—
334C22⋊C4—61no—
335C22⋊C4—61no—
336C22⋊C4—181no—
337C22⋊C4—181no—
338C22⋊C4—181no—
339C22⋊C4—181no—
340C42C2×D3211yescharacteristic
341C22×C3—21no—
342C22×C3—121no—
343C22×C3—121no—
344C22×C3—121no—
345C22×C3#93711yescharacteristic
346C22×C3#93711yescharacteristic
347C2×D3—41no—
348C2×D3—41no—
349C2×D3—41no—
350C2×D3—121no—
351C2×D3—121no—
352C2×D3—121no—
353C2×D3—121no—
354C2×D3—121no—
355C2×D3—121no—
356C2×D3—241no—
357C2×D3—241no—
358C2×D3—241no—
359C3×C4—22no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—82no—
369C3×C4—81no—
370C3×C4—81no—
371C3×C4—121no—
372C3×C4—121no—
373C3×C4—121no—
374Dic3—41no—
375Dic3—41no—
376Dic3—41no—
377Dic3—121no—
378Dic3—121no—
379Dic3—241no—
380C32#166111yescharacteristic, complemented, Sylow
381C23—61no—
382C23—181no—
383Q8—41no—
384Q8—41no—
385Q8—121no—
386Q8—361no—
387D4—121no—
388D4—361no—
389D4—721no—
390D4—721no—
391C2×C4—41no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—181no—
396C2×C4—721no—
397C2×C4—721no—
398C2×C4D3×#6711yescharacteristic
399C2×C4D3×#6711yescharacteristic
400C2×C4#381111yescharacteristic
401C8—62no—
402C8—121no—
403C8—182no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—241no—
408C2×C3#506111yescharacteristic
409C2×C3#509511yescharacteristic
410C2×C3#519811yescharacteristic
411C2×C3#519811yescharacteristic
412C2×C3#520211yescharacteristic
413C2×C3#520511yescharacteristic
414D3—81no—
415D3—241no—
416D3—241no—
417D3—481no—
418C22—121no—
419C22—121no—
420C22—121no—
421C22—361no—
422C22—361no—
423C22—361no—
424C22#6398311yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—81no—
429C4—121no—
430C4—121no—
431C4—121no—
432C4—361no—
433C3—21no—
434C3#7124511yescharacteristic, complemented
435C3#7139211yescharacteristic, complemented
436C2—241no—
437C2—721no—
438C2#1059152211yescharacteristic
439C2#1059165911yescharacteristic
440C2#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. #10592785C2semidirect
3. C3×#5089C2semidirect
4. C3×#5081C2semidirect
5. #10589088C2semidirect
6. #10589087C2semidirect
7. #10589086C2semidirect
33. #5089D3semidirect
37. #5081D3semidirect
380. C32#1661semidirect
434. C3#71245semidirect
435. C3#71392semidirect

Maximal subgroups

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

subgroupindex
#105939532
#105927852
C3×#50892
C3×#50812
#105890882
#105890872
#105890862
#713923
#712453