Finite Group Databasebeta

← #11792352

Subgroups — #11792352

Order 1152.

1044 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 1044 conjugacy classes of subgroups — too many to draw. Only its 179 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
1C32×#536C211yesmaximal, characteristic, complemented
2#10596293C211yesmaximal, characteristic
3C2×#64151C211yesmaximal, characteristic, complemented
4#10592935C211yesmaximal, characteristic, complemented
5#10592924C211yesmaximal, characteristic, complemented
6#10592705C211yesmaximal, characteristic, complemented
7#10589399C211yesmaximal, characteristic, complemented
8#71869—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C22×C32×Q8C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C32×C4⋊Q8—21no—
13C32×#124—21no—
14C32×#123—22no—
15C32×C22⋊Q8—22no—
16C32×#117C2211yescharacteristic
17#64160—21no—
18#64159—22no—
19#64158—21no—
20C2×#3756—21no—
21#64151—22no—
22#64151—21no—
23#64151—22no—
24C2×#3755—21no—
25#64141—21no—
26#64135C2211yescharacteristic
27C2×#3748C2211yescharacteristic
28C2×#3748C2211yescharacteristic
29#63664—22no—
30#63662—22no—
31#63633—22no—
32C3×#536D314yescomplemented
33#5822—34no—
34C2×#942—34no—
35#5236—34no—
36#5225—34no—
37#5006—34no—
38#4533—34no—
39C32×#41—21no—
40C32×#41—21no—
41C32×#41—21no—
42C32×#41—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8D412yes—
49C2×C32×Q8D411yescharacteristic
50C2×C32×D4—21no—
51C2×C32×D4D411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×#638—21no—
56#3828—21no—
57#3828—21no—
58#3828—21no—
59#3828—21no—
60C2×C4⋊(C3⋊D3)D411yescharacteristic
61C2×C4×C3⋊D3—21no—
62C2×#634D411yescharacteristic
63C32×C4⋊C4—24no—
64C32×C4⋊C4—21no—
65C32×C22⋊C4—24no—
66C32×C22⋊C4D412yes—
67C32×C42—21no—
68#3757—21no—
69#3756—24no—
70#3756—22no—
71#3755—24no—
72#3755—22no—
73#3754—22no—
74#3753—22no—
75C4⋊(C3⋊Dic3)—21no—
76C4×C3⋊Dic3—21no—
77#3748—21no—
78#3748—21no—
79#3748—21no—
80#3748D412yes—
81C2×C3⋊(C3⋊C8)—21no—
82C2×C3⋊(C3⋊C8)D412yes—
83#2009—91noSylow
84C2×C3×#41C2×D314yes—
85C22×C3×Q8C2×D314yes—
86C2×#235—34no—
87C3×C4⋊Q8—24no—
88C3×#124—24no—
89C3×#123—28no—
90C3×C22⋊Q8—28no—
91C3×#117C2×D314yes—
92#951—64no—
93#950—68no—
94#949—64no—
95C2×#216—64no—
96#942—68no—
97#942—68no—
98#942—64no—
99C2×#215—64no—
100#932—64no—
101#926—34no—
102C2×#208—34no—
103C2×#208—34no—
104#837—68no—
105#835—68no—
106#806—68no—
107C23×C32—21no—
108C23×C32C2×D411yescharacteristic
109C22×C3⋊D3—21no—
110C32×Q8—22no—
111C32×Q8—21no—
112C32×Q8—22no—
113C32×Q8—21no—
114C32×Q8—41no—
115C32×Q8—41no—
116C32×D4—21no—
117C32×D4—21no—
118C32×D4—41no—
119C32×D4—41no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—21no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133#638—41no—
134#638—41no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—41no—
137C4⋊(C3⋊D3)—21no—
138C4⋊(C3⋊D3)—21no—
139C4×C3⋊D3—41no—
140C4×C3⋊D3—41no—
141#634—21no—
142#634—21no—
143C3⋊(C3⋊C8)—22no—
144C3⋊(C3⋊C8)—22no—
145#575—91no—
146C2×#137—91no—
147#536C3⋊D311yescharacteristic, complemented
148#421—91no—
149#419—91no—
150#410—91no—
151#344—91no—
152C3×#41—24no—
153C3×#41—24no—
154C3×#41—24no—
155C3×#41—24no—
156C2×C3×Q8—24no—
157C2×C3×Q8—24no—
158C2×C3×Q8—24no—
159C2×C3×Q8—24no—
160C2×C3×Q8—24no—
161C2×C3×Q8#6718yes—
162C2×C3×Q8#6714yes—
163C2×C3×D4—24no—
164C2×C3×D4#6714yes—
165C22×C3×C4—24no—
166C22×C3×C4—24no—
167C22×C3×C4C22×D314yes—
168C2×#67—64no—
169#235—64no—
170#235—64no—
171#235—64no—
172#235—64no—
173C2×D12—34no—
174C2×C4×D3—64no—
175C2×Dic6—34no—
176C3×C4⋊C4—216no—
177C3×C4⋊C4—24no—
178C3×C22⋊C4—216no—
179C3×C22⋊C4#6718yes—
180C3×C42—24no—
181#217—64no—
182#216—616no—
183#216—68no—
184#215—616no—
185#215—68no—
186#214—68no—
187#213—68no—
188C4⋊Dic3—64no—
189C4×Dic3—64no—
190#208—38no—
191#208—64no—
192#208—64no—
193#208—64no—
194C2×C3⋊C8—38no—
195C2×C3⋊C8—64no—
196C22×C32—41no—
197C22×C32—42no—
198C22×C32—41no—
199C22×C32#12011yescharacteristic
200C22×C32#12111yescharacteristic
201C22×C32#12711yescharacteristic
202C2×C3⋊D3—41no—
203C2×C3⋊D3—81no—
204C32×C4—42no—
205C32×C4—41no—
206C32×C4—42no—
207C32×C4#12011yescharacteristic
208C32×C4#12011yescharacteristic
209C32×C4#12111yescharacteristic
210C32×C4#12111yescharacteristic
211C3⋊Dic3—41no—
212C3⋊Dic3—81no—
213C2×#41—91no—
214C2×#41C2×C3⋊D311yescharacteristic
215C22×Q8C2×C3⋊D311yescharacteristic
216#137—182no—
217#137—181no—
218#137—182no—
219#137—181no—
220AGL(1,ℤ/8)—181no—
221AGL(1,ℤ/8)—181no—
222#135—182no—
223C2×Q16—181no—
224C2×SD16—181no—
225C2×M16—91no—
226C2×M16—91no—
227C4⋊Q8—21no—
228#124—21no—
229#123—22no—
230C22⋊Q8—22no—
231#117—91no—
232#117C2×C3⋊D311yescharacteristic
233#104—182no—
234#103—182no—
235#99—182no—
236C23×C3—24no—
237C23×C3C2×#6714yes—
238C22×D3—64no—
239C3×Q8—28no—
240C3×Q8—24no—
241C3×Q8—28no—
242C3×Q8—24no—
243C3×Q8—44no—
244C3×Q8—44no—
245C3×D4—24no—
246C3×D4—24no—
247C3×D4—44no—
248C3×D4—44no—
249C2×C3×C4—28no—
250C2×C3×C4—28no—
251C2×C3×C4—24no—
252C2×C3×C4—44no—
253C2×C3×C4—44no—
254C2×C3×C4—44no—
255C2×C3×C4—44no—
256C2×C3×C4D3×D414yes—
257C2×C3×C4D3×D414yes—
258C2×C3×C4D3×D414yes—
259C2×C3×C4#23714yes—
260C2×C3×C4C2×#6714yes—
261C2×C3×C4C2×#6714yes—
262#67—124no—
263#67—124no—
264C2×Dic3—64no—
265C2×Dic3—124no—
266D12—64no—
267D12—64no—
268C4×D3—124no—
269C4×D3—124no—
270Dic6—64no—
271Dic6—64no—
272C3⋊C8—68no—
273C3⋊C8—68no—
274C2×C32—21no—
275C2×C32—21no—
276C2×C32—21no—
277C2×C32—81no—
278C2×C32#39211yescharacteristic
279C3⋊D3—81no—
280#41—21no—
281#41—21no—
282#41—21no—
283#41—21no—
284#41—181no—
285#41—181no—
286#41—181no—
287#41—181no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—91no—
294C2×Q8#63812yes—
295C2×Q8#63811yescharacteristic
296C2×D4—21no—
297C2×D4—91no—
298C2×D4—181no—
299C2×D4#63811yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—181no—
303C22×C4C22×C3⋊D311yescharacteristic
304Q16—184no—
305Q16—182no—
306SD16—182no—
307SD16—184no—
308SD16—182no—
309D8—182no—
310M16—92no—
311M16—181no—
312M16—181no—
313M16—181no—
314C2×C8—92no—
315C2×C8—181no—
316C4⋊C4—24no—
317C4⋊C4—21no—
318C4⋊C4—181no—
319C22⋊C4—24no—
320C22⋊C4—181no—
321C22⋊C4#63812yes—
322C42—21no—
323C42—181no—
324C22×C3—44no—
325C22×C3—48no—
326C22×C3—44no—
327C22×C3#93814yes—
328C22×C3#94014yes—
329C22×C3#95314yes—
330C2×D3—124no—
331C2×D3—244no—
332C3×C4—48no—
333C3×C4—44no—
334C3×C4—48no—
335C3×C4#93714yes—
336C3×C4#93714yes—
337C3×C4#93914yes—
338C3×C4#93914yes—
339Dic3—124no—
340Dic3—244no—
341C32#200911yescharacteristic, complemented, Sylow
342C23—21no—
343C23—181no—
344C23C2×#63811yescharacteristic
345Q8—22no—
346Q8—21no—
347Q8—22no—
348Q8—21no—
349Q8—41no—
350Q8—41no—
351Q8—181no—
352Q8—181no—
353D4—21no—
354D4—21no—
355D4—41no—
356D4—41no—
357D4—181no—
358D4—181no—
359D4—361no—
360D4—361no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—181no—
369C2×C4—361no—
370C2×C4—361no—
371C2×C4—361no—
372C2×C4D4×C3⋊D311yescharacteristic
373C2×C4D4×C3⋊D311yescharacteristic
374C2×C4D4×C3⋊D311yescharacteristic
375C2×C4#383011yescharacteristic
376C2×C4C2×#63811yescharacteristic
377C2×C4C2×#63811yescharacteristic
378C8—182no—
379C8—182no—
380C2×C3—24no—
381C2×C3—24no—
382C2×C3—24no—
383C2×C3—84no—
384C2×C3#522314yes—
385D3—244no—
386C22—41no—
387C22—42no—
388C22—41no—
389C22—361no—
390C22—721no—
391C22#6414711yescharacteristic
392C22#6414911yescharacteristic
393C22#6416211yescharacteristic
394C4—42no—
395C4—41no—
396C4—42no—
397C4—361no—
398C4—721no—
399C4#6414611yescharacteristic
400C4#6414611yescharacteristic
401C4#6414811yescharacteristic
402C4#6414811yescharacteristic
403C3#7186914yescomplemented
404C2—21no—
405C2—21no—
406C2—21no—
407C2—81no—
408C2—721no—
409C2#1059292211yescharacteristic
subgroupG/H
centerC2#10592922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#536C2
socleC2×C32#392
prime radical#10596293C2
hypercenter#536C3⋊D3
hypocenterC32#2009
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C32×#536C2semidirect
3. C2×#64151C2semidirect
4. #10592935C2semidirect
5. #10592924C2semidirect
6. #10592705C2semidirect
7. #10589399C2semidirect
32. C3×#536D3semidirect
147. #536C3⋊D3semidirect
341. C32#2009semidirect
403. C3#71869semidirect

Maximal subgroups

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

subgroupindex
C32×#5362
#105962932
C2×#641512
#105929352
#105929242
#105927052
#105893992
#718693