Finite Group Databasebeta

← #11779343

Subgroups — #11779343

Order 1152.

554 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 88 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#10596056C211yesmaximal, characteristic
2C3×#5021C211yesmaximal, characteristic, complemented
3#10590373C211yesmaximal, characteristic
4#10590284C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589091C211yesmaximal, characteristic
7#10589085C211yesmaximal, characteristic, complemented
8#71159—31nomaximal
9#68260—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11#64156—21no—
12#64103—22no—
13#64102—21no—
14#64084—21no—
15#64083C2211yescharacteristic
16C4×C4⋊(C3⋊D3)—21no—
17C4×#634C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×#3717—22no—
20C3×#835—21no—
21C3×#807—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63575—21no—
26#63567—21no—
27#5585—31no—
28#5585—31no—
29#5585—61no—
30C3×#477—31no—
31#5091—31no—
32#5085—31no—
33#5021D311yescharacteristic, complemented
34#4850—31no—
35#4693—31no—
36C3×Q8⋊C8—31no—
37#4535D311yescharacteristic, complemented
38#4485—31no—
39#4485—31no—
40#4484—31no—
41#4456—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)D412yes—
46C2×C4×C3⋊D3—22no—
47C2×#634D411yescharacteristic
48C2×C3×Dic6—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4D411yescharacteristic
51C32×C42—21no—
52C32×C42C2311yescharacteristic
53#3752—22no—
54#3752—22no—
55#3752—22no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3750—21no—
58C4×C3⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3717—44no—
65#1630—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×Q8—21no—
68C3×C4×Q8C2×D311yescharacteristic
69C3×C4×Q8C2×D311yescharacteristic
70#947—62no—
71#947—61no—
72#947—61no—
73C2×#215—62no—
74C2×#204—62no—
75#894—62no—
76#894—62no—
77#894—64no—
78#893—62no—
79#893—61no—
80#893—61no—
81#875—61no—
82#875—61no—
83#875—62no—
84#874—31no—
85#874—31no—
86#874—61no—
87C4×D12—61no—
88C4×D12—61no—
89C4×D12—62no—
90#869C2×D311yescharacteristic
91C4×Dic6—31no—
92C4×Dic6—31no—
93C4×Dic6—61no—
94C3×#107—61no—
95C3×C4⋊C8—31no—
96C3×C4⋊C8—31no—
97C3×#103—61no—
98C3×C4×C8—31no—
99#835—21no—
100#818—61no—
101#816—61no—
102#810—61no—
103#807—21no—
104#807—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4×C3⋊C8C2×D311yescharacteristic
108C22×C3⋊D3—22no—
109C32×Q8—21no—
110C32×Q8—21no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—21no—
118C4⋊(C3⋊D3)—41no—
119C4⋊(C3⋊D3)—41no—
120C4⋊(C3⋊D3)—41no—
121C4⋊(C3⋊D3)—41no—
122C4⋊(C3⋊D3)—42no—
123C4×C3⋊D3—82no—
124#634—21no—
125#634—21no—
126C2×C3×Dic3—41no—
127C3×Dic6—42no—
128C3×C3⋊C8—22no—
129C3×C3⋊C8—41no—
130C3×C3⋊C8—41no—
131#559—91no—
132#492—91no—
133#477—31no—
134#477—91no—
135#331—91no—
136Q8⋊C8—31no—
137Q8⋊C8—91no—
138C2×C3×Q8—21no—
139C2×C3×Q8—61no—
140C2×C3×Q8D1211yescharacteristic
141C2×C3×Q8#6711yescharacteristic
142C2×D12—32no—
143C2×D12—32no—
144C2×D12—62no—
145C2×D12—62no—
146C2×D12—62no—
147C2×D12—61no—
148C2×D12—61no—
149C2×D12—61no—
150C2×D12—61no—
151C2×C4×D3—64no—
152C2×C4×D3—62no—
153C2×C4×D3—62no—
154C2×Dic6—21no—
155C2×Dic6—31no—
156C2×Dic6—31no—
157C2×Dic6—61no—
158C2×C3×C8—61no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4D1211yescharacteristic
168C3×C4⋊C4#6711yescharacteristic
169C3×C42—22no—
170C3×C42—21no—
171C3×C42—21no—
172C3×C42—21no—
173C3×C42C22×D311yescharacteristic
174C3×C42C22×D311yescharacteristic
175#215—124no—
176(C2×D3)⋊C4—64no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—64no—
180(C2×D3)⋊C4—62no—
181(C2×D3)⋊C4—62no—
182(C2×D3)⋊C4—64no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—62no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—31no—
188C4⋊Dic3—31no—
189C4⋊Dic3—61no—
190Dic3⋊C4—62no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193C4×Dic3—62no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199#204—124no—
200C22×C32#12011yescharacteristic
201C2×C3⋊D3—42no—
202C2×C3⋊D3—42no—
203C2×C3⋊D3—42no—
204C32×C4—21no—
205C32×C4—41no—
206C32×C4—41no—
207C32×C4#13511yescharacteristic
208C32×C4#13511yescharacteristic
209C32×C4#13711yescharacteristic
210C32×C4#13711yescharacteristic
211C3⋊Dic3—41no—
212C3⋊Dic3—41no—
213C3×Dic3—81no—
214C2×SD16—182no—
215C4⋊Q8—31no—
216#127—91no—
217#124—181no—
218#124—181no—
219#123—182no—
220C4×Q8—91no—
221C4×Q8D3211yescharacteristic
222C4×D4—181no—
223C4×D4—181no—
224#107—61no—
225#107—181no—
226C4⋊C8—31no—
227C4⋊C8—31no—
228#103—61no—
229#103—181no—
230C4×C8—31no—
231C22×D3—64no—
232C22×D3—62no—
233C22×D3—62no—
234C3×Q8—21no—
235C3×Q8—21no—
236C3×Q8—21no—
237C3×Q8—21no—
238C3×Q8—41no—
239C3×Q8—41no—
240C3×Q8—122no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—121no—
251C2×C3×C4C2×D1211yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×Dic3—41no—
258C2×Dic3—62no—
259C2×Dic3—62no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264D12—122no—
265D12—122no—
266D12—122no—
267D12—122no—
268D12—122no—
269D12—122no—
270D12—121no—
271D12—121no—
272D12—121no—
273D12—121no—
274D12—121no—
275D12—121no—
276D12—121no—
277D12—121no—
278D12—242no—
279C4×D3—244no—
280C4×D3—242no—
281C4×D3—242no—
282Dic6—42no—
283Dic6—61no—
284Dic6—61no—
285Dic6—61no—
286Dic6—61no—
287Dic6—121no—
288Dic6—121no—
289C3×C8—62no—
290C3×C8—121no—
291C3×C8—121no—
292C3⋊C8—22no—
293C3⋊C8—41no—
294C3⋊C8—41no—
295C2×C32#45211yescharacteristic
296C2×C32#45211yescharacteristic
297C2×C32#45311yescharacteristic
298C3⋊D3—82no—
299C2×Q8—61no—
300C2×Q8—91no—
301C2×Q8#62611yescharacteristic
302C2×D4—92no—
303C2×D4—181no—
304C2×D4—181no—
305C22×C4—182no—
306SD16—364no—
307C2×C8—61no—
308C2×C8—61no—
309C2×C8—61no—
310C4⋊C4—21no—
311C4⋊C4—61no—
312C4⋊C4—61no—
313C4⋊C4—91no—
314C4⋊C4—181no—
315C4⋊C4#62611yescharacteristic
316C22⋊C4—182no—
317C22⋊C4—182no—
318C22⋊C4—182no—
319C42—21no—
320C42—181no—
321C42C2×D3211yescharacteristic
322C22×C3—21no—
323C22×C3#88211yescharacteristic
324C22×C3#93711yescharacteristic
325C2×D3—124no—
326C2×D3—124no—
327C2×D3—124no—
328C2×D3—122no—
329C2×D3—122no—
330C2×D3—122no—
331C2×D3—122no—
332C2×D3—122no—
333C2×D3—122no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—41no—
341C3×C4—42no—
342C3×C4—42no—
343C3×C4—41no—
344C3×C4—41no—
345C3×C4—41no—
346C3×C4—41no—
347C3×C4—241no—
348C3×C4#90411yescharacteristic
349C3×C4#90911yescharacteristic
350C3×C4#91611yescharacteristic
351C3×C4#91811yescharacteristic
352C3×C4#91811yescharacteristic
353C3×C4#91911yescharacteristic
354C3×C4#94211yescharacteristic
355C3×C4#95011yescharacteristic
356Dic3—81no—
357Dic3—122no—
358Dic3—122no—
359Dic3—121no—
360Dic3—121no—
361Dic3—121no—
362Dic3—121no—
363C32#163011yescharacteristic, complemented, Sylow
364C23—182no—
365Q8—21no—
366Q8—21no—
367Q8—122no—
368Q8—181no—
369Q8—181no—
370D4—362no—
371D4—361no—
372D4—361no—
373D4—361no—
374D4—361no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—121no—
378C2×C4—181no—
379C2×C4—181no—
380C2×C4—722no—
381C2×C4C2×#62611yescharacteristic
382C2×C4#381111yescharacteristic
383C2×C4#381111yescharacteristic
384C8—62no—
385C8—121no—
386C8—121no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3#473311yescharacteristic
391C2×C3#480811yescharacteristic
392C2×C3#482211yescharacteristic
393C2×C3#504711yescharacteristic
394C2×C3#518711yescharacteristic
395C2×C3#519811yescharacteristic
396D3—244no—
397D3—242no—
398D3—242no—
399C22—362no—
400C22—362no—
401C22—362no—
402C22#6398111yescharacteristic
403C4—21no—
404C4—41no—
405C4—41no—
406C4—241no—
407C4—361no—
408C4—361no—
409C4#6382911yescharacteristic
410C4#6383311yescharacteristic
411C4#6394511yescharacteristic
412C4#6395011yescharacteristic
413C3—21no—
414C3#6826011yescharacteristic, complemented
415C3#7115911yescharacteristic, complemented
416C2—722no—
417C2#1059118411yescharacteristic
418C2#1059160211yescharacteristic
419C2#1059166711yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radical#64083C22
hypercenterC4×Q8D32
hypocenterC32#1630
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. C3×#5021C2semidirect
4. #10590284C2semidirect
5. C3×#4535C2semidirect
7. #10589085C2semidirect
33. #5021D3semidirect
37. #4535D3semidirect
363. C32#1630semidirect
414. C3#68260semidirect
415. C3#71159semidirect

Maximal subgroups

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

subgroupindex
#105960562
C3×#50212
#105903732
#105902842
C3×#45352
#105890912
#105890852
#711593
#682603