Finite Group Databasebeta

← #11779598

Subgroups — #11779598

Order 1152.

411 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 411 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593861C211yesmaximal, characteristic
2C3×#4850C211yesmaximal, characteristic
3#10590290C211yesmaximal, characteristic
4#10590284C211yesmaximal, characteristic
5#10589350C211yesmaximal, characteristic
6C3×#4486C211yesmaximal, characteristic
7#10589083C211yesmaximal, characteristic
8#71158—31nomaximal
9#68458—31nomaximal
10C4×#634C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63872—21no—
15#63866—21no—
16#63846—22no—
17#63843—21no—
18Dic3×Dic6—21no—
19C32×C4⋊C8C2211yescharacteristic
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C3×#818—21no—
22C3×#816—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63575—21no—
25#63567—21no—
26#63565—22no—
27#5721—31no—
28#5570—31no—
29C3×#477—31no—
30#5093—31no—
31#5091—31no—
32#5079—31no—
33#4850—31no—
34#4850D311yescharacteristic
35C3×#332—31no—
36#4535—31no—
37#4486D311yescharacteristic
38#4484—31no—
39#4484—31no—
40#4484—31no—
41#4484—61no—
42C2×#634D411yescharacteristic
43C2×C3×Dic6—21no—
44C2×C3×Dic6—21no—
45C2×C3×Dic6D411yescharacteristic
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48C4⋊(C3⋊Dic3)D411yescharacteristic
49#3750—21no—
50C4×C3⋊Dic3—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3D412yes—
56C3×C4⋊Dic3D411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C2×C3×C3⋊C8—21no—
60Dic3⋊Dic3—22no—
61Dic3⋊Dic3—22no—
62Dic3⋊Dic3—22no—
63Dic32—22no—
64#1636—91noSylow
65C3×C4⋊Q8—31no—
66C3×C4⋊Q8—31no—
67C3×C4×Q8—31no—
68Q8×Dic3—61no—
69Q8×Dic3—61no—
70#944—61no—
71#890—61no—
72#890—62no—
73#890—61no—
74#889—62no—
75#887—61no—
76#869—61no—
77#869C2×D311yescharacteristic
78#869C2×D311yescharacteristic
79C4×Dic6—31no—
80C4×Dic6—31no—
81C4×Dic6—61no—
82C4×Dic6—61no—
83C4×Dic6C2×D311yescharacteristic
84C3×#107—61no—
85C3×C4⋊C8—21no—
86C3×C4⋊C8—31no—
87C3×C4⋊C8C2×D311yescharacteristic
88C3×C4⋊C8C2×D311yescharacteristic
89C3×#103—61no—
90#835—62no—
91#818—21no—
92#818—61no—
93#816—21no—
94#816—61no—
95#810—61no—
96#810—62no—
97#807—61no—
98C4⋊(C3⋊C8)C2×D311yescharacteristic
99C4×C3⋊C8—31no—
100C4×C3⋊C8—31no—
101C4×C3⋊C8—61no—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—21no—
107#634—21no—
108#634—21no—
109C2×C3×Dic3—21no—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—41no—
113C3×Dic6—21no—
114C3×Dic6—41no—
115C3×Dic6—41no—
116C3×Dic6—42no—
117C3×Dic6Q1612yes—
118C32×C8—41no—
119C3⋊(C3⋊C8)—41no—
120C3×C3⋊C8—41no—
121#557—91no—
122#487—91no—
123#477—31no—
124#477—91no—
125#332—31no—
126Q8⋊C8—91no—
127Q8⋊C8—91no—
128C2×C3×Q8—31no—
129C2×C3×Q8—61no—
130C2×C3×Q8—61no—
131C2×Dic6—21no—
132C2×Dic6—21no—
133C2×Dic6—31no—
134C2×Dic6—31no—
135C2×Dic6—61no—
136C2×Dic6#6711yescharacteristic
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—41no—
140C2×C3×C8—61no—
141C3×C4⋊C4—32no—
142C3×C4⋊C4—31no—
143C3×C4⋊C4—61no—
144C3×C4⋊C4—61no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—61no—
147C3×C42—21no—
148C3×C42—61no—
149C3×C42C22×D311yescharacteristic
150C3×C42C22×D311yescharacteristic
151C4⋊Dic3—21no—
152C4⋊Dic3—21no—
153C4⋊Dic3—21no—
154C4⋊Dic3—31no—
155C4⋊Dic3—31no—
156C4⋊Dic3—61no—
157C4⋊Dic3—62no—
158C4⋊Dic3—62no—
159C4⋊Dic3—62no—
160C4⋊Dic3D1212yes—
161C4⋊Dic3#6711yescharacteristic
162Dic3⋊C4—21no—
163Dic3⋊C4—62no—
164Dic3⋊C4—62no—
165Dic3⋊C4—62no—
166Dic3⋊C4—61no—
167Dic3⋊C4—61no—
168Dic3⋊C4—121no—
169C4×Dic3—21no—
170C4×Dic3—62no—
171C4×Dic3—62no—
172C4×Dic3—61no—
173C4×Dic3—61no—
174C4×Dic3—121no—
175C2×C3⋊C8—21no—
176C2×C3⋊C8—61no—
177C2×C3⋊C8—61no—
178C2×C3⋊C8—121no—
179C22×C32#12011yescharacteristic
180C32×C4—21no—
181C32×C4C2×Q1611yescharacteristic
182C32×C4#13511yescharacteristic
183C32×C4#13711yescharacteristic
184C32×C4#13711yescharacteristic
185C3⋊Dic3—41no—
186C3⋊Dic3—41no—
187C3×Dic3—22no—
188C3×Dic3—42no—
189C3×Dic3—41no—
190C3×Dic3—81no—
191C4⋊Q8—31no—
192C4⋊Q8—31no—
193C4⋊Q8—181no—
194#125—182no—
195#125—181no—
196C4×Q8—31no—
197C4×Q8—91no—
198C4×Q8—181no—
199C4×Q8—181no—
200#107—61no—
201#107—181no—
202C4⋊C8—31no—
203C4⋊C8D3211yescharacteristic
204#103—61no—
205#103—182no—
206#103—181no—
207C4×C8—91no—
208C3×Q8—32no—
209C3×Q8—61no—
210C3×Q8—122no—
211C3×Q8—121no—
212C3×Q8—121no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—61no—
217C2×C3×C4—61no—
218C2×C3×C4—62no—
219C2×C3×C4—121no—
220C2×C3×C4C2×D1211yescharacteristic
221C2×C3×C4D3×D411yescharacteristic
222C2×C3×C4D3×D411yescharacteristic
223C2×C3×C4D3×D411yescharacteristic
224C2×C3×C4D3×D411yescharacteristic
225C2×C3×C4C2×#6711yescharacteristic
226C2×Dic3—21no—
227C2×Dic3—22no—
228C2×Dic3—21no—
229C2×Dic3—41no—
230C2×Dic3—61no—
231C2×Dic3—61no—
232C2×Dic3—61no—
233C2×Dic3—61no—
234C2×Dic3—121no—
235C2×Dic3—121no—
236Dic6—21no—
237Dic6—41no—
238Dic6—41no—
239Dic6—42no—
240Dic6—62no—
241Dic6—61no—
242Dic6—61no—
243Dic6—61no—
244Dic6—61no—
245Dic6—121no—
246Dic6#21612yes—
247C3×C8—41no—
248C3×C8—41no—
249C3×C8—81no—
250C3×C8—121no—
251C3⋊C8—41no—
252C3⋊C8—121no—
253C3⋊C8—121no—
254C3⋊C8—122no—
255C2×C32#45111yescharacteristic
256C2×C32#45211yescharacteristic
257C2×C32#45411yescharacteristic
258C2×Q8—31no—
259C2×Q8—61no—
260C2×Q8—61no—
261C2×Q8—91no—
262C2×C8—21no—
263C2×C8—61no—
264C2×C8—181no—
265C4⋊C4—32no—
266C4⋊C4—31no—
267C4⋊C4—61no—
268C4⋊C4—61no—
269C4⋊C4—61no—
270C4⋊C4—61no—
271C4⋊C4—91no—
272C4⋊C4—182no—
273C4⋊C4—182no—
274C4⋊C4—182no—
275C4⋊C4—181no—
276C42—61no—
277C42—182no—
278C42—181no—
279C42C2×D3211yescharacteristic
280C22×C3—21no—
281C22×C3#88211yescharacteristic
282C22×C3#93711yescharacteristic
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—62no—
291C3×C4—122no—
292C3×C4—121no—
293C3×C4—241no—
294C3×C4#91211yescharacteristic
295C3×C4#91511yescharacteristic
296C3×C4#91511yescharacteristic
297C3×C4D3×Q1611yescharacteristic
298C3×C4#91811yescharacteristic
299C3×C4#91911yescharacteristic
300C3×C4C2×#21611yescharacteristic
301C3×C4#95111yescharacteristic
302Dic3—22no—
303Dic3—41no—
304Dic3—42no—
305Dic3—81no—
306Dic3—122no—
307Dic3—121no—
308Dic3—121no—
309Dic3—121no—
310Dic3—121no—
311Dic3—241no—
312C32#163611yescharacteristic, complemented, Sylow
313Q8—32no—
314Q8—61no—
315Q8—122no—
316Q8—121no—
317Q8—121no—
318Q8—181no—
319Q8—181no—
320C2×C4—61no—
321C2×C4—61no—
322C2×C4—62no—
323C2×C4—121no—
324C2×C4—181no—
325C2×C4—181no—
326C2×C4D3×D1211yescharacteristic
327C2×C4#380211yescharacteristic
328C2×C4D3×#6711yescharacteristic
329C8—41no—
330C8—121no—
331C8—361no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3#475311yescharacteristic
336C2×C3#478311yescharacteristic
337C2×C3#480911yescharacteristic
338C2×C3#505011yescharacteristic
339C2×C3#518711yescharacteristic
340C2×C3#520111yescharacteristic
341C22#6392211yescharacteristic
342C4—21no—
343C4—62no—
344C4—121no—
345C4—122no—
346C4—241no—
347C4—361no—
348C4—361no—
349C4#6381011yescharacteristic
350C4#6381111yescharacteristic
351C4#6392911yescharacteristic
352C4D3×#21611yescharacteristic
353C3—21no—
354C3#6845811yescharacteristic, complemented
355C3#7115811yescharacteristic, complemented
356C2#1059060411yescharacteristic
357C2#1059096511yescharacteristic
358C2#1059102011yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#120
hypercenterC4⋊C8D32
hypocenterC32#1636
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
312. C32#1636semidirect
354. C3#68458semidirect
355. C3#71158semidirect

Maximal subgroups

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

subgroupindex
#105938612
C3×#48502
#105902902
#105902842
#105893502
C3×#44862
#105890832
#711583
#684583