Finite Group Databasebeta

← #11779470

Subgroups — #11779470

Order 1152.

447 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 447 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C3×Q8×Dic6C211yesmaximal, characteristic
2C3×#5021C211yesmaximal, characteristic
3#10590387C211yesmaximal, characteristic
4#10590310C211yesmaximal, characteristic
5#10589401C211yesmaximal, characteristic
6#10589095C211yesmaximal, characteristic
7#10589083C211yesmaximal, characteristic
8#71940—31nomaximal
9#71161—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C3×Q8×Dic3—21no—
12C3×#888—22no—
13C3×#888—21no—
14C3×#869—21no—
15C3×#869C2211yescharacteristic
16C3×#869C2211yescharacteristic
17C3×C4×Dic6—21no—
18C3×C4×Dic6C2211yescharacteristic
19C2×#3718—22no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#835—21no—
23C3×#807—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63576—21no—
26#63565—21no—
27C3×Q82—31no—
28Q8×Dic6D311yescharacteristic
29C3×#477—31no—
30#5092—31no—
31#5092—31no—
32#5091—31no—
33#5021—31no—
34#5021D311yescharacteristic
35#4546—31no—
36#4535—31no—
37#4535—31no—
38#4535—31no—
39#4535—61no—
40#4484—31no—
41#4481—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C3×Dic6—21no—
44C2×C3×Dic6—22no—
45C2×C3×Dic6D411yescharacteristic
46C2×C3×Dic6D412yes—
47C32×C4⋊C4—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C42—21no—
50C32×C42C2311yescharacteristic
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×C4⋊Dic3—22no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×Dic3⋊C4—22no—
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—22no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64#3718—44no—
65#1633—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8—31no—
68C3×C4⋊Q8—61no—
69C3×C4⋊Q8—62no—
70C3×C4⋊Q8—61no—
71C3×C4×Q8—21no—
72C3×C4×Q8—31no—
73C3×C4×Q8—61no—
74C3×C4×Q8—61no—
75C3×C4×Q8C2×D311yescharacteristic
76C3×C4×Q8C2×D311yescharacteristic
77Q8×Dic3—21no—
78C2×#216—62no—
79C2×#216—62no—
80#888—22no—
81#888—21no—
82#869—21no—
83#869C2×D311yescharacteristic
84#869C2×D311yescharacteristic
85C4×Dic6—21no—
86C4×Dic6C2×D311yescharacteristic
87C3×#107—61no—
88C3×C4⋊C8—31no—
89C3×#103—61no—
90#835—21no—
91#835—61no—
92#810—61no—
93#807—21no—
94#807—61no—
95#807—61no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—61no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4×C3⋊C8—31no—
101C4×C3⋊C8—31no—
102C4×C3⋊C8—61no—
103C32×Q8—21no—
104C32×Q8Q1612yescomplemented
105C2×C32×C4—21no—
106C2×C32×C4—21no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3×Dic3—21no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—41no—
114C3×Dic6—21no—
115C3×Dic6—42no—
116C3×Dic6—42no—
117C3×Dic6—82no—
118C3×Dic6Q1612yescomplemented
119C3⋊(C3⋊C8)—22no—
120C3⋊(C3⋊C8)—41no—
121C3×C3⋊C8—41no—
122Q82—31no—
123#494—91no—
124#477—31no—
125#477—91no—
126#333—91no—
127Q8⋊C8—91no—
128Q8⋊C8—91no—
129C2×C3×Q8—21no—
130C2×C3×Q8—31no—
131C2×C3×Q8—32no—
132C2×C3×Q8—62no—
133C2×C3×Q8—61no—
134C2×C3×Q8#6711yescharacteristic
135C2×C3×Q8#6711yescharacteristic
136C2×Dic6—21no—
137C2×Dic6—22no—
138C2×Dic6#6711yescharacteristic
139C2×Dic6#6712yes—
140C2×C3×C8—61no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—31no—
145C3×C4⋊C4—41no—
146C3×C4⋊C4—62no—
147C3×C4⋊C4—62no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4#6711yescharacteristic
154C3×C4⋊C4#6711yescharacteristic
155C3×C42—21no—
156C3×C42—21no—
157C3×C42—21no—
158C3×C42—41no—
159C3×C42—62no—
160C3×C42—61no—
161C3×C42C22×D311yescharacteristic
162C3×C42C22×D311yescharacteristic
163#216—124no—
164#216—124no—
165C4⋊Dic3—22no—
166C4⋊Dic3—21no—
167C4⋊Dic3—21no—
168C4⋊Dic3—21no—
169C4⋊Dic3—21no—
170C4⋊Dic3#6711yescharacteristic
171Dic3⋊C4—22no—
172Dic3⋊C4—21no—
173C4×Dic3—22no—
174C4×Dic3—21no—
175C2×C3⋊C8—21no—
176C2×C3⋊C8—61no—
177C2×C3⋊C8—61no—
178C2×C3⋊C8—61no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—121no—
181C2×C3⋊C8—121no—
182C22×C32#12011yescharacteristic
183C32×C4—22no—
184C32×C4—21no—
185C32×C4—41no—
186C32×C4C2×Q1611yescharacteristic
187C32×C4C2×Q1611yescharacteristic
188C32×C4#13711yescharacteristic
189C32×C4#13711yescharacteristic
190C3×Dic3—22no—
191C3×Dic3—42no—
192C3×Dic3—41no—
193C3×Dic3—81no—
194C2×Q16—182no—
195C4⋊Q8—31no—
196C4⋊Q8—31no—
197C4⋊Q8—61no—
198C4⋊Q8—62no—
199C4⋊Q8—61no—
200C4×Q8—31no—
201C4×Q8—61no—
202C4×Q8—61no—
203C4×Q8D3211yescharacteristic
204#107—61no—
205#107—181no—
206C4⋊C8—31no—
207C4⋊C8—91no—
208#103—61no—
209#103—181no—
210C4×C8—91no—
211C3×Q8—21no—
212C3×Q8—21no—
213C3×Q8—22no—
214C3×Q8—32no—
215C3×Q8—41no—
216C3×Q8—61no—
217C3×Q8—122no—
218C3×Q8—122no—
219C3×Q8—242no—
220C3×Q8#21612yescomplemented
221C3×Q8#21612yescomplemented
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—61no—
232C2×C3×C4—61no—
233C2×C3×C4—62no—
234C2×C3×C4—121no—
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×C3×C4C2×#6711yescharacteristic
239C2×C3×C4C2×#6711yescharacteristic
240C2×C3×C4C2×#6711yescharacteristic
241C2×Dic3—21no—
242C2×Dic3—22no—
243C2×Dic3—21no—
244C2×Dic3—41no—
245Dic6—21no—
246Dic6—42no—
247Dic6—42no—
248Dic6—82no—
249Dic6#21612yescomplemented
250C3×C8—121no—
251C3⋊C8—41no—
252C3⋊C8—62no—
253C3⋊C8—62no—
254C3⋊C8—122no—
255C3⋊C8—121no—
256C3⋊C8—121no—
257C3⋊C8—241no—
258C2×C32#45111yescharacteristic
259C2×C32#45111yescharacteristic
260C2×C32#45311yescharacteristic
261C2×Q8—31no—
262C2×Q8—32no—
263C2×Q8—62no—
264C2×Q8—61no—
265C2×Q8#62511yescharacteristic
266Q16—364no—
267C2×C8—61no—
268C2×C8—181no—
269C2×C8—181no—
270C4⋊C4—21no—
271C4⋊C4—31no—
272C4⋊C4—62no—
273C4⋊C4—62no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C4⋊C4#62511yescharacteristic
280C42—21no—
281C42—62no—
282C42—61no—
283C42C2×D3211yescharacteristic
284C22×C3—21no—
285C22×C3#93711yescharacteristic
286C22×C3#95311yescharacteristic
287C3×C4—21no—
288C3×C4—22no—
289C3×C4—21no—
290C3×C4—22no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—41no—
296C3×C4—42no—
297C3×C4—41no—
298C3×C4—41no—
299C3×C4—62no—
300C3×C4—81no—
301C3×C4—122no—
302C3×C4—121no—
303C3×C4—241no—
304C3×C4D3×Q1611yescharacteristic
305C3×C4#91811yescharacteristic
306C3×C4#94211yescharacteristic
307C3×C4#94211yescharacteristic
308C3×C4C2×#21611yescharacteristic
309C3×C4C2×#21611yescharacteristic
310C3×C4C2×#21611yescharacteristic
311C3×C4#95111yescharacteristic
312Dic3—22no—
313Dic3—42no—
314Dic3—41no—
315Dic3—81no—
316C32#163311yescharacteristic, complemented, Sylow
317Q8—21no—
318Q8—32no—
319Q8—61no—
320Q8—122no—
321Q8—122no—
322Q8—242no—
323Q8#371812yescomplemented
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—62no—
329C2×C4—121no—
330C2×C4C2×#62511yescharacteristic
331C2×C4D3×#6711yescharacteristic
332C2×C4D3×#6711yescharacteristic
333C8—121no—
334C8—182no—
335C8—361no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3#505011yescharacteristic
340C2×C3#518611yescharacteristic
341C2×C3#519811yescharacteristic
342C2×C3#522811yescharacteristic
343C2×C3#522811yescharacteristic
344C2×C3#524111yescharacteristic
345C22#6397611yescharacteristic
346C4—21no—
347C4—22no—
348C4—41no—
349C4—62no—
350C4—122no—
351C4—121no—
352C4—241no—
353C4#6382711yescharacteristic
354C4C2×#371811yescharacteristic
355C4D3×#21611yescharacteristic
356C4#6394811yescharacteristic
357C3—21no—
358C3#7116111yescharacteristic, complemented
359C3#7194011yescharacteristic, complemented
360C2#1059118511yescharacteristic
361C2#1059159411yescharacteristic
362C2#1059166511yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#120
hypercenterC4×Q8D32
hypocenterC32#1633
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
104. C32×Q8Q16semidirect
118. C3×Dic6Q16semidirect
220. C3×Q8#216semidirect
221. C3×Q8#216semidirect
249. Dic6#216semidirect
316. C32#1633semidirect
323. Q8#3718semidirect
358. C3#71161semidirect
359. C3#71940semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
C3×#50212
#105903872
#105903102
#105894012
#105890952
#105890832
#719403
#711613