Finite Group Databasebeta

← #11779468

Subgroups — #11779468

Order 1152.

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

normal subgroups only

This group has 460 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
2#10592720C211yesmaximal, characteristic
3#10590386C211yesmaximal, characteristic
4#10590283C211yesmaximal, characteristic
5C3×#4535C211yesmaximal, characteristic
6#10589095C211yesmaximal, characteristic
7#10589084C211yesmaximal, characteristic
8#71940—31nomaximal
9#68267—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×Q8×Dic3—21no—
13C3×#888—22no—
14C3×#888—21no—
15C3×#869—21no—
16C3×#869C2211yescharacteristic
17C3×C4×Dic6—21no—
18C3×C4×Dic6C2211yescharacteristic
19C2×#3719—22no—
20#63662—21no—
21#63634—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63575—21no—
26#63566—21no—
27C3×Q82—31no—
28Q8×Dic6D311yescharacteristic
29#5092—31no—
30#5021—31no—
31#5021—31no—
32#5021—31no—
33#5021—61no—
34#4850—31no—
35#4699—31no—
36C3×Q8⋊C8—31no—
37#4546—31no—
38#4535—31no—
39#4535D311yescharacteristic
40#4481—31no—
41#4456—31no—
42C2×C32×Q8D411yescharacteristic
43C2×#634—21no—
44C2×C3×Dic6—22no—
45C2×C3×Dic6D411yescharacteristic
46C2×C3×Dic6D412yes—
47C32×C4⋊C4—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C42—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×C4⋊Dic3—22no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—22no—
59C3×Dic3⋊C4—21no—
60C3×C4×Dic3—22no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3719—44no—
65#1633—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8—61no—
68C3×C4⋊Q8—62no—
69C3×C4⋊Q8—61no—
70C3×C4×Q8—21no—
71C3×C4×Q8—31no—
72C3×C4×Q8—61no—
73C3×C4×Q8—61no—
74C3×C4×Q8C2×D311yescharacteristic
75C3×C4×Q8C2×D311yescharacteristic
76Q8×Dic3—21no—
77C2×#216—62no—
78C2×Dic12—62no—
79#888—22no—
80#888—21no—
81#869—21no—
82#869—31no—
83#869—31no—
84#869—61no—
85#869C2×D311yescharacteristic
86C4×Dic6—21no—
87C4×Dic6C2×D311yescharacteristic
88C3×C4⋊C8—31no—
89C3×C4×C8—31no—
90#835—61no—
91#835—62no—
92#835—61no—
93#835—61no—
94#818—61no—
95#816—61no—
96#807—61no—
97#807—62no—
98#807—61no—
99#807—61no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C32×Q8—21no—
106C32×Q8Q1612yescomplemented
107C2×C32×C4—21no—
108C2×C32×C4—21no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—41no—
113#634—42no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—21no—
117C3×Dic6—21no—
118C3×Dic6—42no—
119C3×Dic6—82no—
120C3×Dic6Q1612yescomplemented
121C3⋊(C3⋊C8)—41no—
122C3×C3⋊C8—22no—
123C3×C3⋊C8—41no—
124Q82—31no—
125#494—91no—
126#477—91no—
127#477—91no—
128#333—91no—
129Q8⋊C8—31no—
130Q8⋊C8—91no—
131C2×C3×Q8—21no—
132C2×C3×Q8—31no—
133C2×C3×Q8—32no—
134C2×C3×Q8—62no—
135C2×C3×Q8D1211yescharacteristic
136C2×C3×Q8#6711yescharacteristic
137C2×Dic6—22no—
138C2×Dic6—61no—
139C2×Dic6—61no—
140C2×Dic6—121no—
141C2×Dic6#6711yescharacteristic
142C2×Dic6#6712yes—
143C2×C3×C8—61no—
144C2×C3×C8—61no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—41no—
150C3×C4⋊C4—62no—
151C3×C4⋊C4—62no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4D1211yescharacteristic
156C3×C4⋊C4#6711yescharacteristic
157C3×C42—21no—
158C3×C42—21no—
159C3×C42—21no—
160C3×C42—41no—
161C3×C42—62no—
162C3×C42—61no—
163C3×C42C22×D311yescharacteristic
164C3×C42C22×D311yescharacteristic
165#216—124no—
166C4⋊Dic3—22no—
167C4⋊Dic3—21no—
168C4⋊Dic3—21no—
169C4⋊Dic3—62no—
170C4⋊Dic3—61no—
171C4⋊Dic3—61no—
172C4⋊Dic3—61no—
173C4⋊Dic3—61no—
174C4⋊Dic3—121no—
175C4⋊Dic3#6711yescharacteristic
176Dic3⋊C4—22no—
177Dic3⋊C4—21no—
178C4×Dic3—22no—
179C4×Dic3—21no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—62no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185Dic12—124no—
186C22×C32#12011yescharacteristic
187C32×C4—22no—
188C32×C4—21no—
189C32×C4—41no—
190C32×C4C2×Q1611yescharacteristic
191C32×C4C2×Q1611yescharacteristic
192C32×C4#13711yescharacteristic
193C32×C4#13711yescharacteristic
194C3⋊Dic3—81no—
195C3×Dic3—22no—
196C3×Dic3—42no—
197C3×Dic3—41no—
198C2×Q16—182no—
199C4⋊Q8—31no—
200C4⋊Q8—61no—
201C4⋊Q8—62no—
202C4⋊Q8—61no—
203C4⋊Q8—91no—
204C4×Q8—31no—
205C4×Q8—61no—
206C4×Q8—61no—
207C4×Q8D3211yescharacteristic
208#107—181no—
209#107—181no—
210C4⋊C8—31no—
211C4⋊C8—91no—
212#103—181no—
213#103—181no—
214C4×C8—31no—
215C3×Q8—21no—
216C3×Q8—21no—
217C3×Q8—22no—
218C3×Q8—32no—
219C3×Q8—41no—
220C3×Q8—61no—
221C3×Q8—122no—
222C3×Q8—242no—
223C3×Q8Dic1212yescomplemented
224C3×Q8#21612yescomplemented
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4—61no—
235C2×C3×C4—61no—
236C2×C3×C4—62no—
237C2×C3×C4C2×D1211yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4C2×#6711yescharacteristic
241C2×C3×C4C2×#6711yescharacteristic
242C2×C3×C4C2×#6711yescharacteristic
243C2×Dic3—21no—
244C2×Dic3—22no—
245C2×Dic3—21no—
246C2×Dic3—122no—
247C2×Dic3—121no—
248C2×Dic3—121no—
249Dic6—21no—
250Dic6—42no—
251Dic6—82no—
252Dic6—122no—
253Dic6—122no—
254Dic6—242no—
255Dic6#21612yescomplemented
256C3×C8—62no—
257C3×C8—121no—
258C3⋊C8—22no—
259C3⋊C8—41no—
260C3⋊C8—122no—
261C3⋊C8—121no—
262C3⋊C8—121no—
263C2×C32#45111yescharacteristic
264C2×C32#45111yescharacteristic
265C2×C32#45311yescharacteristic
266C2×Q8—31no—
267C2×Q8—32no—
268C2×Q8—62no—
269C2×Q8—181no—
270C2×Q8#62611yescharacteristic
271Q16—364no—
272C2×C8—61no—
273C2×C8—61no—
274C2×C8—181no—
275C4⋊C4—21no—
276C4⋊C4—31no—
277C4⋊C4—62no—
278C4⋊C4—62no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4—61no—
282C4⋊C4—181no—
283C4⋊C4—181no—
284C4⋊C4#62611yescharacteristic
285C42—21no—
286C42—62no—
287C42—61no—
288C42C2×D3211yescharacteristic
289C22×C3—21no—
290C22×C3#88211yescharacteristic
291C22×C3#95311yescharacteristic
292C3×C4—22no—
293C3×C4—21no—
294C3×C4—22no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—41no—
301C3×C4—42no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—62no—
305C3×C4—81no—
306C3×C4—122no—
307C3×C4—121no—
308C3×C4C2×Dic1211yescharacteristic
309C3×C4#90911yescharacteristic
310C3×C4#91511yescharacteristic
311C3×C4D3×Q1611yescharacteristic
312C3×C4#94211yescharacteristic
313C3×C4#94211yescharacteristic
314C3×C4C2×#21611yescharacteristic
315C3×C4C2×#21611yescharacteristic
316Dic3—22no—
317Dic3—42no—
318Dic3—41no—
319Dic3—242no—
320Dic3—241no—
321Dic3—241no—
322C32#163311yescharacteristic, complemented, Sylow
323Q8—21no—
324Q8—32no—
325Q8—61no—
326Q8—122no—
327Q8—242no—
328Q8—362no—
329Q8#371912yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—62no—
335C2×C4—361no—
336C2×C4C2×#62611yescharacteristic
337C2×C4D3×#6711yescharacteristic
338C2×C4D3×#6711yescharacteristic
339C8—62no—
340C8—121no—
341C8—361no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3#473911yescharacteristic
346C2×C3#480911yescharacteristic
347C2×C3#482211yescharacteristic
348C2×C3#522811yescharacteristic
349C2×C3#522811yescharacteristic
350C2×C3#524111yescharacteristic
351C22#6397711yescharacteristic
352C4—21no—
353C4—22no—
354C4—41no—
355C4—62no—
356C4—122no—
357C4—121no—
358C4—721no—
359C4#6383311yescharacteristic
360C4C2×#371911yescharacteristic
361C4D3×#21611yescharacteristic
362C4#6394611yescharacteristic
363C3—21no—
364C3#6826711yescharacteristic, complemented
365C3#7194011yescharacteristic, complemented
366C2#1059118611yescharacteristic
367C2#1059159511yescharacteristic
368C2#1059166611yescharacteristic
subgroupG/H
centerC22#63977
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
106. C32×Q8Q16semidirect
120. C3×Dic6Q16semidirect
223. C3×Q8Dic12semidirect
224. C3×Q8#216semidirect
255. Dic6#216semidirect
322. C32#1633semidirect
329. Q8#3719semidirect
364. C3#68267semidirect
365. 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
#105927202
#105903862
#105902832
C3×#45352
#105890952
#105890842
#719403
#682673