Finite Group Databasebeta

← #11779594

Subgroups — #11779594

Order 1152.

424 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5570C211yesmaximal, characteristic
2#10592720C211yesmaximal, characteristic
3#10590288C211yesmaximal, characteristic
4#10590283C211yesmaximal, characteristic
5C3×#4535C211yesmaximal, characteristic
6#10589093C211yesmaximal, characteristic
7#10589084C211yesmaximal, characteristic
8#71936—31nomaximal
9#68253—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×Q8×Dic3—21no—
13C3×#890—21no—
14C3×#890—22no—
15C3×#869—21no—
16C3×#869C2211yescharacteristic
17C3×C4×Dic6—21no—
18C3×C4×Dic6C2211yescharacteristic
19#63662—21no—
20#63634—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63575—21no—
25#63567—22no—
26#63566—21no—
27C3×#557—31no—
28#5570D311yescharacteristic
29#5093—31no—
30#5021—31no—
31#5021—31no—
32#5021—31no—
33#5021—61no—
34#4850—31no—
35#4681—31no—
36C3×Q8⋊C8—31no—
37#4547—31no—
38#4535—31no—
39#4535D311yescharacteristic
40#4482—31no—
41#4456—31no—
42C2×C32×Q8D411yescharacteristic
43C2×#634—21no—
44C2×C3×Dic6—21no—
45C2×C3×Dic6D411yescharacteristic
46C32×C4⋊C4—21no—
47C32×C4⋊C4D411yescharacteristic
48C32×C42—21no—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×C4⋊Dic3—22no—
54C3×C4⋊Dic3—22no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3D412yes—
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#1636—91noSylow
65C3×C4⋊Q8—31no—
66C3×C4⋊Q8—61no—
67C3×#125—62no—
68C3×#125—61no—
69C3×C4×Q8—21no—
70C3×C4×Q8—31no—
71C3×C4×Q8—61no—
72C3×C4×Q8—61no—
73C3×C4×Q8C2×D311yescharacteristic
74C3×C4×Q8C2×D311yescharacteristic
75Q8×Dic3—21no—
76#890—21no—
77#890—22no—
78#869—21no—
79#869—31no—
80#869—31no—
81#869—61no—
82#869C2×D311yescharacteristic
83C4×Dic6—21no—
84C4×Dic6C2×D311yescharacteristic
85C3×C4⋊C8—31no—
86C3×C4×C8—31no—
87#835—61no—
88#835—62no—
89#835—61no—
90#835—61no—
91#818—61no—
92#816—61no—
93#816—62no—
94#810—62no—
95#807—61no—
96#807—62no—
97#807—61no—
98#807—61no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4×C3⋊C8C2×D311yescharacteristic
104C32×Q8—21no—
105C32×Q8Q1612yes—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—41no—
112#634—42no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—22no—
116C3×Dic6—21no—
117C3×Dic6—21no—
118C3×Dic6—41no—
119C3×Dic6—41no—
120C3⋊(C3⋊C8)—41no—
121C3×C3⋊C8—41no—
122C3×C3⋊C8—41no—
123#557—31no—
124#487—91no—
125#477—91no—
126#477—91no—
127#332—91no—
128Q8⋊C8—31no—
129Q8⋊C8—91no—
130C2×C3×Q8—21no—
131C2×C3×Q8—31no—
132C2×C3×Q8—61no—
133C2×C3×Q8D1211yescharacteristic
134C2×C3×Q8#6711yescharacteristic
135C2×Dic6—21no—
136C2×Dic6—61no—
137C2×Dic6—61no—
138C2×Dic6—121no—
139C2×Dic6#6711yescharacteristic
140C2×C3×C8—61no—
141C2×C3×C8—61no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—31no—
146C3×C4⋊C4—32no—
147C3×C4⋊C4—41no—
148C3×C4⋊C4—62no—
149C3×C4⋊C4—62no—
150C3×C4⋊C4—62no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4D1211yescharacteristic
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
163C4⋊Dic3—22no—
164C4⋊Dic3—22no—
165C4⋊Dic3—21no—
166C4⋊Dic3—62no—
167C4⋊Dic3—61no—
168C4⋊Dic3—61no—
169C4⋊Dic3—61no—
170C4⋊Dic3—61no—
171C4⋊Dic3—121no—
172C4⋊Dic3#6712yes—
173C4⋊Dic3#6711yescharacteristic
174Dic3⋊C4—22no—
175Dic3⋊C4—21no—
176C4×Dic3—22no—
177C4×Dic3—21no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—21no—
180C2×C3⋊C8—62no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C22×C32#12011yescharacteristic
184C32×C4—22no—
185C32×C4—21no—
186C32×C4—41no—
187C32×C4C2×Q1611yescharacteristic
188C32×C4#13511yescharacteristic
189C32×C4#13711yescharacteristic
190C32×C4#13711yescharacteristic
191C3⋊Dic3—81no—
192C3×Dic3—41no—
193C3×Dic3—42no—
194C3×Dic3—41no—
195C4⋊Q8—31no—
196C4⋊Q8—61no—
197C4⋊Q8—91no—
198#125—62no—
199#125—61no—
200C4×Q8—31no—
201C4×Q8—61no—
202C4×Q8—61no—
203C4×Q8D3211yescharacteristic
204#107—181no—
205#107—181no—
206C4⋊C8—31no—
207C4⋊C8—91no—
208#103—182no—
209#103—181no—
210#103—181no—
211C4×C8—31no—
212C3×Q8—21no—
213C3×Q8—21no—
214C3×Q8—22no—
215C3×Q8—41no—
216C3×Q8—61no—
217C3×Q8—61no—
218C3×Q8—121no—
219C3×Q8—121no—
220C3×Q8Dic1212yes—
221C3×Q8#21612yes—
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—62no—
233C2×C3×C4—61no—
234C2×C3×C4C2×D1211yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×C3×C4C2×#6711yescharacteristic
239C2×C3×C4C2×#6711yescharacteristic
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—22no—
243C2×Dic3—122no—
244C2×Dic3—121no—
245C2×Dic3—121no—
246Dic6—21no—
247Dic6—21no—
248Dic6—41no—
249Dic6—41no—
250Dic6—122no—
251Dic6—122no—
252Dic6—242no—
253C3×C8—121no—
254C3×C8—121no—
255C3⋊C8—41no—
256C3⋊C8—41no—
257C3⋊C8—122no—
258C3⋊C8—121no—
259C3⋊C8—121no—
260C2×C32#45111yescharacteristic
261C2×C32#45211yescharacteristic
262C2×C32#45411yescharacteristic
263C2×Q8—31no—
264C2×Q8—61no—
265C2×Q8—181no—
266C2×Q8#62611yescharacteristic
267C2×C8—61no—
268C2×C8—61no—
269C2×C8—181no—
270C4⋊C4—21no—
271C4⋊C4—32no—
272C4⋊C4—31no—
273C4⋊C4—62no—
274C4⋊C4—62no—
275C4⋊C4—62no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—181no—
279C4⋊C4—181no—
280C4⋊C4#62611yescharacteristic
281C42—21no—
282C42—62no—
283C42—61no—
284C42C2×D3211yescharacteristic
285C22×C3—21no—
286C22×C3#88211yescharacteristic
287C22×C3#95311yescharacteristic
288C3×C4—22no—
289C3×C4—21no—
290C3×C4—22no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—41no—
297C3×C4—42no—
298C3×C4—41no—
299C3×C4—41no—
300C3×C4—81no—
301C3×C4—121no—
302C3×C4—122no—
303C3×C4—121no—
304C3×C4C2×Dic1211yescharacteristic
305C3×C4#90911yescharacteristic
306C3×C4#91611yescharacteristic
307C3×C4#91811yescharacteristic
308C3×C4#94211yescharacteristic
309C3×C4C2×#21611yescharacteristic
310C3×C4#95011yescharacteristic
311C3×C4#95111yescharacteristic
312Dic3—41no—
313Dic3—42no—
314Dic3—41no—
315Dic3—242no—
316Dic3—241no—
317Dic3—241no—
318C32#163611yescharacteristic, complemented, Sylow
319Q8—21no—
320Q8—61no—
321Q8—61no—
322Q8—121no—
323Q8—121no—
324Q8—362no—
325Q8#371912yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—61no—
329C2×C4—62no—
330C2×C4—61no—
331C2×C4—361no—
332C2×C4C2×#62611yescharacteristic
333C2×C4D3×#6711yescharacteristic
334C2×C4D3×#6711yescharacteristic
335C8—121no—
336C8—121no—
337C8—361no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3#473911yescharacteristic
342C2×C3#480811yescharacteristic
343C2×C3#482711yescharacteristic
344C2×C3#522811yescharacteristic
345C2×C3#523911yescharacteristic
346C2×C3#524511yescharacteristic
347C22#6397711yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—121no—
352C4—122no—
353C4—121no—
354C4—721no—
355C4#6383311yescharacteristic
356C4C2×#371911yescharacteristic
357C4#6394311yescharacteristic
358C4#6394711yescharacteristic
359C3—21no—
360C3#6825311yescharacteristic, complemented
361C3#7193611yescharacteristic, complemented
362C2#1059118611yescharacteristic
363C2#1059159911yescharacteristic
364C2#1059168511yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#120
hypercenterC4×Q8D32
hypocenterC32#1636
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
318. C32#1636semidirect
360. C3#68253semidirect
361. C3#71936semidirect

Maximal subgroups

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

subgroupindex
C3×#55702
#105927202
#105902882
#105902832
C3×#45352
#105890932
#105890842
#719363
#682533