Finite Group Databasebeta

← #11779464

Subgroups — #11779464

Order 1152.

460 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 92 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#10593856C211yesmaximal, characteristic
2#10592790C211yesmaximal, characteristic
3C3×#5092C211yesmaximal, characteristic
4C3×#5091C211yesmaximal, characteristic
5#10589095C211yesmaximal, characteristic
6#10589085C211yesmaximal, characteristic
7#10589084C211yesmaximal, characteristic
8#71307—31nomaximal
9#71161—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C2×C3×#216—22no—
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63919—21no—
16#63918—21no—
17#63844—21no—
18#63843—21no—
19#63839—22no—
20#63637—21no—
21#63634—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#810—21no—
24C3×#807—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27#5722—31no—
28Q8×Dic6—31no—
29C3×#494—31no—
30C3×#477—31no—
31#5092D311yescharacteristic
32#5091—31no—
33#5091—31no—
34#5091—61no—
35#5091D311yescharacteristic
36#4546—31no—
37#4535—31no—
38#4484—31no—
39#4481—31no—
40#4456—31no—
41#4456—31no—
42C2×C32×Q8—21no—
43C2×#634D411yescharacteristic
44C2×C3×Dic6D411yescharacteristic
45C2×C3×Dic6D412yes—
46C2×#627—22no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)D411yescharacteristic
51#3750—21no—
52C4×C3⋊Dic3—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×#216—44no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62#3724—22no—
63Dic3⋊Dic3—22no—
64Dic32—22no—
65#1633—91noSylow
66C2×C3×Q16—62no—
67C3×C4⋊Q8—21no—
68C3×C4⋊Q8—31no—
69C3×C4⋊Q8C2×D311yescharacteristic
70C3×C4⋊Q8C2×D311yescharacteristic
71C3×C4×Q8—31no—
72Q8×Dic3—61no—
73#944—62no—
74C2×#216—22no—
75#888—61no—
76#888—61no—
77#888—62no—
78#888—61no—
79#887—61no—
80#887—61no—
81#869—61no—
82#869C2×D311yescharacteristic
83C4×Dic6—31no—
84C4×Dic6—31no—
85C4×Dic6—61no—
86C4×Dic6—61no—
87C4×Dic6C2×D311yescharacteristic
88C3×#107—61no—
89C3×C4⋊C8—31no—
90C3×#103—61no—
91C3×C4×C8—31no—
92#810—21no—
93#810—61no—
94#810—61no—
95#810—62no—
96#807—21no—
97#807—61no—
98#807—61no—
99#807—62no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C32×Q8—42no—
106C2×C32×C4—41no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—21no—
112#634—21no—
113#634Q1612yescomplemented
114C2×C3×Dic3—21no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—21no—
117C3×Dic6—21no—
118C3×Dic6—42no—
119C3×Dic6Q1612yescomplemented
120#627—82no—
121C3⋊(C3⋊C8)—41no—
122C3×C3⋊C8—22no—
123C3×C3⋊C8—41no—
124Q82—91no—
125#494—31no—
126#477—31no—
127#477—91no—
128#333—91no—
129Q8⋊C8—91no—
130Q8⋊C8—91no—
131C2×C3×Q8—21no—
132C2×C3×Q8—21no—
133C2×C3×Q8—31no—
134C2×C3×Q8—32no—
135C2×C3×Q8—41no—
136C2×Dic6—31no—
137C2×Dic6—31no—
138C2×Dic6—61no—
139C2×Dic6—62no—
140C2×Dic6—62no—
141C2×Dic6#6711yescharacteristic
142C2×Dic6#6712yes—
143C3×Q16—124no—
144C2×C3×C8—61no—
145C2×C3×C8—61no—
146C3×C4⋊C4—22no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—31no—
152C3×C4⋊C4—41no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C42—21no—
157C3×C42—61no—
158C3×C42C22×D311yescharacteristic
159C3×C42C22×D311yescharacteristic
160#216—44no—
161C4⋊Dic3—21no—
162C4⋊Dic3—21no—
163C4⋊Dic3—31no—
164C4⋊Dic3—31no—
165C4⋊Dic3—61no—
166C4⋊Dic3—62no—
167C4⋊Dic3#6711yescharacteristic
168Dic3⋊C4—21no—
169Dic3⋊C4—62no—
170Dic3⋊C4—62no—
171Dic3⋊C4—62no—
172Dic3⋊C4—61no—
173Dic3⋊C4—61no—
174Dic3⋊C4—121no—
175C4×Dic3—21no—
176C4×Dic3—62no—
177C4×Dic3—62no—
178C4×Dic3—61no—
179C4×Dic3—61no—
180C4×Dic3—121no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—62no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—61no—
186C22×C32#12011yescharacteristic
187C32×C4—21no—
188C32×C4—81no—
189C32×C4C2×Q1611yescharacteristic
190C32×C4C2×Q1611yescharacteristic
191C32×C4#13711yescharacteristic
192C32×C4#13711yescharacteristic
193C3⋊Dic3—22no—
194C3⋊Dic3—41no—
195C3×Dic3—22no—
196C3×Dic3—41no—
197C3×Dic3—42no—
198C2×Q16—62no—
199C4⋊Q8—31no—
200C4⋊Q8—181no—
201C4⋊Q8—181no—
202C4⋊Q8—182no—
203C4⋊Q8D3211yescharacteristic
204C4×Q8—31no—
205C4×Q8—91no—
206C4×Q8—181no—
207C4×Q8—181no—
208#107—61no—
209#107—181no—
210C4⋊C8—31no—
211C4⋊C8—91no—
212#103—61no—
213#103—181no—
214C4×C8—31no—
215C3×Q8—32no—
216C3×Q8—42no—
217C3×Q8—42no—
218C3×Q8—61no—
219C3×Q8—82no—
220C3×Q8—122no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—42no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—61no—
228C2×C3×C4—62no—
229C2×C3×C4—61no—
230C2×C3×C4D3×D411yescharacteristic
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4C2×#6711yescharacteristic
235C2×C3×C4C2×#6711yescharacteristic
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3—22no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—121no—
244C2×Dic3—121no—
245Dic6—21no—
246Dic6—32no—
247Dic6—32no—
248Dic6—42no—
249Dic6—62no—
250Dic6—61no—
251Dic6—61no—
252Dic6—121no—
253Dic6—242no—
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—21no—
267C2×Q8—31no—
268C2×Q8—32no—
269C2×Q8—91no—
270C2×Q8—182no—
271Q16—124no—
272C2×C8—61no—
273C2×C8—61no—
274C2×C8—181no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—31no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4—91no—
282C4⋊C4—182no—
283C4⋊C4—182no—
284C4⋊C4—181no—
285C42—61no—
286C42—182no—
287C42—181no—
288C42C2×D3211yescharacteristic
289C22×C3—21no—
290C22×C3#93711yescharacteristic
291C22×C3#93711yescharacteristic
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—41no—
299C3×C4—62no—
300C3×C4—82no—
301C3×C4—81no—
302C3×C4—81no—
303C3×C4—122no—
304C3×C4—121no—
305C3×C4D3×Q1611yescharacteristic
306C3×C4D3×Q1611yescharacteristic
307C3×C4D3×Q1611yescharacteristic
308C3×C4#91811yescharacteristic
309C3×C4#91811yescharacteristic
310C3×C4#91811yescharacteristic
311C3×C4C2×#21611yescharacteristic
312C3×C4#95111yescharacteristic
313Dic3—22no—
314Dic3—41no—
315Dic3—42no—
316Dic3—62no—
317Dic3—62no—
318Dic3—122no—
319Dic3—121no—
320Dic3—121no—
321Dic3—241no—
322C32#163311yescharacteristic, complemented, Sylow
323Q8—32no—
324Q8—42no—
325Q8—61no—
326Q8—92no—
327Q8—122no—
328Q8—181no—
329Q8—722no—
330C2×C4—41no—
331C2×C4—61no—
332C2×C4—61no—
333C2×C4—62no—
334C2×C4—181no—
335C2×C4—181no—
336C2×C4D3×#6711yescharacteristic
337C2×C4D3×#6711yescharacteristic
338C2×C4#381111yescharacteristic
339C8—62no—
340C8—121no—
341C8—361no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3#505011yescharacteristic
346C2×C3#507711yescharacteristic
347C2×C3#518611yescharacteristic
348C2×C3#518611yescharacteristic
349C2×C3#518611yescharacteristic
350C2×C3#519811yescharacteristic
351C22#6398311yescharacteristic
352C4—21no—
353C4—62no—
354C4—81no—
355C4—122no—
356C4—121no—
357C4—182no—
358C4—361no—
359C4D3×#21611yescharacteristic
360C4#6394311yescharacteristic
361C4#6394411yescharacteristic
362C4#6394511yescharacteristic
363C3—21no—
364C3#7116111yescharacteristic, complemented
365C3#7130711yescharacteristic, complemented
366C2#1059152311yescharacteristic
367C2#1059165311yescharacteristic
368C2#1059165411yescharacteristic
subgroupG/H
centerC22#63983
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
113. #634Q16semidirect
119. C3×Dic6Q16semidirect
255. Dic6#216semidirect
322. C32#1633semidirect
364. C3#71161semidirect
365. C3#71307semidirect

Maximal subgroups

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

subgroupindex
#105938562
#105927902
C3×#50922
C3×#50912
#105890952
#105890852
#105890842
#713073
#711613