Finite Group Databasebeta

← #11780007

Subgroups — #11780007

Order 1152.

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

normal subgroups only

This group has 454 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#10592789C211yesmaximal, characteristic
3C3×#5094C211yesmaximal, characteristic
4C3×#5093C211yesmaximal, characteristic
5#10589095C211yesmaximal, characteristic
6#10589085C211yesmaximal, characteristic
7#10589084C211yesmaximal, characteristic
8#71239—31nomaximal
9#71129—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3756—21no—
12C4×#634C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63919—21no—
16#63918—21no—
17#63844—21no—
18#63843—21no—
19#63839—22no—
20#63662—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#810—22no—
23C3×#810—21no—
24C3×#808—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27#5722—31no—
28Q8×Dic6—31no—
29C3×#487—31no—
30C3×#475—31no—
31#5094D311yescharacteristic
32#5093D311yescharacteristic
33#5090—31no—
34#5090—31no—
35#5090—61no—
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
50#3756—42no—
51C4⋊(C3⋊Dic3)D411yescharacteristic
52#3750—21no—
53C4×C3⋊Dic3—21no—
54C2×C3⋊(C3⋊C8)—21no—
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#1645—91noSylow
66C3×C4⋊Q8—21no—
67C3×C4⋊Q8—31no—
68C3×C4⋊Q8C2×D311yescharacteristic
69C3×C4⋊Q8C2×D311yescharacteristic
70C3×C4×Q8—31no—
71Q8×Dic3—61no—
72#944—62no—
73C2×#216—61no—
74C2×#216—61no—
75C2×#216—62no—
76#888—61no—
77#888—61no—
78#888—62no—
79#888—61no—
80#887—61no—
81#887—61no—
82#869—61no—
83#869C2×D311yescharacteristic
84C4×Dic6—31no—
85C4×Dic6—31no—
86C4×Dic6—61no—
87C4×Dic6—61no—
88C4×Dic6C2×D311yescharacteristic
89C3×#106—61no—
90C3×C4⋊C8—31no—
91C3×#103—61no—
92C3×#103—62no—
93C3×C4×C8—31no—
94#835—61no—
95#835—61no—
96#835—62no—
97#810—22no—
98#810—21no—
99#808—21no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C32×Q8—41no—
106C32×Q8—41no—
107C2×C32×C4—41no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—21no—
113#634—21no—
114#634SD1612yes—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—21no—
118C3×Dic6—21no—
119C3×Dic6—42no—
120C3×Dic6Q1612yescomplemented
121#627—82no—
122C3⋊(C3⋊C8)—41no—
123C3×C3⋊C8—41no—
124C3×C3⋊C8—41no—
125Q82—91no—
126#487—31no—
127#475—31no—
128#462—91no—
129#333—91no—
130Q8⋊C8—91no—
131Q8⋊C8—91no—
132C2×C3×Q8—22no—
133C2×C3×Q8—21no—
134C2×C3×Q8—21no—
135C2×C3×Q8—31no—
136C2×C3×Q8—32no—
137C2×Dic6—31no—
138C2×Dic6—31no—
139C2×Dic6—61no—
140C2×Dic6—62no—
141C2×Dic6—62no—
142C2×Dic6#6711yescharacteristic
143C2×Dic6#6712yes—
144C2×C3×C8—61no—
145C2×C3×C8—61no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—31no—
151C3×C4⋊C4—41no—
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—122no—
161#216—122no—
162#216—124no—
163C4⋊Dic3—21no—
164C4⋊Dic3—21no—
165C4⋊Dic3—31no—
166C4⋊Dic3—31no—
167C4⋊Dic3—61no—
168C4⋊Dic3—62no—
169C4⋊Dic3#6711yescharacteristic
170Dic3⋊C4—21no—
171Dic3⋊C4—62no—
172Dic3⋊C4—62no—
173Dic3⋊C4—62no—
174Dic3⋊C4—61no—
175Dic3⋊C4—61no—
176Dic3⋊C4—121no—
177C4×Dic3—21no—
178C4×Dic3—62no—
179C4×Dic3—62no—
180C4×Dic3—61no—
181C4×Dic3—61no—
182C4×Dic3—121no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—62no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188C22×C32#12011yescharacteristic
189C32×C4—21no—
190C32×C4—81no—
191C32×C4C2×SD1611yescharacteristic
192C32×C4C2×Q1611yescharacteristic
193C32×C4#13711yescharacteristic
194C32×C4#13711yescharacteristic
195C3⋊Dic3—22no—
196C3⋊Dic3—41no—
197C3×Dic3—22no—
198C3×Dic3—41no—
199C3×Dic3—42no—
200C2×Q16—181no—
201C4⋊Q8—31no—
202C4⋊Q8—181no—
203C4⋊Q8—181no—
204C4⋊Q8—182no—
205C4⋊Q8D3211yescharacteristic
206C4×Q8—31no—
207C4×Q8—91no—
208C4×Q8—181no—
209C4×Q8—181no—
210#106—61no—
211C4⋊C8—31no—
212C4⋊C8—91no—
213#103—61no—
214#103—62no—
215#103—181no—
216C4×C8—31no—
217C3×Q8—32no—
218C3×Q8—42no—
219C3×Q8—42no—
220C3×Q8—41no—
221C3×Q8—41no—
222C3×Q8—41no—
223C3×Q8—41no—
224C3×Q8—61no—
225C3×Q8—122no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—42no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4—61no—
233C2×C3×C4—62no—
234C2×C3×C4—61no—
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4C2×#6711yescharacteristic
240C2×C3×C4C2×#6711yescharacteristic
241C2×Dic3—21no—
242C2×Dic3—21no—
243C2×Dic3—22no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—121no—
249C2×Dic3—121no—
250Dic6—21no—
251Dic6—32no—
252Dic6—32no—
253Dic6—42no—
254Dic6—62no—
255Dic6—61no—
256Dic6—61no—
257Dic6—121no—
258Dic6—242no—
259Dic6—242no—
260Dic6#21612yescomplemented
261C3×C8—121no—
262C3×C8—121no—
263C3⋊C8—41no—
264C3⋊C8—41no—
265C3⋊C8—122no—
266C3⋊C8—121no—
267C3⋊C8—121no—
268C2×C32#44811yescharacteristic
269C2×C32#45111yescharacteristic
270C2×C32#45511yescharacteristic
271C2×Q8—21no—
272C2×Q8—31no—
273C2×Q8—32no—
274C2×Q8—91no—
275C2×Q8—182no—
276Q16—362no—
277C2×C8—61no—
278C2×C8—61no—
279C2×C8—181no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—31no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4—61no—
286C4⋊C4—91no—
287C4⋊C4—182no—
288C4⋊C4—182no—
289C4⋊C4—181no—
290C42—61no—
291C42—182no—
292C42—181no—
293C42C2×D3211yescharacteristic
294C22×C3—21no—
295C22×C3#93711yescharacteristic
296C22×C3#93711yescharacteristic
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—41no—
304C3×C4—62no—
305C3×C4—82no—
306C3×C4—81no—
307C3×C4—81no—
308C3×C4—122no—
309C3×C4—121no—
310C3×C4D3×SD1611yescharacteristic
311C3×C4D3×SD1611yescharacteristic
312C3×C4#91511yescharacteristic
313C3×C4#91511yescharacteristic
314C3×C4D3×Q1611yescharacteristic
315C3×C4#91811yescharacteristic
316C3×C4C2×#21611yescharacteristic
317C3×C4#95111yescharacteristic
318Dic3—22no—
319Dic3—41no—
320Dic3—42no—
321Dic3—62no—
322Dic3—62no—
323Dic3—122no—
324Dic3—121no—
325Dic3—121no—
326Dic3—241no—
327C32#164511yescharacteristic, complemented, Sylow
328Q8—32no—
329Q8—41no—
330Q8—41no—
331Q8—61no—
332Q8—92no—
333Q8—122no—
334Q8—181no—
335Q8—722no—
336C2×C4—41no—
337C2×C4—61no—
338C2×C4—61no—
339C2×C4—62no—
340C2×C4—181no—
341C2×C4—181no—
342C2×C4D3×#6711yescharacteristic
343C2×C4D3×#6711yescharacteristic
344C2×C4#381111yescharacteristic
345C8—121no—
346C8—121no—
347C8—361no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3#505011yescharacteristic
352C2×C3#506111yescharacteristic
353C2×C3#517011yescharacteristic
354C2×C3#517011yescharacteristic
355C2×C3#518611yescharacteristic
356C2×C3#520211yescharacteristic
357C22#6398311yescharacteristic
358C4—21no—
359C4—62no—
360C4—81no—
361C4—122no—
362C4—121no—
363C4—182no—
364C4—361no—
365C4#6393011yescharacteristic
366C4#6393111yescharacteristic
367C4D3×#21611yescharacteristic
368C4#6394311yescharacteristic
369C3—21no—
370C3#7112911yescharacteristic, complemented
371C3#7123911yescharacteristic, complemented
372C2#1059151811yescharacteristic
373C2#1059165311yescharacteristic
374C2#1059165911yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#120
hypercenterC4⋊Q8D32
hypocenterC32#1645
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
120. C3×Dic6Q16semidirect
260. Dic6#216semidirect
327. C32#1645semidirect
370. C3#71129semidirect
371. C3#71239semidirect

Maximal subgroups

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

subgroupindex
#105938562
#105927892
C3×#50942
C3×#50932
#105890952
#105890852
#105890842
#712393
#711293