Finite Group Databasebeta

← #11780008

Subgroups — #11780008

Order 1152.

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

normal subgroups only

This group has 448 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#10592793C211yesmaximal, characteristic
3C3×#5093C211yesmaximal, characteristic
4C3×#5090C211yesmaximal, characteristic
5#10589095C211yesmaximal, characteristic
6#10589085C211yesmaximal, characteristic
7#10589084C211yesmaximal, characteristic
8#71239—31nomaximal
9#71063—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C2×C3×#216—21no—
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63919—21no—
16#63918—21no—
17#63844—21no—
18#63843—21no—
19#63839—22no—
20#63637—21no—
21#63635—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#835—21no—
24C3×#810—22no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27#5722—31no—
28Q8×Dic6—31no—
29C3×#487—31no—
30C3×#462—31no—
31#5094—31no—
32#5094—31no—
33#5094—61no—
34#5093D311yescharacteristic
35#5090D311yescharacteristic
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—42no—
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
66C2×C3×Q16—61no—
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—21no—
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×C4⋊C8—31no—
89C3×#103—62no—
90C3×#103—61no—
91C3×C4×C8—31no—
92#835—21no—
93#810—22no—
94#810—61no—
95#810—61no—
96#810—62no—
97#808—61no—
98#808—61no—
99#808—62no—
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#634Q1612yescomplemented
115C2×C3×Dic3—21no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—21no—
118C3×Dic6—21no—
119C3×Dic6—42no—
120C3×Dic6SD1612yes—
121#627—82no—
122C3⋊(C3⋊C8)—41no—
123C3×C3⋊C8—41no—
124C3×C3⋊C8—41no—
125Q82—91no—
126#487—31no—
127#475—91no—
128#462—31no—
129#333—91no—
130Q8⋊C8—91no—
131Q8⋊C8—91no—
132C2×C3×Q8—21no—
133C2×C3×Q8—21no—
134C2×C3×Q8—31no—
135C2×C3×Q8—32no—
136C2×C3×Q8—41no—
137C2×Dic6—31no—
138C2×Dic6—31no—
139C2×Dic6—61no—
140C2×Dic6—62no—
141C2×Dic6—62no—
142C2×Dic6#6711yescharacteristic
143C2×Dic6#6712yes—
144C3×Q16—122no—
145C2×C3×C8—61no—
146C2×C3×C8—61no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—41no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C42—21no—
158C3×C42—61no—
159C3×C42C22×D311yescharacteristic
160C3×C42C22×D311yescharacteristic
161#216—42no—
162C4⋊Dic3—21no—
163C4⋊Dic3—21no—
164C4⋊Dic3—31no—
165C4⋊Dic3—31no—
166C4⋊Dic3—61no—
167C4⋊Dic3—62no—
168C4⋊Dic3#6711yescharacteristic
169Dic3⋊C4—21no—
170Dic3⋊C4—62no—
171Dic3⋊C4—62no—
172Dic3⋊C4—62no—
173Dic3⋊C4—61no—
174Dic3⋊C4—61no—
175Dic3⋊C4—121no—
176C4×Dic3—21no—
177C4×Dic3—62no—
178C4×Dic3—62no—
179C4×Dic3—61no—
180C4×Dic3—61no—
181C4×Dic3—121no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—62no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C22×C32#12011yescharacteristic
188C32×C4—21no—
189C32×C4—81no—
190C32×C4C2×SD1611yescharacteristic
191C32×C4C2×Q1611yescharacteristic
192C32×C4#13711yescharacteristic
193C32×C4#13711yescharacteristic
194C3⋊Dic3—22no—
195C3⋊Dic3—41no—
196C3×Dic3—22no—
197C3×Dic3—41no—
198C3×Dic3—42no—
199C2×Q16—61no—
200C4⋊Q8—31no—
201C4⋊Q8—181no—
202C4⋊Q8—181no—
203C4⋊Q8—182no—
204C4⋊Q8D3211yescharacteristic
205C4×Q8—31no—
206C4×Q8—91no—
207C4×Q8—181no—
208C4×Q8—181no—
209#106—181no—
210C4⋊C8—31no—
211C4⋊C8—91no—
212#103—62no—
213#103—61no—
214#103—181no—
215C4×C8—31no—
216C3×Q8—32no—
217C3×Q8—41no—
218C3×Q8—41no—
219C3×Q8—41no—
220C3×Q8—41no—
221C3×Q8—61no—
222C3×Q8—81no—
223C3×Q8—81no—
224C3×Q8—122no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—42no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—61no—
232C2×C3×C4—62no—
233C2×C3×C4—61no—
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4C2×#6711yescharacteristic
239C2×C3×C4C2×#6711yescharacteristic
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—22no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—121no—
248C2×Dic3—121no—
249Dic6—21no—
250Dic6—32no—
251Dic6—32no—
252Dic6—42no—
253Dic6—62no—
254Dic6—61no—
255Dic6—61no—
256Dic6—121no—
257Dic6—242no—
258Dic6—242no—
259Dic6#21412yes—
260C3×C8—121no—
261C3×C8—121no—
262C3⋊C8—41no—
263C3⋊C8—41no—
264C3⋊C8—122no—
265C3⋊C8—121no—
266C3⋊C8—121no—
267C2×C32#44811yescharacteristic
268C2×C32#45111yescharacteristic
269C2×C32#45511yescharacteristic
270C2×Q8—21no—
271C2×Q8—31no—
272C2×Q8—32no—
273C2×Q8—91no—
274C2×Q8—182no—
275Q16—122no—
276C2×C8—61no—
277C2×C8—61no—
278C2×C8—181no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—31no—
282C4⋊C4—61no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4—91no—
286C4⋊C4—182no—
287C4⋊C4—182no—
288C4⋊C4—181no—
289C42—61no—
290C42—182no—
291C42—181no—
292C42C2×D3211yescharacteristic
293C22×C3—21no—
294C22×C3#93711yescharacteristic
295C22×C3#93711yescharacteristic
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—41no—
303C3×C4—62no—
304C3×C4—82no—
305C3×C4—81no—
306C3×C4—81no—
307C3×C4—122no—
308C3×C4—121no—
309C3×C4D3×SD1611yescharacteristic
310C3×C4#91511yescharacteristic
311C3×C4D3×Q1611yescharacteristic
312C3×C4D3×Q1611yescharacteristic
313C3×C4#91811yescharacteristic
314C3×C4#91811yescharacteristic
315C3×C4C2×#21411yescharacteristic
316C3×C4#95111yescharacteristic
317Dic3—22no—
318Dic3—41no—
319Dic3—42no—
320Dic3—62no—
321Dic3—62no—
322Dic3—122no—
323Dic3—121no—
324Dic3—121no—
325Dic3—241no—
326C32#164511yescharacteristic, complemented, Sylow
327Q8—32no—
328Q8—41no—
329Q8—41no—
330Q8—61no—
331Q8—92no—
332Q8—122no—
333Q8—181no—
334Q8—722no—
335C2×C4—41no—
336C2×C4—61no—
337C2×C4—61no—
338C2×C4—62no—
339C2×C4—181no—
340C2×C4—181no—
341C2×C4D3×#6711yescharacteristic
342C2×C4D3×#6711yescharacteristic
343C2×C4#381111yescharacteristic
344C8—121no—
345C8—121no—
346C8—361no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3#504011yescharacteristic
351C2×C3#506111yescharacteristic
352C2×C3#517011yescharacteristic
353C2×C3#518611yescharacteristic
354C2×C3#518611yescharacteristic
355C2×C3#520211yescharacteristic
356C22#6398311yescharacteristic
357C4—21no—
358C4—62no—
359C4—81no—
360C4—122no—
361C4—121no—
362C4—182no—
363C4—361no—
364C4D3×#21411yescharacteristic
365C4#6392911yescharacteristic
366C4#6394411yescharacteristic
367C4#6394511yescharacteristic
368C3—21no—
369C3#7106311yescharacteristic, complemented
370C3#7123911yescharacteristic, complemented
371C2#1059151711yescharacteristic
372C2#1059165411yescharacteristic
373C2#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
114. #634Q16semidirect
326. C32#1645semidirect
369. C3#71063semidirect
370. C3#71239semidirect

Maximal subgroups

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

subgroupindex
#105938562
#105927932
C3×#50932
C3×#50902
#105890952
#105890852
#105890842
#712393
#710633