Finite Group Databasebeta

← #11780017

Subgroups — #11780017

Order 1152.

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

normal subgroups only

This group has 435 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
2C3×#4681C211yesmaximal, characteristic
3#10590384C211yesmaximal, characteristic
4#10590307C211yesmaximal, characteristic
5#10589322C211yesmaximal, characteristic
6C3×#4456C211yesmaximal, characteristic
7#10589095C211yesmaximal, characteristic
8#71239—31nomaximal
9#68271—31nomaximal
10C4×#634C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63919—21no—
15#63918—21no—
16#63844—21no—
17#63843—21no—
18#63839—22no—
19C2×#3718—21no—
20C32×C4×C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#816—22no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63573—21no—
25#63567—21no—
26#63565—21no—
27#5722—31no—
28Q8×Dic6—31no—
29C3×#487—31no—
30#5094—31no—
31#5090—31no—
32#5031—31no—
33#4851—31no—
34#4681D311yescharacteristic
35C3×Q8⋊C8—31no—
36#4546—31no—
37#4481—31no—
38#4456—31no—
39#4456—31no—
40#4456—61no—
41#4456D311yescharacteristic
42C2×#634D411yescharacteristic
43C2×C3×Dic6—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C3×Dic6D412yes—
46C2×#627—22no—
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)D411yescharacteristic
50#3750—21no—
51C4×C3⋊Dic3—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—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—
61#3724—22no—
62Dic3⋊Dic3—22no—
63Dic32—22no—
64#3718—42no—
65#1645—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8—31no—
68C3×C4×Q8—31no—
69Q8×Dic3—61no—
70#944—62no—
71C2×#216—61no—
72C2×#216—61no—
73#888—61no—
74#888—61no—
75#888—62no—
76#888—61no—
77#887—61no—
78#887—61no—
79#869—61no—
80#869C2×D311yescharacteristic
81#869C2×D311yescharacteristic
82C4×Dic6—31no—
83C4×Dic6—31no—
84C4×Dic6—61no—
85C4×Dic6—61no—
86C4×Dic6C2×D311yescharacteristic
87C3×C4⋊C8—31no—
88C3×#103—62no—
89C3×C4×C8—21no—
90C3×C4×C8C2×D311yescharacteristic
91C3×C4×C8C2×D311yescharacteristic
92#835—61no—
93#817—61no—
94#816—22no—
95#816—61no—
96#810—61no—
97#810—61no—
98#808—61no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C3⋊Dic3—21no—
107C2×C3⋊Dic3—21no—
108#634—21no—
109#634Q1612yescomplemented
110C2×C3×Dic3—21no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—41no—
114C3×Dic6—21no—
115C3×Dic6—42no—
116C3×Dic6—41no—
117C3×Dic6—41no—
118C3×Dic6SD1612yes—
119#627—82no—
120C32×C8—41no—
121C3⋊(C3⋊C8)—41no—
122C3×C3⋊C8—41no—
123Q82—91no—
124#487—31no—
125#475—91no—
126#462—91no—
127#333—91no—
128Q8⋊C8—31no—
129Q8⋊C8—91no—
130C2×C3×Q8—31no—
131C2×C3×Q8—32no—
132C2×C3×Q8—61no—
133C2×Dic6—21no—
134C2×Dic6—31no—
135C2×Dic6—31no—
136C2×Dic6—61no—
137C2×Dic6—62no—
138C2×Dic6—62no—
139C2×Dic6D1211yescharacteristic
140C2×Dic6#6712yes—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C2×C3×C8—41no—
144C2×C3×C8—61no—
145C3×C4⋊C4—31no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C42—21no—
152C3×C42—61no—
153C3×C42C22×D311yescharacteristic
154C3×C42C22×D311yescharacteristic
155#216—122no—
156#216—122no—
157C4⋊Dic3—21no—
158C4⋊Dic3—21no—
159C4⋊Dic3—21no—
160C4⋊Dic3—21no—
161C4⋊Dic3—31no—
162C4⋊Dic3—31no—
163C4⋊Dic3—61no—
164C4⋊Dic3—62no—
165C4⋊Dic3D1211yescharacteristic
166Dic3⋊C4—21no—
167Dic3⋊C4—62no—
168Dic3⋊C4—62no—
169Dic3⋊C4—62no—
170Dic3⋊C4—61no—
171Dic3⋊C4—61no—
172Dic3⋊C4—121no—
173C4×Dic3—21no—
174C4×Dic3—62no—
175C4×Dic3—62no—
176C4×Dic3—61no—
177C4×Dic3—61no—
178C4×Dic3—121no—
179C2×C3⋊C8—21no—
180C2×C3⋊C8—61no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—121no—
183C22×C32#12011yescharacteristic
184C32×C4—21no—
185C32×C4C2×SD1611yescharacteristic
186C32×C4C2×Q1611yescharacteristic
187C32×C4#13711yescharacteristic
188C32×C4#13711yescharacteristic
189C3⋊Dic3—22no—
190C3⋊Dic3—41no—
191C3×Dic3—22no—
192C3×Dic3—41no—
193C3×Dic3—42no—
194C3×Dic3—81no—
195C2×Q16—181no—
196C4⋊Q8—31no—
197C4⋊Q8—31no—
198C4⋊Q8—181no—
199C4⋊Q8—181no—
200C4⋊Q8—182no—
201C4×Q8—31no—
202C4×Q8—91no—
203C4×Q8—181no—
204C4×Q8—181no—
205#106—181no—
206C4⋊C8—31no—
207C4⋊C8—91no—
208#103—62no—
209#103—181no—
210#103—181no—
211C4×C8D3211yescharacteristic
212C3×Q8—32no—
213C3×Q8—61no—
214C3×Q8—122no—
215C3×Q8—121no—
216C3×Q8—121no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—61no—
221C2×C3×C4—62no—
222C2×C3×C4—61no—
223C2×C3×C4—121no—
224C2×C3×C4C2×D1211yescharacteristic
225C2×C3×C4D3×D411yescharacteristic
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4D3×D411yescharacteristic
228C2×C3×C4D3×D411yescharacteristic
229C2×C3×C4C2×#6711yescharacteristic
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—22no—
233C2×Dic3—41no—
234C2×Dic3—61no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—121no—
239C2×Dic3—121no—
240Dic6—21no—
241Dic6—32no—
242Dic6—32no—
243Dic6—42no—
244Dic6—41no—
245Dic6—41no—
246Dic6—62no—
247Dic6—61no—
248Dic6—61no—
249Dic6—121no—
250Dic6—242no—
251Dic6—242no—
252Dic6#20412yes—
253C3×C8—41no—
254C3×C8—41no—
255C3×C8—42no—
256C3×C8—121no—
257C3⋊C8—41no—
258C3⋊C8—121no—
259C3⋊C8—121no—
260C3⋊C8—241no—
261C2×C32#44811yescharacteristic
262C2×C32#45111yescharacteristic
263C2×C32#45511yescharacteristic
264C2×Q8—31no—
265C2×Q8—32no—
266C2×Q8—61no—
267C2×Q8—91no—
268C2×Q8—182no—
269Q16—362no—
270C2×C8—21no—
271C2×C8—61no—
272C2×C8—181no—
273C4⋊C4—31no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C4⋊C4—91no—
280C4⋊C4—182no—
281C4⋊C4—182no—
282C4⋊C4—181no—
283C42—61no—
284C42—182no—
285C42—181no—
286C42C2×D3211yescharacteristic
287C22×C3—21no—
288C22×C3#88211yescharacteristic
289C22×C3#93711yescharacteristic
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—41no—
297C3×C4—62no—
298C3×C4—121no—
299C3×C4—122no—
300C3×C4—241no—
301C3×C4C2×#20411yescharacteristic
302C3×C4#90911yescharacteristic
303C3×C4D3×SD1611yescharacteristic
304C3×C4#91511yescharacteristic
305C3×C4#91511yescharacteristic
306C3×C4D3×Q1611yescharacteristic
307C3×C4D3×Q1611yescharacteristic
308C3×C4#91811yescharacteristic
309Dic3—22no—
310Dic3—42no—
311Dic3—41no—
312Dic3—62no—
313Dic3—62no—
314Dic3—81no—
315Dic3—122no—
316Dic3—121no—
317Dic3—121no—
318Dic3—241no—
319C32#164511yescharacteristic, complemented, Sylow
320Q8—32no—
321Q8—61no—
322Q8—92no—
323Q8—122no—
324Q8—121no—
325Q8—121no—
326Q8—181no—
327Q8—722no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—62no—
331C2×C4—121no—
332C2×C4—181no—
333C2×C4—181no—
334C2×C4D3×D1211yescharacteristic
335C2×C4#380211yescharacteristic
336C2×C4D3×#6711yescharacteristic
337C8—41no—
338C8—121no—
339C8—361no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3#473811yescharacteristic
344C2×C3#480911yescharacteristic
345C2×C3#482511yescharacteristic
346C2×C3#506111yescharacteristic
347C2×C3#517011yescharacteristic
348C2×C3#518611yescharacteristic
349C22#6392211yescharacteristic
350C4—21no—
351C4—62no—
352C4—122no—
353C4—121no—
354C4—182no—
355C4—241no—
356C4—361no—
357C4D3×#20411yescharacteristic
358C4#6380011yescharacteristic
359C4#6380211yescharacteristic
360C4#6381111yescharacteristic
361C3—21no—
362C3#6827111yescharacteristic, complemented
363C3#7123911yescharacteristic, complemented
364C2#1059039611yescharacteristic
365C2#1059082211yescharacteristic
366C2#1059095011yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#120
hypercenterC4×C8D32
hypocenterC32#1645
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
109. #634Q16semidirect
319. C32#1645semidirect
362. C3#68271semidirect
363. C3#71239semidirect

Maximal subgroups

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

subgroupindex
#105938562
C3×#46812
#105903842
#105903072
#105893222
C3×#44562
#105890952
#712393
#682713