Finite Group Databasebeta

← #11780167

Subgroups — #11780167

Order 1152.

423 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 423 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593861C211yesmaximal, characteristic
2C3×#4851C211yesmaximal, characteristic
3#10590388C211yesmaximal, characteristic
4#10590312C211yesmaximal, characteristic
5#10589350C211yesmaximal, characteristic
6C3×#4486C211yesmaximal, characteristic
7#10589083C211yesmaximal, characteristic
8#71130—31nomaximal
9#68460—31nomaximal
10C4×#634C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63872—21no—
15#63866—21no—
16#63846—22no—
17#63843—21no—
18Dic3×Dic6—21no—
19C2×#3719—21no—
20C32×C4⋊C8C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#817—21no—
23C3×#816—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63576—22no—
26#63566—21no—
27#5721—31no—
28#5570—31no—
29C3×#475—31no—
30#5090—31no—
31#5078—31no—
32#5078—31no—
33#4851D311yescharacteristic
34#4849—31no—
35C3×#332—31no—
36#4535—31no—
37#4486D311yescharacteristic
38#4484—31no—
39#4484—31no—
40#4484—31no—
41#4484—61no—
42C2×#634D411yescharacteristic
43C2×C3×Dic6—21no—
44C2×C3×Dic6—21no—
45C2×C3×Dic6D411yescharacteristic
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48C4⋊(C3⋊Dic3)D411yescharacteristic
49#3750—21no—
50C4×C3⋊Dic3—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3D412yes—
56C3×C4⋊Dic3D411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C2×C3×C3⋊C8—21no—
60Dic3⋊Dic3—22no—
61Dic3⋊Dic3—22no—
62Dic3⋊Dic3—22no—
63Dic32—22no—
64#3719—42no—
65#1648—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8—31no—
68C3×C4×Q8—31no—
69Q8×Dic3—61no—
70Q8×Dic3—61no—
71#944—61no—
72C2×#216—61no—
73C2×Dic12—61no—
74#890—61no—
75#890—62no—
76#890—61no—
77#889—62no—
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×#106—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C2×D311yescharacteristic
92C3×#103—61no—
93#835—61no—
94#817—21no—
95#816—21no—
96#816—61no—
97#807—62no—
98#807—62no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4×C3⋊C8—31no—
101C4×C3⋊C8—31no—
102C4×C3⋊C8—61no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C3⋊Dic3—21no—
107C2×C3⋊Dic3—21no—
108#634—21no—
109#634—21no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—41no—
114C3×Dic6—21no—
115C3×Dic6—41no—
116C3×Dic6—41no—
117C3×Dic6—41no—
118C3×Dic6—41no—
119C3×Dic6Q1612yescomplemented
120C32×C8—41no—
121C3⋊(C3⋊C8)—22no—
122C3×C3⋊C8—41no—
123#557—91no—
124#500—91no—
125#475—31no—
126#462—91no—
127#332—31no—
128Q8⋊C8—91no—
129Q8⋊C8—91no—
130C2×C3×Q8—31no—
131C2×C3×Q8—61no—
132C2×C3×Q8—61no—
133C2×Dic6—21no—
134C2×Dic6—21no—
135C2×Dic6—31no—
136C2×Dic6—31no—
137C2×Dic6—61no—
138C2×Dic6#6711yescharacteristic
139C2×C3×C8—21no—
140C2×C3×C8—21no—
141C2×C3×C8—41no—
142C2×C3×C8—61no—
143C3×C4⋊C4—32no—
144C3×C4⋊C4—31no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C42—21no—
150C3×C42—61no—
151C3×C42C22×D311yescharacteristic
152C3×C42C22×D311yescharacteristic
153#216—122no—
154C4⋊Dic3—21no—
155C4⋊Dic3—21no—
156C4⋊Dic3—21no—
157C4⋊Dic3—31no—
158C4⋊Dic3—31no—
159C4⋊Dic3—61no—
160C4⋊Dic3—62no—
161C4⋊Dic3—62no—
162C4⋊Dic3—62no—
163C4⋊Dic3D1212yes—
164C4⋊Dic3#6711yescharacteristic
165Dic3⋊C4—21no—
166Dic3⋊C4—62no—
167Dic3⋊C4—62no—
168Dic3⋊C4—62no—
169Dic3⋊C4—61no—
170Dic3⋊C4—61no—
171Dic3⋊C4—121no—
172C4×Dic3—21no—
173C4×Dic3—62no—
174C4×Dic3—62no—
175C4×Dic3—61no—
176C4×Dic3—61no—
177C4×Dic3—121no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—61no—
181C2×C3⋊C8—121no—
182Dic12—122no—
183C22×C32#12011yescharacteristic
184C32×C4—21no—
185C32×C4C2×Q1611yescharacteristic
186C32×C4#13511yescharacteristic
187C32×C4AGL(1,ℤ/8)11yescharacteristic
188C32×C4#13711yescharacteristic
189C3⋊Dic3—41no—
190C3⋊Dic3—41no—
191C3×Dic3—22no—
192C3×Dic3—42no—
193C3×Dic3—41no—
194C3×Dic3—81no—
195C2×Q16—181no—
196C4⋊Q8—31no—
197C4⋊Q8—31no—
198C4⋊Q8—181no—
199#125—182no—
200#125—181no—
201C4×Q8—31no—
202C4×Q8—91no—
203C4×Q8—181no—
204C4×Q8—181no—
205#107—182no—
206#106—61no—
207C4⋊C8—31no—
208C4⋊C8D3211yescharacteristic
209#103—61no—
210#103—181no—
211C4×C8—91no—
212C3×Q8—32no—
213C3×Q8—61no—
214C3×Q8—121no—
215C3×Q8—121no—
216C3×Q8—121no—
217C3×Q8—121no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—61no—
222C2×C3×C4—61no—
223C2×C3×C4—62no—
224C2×C3×C4—121no—
225C2×C3×C4C2×D1211yescharacteristic
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4D3×D411yescharacteristic
228C2×C3×C4D3×D411yescharacteristic
229C2×C3×C4D3×D411yescharacteristic
230C2×C3×C4C2×#6711yescharacteristic
231C2×Dic3—21no—
232C2×Dic3—22no—
233C2×Dic3—21no—
234C2×Dic3—41no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—121no—
240C2×Dic3—121no—
241Dic6—21no—
242Dic6—41no—
243Dic6—41no—
244Dic6—41no—
245Dic6—41no—
246Dic6—62no—
247Dic6—61no—
248Dic6—61no—
249Dic6—61no—
250Dic6—61no—
251Dic6—121no—
252Dic6#21612yescomplemented
253C3×C8—41no—
254C3×C8—41no—
255C3×C8—81no—
256C3×C8—121no—
257C3⋊C8—41no—
258C3⋊C8—62no—
259C3⋊C8—62no—
260C3⋊C8—122no—
261C2×C32#44911yescharacteristic
262C2×C32#45111yescharacteristic
263C2×C32#45611yescharacteristic
264C2×Q8—31no—
265C2×Q8—61no—
266C2×Q8—61no—
267C2×Q8—91no—
268Q16—362no—
269C2×C8—21no—
270C2×C8—61no—
271C2×C8—181no—
272C4⋊C4—32no—
273C4⋊C4—31no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—91no—
279C4⋊C4—182no—
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—122no—
299C3×C4—121no—
300C3×C4—241no—
301C3×C4#91111yescharacteristic
302C3×C4#91411yescharacteristic
303C3×C4#91511yescharacteristic
304C3×C4#91611yescharacteristic
305C3×C4#91611yescharacteristic
306C3×C4D3×Q1611yescharacteristic
307C3×C4C2×#21611yescharacteristic
308C3×C4#95111yescharacteristic
309Dic3—22no—
310Dic3—41no—
311Dic3—42no—
312Dic3—81no—
313Dic3—122no—
314Dic3—121no—
315Dic3—121no—
316Dic3—121no—
317Dic3—121no—
318Dic3—241no—
319C32#164811yescharacteristic, complemented, Sylow
320Q8—32no—
321Q8—61no—
322Q8—121no—
323Q8—121no—
324Q8—121no—
325Q8—121no—
326Q8—181no—
327Q8—181no—
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—182no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3#475211yescharacteristic
344C2×C3#478111yescharacteristic
345C2×C3#480911yescharacteristic
346C2×C3#505011yescharacteristic
347C2×C3#517211yescharacteristic
348C2×C3#520511yescharacteristic
349C22#6392211yescharacteristic
350C4—21no—
351C4—62no—
352C4—121no—
353C4—122no—
354C4—241no—
355C4—361no—
356C4—361no—
357C4#6379811yescharacteristic
358C4#6380911yescharacteristic
359C4#6392911yescharacteristic
360C4D3×#21611yescharacteristic
361C3—21no—
362C3#6846011yescharacteristic, complemented
363C3#7113011yescharacteristic, complemented
364C2#1059060411yescharacteristic
365C2#1059096411yescharacteristic
366C2#1059101811yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#120
hypercenterC4⋊C8D32
hypocenterC32#1648
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
119. C3×Dic6Q16semidirect
252. Dic6#216semidirect
319. C32#1648semidirect
362. C3#68460semidirect
363. C3#71130semidirect

Maximal subgroups

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

subgroupindex
#105938612
C3×#48512
#105903882
#105903122
#105893502
C3×#44862
#105890832
#711303
#684603