Finite Group Databasebeta

← #11795047

Subgroups — #11795047

Order 1152.

441 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 441 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C2×#63663C211yesmaximal, characteristic
2C3×#5225C211yesmaximal, characteristic
3C3×#5225C211yesmaximal, characteristic
4#10591141C211yesmaximal, characteristic
5#10589170C211yesmaximal, characteristic
6#10589169C211yesmaximal, characteristic
7#10589157C211yesmaximal, characteristic
8#70342—31nomaximal
9#70341—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3748C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63663—22no—
18C3×#835—22no—
19C3×#835—22no—
20#63577—22no—
21C3×#419—31no—
22C3×#419—31no—
23C2×#836—31no—
24C2×#836—31no—
25C2×#836—61no—
26#5225D311yescharacteristic
27#5225D311yescharacteristic
28#5125—31no—
29#5124—31no—
30#4559—31no—
31#4556—31no—
32#4533—31no—
33#4533—31no—
34#4531—31no—
35#4531—31no—
36C2×C32×Q8—21no—
37C2×C32×Q8—21no—
38C2×C32×Q8—21no—
39C2×C32×Q8—21no—
40C2×C32×Q8—21no—
41C2×C32×Q8D412yes—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44#3748—21no—
45#3748—21no—
46#3748—21no—
47#3748—21no—
48C2×C3⋊(C3⋊C8)—21no—
49C2×C3⋊(C3⋊C8)—21no—
50C3×#217—21no—
51C3×#217—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4×Dic3—21no—
55C3×C4×Dic3—21no—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208—21no—
59C3×#208—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8D412yes—
62#2082—91noSylow
63C22×C3×Q8—21no—
64C22×C3×Q8C2×D311yescharacteristic
65C22×C3×Q8C2×D311yescharacteristic
66C2×C3×M16—31no—
67C2×C3×M16—31no—
68C3×#117—31no—
69C3×#117—31no—
70#926C2×D311yescharacteristic
71#926C2×D311yescharacteristic
72C2×#208—31no—
73C2×#208—31no—
74C2×#208—31no—
75C2×#208—31no—
76C2×#208—61no—
77C2×#208—61no—
78C2×#208C2×D311yescharacteristic
79C2×#208C2×D311yescharacteristic
80C3×#103—62no—
81C3×#103—62no—
82#836—64no—
83#836—62no—
84#836—62no—
85#835—22no—
86#835—22no—
87#822—62no—
88#819—62no—
89C23×C32#4111yescharacteristic
90C32×Q8—22no—
91C32×Q8—22no—
92C32×Q8—41no—
93C32×Q8—41no—
94C2×C32×C4—22no—
95C2×C32×C4—41no—
96C2×C32×C4—41no—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C3×Dic3—41no—
104C2×C3×Dic3—41no—
105C3⋊(C3⋊C8)—41no—
106C3⋊(C3⋊C8)—41no—
107C3×C3⋊C8—22no—
108C3×C3⋊C8—41no—
109#430—91no—
110#419—31no—
111#419—31no—
112C2×#101—91no—
113#344—91no—
114#344—91no—
115H(3,ℤ/4)—91no—
116C2×C3×Q8—22no—
117C2×C3×Q8—21no—
118C2×C3×Q8—21no—
119C2×C3×Q8—21no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—21no—
123C2×C3×Q8—21no—
124C2×C3×Q8—21no—
125C2×C3×Q8—21no—
126C2×C3×Q8—21no—
127C2×C3×Q8—22no—
128C2×C3×Q8—41no—
129C2×C3×Q8—41no—
130C2×C3×Q8—41no—
131C2×C3×Q8—41no—
132C2×C3×Q8D1212yes—
133C2×C3×Q8#6712yes—
134C22×C3×C4—22no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4C22×D311yescharacteristic
139C22×C3×C4C22×D311yescharacteristic
140C3×M16—61no—
141C3×M16—61no—
142C3×M16—61no—
143C3×M16—61no—
144C2×C3×C8—32no—
145C2×C3×C8—61no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C22⋊C4—61no—
149C3×C22⋊C4—61no—
150C3×C42—61no—
151C3×C42—61no—
152#217—21no—
153#217—21no—
154C4⋊Dic3—21no—
155C4⋊Dic3—21no—
156C4×Dic3—21no—
157C4×Dic3—21no—
158#208—21no—
159#208—21no—
160#208—21no—
161#208—21no—
162#208—62no—
163#208—62no—
164#208—61no—
165#208—61no—
166#208—61no—
167#208—61no—
168#208—61no—
169#208—61no—
170#208—61no—
171#208—61no—
172#208—121no—
173#208—121no—
174C2×C3⋊C8—21no—
175C2×C3⋊C8—61no—
176C2×C3⋊C8—61no—
177C2×C3⋊C8—61no—
178C2×C3⋊C8—61no—
179C2×C3⋊C8—121no—
180C2×C3⋊C8—121no—
181C2×C3⋊C8#6712yes—
182C22×C32—41no—
183C22×C32#12311yescharacteristic
184C22×C32#12411yescharacteristic
185C22×C32#12611yescharacteristic
186C32×C4—42no—
187C32×C4#12111yescharacteristic
188C32×C4#12311yescharacteristic
189C32×C4#12311yescharacteristic
190C32×C4#12611yescharacteristic
191C3×Dic3—81no—
192C3×Dic3—81no—
193C22×Q8D3211yescharacteristic
194C2×M16—31no—
195C2×M16—31no—
196C2×M16—91no—
197C2×M16—91no—
198#117—31no—
199#117—31no—
200#108—182no—
201#103—62no—
202#103—62no—
203#101—182no—
204C23×C3—21no—
205C23×C3#23711yescharacteristic
206C23×C3#23711yescharacteristic
207C3×Q8—22no—
208C3×Q8—22no—
209C3×Q8—22no—
210C3×Q8—22no—
211C3×Q8—42no—
212C3×Q8—42no—
213C3×Q8—42no—
214C3×Q8—42no—
215C3×Q8—41no—
216C3×Q8—41no—
217C3×Q8—41no—
218C3×Q8—41no—
219C2×C3×C4—24no—
220C2×C3×C4—22no—
221C2×C3×C4—22no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4—121no—
235C2×C3×C4—121no—
236C2×C3×C4C2×D1211yescharacteristic
237C2×C3×C4#23511yescharacteristic
238C2×C3×C4#23511yescharacteristic
239C2×C3×C4#23511yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4#23711yescharacteristic
242C2×C3×C4#23711yescharacteristic
243C2×C3×C4#23711yescharacteristic
244C2×C3×C4#23711yescharacteristic
245C2×C3×C4#23711yescharacteristic
246C2×C3×C4C2×#6711yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248C2×Dic3—41no—
249C2×Dic3—41no—
250C3×C8—62no—
251C3×C8—121no—
252C3⋊C8—22no—
253C3⋊C8—41no—
254C3⋊C8—122no—
255C3⋊C8—122no—
256C3⋊C8—121no—
257C3⋊C8—121no—
258C3⋊C8—121no—
259C3⋊C8—121no—
260C2×C32—21no—
261C2×C32—21no—
262C2×C32—21no—
263C2×C32#39711yescharacteristic
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8#62612yes—
270C22×C4—21no—
271C22×C4C2×D3211yescharacteristic
272M16—61no—
273M16—61no—
274M16—61no—
275M16—61no—
276M16—181no—
277M16—181no—
278M16—181no—
279M16—181no—
280C2×C8—32no—
281C2×C8—61no—
282C2×C8—181no—
283C2×C8—181no—
284C4⋊C4—61no—
285C4⋊C4—61no—
286C22⋊C4—61no—
287C22⋊C4—61no—
288C42—61no—
289C42—61no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—42no—
296C22×C3#87911yescharacteristic
297C22×C3#87911yescharacteristic
298C22×C3#88511yescharacteristic
299C22×C3#88611yescharacteristic
300C22×C3#93511yescharacteristic
301C22×C3#93611yescharacteristic
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—44no—
307C3×C4—42no—
308C3×C4—42no—
309C3×C4—241no—
310C3×C4—241no—
311C3×C4#87911yescharacteristic
312C3×C4#87911yescharacteristic
313C3×C4#88311yescharacteristic
314C3×C4#88611yescharacteristic
315C3×C4#92911yescharacteristic
316C3×C4#93011yescharacteristic
317C3×C4#93511yescharacteristic
318C3×C4#93911yescharacteristic
319Dic3—81no—
320Dic3—81no—
321C32#208211yescharacteristic, complemented, Sylow
322C23#380511yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—121no—
331C2×C4—121no—
332C2×C4#380411yescharacteristic
333C2×C4#380411yescharacteristic
334C2×C4#380411yescharacteristic
335C2×C4#380511yescharacteristic
336C2×C4C2×#62611yescharacteristic
337C2×C4D3×#6711yescharacteristic
338C8—62no—
339C8—121no—
340C8—361no—
341C8—361no—
342C2×C3—22no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—41no—
351C2×C3—41no—
352C2×C3#495211yescharacteristic
353C2×C3#495311yescharacteristic
354C22—41no—
355C22#6395611yescharacteristic
356C22#6395911yescharacteristic
357C22#6396211yescharacteristic
358C4—42no—
359C4—241no—
360C4—241no—
361C4#6395611yescharacteristic
362C4#6396611yescharacteristic
363C4#6396911yescharacteristic
364C4#6397811yescharacteristic
365C3—21no—
366C3#7034111yescharacteristic, complemented
367C3#7034211yescharacteristic, complemented
368C2—21no—
369C2—21no—
370C2—21no—
371C2#1059171711yescharacteristic
subgroupG/H
centerC2#10591717
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC2×C32#397
prime radicalC23×C32#41
hypercenterC22×Q8D32
hypocenterC32#2082
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
321. C32#2082semidirect
366. C3#70341semidirect
367. C3#70342semidirect

Maximal subgroups

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

subgroupindex
C2×#636632
C3×#52252
#105911412
#105891702
#105891692
#105891572
#703423
#703413