Finite Group Databasebeta

← #11795053

Subgroups — #11795053

Order 1152.

415 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 415 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×#5004C211yesmaximal, characteristic
2#10591141C211yesmaximal, characteristic
3#10591100C211yesmaximal, characteristic
4C2×#63560C211yesmaximal, characteristic
5#10589397C211yesmaximal, characteristic
6C3×#4533C211yesmaximal, characteristic
7#10589171C211yesmaximal, characteristic
8#70341—31nomaximal
9#69023—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C32×#117C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#810—22no—
18#63577—22no—
19#63566—22no—
20#63560—22no—
21C3×#419—31no—
22C2×#836—31no—
23#5225—31no—
24C2×#824—31no—
25#5125—31no—
26#5124—31no—
27#5120—31no—
28#5004D311yescharacteristic
29C3×#344—31no—
30#4559—31no—
31#4556—31no—
32#4533D311yescharacteristic
33#4531—31no—
34#4531—31no—
35#4531—61no—
36C22×C32×C4C2311yescharacteristic
37C22×C3×Dic3—21no—
38C2×C3×Dic6—21no—
39C2×C3×Dic6—21no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6D412yes—
44C32×C4⋊C4—21no—
45C32×C22⋊C4—21no—
46C32×C42—21no—
47#3757—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4×C3⋊Dic3—21no—
50#3748—21no—
51#3748—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×#208—21no—
54C3×#208—21no—
55C3×#208—21no—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8D412yes—
62#2082—91noSylow
63C22×C3×Q8—31no—
64C22×Dic6C2×D311yescharacteristic
65C2×C3×M16—31no—
66C2×C3×M16—31no—
67C2×C3×M16—31no—
68C3×#117—21no—
69C3×#117C2×D311yescharacteristic
70C3×#117C2×D311yescharacteristic
71#926—31no—
72#926—31no—
73#926—61no—
74C2×#208—31no—
75C2×#208—31no—
76C2×#208—61no—
77C2×#208C2×D311yescharacteristic
78C2×#208C2×D311yescharacteristic
79C2×#208C2×D311yescharacteristic
80C3×#103—62no—
81#836—62no—
82#835—62no—
83#824—62no—
84#822—62no—
85#819—62no—
86#816—62no—
87#810—22no—
88C23×C32#4111yescharacteristic
89C2×C32×C4—41no—
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4#4111yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3⋊Dic3—41no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—41no—
100C3×Dic6—22no—
101C3×Dic6—22no—
102C3×Dic6—41no—
103C3×Dic6—41no—
104C3⋊(C3⋊C8)—41no—
105C3×C3⋊C8—22no—
106C3×C3⋊C8—41no—
107C3×C3⋊C8—41no—
108#430—91no—
109#419—31no—
110#419—91no—
111C2×#101—91no—
112#344—31no—
113#344—91no—
114H(3,ℤ/4)—91no—
115C2×C3×Q8—32no—
116C2×C3×Q8—61no—
117C2×C3×Q8—61no—
118C2×C3×Q8—61no—
119C2×C3×Q8—61no—
120C2×C3×Q8—61no—
121C22×C3×C4—21no—
122C22×C3×C4—61no—
123C22×C3×C4C22×D311yescharacteristic
124C22×C3×C4C22×D311yescharacteristic
125C22×Dic3—21no—
126C2×Dic6—21no—
127C2×Dic6—21no—
128C2×Dic6—21no—
129C2×Dic6—21no—
130C2×Dic6—21no—
131C2×Dic6D1212yes—
132C3×M16—61no—
133C3×M16—61no—
134C3×M16—61no—
135C3×M16—61no—
136C3×M16—61no—
137C3×M16—61no—
138C2×C3×C8—32no—
139C2×C3×C8—61no—
140C2×C3×C8—61no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—41no—
144C3×C22⋊C4—21no—
145C3×C22⋊C4—21no—
146C3×C22⋊C4—41no—
147C3×C42—22no—
148C3×C42—21no—
149C3×C42—21no—
150#217—61no—
151#217—61no—
152#217—121no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—121no—
156C4×Dic3—62no—
157C4×Dic3—61no—
158C4×Dic3—61no—
159#208—21no—
160#208—21no—
161#208—21no—
162#208—21no—
163#208—21no—
164#208—21no—
165#208—61no—
166#208—61no—
167#208—61no—
168#208—61no—
169#208—121no—
170#208—121no—
171C2×C3⋊C8—21no—
172C2×C3⋊C8—21no—
173C2×C3⋊C8—62no—
174C2×C3⋊C8—61no—
175C2×C3⋊C8—61no—
176C2×C3⋊C8#6712yes—
177C22×C32—41no—
178C22×C32#12311yescharacteristic
179C22×C32#12411yescharacteristic
180C22×C32#12611yescharacteristic
181C32×C4—81no—
182C32×C4#12111yescharacteristic
183C32×C4#12311yescharacteristic
184C32×C4#12311yescharacteristic
185C32×C4#12611yescharacteristic
186C3⋊Dic3—81no—
187C3×Dic3—42no—
188C22×Q8—31no—
189C2×M16—31no—
190C2×M16—31no—
191C2×M16—31no—
192C2×M16—91no—
193#117—91no—
194#117D3211yescharacteristic
195#108—182no—
196#103—62no—
197#103—182no—
198#101—182no—
199C23×C3—21no—
200C23×C3#23511yescharacteristic
201C23×C3#23711yescharacteristic
202C3×Q8—62no—
203C3×Q8—62no—
204C3×Q8—121no—
205C3×Q8—121no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—42no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—62no—
216C2×C3×C4—121no—
217C2×C3×C4—121no—
218C2×C3×C4C2×D1211yescharacteristic
219C2×C3×C4#23511yescharacteristic
220C2×C3×C4#23511yescharacteristic
221C2×C3×C4#23511yescharacteristic
222C2×C3×C4D3×D411yescharacteristic
223C2×C3×C4D3×D411yescharacteristic
224C2×C3×C4#23711yescharacteristic
225C2×C3×C4#23711yescharacteristic
226C2×C3×C4#23711yescharacteristic
227C2×C3×C4#23711yescharacteristic
228C2×C3×C4#23911yescharacteristic
229C2×C3×C4C2×#6711yescharacteristic
230C2×Dic3—22no—
231C2×Dic3—41no—
232C2×Dic3—41no—
233C2×Dic3—122no—
234C2×Dic3—121no—
235C2×Dic3—121no—
236Dic6—22no—
237Dic6—22no—
238Dic6—41no—
239Dic6—41no—
240C3×C8—62no—
241C3×C8—121no—
242C3×C8—121no—
243C3⋊C8—22no—
244C3⋊C8—41no—
245C3⋊C8—41no—
246C3⋊C8—122no—
247C3⋊C8—121no—
248C3⋊C8—121no—
249C2×C32—21no—
250C2×C32—21no—
251C2×C32—21no—
252C2×C32#39711yescharacteristic
253C2×Q8—32no—
254C2×Q8—61no—
255C2×Q8—61no—
256C2×Q8—61no—
257C2×Q8—61no—
258C2×Q8—61no—
259C22×C4—61no—
260C22×C4C2×D3211yescharacteristic
261M16—61no—
262M16—61no—
263M16—61no—
264M16—61no—
265M16—61no—
266M16—61no—
267M16—181no—
268M16—181no—
269C2×C8—32no—
270C2×C8—61no—
271C2×C8—61no—
272C2×C8—181no—
273C4⋊C4—21no—
274C4⋊C4—181no—
275C22⋊C4—21no—
276C22⋊C4—181no—
277C42—21no—
278C42—181no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—81no—
285C22×C3#87611yescharacteristic
286C22×C3#87911yescharacteristic
287C22×C3#88511yescharacteristic
288C22×C3#88611yescharacteristic
289C22×C3#89411yescharacteristic
290C22×C3#93611yescharacteristic
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—81no—
296C3×C4—81no—
297C3×C4—82no—
298C3×C4—122no—
299C3×C4#87911yescharacteristic
300C3×C4#88311yescharacteristic
301C3×C4#88411yescharacteristic
302C3×C4#88611yescharacteristic
303C3×C4#89411yescharacteristic
304C3×C4#89811yescharacteristic
305C3×C4#93011yescharacteristic
306C3×C4#93511yescharacteristic
307Dic3—42no—
308Dic3—241no—
309Dic3—241no—
310Dic3—242no—
311C32#208211yescharacteristic, complemented, Sylow
312C23#380411yescharacteristic
313Q8—62no—
314Q8—62no—
315Q8—121no—
316Q8—121no—
317C2×C4—41no—
318C2×C4—62no—
319C2×C4—121no—
320C2×C4—121no—
321C2×C4—361no—
322C2×C4#379511yescharacteristic
323C2×C4#379611yescharacteristic
324C2×C4#379811yescharacteristic
325C2×C4D3×D1211yescharacteristic
326C2×C4#380511yescharacteristic
327C2×C4D3×#6711yescharacteristic
328C8—62no—
329C8—121no—
330C8—121no—
331C8—361no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—41no—
340C2×C3—41no—
341C2×C3—41no—
342C2×C3#467511yescharacteristic
343C2×C3#495311yescharacteristic
344C22—41no—
345C22#6385911yescharacteristic
346C22#6389011yescharacteristic
347C22#6395911yescharacteristic
348C4—81no—
349C4—122no—
350C4—721no—
351C4#6386211yescharacteristic
352C4#6388411yescharacteristic
353C4#6389111yescharacteristic
354C4#6390611yescharacteristic
355C3—21no—
356C3#6902311yescharacteristic, complemented
357C3#7034111yescharacteristic, complemented
358C2—21no—
359C2—21no—
360C2—21no—
361C2#1059129711yescharacteristic
subgroupG/H
centerC2#10591297
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#397
prime radicalC23×C32#41
hypercenter#117D32
hypocenterC32#2082
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
311. C32#2082semidirect
356. C3#69023semidirect
357. C3#70341semidirect

Maximal subgroups

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

subgroupindex
C3×#50042
#105911412
#105911002
C2×#635602
#105893972
C3×#45332
#105891712
#703413
#690233