Finite Group Databasebeta

← #11785592

Subgroups — #11785592

Order 1152.

661 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 661 conjugacy classes of subgroups — too many to draw. Only its 156 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×#64157C211yesmaximal, characteristic
2C3×#5232C212yesmaximal
3C2×#63578C211yesmaximal, characteristic, complemented
4C2×#63574C211yesmaximal, characteristic, complemented
5#10589167C212yesmaximal, complemented
6#70299—32nomaximal
7C2×C32×#41C2211yescharacteristic
8#64157—22no—
9#64157C414yescomplemented
10C2×#3748—21no—
11C2×#3748C2211yescharacteristic
12C22×C3⋊(C3⋊C8)—21no—
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C2×C3×#208C2212yes—
16C3×#835—22no—
17C3×#832—22no—
18#63578—22no—
19#63574—21no—
20#63574—21no—
21C2×#948—32no—
22C2×#948—61no—
23C3×#417—32no—
24#5232D312yes—
25C2×#822—32no—
26C2×#808—32no—
27#4554—32no—
28#4530—32no—
29C32×#41—21no—
30C32×#41—21no—
31C32×#41C2×C412yes—
32C32×#41Q812yes—
33C2×C32×Q8D411yescharacteristic
34C2×C32×D4—21no—
35C2×C32×D4D411yescharacteristic
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C22×C3×Dic3—22no—
39#3748—21no—
40#3748—24no—
41#3748C2×C412yes—
42C2×C3⋊(C3⋊C8)—21no—
43C2×C3⋊(C3⋊C8)—24no—
44C2×C3⋊(C3⋊C8)C2×C412yes—
45C2×C3⋊(C3⋊C8)D411yescharacteristic
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47C2×C3⋊(C3⋊C8)D412yes—
48C3×C4⋊Dic3—22no—
49C3×C4⋊Dic3—22no—
50C3×#208—22no—
51C3×#208—22no—
52C2×C3×C3⋊C8—22no—
53#1815—91noSylow
54C2×C3×#41—21no—
55C2×C3×#41C2×D312yes—
56C2×C3×M16—32no—
57C2×C3×C4⋊C4—32no—
58#948—38no—
59#948—64no—
60#948—64no—
61#948—64no—
62C2×C4⋊Dic3C2×D312yes—
63C2×#208—32no—
64C2×#208—61no—
65C2×#208—62no—
66C2×#208—62no—
67C2×#208C2×D312yes—
68C22×C3⋊C8—32no—
69C22×C3⋊C8—61no—
70C22×C3⋊C8—62no—
71C22×C3⋊C8—62no—
72C3×#103—62no—
73C3×#102—62no—
74#835—22no—
75#832—22no—
76#822—64no—
77#808—62no—
78#808—62no—
79C23×C32—21no—
80C23×C32#4111yescharacteristic
81C32×Q8—21no—
82C32×Q8C4⋊C412yes—
83C32×D4—22no—
84C32×D4—22no—
85C32×D4—21no—
86C32×D4C4⋊C412yes—
87C2×C32×C4—21no—
88C2×C32×C4—22no—
89C2×C32×C4—22no—
90C2×C32×C4C22×C411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×Q811yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3×Dic3—42no—
97C2×C3×Dic3—82no—
98C3⋊(C3⋊C8)—22no—
99C3⋊(C3⋊C8)C22⋊C412yes—
100C3⋊(C3⋊C8)C22⋊C412yes—
101C3×C3⋊C8—42no—
102C2×#131—91no—
103C2×#108—91no—
104C2×#106—91no—
105#417—32no—
106#343—92no—
107C3×#41—22no—
108C3×#41—22no—
109C3×#41—22no—
110C3×#41—22no—
111C3×#41—22no—
112C3×#41—22no—
113C3×#41Dic614yes—
114C3×#41C4×D314yes—
115C2×C3×Q8—21no—
116C2×C3×Q8#6712yes—
117C2×C3×D4—22no—
118C2×C3×D4—22no—
119C2×C3×D4—21no—
120C2×C3×D4#6712yes—
121C22×C3×C4—22no—
122C22×C3×C4—22no—
123C22×C3×C4—21no—
124C22×C3×C4—62no—
125C22×C3×C4C22×D312yes—
126C22×Dic3—22no—
127C3×M16—62no—
128C3×M16—62no—
129C2×C3×C8—62no—
130C3×C4⋊C4—62no—
131C3×C4⋊C4—62no—
132C4⋊Dic3—22no—
133C4⋊Dic3—22no—
134#208—22no—
135#208—22no—
136#208—34no—
137#208—62no—
138#208—68no—
139#208—68no—
140#208—62no—
141#208—62no—
142C2×C3⋊C8—22no—
143C2×C3⋊C8—34no—
144C2×C3⋊C8—32no—
145C2×C3⋊C8—32no—
146C2×C3⋊C8—34no—
147C2×C3⋊C8—61no—
148C2×C3⋊C8—61no—
149C2×C3⋊C8—62no—
150C2×C3⋊C8—62no—
151C2×C3⋊C8—68no—
152C2×C3⋊C8—62no—
153C2×C3⋊C8—68no—
154C2×C3⋊C8—62no—
155C22×C32—22no—
156C22×C32—22no—
157C22×C32—42no—
158C22×C32#11711yescharacteristic
159C22×C32#12111yescharacteristic
160C22×C32C22⋊Q811yescharacteristic
161C32×C4—22no—
162C32×C4C2×C22⋊C411yescharacteristic
163C32×C4C2×C4⋊C411yescharacteristic
164C32×C4#12111yescharacteristic
165C32×C4C22⋊Q811yescharacteristic
166C3×Dic3—82no—
167C2×#41D3211yescharacteristic
168#131—94no—
169#131—182no—
170C2×M16—32no—
171C2×M16—91no—
172C2×M16—181no—
173C22×C8—91no—
174C22×C8—181no—
175C2×C4⋊C4—32no—
176#108—182no—
177#106—181no—
178#106—181no—
179#103—62no—
180#102—62no—
181C23×C3—22no—
182C23×C3—22no—
183C23×C3—21no—
184C23×C3#23712yes—
185C3×Q8—22no—
186C3×Q8—22no—
187C3×Q8—22no—
188C3×Q8Dic3⋊C414yes—
189C3×D4—24no—
190C3×D4—24no—
191C3×D4—22no—
192C3×D4—24no—
193C3×D4—24no—
194C3×D4—22no—
195C3×D4—22no—
196C3×D4Dic3⋊C414yes—
197C2×C3×C4—24no—
198C2×C3×C4—22no—
199C2×C3×C4—24no—
200C2×C3×C4—22no—
201C2×C3×C4—24no—
202C2×C3×C4—24no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—122no—
210C2×C3×C4—242no—
211C2×C3×C4C2×Dic612yes—
212C2×C3×C4C2×C4×D312yes—
213C2×C3×C4D3×D412yes—
214C2×C3×C4D3×D412yes—
215C2×C3×C4#23712yes—
216C2×C3×C4C2×#6712yes—
217C2×Dic3—42no—
218C2×Dic3—82no—
219C3×C8—122no—
220C3⋊C8—34no—
221C3⋊C8—34no—
222C3⋊C8—42no—
223C3⋊C8—62no—
224C3⋊C8—62no—
225C3⋊C8—64no—
226C3⋊C8—64no—
227C2×C32—21no—
228C2×C32—21no—
229C2×C32—42no—
230C2×C32#38011yescharacteristic
231C2×C32#47112yes—
232#41—21no—
233#41—21no—
234#41#62412yes—
235#41#62712yes—
236C2×Q8#62511yescharacteristic
237C2×D4—21no—
238C2×D4#62511yescharacteristic
239C22×C4—21no—
240C22×C4—62no—
241C22×C4C2×D3211yescharacteristic
242M16—62no—
243M16—62no—
244M16—92no—
245M16—184no—
246M16—181no—
247C2×C8—62no—
248C2×C8—92no—
249C2×C8—91no—
250C2×C8—91no—
251C2×C8—92no—
252C2×C8—184no—
253C2×C8—181no—
254C4⋊C4—62no—
255C4⋊C4—62no—
256C22×C3—22no—
257C22×C3—22no—
258C22×C3—24no—
259C22×C3—24no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—42no—
264C22×C3—44no—
265C22×C3—42no—
266C22×C3—42no—
267C22×C3#87712yes—
268C22×C3#87812yes—
269C22×C3#93912yes—
270C3×C4—24no—
271C3×C4—24no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—242no—
277C3×C4#87812yes—
278C3×C4D3×C22⋊C412yes—
279C3×C4C2×Dic3⋊C412yes—
280C3×C4#93912yes—
281Dic3—82no—
282C32#181511yescharacteristic, complemented, Sylow
283C23—21no—
284C23#380511yescharacteristic
285Q8—21no—
286Q8#372412yes—
287D4—22no—
288D4—22no—
289D4—21no—
290D4#372412yes—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—122no—
295C2×C4—242no—
296C2×C4#380511yescharacteristic
297C2×C4C2×#62411yescharacteristic
298C2×C4C2×#62511yescharacteristic
299C2×C4C2×#62711yescharacteristic
300C2×C4#381111yescharacteristic
301C2×C4#381111yescharacteristic
302C8—92no—
303C8—92no—
304C8—122no—
305C8—182no—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—22no—
309C2×C3—21no—
310C2×C3—41no—
311C2×C3—41no—
312C2×C3—44no—
313C2×C3—44no—
314C2×C3#494212yes—
315C2×C3#520012yes—
316C2×C3#520312yes—
317C22—22no—
318C22—22no—
319C22—42no—
320C22#6395711yescharacteristic
321C22#6398011yescharacteristic
322C22#6398211yescharacteristic
323C4—22no—
324C4—242no—
325C4C2×#372411yescharacteristic
326C4#6397411yescharacteristic
327C4#6398011yescharacteristic
328C4#6398211yescharacteristic
329C3—21no—
330C3#7029912yescomplemented
331C2—21no—
332C2—21no—
333C2—42no—
334C2#1059168112yes—
335C2#1059172011yescharacteristic
subgroupG/H
centerC22#63980
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32#121
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1815
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
3. C2×#63578C2semidirect
4. C2×#63574C2semidirect
5. #10589167C2semidirect
9. #64157C4semidirect
282. C32#1815semidirect
330. C3#70299semidirect

Maximal subgroups

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

subgroupindex
C2×#641572
C3×#52322
C2×#635782
C2×#635742
#105891672
#702993