Finite Group Databasebeta

← #11784930

Subgroups — #11784930

Order 1152.

1644 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 1644 conjugacy classes of subgroups — too many to draw. Only its 221 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#10596756C211yesmaximal, characteristic
2C32×#410C211yesmaximal, characteristic, complemented
3#10592933C211yesmaximal, characteristic, complemented
4#10592704C212yesmaximal, complemented
5#10592701C212yesmaximal, complemented
6#70054—34nomaximal
7C2×C32×#41C2211yescharacteristic
8#64367—22no—
9#64366—22no—
10#41×C3⋊D3—24no—
11#64364C412yescomplemented
12#64361—22no—
13#64361C412yescomplemented
14C2×#3828—22no—
15C2×#3828C2212yes—
16C32×#117C2212yescomplemented
17C2×#3748C2211yescharacteristic, complemented
18C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
19C32×#99—22no—
20#63657—22no—
21#63637—22no—
22#63636—22no—
23#63632—24no—
24#5964—34no—
25C3×#410D314yescomplemented
26#5234—34no—
27#5005—38no—
28#5002—38no—
29C32×#41—22no—
30C32×#41—22no—
31C2×C32×Q8C2×C411yescharacteristic
32C2×C32×D4C2×C411yescharacteristic
33C2×C32×D4D412yes—
34C22×C32×C4D412yes—
35C22×C32×C4C2311yescharacteristic
36C2×#638—24no—
37C2×#638—22no—
38#3832—24no—
39Q8×C3⋊D3—24no—
40#3830—28no—
41#3830—24no—
42D4×C3⋊D3—28no—
43D4×C3⋊D3—24no—
44#3828—24no—
45#3828—24no—
46#3828—24no—
47#3828—22no—
48#3828—22no—
49#3828C2×C414yes—
50#3828D414yes—
51C2×C4⋊(C3⋊D3)—22no—
52C2×C4⋊(C3⋊D3)D412yes—
53C2×C4×C3⋊D3—24no—
54C2×C4×C3⋊D3—22no—
55C2×#634—22no—
56C2×#634D412yes—
57C32×C4⋊C4—22no—
58C32×C22⋊C4—22no—
59C32×C42—22no—
60#3748—22no—
61C2×C3⋊(C3⋊C8)—22no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64#1794—91noSylow
65C2×C3×#41C2×D314yes—
66#1010—68no—
67#1009—68no—
68D3×#41—616no—
69#1007—38no—
70#1004—38no—
71#1004—68no—
72C2×#235—38no—
73C2×#235—68no—
74C3×#117C2×D318yescomplemented
75C2×#208—34no—
76C22×C3⋊C8—34no—
77C3×#99—28no—
78#830—68no—
79#810—68no—
80#809—68no—
81#805—616no—
82C23×C32C22⋊C412yes—
83C23×C32C2×D411yescharacteristic
84C22×C3⋊D3—24no—
85C22×C3⋊D3—22no—
86C32×Q8—22no—
87C32×D4—24no—
88C32×D4—22no—
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4—42no—
92C2×C32×C4C22⋊C412yes—
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D412yes—
96C2×C32×C4C2×D412yes—
97#638—28no—
98#638—24no—
99#638—24no—
100C2×C3⋊Dic3—24no—
101C2×C3⋊Dic3—22no—
102C4⋊(C3⋊D3)—24no—
103C4⋊(C3⋊D3)—22no—
104C4⋊(C3⋊D3)C22⋊C414yes—
105C4×C3⋊D3—28no—
106C4×C3⋊D3—24no—
107C4×C3⋊D3—24no—
108#634—24no—
109#634—22no—
110#634C22⋊C414yes—
111C3⋊(C3⋊C8)—41no—
112C3⋊(C3⋊C8)—41no—
113#585—91no—
114#421—92no—
115#416—92no—
116#410C3⋊D311yescharacteristic, complemented
117#408—91no—
118C3×#41—28no—
119C3×#41—28no—
120C2×C3×Q8C4×D314yes—
121C2×C3×D4C4×D314yes—
122C2×C3×D4#6718yes—
123C22×C3×C4D1218yes—
124C22×C3×C4C22×D314yes—
125C2×#67—616no—
126C2×#67—68no—
127#239—616no—
128D3×Q8—616no—
129#237—616no—
130#237—632no—
131D3×D4—616no—
132D3×D4—632no—
133#235—316no—
134#235—316no—
135#235—616no—
136#235—616no—
137#235—616no—
138#235—68no—
139#235—68no—
140C2×D12—38no—
141C2×D12—68no—
142C2×C4×D3—616no—
143C2×C4×D3—68no—
144C2×Dic6—38no—
145C2×Dic6—68no—
146C3×C4⋊C4—28no—
147C3×C22⋊C4—28no—
148C3×C42—28no—
149#208—68no—
150C2×C3⋊C8—64no—
151C2×C3⋊C8—64no—
152C2×C3⋊C8—68no—
153C22×C32—22no—
154C22×C32—41no—
155C22×C32—42no—
156C22×C32C2×C22⋊C411yescharacteristic
157C22×C32#12012yes—
158C2×C3⋊D3—24no—
159C2×C3⋊D3—82no—
160C2×C3⋊D3—84no—
161C32×C4—22no—
162C32×C4—82no—
163C32×C4C2×C22⋊C412yes—
164C32×C4#12011yescharacteristic
165C32×C4#12011yescharacteristic
166C3⋊Dic3—24no—
1672−1+4—92no—
1682−1+4—182no—
169H(5,𝔽2)—92no—
170H(5,𝔽2)—182no—
171H(5,𝔽2)—182no—
172C2×#41—92no—
173C2×#41—184no—
174C2×#41—182no—
175C2×#41C2×C3⋊D311yescharacteristic
176C2×M16—91no—
177C22×C8—91no—
178#117C2×C3⋊D312yescomplemented
179#104—184no—
180#103—182no—
181#102—182no—
182#99—22no—
183C22⋊C8—182no—
184C23×C3(C2×D3)⋊C418yes—
185C23×C3C2×#6714yes—
186C22×D3—616no—
187C22×D3—68no—
188C3×Q8—28no—
189C3×D4—216no—
190C3×D4—28no—
191C2×C3×C4—28no—
192C2×C3×C4—28no—
193C2×C3×C4—48no—
194C2×C3×C4(C2×D3)⋊C418yes—
195C2×C3×C4C2×C4×D314yes—
196C2×C3×C4C2×D1214yes—
197C2×C3×C4D3×D418yes—
198C2×C3×C4D3×D418yes—
199#67—632no—
200#67—616no—
201#67—616no—
202C2×Dic3—616no—
203C2×Dic3—68no—
204D12—316no—
205D12—616no—
206D12—68no—
207C4×D3—632no—
208C4×D3—616no—
209C4×D3—616no—
210Dic6—316no—
211Dic6—616no—
212Dic6—68no—
213C3⋊C8—124no—
214C3⋊C8—124no—
215C2×C32—22no—
216C2×C32—21no—
217C2×C32—42no—
218C2×C32#37911yescharacteristic
219C3⋊D3—44no—
220#41—22no—
221#41—22no—
222#41—94no—
223#41—94no—
224#41—184no—
225#41—184no—
226#41—184no—
227#41—188no—
228#41—184no—
229#41—184no—
230#41—182no—
231#41—182no—
232C2×Q8—92no—
233C2×Q8—182no—
234C2×Q8—184no—
235C2×Q8C4×C3⋊D311yescharacteristic
236C2×D4—92no—
237C2×D4—182no—
238C2×D4—184no—
239C2×D4—188no—
240C2×D4—184no—
241C2×D4—182no—
242C2×D4C4×C3⋊D311yescharacteristic
243C2×D4#63812yes—
244C22×C4—184no—
245C22×C4—182no—
246C22×C4C4⋊(C3⋊D3)12yes—
247C22×C4C22×C3⋊D311yescharacteristic
248M16—182no—
249C2×C8—181no—
250C2×C8—181no—
251C2×C8—182no—
252C4⋊C4—22no—
253C22⋊C4—22no—
254C42—22no—
255C22×C3—28no—
256C22×C3—44no—
257C22×C3—48no—
258C22×C3C2×(C2×D3)⋊C414yes—
259C22×C3#93718yes—
260C2×D3—616no—
261C2×D3—248no—
262C2×D3—2416no—
263C3×C4—28no—
264C3×C4—88no—
265C3×C4D3×C22⋊C418yes—
266C3×C4#88214yes—
267C3×C4#88214yes—
268Dic3—616no—
269C32#179411yescharacteristic, complemented, Sylow
270C23—184no—
271C23—182no—
272C23#375212yes—
273C23C2×#63811yescharacteristic
274Q8—22no—
275Q8—94no—
276Q8—184no—
277Q8—182no—
278D4—24no—
279D4—22no—
280D4—94no—
281D4—184no—
282D4—188no—
283D4—184no—
284D4—184no—
285D4—182no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—42no—
289C2×C4—188no—
290C2×C4—184no—
291C2×C4—182no—
292C2×C4—184no—
293C2×C4—184no—
294C2×C4#375212yes—
295C2×C4C2×C4×C3⋊D311yescharacteristic
296C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
297C2×C4D4×C3⋊D312yes—
298C2×C4D4×C3⋊D312yes—
299C8—361no—
300C8—361no—
301C2×C3—28no—
302C2×C3—24no—
303C2×C3—48no—
304C2×C3#495514yes—
305D3—1216no—
306C22—22no—
307C22—41no—
308C22—42no—
309C22—184no—
310C22—722no—
311C22—724no—
312C22C2×#375211yescharacteristic
313C22#6414612yes—
314C4—22no—
315C4—82no—
316C4—184no—
317C4C22⋊C4×C3⋊D312yes—
318C4#6409111yescharacteristic
319C4#6409111yescharacteristic
320C3#7005414yescomplemented
321C2—22no—
322C2—21no—
323C2—42no—
324C2—364no—
325C2#1059265411yescharacteristic
subgroupG/H
centerC4#64091
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#410C2
socleC2×C32#379
prime radical#10596756C2
cosocleC22×C32×C4C23
hypercenter#410C3⋊D3
hypocenterC32#1794
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. C32×#410C2semidirect
3. #10592933C2semidirect
4. #10592704C2semidirect
5. #10592701C2semidirect
11. #64364C4semidirect
13. #64361C4semidirect
16. C32×#117C22semidirect
17. C2×#3748C22semidirect
18. C22×C3⋊(C3⋊C8)C22semidirect
25. C3×#410D3semidirect
74. C3×#117C2×D3semidirect
116. #410C3⋊D3semidirect
178. #117C2×C3⋊D3semidirect
269. C32#1794semidirect
320. C3#70054semidirect

Maximal subgroups

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

subgroupindex
#105967562
C32×#4102
#105929332
#105927042
#105927012
#700543