Finite Group Databasebeta

← #11789944

Subgroups — #11789944

Order 1152.

388 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 60 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#10593823C211yesmaximal, characteristic
2C2×#63783C211yesmaximal, characteristic
3C2×C8×#157C211yesmaximal, characteristic, complemented
4#10593755C211yesmaximal, characteristic, complemented
5#10592471C211yesmaximal, characteristic
6#10590185C211yesmaximal, characteristic, complemented
7#10590164C211yesmaximal, characteristic, complemented
8C2×#3830C2211yescharacteristic
9C2×C4×#157C2211yescharacteristic
10C2×#3788C2211yescharacteristic
11C2×#3788C2211yescharacteristic
12C2×#3787C2211yescharacteristic
13C2×C8×C3⋊D3C2211yescharacteristic
14#64101C2211yescharacteristic
15C22⋊#622—21no—
16C22⋊#622—21no—
17#63783—22no—
18#63779—21no—
19C4⋊#622—21no—
20C8×#157—22no—
21C32×#102C411yescharacteristic, complemented
22#63659C411yescharacteristic, complemented
23#63643C411yescharacteristic, complemented
24#63637C411yescharacteristic, complemented
25#4772—62no—
26C22×#157—21no—
27C2×C32×D4C2×C411yescharacteristic
28C2×#638—21no—
29C22×C3⋊Dic3—21no—
30#3830—21no—
31#3830—21no—
32#3830—21no—
33#3830—21no—
34C2×C4×C3⋊D3C2311yescharacteristic
35C2×#634C2×C411yescharacteristic
36C2×#622—21no—
37C2×#622—21no—
38C2×#622D411yescharacteristic
39C2×#622D411yescharacteristic
40C4×#157—21no—
41C4×#157D412yes—
42#3788—21no—
43#3788—21no—
44#3788—21no—
45#3788—21no—
46#3787—21no—
47#3787—21no—
48C2×C32×C8C2×C411yescharacteristic
49C32×C4⋊C4C2×C411yescharacteristic
50#3752—21no—
51C4⋊(C3⋊Dic3)C2×C411yescharacteristic
52C4×C3⋊Dic3—21no—
53C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
54C8×C3⋊D3—21no—
55C8×C3⋊D3—21no—
56#1937—91nomaximal, Sylow
57C2×#237—62no—
58C2×D3×C8—62no—
59#892—62no—
60C3×#102—22no—
61#832—62no—
62#816—62no—
63#810—62no—
64C23×C32—21no—
65C22×C3⋊D3#4111yescharacteristic
66C2×#157—22no—
67C2×#157—22no—
68C2×#157—22no—
69C32×D4—21no—
70C32×D4—21no—
71C2×C32×C4—21no—
72C2×C32×C4C22×C411yescharacteristic
73#638—41no—
74#638—41no—
75C2×C3⋊Dic3—21no—
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3—41no—
78C2×C3⋊Dic3—41no—
79C2×C3⋊Dic3C2×D411yescharacteristic
80C4×C3⋊D3C2×D411yescharacteristic
81C4×C3⋊D3#4111yescharacteristic
82C4×C3⋊D3#4111yescharacteristic
83C4×C3⋊D3#4111yescharacteristic
84#634—21no—
85#634—21no—
86#622—21no—
87#622—21no—
88#622—41no—
89#622—41no—
90C32×C8—21no—
91C3⋊(C3⋊C8)—21no—
92#424—91no—
93C2×#104—91no—
94#416—91no—
95#408—91no—
96C2×C4×C8—91no—
97#341—91no—
98#339—91no—
99C2×C3×D4—22no—
100C2×#67—122no—
101C22×Dic3—122no—
102#237—64no—
103#237—64no—
104#237—122no—
105#237—122no—
106C2×C4×D3—62no—
107C2×Dic6—62no—
108C2×C3×C8—22no—
109C3×C4⋊C4—22no—
110(C2×D3)⋊C4—122no—
111C4⋊Dic3—62no—
112C4×Dic3—122no—
113C2×C3⋊C8—62no—
114D3×C8—122no—
115D3×C8—122no—
116C22×C32—41no—
117C22×C32—41no—
118C22×C32—41no—
119C22×C32C4×D411yescharacteristic
120C2×C3⋊D3—21no—
121C2×C3⋊D3—21no—
122C2×C3⋊D3#12311yescharacteristic
123C2×C3⋊D3#12611yescharacteristic
124#157—24no—
125C32×C4—41no—
126C32×C4#11711yescharacteristic
127C32×C4C4×D411yescharacteristic
128C3⋊Dic3—41no—
129C3⋊Dic3—41no—
130C3⋊Dic3#12111yescharacteristic
131C3⋊Dic3#12411yescharacteristic
132C2×#41—91no—
133C2×M16—91no—
134C2×M16—91no—
135C22×C8—91no—
136C22×C8—91no—
137#117—91no—
138C2×C42—91no—
139C4⋊C8—181no—
140C4⋊C8—181no—
141#104—182no—
142#103—91no—
143#103—91no—
144#102—91no—
145#102#15711yescharacteristic, complemented
146C22⋊C8—181no—
147C22⋊C8—181no—
148C4×C8—182no—
149C23×C3—42no—
150C22×D3—62no—
151C3×D4—24no—
152C3×D4—42no—
153C2×C3×C4—22no—
154C2×C3×C4—42no—
155#67—124no—
156#67—124no—
157C2×Dic3—62no—
158C2×Dic3—122no—
159C2×Dic3—122no—
160C2×Dic3—124no—
161C2×Dic3—124no—
162C4×D3—62no—
163C4×D3—62no—
164C4×D3—62no—
165C4×D3—62no—
166Dic6—64no—
167Dic6—122no—
168C3×C8—42no—
169C3⋊C8—122no—
170C2×C32—81no—
171C2×C32#38811yescharacteristic
172C2×C32#44311yescharacteristic
173C2×C32#44311yescharacteristic
174C3⋊D3—21no—
175C3⋊D3—21no—
176#41—181no—
177#41—181no—
178#41—181no—
179#41—181no—
180C2×Q8—91no—
181C2×D4—181no—
182C2×D4C2×#15711yescharacteristic
183C22×C4—91no—
184C22×C4—181no—
185C22×C4—181no—
186M16—181no—
187M16—181no—
188M16—181no—
189M16—181no—
190C2×C8—91no—
191C2×C8—91no—
192C2×C8—91no—
193C2×C8—181no—
194C2×C8—181no—
195C2×C8—181no—
196C2×C8—181no—
197C2×C8—181no—
198C2×C8—181no—
199C2×C8C2×#15711yescharacteristic
200C4⋊C4—91no—
201C4⋊C4C2×#15711yescharacteristic
202C22⋊C4—181no—
203C42—92no—
204C42—181no—
205C42—181no—
206C22×C3—22no—
207C22×C3—44no—
208C22×C3—82no—
209C22×C3—82no—
210C2×D3—62no—
211C2×D3—62no—
212C2×D3—122no—
213C2×D3—122no—
214C3×C4—22no—
215C3×C4—22no—
216C3×C4—82no—
217Dic3—62no—
218Dic3—62no—
219Dic3—124no—
220Dic3—242no—
221C32#193711yescharacteristic, complemented, Sylow
222C23—21no—
223C23—91no—
224Q8—181no—
225Q8—181no—
226D4—21no—
227D4—21no—
228D4—361no—
229D4—361no—
230C2×C4—21no—
231C2×C4—91no—
232C2×C4—91no—
233C2×C4—91no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—182no—
237C2×C4—182no—
238C2×C4—182no—
239C2×C4—181no—
240C2×C4—181no—
241C2×C4—361no—
242C2×C4—361no—
243C2×C4C22×#15711yescharacteristic
244C8—21no—
245C8—181no—
246C8—181no—
247C8—181no—
248C8—361no—
249C8—361no—
250C2×C3—22no—
251C2×C3—22no—
252C2×C3—22no—
253C2×C3—84no—
254D3—122no—
255D3—122no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—91no—
260C22—91no—
261C22—181no—
262C22—181no—
263C22D4×#15711yescharacteristic
264C4—41no—
265C4—91no—
266C4—91no—
267C4—184no—
268C4—361no—
269C4—361no—
270C4#6428611yescharacteristic
271C4D4×#15711yescharacteristic
272C3—22no—
273C2—81no—
274C2—181no—
275C2—181no—
276C2#1059374711yescharacteristic
277C2#1059377911yescharacteristic
278C2#1059378311yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#102C4
socleC22×C32C4×D4
prime radicalC2×#3830C22
cosocleC2×C4×C3⋊D3C23
hypercenter#102#157
hypocenterC32#1937
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
3. C2×C8×#157C2semidirect
4. #10593755C2semidirect
6. #10590185C2semidirect
7. #10590164C2semidirect
21. C32×#102C4semidirect
22. #63659C4semidirect
23. #63643C4semidirect
24. #63637C4semidirect
145. #102#157semidirect
221. C32#1937semidirect

Maximal subgroups

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

subgroupindex
#105938232
C2×#637832
C2×C8×#1572
#105937552
#105924712
#105901852
#105901642
#19379