Finite Group Databasebeta

← #11859098

Subgroups — #11859098

Order 1152.

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

normal subgroups only

This group has 702 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
1C4×#3830C211yesmaximal, characteristic
2#10593823C212yesmaximal
3#10593804C212yesmaximal, complemented
4#10593801C212yesmaximal, complemented
5#10593748C212yesmaximal, complemented
6#10593744C214yesmaximal, complemented
7#10593729C211yesmaximal, characteristic, complemented
8#10593726C211yesmaximal, characteristic, complemented
9C2×#3830C2211yescharacteristic
10C2×#3788C2212yes—
11C2×#3787C2212yes—
12C32×C4×D4C411yescharacteristic
13D4×C3⋊Dic3C411yescharacteristic
14C4×#638C412yes—
15C2×C4×C3⋊Dic3C2212yes—
16#64101C2211yescharacteristic
17#64096C411yescharacteristic
18#64090C412yes—
19#64086C2212yes—
20C42×C3⋊D3C2211yescharacteristic
21C4×#634C411yescharacteristic
22C22⋊#622C2214yes—
23C22⋊#622C2214yes—
24#63779C2211yescharacteristic
25#63779C2212yes—
26#63779C2211yescharacteristic
27#63779C2212yes—
28#63777C2214yes—
29C4⋊#622C2212yes—
30C4×#622C2214yes—
31C4×#237—62no—
32C2×C32×D4C2×C411yescharacteristic
33C22×C32×C4C2×C412yes—
34C2×#638C2×C412yes—
35C22×C3⋊Dic3C2×C412yes—
36C22×C3⋊Dic3C2312yes—
37#3830—22no—
38#3830—22no—
39C2×C4×C3⋊D3C2×C411yescharacteristic
40C2×C4×C3⋊D3C2×C411yescharacteristic
41C2×C4×C3⋊D3C2311yescharacteristic
42C2×#634C2×C411yescharacteristic
43C2×#622C2312yes—
44C2×#622C2312yes—
45C2×#622C2314yes—
46#3788—24no—
47#3787—24no—
48C32×C4⋊C4C2×C411yescharacteristic
49C32×C22⋊C4C2×C412yes—
50C32×C42C2×C411yescharacteristic
51#3757C2×C412yes—
52#3752C2×C412yes—
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54#3750C2×C412yes—
55#3750C2×C412yes—
56C4×C3⋊Dic3C2×C412yes—
57C4×C3⋊Dic3C2×C411yescharacteristic
58C4×C3⋊Dic3C2×C412yes—
59C4×C3⋊Dic3C2312yes—
60C4×C3⋊Dic3C2311yescharacteristic
61C4×C3⋊Dic3C2311yescharacteristic
62#2925—91nomaximal, Sylow
63C2×#237—62no—
64C3×C4×D4—22no—
65D4×Dic3—62no—
66C4×#67—64no—
67C2×C4×Dic3—64no—
68#892—62no—
69#887—62no—
70#67⋊C4—64no—
71#877—64no—
72C42×D3—62no—
73C4×Dic6—62no—
74C23×C32C22×C412yes—
75C22×C3⋊D3C22×C411yescharacteristic
76C32×D4—22no—
77C2×C32×C4—42no—
78C2×C32×C4C22×C411yescharacteristic
79C2×C32×C4C22×C412yes—
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C22×C411yescharacteristic
82#638—24no—
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—24no—
86C2×C3⋊Dic3C22×C412yes—
87C2×C3⋊Dic3C22×C411yescharacteristic
88C2×C3⋊Dic3C22×C412yes—
89C2×C3⋊Dic3C22×C411yescharacteristic
90C2×C3⋊Dic3C2411yescharacteristic
91C4×C3⋊D3—22no—
92C4×C3⋊D3—41no—
93C4×C3⋊D3#4112yes—
94C4×C3⋊D3#4112yes—
95#634—22no—
96#622—22no—
97#622—22no—
98#622—24no—
99C4×#41—91no—
100#433—94no—
101#432—92no—
102#431—92no—
103#423—91no—
104C2×C4⋊C8—91no—
105#408—92no—
106#405—92no—
107C2×C3×D4—22no—
108C22×C3×C4—24no—
109C2×#67—64no—
110C22×Dic3—64no—
111C22×Dic3—64no—
112#237—68no—
113#237—68no—
114C2×C4×D3—62no—
115C2×C4×D3—62no—
116C2×C4×D3—62no—
117C2×Dic6—62no—
118C3×C4⋊C4—22no—
119C3×C22⋊C4—24no—
120C3×C42—22no—
121#217—64no—
122(C2×D3)⋊C4—64no—
123C4⋊Dic3—62no—
124Dic3⋊C4—64no—
125Dic3⋊C4—64no—
126C4×Dic3—64no—
127C4×Dic3—62no—
128C4×Dic3—62no—
129C4×Dic3—62no—
130C4×Dic3—64no—
131C4×Dic3—64no—
132C22×C32—22no—
133C22×C32—22no—
134C22×C32—22no—
135C22×C32C23×C411yescharacteristic
136C2×C3⋊D3—21no—
137C2×C3⋊D3—21no—
138C2×C3⋊D3#11712yes—
139C32×C4—21no—
140C32×C4—21no—
141C32×C4—22no—
142C32×C4#11712yes—
143C3⋊Dic3—22no—
144C3⋊Dic3—22no—
145C3⋊Dic3—21no—
146C3⋊Dic3#13112yes—
147C3⋊Dic3C2×#4111yescharacteristic
148C3⋊Dic3C2×#4111yescharacteristic
149C2×#41—91no—
150C2×M16—92no—
151C22×C8—92no—
152C4×Q8—91no—
153C4×Q8—91no—
154C4×D4—91no—
155C4×D4—92no—
156C4×D4—92no—
157C4×D4#15711yescharacteristic
158#117—91no—
159#117—92no—
160C2×C42—92no—
161C2×C42—91no—
162C4⋊C8—92no—
163C4⋊C8—91no—
164C4⋊C8—91no—
165C4⋊C8—92no—
166C4⋊C8—92no—
167C22⋊C8—94no—
168C22⋊C8—94no—
169#97—94no—
170C4×C8—94no—
171C23×C3—24no—
172C22×D3—62no—
173C3×D4—28no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—24no—
177C2×C3×C4—22no—
178C2×C3×C4—48no—
179#67—616no—
180C2×Dic3—62no—
181C2×Dic3—64no—
182C2×Dic3—62no—
183C2×Dic3—62no—
184C2×Dic3—64no—
185C2×Dic3—68no—
186C2×Dic3—68no—
187C2×Dic3—128no—
188C4×D3—64no—
189C4×D3—64no—
190C4×D3—124no—
191C4×D3—124no—
192Dic6—68no—
193C2×C32—42no—
194C2×C32C2×#11711yescharacteristic
195C2×C32C2×#13111yescharacteristic
196C2×C32#56811yescharacteristic
197C3⋊D3—22no—
198#41—182no—
199#41—182no—
200C2×Q8—91no—
201C2×D4—92no—
202C2×D4C2×#15711yescharacteristic
203C22×C4—91no—
204C22×C4—92no—
205C22×C4—92no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4C2×#15712yes—
209M16—184no—
210C2×C8—92no—
211C2×C8—94no—
212C2×C8—92no—
213C2×C8—184no—
214C4⋊C4—92no—
215C4⋊C4—92no—
216C4⋊C4—91no—
217C4⋊C4C2×#15711yescharacteristic
218C22⋊C4—92no—
219C22⋊C4—92no—
220C22⋊C4C2×#15712yes—
221C42—92no—
222C42—91no—
223C42—91no—
224C42—91no—
225C42—92no—
226C42—92no—
227C42C2×#15711yescharacteristic
228C22×C3—28no—
229C22×C3—22no—
230C22×C3—44no—
231C22×C3—44no—
232C2×D3—64no—
233C2×D3—122no—
234C2×D3—122no—
235C3×C4—24no—
236C3×C4—24no—
237C3×C4—42no—
238C3×C4—44no—
239Dic3—62no—
240Dic3—62no—
241Dic3—64no—
242Dic3—68no—
243Dic3—122no—
244Dic3—124no—
245C32#292511yescharacteristic, complemented, Sylow
246C23—91no—
247C23C22×#15712yes—
248Q8—182no—
249D4—22no—
250D4—184no—
251C2×C4—42no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—92no—
255C2×C4—92no—
256C2×C4—91no—
257C2×C4—92no—
258C2×C4—92no—
259C2×C4—182no—
260C2×C4—182no—
261C2×C4—182no—
262C2×C4—184no—
263C2×C4—361no—
264C2×C4C22×#15711yescharacteristic
265C2×C4C22×#15712yes—
266C2×C4C22×#15711yescharacteristic
267C2×C4C22×#15711yescharacteristic
268C8—182no—
269C8—182no—
270C8—184no—
271C2×C3—22no—
272C2×C3—22no—
273C2×C3—22no—
274C2×C3—48no—
275D3—124no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—92no—
280C22—181no—
281C22—181no—
282C22C23×#15711yescharacteristic
283C4—21no—
284C4—22no—
285C4—21no—
286C4—91no—
287C4—91no—
288C4—92no—
289C4—182no—
290C4—181no—
291C4—182no—
292C4#6428612yes—
293C3—22no—
294C2—42no—
295C2—182no—
296C2C2×#6428611yescharacteristic
297C2#1059664011yescharacteristic
298C2#1059664711yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C4×D4C4
prime radicalC2×#3830C22
cosocleC2×C3⋊Dic3C24
hypercenterC4×D4#157
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10593804C2semidirect
4. #10593801C2semidirect
5. #10593748C2semidirect
6. #10593744C2semidirect
7. #10593729C2semidirect
8. #10593726C2semidirect
245. C32#2925semidirect

Maximal subgroups

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

subgroupindex
C4×#38302
#105938232
#105938042
#105938012
#105937482
#105937442
#105937292
#105937262
#29259