Finite Group Databasebeta

← #11773715

Subgroups — #11773715

Order 1152.

1130 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 84 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×C22⋊C4×C3⋊D3C211yesmaximal, characteristic
2#10593800C212yesmaximal, complemented
3#10590222C212yesmaximal, complemented
4#10590204C212yesmaximal, complemented
5C24×C3⋊D3C411yescharacteristic
6C22×C4×C3⋊D3C411yescharacteristic
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×#3787—22no—
9C2×C32×C22⋊C4C411yescharacteristic
10C2×#3757C2211yescharacteristic
11C2×#3752C411yescharacteristic
12C2×#3752C2211yescharacteristic
13C22⋊C4×C3⋊D3—22no—
14C22⋊C4×C3⋊D3—22no—
15C22⋊#622C2214yescomplemented
16#63778—22no—
17C2×D3×C22⋊C4—62no—
18C24×C32C2×C411yescharacteristic
19C23×C3⋊D3—21no—
20C23×C3⋊D3—21no—
21C23×C3⋊D3—22no—
22C23×C3⋊D3—42no—
23C23×C3⋊D3—42no—
24C23×C3⋊D3C814yescomplemented
25C23×C3⋊D3C2×C411yescharacteristic
26C23×C3⋊D3C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2311yescharacteristic
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3—42no—
34C2×C4×C3⋊D3—42no—
35C2×C4×C3⋊D3D412yes—
36C2×C4×C3⋊D3D412yes—
37C2×#622—24no—
38#3787—44no—
39C32×C22⋊C4—22no—
40#3757—22no—
41#3752—22no—
42#3752—22no—
43C2×#323—91nomaximal, Sylow
44C24×D3—62no—
45C22×C4×D3—62no—
46C22×C4×D3—62no—
47C2×C3×C22⋊C4—22no—
48C2×#217—62no—
49C2×(C2×D3)⋊C4—62no—
50C2×(C2×D3)⋊C4—62no—
51D3×C22⋊C4—68no—
52D3×C22⋊C4—68no—
53C23×C32—21no—
54C23×C32—21no—
55C23×C32—41no—
56C23×C32—41no—
57C23×C32C2×C812yescomplemented
58C23×C32C22×C411yescharacteristic
59C22×C3⋊D3—22no—
60C22×C3⋊D3—22no—
61C22×C3⋊D3—21no—
62C22×C3⋊D3—21no—
63C22×C3⋊D3—24no—
64C22×C3⋊D3—24no—
65C22×C3⋊D3—42no—
66C22×C3⋊D3—42no—
67C22×C3⋊D3—48no—
68C22×C3⋊D3—48no—
69C22×C3⋊D3—42no—
70C22×C3⋊D3—42no—
71C22×C3⋊D3—41no—
72C22×C3⋊D3—41no—
73C22×C3⋊D3C22⋊C411yescharacteristic
74C22×C3⋊D3C22⋊C411yescharacteristic
75C22×C3⋊D3C2×C812yes—
76C22×C3⋊D3C2×C812yescomplemented
77C22×C3⋊D3M1612yes—
78C2×C32×C4—21no—
79C2×C32×C4—41no—
80C2×C32×C4—41no—
81C2×C32×C4C22⋊C412yes—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3C2×D412yes—
86C4×C3⋊D3—24no—
87C4×C3⋊D3—42no—
88C4×C3⋊D3—42no—
89C4×C3⋊D3—42no—
90#622—44no—
91C22×C22⋊C4—91no—
92C2×C22⋊C8—92no—
93#323—92no—
94#323—92no—
95C24×C3—22no—
96C23×D3—62no—
97C23×D3—68no—
98C23×D3—62no—
99C23×D3—64no—
100C23×D3—64no—
101C23×D3—68no—
102C23×D3—128no—
103C23×D3—128no—
104C22×C3×C4—22no—
105C22×C3×C4—22no—
106C22×Dic3—62no—
107C22×Dic3—62no—
108C2×C4×D3—64no—
109C2×C4×D3—64no—
110C2×C4×D3—64no—
111C2×C4×D3—64no—
112C2×C4×D3—128no—
113C2×C4×D3—128no—
114C3×C22⋊C4—28no—
115#217—68no—
116(C2×D3)⋊C4—68no—
117(C2×D3)⋊C4—68no—
118C22×C32—21no—
119C22×C32—21no—
120C22×C32—22no—
121C22×C32—42no—
122C22×C32—42no—
123C22×C32—41no—
124C22×C32—41no—
125C22×C32C2×C22⋊C411yescharacteristic
126C22×C32C22×C811yescharacteristic
127C22×C32C2×M1611yescharacteristic
128C2×C3⋊D3—21no—
129C2×C3⋊D3—21no—
130C2×C3⋊D3—24no—
131C2×C3⋊D3—24no—
132C2×C3⋊D3—22no—
133C2×C3⋊D3—48no—
134C2×C3⋊D3—42no—
135C2×C3⋊D3—41no—
136C2×C3⋊D3—41no—
137C2×C3⋊D3—48no—
138C2×C3⋊D3—42no—
139C2×C3⋊D3C22⋊C812yes—
140C2×C3⋊D3C22⋊C812yes—
141C2×C3⋊D3#9912yes—
142C2×C3⋊D3#10012yes—
143C32×C4—22no—
144C32×C4—41no—
145C3⋊Dic3—22no—
146C3⋊Dic3—41no—
147C25—91no—
148C23×C4—91no—
149C23×C4—91no—
150C22×C8—182no—
151C2×C22⋊C4—91no—
152C2×C22⋊C4—91no—
153C2×C22⋊C4—91no—
154C2×C22⋊C4—182no—
155C2×C22⋊C4—182no—
156C2×C22⋊C4#15711yescharacteristic
157C22⋊C8—94no—
158C22⋊C8—182no—
159C23×C3—24no—
160C23×C3—24no—
161C23×C3—22no—
162C23×C3—24no—
163C23×C3—44no—
164C23×C3—44no—
165C22×D3—62no—
166C22×D3—62no—
167C22×D3—64no—
168C22×D3—64no—
169C22×D3—64no—
170C22×D3—68no—
171C22×D3—68no—
172C22×D3—64no—
173C22×D3—616no—
174C22×D3—616no—
175C22×D3—64no—
176C22×D3—128no—
177C22×D3—128no—
178C22×D3—1232no—
179C22×D3—128no—
180C22×D3—128no—
181C22×D3—1232no—
182C22×D3—124no—
183C22×D3—124no—
184C2×C3×C4—24no—
185C2×C3×C4—24no—
186C2×C3×C4—44no—
187C2×C3×C4—44no—
188C2×Dic3—64no—
189C2×Dic3—64no—
190C2×Dic3—124no—
191C2×Dic3—124no—
192C4×D3—128no—
193C4×D3—128no—
194C4×D3—128no—
195C4×D3—128no—
196C2×C32—21no—
197C2×C32—21no—
198C2×C32—42no—
199C2×C32C2×C22⋊C811yescharacteristic
200C2×C32C2×#9911yescharacteristic
201C2×C32C2×#10011yescharacteristic
202C3⋊D3—22no—
203C3⋊D3—42no—
204C3⋊D3#32314yescomplemented
205C24—91no—
206C24—91no—
207C24—94no—
208C24—181no—
209C24—181no—
210C24—182no—
211C24—362no—
212C24—362no—
213C24C2×#15711yescharacteristic
214C22×C4—91no—
215C22×C4—92no—
216C22×C4—92no—
217C22×C4—91no—
218C22×C4—181no—
219C22×C4—181no—
220C22×C4—362no—
221C22×C4—362no—
222C22×C4C2×#15711yescharacteristic
223C22×C4C2×#15711yescharacteristic
224C2×C8—184no—
225C2×C8—364no—
226C22⋊C4—22no—
227C22⋊C4—182no—
228C22⋊C4—182no—
229C22⋊C4—182no—
230C22×C3—24no—
231C22×C3—24no—
232C22×C3—28no—
233C22×C3—22no—
234C22×C3—22no—
235C22×C3—22no—
236C22×C3—48no—
237C22×C3—48no—
238C22×C3—44no—
239C22×C3—44no—
240C2×D3—64no—
241C2×D3—64no—
242C2×D3—64no—
243C2×D3—64no—
244C2×D3—64no—
245C2×D3—64no—
246C2×D3—616no—
247C2×D3—616no—
248C2×D3—68no—
249C2×D3—1232no—
250C2×D3—1232no—
251C2×D3—128no—
252C2×D3—128no—
253C2×D3—124no—
254C2×D3—124no—
255C3×C4—44no—
256C3×C4—44no—
257Dic3—124no—
258Dic3—124no—
259C32C2×#32311yescharacteristic, complemented, Sylow
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23—91no—
265C23—92no—
266C23—92no—
267C23—91no—
268C23—92no—
269C23—182no—
270C23—182no—
271C23—184no—
272C23—184no—
273C23—181no—
274C23—181no—
275C23—361no—
276C23—361no—
277C23—362no—
278C23—362no—
279C23—368no—
280C23—368no—
281C23—362no—
282C23—362no—
283C23#378712yescomplemented
284C23C22×#15711yescharacteristic
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—92no—
289C2×C4—184no—
290C2×C4—181no—
291C2×C4—362no—
292C2×C4—362no—
293C2×C4—362no—
294C2×C4—361no—
295C2×C4—361no—
296C2×C4C22⋊#15712yes—
297C8—364no—
298C2×C3—24no—
299C2×C3—24no—
300C2×C3—22no—
301C2×C3—22no—
302C2×C3—22no—
303C2×C3—48no—
304D3—68no—
305D3—68no—
306D3—128no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22—42no—
311C22—42no—
312C22—41no—
313C22—41no—
314C22—92no—
315C22—92no—
316C22—92no—
317C22—92no—
318C22—184no—
319C22—184no—
320C22—181no—
321C22—181no—
322C22—182no—
323C22—362no—
324C22—362no—
325C22—368no—
326C22—368no—
327C22—361no—
328C22—361no—
329C22C2×#378711yescharacteristic
330C22#6428311yescharacteristic
331C22C2×C22⋊#15711yescharacteristic
332C4—22no—
333C4—41no—
334C4—182no—
335C4—361no—
336C3—22no—
337C2—21no—
338C2—21no—
339C2—42no—
340C2—94no—
341C2—182no—
342C2—362no—
343C2#1059380011yescharacteristic
344C2#1059381711yescharacteristic
345C2#1059382511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC22×C32C22×C8
FrattiniC23C22×#157
FittingC2×C32×C22⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC24×C3⋊D3C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C22⋊C4#157
hypocenterC32C2×#323
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10593800C2semidirect
3. #10590222C2semidirect
4. #10590204C2semidirect
15. C22⋊#622C22semidirect
24. C23×C3⋊D3C8semidirect
57. C23×C32C2×C8semidirect
76. C22×C3⋊D3C2×C8semidirect
204. C3⋊D3#323semidirect
259. C32C2×#323semidirect
283. C23#3787semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
#105938002
#105902222
#105902042
C2×#3239