Finite Group Databasebeta

← #11773815

Subgroups — #11773815

Order 1152.

683 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 683 conjugacy classes of subgroups — too many to draw. Only its 112 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×#63902C211yesmaximal, characteristic
2#10592417C211yesmaximal, characteristic, complemented
3#10591061C211yesmaximal, characteristic, complemented
4C3×#4468C212yesmaximal, complemented
5#10589145C212yesmaximal, complemented
6#68101—32nomaximal
7C22×#625C411yescharacteristic
8C22×D3×Dic3C412yes—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×C3×(C2×D3)⋊C4C2212yes—
11C2×#3724C411yescharacteristic
12#63902—21no—
13#63902—21no—
14#63902—21no—
15#63902—21no—
16C32×C22⋊C8C2211yescharacteristic
17#63657C2211yescharacteristic
18#63641—21no—
19C8×C3⋊Dic3—21no—
20C3×#830C2212yes—
21#63572—21no—
22#63553—21no—
23C2×#67⋊C4—32no—
24#4718—32no—
25#4718—32no—
26#4718—61no—
27C3×#323—32no—
28#4525—32no—
29#4468—32no—
30#4468D312yescomplemented
31C23×C3×D3C2×C412yes—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3⋊Dic3C2×C411yescharacteristic
35C22×C3×Dic3C2×C412yes—
36C2×#625—21no—
37C2×#625—21no—
38C2×#625—22no—
39C2×#625C814yescomplemented
40C2×D3×Dic3—22no—
41C2×D3×Dic3—22no—
42C2×D3×Dic3—44no—
43C2×C32×C8—21no—
44C4×C3⋊Dic3D411yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C2×C3⋊(C3⋊C8)—21no—
49C3×(C2×D3)⋊C4—22no—
50C3×(C2×D3)⋊C4—22no—
51C2×C3×C3⋊C8—22no—
52#3724—21no—
53#3724—21no—
54#1460—91noSylow
55C22×#67—32no—
56C23×Dic3—32no—
57C22×C4×D3—32no—
58C2×C3×C22⋊C4—32no—
59C2×(C2×D3)⋊C4C2×D312yes—
60C2×Dic3⋊C4—32no—
61C2×C4×Dic3—32no—
62C2×C4×Dic3—61no—
63#67⋊C4—62no—
64#67⋊C4—62no—
65#67⋊C4—62no—
66#67⋊C4—62no—
67C3×C22⋊C8—21no—
68C3×C22⋊C8—32no—
69C3×C22⋊C8C2×D312yes—
70#830—32no—
71#830—61no—
72#830C2×D312yes—
73Dic3⋊C8—62no—
74Dic3⋊C8—62no—
75Dic3⋊C8—62no—
76C8×Dic3—62no—
77C8×Dic3—62no—
78C8×Dic3—62no—
79C23×C32C22×C411yescharacteristic
80C22×C3×D3—22no—
81C22×C3×D3—22no—
82C22×C3×D3—42no—
83C22×C3×D3—42no—
84C22×C3×D3C2×C814yes—
85C2×C32×C4—41no—
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3C22⋊C411yescharacteristic
90C2×C3⋊Dic3C22⋊C411yescharacteristic
91C2×C3⋊Dic3C22⋊C411yescharacteristic
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C2×C3⋊Dic3C2×C812yes—
94C2×C3⋊Dic3M1612yes—
95C2×C3×Dic3—22no—
96C2×C3×Dic3—42no—
97#625—24no—
98#625—24no—
99D3×Dic3—44no—
100D3×Dic3—44no—
101C32×C8—41no—
102C3⋊(C3⋊C8)—41no—
103C3×C3⋊C8—42no—
104C2×C4×D4—91no—
105#431—91no—
106#431—91no—
107#323—32no—
108#323—92no—
109C24×C3—32no—
110C23×D3C4×D312yes—
111C22×C3×C4—21no—
112C22×C3×C4—32no—
113C22×C3×C4C22×D312yes—
114C2×#67—38no—
115C2×#67—62no—
116C2×#67—62no—
117C2×#67—64no—
118C22×Dic3—32no—
119C22×Dic3—32no—
120C22×Dic3—61no—
121C22×Dic3—61no—
122C22×Dic3—62no—
123C22×Dic3—62no—
124C22×Dic3—124no—
125C22×Dic3C4×D312yes—
126C2×C4×D3—62no—
127C2×C4×D3—62no—
128C2×C4×D3—124no—
129C2×C3×C8—22no—
130C2×C3×C8—22no—
131C2×C3×C8—62no—
132C3×C22⋊C4—62no—
133C3×C22⋊C4—62no—
134(C2×D3)⋊C4—22no—
135(C2×D3)⋊C4—22no—
136Dic3⋊C4—62no—
137Dic3⋊C4—62no—
138C4×Dic3—32no—
139C4×Dic3—32no—
140C4×Dic3—32no—
141C4×Dic3—32no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C2×C3⋊C8—22no—
147C2×C3⋊C8—62no—
148C2×C3⋊C8—62no—
149C22×C32—21no—
150C22×C32—21no—
151C22×C32C2×C22⋊C411yescharacteristic
152C22×C32C22×C811yescharacteristic
153C22×C32C2×M1611yescharacteristic
154C2×C3×D3—24no—
155C2×C3×D3—44no—
156C2×C3×D3—42no—
157C2×C3×D3—42no—
158C2×C3×D3—44no—
159C32×C4—21no—
160C32×C4—21no—
161C3⋊Dic3—21no—
162C3⋊Dic3C22⋊C812yes—
163C3⋊Dic3C22⋊C812yes—
164C3⋊Dic3#10012yes—
165C3×Dic3—42no—
166C22×D4—91no—
167C23×C4—92no—
168C4×D4—181no—
169C4×D4—181no—
170C4×D4—181no—
171C4×D4—181no—
172C2×C4⋊C4—91no—
173C2×C22⋊C4—32no—
174C2×C42—91no—
175C4⋊C8—181no—
176C4⋊C8—181no—
177C22⋊C8—32no—
178C22⋊C8—91no—
179C22⋊C8D3211yescharacteristic
180C4×C8—181no—
181C4×C8—181no—
182C23×C3—21no—
183C23×C3—34no—
184C23×C3—62no—
185C23×C3—62no—
186C23×C3—122no—
187C23×C3—122no—
188C23×C3C2×C4×D312yes—
189C22×D3—22no—
190C22×D3—22no—
191C22×D3—42no—
192C22×D3—42no—
193C22×D3D3×C814yes—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—42no—
197C2×C3×C4—42no—
198C2×C3×C4—62no—
199C2×C3×C4—122no—
200C2×C3×C4D3×D412yes—
201C2×C3×C4D3×D412yes—
202#67—68no—
203#67—68no—
204C2×Dic3—22no—
205C2×Dic3—32no—
206C2×Dic3—32no—
207C2×Dic3—32no—
208C2×Dic3—34no—
209C2×Dic3—34no—
210C2×Dic3—32no—
211C2×Dic3—42no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—61no—
218C2×Dic3—64no—
219C2×Dic3—122no—
220C2×Dic3—124no—
221C2×Dic3—124no—
222C4×D3—124no—
223C4×D3—124no—
224C3×C8—42no—
225C3×C8—42no—
226C3×C8—122no—
227C3⋊C8—42no—
228C3⋊C8—122no—
229C3⋊C8—122no—
230C2×C32—21no—
231C2×C32—21no—
232C2×C32C2×C22⋊C811yescharacteristic
233C2×C32#41011yescharacteristic
234C2×C32C2×#10011yescharacteristic
235C3×D3—44no—
236C24—32no—
237C2×D4—94no—
238C2×D4—181no—
239C2×D4—181no—
240C2×D4—182no—
241C22×C4—32no—
242C22×C4—91no—
243C22×C4—91no—
244C22×C4—182no—
245C22×C4—182no—
246C22×C4—364no—
247C22×C4C2×D3211yescharacteristic
248C2×C8—21no—
249C2×C8—62no—
250C2×C8—181no—
251C4⋊C4—181no—
252C4⋊C4—181no—
253C22⋊C4—62no—
254C22⋊C4—62no—
255C42—91no—
256C42—91no—
257C42—91no—
258C42—91no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—64no—
267C22×C3—124no—
268C22×C3—124no—
269C22×C3—122no—
270C22×C3—122no—
271C22×C3D3×C22⋊C412yes—
272C22×C3C2×D3×C812yes—
273C22×C3D3×M1612yes—
274C2×D3—24no—
275C2×D3—44no—
276C2×D3—42no—
277C2×D3—42no—
278C2×D3—44no—
279C3×C4—22no—
280C3×C4—22no—
281C3×C4—22no—
282C3×C4—41no—
283C3×C4—122no—
284Dic3—34no—
285Dic3—34no—
286Dic3—34no—
287Dic3—42no—
288Dic3—62no—
289Dic3—62no—
290Dic3—62no—
291Dic3—62no—
292Dic3—121no—
293C32#146011yescharacteristic, complemented, Sylow
294C23—34no—
295C23—62no—
296C23—62no—
297C23—122no—
298C23—122no—
299C23C4×D3211yescharacteristic
300D4—184no—
301D4—184no—
302C2×C4—41no—
303C2×C4—62no—
304C2×C4—92no—
305C2×C4—92no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—91no—
309C2×C4—91no—
310C2×C4—122no—
311C2×C4—182no—
312C2×C4—364no—
313C2×C4—364no—
314C2×C4#380211yescharacteristic
315C2×C4#381111yescharacteristic
316C8—41no—
317C8—122no—
318C8—361no—
319C2×C3—22no—
320C2×C3—22no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—41no—
325C2×C3—41no—
326C2×C3—124no—
327C2×C3D3×C22⋊C812yes—
328C2×C3#474012yes—
329C2×C3D3×#10012yes—
330D3—44no—
331C22—21no—
332C22—21no—
333C22—64no—
334C22—124no—
335C22—124no—
336C22—122no—
337C22—122no—
338C22D32×C811yescharacteristic
339C22#6379111yescharacteristic
340C22#6392111yescharacteristic
341C4—21no—
342C4—21no—
343C4—92no—
344C4—92no—
345C4—92no—
346C4—122no—
347C4—181no—
348C3—21no—
349C3#6810112yescomplemented
350C2—21no—
351C2—21no—
352C2—124no—
353C2#1059040611yescharacteristic
354C2#1059093511yescharacteristic
355C2#1059100111yescharacteristic
subgroupG/H
centerC22#63921
commutatorC22×C32C22×C8
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#625C4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1460
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592417C2semidirect
3. #10591061C2semidirect
4. C3×#4468C2semidirect
5. #10589145C2semidirect
30. #4468D3semidirect
39. C2×#625C8semidirect
293. C32#1460semidirect
349. C3#68101semidirect

Maximal subgroups

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

subgroupindex
C2×#639022
#105924172
#105910612
C3×#44682
#105891452
#681013