Finite Group Databasebeta

← #11775152

Subgroups — #11775152

Order 1152.

633 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 633 conjugacy classes of subgroups — too many to draw. Only its 92 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#10594929C211yesmaximal, characteristic
2#10592347C211yesmaximal, characteristic, complemented
3#10591066C211yesmaximal, characteristic, complemented
4C3×#4451C212yesmaximal, complemented
5#10589150C212yesmaximal, complemented
6#68278—32nomaximal
7C2×#3805—21no—
8C2×C4×C3⋊Dic3—21no—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C3×#930C2212yes—
11#63980—21no—
12#63919C411yescharacteristic, complemented
13#63915—21no—
14#63914C411yescharacteristic, complemented
15#63902—21no—
16#63898C412yescomplemented
17C32×#95C2211yescharacteristic
18#63658—21no—
19#63658C2211yescharacteristic
20C3×#830C2212yes—
21#63572—21no—
22#63555—21no—
23#5596—32no—
24#4719—32no—
25#4648—32no—
26#4648—61no—
27C3×#327—32no—
28#4537—32no—
29#4470—32no—
30#4451D312yescomplemented
31C22×C32×C4—21no—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36C2×C3×#67—22no—
37C2×C3×D12C2×C412yes—
38C2×#627—21no—
39C2×#625—21no—
40C2×#625—21no—
41#3805—42no—
42#3805—42no—
43C2×D3×Dic3—22no—
44C4×C3⋊Dic3—24no—
45C4×C3⋊Dic3C2×C411yescharacteristic
46C4×C3⋊Dic3C2×C411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C3×(C2×D3)⋊C4—22no—
50C3×C4⋊Dic3C2×C412yes—
51C2×C3×C3⋊C8—22no—
52#3724—21no—
53(C2×D3)⋊Dic3—22no—
54#1505—91noSylow
55C2×#237—62no—
56C3×#121—32no—
57#940—32no—
58#939—62no—
59D4×Dic3—32no—
60#930C2×D312yes—
61C2×C4×Dic3—32no—
62C2×C4×Dic3—61no—
63C2×C4×Dic3—62no—
64C2×C4×Dic3—62no—
65#893—32no—
66#888—32no—
67#885—62no—
68#67⋊C4—62no—
69C3×C22⋊C8—32no—
70C3×#95—21no—
71C3×#95C2×D312yes—
72C3⋊#95—32no—
73C3⋊#95—61no—
74C3⋊#95—62no—
75C3⋊#95—62no—
76#830C2×D312yes—
77#815—62no—
78Dic3⋊C8—62no—
79C23×C32C2×D411yescharacteristic
80C22×C3×D3—22no—
81C2×C32×C4—22no—
82C2×C32×C4—41no—
83C2×C32×C4—41no—
84C2×C32×C4—41no—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—21no—
91C2×C3⋊Dic3—41no—
92C2×C3⋊Dic3—41no—
93C2×C3⋊Dic3C22⋊C411yescharacteristic
94C2×C3⋊Dic3C22⋊C411yescharacteristic
95C2×C3⋊Dic3C22⋊C411yescharacteristic
96C2×C3⋊Dic3C22⋊C411yescharacteristic
97C3×#67—42no—
98C3×#67—42no—
99C2×C3×Dic3—22no—
100C3×D12—42no—
101#627—42no—
102#625—42no—
103#625—42no—
104D3×Dic3—44no—
105C3×C3⋊C8—42no—
106#532—91no—
107#432—91no—
108#376—91no—
109#327—32no—
110#327—92no—
111C2×C3×D4—32no—
112C2×C3×D4—62no—
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—21no—
116C22×C3×C4C22×D312yes—
117C2×#67—22no—
118C2×#67—62no—
119C2×#67—62no—
120C22×Dic3—32no—
121C22×Dic3—32no—
122C22×Dic3—61no—
123C22×Dic3—61no—
124C22×Dic3—62no—
125C22×Dic3—62no—
126C22×Dic3—62no—
127#237—124no—
128#237—124no—
129C2×D12C4×D312yes—
130C2×C4×D3—62no—
131C2×Dic6—62no—
132C2×C3×C8—62no—
133C3×C4⋊C4—32no—
134C3×C22⋊C4—62no—
135#217—62no—
136(C2×D3)⋊C4—22no—
137(C2×D3)⋊C4—62no—
138C4⋊Dic3C4×D312yes—
139Dic3⋊C4—62no—
140C4×Dic3—32no—
141C4×Dic3—32no—
142C4×Dic3—32no—
143C4×Dic3—32no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C4×Dic3—68no—
149C4×Dic3—68no—
150C2×C3⋊C8—22no—
151C22×C32—21no—
152C22×C32—21no—
153C22×C32C2×C22⋊C411yescharacteristic
154C22×C32AGL(1,ℤ/8)11yescharacteristic
155C22×C32AGL(1,ℤ/8)11yescharacteristic
156C2×C3×D3—42no—
157C2×C3×D3—42no—
158C2×C3×D3—42no—
159C32×C4—21no—
160C32×C4—21no—
161C32×C4—42no—
162C3⋊Dic3—21no—
163C3⋊Dic3—21no—
164C3⋊Dic3—21no—
165C3⋊Dic3—42no—
166C3⋊Dic3#10412yes—
167C3×Dic3—42no—
168C2×#41—181no—
169C4⋊Q8—91no—
170#127—91no—
171#124—181no—
172#121—32no—
173#121—181no—
174C4×D4—92no—
175C4×D4—181no—
176C2×C42—91no—
177C2×C42—181no—
178C4⋊C8—181no—
179C22⋊C8—32no—
180#97—181no—
181#95—91no—
182#95—181no—
183#95D3211yescharacteristic
184C23×C3—21no—
185C23×C3—62no—
186C23×C3D3×D412yes—
187C22×D3—22no—
188C3×D4—122no—
189C3×D4—122no—
190C3×D4—122no—
191C2×C3×C4—24no—
192C2×C3×C4—24no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—42no—
196C2×C3×C4—42no—
197C2×C3×C4—42no—
198C2×C3×C4—42no—
199C2×C3×C4—42no—
200C2×C3×C4—42no—
201C2×C3×C4—62no—
202C2×C3×C4C2×C4×D312yes—
203C2×C3×C4D3×D412yes—
204#67—42no—
205#67—42no—
206#67—124no—
207#67—124no—
208C2×Dic3—22no—
209C2×Dic3—32no—
210C2×Dic3—32no—
211C2×Dic3—32no—
212C2×Dic3—32no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—64no—
218C2×Dic3—64no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—64no—
222C2×Dic3—64no—
223C2×Dic3—121no—
224C2×Dic3—121no—
225C2×Dic3—124no—
226C2×Dic3—122no—
227C2×Dic3—122no—
228C2×Dic3—122no—
229C2×Dic3—122no—
230D12—42no—
231C4×D3—124no—
232Dic6—124no—
233C3×C8—122no—
234C3⋊C8—42no—
235C2×C32—21no—
236C2×C32—21no—
237C2×C32#41011yescharacteristic
238C2×C32#41811yescharacteristic
239C2×C32C2×#10411yescharacteristic
240C3×D3—82no—
241#41—362no—
242#41—362no—
243C2×Q8—181no—
244C2×D4—32no—
245C2×D4—62no—
246C2×D4—181no—
247C2×D4—181no—
248C22×C4—21no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—182no—
252C22×C4—181no—
253C22×C4C2×D3211yescharacteristic
254C2×C8—62no—
255C4⋊C4—32no—
256C4⋊C4—181no—
257C22⋊C4—62no—
258C22⋊C4—182no—
259C42—91no—
260C42—91no—
261C42—91no—
262C42—91no—
263C42—184no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—122no—
272C22×C3—122no—
273C22×C3—122no—
274C22×C3D3×C22⋊C412yes—
275C22×C3#91112yes—
276C22×C3#91412yes—
277C2×D3—42no—
278C2×D3—42no—
279C2×D3—42no—
280C3×C4—22no—
281C3×C4—22no—
282C3×C4—41no—
283C3×C4—41no—
284C3×C4—44no—
285C3×C4—44no—
286C3×C4—122no—
287Dic3—34no—
288Dic3—42no—
289Dic3—62no—
290Dic3—62no—
291Dic3—62no—
292Dic3—62no—
293Dic3—62no—
294Dic3—121no—
295Dic3—121no—
296Dic3—124no—
297Dic3—124no—
298C32#150511yescharacteristic, complemented, Sylow
299C23—62no—
300C23#381111yescharacteristic
301Q8—362no—
302D4—122no—
303D4—122no—
304D4—122no—
305D4—362no—
306D4—362no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—62no—
312C2×C4—91no—
313C2×C4—91no—
314C2×C4—91no—
315C2×C4—91no—
316C2×C4—182no—
317C2×C4—181no—
318C2×C4—181no—
319C2×C4—182no—
320C2×C4—364no—
321C2×C4—361no—
322C2×C4—361no—
323C2×C4C4×D3211yescharacteristic
324C2×C4#380211yescharacteristic
325C8—122no—
326C2×C3—22no—
327C2×C3—22no—
328C2×C3—22no—
329C2×C3—22no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—242no—
334C2×C3#474012yes—
335C2×C3#477012yes—
336C2×C3D3×#10412yes—
337D3—82no—
338C22—21no—
339C22—21no—
340C22—122no—
341C22—122no—
342C22—122no—
343C22#6392111yescharacteristic
344C22#6392711yescharacteristic
345C22#6394111yescharacteristic
346C4—21no—
347C4—21no—
348C4—42no—
349C4—92no—
350C4—122no—
351C4—181no—
352C4—181no—
353C4—181no—
354C4—362no—
355C3—21no—
356C3#6827812yescomplemented
357C2—21no—
358C2—21no—
359C2—242no—
360C2#1059039311yescharacteristic
361C2#1059040611yescharacteristic
362C2#1059059411yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32C2×C22⋊C4
prime radical#10594929C2
cosocleC22×C32×C4C23
hypercenter#95D32
hypocenterC32#1505
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592347C2semidirect
3. #10591066C2semidirect
4. C3×#4451C2semidirect
5. #10589150C2semidirect
12. #63919C4semidirect
14. #63914C4semidirect
16. #63898C4semidirect
30. #4451D3semidirect
298. C32#1505semidirect
356. C3#68278semidirect

Maximal subgroups

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

subgroupindex
#105949292
#105923472
#105910662
C3×#44512
#105891502
#682783