Finite Group Databasebeta

← #11860247

Subgroups — #11860247

Order 1152.

802 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 151 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×#64237C211yesmaximal, characteristic
2C4×#3805C212yesmaximal, complemented
3C2×#63777C211yesmaximal, characteristic, complemented
4#10593511C211yesmaximal, characteristic, complemented
5#10593498C212yesmaximal, complemented
6#10593432C212yesmaximal, complemented
7#10593431C212yesmaximal, complemented
8#10593419C212yesmaximal, complemented
9#10593369C212yesmaximal, complemented
10C2×#3805C2212yes—
11C22×#622C2211yescharacteristic
12C22×#622C2211yescharacteristic
13C2×#3776C2211yescharacteristic
14C2×#3775C2212yes—
15#64237C418yescomplemented
16C2×#3774C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C3×C4×#67—22no—
19#67⋊Dic3—22no—
20#63957C2212yes—
21C4×#627C2212yes—
22#63902C2212yes—
23C4×#625C2212yes—
24#63878—22no—
25C4×D3×Dic3—22no—
26#63838C2212yes—
27#63777C2212yes—
28#63777C2212yes—
29#63743C2211yescharacteristic
30#63743C2211yescharacteristic
31#63742C2212yes—
32#63740C2212yes—
33#63740C2212yes—
34#63739C2212yes—
35#63739C2212yes—
36C4×#237—62no—
37C22×C32×C4D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C22×C3⋊Dic3C2311yescharacteristic
40C2×C3×#67—22no—
41C2×C3×C4×D3—22no—
42C2×#627C2312yes—
43C2×#625C2312yes—
44#3805—24no—
45#3805C2×C418yescomplemented
46C2×D3×Dic3—22no—
47C2×D3×Dic3—22no—
48C2×#622—22no—
49C2×#622C2×C414yescomplemented
50C2×#622C2312yes—
51C2×#622C2311yescharacteristic
52C2×#622C2311yescharacteristic
53#3776C2×C414yescomplemented
54#3775C2×C418yescomplemented
55#3774C2×C414yescomplemented
56C4×C3⋊Dic3D412yes—
57C4×C3⋊Dic3C2312yes—
58C3×#217—22no—
59C3×(C2×D3)⋊C4—22no—
60C3×Dic3⋊C4—22no—
61C3×C4×Dic3—22no—
62#3724C2312yes—
63#3724C2312yes—
64Dic3⋊Dic3—22no—
65(C2×D3)⋊Dic3—22no—
66Dic32—22no—
67Dic32—22no—
68#2943—91nomaximal, Sylow
69C2×#237—62no—
70C3×C4×D4—62no—
71D4×Dic3—62no—
72C4×#67—22no—
73C4×#67—62no—
74C2×C4×Dic3—62no—
75C2×C4×Dic3—62no—
76#892—62no—
77#887—62no—
78#67⋊C4—62no—
79#67⋊C4—62no—
80#877—62no—
81#877—62no—
82C42×D3—62no—
83C4×Dic6—62no—
84C23×C32C2×D411yescharacteristic
85C22×C3×D3—22no—
86C2×C32×C4—41no—
87C2×C32×C4C2×D412yes—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3C22×C412yes—
90C2×C3⋊Dic3C2×D412yes—
91C2×C3⋊Dic3C2×D411yescharacteristic
92C2×C3⋊Dic3#4112yes—
93C2×C3⋊Dic3C2411yescharacteristic
94C3×#67—28no—
95C2×C3×Dic3—22no—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—22no—
98C3×C4×D3—44no—
99#627—22no—
100#627C22×C414yes—
101#625—22no—
102#625C22×C414yes—
103D3×Dic3—28no—
104D3×Dic3—44no—
105#622—22no—
106#622C22×C412yes—
107#622C22×C412yes—
108C2×#135—91no—
109C4×#41—92no—
110#442—92no—
111#441—92no—
112#440—92no—
113#440—92no—
114#427—91no—
115#416—92no—
116C2×#97—91no—
117C2×C3×D4—62no—
118C22×C3×C4—22no—
119C22×C3×C4—62no—
120C2×#67—22no—
121C2×#67—62no—
122C22×Dic3—62no—
123C22×Dic3—62no—
124C22×Dic3—62no—
125C22×Dic3—62no—
126#237—68no—
127#237—68no—
128C2×C4×D3—22no—
129C2×C4×D3—62no—
130C2×C4×D3—62no—
131C2×Dic6—62no—
132C3×C4⋊C4—62no—
133C3×C22⋊C4—62no—
134C3×C22⋊C4—62no—
135C3×C42—62no—
136#217—22no—
137#217—62no—
138(C2×D3)⋊C4—22no—
139(C2×D3)⋊C4—62no—
140C4⋊Dic3—62no—
141Dic3⋊C4—22no—
142Dic3⋊C4—62no—
143Dic3⋊C4—62no—
144Dic3⋊C4—62no—
145C4×Dic3—22no—
146C4×Dic3—62no—
147C4×Dic3—62no—
148C4×Dic3—62no—
149C4×Dic3—62no—
150C4×Dic3—62no—
151C4×Dic3—62no—
152C4×Dic3—62no—
153C4×Dic3—62no—
154C22×C32—21no—
155C22×C32—21no—
156C22×C32C4×D412yes—
157C22×C32C22×D411yescharacteristic
158C2×C3×D3—24no—
159C2×C3×D3—42no—
160C2×C3×D3—42no—
161C32×C4—22no—
162C3⋊Dic3—22no—
163C3⋊Dic3C4×D412yes—
164C3⋊Dic3C23×C411yescharacteristic
165C3⋊Dic3C2×#4111yescharacteristic
166C3×Dic3—24no—
167C3×Dic3—42no—
168C3×Dic3—42no—
169C2×#41—92no—
170#135—98no—
171C2×Q16—91no—
172C2×SD16—92no—
173C2×D8—91no—
174C22×C8—91no—
175C22×C8—91no—
176C4×Q8—92no—
177C4×Q8—92no—
178C4×D4—62no—
179C4×D4—92no—
180C4×D4—92no—
181C4×D4—182no—
182#117—92no—
183#117—182no—
184C2×C42—91no—
185C2×C42—182no—
186#107—91no—
187#107—91no—
188#106—92no—
189#103—92no—
190#103—92no—
191#102—92no—
192#102—92no—
193#97—92no—
194#97—92no—
195C23×C3—22no—
196C23×C3—62no—
197C22×D3—22no—
198C3×D4—68no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—44no—
202C2×C3×C4—62no—
203C2×C3×C4—62no—
204C2×C3×C4—62no—
205C2×C3×C4—124no—
206#67—28no—
207#67—64no—
208#67—64no—
209C2×Dic3—22no—
210C2×Dic3—22no—
211C2×Dic3—22no—
212C2×Dic3—64no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—64no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218C2×Dic3—68no—
219C2×Dic3—124no—
220C2×Dic3—124no—
221C4×D3—44no—
222C4×D3—68no—
223C4×D3—124no—
224Dic6—64no—
225Dic6—64no—
226C2×C32—22no—
227C2×C32C2×C4×D411yescharacteristic
228C2×C32#57511yescharacteristic
229C2×C32#57511yescharacteristic
230C3×D3—44no—
231#41—98no—
232#41—184no—
233C2×Q8—92no—
234C2×D4—62no—
235C2×D4—92no—
236C22×C4—62no—
237C22×C4—91no—
238C22×C4—91no—
239C22×C4—182no—
240C22×C4—182no—
241C22×C4GO+(4,𝔽2)11yescharacteristic
242Q16—94no—
243SD16—98no—
244D8—94no—
245C2×C8—91no—
246C2×C8—91no—
247C2×C8—94no—
248C2×C8—92no—
249C2×C8—182no—
250C4⋊C4—62no—
251C4⋊C4—92no—
252C4⋊C4—92no—
253C4⋊C4—182no—
254C22⋊C4—62no—
255C22⋊C4—62no—
256C22⋊C4—182no—
257C42—62no—
258C42—92no—
259C42—92no—
260C42—182no—
261C42—182no—
262C22×C3—22no—
263C22×C3—24no—
264C22×C3—42no—
265C22×C3—42no—
266C22×C3—64no—
267C22×C3—122no—
268C22×C3—122no—
269C2×D3—24no—
270C2×D3—42no—
271C2×D3—42no—
272C3×C4—24no—
273C3×C4—42no—
274C3×C4—64no—
275C3×C4—122no—
276C3×C4—122no—
277Dic3—24no—
278Dic3—42no—
279Dic3—42no—
280Dic3—62no—
281Dic3—62no—
282Dic3—64no—
283Dic3—64no—
284Dic3—122no—
285C32#294311yescharacteristic, complemented, Sylow
286C23—62no—
287C23C2×GO+(4,𝔽2)11yescharacteristic
288Q8—94no—
289Q8—182no—
290D4—68no—
291D4—94no—
292D4—182no—
293C2×C4—41no—
294C2×C4—62no—
295C2×C4—62no—
296C2×C4—62no—
297C2×C4—91no—
298C2×C4—91no—
299C2×C4—92no—
300C2×C4—92no—
301C2×C4—92no—
302C2×C4—124no—
303C2×C4—188no—
304C2×C4—364no—
305C2×C4—361no—
306C2×C4C2×GO+(4,𝔽2)12yes—
307C8—92no—
308C8—92no—
309C8—182no—
310C2×C3—22no—
311C2×C3—22no—
312C2×C3—22no—
313C2×C3—44no—
314C2×C3—124no—
315D3—44no—
316C22—21no—
317C22—21no—
318C22—64no—
319C22—122no—
320C22—122no—
321C22C4×GO+(4,𝔽2)12yes—
322C22C22×GO+(4,𝔽2)11yescharacteristic
323C4—22no—
324C4—64no—
325C4—91no—
326C4—91no—
327C4—92no—
328C4—122no—
329C4—122no—
330C4—182no—
331C3—22no—
332C2—22no—
333C2—124no—
334C2#1059650211yescharacteristic
335C2C2×C4×GO+(4,𝔽2)11yescharacteristic
336C2#1059653211yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC2×#64237C2
cosocleC2×C3⋊Dic3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2943
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×#3805C2semidirect
3. C2×#63777C2semidirect
4. #10593511C2semidirect
5. #10593498C2semidirect
6. #10593432C2semidirect
7. #10593431C2semidirect
8. #10593419C2semidirect
9. #10593369C2semidirect
15. #64237C4semidirect
45. #3805C2×C4semidirect
49. C2×#622C2×C4semidirect
53. #3776C2×C4semidirect
54. #3775C2×C4semidirect
55. #3774C2×C4semidirect
285. C32#2943semidirect

Maximal subgroups

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

subgroupindex
C2×#642372
C4×#38052
C2×#637772
#105935112
#105934982
#105934322
#105934312
#105934192
#105933692
#29439