Finite Group Databasebeta

← #11868770

Subgroups — #11868770

Order 1152.

636 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 115 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×C4×#627C211yesmaximal, characteristic
2#10594810C211yesmaximal, characteristic
3#10593805C211yesmaximal, characteristic
4#10593507C212yesmaximal
5#10593503C212yesmaximal
6#10593393C212yesmaximal, complemented
7#10593382C214yesmaximal, complemented
8#10593376C212yesmaximal, complemented
9C22×#627C2211yescharacteristic
10C2×#3792C2212yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C3×#924—21no—
13C2×C3×C4×Dic3—21no—
14#63982—21no—
15C2×#3724C2211yescharacteristic
16C2×Dic3⋊Dic3—21no—
17#63957C2212yes—
18#63919C2211yescharacteristic
19C4×#627—21no—
20C4×#627—21no—
21C4×#627C2212yes—
22C4×#627C2212yes—
23#63873C2211yescharacteristic
24#63870C2212yes—
25#63843—21no—
26#63838—21no—
27#63779C2212yes—
28C4⋊#622C2212yes—
29#63743C2214yes—
30#63742C2214yes—
31#63740C2214yes—
32#63740C2214yes—
33#5622—61no—
34C2×C4×Dic6—61no—
35C22×C32×C4D411yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3C2311yescharacteristic
38C22×C3×Dic3—21no—
39C22×C3×Dic3—21no—
40C2×C3×Dic6—21no—
41C2×#627—21no—
42C2×#627—22no—
43C2×#627—21no—
44C2×#627Q814yescomplemented
45C2×#627C2312yes—
46#3792—24no—
47C2×#622C2314yes—
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3D411yescharacteristic
50C4×C3⋊Dic3C2311yescharacteristic
51C4×C3⋊Dic3C2311yescharacteristic
52C3×#217—22no—
53C3×C4⋊Dic3—21no—
54C3×Dic3⋊C4—22no—
55C3×C4×Dic3—22no—
56C3×C4×Dic3—22no—
57#3724—21no—
58#3724—21no—
59#3724C2312yes—
60#3724C2312yes—
61#3724C2312yes—
62Dic3⋊Dic3—22no—
63Dic3⋊Dic3—22no—
64Dic3⋊Dic3—22no—
65Dic32—22no—
66#3078—91nomaximal, Sylow
67C22×Dic6—61no—
68C3×C22⋊Q8—61no—
69C2×C3×C42—61no—
70Q8×Dic3—61no—
71#944—61no—
72C2×C4⋊Dic3—61no—
73#924—21no—
74C2×Dic3⋊C4—61no—
75C2×Dic3⋊C4—61no—
76C2×C4×Dic3—21no—
77C2×C4×Dic3—61no—
78C2×C4×Dic3—61no—
79#889—62no—
80#888—61no—
81#887—62no—
82#887—61no—
83#878—62no—
84#877—62no—
85C4×Dic6—62no—
86C4×Dic6—62no—
87C4×Dic6—62no—
88C4×Dic6—62no—
89C23×C32C2×D411yescharacteristic
90C2×C32×C4—22no—
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C3⋊Dic3—41no—
94C2×C3⋊Dic3C2×D411yescharacteristic
95C2×C3⋊Dic3C2×D411yescharacteristic
96C2×C3⋊Dic3C2×D411yescharacteristic
97C2×C3⋊Dic3C2×Q812yes—
98C2×C3⋊Dic3#4112yes—
99C2×C3⋊Dic3C2411yescharacteristic
100C2×C3×Dic3—24no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—42no—
106C3×Dic6—42no—
107#627—24no—
108#627—22no—
109#627—42no—
110#627C2×Q814yes—
111#622—24no—
112#533—91no—
113C2×C4×Q8—91no—
114#479—94no—
115#477—92no—
116#475—92no—
117#428—92no—
118#423—91no—
119#419—92no—
120C2×C3×Q8—61no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—61no—
124C22×C3×C4—61no—
125C22×Dic3—21no—
126C22×Dic3—21no—
127C22×Dic3—61no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131C2×Dic6—21no—
132C2×Dic6—62no—
133C2×Dic6—64no—
134C2×Dic6—62no—
135C2×Dic6—64no—
136C2×Dic6—62no—
137C3×C4⋊C4—61no—
138C3×C4⋊C4—62no—
139C3×C22⋊C4—62no—
140C3×C42—62no—
141C3×C42—62no—
142#217—22no—
143C4⋊Dic3—21no—
144C4⋊Dic3—62no—
145C4⋊Dic3—62no—
146C4⋊Dic3—62no—
147Dic3⋊C4—22no—
148Dic3⋊C4—62no—
149Dic3⋊C4—62no—
150Dic3⋊C4—62no—
151Dic3⋊C4—62no—
152Dic3⋊C4—62no—
153Dic3⋊C4—62no—
154Dic3⋊C4—62no—
155Dic3⋊C4—62no—
156C4×Dic3—22no—
157C4×Dic3—22no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—61no—
162C4×Dic3—61no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3—61no—
166C4×Dic3—62no—
167C4×Dic3—62no—
168C22×C32—21no—
169C22×C32—21no—
170C22×C32C22⋊Q812yes—
171C22×C32C22×D411yescharacteristic
172C32×C4—21no—
173C32×C4#13712yes—
174C3⋊Dic3—21no—
175C3⋊Dic3—21no—
176C3⋊Dic3C22⋊Q812yes—
177C3⋊Dic3C22×Q811yescharacteristic
178C3⋊Dic3C2×#4111yescharacteristic
179C3×Dic3—24no—
180C3×Dic3—42no—
181C3×Dic3—42no—
182C3×Dic3—42no—
183C22×Q8—91no—
184C2×M16—92no—
185C4⋊Q8—91no—
186C4⋊Q8—91no—
187#125—92no—
188C22⋊Q8—61no—
189C22⋊Q8—181no—
190C4×Q8—92no—
191C4×Q8—92no—
192C4×Q8—181no—
193C4×Q8—181no—
194C4×Q8—181no—
195C4×Q8—181no—
196#117—92no—
197C2×C4⋊C4—91no—
198C2×C4⋊C4—181no—
199C2×C42—61no—
200C2×C42—91no—
201#107—94no—
202#106—94no—
203C4⋊C8—92no—
204C4⋊C8—92no—
205#103—94no—
206#103—94no—
207C23×C3—21no—
208C23×C3—21no—
209C3×Q8—122no—
210C2×C3×C4—24no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—42no—
216C2×C3×C4—62no—
217C2×C3×C4—64no—
218C2×C3×C4—62no—
219C2×C3×C4—62no—
220C2×C3×C4—62no—
221C2×C3×C4—122no—
222C2×Dic3—22no—
223C2×Dic3—24no—
224C2×Dic3—22no—
225C2×Dic3—22no—
226C2×Dic3—22no—
227C2×Dic3—42no—
228C2×Dic3—61no—
229C2×Dic3—61no—
230C2×Dic3—61no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3—122no—
241C2×Dic3—122no—
242Dic6—42no—
243Dic6—64no—
244Dic6—68no—
245Dic6—64no—
246Dic6—124no—
247C2×C32—22no—
248C2×C32C2×C22⋊Q811yescharacteristic
249C2×C32C2×#13711yescharacteristic
250C2×C32#57511yescharacteristic
251C2×Q8—61no—
252C2×Q8—92no—
253C2×Q8—94no—
254C2×Q8—181no—
255C2×Q8—182no—
256C2×Q8—181no—
257C22×C4—61no—
258C22×C4—61no—
259C22×C4—91no—
260C22×C4—91no—
261C22×C4GO+(4,𝔽2)11yescharacteristic
262M16—184no—
263C2×C8—94no—
264C4⋊C4—62no—
265C4⋊C4—61no—
266C4⋊C4—92no—
267C4⋊C4—92no—
268C4⋊C4—92no—
269C4⋊C4—181no—
270C4⋊C4—182no—
271C4⋊C4—182no—
272C4⋊C4—182no—
273C4⋊C4—181no—
274C22⋊C4—62no—
275C42—62no—
276C42—62no—
277C42—91no—
278C42—91no—
279C42—91no—
280C42—91no—
281C42—182no—
282C22×C3—22no—
283C22×C3—22no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—41no—
289C22×C3—41no—
290C3×C4—22no—
291C3×C4—22no—
292C3×C4—22no—
293C3×C4—41no—
294C3×C4—64no—
295C3×C4—122no—
296C3×C4—122no—
297C3×C4—122no—
298Dic3—24no—
299Dic3—42no—
300Dic3—42no—
301Dic3—42no—
302Dic3—62no—
303Dic3—61no—
304Dic3—61no—
305Dic3—62no—
306Dic3—61no—
307Dic3—61no—
308Dic3—62no—
309Dic3—121no—
310Dic3—121no—
311Dic3—121no—
312C32#307811yescharacteristic, complemented, Sylow
313C23C2×GO+(4,𝔽2)11yescharacteristic
314Q8—94no—
315Q8—122no—
316Q8—182no—
317Q8—184no—
318Q8—362no—
319C2×C4—22no—
320C2×C4—62no—
321C2×C4—64no—
322C2×C4—62no—
323C2×C4—62no—
324C2×C4—62no—
325C2×C4—91no—
326C2×C4—91no—
327C2×C4—92no—
328C2×C4—92no—
329C2×C4—91no—
330C2×C4—91no—
331C2×C4—122no—
332C2×C4—361no—
333C2×C4C2×GO+(4,𝔽2)11yescharacteristic
334C2×C4C2×GO+(4,𝔽2)11yescharacteristic
335C8—184no—
336C2×C3—24no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—42no—
344C22—21no—
345C22—21no—
346C22D32⋊Q812yes—
347C22C22×GO+(4,𝔽2)11yescharacteristic
348C4—21no—
349C4—64no—
350C4—91no—
351C4—91no—
352C4—92no—
353C4—122no—
354C4—122no—
355C4—122no—
356C4—181no—
357C4—181no—
358C4#6423912yes—
359C3—21no—
360C3—21no—
361C2—22no—
362C2C2×D32⋊Q811yescharacteristic
363C2#1059649911yescharacteristic
364C2C2×#6423911yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3078
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #10593393C2semidirect
7. #10593382C2semidirect
8. #10593376C2semidirect
44. C2×#627Q8semidirect
312. C32#3078semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
#105948102
#105938052
#105935072
#105935032
#105933932
#105933822
#105933762
#30789