Finite Group Databasebeta

← #11775614

Subgroups — #11775614

Order 1152.

677 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 677 conjugacy classes of subgroups — too many to draw. Only its 100 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#10594925C211yesmaximal, characteristic
2C3⋊D3×C22⋊C8C211yesmaximal, characteristic
3#10591355C211yesmaximal, characteristic
4C3×#4467C212yesmaximal, complemented
5#10589153C212yesmaximal, complemented
6#68339—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×#3797C411yescharacteristic, complemented
9C2×C8×C3⋊D3—21no—
10C3×#924C2212yes—
11#63982—21no—
12#63974—21no—
13C2×#3724—21no—
14C2×#3722—21no—
15#63900C411yescharacteristic, complemented
16#63883—21no—
17#63871C412yescomplemented
18#63865—21no—
19C32×C22⋊C8C2211yescharacteristic
20#63657C2211yescharacteristic
21#63647—21no—
22C3×C3⋊#95C2212yes—
23D3×C22⋊Q8—32no—
24D3×C22⋊C8—32no—
25D3×C22⋊C8—61no—
26#4667—32no—
27C3×#328—32no—
28#4538—32no—
29#4467D312yescomplemented
30#4452—32no—
31C23×C3⋊D3D411yescharacteristic
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C2×C4×C3⋊D3—42no—
35C2×C4×C3⋊D3C2×C411yescharacteristic
36C2×C4×C3⋊D3C2×C411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C22×C3×Dic3—22no—
40C2×C3×Dic6C2×C412yes—
41C2×#627—21no—
42C2×#624—21no—
43C2×#624—21no—
44#3797—42no—
45C2×C32×C8—21no—
46C2×C3⋊(C3⋊C8)—21no—
47C8×C3⋊D3—42no—
48C3×#217—22no—
49C3×C4⋊Dic3C2×C412yes—
50C3×Dic3⋊C4—22no—
51#3724—21no—
52#3724—42no—
53Dic3⋊Dic3—22no—
54#3722—22no—
55#3722—42no—
56#1520—91noSylow
57C2×D3×Q8—32no—
58C22×C4×D3—32no—
59C22×C4×D3—61no—
60C3×C22⋊Q8—32no—
61#946—32no—
62C2×(C2×D3)⋊C4—62no—
63#924C2×D312yes—
64C2×Dic3⋊C4—62no—
65C2×D3×C8—62no—
66C2×D3×C8—62no—
67#897—32no—
68#896—62no—
69D3×C4⋊C4—32no—
70D3×C4⋊C4—62no—
71D3×C22⋊C4—62no—
72#878—62no—
73C3×C22⋊C8—21no—
74C3×C22⋊C8C2×D312yes—
75C3×#95—32no—
76C3⋊#95C2×D312yes—
77#830—32no—
78#830—61no—
79(C2×D3)⋊C8—62no—
80(C2×D3)⋊C8—62no—
81C23×C32C2×D411yescharacteristic
82C22×C3⋊D3—41no—
83C22×C3⋊D3—41no—
84C22×C3⋊D3C22⋊C411yescharacteristic
85C22×C3⋊D3C22⋊C411yescharacteristic
86C22×C3⋊D3SD1612yes—
87C22×C3⋊D3Q1612yes—
88C2×C32×C4—41no—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C2×C3⋊Dic3C22⋊C411yescharacteristic
94C4×C3⋊D3—22no—
95C4×C3⋊D3—22no—
96C4×C3⋊D3—41no—
97C4×C3⋊D3—41no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—42no—
101C2×C3×Dic3—42no—
102C2×C3×Dic3—42no—
103C3×Dic6—42no—
104#627—42no—
105#624—42no—
106#624—42no—
107C32×C8—41no—
108C3⋊(C3⋊C8)—41no—
109C2×C22⋊Q8—91no—
110C2×C22⋊C8—91no—
111#380—91no—
112#328—32no—
113#328—92no—
114C23×D3—32no—
115C23×D3—61no—
116C2×C3×Q8—32no—
117C22×C3×C4—21no—
118C22×C3×C4—62no—
119C22×C3×C4C22×D312yes—
120C22×Dic3—22no—
121C22×Dic3—32no—
122C22×Dic3—61no—
123D3×Q8—124no—
124C2×C4×D3—32no—
125C2×C4×D3—32no—
126C2×C4×D3—32no—
127C2×C4×D3—32no—
128C2×C4×D3—61no—
129C2×C4×D3—61no—
130C2×C4×D3—61no—
131C2×C4×D3—61no—
132C2×C4×D3—62no—
133C2×C4×D3—62no—
134C2×C4×D3—124no—
135C2×C4×D3—124no—
136C2×Dic6—62no—
137C2×Dic6C4×D312yes—
138C2×C3×C8—22no—
139C2×C3×C8—22no—
140C3×C4⋊C4—32no—
141C3×C4⋊C4—62no—
142C3×C22⋊C4—62no—
143#217—22no—
144(C2×D3)⋊C4—62no—
145(C2×D3)⋊C4—62no—
146(C2×D3)⋊C4—124no—
147C4⋊Dic3—62no—
148C4⋊Dic3C4×D312yes—
149Dic3⋊C4—22no—
150Dic3⋊C4—62no—
151Dic3⋊C4—62no—
152Dic3⋊C4—124no—
153C2×C3⋊C8—62no—
154C2×C3⋊C8—62no—
155D3×C8—124no—
156D3×C8—124no—
157C22×C32—21no—
158C22×C32—21no—
159C22×C32C2×C22⋊C411yescharacteristic
160C22×C32C2×SD1611yescharacteristic
161C22×C32C2×Q1611yescharacteristic
162C2×C3⋊D3—21no—
163C2×C3⋊D3—21no—
164C2×C3⋊D3—21no—
165C2×C3⋊D3—21no—
166C2×C3⋊D3—42no—
167C2×C3⋊D3—42no—
168C2×C3⋊D3#10312yes—
169C2×C3⋊D3#10312yes—
170C32×C4—21no—
171C32×C4—21no—
172C3⋊Dic3—21no—
173C3⋊Dic3#9912yes—
174C3×Dic3—42no—
175C3×Dic3—42no—
176C3×Dic3—82no—
177C22×Q8—91no—
178C23×C4—91no—
179C22×C8—181no—
180C22⋊Q8—32no—
181C22⋊Q8—92no—
182C22⋊Q8—181no—
183C22⋊Q8—181no—
184C2×C4⋊C4—91no—
185C2×C4⋊C4—181no—
186C2×C4⋊C4—181no—
187C2×C22⋊C4—181no—
188C2×C22⋊C4—181no—
189C22⋊C8—91no—
190C22⋊C8—181no—
191C22⋊C8D3211yescharacteristic
192#95—32no—
193C23×C3—21no—
194C23×C3D3×D412yes—
195C22×D3—32no—
196C22×D3—32no—
197C22×D3—34no—
198C22×D3—34no—
199C22×D3—61no—
200C22×D3—61no—
201C22×D3—62no—
202C22×D3—62no—
203C22×D3—122no—
204C22×D3—122no—
205C22×D3—122no—
206C22×D3—122no—
207C3×Q8—122no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—42no—
211C2×C3×C4—42no—
212C2×C3×C4—62no—
213C2×C3×C4—62no—
214C2×C3×C4—122no—
215C2×C3×C4—122no—
216C2×C3×C4—122no—
217C2×C3×C4C2×C4×D312yes—
218C2×C3×C4D3×D412yes—
219C2×Dic3—22no—
220C2×Dic3—22no—
221C2×Dic3—32no—
222C2×Dic3—32no—
223C2×Dic3—42no—
224C2×Dic3—42no—
225C2×Dic3—42no—
226C2×Dic3—61no—
227C2×Dic3—61no—
228C2×Dic3—64no—
229C2×Dic3—122no—
230C4×D3—64no—
231C4×D3—64no—
232C4×D3—64no—
233C4×D3—122no—
234C4×D3—124no—
235C4×D3—124no—
236C4×D3—122no—
237C4×D3—122no—
238C4×D3—122no—
239C4×D3—122no—
240Dic6—42no—
241Dic6—124no—
242C3×C8—42no—
243C3×C8—42no—
244C3⋊C8—122no—
245C3⋊C8—122no—
246C2×C32—21no—
247C2×C32—21no—
248C2×C32C2×#9911yescharacteristic
249C2×C32C2×#10311yescharacteristic
250C2×C32#42111yescharacteristic
251C3⋊D3—22no—
252C3⋊D3—22no—
253C24—91no—
254C2×Q8—32no—
255C2×Q8—181no—
256C2×Q8—362no—
257C22×C4—62no—
258C22×C4—91no—
259C22×C4—91no—
260C22×C4—91no—
261C22×C4—91no—
262C22×C4—91no—
263C22×C4—181no—
264C22×C4—181no—
265C22×C4—362no—
266C22×C4C2×D3211yescharacteristic
267C2×C8—21no—
268C2×C8—181no—
269C2×C8—362no—
270C4⋊C4—32no—
271C4⋊C4—62no—
272C4⋊C4—181no—
273C4⋊C4—182no—
274C4⋊C4—362no—
275C22⋊C4—62no—
276C22⋊C4—182no—
277C22⋊C4—362no—
278C22×C3—22no—
279C22×C3—22no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3D3×C22⋊C412yes—
286C22×C3D3×SD1612yes—
287C22×C3D3×Q1612yes—
288C2×D3—34no—
289C2×D3—34no—
290C2×D3—62no—
291C2×D3—62no—
292C2×D3—62no—
293C2×D3—62no—
294C2×D3—62no—
295C2×D3—62no—
296C2×D3—62no—
297C2×D3—62no—
298C2×D3—121no—
299C2×D3—121no—
300C2×D3—124no—
301C2×D3—124no—
302C2×D3—124no—
303C2×D3—124no—
304C3×C4—22no—
305C3×C4—22no—
306C3×C4—22no—
307C3×C4—41no—
308C3×C4—122no—
309C3×C4—122no—
310C3×C4—242no—
311Dic3—34no—
312Dic3—42no—
313Dic3—42no—
314Dic3—62no—
315Dic3—62no—
316Dic3—82no—
317Dic3—121no—
318C32#152011yescharacteristic, complemented, Sylow
319C23—91no—
320C23—91no—
321C23—92no—
322C23—92no—
323C23—361no—
324C23—361no—
325C23#380211yescharacteristic
326Q8—122no—
327Q8—362no—
328C2×C4—41no—
329C2×C4—62no—
330C2×C4—62no—
331C2×C4—91no—
332C2×C4—91no—
333C2×C4—122no—
334C2×C4—122no—
335C2×C4—122no—
336C2×C4—182no—
337C2×C4—182no—
338C2×C4—182no—
339C2×C4—361no—
340C2×C4—361no—
341C2×C4—362no—
342C2×C4—362no—
343C2×C4C4×D3211yescharacteristic
344C2×C4#381111yescharacteristic
345C8—41no—
346C8—361no—
347C2×C3—22no—
348C2×C3—22no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—41no—
353C2×C3—41no—
354C2×C3D3×#9912yes—
355C2×C3D3×#10312yes—
356C2×C3#482112yes—
357D3—64no—
358D3—64no—
359D3—64no—
360D3—122no—
361C22—21no—
362C22—21no—
363C22—92no—
364C22—92no—
365C22—181no—
366C22—181no—
367C22—181no—
368C22—181no—
369C22—362no—
370C22—362no—
371C22#6379611yescharacteristic
372C22#6380211yescharacteristic
373C22#6392111yescharacteristic
374C4—21no—
375C4—21no—
376C4—92no—
377C4—122no—
378C4—122no—
379C4—181no—
380C4—242no—
381C3—21no—
382C3#6833912yescomplemented
383C2—21no—
384C2—21no—
385C2—182no—
386C2—182no—
387C2#1059040411yescharacteristic
388C2#1059067211yescharacteristic
389C2#1059100911yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1520
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4467C2semidirect
5. #10589153C2semidirect
8. C2×#3797C4semidirect
15. #63900C4semidirect
17. #63871C4semidirect
29. #4467D3semidirect
318. C32#1520semidirect
382. C3#68339semidirect

Maximal subgroups

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

subgroupindex
#105949252
C3⋊D3×C22⋊C82
#105913552
C3×#44672
#105891532
#683393