Finite Group Databasebeta

← #11786502

Subgroups — #11786502

Order 1152.

518 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 78 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×#64286C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic
3C2×#63769C211yesmaximal, characteristic, complemented
4C2×#63768C211yesmaximal, characteristic, complemented
5C3⋊D3×C22⋊C8C211yesmaximal, characteristic
6#10590182C211yesmaximal, characteristic, complemented
7#10590182C211yesmaximal, characteristic, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C22⋊#157—21no—
10C2×C22⋊#157—21no—
11#64286—22no—
12#64286—22no—
13C2×C4⋊#157C2211yescharacteristic
14C2×C4⋊#157C2211yescharacteristic
15C2×C4⋊#157C2211yescharacteristic
16C2×C4⋊#157C2211yescharacteristic
17C2×C4×#157—21no—
18C2×C8×C3⋊D3C2211yescharacteristic
19C2×C8×C3⋊D3C2211yescharacteristic
20#63781—21no—
21#63769—22no—
22#63768—22no—
23C32×C22⋊C8C411yescharacteristic, complemented
24#63657C411yescharacteristic, complemented
25#63647C411yescharacteristic, complemented
26#63647C411yescharacteristic, complemented
27D3×C22⋊C8—62no—
28C23×C3⋊D3D411yescharacteristic
29C22×#157—21no—
30C22×#157—21no—
31C22×#157—21no—
32C22×#157—21no—
33C22×C32×C4C2×C411yescharacteristic
34C22×C3⋊Dic3Q811yescharacteristic
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3—21no—
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3C2×C411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3Q811yescharacteristic
42C2×C4×C3⋊D3C2311yescharacteristic
43C22⋊#157—24no—
44C22⋊#157—42no—
45C4⋊#157—21no—
46C4⋊#157—21no—
47C4⋊#157—21no—
48C4⋊#157—21no—
49C4⋊#157—21no—
50C4⋊#157—21no—
51C4⋊#157D412yes—
52C4⋊#157D412yes—
53C4×#157—24no—
54C2×C32×C8C2×C411yescharacteristic
55C2×C32×C8C2×C411yescharacteristic
56C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
57C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
58C8×C3⋊D3—21no—
59C8×C3⋊D3—21no—
60C8×C3⋊D3—21no—
61C8×C3⋊D3—21no—
62#1854—91nomaximal, Sylow
63C22×C4×D3—62no—
64C2×D3×C8—62no—
65C2×D3×C8—62no—
66C3×C22⋊C8—22no—
67#830—62no—
68(C2×D3)⋊C8—62no—
69(C2×D3)⋊C8—62no—
70C23×C32C4⋊C411yescharacteristic
71C22×C3⋊D3—21no—
72C22×C3⋊D3—21no—
73C22×C3⋊D3—21no—
74C22×C3⋊D3—21no—
75C22×C3⋊D3—21no—
76C22×C3⋊D3—21no—
77C22×C3⋊D3C4⋊C411yescharacteristic
78C22×C3⋊D3C2×D411yescharacteristic
79C2×#157—22no—
80C2×#157—22no—
81C2×#157—41no—
82C2×#157—41no—
83C2×#157—41no—
84C2×#157—41no—
85C2×#157—41no—
86C2×#157—41no—
87C2×#157—41no—
88C2×#157—41no—
89C2×#157—41no—
90C2×#157—41no—
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4C4⋊C411yescharacteristic
94C2×C32×C4C22×C411yescharacteristic
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3C4⋊C411yescharacteristic
98C2×C3⋊Dic3C2×Q811yescharacteristic
99C4×C3⋊D3—21no—
100C4×C3⋊D3—21no—
101C4×C3⋊D3—21no—
102C4×C3⋊D3—21no—
103C4×C3⋊D3—21no—
104C4×C3⋊D3—21no—
105C4×C3⋊D3C2×D411yescharacteristic
106C4×C3⋊D3C2×D411yescharacteristic
107C4×C3⋊D3#4111yescharacteristic
108C4×C3⋊D3#4111yescharacteristic
109C32×C8—21no—
110C32×C8—21no—
111C3⋊(C3⋊C8)—21no—
112C3⋊(C3⋊C8)—21no—
113C2×#117—91no—
114C2×#107—91no—
115C2×#106—91no—
116C2×C22⋊C8—91no—
117#380—91no—
118#340—91no—
119#340—91no—
120C23×D3—62no—
121C22×C3×C4—22no—
122C22×Dic3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—62no—
126C2×C4×D3—62no—
127C2×C4×D3—122no—
128C2×C4×D3—122no—
129C2×C4×D3—122no—
130C2×C4×D3—122no—
131C2×C3×C8—22no—
132C2×C3×C8—22no—
133C2×C3⋊C8—62no—
134C2×C3⋊C8—62no—
135D3×C8—122no—
136D3×C8—122no—
137D3×C8—122no—
138D3×C8—122no—
139C22×C32—21no—
140C22×C32—21no—
141C22×C32—21no—
142C22×C32C2×C4⋊C411yescharacteristic
143C2×C3⋊D3—21no—
144C2×C3⋊D3—21no—
145C2×C3⋊D3—21no—
146C2×C3⋊D3—41no—
147C2×C3⋊D3—41no—
148C2×C3⋊D3—41no—
149C2×C3⋊D3—41no—
150C2×C3⋊D3#12011yescharacteristic
151C2×C3⋊D3#12311yescharacteristic
152C2×C3⋊D3#13511yescharacteristic
153C2×C3⋊D3#13511yescharacteristic
154C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
155C2×C3⋊D3#13711yescharacteristic
156#157—42no—
157#157—42no—
158#157—81no—
159#157—81no—
160C32×C4—21no—
161C32×C4C4×D411yescharacteristic
162C32×C4C4×D411yescharacteristic
163C3⋊Dic3—21no—
164C3⋊Dic3C22⋊Q811yescharacteristic
165C3⋊Dic3C22⋊Q811yescharacteristic
166C23×C4—91no—
167C22×C8—91no—
168C22×C8—91no—
169#117—182no—
170#117—182no—
171C2×C4⋊C4—91no—
172C2×C4⋊C4—91no—
173C2×C4⋊C4—91no—
174C2×C4⋊C4—91no—
175C2×C22⋊C4—181no—
176C2×C22⋊C4—181no—
177C2×C42—181no—
178#107—182no—
179#106—182no—
180C22⋊C8—91no—
181C22⋊C8—91no—
182C22⋊C8—91no—
183C22⋊C8#15711yescharacteristic, complemented
184#95—181no—
185C23×C3—22no—
186C22×D3—62no—
187C22×D3—62no—
188C22×D3—64no—
189C22×D3—64no—
190C22×D3—122no—
191C22×D3—122no—
192C22×D3—122no—
193C22×D3—122no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—42no—
197C2×C3×C4—42no—
198C2×Dic3—62no—
199C2×Dic3—62no—
200C2×Dic3—122no—
201C2×Dic3—122no—
202C4×D3—62no—
203C4×D3—62no—
204C4×D3—62no—
205C4×D3—62no—
206C4×D3—122no—
207C4×D3—122no—
208C4×D3—122no—
209C4×D3—122no—
210C4×D3—122no—
211C4×D3—122no—
212C3×C8—42no—
213C3×C8—42no—
214C3⋊C8—122no—
215C3⋊C8—122no—
216C2×C32—41no—
217C2×C32#38511yescharacteristic
218C2×C32#42711yescharacteristic
219C2×C32#42811yescharacteristic
220C3⋊D3—41no—
221C3⋊D3#44911yescharacteristic
222C3⋊D3#45211yescharacteristic
223C3⋊D3#48211yescharacteristic
224C3⋊D3#48511yescharacteristic
225C24—91no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—91no—
229C22×C4—91no—
230C22×C4—91no—
231C22×C4—181no—
232C22×C4—181no—
233C22×C4—181no—
234C22×C4—181no—
235C22×C4—181no—
236C22×C4—181no—
237C22×C4—181no—
238C22×C4—181no—
239C22×C4C2×#15711yescharacteristic
240C2×C8—91no—
241C2×C8—91no—
242C2×C8—181no—
243C2×C8—181no—
244C2×C8—181no—
245C2×C8—181no—
246C2×C8C2×#15711yescharacteristic
247C2×C8C2×#15711yescharacteristic
248C4⋊C4—92no—
249C4⋊C4—92no—
250C4⋊C4—181no—
251C4⋊C4—181no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C4⋊C4—181no—
255C4⋊C4—181no—
256C22⋊C4—184no—
257C22⋊C4—362no—
258C42—184no—
259C22×C3—24no—
260C22×C3—22no—
261C22×C3—42no—
262C22×C3—42no—
263C2×D3—62no—
264C2×D3—62no—
265C2×D3—62no—
266C2×D3—62no—
267C2×D3—62no—
268C2×D3—62no—
269C2×D3—64no—
270C2×D3—122no—
271C2×D3—122no—
272C2×D3—124no—
273C2×D3—124no—
274C2×D3—124no—
275C2×D3—124no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—42no—
279Dic3—62no—
280Dic3—62no—
281Dic3—122no—
282C32#185411yescharacteristic, complemented, Sylow
283C23—91no—
284C23—91no—
285C23—181no—
286C23—181no—
287C23—181no—
288C23—181no—
289C23—181no—
290C23—181no—
291C23C4⋊#15711yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—91no—
295C2×C4—91no—
296C2×C4—91no—
297C2×C4—91no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—181no—
301C2×C4—181no—
302C2×C4—181no—
303C2×C4—181no—
304C2×C4—181no—
305C2×C4—181no—
306C2×C4—181no—
307C2×C4—181no—
308C2×C4—182no—
309C2×C4—182no—
310C2×C4—361no—
311C2×C4—361no—
312C2×C4—361no—
313C2×C4—361no—
314C2×C4—361no—
315C2×C4—361no—
316C2×C4—361no—
317C2×C4—361no—
318C2×C4—361no—
319C2×C4—361no—
320C2×C4C4⋊#15711yescharacteristic
321C2×C4C22×#15711yescharacteristic
322C8—21no—
323C8—21no—
324C8—181no—
325C8—181no—
326C2×C3—22no—
327C2×C3—22no—
328C2×C3—22no—
329C2×C3—44no—
330D3—62no—
331D3—62no—
332D3—62no—
333D3—62no—
334D3—124no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—91no—
339C22—91no—
340C22—91no—
341C22—91no—
342C22—91no—
343C22—91no—
344C22—181no—
345C22—181no—
346C22—181no—
347C22—361no—
348C22—361no—
349C22—361no—
350C22—361no—
351C22C2×C4⋊#15711yescharacteristic
352C4—21no—
353C4—91no—
354C4—91no—
355C4—181no—
356C4—362no—
357C4—362no—
358C4—721no—
359C4—721no—
360C4D4×#15711yescharacteristic
361C4D4×#15711yescharacteristic
362C3—22no—
363C2—41no—
364C2—91no—
365C2—91no—
366C2—91no—
367C2—91no—
368C2—361no—
369C2#1059374611yescharacteristic
370C2#1059376811yescharacteristic
371C2#1059377411yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C22⋊C8C4
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22⋊C8#157
hypocenterC32#1854
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#63769C2semidirect
4. C2×#63768C2semidirect
6. #10590182C2semidirect
7. #10590182C2semidirect
23. C32×C22⋊C8C4semidirect
24. #63657C4semidirect
25. #63647C4semidirect
26. #63647C4semidirect
183. C22⋊C8#157semidirect
282. C32#1854semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
#105938122
C2×#637692
C2×#637682
C3⋊D3×C22⋊C82
#105901822
#18549