Finite Group Databasebeta

← #11801143

Subgroups — #11801143

Order 1152.

1066 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×C3⋊D3C211yesmaximal, characteristic
2#10593812C212yesmaximal
3#10593811C212yesmaximal
4C4×C22⋊#157C212yesmaximal
5#10593737C212yesmaximal, complemented
6#10593736C212yesmaximal, complemented
7C4×C4⋊#157C212yesmaximal, complemented
8#10593733C212yesmaximal, complemented
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×C22⋊#157C2214yes—
13C2×C4⋊#157C2214yes—
14C2×C4×#157C2214yes—
15C2×C32×C42C411yescharacteristic, complemented
16C2×C4×C3⋊Dic3C411yescharacteristic, complemented
17C2×C4×C3⋊Dic3C411yescharacteristic, complemented
18C2×C4×C3⋊Dic3C411yescharacteristic, complemented
19C42×C3⋊D3C411yescharacteristic, complemented
20C42×C3⋊D3C411yescharacteristic, complemented
21C42×C3⋊D3C411yescharacteristic, complemented
22C42×C3⋊D3C411yescharacteristic, complemented
23C42×C3⋊D3C2211yescharacteristic
24C42×C3⋊D3C2211yescharacteristic
25C42×C3⋊D3C2211yescharacteristic
26C42×C3⋊D3C2211yescharacteristic
27#63781C2214yes—
28#63781C2214yes—
29#63781C2214yes—
30#63781C2214yes—
31C2×C42×D3—62no—
32C23×C3⋊D3C2311yescharacteristic
33C22×#157C2318yes—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4C2×C411yescharacteristic
37C22×C3⋊Dic3C2×C411yescharacteristic
38C22×C3⋊Dic3C2×C411yescharacteristic
39C22×C3⋊Dic3C2×C411yescharacteristic
40C2×C4×C3⋊D3—24no—
41C2×C4×C3⋊D3—24no—
42C2×C4×C3⋊D3—24no—
43C2×C4×C3⋊D3C2×C411yescharacteristic
44C2×C4×C3⋊D3C2×C411yescharacteristic
45C2×C4×C3⋊D3C2×C411yescharacteristic
46C2×C4×C3⋊D3C2×C411yescharacteristic
47C2×C4×C3⋊D3C2×C411yescharacteristic
48C2×C4×C3⋊D3C2×C411yescharacteristic
49C2×C4×C3⋊D3C2311yescharacteristic
50C2×C4×C3⋊D3C2311yescharacteristic
51C2×C4×C3⋊D3C2311yescharacteristic
52C2×C4×C3⋊D3C2311yescharacteristic
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×C4×C3⋊D3C2311yescharacteristic
55C22⋊#157—28no—
56C4⋊#157—28no—
57C4×#157—28no—
58C32×C42C2×C411yescharacteristic
59C32×C42C2×C411yescharacteristic
60C32×C42C2×C411yescharacteristic
61C32×C42C2×C411yescharacteristic
62C4×C3⋊Dic3C2×C411yescharacteristic
63C4×C3⋊Dic3C2×C411yescharacteristic
64C4×C3⋊Dic3C2×C411yescharacteristic
65C4×C3⋊Dic3C2×C411yescharacteristic
66C4×C3⋊Dic3C2×C411yescharacteristic
67C4×C3⋊Dic3C2×C411yescharacteristic
68C4×C3⋊Dic3C2×C411yescharacteristic
69C4×C3⋊Dic3C2×C411yescharacteristic
70C4×C3⋊Dic3C2×C411yescharacteristic
71C4×C3⋊Dic3C2×C411yescharacteristic
72C4×C3⋊Dic3C2×C411yescharacteristic
73C4×C3⋊Dic3C2×C411yescharacteristic
74#2283—91nomaximal, Sylow
75C22×C4×D3—62no—
76C22×C4×D3—62no—
77C22×C4×D3—62no—
78C2×C3×C42—22no—
79C2×C4×Dic3—62no—
80C2×C4×Dic3—62no—
81C2×C4×Dic3—62no—
82C42×D3—62no—
83C42×D3—62no—
84C42×D3—62no—
85C42×D3—62no—
86C42×D3—62no—
87C42×D3—62no—
88C42×D3—62no—
89C42×D3—62no—
90C23×C32C22×C411yescharacteristic
91C22×C3⋊D3—22no—
92C22×C3⋊D3—22no—
93C22×C3⋊D3C22×C411yescharacteristic
94C22×C3⋊D3#4114yes—
95C22×C3⋊D3C2411yescharacteristic
96C2×#157—28no—
97C2×#157—28no—
98C2×#157—28no—
99C2×C32×C4—22no—
100C2×C32×C4—22no—
101C2×C32×C4—22no—
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C22×C411yescharacteristic
104C2×C32×C4C22×C411yescharacteristic
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C22×C411yescharacteristic
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3C22×C411yescharacteristic
112C2×C3⋊Dic3C22×C411yescharacteristic
113C2×C3⋊Dic3C22×C411yescharacteristic
114C2×C3⋊Dic3C22×C411yescharacteristic
115C2×C3⋊Dic3C22×C411yescharacteristic
116C2×C3⋊Dic3C22×C411yescharacteristic
117C4×C3⋊D3—22no—
118C4×C3⋊D3—22no—
119C4×C3⋊D3—22no—
120C4×C3⋊D3—22no—
121C4×C3⋊D3—22no—
122C4×C3⋊D3—22no—
123C4×C3⋊D3—22no—
124C4×C3⋊D3—22no—
125C4×C3⋊D3—22no—
126C4×C3⋊D3—22no—
127C4×C3⋊D3#4114yes—
128C4×C3⋊D3#4114yes—
129C22×C42—91no—
130#383—92no—
131#382—92no—
132#381—92no—
133#380—92no—
134C4×C4⋊C4—92no—
135C4×C22⋊C4—92no—
136#376—92no—
137C23×D3—62no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×Dic3—62no—
142C22×Dic3—62no—
143C22×Dic3—62no—
144C2×C4×D3—62no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×C4×D3—62no—
153C2×C4×D3—62no—
154C2×C4×D3—62no—
155C2×C4×D3—62no—
156C2×C4×D3—616no—
157C2×C4×D3—616no—
158C2×C4×D3—616no—
159C3×C42—22no—
160C3×C42—22no—
161C3×C42—22no—
162C3×C42—22no—
163C4×Dic3—62no—
164C4×Dic3—62no—
165C4×Dic3—62no—
166C4×Dic3—62no—
167C4×Dic3—62no—
168C4×Dic3—62no—
169C4×Dic3—62no—
170C4×Dic3—62no—
171C4×Dic3—62no—
172C4×Dic3—62no—
173C4×Dic3—62no—
174C4×Dic3—62no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32#11712yes—
178C22×C32C23×C411yescharacteristic
179C2×C3⋊D3—21no—
180C2×C3⋊D3—21no—
181C2×C3⋊D3—28no—
182C2×C3⋊D3#11712yes—
183C2×C3⋊D3C2×#4112yes—
184C2×C3⋊D3C2×#4112yes—
185C2×C3⋊D3C2×#4112yes—
186#157—48no—
187C32×C4—21no—
188C32×C4—21no—
189C32×C4—21no—
190C32×C4—21no—
191C32×C4#11712yes—
192C32×C4#11712yes—
193C3⋊Dic3—21no—
194C3⋊Dic3—21no—
195C3⋊Dic3—21no—
196C3⋊Dic3—21no—
197C3⋊Dic3#11712yes—
198C3⋊Dic3#11712yes—
199C23×C4—91no—
200C23×C4—91no—
201C23×C4—91no—
202C2×C4⋊C4—94no—
203C2×C22⋊C4—94no—
204C2×C42—91no—
205C2×C42—91no—
206C2×C42—91no—
207C2×C42—91no—
208C2×C42—91no—
209C2×C42—91no—
210C2×C42—91no—
211C2×C42—91no—
212C2×C42—91no—
213C2×C42—91no—
214C2×C42—91no—
215C2×C42—94no—
216C2×C42#15711yescharacteristic, complemented
217#95—94no—
218#95—94no—
219#95—94no—
220#95—94no—
221C23×C3—22no—
222C22×D3—62no—
223C22×D3—68no—
224C22×D3—62no—
225C22×D3—68no—
226C22×D3—68no—
227C2×C3×C4—28no—
228C2×C3×C4—28no—
229C2×C3×C4—28no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—68no—
243C2×Dic3—68no—
244C2×Dic3—68no—
245C4×D3—68no—
246C4×D3—68no—
247C4×D3—68no—
248C4×D3—68no—
249C4×D3—68no—
250C4×D3—68no—
251C4×D3—68no—
252C4×D3—68no—
253C4×D3—68no—
254C4×D3—68no—
255C4×D3—68no—
256C4×D3—68no—
257C2×C32—22no—
258C2×C32C2×#11711yescharacteristic
259C2×C32C2×#11711yescharacteristic
260C2×C32C2×#11711yescharacteristic
261C3⋊D3—22no—
262C3⋊D3#52914yes—
263C24—91no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—91no—
267C22×C4—91no—
268C22×C4—91no—
269C22×C4—91no—
270C22×C4—91no—
271C22×C4—91no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—91no—
278C22×C4—91no—
279C22×C4—98no—
280C22×C4—184no—
281C22×C4—184no—
282C22×C4—184no—
283C22×C4C2×#15711yescharacteristic
284C22×C4C2×#15711yescharacteristic
285C22×C4C2×#15711yescharacteristic
286C4⋊C4—188no—
287C22⋊C4—188no—
288C42—91no—
289C42—91no—
290C42—91no—
291C42—91no—
292C42—91no—
293C42—91no—
294C42—91no—
295C42—91no—
296C42—91no—
297C42—91no—
298C42—91no—
299C42—91no—
300C42—188no—
301C42C2×#15711yescharacteristic
302C42C2×#15711yescharacteristic
303C42C2×#15711yescharacteristic
304C42C2×#15711yescharacteristic
305C22×C3—24no—
306C22×C3—24no—
307C22×C3—24no—
308C22×C3—22no—
309C2×D3—64no—
310C2×D3—64no—
311C2×D3—64no—
312C2×D3—64no—
313C2×D3—64no—
314C2×D3—64no—
315C2×D3—632no—
316C3×C4—24no—
317C3×C4—24no—
318C3×C4—24no—
319C3×C4—24no—
320C3×C4—24no—
321C3×C4—24no—
322Dic3—64no—
323Dic3—64no—
324Dic3—64no—
325Dic3—64no—
326Dic3—64no—
327Dic3—64no—
328C32#228311yescharacteristic, complemented, Sylow
329C23—91no—
330C23—94no—
331C23—91no—
332C23—182no—
333C23—182no—
334C23C22×#15711yescharacteristic
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—91no—
339C2×C4—91no—
340C2×C4—94no—
341C2×C4—94no—
342C2×C4—91no—
343C2×C4—91no—
344C2×C4—91no—
345C2×C4—91no—
346C2×C4—182no—
347C2×C4—182no—
348C2×C4—182no—
349C2×C4—182no—
350C2×C4—182no—
351C2×C4—182no—
352C2×C4—182no—
353C2×C4—182no—
354C2×C4—182no—
355C2×C4—182no—
356C2×C4—182no—
357C2×C4—182no—
358C2×C4—182no—
359C2×C4—188no—
360C2×C4—188no—
361C2×C4—188no—
362C2×C4C22×#15711yescharacteristic
363C2×C4C22×#15711yescharacteristic
364C2×C4C22×#15711yescharacteristic
365C2×C4C22×#15711yescharacteristic
366C2×C4C22×#15711yescharacteristic
367C2×C4C22×#15711yescharacteristic
368C2×C3—28no—
369C2×C3—22no—
370C2×C3—22no—
371C2×C3—22no—
372D3—68no—
373D3—68no—
374C22—21no—
375C22—21no—
376C22—92no—
377C22—92no—
378C22—92no—
379C22—92no—
380C22—188no—
381C22—181no—
382C22—181no—
383C22#6428612yes—
384C22C23×#15711yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—92no—
390C4—92no—
391C4—181no—
392C4—181no—
393C4—181no—
394C4—181no—
395C4—368no—
396C4#6428612yes—
397C4#6428612yes—
398C3—22no—
399C2—22no—
400C2—94no—
401C2—182no—
402C2C2×#6428611yescharacteristic
403C2C2×#6428611yescharacteristic
404C2C2×#6428611yescharacteristic
subgroupG/H
centerC2×C4C22×#157
commutator, socleC22×C32C23×C4
FrattiniC22C23×#157
FittingC2×C32×C42C4
prime radicalC23×C3⋊D3C23
cosocleC22×C3⋊D3C24
hypercenterC2×C42#157
hypocenterC32#2283
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
5. #10593737C2semidirect
6. #10593736C2semidirect
7. C4×C4⋊#157C2semidirect
8. #10593733C2semidirect
15. C2×C32×C42C4semidirect
16. C2×C4×C3⋊Dic3C4semidirect
17. C2×C4×C3⋊Dic3C4semidirect
18. C2×C4×C3⋊Dic3C4semidirect
19. C42×C3⋊D3C4semidirect
20. C42×C3⋊D3C4semidirect
21. C42×C3⋊D3C4semidirect
22. C42×C3⋊D3C4semidirect
216. C2×C42#157semidirect
328. C32#2283semidirect

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
#105938122
#105938112
C4×C22⋊#1572
#105937372
#105937362
C4×C4⋊#1572
#105937332
#22839