Finite Group Databasebeta

← #11772618

Subgroups — #11772618

Order 1152.

417 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63663C211yesmaximal, characteristic
2C3×#5229C211yesmaximal, characteristic
3C2×C3×#836C211yesmaximal, characteristic
4#67699—31nomaximal
5#67644—31nomaximal
6C22×C32×Q8C2211yescharacteristic
7C2×#3748—21no—
8C2×C3×C4⋊Dic3C411yescharacteristic
9C2×C3×C4×Dic3C411yescharacteristic
10C2×C3×#208—21no—
11#63663—21no—
12#63663C412yescomplemented
13C3×#836—21no—
14C3×#836C412yescomplemented
15C3×C3⋊#95—21no—
16C3×C3⋊#95—21no—
17C2×C3×#101—31no—
18C3×#391—31no—
19#5229D311yescharacteristic
20C2×#836—31no—
21C2×#836—31no—
22C2×#836—61no—
23C2×#836D311yescharacteristic
24C2×C32×Q8—41no—
25C2×C32×Q8—41no—
26C2×C32×Q8C2×C411yescharacteristic
27C2×C32×Q8C2×C411yescharacteristic
28C2×C32×Q8D411yescharacteristic
29C2×C32×Q8Q811yescharacteristic
30C22×C32×C4C2×C411yescharacteristic
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C3×Dic3—21no—
34C22×C3×Dic3—21no—
35#3748—22no—
36#3748—41no—
37C2×C3⋊(C3⋊C8)—41no—
38C3×C4⋊Dic3—41no—
39C3×C4×Dic3—41no—
40C3×#208—22no—
41C3×#208—41no—
42C2×C3×C3⋊C8—41no—
43#1394—91noSylow
44C22×C3×Q8—21no—
45C22×C3×Q8C2×D311yescharacteristic
46C22×C3×Q8C2×D311yescharacteristic
47C2×C3×M16—61no—
48C2×C3×C4⋊C4—31no—
49C2×C3×C42—31no—
50C2×C4⋊Dic3Dic311yescharacteristic
51C2×C4×Dic3Dic311yescharacteristic
52C2×#208—21no—
53C2×#208—62no—
54C2×#208—61no—
55C2×#208—61no—
56C3×#101—32no—
57C3×#101—61no—
58C3×#95—61no—
59C3×#95—61no—
60#836—21no—
61#836—32no—
62#836—32no—
63#836—62no—
64#836—62no—
65#836—61no—
66#836—61no—
67#836Dic312yescomplemented
68C3⋊#95—21no—
69C3⋊#95—21no—
70C23×C32C22⋊C411yescharacteristic
71C32×Q8—41no—
72C32×Q8—41no—
73C32×Q8—41no—
74C32×Q8—41no—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—21no—
81C2×C32×C4C4211yescharacteristic
82C2×C32×C4C22⋊C411yescharacteristic
83C2×C32×C4C22⋊C411yescharacteristic
84C2×C32×C4C4⋊C411yescharacteristic
85C2×C32×C4C4⋊C411yescharacteristic
86C2×C32×C4C4⋊C411yescharacteristic
87C2×C3×Dic3—22no—
88C2×C3×Dic3—41no—
89C2×C3×Dic3—41no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3—41no—
92C3⋊(C3⋊C8)—42no—
93C3×C3⋊C8—42no—
94C2×#101—31no—
95C2×#101—91no—
96#391—31no—
97C2×C3×Q8—21no—
98C2×C3×Q8—21no—
99C2×C3×Q8—21no—
100C2×C3×Q8—21no—
101C2×C3×Q8—41no—
102C2×C3×Q8—41no—
103C2×C3×Q8—41no—
104C2×C3×Q8—41no—
105C2×C3×Q8—42no—
106C2×C3×Q8—42no—
107C2×C3×Q8Dic611yescharacteristic
108C2×C3×Q8Dic611yescharacteristic
109C2×C3×Q8C4×D311yescharacteristic
110C2×C3×Q8C4×D311yescharacteristic
111C2×C3×Q8C4×D311yescharacteristic
112C2×C3×Q8D1211yescharacteristic
113C2×C3×Q8C2×Dic311yescharacteristic
114C2×C3×Q8#6711yescharacteristic
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—61no—
119C22×C3×C4—61no—
120C22×C3×C4C4×D311yescharacteristic
121C22×C3×C4D1211yescharacteristic
122C22×C3×C4C2×Dic311yescharacteristic
123C22×C3×C4#6711yescharacteristic
124C22×C3×C4#6711yescharacteristic
125C22×C3×C4#6711yescharacteristic
126C22×Dic3—21no—
127C22×Dic3—21no—
128C3×M16—62no—
129C3×M16—121no—
130C2×C3×C8—121no—
131C3×C4⋊C4—121no—
132C3×C42—121no—
133C4⋊Dic3—41no—
134C4×Dic3—41no—
135#208—22no—
136#208—41no—
137#208—64no—
138#208—62no—
139#208—62no—
140#208—122no—
141#208—121no—
142#208—121no—
143C2×C3⋊C8—41no—
144C2×C3⋊C8—122no—
145C2×C3⋊C8—121no—
146C2×C3⋊C8—121no—
147C22×C32—21no—
148C22×C32—21no—
149C22×C32#9511yescharacteristic
150C22×C32#9911yescharacteristic
151C22×C32#9911yescharacteristic
152C32×C4—21no—
153C32×C4—21no—
154C32×C4—21no—
155C32×C4—21no—
156C32×C4—21no—
157C32×C4—21no—
158C3×Dic3—42no—
159C3×Dic3—81no—
160C22×Q8D3211yescharacteristic
161C2×M16—61no—
162C2×M16—181no—
163C2×C4⋊C4—31no—
164C2×C42—31no—
165#101—32no—
166#101—61no—
167#101—92no—
168#101—181no—
169#95—61no—
170#95—61no—
171C23×C3—21no—
172C23×C3(C2×D3)⋊C411yescharacteristic
173C23×C3#21711yescharacteristic
174C3×Q8—41no—
175C3×Q8—41no—
176C3×Q8—41no—
177C3×Q8—41no—
178C3×Q8—41no—
179C3×Q8—41no—
180C3×Q8—41no—
181C3×Q8—41no—
182C3×Q8—42no—
183C3×Q8—42no—
184C3×Q8—42no—
185C3×Q8—42no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—62no—
211C2×C3×C4—121no—
212C2×C3×C4—121no—
213C2×C3×C4—122no—
214C2×C3×C4—121no—
215C2×C3×C4C4×Dic311yescharacteristic
216C2×C3×C4C4×Dic311yescharacteristic
217C2×C3×C4Dic3⋊C411yescharacteristic
218C2×C3×C4Dic3⋊C411yescharacteristic
219C2×C3×C4Dic3⋊C411yescharacteristic
220C2×C3×C4Dic3⋊C411yescharacteristic
221C2×C3×C4C4⋊Dic311yescharacteristic
222C2×C3×C4C4⋊Dic311yescharacteristic
223C2×C3×C4(C2×D3)⋊C411yescharacteristic
224C2×C3×C4(C2×D3)⋊C411yescharacteristic
225C2×C3×C4(C2×D3)⋊C411yescharacteristic
226C2×C3×C4#21711yescharacteristic
227C2×Dic3—22no—
228C2×Dic3—41no—
229C2×Dic3—41no—
230C2×Dic3—42no—
231C2×Dic3—41no—
232C3×C8—122no—
233C3⋊C8—42no—
234C3⋊C8—124no—
235C3⋊C8—122no—
236C3⋊C8—122no—
237C2×C32—21no—
238C2×C32—21no—
239C2×C32#34211yescharacteristic
240C2×C32#35511yescharacteristic
241C2×C32#35611yescharacteristic
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8D3×Dic311yescharacteristic
245C2×Q8#62411yescharacteristic
246C2×Q8#62611yescharacteristic
247C2×Q8#62711yescharacteristic
248C22×C4—61no—
249C22×C4—61no—
250C22×C4D3×Dic311yescharacteristic
251C22×C4#62511yescharacteristic
252C22×C4#62611yescharacteristic
253M16—62no—
254M16—121no—
255M16—182no—
256M16—361no—
257C2×C8—121no—
258C2×C8—361no—
259C4⋊C4—121no—
260C42—121no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3#80611yescharacteristic
271C22×C3#80611yescharacteristic
272C22×C3C3⋊#9511yescharacteristic
273C22×C3C3⋊#9511yescharacteristic
274C22×C3#83411yescharacteristic
275C22×C3#83411yescharacteristic
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—41no—
291C3×C4—41no—
292C3×C4—41no—
293C3×C4—41no—
294C3×C4—122no—
295C3×C4—241no—
296Dic3—42no—
297Dic3—81no—
298C32#139411yescharacteristic, complemented, Sylow
299C23(C2×D3)⋊Dic311yescharacteristic
300Q8—41no—
301Q8—41no—
302Q8—41no—
303Q8—41no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—62no—
311C2×C4—121no—
312C2×C4—121no—
313C2×C4—122no—
314C2×C4—121no—
315C2×C4Dic3211yescharacteristic
316C2×C4(C2×D3)⋊Dic311yescharacteristic
317C2×C4#372211yescharacteristic
318C2×C4Dic3⋊Dic311yescharacteristic
319C2×C4Dic3⋊Dic311yescharacteristic
320C2×C4#372411yescharacteristic
321C8—122no—
322C8—362no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—41no—
331C2×C3—41no—
332C2×C3#447711yescharacteristic
333C2×C3#447811yescharacteristic
334C2×C3#452611yescharacteristic
335C2×C3#452711yescharacteristic
336C2×C3#454211yescharacteristic
337C2×C3#454811yescharacteristic
338C22—21no—
339C22—21no—
340C22#6357911yescharacteristic
341C22#6358011yescharacteristic
342C22#6358011yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—122no—
350C4—241no—
351C3—21no—
352C3#6764411yescharacteristic, complemented
353C3#6769911yescharacteristic, complemented
354C2—21no—
355C2—21no—
356C2#1058918211yescharacteristic
357C2#1058918411yescharacteristic
358C2#1058918611yescharacteristic
subgroupG/H
centerC22#63580
commutatorC2×C32×C4C42
Frattini, hypercenterC22×Q8D32
Fitting, cosocleC22×C32×Q8C22
socleC22×C32#99
prime radicalC23×C32C22⋊C4
hypocenterC32#1394
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
12. #63663C4semidirect
14. C3×#836C4semidirect
67. #836Dic3semidirect
298. C32#1394semidirect
352. C3#67644semidirect
353. C3#67699semidirect

Maximal subgroups

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

subgroupindex
C2×#636632
C3×#52292
C2×C3×#8362
#676993
#676443