Finite Group Databasebeta

← #16790711

Subgroups — #16790711

Order 3328.

394 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊#6092C211yesmaximal, characteristic, complemented
2C2×C22⋊#6092C211yesmaximal, characteristic
3C2×C22⋊#6092C211yesmaximal, characteristic
4C2×C4×#6092C211yesmaximal, characteristic, complemented
5#13129874C211yesmaximal, characteristic, complemented
6#13129874C211yesmaximal, characteristic, complemented
7C22⋊C4×#1055C211yesmaximal, characteristic
8C23×#1055C2211yescharacteristic
9C22×#6092C2211yescharacteristic
10C22×#6092C2211yescharacteristic
11C22×#6092C2211yescharacteristic
12C22×#6092C2211yescharacteristic
13C4×C13×C22⋊C4C411yescharacteristic
14C2×C22⋊#1055C411yescharacteristic
15C2×C4×#1055C2211yescharacteristic
16C2×C4×#1055C2211yescharacteristic
17C22⋊#6092—22no—
18C22⋊#6092—22no—
19C4⋊#6092—22no—
20C4×#6092—22no—
21#11718116C411yescharacteristic
22#11718116C411yescharacteristic
23C23×C4×C13C2×C411yescharacteristic
24C2×C13×C22⋊C4C811yescharacteristic
25C2×C13×C22⋊C4C811yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27C2×C42×C13C2×C411yescharacteristic
28C22×#1055—21no—
29C22×#1055—21no—
30C22×#1055—21no—
31C22×#1055—21no—
32C22×#1055—21no—
33C22×#1055—21no—
34C22×#1055C2×C411yescharacteristic
35C22×#1055C2×C411yescharacteristic
36C22×#1055C2×C411yescharacteristic
37C22×#1055C2311yescharacteristic
38C2×#6092—21no—
39C2×#6092—21no—
40C2×#6092—21no—
41C2×#6092—21no—
42C2×#6092—21no—
43C2×#6092—21no—
44C2×#6092—21no—
45C2×#6092—21no—
46C2×#6092—21no—
47C2×#6092—21no—
48C2×#6092D412yes—
49C2×#6092D412yes—
50C13×#95C811yescharacteristic
51C13×#95C811yescharacteristic
52C22⋊#1055—22no—
53C4×#1055—21no—
54C4×#1055—21no—
55C4×#1055—21no—
56C4×#1055—21no—
57#13120—131nomaximal, Sylow
58C24×C13C2×C811yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13C2×C811yescharacteristic
66C22×C4×C13C2×C811yescharacteristic
67C22×C4×C13C2×C811yescharacteristic
68C22×C4×C13C2×C811yescharacteristic
69C22×C4×C13C2×C811yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C13×C22⋊C4—22no—
72C13×C22⋊C4C1614yescomplemented
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—21no—
77C2×#1055—21no—
78C2×#1055—21no—
79C2×#1055—21no—
80C2×#1055—21no—
81C2×#1055—21no—
82C2×#1055—21no—
83C2×#1055—21no—
84C2×#1055—21no—
85C2×#1055—41no—
86C2×#1055—41no—
87C2×#1055—41no—
88C2×#1055—41no—
89C2×#1055M1612yes—
90C2×#1055C2×D411yescharacteristic
91C2×#1055C2×D411yescharacteristic
92C2×#1055#4111yescharacteristic
93C2×#1055#4111yescharacteristic
94C2×#1055#4111yescharacteristic
95C2×#1055#4111yescharacteristic
96#6092—22no—
97#6092—22no—
98#6092—41no—
99#6092—41no—
100C2×C4⋊C16—131no—
101C2×C22⋊C16—131no—
102C2×C22⋊C16—131no—
103C2×C4×C16—131no—
104C8×C22⋊C4—131no—
105#1374—131no—
106#1374—131no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13C2×C1612yes—
114C23×C13C22×C811yescharacteristic
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13C2×C1612yes—
132C2×C4×C13C2×C1612yes—
133C2×C4×C13M3212yes—
134C2×C4×C13#11711yescharacteristic
135C2×C4×C13C4×D411yescharacteristic
136C2×C4×C13C4×D411yescharacteristic
137C2×C4×C13C2×M1611yescharacteristic
138C2×C4×C13#13111yescharacteristic
139C2×C4×C13#13111yescharacteristic
140#1055—22no—
141#1055—41no—
142#1055—41no—
143#1055#12111yescharacteristic
144#1055#12311yescharacteristic
145#1055#12411yescharacteristic
146#1055#12611yescharacteristic
147C23×C8—131no—
148C22×C16—131no—
149C22×C16—131no—
150C22×C16—131no—
151C22×C16—131no—
152C2×C22⋊C8—131no—
153C2×C4×C8—131no—
154C2×C4×C8—131no—
155C4×C22⋊C4#26111yescharacteristic
156C4⋊C16—262no—
157C22⋊C16—262no—
158C22⋊C16—262no—
159C4×C16—262no—
160#336—131no—
161#336—131no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13—22no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13#43111yescharacteristic
170C22×C13C8×D411yescharacteristic
171C22×C13C8×D411yescharacteristic
172C22×C13C22×C1611yescharacteristic
173C22×C13C2×M3211yescharacteristic
174C22×C13#50411yescharacteristic
175C22×C13#50411yescharacteristic
176C4×C13—22no—
177C4×C13—22no—
178C4×C13—22no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13#38811yescharacteristic
182C4×C13#43311yescharacteristic
183C4×C13#43511yescharacteristic
184C4×C13#43611yescharacteristic
185C23×C4C2×#26111yescharacteristic
186C22×C8—131no—
187C22×C8—131no—
188C22×C8—131no—
189C22×C8—131no—
190C22×C8—261no—
191C22×C8—261no—
192C22×C8—261no—
193C22×C8—261no—
194C22×C8—261no—
195C22×C8—261no—
196C2×C22⋊C4#105711yescharacteristic
197C2×C22⋊C4#105711yescharacteristic
198C2×C42C2×#26111yescharacteristic
199C2×C42C2×#26111yescharacteristic
200C2×C16—132no—
201C2×C16—132no—
202C2×C16—261no—
203C2×C16—261no—
204C2×C16—261no—
205C2×C16—261no—
206C2×C16—261no—
207C2×C16—261no—
208C2×C16—261no—
209C2×C16—261no—
210C2×C16—261no—
211C2×C16—261no—
212C22⋊C8—262no—
213C4×C8—261no—
214C4×C8—261no—
215C4×C8—261no—
216C4×C8—261no—
217#95#105711yescharacteristic
218#95#105711yescharacteristic
219C2×C13—42no—
220C2×C13#192311yescharacteristic
221C2×C13#216211yescharacteristic
222C2×C13#216411yescharacteristic
223C2×C13D4×C1611yescharacteristic
224C2×C13D4×C1611yescharacteristic
225C2×C13#216811yescharacteristic
226C2×C13#216911yescharacteristic
227C24C2×#105711yescharacteristic
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4C2×#105711yescharacteristic
235C22×C4C2×#105711yescharacteristic
236C22×C4C2×#105711yescharacteristic
237C22×C4C2×#105711yescharacteristic
238C22×C4C2×#105711yescharacteristic
239C22×C4C22×#26111yescharacteristic
240C2×C8—131no—
241C2×C8—131no—
242C2×C8—131no—
243C2×C8—131no—
244C2×C8—131no—
245C2×C8—131no—
246C2×C8—132no—
247C2×C8—261no—
248C2×C8—261no—
249C2×C8—261no—
250C2×C8—261no—
251C2×C8—261no—
252C2×C8—261no—
253C2×C8—261no—
254C2×C8—261no—
255C2×C8—521no—
256C2×C8—521no—
257C2×C8—521no—
258C2×C8—521no—
259C22⋊C4—22no—
260C22⋊C4#609214yescomplemented
261C42—21no—
262C42—21no—
263C42—21no—
264C42—21no—
265C16—262no—
266C16—262no—
267C16—521no—
268C16—521no—
269C13#1312011yescharacteristic, complemented, Sylow
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23C2×#609212yes—
277C23C22×#105711yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4C2×#609212yes—
295C2×C4C2×#609212yes—
296C2×C4#8810612yes—
297C2×C4D13⋊M1611yescharacteristic
298C2×C4#8823711yescharacteristic
299C2×C4#8823811yescharacteristic
300C2×C4#8823811yescharacteristic
301C2×C4D4×#26111yescharacteristic
302C2×C4D4×#26111yescharacteristic
303C8—131no—
304C8—131no—
305C8—131no—
306C8—131no—
307C8—262no—
308C8—521no—
309C8—521no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C22×#609211yescharacteristic
318C22C2×#8810611yescharacteristic
319C22#1171911911yescharacteristic
320C22D4×#105711yescharacteristic
321C22D4×#105711yescharacteristic
322C22#1171916211yescharacteristic
323C22#1171916211yescharacteristic
324C4—22no—
325C4—22no—
326C4—22no—
327C4—41no—
328C4—41no—
329C4#1171906511yescharacteristic
330C4#1171906611yescharacteristic
331C4#1171906811yescharacteristic
332C4#1171907111yescharacteristic
333C2—42no—
334C2#1313090511yescharacteristic
335C2#1313119311yescharacteristic
336C2#1313120111yescharacteristic
337C2D4×#609211yescharacteristic
338C2D4×#609211yescharacteristic
339C2#1313121611yescharacteristic
340C2#1313122011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×#261
commutatorC22×C13C22×C16
FittingC4×C13×C22⋊C4C4
socleC23×C13C22×C8
prime radicalC24×C13C2×C8
cosocleC22×#1055C23
hypercenterC4×C22⋊C4#261
hypocenterC13#13120
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊#6092C2semidirect
4. C2×C4×#6092C2semidirect
5. #13129874C2semidirect
6. #13129874C2semidirect
72. C13×C22⋊C4C16semidirect
260. C22⋊C4#6092semidirect
269. C13#13120semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#60922
C2×C22⋊#60922
C2×C4×#60922
#131298742
C22⋊C4×#10552
#1312013