Finite Group Databasebeta

← #16790281

Subgroups — #16790281

Order 3328.

438 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88098C211yesmaximal, characteristic
2C2×#11718260C211yesmaximal, characteristic, complemented
3C2×C4⋊#6092C211yesmaximal, characteristic, complemented
4C2×#11718259C211yesmaximal, characteristic
5#13129875C211yesmaximal, characteristic, complemented
6#13129874C211yesmaximal, characteristic, complemented
7#13114606C211yesmaximal, characteristic
8C22×C8×D13C2211yescharacteristic
9C22×#6092C2211yescharacteristic
10C22×#6092C2211yescharacteristic
11C22×#6092C2211yescharacteristic
12C22×#6092C2211yescharacteristic
13C2×#88098—22no—
14C2×#88098—22no—
15C2×#88098—22no—
16C2×#88060C411yescharacteristic
17C2×C8×Dic13C2211yescharacteristic
18C4×#6103C411yescharacteristic
19C2×C4×#1055C2211yescharacteristic
20#11718260—22no—
21#11718259—22no—
22C4⋊#6092—22no—
23C13×#336C411yescharacteristic
24#11718142C411yescharacteristic
25C22×C4×D13C2×C411yescharacteristic
26C22×C8×C13C2×C411yescharacteristic
27C22×C8×C13C2×C411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×#6103C811yescharacteristic
30C2×#6103C811yescharacteristic
31C2×C4×Dic13C2×C411yescharacteristic
32C22×#1055C2×C411yescharacteristic
33C22×#1055C2311yescharacteristic
34C2×C8×D13—21no—
35C2×C8×D13—21no—
36C2×C8×D13—21no—
37C2×C8×D13—21no—
38C2×C8×D13D412yes—
39C2×C8×D13Q812yes—
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×#6092—21no—
49C2×#6092—21no—
50C2×#6092D412yes—
51C2×#6092D412yes—
52#88098—28no—
53#88071C811yescharacteristic
54#88071C811yescharacteristic
55#88060—22no—
56C8×Dic13—21no—
57C8×Dic13—21no—
58C4×#1055—21no—
59C4×#1055—21no—
60#12913—131nomaximal, Sylow
61C23×D13C2×C811yescharacteristic
62C22×C4×C13C2×C811yescharacteristic
63C22×C4×C13C2×C811yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×Dic13C2×C811yescharacteristic
66C22×Dic13C2×C811yescharacteristic
67C22×Dic13C2×C811yescharacteristic
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13C4⋊C412yes—
73C2×C4×D13M1612yes—
74C2×C8×C13—21no—
75C2×C8×C13—21no—
76C2×C8×C13—21no—
77C2×C8×C13—21no—
78C2×C8×C13—21no—
79C2×C8×C13C4⋊C412yes—
80C42×C13—21no—
81C42×C13—21no—
82#6103—22no—
83#6103—22no—
84C4×Dic13—21no—
85C4×Dic13—21no—
86C2×#1055—21no—
87C2×#1055—21no—
88C2×#1055—21no—
89C2×#1055C2×D411yescharacteristic
90C2×#1055C2×D411yescharacteristic
91C2×#1055C2×D411yescharacteristic
92C2×#1055C2×Q811yescharacteristic
93C2×#1055#4111yescharacteristic
94C2×#1055#4111yescharacteristic
95C8×D13—22no—
96C8×D13—22no—
97C8×D13—22no—
98C8×D13—22no—
99#6092—22no—
100#6092—22no—
101#6092—41no—
102#6092—41no—
103C22×M32—131no—
104C2×C4⋊C16—131no—
105C2×C4⋊C16—131no—
106C2×C22⋊C16—131no—
107C8×C22⋊C4—131no—
108#1374—131no—
109#1374—131no—
110C23×C13C22×C811yescharacteristic
111C22×D13—21no—
112C22×D13—21no—
113C22×D13—21no—
114C22×D13—21no—
115C22×D13—21no—
116C22×D13—21no—
117C22×D13C4⋊C812yes—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13M3212yescomplemented
124C2×C4×C13C2×C4⋊C411yescharacteristic
125C2×C4×C13C4×D411yescharacteristic
126C2×C4×C13C4×D411yescharacteristic
127C2×C4×C13C2×M1611yescharacteristic
128C2×C4×C13#13111yescharacteristic
129C2×C4×C13#13111yescharacteristic
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13C4⋊C812yes—
138C2×Dic13M3212yescomplemented
139C4×D13—22no—
140C4×D13—22no—
141C4×D13—22no—
142C4×D13—22no—
143C8×C13—22no—
144C8×C13—41no—
145#1055—41no—
146#1055#12011yescharacteristic
147#1055C22⋊Q811yescharacteristic
148#1055C22⋊Q811yescharacteristic
149#1055#12311yescharacteristic
150C23×C8—131no—
151C2×M32—262no—
152C2×M32—262no—
153C2×M32—262no—
154C22×C16—131no—
155C22×C16—131no—
156C22×C16—131no—
157C22×C16—131no—
158C2×C22⋊C8—131no—
159C2×C4×C8—131no—
160C2×C4×C8—131no—
161C4×C22⋊C4—131no—
162C4⋊C16—262no—
163C4⋊C16—262no—
164C22⋊C16—262no—
165#336—131no—
166#336#26111yescharacteristic
167C22×C13C2×C4⋊C811yescharacteristic
168C22×C13C8×D411yescharacteristic
169C22×C13C8×D411yescharacteristic
170C22×C13C2×M3211yescharacteristic
171C22×C13C2×M3211yescharacteristic
172C22×C13#50411yescharacteristic
173C22×C13#50411yescharacteristic
174C2×D13—22no—
175C2×D13—22no—
176C2×D13—22no—
177C2×D13—41no—
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C4×C13—22no—
182C4×C13—41no—
183C4×C13#38511yescharacteristic
184C4×C13#42411yescharacteristic
185C4×C13#43511yescharacteristic
186C4×C13#43511yescharacteristic
187Dic13—22no—
188Dic13—22no—
189Dic13—41no—
190C23×C4—131no—
191C22×C8—131no—
192C22×C8—132no—
193C22×C8—132no—
194C22×C8—131no—
195C22×C8—261no—
196C22×C8—261no—
197C22×C8—261no—
198C22×C8—261no—
199C22×C8C2×#26111yescharacteristic
200C22×C8C2×#26111yescharacteristic
201C2×C22⋊C4—131no—
202C2×C22⋊C4—131no—
203C2×C42—131no—
204C2×C42C2×#26111yescharacteristic
205M32—268no—
206C2×C16—132no—
207C2×C16—132no—
208C2×C16—261no—
209C2×C16—261no—
210C2×C16—261no—
211C2×C16—261no—
212C2×C16—261no—
213C2×C16—261no—
214C2×C16—261no—
215C2×C16—261no—
216C2×C16—261no—
217C2×C16—261no—
218C22⋊C8—262no—
219C4×C8—261no—
220C4×C8—261no—
221C4×C8—261no—
222C4×C8—261no—
223#95—131no—
224#95—131no—
225C2×C13#185011yescharacteristic
226C2×C13#215011yescharacteristic
227C2×C13#215111yescharacteristic
228C2×C13#216811yescharacteristic
229C2×C13#216811yescharacteristic
230C2×C13#216911yescharacteristic
231C2×C13#216911yescharacteristic
232D13—42no—
233C24—131no—
234C22×C4—131no—
235C22×C4—131no—
236C22×C4—132no—
237C22×C4—132no—
238C22×C4—131no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4D13⋊C811yescharacteristic
244C22×C4D13⋊C811yescharacteristic
245C22×C4C22×#26111yescharacteristic
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—131no—
252C2×C8—131no—
253C2×C8—131no—
254C2×C8—131no—
255C2×C8—131no—
256C2×C8—131no—
257C2×C8—262no—
258C2×C8—262no—
259C2×C8—262no—
260C2×C8—262no—
261C2×C8—261no—
262C2×C8—261no—
263C2×C8—261no—
264C2×C8C4⋊#26112yes—
265C22⋊C4—262no—
266C22⋊C4—262no—
267C42—21no—
268C42—21no—
269C42—261no—
270C42—261no—
271C16—262no—
272C16—262no—
273C16—521no—
274C16—521no—
275C13#1291311yescharacteristic, complemented, Sylow
276C23—132no—
277C23—261no—
278C23—261no—
279C23—261no—
280C23—261no—
281C23—261no—
282C23—261no—
283C23C2×D13⋊C811yescharacteristic
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—132no—
290C2×C4—132no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—262no—
296C2×C4—262no—
297C2×C4—262no—
298C2×C4—262no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4#8809812yescomplemented
303C2×C4D13⋊M1611yescharacteristic
304C2×C4C2×C4⋊#26111yescharacteristic
305C2×C4#8823811yescharacteristic
306C2×C4D4×#26111yescharacteristic
307C2×C4D4×#26111yescharacteristic
308C2×C4#8824011yescharacteristic
309C8—22no—
310C8—41no—
311C8—131no—
312C8—131no—
313C8—131no—
314C8—131no—
315C8—521no—
316C22—262no—
317C22—262no—
318C22—262no—
319C22—521no—
320C22—521no—
321C22—521no—
322C22—521no—
323C22D13⋊(C4⋊C8)11yescharacteristic
324C22#1171906311yescharacteristic
325C22#1171907311yescharacteristic
326C22C2×#8809811yescharacteristic
327C22D13⋊M3211yescharacteristic
328C22#1171909611yescharacteristic
329C22#1171909611yescharacteristic
330C4—22no—
331C4—41no—
332C4—262no—
333C4—262no—
334C4—521no—
335C4#1171906511yescharacteristic
336C4#1171907011yescharacteristic
337C4#1171907511yescharacteristic
338C4#1171907911yescharacteristic
339C2—522no—
340C2#1313078111yescharacteristic
341C2#1313116911yescharacteristic
342C2#1313117211yescharacteristic
343C2#1313121811yescharacteristic
344C2#1313121911yescharacteristic
345C2#1313122111yescharacteristic
346C2#1313122211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×#261
commutator, socleC23×C13C22×C8
FittingC13×#336C4
prime radicalC23×D13C2×C8
cosocleC22×#1055C23
hypercenter#336#261
hypocenterC13#12913
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #336

Complements

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

NH ≅ G/Ntype
2. C2×#11718260C2semidirect
3. C2×C4⋊#6092C2semidirect
5. #13129875C2semidirect
6. #13129874C2semidirect
123. C2×C4×C13M32semidirect
138. C2×Dic13M32semidirect
275. C13#12913semidirect
302. C2×C4#88098semidirect

Maximal subgroups

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

subgroupindex
C22×#880982
C2×#117182602
C2×C4⋊#60922
C2×#117182592
#131298752
#131298742
#131146062
#1291313