Finite Group Databasebeta

← #15772054

Subgroups — #15772054

Order 3328.

392 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11718500C211yesmaximal, characteristic
2#13116445C211yesmaximal, characteristic
3D13×C22⋊C16C211yesmaximal, characteristic
4#13112776C211yesmaximal, characteristic, complemented
5#13112775C211yesmaximal, characteristic, complemented
6#13112775C211yesmaximal, characteristic, complemented
7C13×#1322C211yesmaximal, characteristic, complemented
8C22×#6094C411yescharacteristic
9C22×C8×D13C2211yescharacteristic
10C2×#88126C411yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88054C411yescharacteristic
13C2×#88054C2211yescharacteristic
14C2×C4⋊#1055C411yescharacteristic
15C2×#88038—21no—
16C2×C16×D13—21no—
17#11718500—21no—
18#11718500—21no—
19#11718500—21no—
20#11718500—21no—
21C13×C22⋊C16C2211yescharacteristic
22C13×C22⋊C16C2211yescharacteristic
23C22⋊#6090C2211yescharacteristic
24C22⋊#6090C2211yescharacteristic
25#11718099—21no—
26#11718099—21no—
27C22×C4×D13C2×C411yescharacteristic
28C22×C8×C13C2×C411yescharacteristic
29C22×C8×C13C2311yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×#6103C811yescharacteristic
32C2×#6103C811yescharacteristic
33C2×#6101C811yescharacteristic
34C2×#6101C811yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C22×#1055C2×C411yescharacteristic
37C22×#1055C2×C411yescharacteristic
38C2×#6094—21no—
39C2×#6094—21no—
40C2×#6094—42no—
41C2×C8×D13—42no—
42C2×C8×D13D411yescharacteristic
43C2×C8×D13D411yescharacteristic
44C2×C8×D13D411yescharacteristic
45C2×C8×D13D411yescharacteristic
46#88126—21no—
47#88126—21no—
48#88126—21no—
49#88126—21no—
50C2×C13×C16—21no—
51C2×C13×C16—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54#88054—21no—
55#88054—21no—
56#88054—21no—
57#88054—21no—
58C2×#6090—21no—
59C2×#6090—21no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62#88038—42no—
63C16×D13—42no—
64#11441—131nomaximal, Sylow
65C23×D13C2×C811yescharacteristic
66C22×C4×C13C2×C811yescharacteristic
67C22×C4×C13C2×C811yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×Dic13C2×C811yescharacteristic
70C22×Dic13C2×C811yescharacteristic
71C22×Dic13C2×C811yescharacteristic
72C2×C4×D13—22no—
73C2×C4×D13—22no—
74C2×C4×D13C22⋊C411yescharacteristic
75C2×C4×D13C22⋊C411yescharacteristic
76C2×C4×D13M1611yescharacteristic
77C2×C4×D13M1611yescharacteristic
78C2×C8×C13—21no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C2×C8×C13C2×D411yescharacteristic
82C2×C8×C13C2×D411yescharacteristic
83C42×C13—21no—
84C42×C13—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93C4×Dic13—21no—
94C4×Dic13—21no—
95C2×#1055—21no—
96C2×#1055—41no—
97C2×#1055—41no—
98C2×#1055C22⋊C411yescharacteristic
99C2×#1055C22⋊C411yescharacteristic
100#6094—42no—
101#6094—42no—
102C8×D13—22no—
103C8×D13—22no—
104C8×D13—41no—
105C8×D13—41no—
106C13×C16—41no—
107C13×C16—41no—
108#6090—41no—
109#6090—41no—
110C2×#424—131no—
111#2112—131no—
112C2×C22⋊C16—131no—
113#1322—131no—
114#1322—131no—
115#1322—131no—
116#1322D1311yescharacteristic, complemented
117C23×C13C22×C811yescharacteristic
118C22×D13—21no—
119C22×D13—21no—
120C22×D13—22no—
121C22×D13—41no—
122C22×D13C22⋊C811yescharacteristic
123C22×D13C22⋊C811yescharacteristic
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—41no—
131C2×C4×C13C2×C22⋊C411yescharacteristic
132C2×C4×C13C2×M1611yescharacteristic
133C2×Dic13—22no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—41no—
139C2×Dic13C22⋊C811yescharacteristic
140C2×Dic13C22⋊C811yescharacteristic
141C4×D13—22no—
142C4×D13—21no—
143C4×D13—21no—
144C4×D13—22no—
145C4×D13#9912yes—
146C4×D13#10112yes—
147C8×C13—21no—
148C8×C13—21no—
149C8×C13—41no—
150#1055—21no—
151#1055—21no—
152#1055—41no—
153C22×M16—131no—
154C23×C8—131no—
155C2×#117—131no—
156C2×M32—261no—
157C22×C16—261no—
158#424—261no—
159#424—261no—
160#424—261no—
161#424—261no—
162C2×C4⋊C8—131no—
163C2×C4⋊C8—131no—
164C2×C4⋊C8—131no—
165C2×C4⋊C8C2×D1311yescharacteristic
166C22⋊C16—131no—
167C22⋊C16—131no—
168C22⋊C16—261no—
169C22⋊C16—261no—
170C22⋊C16C2×D1311yescharacteristic
171C22⋊C16C2×D1311yescharacteristic
172C22×C13—21no—
173C22×C13—21no—
174C22×C13C2×C22⋊C811yescharacteristic
175C22×C13#50411yescharacteristic
176C22×C13#50411yescharacteristic
177C2×D13—21no—
178C2×D13—21no—
179C2×D13—21no—
180C2×D13—21no—
181C2×D13—21no—
182C2×D13—42no—
183C2×D13—42no—
184C2×D13#32412yes—
185C4×C13—21no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13C2×#9911yescharacteristic
189C4×C13C2×#10111yescharacteristic
190Dic13—21no—
191Dic13—41no—
192Dic13—41no—
193Dic13#32412yes—
194C23×C4—131no—
195C2×M16—261no—
196C2×M16—261no—
197C2×M16—522no—
198C22×C8—131no—
199C22×C8—131no—
200C22×C8—131no—
201C22×C8—131no—
202C22×C8—131no—
203C22×C8—131no—
204C22×C8—522no—
205C22×C8C4×D1311yescharacteristic
206C22×C8C22×D1311yescharacteristic
207#117—261no—
208#117—261no—
209#117—261no—
210#117—261no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C22⋊C4—131no—
214C2×C22⋊C4—131no—
215C2×C42—131no—
216C2×C42C4×D1311yescharacteristic
217M32—522no—
218C2×C16—21no—
219C2×C16—21no—
220C2×C16—261no—
221C2×C16—261no—
222C2×C16—522no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—261no—
226C4⋊C8—261no—
227C4⋊C8—261no—
228C4⋊C8—261no—
229C4⋊C8—261no—
230C4⋊C8—261no—
231C2×C13—21no—
232C2×C13—21no—
233C2×C13C2×#32411yescharacteristic
234C2×C13#211311yescharacteristic
235C2×C13#211511yescharacteristic
236D13—22no—
237D13—41no—
238C24—131no—
239C22×C4—131no—
240C22×C4—131no—
241C22×C4—131no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—262no—
247C22×C4—262no—
248C22×C4C8×D1311yescharacteristic
249C22×C4C8×D1311yescharacteristic
250C22×C4C2×C4×D1311yescharacteristic
251M16—522no—
252M16—522no—
253C2×C8—21no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—131no—
257C2×C8—131no—
258C2×C8—262no—
259C2×C8—262no—
260C2×C8—261no—
261C2×C8—521no—
262C2×C8—521no—
263C2×C8—521no—
264C2×C8—521no—
265C2×C8D4×D1311yescharacteristic
266C2×C8D4×D1311yescharacteristic
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C42—21no—
276C42—21no—
277C42—261no—
278C42—261no—
279C16—41no—
280C16—41no—
281C16—521no—
282C16—521no—
283C13#1144111yescharacteristic, complemented, Sylow
284C23—131no—
285C23—131no—
286C23—262no—
287C23—261no—
288C23—261no—
289C23—521no—
290C23C2×C8×D1311yescharacteristic
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—131no—
299C2×C4—132no—
300C2×C4—132no—
301C2×C4—131no—
302C2×C4—262no—
303C2×C4—262no—
304C2×C4—262no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—521no—
312C2×C4C22⋊C4×D1311yescharacteristic
313C2×C4M16×D1311yescharacteristic
314C8—21no—
315C8—21no—
316C8—41no—
317C8—261no—
318C8—261no—
319C8—521no—
320C22—21no—
321C22—21no—
322C22—132no—
323C22—261no—
324C22—261no—
325C22—261no—
326C22—261no—
327C22—261no—
328C22—522no—
329C22—522no—
330C22D13×C22⋊C811yescharacteristic
331C22#1171856211yescharacteristic
332C22#1171856811yescharacteristic
333C4—21no—
334C4—41no—
335C4—41no—
336C4—132no—
337C4—261no—
338C4—521no—
339C4—521no—
340C4D13×#9911yescharacteristic
341C4D13×#10111yescharacteristic
342C2—21no—
343C2—21no—
344C2—262no—
345C2—521no—
346C2D13×#32411yescharacteristic
347C2#1311644811yescharacteristic
348C2#1311645511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC23×C13C22×C8
FrattiniC22×C8C22×D13
FittingC13×#1322C2
socleC22×C13C2×C22⋊C8
prime radicalC23×D13C2×C8
cosocleC22×C8×C13C23
hypercenter#1322D13
hypocenterC13#11441
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
4. #13112776C2semidirect
5. #13112775C2semidirect
6. #13112775C2semidirect
7. C13×#1322C2semidirect
116. #1322D13semidirect
283. C13#11441semidirect

Maximal subgroups

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

subgroupindex
C2×#117185002
#131164452
D13×C22⋊C162
#131127762
#131127752
C13×#13222
#1144113