Finite Group Databasebeta

← #15773745

Subgroups — #15773745

Order 3328.

382 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#13114832C211yesmaximal, characteristic, complemented
2#13113180C211yesmaximal, characteristic, complemented
3#13112866C212yesmaximal, complemented
4#13112839C212yesmaximal
5C13×#2632C211yesmaximal, characteristic
6C2×C13×#124C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#399—21no—
9C13×#395C411yescharacteristic
10C13×#395C2211yescharacteristic
11C13×#394C411yescharacteristic
12C13×#394C2211yescharacteristic
13C13×#393—21no—
14C13×#388—21no—
15C13×#388—21no—
16C13×#383C411yescharacteristic
17C2×#88076—21no—
18#11718587—21no—
19#11718585—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×Q8×C13D411yescharacteristic
25C22×D4×C13C2×C411yescharacteristic
26C13×#124—41no—
27C13×#124—41no—
28C4×Q8×C13—41no—
29C4×Q8×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C42×C13C2×C411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×#6099—22no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95C2×C411yescharacteristic
50C13×#95C2×C411yescharacteristic
51#88076—42no—
52C22⋊#1055—22no—
53C4⋊#1055—41no—
54C4⋊#1055—41no—
55C4⋊#1055—41no—
56#88043—41no—
57#11833—131nomaximal, Sylow
58C24×C13—21no—
59C2×Q8×C13—21no—
60C2×Q8×C13—21no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C2×Q8×C13—41no—
64C2×Q8×C13—81no—
65C2×D4×C13—41no—
66C2×D4×C13—81no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—81no—
81C13×C4⋊C4—81no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—81no—
89C13×C22⋊C4—81no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—21no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—21no—
96#6099—42no—
97#6099—42no—
98C2×#1055—42no—
99C2×#1055—42no—
100#2632D1311yescharacteristic
101#1801—131no—
102#1467—131no—
103#1354—132no—
104#1345—132no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13C2×C22⋊C411yescharacteristic
113Q8×C13—42no—
114Q8×C13—42no—
115Q8×C13—82no—
116D4×C13—82no—
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—21no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13#9911yescharacteristic
142C2×C4×C13#9911yescharacteristic
143C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C13#13711yescharacteristic
145#1055—82no—
146#1055—82no—
147C2×#124Dic1311yescharacteristic
148C2×C4×Q8C2×D1311yescharacteristic
149#432—261no—
150#423—261no—
151C2×#101—261no—
152#399—21no—
153#395Dic1311yescharacteristic
154#395C2×D1311yescharacteristic
155#394Dic1311yescharacteristic
156#394C2×D1311yescharacteristic
157#393—21no—
158#388—21no—
159#388—21no—
160#383Dic1311yescharacteristic
161#343—132no—
162#324—132no—
163#324—261no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—81no—
167C22×C13—81no—
168C22×C13—81no—
169C22×C13—81no—
170C22×C13—81no—
171C22×C13—81no—
172C22×C13—81no—
173C22×C13C2×#9911yescharacteristic
174C22×C13#41711yescharacteristic
175C22×C13#42111yescharacteristic
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—81no—
186C4×C13—81no—
187C4×C13—81no—
188C22×Q8C2×Dic1311yescharacteristic
189C22×Q8C22⋊D1311yescharacteristic
190C22×D4C2×Dic1311yescharacteristic
191C2×M16—262no—
192#124—41no—
193#124—41no—
194C4×Q8—41no—
195C4×Q8—41no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C2×Dic1311yescharacteristic
199C2×C4⋊C4C22⋊D1311yescharacteristic
200C2×C4⋊C4C22×D1311yescharacteristic
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C42C2×Dic1311yescharacteristic
208C2×C42C22⋊D1311yescharacteristic
209C2×C42C22⋊D1311yescharacteristic
210C4⋊C8—521no—
211C4⋊C8—521no—
212C4⋊C8—521no—
213#101—522no—
214C22⋊C8—262no—
215#97—521no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95C2×Dic1311yescharacteristic
221#95C2×Dic1311yescharacteristic
222C2×C13—21no—
223C2×C13—21no—
224C2×C13—161no—
225C2×C13#151311yescharacteristic
226C2×C13#212211yescharacteristic
227C2×C13#213311yescharacteristic
228C24—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—81no—
235C2×D4—41no—
236C2×D4—81no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4C22⋊Dic1311yescharacteristic
241C22×C4C22⋊Dic1311yescharacteristic
242C22×C4C22⋊Dic1311yescharacteristic
243C22×C4C22⋊Dic1311yescharacteristic
244C22×C4C22×Dic1311yescharacteristic
245C22×C4C2×C22⋊D1311yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247M16—522no—
248M16—522no—
249C2×C8—522no—
250C2×C8—522no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—81no—
255C4⋊C4—81no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—81no—
263C22⋊C4—81no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C13#1183311yescharacteristic, complemented, Sylow
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23C2×C22⋊Dic1311yescharacteristic
279Q8—42no—
280Q8—42no—
281Q8—82no—
282D4—82no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4#8807411yescharacteristic
308C2×C4#8807411yescharacteristic
309C2×C4#8820311yescharacteristic
310C2×C4#8820511yescharacteristic
311C8—1042no—
312C8—1042no—
313C22—21no—
314C22—21no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22C2×#8807411yescharacteristic
323C22#1171889311yescharacteristic
324C22#1171889711yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C2—21no—
338C2—21no—
339C2—161no—
340C2#1311337911yescharacteristic
341C2#1311648611yescharacteristic
342C2#1311652511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2632C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2632D13
hypocenterC13#11833
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2632

Complements

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

NH ≅ G/Ntype
1. #13114832C2semidirect
2. #13113180C2semidirect
3. #13112866C2semidirect
270. C13#11833semidirect

Maximal subgroups

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

subgroupindex
#131148322
#131131802
#131128662
#131128392
C13×#26322
#1183313