Finite Group Databasebeta

← #15773314

Subgroups — #15773314

Order 3328.

420 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 83 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#13120753C211yesmaximal, characteristic
2C4×#88073C211yesmaximal, characteristic
3#13112867C212yesmaximal, complemented
4#13112843C212yesmaximal, complemented
5C13×#1459C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88178C411yescharacteristic
8C2×C13×C22⋊C8—21no—
9#11718883—21no—
10C2×#88073—21no—
11#11718872C411yescharacteristic
12#11718871—21no—
13#11718644C2211yescharacteristic
14#11718640C2211yescharacteristic
15#11718614C411yescharacteristic
16#11718613—21no—
17#11718608C411yescharacteristic
18#11718594—21no—
19C4×#6099—21no—
20C13×#324C2212yes—
21C13×#323—21no—
22#11718122C2212yes—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C22×C8×C13—41no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4C2311yescharacteristic
31C2×C13×C22⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39#88178—41no—
40#88178—41no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6099—22no—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—41no—
47#88073—24no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071C2×C411yescharacteristic
54#88071C2×C411yescharacteristic
55#88043—41no—
56C4×#1055—41no—
57#11739—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C22⋊C411yescharacteristic
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13—41no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—81no—
68C22×C4×C13—81no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C2×Dic26—41no—
79C2×Dic26—81no—
80C2×C8×C13—42no—
81C2×C8×C13—82no—
82C13×C4⋊C4—41no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—41no—
85C42×C13—21no—
86C42×C13—21no—
87C22⋊Dic13—42no—
88C22⋊Dic13—42no—
89C22⋊Dic13—81no—
90C22⋊Dic13—81no—
91C4⋊Dic13—41no—
92#6101—41no—
93#6101—41no—
94#6101—42no—
95#6101—81no—
96#6099—24no—
97#6099—42no—
98C2×#1055—42no—
99#2638—131no—
100C4×#100—131no—
101#1459D1311yescharacteristic
102#1354—132no—
103#1346—132no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13#10412yes—
114C23×C13C2×C22⋊C411yescharacteristic
115D4×C13—44no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—41no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—81no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13#9911yescharacteristic
130C2×C4×C13#9911yescharacteristic
131C2×C4×C13#13512yes—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144Dic26—82no—
145C8×C13—82no—
146#1055—44no—
147C2×C22⋊Q8—131no—
148C2×C4×D4C2×D1311yescharacteristic
149C2×#100—261no—
150C2×C22⋊C8—21no—
151C4×M16—261no—
152#398—131no—
153#397—131no—
154#397—261no—
155#395—131no—
156#394—261no—
157#393—131no—
158#387—261no—
159#385—261no—
160#381—131no—
161#343—132no—
162#324C2×D1312yes—
163#323—21no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—22no—
167C22×C13—42no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—81no—
174C22×C13—81no—
175C22×C13—81no—
176C22×C13C2×#9911yescharacteristic
177C22×C13#41611yescharacteristic
178C22×C13C2×#10411yescharacteristic
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—22no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185Dic13—81no—
186Dic13—81no—
187Dic13—81no—
188Dic13—81no—
189C22×Q8—131no—
190C22×D4D5211yescharacteristic
191C23×C4C4×D1311yescharacteristic
192C23×C4C22⋊D1311yescharacteristic
193C2×M16—262no—
194C22×C8—41no—
195C22⋊Q8—521no—
196C22⋊Q8—521no—
197C4×D4—41no—
198C4×D4—41no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4C22×D1311yescharacteristic
204C2×C22⋊C4—261no—
205C2×C22⋊C4—261no—
206C2×C22⋊C4—261no—
207C2×C22⋊C4—261no—
208C2×C22⋊C4C4×D1311yescharacteristic
209C2×C22⋊C4C22⋊D1311yescharacteristic
210C2×C42D5211yescharacteristic
211#100—264no—
212C22⋊C8—22no—
213C22⋊C8—41no—
214#97—521no—
215C4×C8—521no—
216#95—131no—
217#95—131no—
218#95—261no—
219#95—261no—
220#95—261no—
221#95—261no—
222#95—261no—
223C2×C13—21no—
224C2×C13—21no—
225C2×C13—42no—
226C2×C13—81no—
227C2×C13#150111yescharacteristic
228C2×C13#212111yescharacteristic
229C2×C13#213511yescharacteristic
230C24#610311yescharacteristic
231C24#610311yescharacteristic
232C2×Q8—521no—
233C2×Q8—1041no—
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—41no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—81no—
242C22×C4—81no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4#610311yescharacteristic
248C22×C4#610311yescharacteristic
249C22×C4C2×C4×D1311yescharacteristic
250C22×C4C2×D5211yescharacteristic
251C22×C4C2×C22⋊D1311yescharacteristic
252M16—264no—
253M16—522no—
254C2×C8—42no—
255C2×C8—82no—
256C2×C8—522no—
257C4⋊C4—41no—
258C4⋊C4—521no—
259C4⋊C4—522no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—1041no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—522no—
266C22⋊C4—522no—
267C22⋊C4—1041no—
268C22⋊C4—1041no—
269C42—21no—
270C42—21no—
271C13#1173911yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23#8806512yes—
282C23C2×#610311yescharacteristic
283Q8—1042no—
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4#8804611yescharacteristic
311C2×C4#8804611yescharacteristic
312C2×C4#8815812yes—
313C8—82no—
314C8—524no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22C2×#8804611yescharacteristic
328C22#1171877411yescharacteristic
329C22C2×#8806511yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—1041no—
337C4—1041no—
338C4—1041no—
339C4—1041no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#1311332811yescharacteristic
345C2#1311648011yescharacteristic
346C2#1311653011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1459C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C4⋊C4C23
hypercenter#1459D13
hypocenterC13#11739
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13112867C2semidirect
4. #13112843C2semidirect
271. C13#11739semidirect

Maximal subgroups

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

subgroupindex
#131207532
C4×#880732
#131128672
#131128432
C13×#14592
#1173913