Finite Group Databasebeta

← #15773564

Subgroups — #15773564

Order 3328.

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

normal subgroups only

This group has 444 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#13120012C211yesmaximal, characteristic
2C4×#88073C211yesmaximal, characteristic
3#13112867C212yesmaximal, complemented
4#13112864C212yesmaximal, complemented
5C13×#1465C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88178C411yescharacteristic
8C13×#407—21no—
9#11718881—21no—
10C2×#88073—21no—
11#11718871—21no—
12C2×#88071C411yescharacteristic
13#11718647C2211yescharacteristic
14#11718640C2211yescharacteristic
15#11718610C411yescharacteristic
16#11718608C411yescharacteristic
17#11718603—21no—
18#11718594—21no—
19C4×#6099—21no—
20C13×#324C2212yes—
21C13×#323—21no—
22#11718122C2212yes—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×Dic13—21no—
27C22×Dic26C2×C411yescharacteristic
28C2×C13×M16—41no—
29C4×D4×C13—41no—
30C4×D4×C13—41no—
31C2×C13×C4⋊C4C2311yescharacteristic
32C2×C13×C22⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C42×C13D411yescharacteristic
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#11793—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—
78C22×Dic13—42no—
79C22×Dic13—42no—
80C22×Dic13—81no—
81C2×Dic26—41no—
82C2×Dic26—81no—
83C13×M16—82no—
84C2×C8×C13—42no—
85C13×C4⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C42×C13—21no—
89C42×C13—21no—
90C22⋊Dic13—42no—
91C22⋊Dic13—42no—
92C22⋊Dic13—81no—
93C4⋊Dic13—41no—
94#6101—42no—
95#6101—41no—
96#6101—41no—
97#6101—81no—
98#6099—24no—
99#6099—42no—
100C2×#1055—42no—
101#2564—131no—
102C4×#100—131no—
103#1465D1311yescharacteristic
104#1354—132no—
105#1353—132no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13#10412yes—
116C23×C13C2×C22⋊C411yescharacteristic
117D4×C13—44no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13—81no—
131C2×C4×C13#9911yescharacteristic
132C2×C4×C13#9911yescharacteristic
133C2×C4×C13#13712yes—
134C2×Dic13—22no—
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—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—84no—
147Dic26—82no—
148C8×C13—82no—
149#1055—44no—
150C2×C22⋊Q8—131no—
151C2×C4×D4C2×D1311yescharacteristic
152C2×#100—261no—
153#407—21no—
154C4×M16—261no—
155#400—131no—
156#399—131no—
157#395—131no—
158#393—131no—
159#387—261no—
160#386—261no—
161#385—261no—
162#380—261no—
163C2×#95—131no—
164#343—132no—
165#324C2×D1312yes—
166#323—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—22no—
170C22×C13—42no—
171C22×C13—42no—
172C22×C13—42no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—81no—
179C22×C13C2×#9911yescharacteristic
180C22×C13#41911yescharacteristic
181C22×C13C2×#10411yescharacteristic
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—22no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—41no—
188Dic13—42no—
189Dic13—81no—
190Dic13—81no—
191Dic13—81no—
192C22×Q8—131no—
193C22×D4D5211yescharacteristic
194C23×C4—261no—
195C23×C4C4×D1311yescharacteristic
196C23×C4C22⋊D1311yescharacteristic
197C2×M16—41no—
198C2×M16—262no—
199C22⋊Q8—521no—
200C22⋊Q8—521no—
201C4×D4—41no—
202C4×D4—41no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4C22×D1311yescharacteristic
208C2×C22⋊C4—261no—
209C2×C22⋊C4—261no—
210C2×C22⋊C4—261no—
211C2×C22⋊C4C4×D1311yescharacteristic
212C2×C22⋊C4C22⋊D1311yescharacteristic
213C2×C42D5211yescharacteristic
214#100—264no—
215C22⋊C8—22no—
216C22⋊C8—41no—
217#97—521no—
218C4×C8—521no—
219#95—131no—
220#95—131no—
221#95—261no—
222#95—261no—
223#95—261no—
224#95—261no—
225#95—261no—
226C2×C13—21no—
227C2×C13—21no—
228C2×C13—42no—
229C2×C13—81no—
230C2×C13#150811yescharacteristic
231C2×C13#212111yescharacteristic
232C2×C13#213211yescharacteristic
233C24#610311yescharacteristic
234C24#610311yescharacteristic
235C2×Q8—521no—
236C2×Q8—1041no—
237C2×D4—22no—
238C2×D4—22no—
239C2×D4—41no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—81no—
245C22×C4—81no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4—261no—
250C22×C4—522no—
251C22×C4—522no—
252C22×C4—1041no—
253C22×C4#610311yescharacteristic
254C22×C4#610311yescharacteristic
255C22×C4C2×C4×D1311yescharacteristic
256C22×C4C2×D5211yescharacteristic
257C22×C4C2×C22⋊D1311yescharacteristic
258M16—82no—
259M16—264no—
260M16—522no—
261C2×C8—42no—
262C2×C8—522no—
263C4⋊C4—41no—
264C4⋊C4—521no—
265C4⋊C4—522no—
266C4⋊C4—521no—
267C4⋊C4—521no—
268C4⋊C4—1041no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—522no—
272C22⋊C4—522no—
273C22⋊C4—1041no—
274C42—21no—
275C42—21no—
276C13#1179311yescharacteristic, complemented, Sylow
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23#8806512yes—
287C23C2×#610311yescharacteristic
288Q8—1042no—
289D4—44no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—262no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—1044no—
316C2×C4#8804611yescharacteristic
317C2×C4#8804611yescharacteristic
318C2×C4#8816312yes—
319C8—82no—
320C8—524no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22C2×#8804611yescharacteristic
334C22#1171878111yescharacteristic
335C22C2×#8806511yescharacteristic
336C4—22no—
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—522no—
343C4—1041no—
344C4—1041no—
345C4—1041no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—81no—
350C2#1311335711yescharacteristic
351C2#1311648011yescharacteristic
352C2#1311651911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1465C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C4⋊C4C23
hypercenter#1465D13
hypocenterC13#11793
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #13112867C2semidirect
4. #13112864C2semidirect
276. C13#11793semidirect

Maximal subgroups

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

subgroupindex
#131200122
C4×#880732
#131128672
#131128642
C13×#14652
#1179313