Finite Group Databasebeta

← #15773259

Subgroups — #15773259

Order 3328.

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

normal subgroups only

This group has 470 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#13118120C211yesmaximal, characteristic
2C4×#88074C211yesmaximal, characteristic
3#13112858C212yesmaximal, complemented
4#13112837C212yesmaximal, complemented
5C13×#1459C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×C4×Dic26C411yescharacteristic, complemented
8C2×C13×C22⋊C8—21no—
9#11718883—21no—
10C2×#88074—21no—
11C4×C22⋊Dic13—21no—
12C4×C22⋊Dic13—21no—
13C4×C22⋊Dic13—21no—
14#11718643—21no—
15#11718614C411yescharacteristic, complemented
16#11718614C2211yescharacteristic
17#11718608C411yescharacteristic, complemented
18#11718608C2211yescharacteristic
19#11718593C411yescharacteristic, complemented
20C13×#324—21no—
21C13×#323C2212yes—
22#11718118C2212yes—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C22×C8×C13—41no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C22⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4C2311yescharacteristic
33C2×C42×C13C2×C411yescharacteristic
34C2×C22⋊Dic13—22no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×#6101—21no—
41C2×C4×Dic13—21no—
42C2×C4×Dic13—21no—
43C2×C4×Dic13—41no—
44C4×Dic26—41no—
45C4×Dic26—41no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—41no—
48#88074—24no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—41no—
55#88071C2×C411yescharacteristic
56#88071C2×C411yescharacteristic
57#11728—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C2×D411yescharacteristic
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—42no—
68C22×C4×C13—42no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—42no—
79C2×Dic26—41no—
80C2×Dic26—42no—
81C2×C8×C13—42no—
82C2×C8×C13—82no—
83C13×C4⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C42×C13—21no—
87C42×C13—21no—
88C22⋊Dic13—24no—
89C22⋊Dic13—42no—
90C22⋊Dic13—42no—
91C22⋊Dic13—42no—
92C22⋊Dic13—42no—
93C22⋊Dic13—42no—
94C4⋊Dic13—41no—
95#6101—42no—
96C4×Dic13—42no—
97C4×Dic13—41no—
98C4×Dic13—41no—
99C4×Dic13—82no—
100#2398—131no—
101C4×#99—131no—
102#1459D1311yescharacteristic
103#1351—132no—
104#1344—132no—
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
115C23×C13#13512yes—
116D4×C13—44no—
117C2×C4×C13—22no—
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—42no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—81no—
130C2×C4×C13—81no—
131C2×C4×C13#9911yescharacteristic
132C2×C4×C13#9911yescharacteristic
133C2×Dic13—22no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—44no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—82no—
147C2×Dic13—82no—
148Dic26—42no—
149Dic26—42no—
150C8×C13—82no—
151C2×C4×Q8—131no—
152C2×C4×D4C2×D1311yescharacteristic
153C2×#99—261no—
154C2×C22⋊C8—21no—
155#400—261no—
156#397—131no—
157#397—131no—
158#394—261no—
159#393—131no—
160#393—131no—
161C4×C22⋊C4—261no—
162C4×C22⋊C4—261no—
163C4×C22⋊C4—261no—
164#376—131no—
165#342—132no—
166#324—21no—
167#323C2×D1312yes—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—22no—
171C22×C13—22no—
172C22×C13—42no—
173C22×C13—42no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—81no—
179C22×C13—81no—
180C22×C13C2×#9911yescharacteristic
181C22×C13#41611yescharacteristic
182C22×C13C2×#10411yescharacteristic
183C4×C13—21no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13#35412yes—
189Dic13—42no—
190Dic13—81no—
191Dic13—81no—
192Dic13—84no—
193Dic13—81no—
194C22×Q8—131no—
195C22×D4D5211yescharacteristic
196C23×C4D5211yescharacteristic
197C23×C4C22⋊D1311yescharacteristic
198C22×C8—41no—
199C4×Q8—521no—
200C4×Q8—521no—
201C4×D4—41no—
202C4×D4—41no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4C22⋊D1311yescharacteristic
206C2×C22⋊C4—262no—
207C2×C22⋊C4—261no—
208C2×C22⋊C4—261no—
209C2×C22⋊C4—261no—
210C2×C22⋊C4—261no—
211C2×C22⋊C4C4×D1311yescharacteristic
212C2×C22⋊C4C22×D1311yescharacteristic
213C2×C42—261no—
214C2×C42—261no—
215C2×C42—521no—
216C2×C42C4×D1311yescharacteristic
217#99—264no—
218C22⋊C8—22no—
219C22⋊C8—41no—
220#95—131no—
221#95—131no—
222#95—261no—
223#95—261no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—521no—
228C2×C13—21no—
229C2×C13—21no—
230C2×C13—42no—
231C2×C13—42no—
232C2×C13#150111yescharacteristic
233C2×C13#212011yescharacteristic
234C2×C13C2×#35411yescharacteristic
235C24#610311yescharacteristic
236C24C2×D5211yescharacteristic
237C2×Q8—521no—
238C2×Q8—522no—
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—41no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—261no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—522no—
253C22×C4#610311yescharacteristic
254C22×C4#610311yescharacteristic
255C22×C4#610311yescharacteristic
256C22×C4C2×C4×D1311yescharacteristic
257C22×C4C2×C22⋊D1311yescharacteristic
258C2×C8—42no—
259C2×C8—82no—
260C4⋊C4—41no—
261C4⋊C4—521no—
262C4⋊C4—522no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—264no—
266C22⋊C4—522no—
267C22⋊C4—522no—
268C22⋊C4—522no—
269C22⋊C4—522no—
270C22⋊C4—522no—
271C42—21no—
272C42—21no—
273C42—522no—
274C42—521no—
275C42—521no—
276C42—1042no—
277C13#1172811yescharacteristic, complemented, Sylow
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23#8806512yes—
287C23#8815812yes—
288C23C2×#610311yescharacteristic
289Q8—522no—
290Q8—522no—
291D4—44no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—262no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—524no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—1042no—
320C2×C4—1042no—
321C2×C4#8804611yescharacteristic
322C2×C4#8804611yescharacteristic
323C8—82no—
324C22—21no—
325C22—21no—
326C22—22no—
327C22—22no—
328C22—42no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—81no—
335C22—81no—
336C22C2×#8804611yescharacteristic
337C22#1171877411yescharacteristic
338C22C2×#8806511yescharacteristic
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—522no—
345C4—1041no—
346C4—1041no—
347C4—1044no—
348C4—1041no—
349C4#1171806512yes—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—42no—
354C2#1311332811yescharacteristic
355C2#1311647811yescharacteristic
356C2C2×#1171806511yescharacteristic
subgroupG/H
centerC2×C4#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1459C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1459D13
hypocenterC13#11728
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13112858C2semidirect
4. #13112837C2semidirect
7. C2×C4×Dic26C4semidirect
15. #11718614C4semidirect
17. #11718608C4semidirect
19. #11718593C4semidirect
277. C13#11728semidirect

Maximal subgroups

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

subgroupindex
#131181202
C4×#880742
#131128582
#131128372
C13×#14592
#1172813