Finite Group Databasebeta

← #15779180

Subgroups — #15779180

Order 3328.

642 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 99 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#13117428C211yesmaximal, characteristic
2#13114754C211yesmaximal, characteristic
3#13112960C214yesmaximal, complemented
4C13×#1782C211yesmaximal, characteristic
5C22×C13×#41C2211yescharacteristic
6C2×#88180C411yescharacteristic, complemented
7C22×C4⋊Dic13C411yescharacteristic, complemented
8C2×C13×#99—21no—
9C2×C13×#99C2212yes—
10C13×#381—21no—
11#11718891C412yescomplemented
12#11718882C2212yes—
13#11718881—21no—
14#11718881—21no—
15C2×#88074—21no—
16C2×#88074C2212yes—
17#11718873—21no—
18#11718873—21no—
19#11718872—21no—
20C2×C13×#41—24no—
21C2×C13×#41—42no—
22C2×C13×#41—42no—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D4×C13D411yescharacteristic
25C22×D4×C13D411yescharacteristic
26C22×D4×C13C2311yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C23×Dic13—21no—
31C2×C13×C22⋊C4—22no—
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13—22no—
35C2×C22⋊Dic13—22no—
36#88180—42no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—42no—
40C2×C4⋊Dic13C2×C412yes—
41C2×C4×Dic13C2×C412yes—
42C13×#99—24no—
43C13×#99—42no—
44C13×#95—42no—
45#88074—24no—
46#88074—42no—
47#88071—22no—
48#88071—22no—
49#88071—42no—
50#12859—131nomaximal, Sylow
51C24×C13C22⋊C411yescharacteristic
52C24×C13C2×D411yescharacteristic
53C24×C13C2×D411yescharacteristic
54C13×#41—416no—
55C2×Q8×C13—22no—
56C2×Q8×C13—41no—
57C2×Q8×C13—41no—
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
66C2×D4×C13#4114yes—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—22no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—42no—
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22×C411yescharacteristic
81C22×Dic13—22no—
82C22×Dic13—22no—
83C22×Dic13—42no—
84C22×Dic13—42no—
85C22×Dic13—82no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C22⋊Dic13—42no—
89C22⋊Dic13—42no—
90C22⋊Dic13—42no—
91C22⋊Dic13—82no—
92C22⋊Dic13—82no—
93C4⋊Dic13—42no—
94C4⋊Dic13—42no—
95C4⋊Dic13—42no—
96C4×Dic13—42no—
97#2311—131no—
98#1782—131no—
99#1782D1311yescharacteristic
100#1393—134no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13#9912yes—
114C23×C13C2×C22⋊C411yescharacteristic
115C23×C13#12312yes—
116C23×C13#12312yes—
117Q8×C13—44no—
118D4×C13—44no—
119D4×C13—44no—
120D4×C13—44no—
121C2×C4×C13—28no—
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—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—44no—
133C2×C4×C13—44no—
134C2×C4×C13—82no—
135C2×C4×C13—82no—
136C2×C4×C13—82no—
137C2×C4×C13#9912yes—
138C2×C4×C13#11712yes—
139C2×Dic13—42no—
140C2×Dic13—42no—
141C2×Dic13—42no—
142C2×Dic13—42no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145C2×Dic13—84no—
146C2×Dic13—82no—
147C2×Dic13—82no—
148C2×Dic13—82no—
149C22×#41C2×D1311yescharacteristic
150C2×#117—131no—
151C22×C4⋊C4—131no—
152C2×#99—21no—
153C2×#99—132no—
154C2×#99—261no—
155C2×#99C2×D1312yes—
156#391—132no—
157#390—132no—
158#386—261no—
159#386—261no—
160#381—21no—
161#381—261no—
162#380—261no—
163#380—261no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—22no—
167C22×C13—22no—
168C22×C13—22no—
169C22×C13—42no—
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—41no—
179C22×C13—81no—
180C22×C13—81no—
181C22×C13#38111yescharacteristic
182C22×C13C2×#9911yescharacteristic
183C22×C13C2×#9911yescharacteristic
184C4×C13—22no—
185C4×C13—22no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—162no—
189Dic13—82no—
190Dic13—82no—
191Dic13—162no—
192C2×#41—24no—
193C2×#41—42no—
194C2×#41—42no—
195C22×Q8C4×D1311yescharacteristic
196C22×D4D5211yescharacteristic
197C22×D4C22⋊D1311yescharacteristic
198C22×D4C22×D1311yescharacteristic
199C23×C4—261no—
200C23×C4C4×D1311yescharacteristic
201C23×C4D5211yescharacteristic
202C23×C4C22⋊D1311yescharacteristic
203#117—522no—
204C2×C4⋊C4—132no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—522no—
208C2×C22⋊C4—22no—
209C2×C22⋊C4—261no—
210C2×C22⋊C4—262no—
211C2×C22⋊C4—262no—
212C2×C22⋊C4—262no—
213C2×C42—132no—
214#99—24no—
215#99—42no—
216#99—264no—
217#99—522no—
218#95—42no—
219#95—262no—
220#95—262no—
221#95—522no—
222C2×C13—21no—
223C2×C13—21no—
224C2×C13—42no—
225C2×C13—42no—
226C2×C13—42no—
227C2×C13#181911yescharacteristic
228C2×C13#212811yescharacteristic
229C2×C13#212911yescharacteristic
230C24#610311yescharacteristic
231C24C2×D5211yescharacteristic
232C24C2×C22⋊D1311yescharacteristic
233#41—416no—
234C2×Q8—22no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×D4—22no—
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4#612914yes—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—42no—
256C22×C4—262no—
257C22×C4—262no—
258C22×C4—522no—
259C22×C4—522no—
260C22×C4—1042no—
261C22×C4#610311yescharacteristic
262C22×C4#610311yescharacteristic
263C22×C4#610311yescharacteristic
264C22×C4C2×C4×D1311yescharacteristic
265C4⋊C4—522no—
266C4⋊C4—522no—
267C4⋊C4—522no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—522no—
271C22⋊C4—522no—
272C22⋊C4—522no—
273C22⋊C4—1042no—
274C22⋊C4—1042no—
275C42—522no—
276C13#1285911yescharacteristic, complemented, Sylow
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23#8804612yes—
290C23#8814012yes—
291C23C2×#610311yescharacteristic
292C23#8818912yes—
293Q8—44no—
294D4—44no—
295D4—44no—
296D4—44no—
297C2×C4—28no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—522no—
314C2×C4—522no—
315C2×C4—522no—
316C2×C4—522no—
317C2×C4—522no—
318C2×C4—522no—
319C2×C4—1044no—
320C2×C4—1042no—
321C2×C4—1042no—
322C2×C4—1042no—
323C2×C4#8804612yes—
324C2×C4#8813112yes—
325C22—21no—
326C22—21no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—42no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—81no—
341C22—81no—
342C22#1171860411yescharacteristic
343C22C2×#8804611yescharacteristic
344C22C2×#8804611yescharacteristic
345C4—22no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—162no—
350C4—1042no—
351C4—1042no—
352C4—2082no—
353C2—21no—
354C2—21no—
355C2—42no—
356C2—42no—
357C2—42no—
358C2#1311490811yescharacteristic
359C2#1311650711yescharacteristic
360C2#1311651011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#1782C2
socleC22×C13C2×#99
prime radicalC22×C13×#41C22
cosocleC22×D4×C13C23
hypercenter#1782D13
hypocenterC13#12859
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #1782

Complements

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

NH ≅ G/Ntype
3. #13112960C2semidirect
6. C2×#88180C4semidirect
7. C22×C4⋊Dic13C4semidirect
11. #11718891C4semidirect
276. C13#12859semidirect

Maximal subgroups

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

subgroupindex
#131174282
#131147542
#131129602
C13×#17822
#1285913