Finite Group Databasebeta

← #15774058

Subgroups — #15774058

Order 3328.

452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 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
2#13113157C211yesmaximal, characteristic
3#13112859C212yesmaximal, complemented
4#13112856C212yesmaximal, complemented
5C13×#1799C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88178C411yescharacteristic, complemented
8C2×C13×#99—21no—
9C13×#380—21no—
10#11718881—21no—
11#11718871—21no—
12C2×#88071C411yescharacteristic, complemented
13#11718647C411yescharacteristic, complemented
14#11718640C411yescharacteristic, complemented
15#11718610C2211yescharacteristic
16#11718608C2211yescharacteristic
17#11718603—21no—
18#11718594—21no—
19#11718586—21no—
20C13×#342C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×Dic13—21no—
27C22×Dic26C2×C411yescharacteristic
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C13×C22⋊C4C2311yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40#88178—41no—
41#88178—41no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C13×#99—42no—
46C13×#95—41no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071C2×C411yescharacteristic
53#88071C2×C411yescharacteristic
54C22⋊#1055—22no—
55C4⋊#1055—41no—
56C4×#1055—41no—
57#11902—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C2×D411yescharacteristic
60C2×D4×C13—41no—
61C2×D4×C13—41no—
62C2×D4×C13SD1612yes—
63C2×D4×C13Q1612yes—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—42no—
69C22×C4×C13—81no—
70C22×C4×C13—81no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—42no—
81C22×Dic13—42no—
82C22×Dic13—81no—
83C2×Dic26—41no—
84C2×Dic26—81no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—82no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—42no—
91C42×C13—21no—
92C42×C13—21no—
93C22⋊Dic13—42no—
94C22⋊Dic13—42no—
95C22⋊Dic13—81no—
96C4⋊Dic13—41no—
97#6101—42no—
98#6101—41no—
99#6101—41no—
100#6101—81no—
101C2×#1055—42no—
102#2564—131no—
103#1799D1311yescharacteristic
104#1460—131no—
105#1352—132no—
106#1351—132no—
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#10312yes—
116C23×C13C2×C22⋊C411yescharacteristic
117C23×C13C2×SD1611yescharacteristic
118C23×C13C2×Q1611yescharacteristic
119D4×C13—42no—
120D4×C13—42no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—41no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13—81no—
134C2×C4×C13—82no—
135C2×C4×C13—82no—
136C2×C4×C13—82no—
137C2×C4×C13#9911yescharacteristic
138C2×C4×C13#9911yescharacteristic
139C2×C4×C13#10312yes—
140C2×Dic13—22no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—84no—
153Dic26—82no—
154#1055—82no—
155C2×C22⋊Q8—131no—
156C2×C4×D4C2×D1311yescharacteristic
157#431—261no—
158C2×#99—21no—
159#400—131no—
160#399—131no—
161#395—131no—
162#393—131no—
163#387—261no—
164#386—261no—
165#385—261no—
166#380—21no—
167#380—261no—
168C2×#95—131no—
169#342C2×D1312yes—
170#323—132no—
171#323—261no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—22no—
176C22×C13—21no—
177C22×C13—42no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—42no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—81no—
186C22×C13C2×#9911yescharacteristic
187C22×C13C2×#10311yescharacteristic
188C22×C13#42111yescharacteristic
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—22no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13—162no—
196Dic13—42no—
197Dic13—81no—
198Dic13—81no—
199Dic13—81no—
200C22×Q8—131no—
201C22×D4C22⋊D1311yescharacteristic
202C23×C4—261no—
203C23×C4C4×D1311yescharacteristic
204C23×C4C22⋊D1311yescharacteristic
205C22⋊Q8—521no—
206C22⋊Q8—521no—
207C4×D4—41no—
208C4×D4—41no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4C4×D1311yescharacteristic
215C2×C22⋊C4—22no—
216C2×C22⋊C4—261no—
217C2×C22⋊C4—261no—
218C2×C22⋊C4—261no—
219C2×C22⋊C4D5211yescharacteristic
220C2×C22⋊C4C22×D1311yescharacteristic
221C2×C42D5211yescharacteristic
222C4⋊C8—521no—
223#99—42no—
224C22⋊C8—262no—
225C4×C8—521no—
226#95—41no—
227#95—131no—
228#95—131no—
229#95—261no—
230#95—261no—
231#95—261no—
232#95—261no—
233#95—261no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—41no—
237C2×C13—42no—
238C2×C13—41no—
239C2×C13#152011yescharacteristic
240C2×C13#212111yescharacteristic
241C2×C13#212611yescharacteristic
242C24#610311yescharacteristic
243C24C2×C22⋊D1311yescharacteristic
244C2×Q8—521no—
245C2×Q8—1041no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4#610512yes—
249C2×D4#610712yes—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—522no—
262C22×C4—522no—
263C22×C4—1041no—
264C22×C4#610311yescharacteristic
265C22×C4#610311yescharacteristic
266C22×C4#610311yescharacteristic
267C22×C4C2×C4×D1311yescharacteristic
268C22×C4C2×D5211yescharacteristic
269C2×C8—522no—
270C4⋊C4—41no—
271C4⋊C4—82no—
272C4⋊C4—521no—
273C4⋊C4—522no—
274C4⋊C4—521no—
275C4⋊C4—521no—
276C4⋊C4—1041no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—522no—
282C22⋊C4—522no—
283C22⋊C4—1041no—
284C42—21no—
285C42—21no—
286C13#1190211yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23#8805012yes—
296C23C2×#610311yescharacteristic
297C23C2×#610511yescharacteristic
298C23C2×#610711yescharacteristic
299Q8—1042no—
300D4—42no—
301D4—42no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—82no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4—262no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—1044no—
331C2×C4#8804611yescharacteristic
332C2×C4#8804611yescharacteristic
333C2×C4#8805012yes—
334C8—1042no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—42no—
343C22—42no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—81no—
349C22C2×#8804611yescharacteristic
350C22C2×#8805011yescharacteristic
351C22#1171866611yescharacteristic
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—162no—
359C4—522no—
360C4—1041no—
361C4—1041no—
362C4—1041no—
363C2—21no—
364C2—21no—
365C2—41no—
366C2—42no—
367C2—41no—
368C2#1311340711yescharacteristic
369C2#1311648011yescharacteristic
370C2#1311649911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1799C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1799D13
hypocenterC13#11902
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #13112859C2semidirect
4. #13112856C2semidirect
7. C2×#88178C4semidirect
12. C2×#88071C4semidirect
13. #11718647C4semidirect
14. #11718640C4semidirect
286. C13#11902semidirect

Maximal subgroups

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

subgroupindex
#131200122
#131131572
#131128592
#131128562
C13×#17992
#1190213