Finite Group Databasebeta

← #15774037

Subgroups — #15774037

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#13120190C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112859C212yesmaximal, complemented
4#13112856C212yesmaximal, complemented
5C13×#1799C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×C4×Dic26C411yescharacteristic, complemented
8C2×C13×#99—21no—
9C13×#380—21no—
10#11718882—21no—
11#11718871—21no—
12#11718871—21no—
13C2×C22⋊#1055—21no—
14#11718634—21no—
15#11718610C411yescharacteristic, complemented
16#11718610C2211yescharacteristic
17#11718608C411yescharacteristic, complemented
18#11718608C2211yescharacteristic
19#11718597C411yescharacteristic, complemented
20C13×#342C2212yes—
21#11718120—21no—
22#11718117C2212yes—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C4×D4×C13—41no—
28C4×D4×C13—41no—
29C2×C13×C4⋊C4—41no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4C2311yescharacteristic
34C2×C42×C13C2×C411yescharacteristic
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×C4×Dic13—21no—
45C22×#1055—41no—
46C4×Dic26—41no—
47C4×Dic26—41no—
48C13×#99—42no—
49C13×#95—41no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071C2×C411yescharacteristic
54#88071C2×C411yescharacteristic
55C22⋊#1055—22no—
56C22⋊#1055—41no—
57#11897—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—
80C2×Dic26—41no—
81C2×Dic26—42no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—82no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C42×C13—21no—
89C42×C13—21no—
90C22⋊Dic13—42no—
91C22⋊Dic13—42no—
92C22⋊Dic13—81no—
93C22⋊Dic13—81no—
94C4⋊Dic13—42no—
95C4⋊Dic13—41no—
96#6101—41no—
97#6101—41no—
98#6101—81no—
99#6101—81no—
100C4×Dic13—42no—
101C2×#1055—42no—
102C2×#1055—82no—
103#2580—131no—
104#1799D1311yescharacteristic
105#1459—131no—
106#1352—132no—
107#1351—132no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13#10312yes—
117C23×C13C2×C22⋊C411yescharacteristic
118C23×C13C2×SD1611yescharacteristic
119C23×C13C2×Q1611yescharacteristic
120D4×C13—42no—
121D4×C13—42no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13—82no—
136C2×C4×C13—82no—
137C2×C4×C13—82no—
138C2×C4×C13#9911yescharacteristic
139C2×C4×C13#9911yescharacteristic
140C2×C4×C13#10312yes—
141C2×Dic13—22no—
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—41no—
153Dic26—42no—
154Dic26—42no—
155#1055—82no—
156C2×C4×Q8—131no—
157C2×C4×D4C2×D1311yescharacteristic
158C2×#99—21no—
159C2×C22⋊C8—261no—
160#399—131no—
161#399—131no—
162#393—131no—
163#393—131no—
164#390—261no—
165#389—261no—
166#385—261no—
167#385—261no—
168#382—131no—
169#380—21no—
170#342C2×D1312yes—
171#324—261no—
172#323—132no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—22no—
177C22×C13—21no—
178C22×C13—42no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13C2×#9911yescharacteristic
188C22×C13C2×#10311yescharacteristic
189C22×C13#42111yescharacteristic
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—22no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—162no—
197Dic13—42no—
198Dic13—81no—
199Dic13—81no—
200Dic13—81no—
201C22×Q8—131no—
202C22×D4C22⋊D1311yescharacteristic
203C23×C4D5211yescharacteristic
204C23×C4C22⋊D1311yescharacteristic
205C22×C8—521no—
206C4×Q8—521no—
207C4×Q8—521no—
208C4×D4—41no—
209C4×D4—41no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4D5211yescharacteristic
217C2×C22⋊C4—22no—
218C2×C22⋊C4—261no—
219C2×C22⋊C4—261no—
220C2×C22⋊C4—261no—
221C2×C22⋊C4—261no—
222C2×C22⋊C4C4×D1311yescharacteristic
223C2×C22⋊C4C22×D1311yescharacteristic
224C2×C42—261no—
225C2×C42C4×D1311yescharacteristic
226#99—42no—
227C22⋊C8—262no—
228C22⋊C8—521no—
229#95—41no—
230#95—131no—
231#95—131no—
232#95—261no—
233#95—261no—
234#95—261no—
235C2×C13—21no—
236C2×C13—21no—
237C2×C13—41no—
238C2×C13—42no—
239C2×C13—41no—
240C2×C13#152011yescharacteristic
241C2×C13#212011yescharacteristic
242C2×C13#212711yescharacteristic
243C24#610311yescharacteristic
244C24C2×C22⋊D1311yescharacteristic
245C2×Q8—521no—
246C2×Q8—522no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4#610512yes—
250C2×D4#610712yes—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4#610311yescharacteristic
263C22×C4#610311yescharacteristic
264C22×C4#610311yescharacteristic
265C22×C4C2×C4×D1311yescharacteristic
266C22×C4C2×D5211yescharacteristic
267C2×C8—522no—
268C2×C8—1042no—
269C4⋊C4—41no—
270C4⋊C4—82no—
271C4⋊C4—521no—
272C4⋊C4—522no—
273C4⋊C4—521no—
274C4⋊C4—521no—
275C4⋊C4—1041no—
276C4⋊C4—1041no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—522no—
282C22⋊C4—522no—
283C22⋊C4—1041no—
284C22⋊C4—1041no—
285C42—21no—
286C42—21no—
287C42—522no—
288C13#1189711yescharacteristic, complemented, Sylow
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#8805012yes—
298C23C2×#610311yescharacteristic
299C23C2×#610511yescharacteristic
300C23C2×#610711yescharacteristic
301Q8—522no—
302Q8—522no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4—262no—
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—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4#8804611yescharacteristic
334C2×C4#8804611yescharacteristic
335C2×C4#8805012yes—
336C8—1042no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—42no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22C2×#8804611yescharacteristic
352C22C2×#8805011yescharacteristic
353C22#1171866611yescharacteristic
354C4—22no—
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—162no—
361C4—522no—
362C4—1041no—
363C4—1041no—
364C4—1041no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—41no—
369C2—42no—
370C2#1311340711yescharacteristic
371C2#1311647511yescharacteristic
372C2#1311650311yescharacteristic
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#11897
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×C4×Dic26C4semidirect
15. #11718610C4semidirect
17. #11718608C4semidirect
19. #11718597C4semidirect
288. C13#11897semidirect

Maximal subgroups

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

subgroupindex
#131201902
#131131542
#131128592
#131128562
C13×#17992
#1189713