Finite Group Databasebeta

← #15773522

Subgroups — #15773522

Order 3328.

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

normal subgroups only

This group has 460 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#13120190C211yesmaximal, characteristic
2#13113174C211yesmaximal, characteristic
3#13112859C212yesmaximal, complemented
4#13112856C212yesmaximal, complemented
5C4×C13×#99C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×C4×Dic26C411yescharacteristic, complemented
8C2×C13×#99—21no—
9C4×C13×C22⋊C4—21no—
10#11718882—21no—
11#11718871—21no—
12#11718871—21no—
13#11718868—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⋊C4D411yescharacteristic
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4C2311yescharacteristic
33C2×C42×C13—41no—
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—
45C2×#6099—41no—
46C4×Dic26—41no—
47C4×Dic26—41no—
48C13×#99—24no—
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#11784—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—81no—
69C22×C4×C13—81no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C2×Dic26—41no—
80C2×Dic26—42no—
81C13×C4⋊C4—41no—
82C13×C22⋊C4—24no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—42no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—82no—
89C22⋊Dic13—42no—
90C22⋊Dic13—42no—
91C22⋊Dic13—81no—
92C22⋊Dic13—81no—
93C4⋊Dic13—42no—
94C4⋊Dic13—41no—
95#6101—41no—
96#6101—41no—
97#6101—81no—
98#6101—81no—
99C4×Dic13—42no—
100#6099—82no—
101C2×#1055—42no—
102#2580—131no—
103C4×#99D1311yescharacteristic
104#1465—131no—
105#1352—132no—
106#1351—132no—
107C23×C13—21no—
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×C13C2×C22⋊C411yescharacteristic
117C23×C13#13712yes—
118D4×C13—44no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—44no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13—82no—
134C2×C4×C13—82no—
135C2×C4×C13#9911yescharacteristic
136C2×C4×C13#9911yescharacteristic
137C2×C4×C13#10412yes—
138C2×Dic13—22no—
139C2×Dic13—41no—
140C2×Dic13—41no—
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—
150Dic26—42no—
151Dic26—42no—
152#1055—82no—
153C2×C4×Q8—131no—
154C2×C4×D4C2×D1311yescharacteristic
155C2×#99—21no—
156#407—261no—
157#399—131no—
158#399—131no—
159#393—131no—
160#393—131no—
161#390—261no—
162#389—261no—
163#385—261no—
164#385—261no—
165#382—131no—
166C4×C22⋊C4—21no—
167#342C2×D1312yes—
168#324—261no—
169#323—132no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—22no—
173C22×C13—42no—
174C22×C13—42no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13C2×#9911yescharacteristic
183C22×C13#41911yescharacteristic
184C22×C13C2×#10411yescharacteristic
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—22no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—84no—
192Dic13—42no—
193Dic13—81no—
194Dic13—81no—
195Dic13—81no—
196C22×Q8—131no—
197C22×D4C22⋊D1311yescharacteristic
198C23×C4D5211yescharacteristic
199C23×C4C22⋊D1311yescharacteristic
200C2×M16—521no—
201C4×Q8—521no—
202C4×Q8—521no—
203C4×D4—41no—
204C4×D4—41no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4—261no—
209C2×C4⋊C4—261no—
210C2×C4⋊C4D5211yescharacteristic
211C2×C22⋊C4—22no—
212C2×C22⋊C4—261no—
213C2×C22⋊C4—261no—
214C2×C22⋊C4—261no—
215C2×C22⋊C4—261no—
216C2×C22⋊C4C4×D1311yescharacteristic
217C2×C22⋊C4C22×D1311yescharacteristic
218C2×C42—41no—
219C2×C42—261no—
220C2×C42C4×D1311yescharacteristic
221#99—24no—
222C22⋊C8—262no—
223C22⋊C8—521no—
224#95—41no—
225#95—131no—
226#95—131no—
227#95—261no—
228#95—261no—
229#95—261no—
230C2×C13—21no—
231C2×C13—21no—
232C2×C13—42no—
233C2×C13—81no—
234C2×C13#150811yescharacteristic
235C2×C13#212011yescharacteristic
236C2×C13#212711yescharacteristic
237C24#610311yescharacteristic
238C24C2×C22⋊D1311yescharacteristic
239C2×Q8—521no—
240C2×Q8—522no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—42no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4#610311yescharacteristic
256C22×C4#610311yescharacteristic
257C22×C4#610311yescharacteristic
258C22×C4C2×C4×D1311yescharacteristic
259C22×C4C2×D5211yescharacteristic
260M16—1042no—
261C2×C8—522no—
262C4⋊C4—41no—
263C4⋊C4—521no—
264C4⋊C4—522no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C4⋊C4—1041no—
268C4⋊C4—1041no—
269C22⋊C4—24no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—42no—
273C22⋊C4—522no—
274C22⋊C4—522no—
275C22⋊C4—1041no—
276C22⋊C4—1041no—
277C42—21no—
278C42—21no—
279C42—82no—
280C42—522no—
281C13#1178411yescharacteristic, complemented, Sylow
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23C2×#610311yescharacteristic
292C23#8820512yes—
293Q8—522no—
294Q8—522no—
295D4—44no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—262no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4#8804512yes—
325C2×C4#8804611yescharacteristic
326C2×C4#8804611yescharacteristic
327C8—1042no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—81no—
339C22—81no—
340C22C2×#8804511yescharacteristic
341C22C2×#8804611yescharacteristic
342C22#1171866511yescharacteristic
343C4—22no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—84no—
350C4—522no—
351C4—1041no—
352C4—1041no—
353C4—1041no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—81no—
358C2#1311335511yescharacteristic
359C2#1311647511yescharacteristic
360C2#1311650311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC4×C13×#99C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenterC4×#99D13
hypocenterC13#11784
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

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
281. C13#11784semidirect

Maximal subgroups

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

subgroupindex
#131201902
#131131742
#131128592
#131128562
C4×C13×#992
#1178413