Finite Group Databasebeta

← #15773751

Subgroups — #15773751

Order 3328.

400 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 79 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#13120753C211yesmaximal, characteristic
2#13114828C211yesmaximal, characteristic
3#13112867C212yesmaximal, complemented
4#13112843C212yesmaximal, complemented
5C13×#1465C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88178C411yescharacteristic
8C13×#407—21no—
9#11718883—21no—
10C2×#88073—21no—
11#11718872C411yescharacteristic
12#11718871—21no—
13#11718644C2211yescharacteristic
14#11718640C2211yescharacteristic
15#11718614C411yescharacteristic
16#11718613—21no—
17#11718608C411yescharacteristic
18#11718594—21no—
19#11718585—21no—
20C13×#324C2212yes—
21C13×#323—21no—
22#11718122C2212yes—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C2×C13×M16—41no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4C2311yescharacteristic
31C2×C13×C22⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39#88178—41no—
40#88178—41no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6099—22no—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—41no—
47#88073—42no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071C2×C411yescharacteristic
54#88071C2×C411yescharacteristic
55C4⋊#1055—41no—
56C4⋊#1055—41no—
57#11834—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C22⋊C411yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—81no—
69C22×C4×C13—81no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C2×Dic26—41no—
80C2×Dic26—81no—
81C13×M16—82no—
82C2×C8×C13—42no—
83C13×C4⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C42×C13—21no—
87C42×C13—21no—
88C22⋊Dic13—42no—
89C22⋊Dic13—42no—
90C22⋊Dic13—81no—
91C22⋊Dic13—81no—
92C4⋊Dic13—41no—
93#6101—41no—
94#6101—41no—
95#6101—41no—
96#6101—41no—
97#6101—81no—
98#6099—42no—
99#6099—42no—
100C2×#1055—42no—
101#2638—131no—
102#1800—131no—
103#1465D1311yescharacteristic
104#1354—132no—
105#1346—132no—
106C23×C13—21no—
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
117D4×C13—42no—
118D4×C13—42no—
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—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—81no—
130C2×C4×C13—81no—
131C2×C4×C13—81no—
132C2×C4×C13#9911yescharacteristic
133C2×C4×C13#9911yescharacteristic
134C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C13#13711yescharacteristic
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
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—
148Dic26—82no—
149C8×C13—82no—
150#1055—82no—
151C2×C22⋊Q8—131no—
152C2×C4×D4C2×D1311yescharacteristic
153#423—261no—
154C2×#100—261no—
155#407—21no—
156#398—131no—
157#397—131no—
158#397—261no—
159#395—131no—
160#394—261no—
161#393—131no—
162#387—261no—
163#385—261no—
164#381—131no—
165#343—132no—
166#324C2×D1312yes—
167#323—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—42no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—81no—
178C22×C13—81no—
179C22×C13—81no—
180C22×C13C2×#9911yescharacteristic
181C22×C13#41711yescharacteristic
182C22×C13#42111yescharacteristic
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190Dic13—81no—
191Dic13—81no—
192Dic13—81no—
193Dic13—81no—
194C22×Q8—131no—
195C22×D4D5211yescharacteristic
196C23×C4C4×D1311yescharacteristic
197C23×C4C22⋊D1311yescharacteristic
198C2×M16—41no—
199C2×M16—262no—
200C22⋊Q8—521no—
201C22⋊Q8—521no—
202C4×D4—41no—
203C4×D4—41no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4C22×D1311yescharacteristic
209C2×C22⋊C4—261no—
210C2×C22⋊C4—261no—
211C2×C22⋊C4—261no—
212C2×C22⋊C4—261no—
213C2×C22⋊C4C4×D1311yescharacteristic
214C2×C22⋊C4C22⋊D1311yescharacteristic
215C2×C42D5211yescharacteristic
216C4⋊C8—521no—
217C4⋊C8—521no—
218#100—522no—
219C22⋊C8—22no—
220C22⋊C8—41no—
221#95—131no—
222#95—131no—
223#95—261no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—261no—
228C2×C13—21no—
229C2×C13—21no—
230C2×C13—81no—
231C2×C13—81no—
232C2×C13#151311yescharacteristic
233C2×C13#212111yescharacteristic
234C2×C13#213511yescharacteristic
235C24#610311yescharacteristic
236C24#610311yescharacteristic
237C2×Q8—521no—
238C2×Q8—1041no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—41no—
242C2×D4—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—81no—
248C22×C4—81no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4#610311yescharacteristic
254C22×C4#610311yescharacteristic
255C22×C4C2×C4×D1311yescharacteristic
256C22×C4C2×D5211yescharacteristic
257C22×C4C2×C22⋊D1311yescharacteristic
258M16—82no—
259M16—522no—
260M16—522no—
261C2×C8—42no—
262C2×C8—522no—
263C4⋊C4—41no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C4⋊C4—521no—
268C4⋊C4—521no—
269C4⋊C4—1041no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—522no—
273C22⋊C4—522no—
274C22⋊C4—1041no—
275C22⋊C4—1041no—
276C42—21no—
277C42—21no—
278C13#1183411yescharacteristic, complemented, Sylow
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23C2×#610311yescharacteristic
290Q8—1042no—
291D4—42no—
292D4—42no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4#8804611yescharacteristic
319C2×C4#8804611yescharacteristic
320C2×C4#8816211yescharacteristic
321C2×C4#8816311yescharacteristic
322C8—82no—
323C8—1042no—
324C22—21no—
325C22—21no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22C2×#8804611yescharacteristic
337C22#1171879411yescharacteristic
338C22#1171880011yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—1041no—
347C4—1041no—
348C4—1041no—
349C4—1041no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—81no—
354C2#1311338011yescharacteristic
355C2#1311648011yescharacteristic
356C2#1311653011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1465C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C4⋊C4C23
hypercenter#1465D13
hypocenterC13#11834
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #13112867C2semidirect
4. #13112843C2semidirect
278. C13#11834semidirect

Maximal subgroups

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

subgroupindex
#131207532
#131148282
#131128672
#131128432
C13×#14652
#1183413