Finite Group Databasebeta

← #16778789

Subgroups — #16778789

Order 3328.

464 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 98 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#13130692C211yesmaximal, characteristic
2#13130690C211yesmaximal, characteristic
3#13129656C212yesmaximal, complemented
4#13129655C212yesmaximal, complemented
5#13123170C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C22×C4×Dic13C2211yescharacteristic
8C2×C22⋊#1057—21no—
9C2×C22⋊#1057—21no—
10C2×#88112—21no—
11C2×C4⋊#1057—21no—
12#11718891C411yescharacteristic
13#11718891C2211yescharacteristic
14#11718873C411yescharacteristic
15#11718639—21no—
16#11718639—21no—
17#11718634C411yescharacteristic
18#11718634C2211yescharacteristic
19#11718607—21no—
20#11718604—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×Dic13D411yescharacteristic
26C23×Dic13D411yescharacteristic
27C22×#1057—22no—
28C22×#1057—22no—
29C13×C22⋊Q8—42no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4—21no—
33C2×C22⋊Dic13—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13—42no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13C2311yescharacteristic
43C22⋊#1057—42no—
44C22⋊#1057—42no—
45#88112—42no—
46C4⋊#1057—42no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#7715—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C2×Q8×C13—22no—
57C2×Q8×C13—41no—
58C2×Q8×C13—41no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—41no—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22×C411yescharacteristic
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—41no—
71C22×Dic13—41no—
72C22×Dic13—41no—
73C22×Dic13—41no—
74C22×Dic13C22⋊C411yescharacteristic
75C22×Dic13C22⋊C411yescharacteristic
76C22×Dic13SD1612yes—
77C22×Dic13Q1612yes—
78C22×Dic13C2×D411yescharacteristic
79C22×Dic13C2×D411yescharacteristic
80C2×#1057—42no—
81C2×#1057—42no—
82C2×#1057—42no—
83C2×#1057—42no—
84C2×#1057—42no—
85C2×#1057—42no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—42no—
88C13×C22⋊C4—42no—
89C22⋊Dic13—42no—
90C4⋊Dic13—22no—
91C4⋊Dic13—41no—
92#6101—42no—
93#6101—41no—
94#6101—41no—
95C4×Dic13—22no—
96C4×Dic13—22no—
97C4×Dic13—41no—
98C4×Dic13—41no—
99#2855—131no—
100#1797—131no—
101#1797—131no—
102#1272—132no—
103#1271—132no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13#10312yes—
111C23×C13C2×C22⋊C411yescharacteristic
112Q8×C13—82no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—44no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13#9912yes—
125C2×C4×C13#13112yes—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13#10312yes—
146C2×Dic13C2×SD1611yescharacteristic
147C2×Dic13C2×Q1611yescharacteristic
148C2×Dic13AGL(1,ℤ/8)11yescharacteristic
149C2×Dic13#13711yescharacteristic
150#1057—82no—
151#1057—82no—
152C2×C22⋊Q8#26111yescharacteristic
153C22×C42—131no—
154C2×C4⋊C8—261no—
155C2×C4⋊C8—261no—
156C2×C22⋊C8—261no—
157C2×C22⋊C8—261no—
158#391—131no—
159#391—131no—
160#389—131no—
161#389—131no—
162#387—261no—
163#387—261no—
164#385—261no—
165#381—261no—
166#380—131no—
167#336—132no—
168#336—132no—
169C22×C13—22no—
170C22×C13—22no—
171C22×C13—22no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13#40811yescharacteristic
177C22×C13C2×#9911yescharacteristic
178C22×C13#41311yescharacteristic
179C22×C13C2×#10311yescharacteristic
180C22×C13#41711yescharacteristic
181C22×C13#42111yescharacteristic
182C22×C13#42111yescharacteristic
183C4×C13—22no—
184C4×C13—22no—
185C4×C13—81no—
186C4×C13—81no—
187Dic13—21no—
188Dic13—21no—
189Dic13—21no—
190Dic13—22no—
191Dic13—21no—
192Dic13—41no—
193Dic13—81no—
194Dic13—81no—
195C22×Q8C2×#26111yescharacteristic
196C23×C4—131no—
197C23×C4—131no—
198C23×C4C2×#26111yescharacteristic
199C22×C8—262no—
200C22×C8—262no—
201C22⋊Q8—42no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4C2×#26111yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—261no—
210C2×C42—131no—
211C2×C42—131no—
212C2×C42—131no—
213C2×C42—131no—
214C2×C42—522no—
215C4⋊C8—522no—
216C4⋊C8—522no—
217C22⋊C8—522no—
218C22⋊C8—522no—
219#95—261no—
220#95—261no—
221#95—261no—
222#95—261no—
223#95—261no—
224#95—261no—
225#95—261no—
226C2×C13—42no—
227C2×C13#146811yescharacteristic
228C2×C13#148111yescharacteristic
229C2×C13#149511yescharacteristic
230C2×C13#151311yescharacteristic
231C2×C13#152011yescharacteristic
232C2×C13#153511yescharacteristic
233C2×C13#155011yescharacteristic
234C24C22⋊#26111yescharacteristic
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—41no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—41no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—132no—
247C22×C4—132no—
248C22×C4—131no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—521no—
254C22×C4—521no—
255C22×C4—521no—
256C22×C4—521no—
257C22×C4C22⋊#26111yescharacteristic
258C22×C4C22×#26111yescharacteristic
259C2×C8—522no—
260C2×C8—522no—
261C2×C8—522no—
262C2×C8—522no—
263C2×C8—522no—
264C2×C8—522no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—262no—
268C4⋊C4—521no—
269C4⋊C4—521no—
270C4⋊C4—521no—
271C4⋊C4—522no—
272C22⋊C4—42no—
273C22⋊C4—522no—
274C42—262no—
275C42—262no—
276C42—521no—
277C42—521no—
278C13#771511yescharacteristic, complemented, Sylow
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23#8811712yes—
286C23C2×C22⋊#26111yescharacteristic
287Q8—82no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—44no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—131no—
300C2×C4—132no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—131no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—522no—
314C2×C4—522no—
315C2×C4—522no—
316C2×C4—522no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4#8811912yes—
324C2×C4#8823812yes—
325C8—1042no—
326C8—1042no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22#1171914611yescharacteristic
335C22#1171914811yescharacteristic
336C22C2×#8811711yescharacteristic
337C22#1171915511yescharacteristic
338C22#1171916411yescharacteristic
339C22#1171916611yescharacteristic
340C22C2×#8811911yescharacteristic
341C4—22no—
342C4—22no—
343C4—81no—
344C4—81no—
345C4—261no—
346C4—261no—
347C4—261no—
348C4—262no—
349C4—261no—
350C4—521no—
351C4—1041no—
352C4—1041no—
353C2—42no—
354C2#1313010111yescharacteristic
355C2#1313014411yescharacteristic
356C2#1313019311yescharacteristic
357C2#1313025111yescharacteristic
358C2#1313027611yescharacteristic
359C2#1313032311yescharacteristic
360C2#1313035411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C22⋊Q8C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C22⋊Q8#261
hypocenterC13#7715
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13129656C2semidirect
4. #13129655C2semidirect
278. C13#7715semidirect

Maximal subgroups

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

subgroupindex
#131306922
#131306902
#131296562
#131296552
#131231702
#771513