Finite Group Databasebeta

← #15773630

Subgroups — #15773630

Order 3328.

616 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#11718610C211yesmaximal, characteristic
2#13113163C211yesmaximal, characteristic
3#13112859C214yesmaximal, complemented
4C13×#1819C211yesmaximal, characteristic
5C22×C13×C22⋊C4C2211yescharacteristic
6C22×C22⋊Dic13—21no—
7C22×C4⋊Dic13C411yescharacteristic, complemented
8C22×#6101—21no—
9C13×#379—21no—
10C2×#88071C411yescharacteristic, complemented
11#11718868—21no—
12#11718610—21no—
13#11718610—21no—
14#11718610C412yescomplemented
15#11718610C2212yes—
16C13×#342—21no—
17C13×#342C2212yes—
18#11718117—21no—
19#11718117C2212yes—
20C25×C13D411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×Dic13—21no—
24C23×Dic13—21no—
25C2×C13×C22⋊C4—22no—
26C2×C13×C22⋊C4—41no—
27C2×C13×C22⋊C4—41no—
28C2×C13×C22⋊C4—41no—
29C2×C13×C22⋊C4—41no—
30C2×C13×C22⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4D411yescharacteristic
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C13×C22⋊C4C2311yescharacteristic
34C2×C22⋊Dic13—22no—
35C2×C22⋊Dic13—22no—
36C2×C22⋊Dic13—44no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—41no—
39C2×C4⋊Dic13—41no—
40C2×C4⋊Dic13C2×C412yes—
41C2×#6101—22no—
42C2×#6101—22no—
43C2×#6101—44no—
44C2×#6099—41no—
45#88071—21no—
46#88071C2×C412yes—
47C22⋊#1055—22no—
48C22⋊#1055—41no—
49#11809—131nomaximal, Sylow
50C24×C13—22no—
51C24×C13—21no—
52C24×C13—21no—
53C24×C13—41no—
54C24×C13—42no—
55C24×C13—42no—
56C24×C13C22⋊C411yescharacteristic
57C24×C13C22⋊C411yescharacteristic
58C24×C13C2×D411yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—24no—
71C22×Dic13—22no—
72C22×Dic13—22no—
73C22×Dic13—42no—
74C22×Dic13—42no—
75C22×Dic13—42no—
76C22×Dic13—42no—
77C22×Dic13—41no—
78C22×Dic13—41no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—82no—
86C13×C22⋊C4—82no—
87C22⋊Dic13—44no—
88C22⋊Dic13—44no—
89C4⋊Dic13—42no—
90C4⋊Dic13—42no—
91#6101—44no—
92#6101—44no—
93#6099—82no—
94C2×#1055—42no—
95C2×#399—131no—
96#1819D1311yescharacteristic
97#1462—131no—
98#1352—134no—
99C23×C13—22no—
100C23×C13—22no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—42no—
109C23×C13—42no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—48no—
115C23×C13—42no—
116C23×C13—42no—
117C23×C13—81no—
118C23×C13—81no—
119C23×C13—84no—
120C23×C13#9911yescharacteristic
121C23×C13#9911yescharacteristic
122C23×C13C2×C22⋊C411yescharacteristic
123C23×C13#13712yes—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—81no—
136C2×C4×C13—82no—
137C2×C4×C13—82no—
138C2×C4×C13—82no—
139C2×Dic13—24no—
140C2×Dic13—48no—
141C2×Dic13—42no—
142C2×Dic13—42no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145C2×Dic13—42no—
146C2×Dic13—82no—
147C2×Dic13—82no—
148#1055—82no—
149C22×C4⋊C4—131no—
150C22×C4⋊C4—261no—
151C22×C22⋊C4—261no—
152C22×C22⋊C4C2×D1311yescharacteristic
153#407—261no—
154#399—132no—
155#399—132no—
156#399—261no—
157#399—261no—
158#379—21no—
159C2×#95—131no—
160#342—21no—
161#342C2×D1312yes—
162#323—132no—
163#323—261no—
164C22×C13—24no—
165C22×C13—24no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
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—84no—
182C22×C13—84no—
183C22×C13—81no—
184C22×C13#35212yes—
185C22×C13#35312yes—
186C22×C13C2×#9911yescharacteristic
187C22×C13#41911yescharacteristic
188C22×C13#42111yescharacteristic
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13—162no—
194Dic13—44no—
195Dic13—82no—
196C25C22⋊D1311yescharacteristic
197C23×C4—261no—
198C23×C4—261no—
199C23×C4C4×D1311yescharacteristic
200C23×C4D5211yescharacteristic
201C2×M16—521no—
202C2×C4⋊C4—132no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—262no—
205C2×C4⋊C4—262no—
206C2×C4⋊C4—521no—
207C2×C4⋊C4—521no—
208C2×C4⋊C4—524no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—41no—
211C2×C22⋊C4—41no—
212C2×C22⋊C4—41no—
213C2×C22⋊C4—41no—
214C2×C22⋊C4—262no—
215C2×C22⋊C4—262no—
216C2×C22⋊C4—524no—
217C2×C22⋊C4C4×D1311yescharacteristic
218C2×C22⋊C4D5211yescharacteristic
219C2×C22⋊C4C22⋊D1311yescharacteristic
220C2×C22⋊C4C22×D1311yescharacteristic
221C22⋊C8—262no—
222C22⋊C8—521no—
223#95—132no—
224#95—261no—
225C2×C13—21no—
226C2×C13—21no—
227C2×C13—22no—
228C2×C13—22no—
229C2×C13—42no—
230C2×C13—81no—
231C2×C13#151111yescharacteristic
232C2×C13C2×#35211yescharacteristic
233C2×C13C2×#35311yescharacteristic
234C24—22no—
235C24—21no—
236C24—21no—
237C24—41no—
238C24—42no—
239C24—42no—
240C24#610311yescharacteristic
241C24#610311yescharacteristic
242C24C2×C22⋊D1311yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—264no—
251C22×C4—262no—
252C22×C4—262no—
253C22×C4—522no—
254C22×C4—522no—
255C22×C4—522no—
256C22×C4—522no—
257C22×C4—521no—
258C22×C4—521no—
259C22×C4#610311yescharacteristic
260C22×C4#610311yescharacteristic
261C22×C4C2×C4×D1311yescharacteristic
262C22×C4C2×D5211yescharacteristic
263M16—1042no—
264C2×C8—522no—
265C4⋊C4—522no—
266C4⋊C4—522no—
267C4⋊C4—524no—
268C4⋊C4—524no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—82no—
276C22⋊C4—82no—
277C22⋊C4—524no—
278C22⋊C4—524no—
279C13#1180911yescharacteristic, complemented, Sylow
280C23—21no—
281C23—21no—
282C23—22no—
283C23—22no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—42no—
290C23—42no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—48no—
296C23—42no—
297C23—42no—
298C23—81no—
299C23—81no—
300C23—84no—
301C23#8804611yescharacteristic
302C23#8804611yescharacteristic
303C23C2×#610311yescharacteristic
304C23#8820512yes—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—264no—
321C2×C4—528no—
322C2×C4—522no—
323C2×C4—522no—
324C2×C4—522no—
325C2×C4—522no—
326C2×C4—522no—
327C2×C4—1042no—
328C2×C4—1042no—
329C8—1042no—
330C22—24no—
331C22—24no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—42no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—84no—
348C22—84no—
349C22—81no—
350C22#1171806412yes—
351C22#1171806612yes—
352C22C2×#8804611yescharacteristic
353C22#1171866511yescharacteristic
354C22#1171866611yescharacteristic
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—162no—
360C4—524no—
361C4—1042no—
362C2—21no—
363C2—21no—
364C2—22no—
365C2—22no—
366C2—42no—
367C2—81no—
368C2#1311336811yescharacteristic
369C2C2×#1171806411yescharacteristic
370C2C2×#1171806611yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1819C2
socleC22×C13C2×#99
prime radicalC25×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1819D13
hypocenterC13#11809
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1819

Complements

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

NH ≅ G/Ntype
3. #13112859C2semidirect
7. C22×C4⋊Dic13C4semidirect
10. C2×#88071C4semidirect
14. #11718610C4semidirect
279. C13#11809semidirect

Maximal subgroups

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

subgroupindex
C2×#117186102
#131131632
#131128592
C13×#18192
#1180913