Finite Group Databasebeta

← #15781589

Subgroups — #15781589

Order 3328.

556 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 107 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#13119789C211yesmaximal, characteristic
2#13114824C211yesmaximal, characteristic
3#13112960C214yesmaximal
4C4×C13×#99C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C2×#88178—21no—
7C2×#88178—21no—
8C2×#88123C411yescharacteristic, complemented
9C2×C13×#99C2212yes—
10C4×C13×C22⋊C4—21no—
11#11718882C2212yes—
12C2×#88074C2212yes—
13#11718873—21no—
14#11718637C412yescomplemented
15#11718610—21no—
16#11718610—21no—
17C4×C4⋊Dic13C411yescharacteristic, complemented
18C13×#342—21no—
19#11718118—21no—
20C22×D4×C13C2311yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C22×Dic26—21no—
24C4×D4×C13—41no—
25C4×D4×C13—41no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4D411yescharacteristic
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C42×C13—41no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C22⋊Dic13—22no—
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13—22no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—41no—
38C2×C4⋊Dic13C2×C412yes—
39#88178—44no—
40#88178—44no—
41C2×#6101—22no—
42C2×#6101—22no—
43C2×C4×Dic13C2×C412yes—
44#88123—41no—
45#88123—41no—
46C13×#99—22no—
47C13×#99Q814yescomplemented
48C13×#95—41no—
49#88074—24no—
50#88071—21no—
51#88071—41no—
52#13298—131nomaximal, Sylow
53C24×C13C2×D411yescharacteristic
54C24×C13C2×D411yescharacteristic
55C2×D4×C13—41no—
56C2×D4×C13—41no—
57C2×D4×C13C2×Q812yes—
58C2×D4×C13#4112yes—
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×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×Dic13—22no—
72C22×Dic13—22no—
73C22×Dic13—42no—
74C2×Dic26—42no—
75C2×Dic26—42no—
76C2×Dic26—41no—
77C2×Dic26—41no—
78C13×C4⋊C4—41no—
79C13×C22⋊C4—24no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—42no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—82no—
86C22⋊Dic13—44no—
87C22⋊Dic13—44no—
88C22⋊Dic13—42no—
89C22⋊Dic13—42no—
90C4⋊Dic13—24no—
91C4⋊Dic13—42no—
92C4⋊Dic13—42no—
93C4⋊Dic13—82no—
94#6101—44no—
95#6101—44no—
96C4×Dic13—42no—
97#2542—131no—
98#1799—131no—
99C4×#99D1311yescharacteristic
100#1393—134no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13C2×C22⋊C411yescharacteristic
110C23×C13C22⋊Q812yes—
111C23×C13#12411yescharacteristic
112C23×C13C4⋊Q811yescharacteristic
113D4×C13—42no—
114D4×C13—42no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—22no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—44no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13—82no—
130C2×C4×C13—82no—
131C2×C4×C13#9911yescharacteristic
132C2×C4×C13#9911yescharacteristic
133C2×C4×C13C4×Q812yes—
134C2×Dic13—24no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140C2×Dic13—82no—
141C2×Dic13—82no—
142C2×Dic13—82no—
143Dic26—82no—
144Dic26—82no—
145C2×C4⋊Q8—131no—
146C2×C22⋊Q8—261no—
147C2×C22⋊Q8—261no—
148C2×C4×D4C2×D1311yescharacteristic
149C2×#99—132no—
150C2×#99C2×D1312yes—
151#399—261no—
152#399—261no—
153#390—132no—
154#384—132no—
155#380—261no—
156C4×C4⋊C4—131no—
157C4×C22⋊C4—21no—
158#342—21no—
159#342—261no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—22no—
164C22×C13—21no—
165C22×C13—42no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—81no—
173C22×C13—81no—
174C22×C13#39111yescharacteristic
175C22×C13C2×#9911yescharacteristic
176C22×C13#41011yescharacteristic
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—84no—
183C4×C13#35312yes—
184Dic13—44no—
185Dic13—82no—
186Dic13—162no—
187C22×Q8—261no—
188C22×D4C22×D1311yescharacteristic
189C23×C4D5211yescharacteristic
190C23×C4C22⋊D1311yescharacteristic
191C4⋊Q8—521no—
192C4⋊Q8—521no—
193C22⋊Q8—524no—
194C22⋊Q8—524no—
195C4×D4—41no—
196C4×D4—41no—
197C2×C4⋊C4—132no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—262no—
200C2×C4⋊C4—262no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—521no—
203C2×C4⋊C4C4×D1311yescharacteristic
204C2×C22⋊C4—22no—
205C2×C22⋊C4—262no—
206C2×C22⋊C4—262no—
207C2×C22⋊C4—262no—
208C2×C22⋊C4D5211yescharacteristic
209C2×C22⋊C4C22⋊D1311yescharacteristic
210C2×C42—41no—
211C2×C42—132no—
212C2×C42C4×D1311yescharacteristic
213#99—22no—
214#99—264no—
215#99Dic2614yescomplemented
216#95—41no—
217#95—261no—
218#95—521no—
219C2×C13—21no—
220C2×C13—21no—
221C2×C13—41no—
222C2×C13—42no—
223C2×C13—41no—
224C2×C13#199611yescharacteristic
225C2×C13C2×#35311yescharacteristic
226C2×C13#212911yescharacteristic
227C24C2×D5211yescharacteristic
228C24C2×C22⋊D1311yescharacteristic
229C2×Q8—522no—
230C2×Q8—522no—
231C2×Q8—521no—
232C2×Q8—521no—
233C2×D4—41no—
234C2×D4—41no—
235C2×D4C2×Dic2612yes—
236C2×D4#612712yes—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—262no—
245C22×C4—262no—
246C22×C4—522no—
247C22×C4#610311yescharacteristic
248C22×C4#610311yescharacteristic
249C22×C4#610311yescharacteristic
250C22×C4#610311yescharacteristic
251C22×C4C2×C4×D1311yescharacteristic
252C4⋊C4—41no—
253C4⋊C4—264no—
254C4⋊C4—522no—
255C4⋊C4—522no—
256C4⋊C4—524no—
257C4⋊C4—524no—
258C4⋊C4—1042no—
259C22⋊C4—24no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—524no—
264C22⋊C4—524no—
265C22⋊C4—522no—
266C22⋊C4—522no—
267C42—21no—
268C42—21no—
269C42—82no—
270C42—522no—
271C13#1329811yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23#8812311yescharacteristic
281C23#8812911yescharacteristic
282C23#8817812yes—
283C23C2×#610311yescharacteristic
284Q8—1042no—
285Q8—1042no—
286D4—42no—
287D4—42no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—44no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—82no—
303C2×C4—82no—
304C2×C4—264no—
305C2×C4—522no—
306C2×C4—522no—
307C2×C4—522no—
308C2×C4—522no—
309C2×C4—522no—
310C2×C4—1042no—
311C2×C4—1042no—
312C2×C4—1042no—
313C2×C4#8804611yescharacteristic
314C2×C4#8804611yescharacteristic
315C2×C4C4×Dic2612yes—
316C22—21no—
317C22—21no—
318C22—22no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—42no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—81no—
329C22—81no—
330C22#1171859011yescharacteristic
331C22C2×#8804611yescharacteristic
332C22#1171866711yescharacteristic
333C4—21no—
334C4—22no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—84no—
339C4—524no—
340C4—1042no—
341C4—2082no—
342C4#1171806612yes—
343C2—21no—
344C2—21no—
345C2—42no—
346C2—41no—
347C2—41no—
348C2#1311582111yescharacteristic
349C2C2×#1171806611yescharacteristic
350C2#1311651011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC4×C13×#99C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenterC4×#99D13
hypocenterC13#13298
LCSG ▷ C22×C4×C13 ▷ C22×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
8. C2×#88123C4semidirect
14. #11718637C4semidirect
17. C4×C4⋊Dic13C4semidirect
47. C13×#99Q8semidirect
215. #99Dic26semidirect
271. C13#13298semidirect

Maximal subgroups

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

subgroupindex
#131197892
#131148242
#131129602
C4×C13×#992
#1329813