Finite Group Databasebeta

← #16019805

Subgroups — #16019805

Order 3328.

548 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13127229C211yesmaximal, characteristic
2#13117063C211yesmaximal, characteristic, complemented
3#13117036C212yesmaximal, complemented
4#13116988C211yesmaximal, characteristic, complemented
5#13116925C212yesmaximal, complemented
6#13116883C211yesmaximal, characteristic, complemented
7#13116770C212yesmaximal, complemented
8C4×#88069C211yesmaximal, characteristic, complemented
9D4×#6090C211yesmaximal, characteristic
10C2×#11718156C212yesmaximal, complemented
11D4×C13×Q16C211yesmaximal, characteristic
12C22×C13×Q16C2212yes—
13D4×Q8×C13—21no—
14#11719248—21no—
15C13×#494C2211yescharacteristic
16C13×#467C2212yes—
17C13×#462—21no—
18C13×#451—22no—
19C4×C13×Q16C2211yescharacteristic
20C8×D4×C13C2211yescharacteristic
21C2×#88069C2211yescharacteristic
22C2×#88069C2212yes—
23#11718777C2212yes—
24C2×#88058C2212yes—
25C22×#6090C2212yes—
26#11718511—21no—
27#11718383—22no—
28C4×Dic52C2211yescharacteristic
29#11718343C2211yescharacteristic
30#11718156C2211yescharacteristic
31#11718156C2212yes—
32#11718156C2212yes—
33#11718156C2212yes—
34#11718156C2212yes—
35C22⋊#6090C2212yes—
36#11718084C2211yescharacteristic
37#11718081C2211yescharacteristic
38#11718081C2212yes—
39C4⋊#6090C2211yescharacteristic
40C4×#6090C2211yescharacteristic
41C22×Q8×C13—22no—
42C2×C13×Q16—24no—
43C2×C13×Q16—22no—
44C2×C13×Q16—21no—
45C2×C13×Q16—42no—
46C2×C13×Q16C2312yes—
47C2×C13×Q16C2311yescharacteristic
48C22×C8×C13C2312yes—
49C13×C4⋊Q8—21no—
50C13×C4⋊Q8—41no—
51C13×C22⋊Q8—22no—
52C13×C22⋊Q8—42no—
53C4×Q8×C13—21no—
54C4×D4×C13—41no—
55C4×D4×C13D411yescharacteristic
56D4×Dic13—41no—
57C2×C4⋊Dic13—22no—
58#88178—22no—
59C2×Dic52C2311yescharacteristic
60#88144—41no—
61#88132—42no—
62#88123—21no—
63C4×Dic26—21no—
64C13×#107C2311yescharacteristic
65C13×C4⋊C8D411yescharacteristic
66C13×#103—21no—
67C13×#103—22no—
68C13×C22⋊C8D412yes—
69C4×C8×C13C2311yescharacteristic
70#88069—22no—
71#88069—42no—
72#88058—22no—
73#88058—21no—
74#88058C2311yescharacteristic
75#88058C2312yes—
76#88056—22no—
77#88056—21no—
78C2×#6090—42no—
79C2×#6090C2311yescharacteristic
80C2×#6090C2312yes—
81C2×#6090C2311yescharacteristic
82#33866—131nomaximal, Sylow
83C2×Q8×C13—21no—
84C2×Q8×C13—22no—
85C2×Q8×C13—44no—
86C2×Q8×C13—42no—
87C2×Q8×C13—82no—
88C2×D4×C13D811yescharacteristic
89C22×C4×C13—42no—
90C22×C4×C13C2×D412yes—
91C22×Dic13—42no—
92C2×Dic26—21no—
93C2×Dic26—41no—
94C13×Q16—22no—
95C13×Q16—21no—
96C13×Q16—22no—
97C13×Q16—44no—
98C13×Q16—81no—
99C13×Q16#4112yes—
100C2×C8×C13—22no—
101C2×C8×C13—22no—
102C2×C8×C13C2×D411yescharacteristic
103C2×C8×C13C2×D412yes—
104C2×C8×C13C2411yescharacteristic
105C13×C4⋊C4—21no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—42no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4D811yescharacteristic
111C13×C22⋊C4—42no—
112C13×C22⋊C4D812yes—
113C42×C13—41no—
114C42×C13C2×D411yescharacteristic
115C22⋊Dic13—42no—
116C4⋊Dic13—21no—
117C4⋊Dic13—22no—
118C4⋊Dic13—41no—
119C4⋊Dic13—42no—
120#6101—41no—
121#6101—42no—
122C4×Dic13—41no—
123Dic52—21no—
124Dic52—21no—
125#6090—21no—
126#6090—22no—
127#6090—21no—
128#3338—131no—
129D4×Q16D1311yescharacteristic
130#2241—131no—
131#2236—132no—
132#2227—131no—
133#2216—132no—
134#2209—131no—
135#2188—132no—
136C4×Q32—131no—
137D4×C16—131no—
138C2×#358—132no—
139C23×C13C2×D812yes—
140Q8×C13—22no—
141Q8×C13—41no—
142Q8×C13—42no—
143Q8×C13—42no—
144Q8×C13—84no—
145D4×C13Q3214yescomplemented
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—42no—
151C2×C4×C13—84no—
152C2×C4×C13C2×D812yes—
153C2×C4×C13C2×D811yescharacteristic
154C2×C4×C13C2×D811yescharacteristic
155C2×C4×C13C22×D411yescharacteristic
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—42no—
159C2×Dic13—162no—
160Dic26—41no—
161Dic26—41no—
162Dic26—161no—
163C8×C13—22no—
164C8×C13—21no—
165C8×C13C2×#4111yescharacteristic
166C8×C13H(5,𝔽2)11yescharacteristic
167C22×Q16C2×D1312yes—
168#554—261no—
169D4×Q8—21no—
170C2×Q32—131no—
171C2×Q32—132no—
172C22×C16—132no—
173#500—131no—
174#494C2×D1311yescharacteristic
175#484—262no—
176#477—261no—
177#467—132no—
178#467C2×D1312yes—
179#462—21no—
180#451—22no—
181C4×Q16—131no—
182C4×Q16C2×D1311yescharacteristic
183C8×D4C2×D1311yescharacteristic
184C2×#107—132no—
185#366—131no—
186#366—132no—
187C4⋊C16—131no—
188#358—131no—
189#358—132no—
190#358—132no—
191#358—132no—
192#358—132no—
193#358—131no—
194C22⋊C16—132no—
195C4×C16—131no—
196C22×C13—22no—
197C22×C13—22no—
198C22×C13C2×Q3214yes—
199C22×C13C22×D811yescharacteristic
200C4×C13—21no—
201C4×C13—22no—
202C4×C13—42no—
203C4×C13—81no—
204C4×C13—82no—
205C4×C13C2×Q3212yes—
206C4×C13#54611yescharacteristic
207C4×C13#57711yescharacteristic
208Dic13—82no—
209Dic13—81no—
210Dic13—81no—
211C22×Q8—22no—
212C2×Q16—24no—
213C2×Q16—22no—
214C2×Q16—21no—
215C2×Q16—42no—
216C2×Q16—131no—
217C2×Q16C22×D1312yes—
218C2×Q16C22×D1311yescharacteristic
219C22×C8C22×D1312yes—
220C4⋊Q8—21no—
221C4⋊Q8—41no—
222C4⋊Q8—261no—
223#125—521no—
224C22⋊Q8—22no—
225C22⋊Q8—42no—
226C22⋊Q8—262no—
227C22⋊Q8—522no—
228C4×Q8—21no—
229C4×Q8—261no—
230C4×D4—41no—
231C4×D4—521no—
232C4×D4C22⋊D1311yescharacteristic
233C2×C4⋊C4—262no—
234Q32—262no—
235Q32—522no—
236C2×C16—131no—
237C2×C16—131no—
238C2×C16—132no—
239C2×C16—522no—
240#107—131no—
241#107—132no—
242#107—262no—
243#107—261no—
244#107C22×D1311yescharacteristic
245C4⋊C8C22⋊D1311yescharacteristic
246#103—21no—
247#103—22no—
248#103—261no—
249#103—262no—
250C22⋊C8C22⋊D1312yes—
251C4×C8C22×D1311yescharacteristic
252C2×C13—24no—
253C2×C13#329411yescharacteristic
254C2×C13C22×Q3211yescharacteristic
255C2×C13#341611yescharacteristic
256C2×Q8—21no—
257C2×Q8—22no—
258C2×Q8—44no—
259C2×Q8—42no—
260C2×Q8—82no—
261C2×Q8—261no—
262C2×Q8—521no—
263C2×D4#610411yescharacteristic
264C22×C4—42no—
265C22×C4—522no—
266C22×C4C2×C22⋊D1312yes—
267Q16—22no—
268Q16—21no—
269Q16—22no—
270Q16—44no—
271Q16—81no—
272Q16—261no—
273Q16—261no—
274Q16#612912yes—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8C2×C22⋊D1311yescharacteristic
278C2×C8C2×C22⋊D1312yes—
279C2×C8C23×D1311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C4⋊C4—41no—
285C4⋊C4—261no—
286C4⋊C4—262no—
287C4⋊C4—522no—
288C4⋊C4—521no—
289C4⋊C4—521no—
290C4⋊C4—522no—
291C4⋊C4#610411yescharacteristic
292C22⋊C4—42no—
293C22⋊C4—522no—
294C22⋊C4#610412yes—
295C42—41no—
296C42—521no—
297C42C2×C22⋊D1311yescharacteristic
298C16—261no—
299C16—261no—
300C16—262no—
301C13#3386611yescharacteristic, complemented, Sylow
302C23C2×#610412yes—
303Q8—22no—
304Q8—41no—
305Q8—42no—
306Q8—42no—
307Q8—84no—
308Q8—521no—
309Q8—521no—
310Q8—2081no—
311D4#8806914yescomplemented
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—84no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—522no—
321C2×C4—2082no—
322C2×C4C2×#610411yescharacteristic
323C2×C4C2×#610412yes—
324C2×C4C2×#610411yescharacteristic
325C2×C4C22×C22⋊D1311yescharacteristic
326C8—22no—
327C8—21no—
328C8C2×#612911yescharacteristic
329C8#8825111yescharacteristic
330C22—22no—
331C22—22no—
332C22C2×#8806914yes—
333C22C22×#610411yescharacteristic
334C4—21no—
335C4—22no—
336C4—42no—
337C4—81no—
338C4—82no—
339C4—1041no—
340C4—1042no—
341C4—1041no—
342C4C2×#8806912yes—
343C4#1171951111yescharacteristic
344C4#1171954111yescharacteristic
345C2—24no—
346C2#1312664911yescharacteristic
347C2C22×#8806911yescharacteristic
348C2#1312798011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingD4×C13×Q16C2
socleC22×C13C22×D8
prime radicalC2×D4×C13D8
hypercenterD4×Q16D13
hypocenterC13#33866
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×Q16

Complements

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

NH ≅ G/Ntype
2. #13117063C2semidirect
3. #13117036C2semidirect
4. #13116988C2semidirect
5. #13116925C2semidirect
6. #13116883C2semidirect
7. #13116770C2semidirect
8. C4×#88069C2semidirect
10. C2×#11718156C2semidirect
145. D4×C13Q32semidirect
301. C13#33866semidirect
311. D4#88069semidirect

Maximal subgroups

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

subgroupindex
#131272292
#131170632
#131170362
#131169882
#131169252
#131168832
#131167702
C4×#880692
D4×#60902
C2×#117181562
D4×C13×Q162
#3386613