Finite Group Databasebeta

← #16018267

Subgroups — #16018267

Order 3328.

570 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125330C211yesmaximal, characteristic
2#13117083C212yesmaximal, complemented
3#13117075C212yesmaximal, complemented
4#13117070C212yesmaximal, complemented
5#13117065C212yesmaximal, complemented
6#13116555C211yesmaximal, characteristic, complemented
7#13116546C211yesmaximal, characteristic
8#13116541C211yesmaximal, characteristic
9C2×#11718084C211yesmaximal, characteristic, complemented
10#13116433C211yesmaximal, characteristic, complemented
11C13×#3164C211yesmaximal, characteristic, complemented
12C13×#544—21no—
13C2×#88163—21no—
14C22×Dic52C2211yescharacteristic
15C2×#88158C2211yescharacteristic
16#11719231—21no—
17C13×#501—22no—
18C13×#500C2212yes—
19C13×#499C2212yes—
20C13×#428—21no—
21C13×#427C2211yescharacteristic
22C2×C13×#107C2211yescharacteristic
23C13×#405C2211yescharacteristic
24C2×#88052C2211yescharacteristic
25C22×#6090C2211yescharacteristic
26#11718376—22no—
27#11718360C2212yes—
28#11718357C2212yes—
29#11718084C2212yes—
30#11718084C2212yes—
31#11718084C2211yescharacteristic
32#11718084C2211yescharacteristic
33#11718084C2212yes—
34#11718084C2212yes—
35#11718084C2212yes—
36#11718083C2211yescharacteristic
37#11718083C2211yescharacteristic
38#11718083C2212yes—
39#11718053C2212yes—
40C4×#6090C2212yes—
41C2×#6127—21no—
42C22×Dic26—21no—
43C2×C13×M16D411yescharacteristic
44C22×C8×C13C2311yescharacteristic
45C13×C4⋊Q8—22no—
46C13×C4⋊Q8—41no—
47C13×#125—22no—
48C13×#125—41no—
49C13×C22⋊Q8—42no—
50C13×#117—21no—
51C13×#117D411yescharacteristic
52C2×C13×C4⋊C4—21no—
53#88163—44no—
54C2×Dic52—22no—
55C2×Dic52—22no—
56C2×Dic52—21no—
57C2×Dic52—22no—
58C2×Dic52C2311yescharacteristic
59C2×Dic52C2312yes—
60#88158—22no—
61#88158—22no—
62C2×D104C2311yescharacteristic
63C2×#6095—21no—
64C2×#6095—22no—
65#88151—41no—
66#88151—41no—
67#88140—42no—
68#88129—22no—
69#88123—22no—
70C13×#107—21no—
71C13×#107—22no—
72C13×#107C2312yes—
73C13×#107C2311yescharacteristic
74C13×#107C2311yescharacteristic
75C13×#106—21no—
76C13×#106—22no—
77C13×#97D412yes—
78C4×C8×C13C2312yes—
79#88052—22no—
80C2×#6090—22no—
81C2×#6090C2311yescharacteristic
82C2×#6090C2311yescharacteristic
83C2×#6090C2312yes—
84#33703—131nomaximal, Sylow
85C2×Q8×C13—42no—
86C22×C4×C13—41no—
87C22×C4×C13C2×D411yescharacteristic
88C2×C22⋊D13—41no—
89C22×Dic13—41no—
90#6127—42no—
91#6127—42no—
92C2×D52—21no—
93C2×C4×D13—41no—
94C2×Dic26—21no—
95C2×Dic26—22no—
96C2×Dic26—42no—
97C2×Dic26—42no—
98C2×Dic26—41no—
99C13×M16SD1614yes—
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×D412yes—
102C2×C8×C13#4112yes—
103C2×C8×C13#4112yes—
104C2×C8×C13C2411yescharacteristic
105C13×C4⋊C4—21no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—42no—
110C13×C4⋊C4—42no—
111C13×C4⋊C4—42no—
112C13×C4⋊C4D811yescharacteristic
113C13×C4⋊C4D811yescharacteristic
114C13×C22⋊C4—41no—
115C13×C22⋊C4D812yes—
116C42×C13—41no—
117C42×C13C2×D412yes—
118#6103—42no—
119#6103—42no—
120C4⋊Dic13—42no—
121C4⋊Dic13—42no—
122Dic52—21no—
123Dic52—21no—
124Dic52—22no—
125Dic52—22no—
126Dic52—42no—
127Dic52—44no—
128D104—21no—
129D104—21no—
130#6095—42no—
131#6095—44no—
132#6090—21no—
133#6090—21no—
134#6090—22no—
135#3164D1311yescharacteristic, complemented
136#3156—131no—
137#2245—132no—
138#2243—132no—
139#2242—132no—
140#2241—132no—
141#2141—131no—
142#2139—131no—
143#2138—131no—
144C2×#358—131no—
145#2108—131no—
146C23×C13C2×D811yescharacteristic
147C22×D13—41no—
148Q8×C13—162no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—42no—
152C2×C4×C13—161no—
153C2×C4×C13#12412yes—
154C2×C4×C13C2×D812yes—
155C2×C4×C13C2×D812yes—
156C2×C4×C13C2×D811yescharacteristic
157C2×C4×C13C2×SD1612yes—
158C2×C4×C13C22×D411yescharacteristic
159C22⋊D13—82no—
160C2×Dic13—41no—
161C2×Dic13—42no—
162C2×Dic13—82no—
163D52—41no—
164D52—41no—
165C4×D13—82no—
166Dic26—41no—
167Dic26—42no—
168Dic26—42no—
169Dic26—41no—
170Dic26—82no—
171C8×C13#12412yes—
172C8×C13C2×SD1614yes—
173C8×C13C2×#4111yescharacteristic
174C8×C13C2×#4111yescharacteristic
175C2×#137—261no—
176C2×#135—131no—
177C22×Q16—131no—
178#544—21no—
179#536—261no—
180C2×M32—131no—
181C22×C16—131no—
182#501—22no—
183#500C2×D1312yes—
184#499C2×D1312yes—
185#497—262no—
186#495—132no—
187#494—132no—
188#428—21no—
189#427C2×D1311yescharacteristic
190C2×#107C2×D1311yescharacteristic
191#405C2×D1311yescharacteristic
192#358—132no—
193#358—132no—
194#358—131no—
195#358—131no—
196#358—132no—
197#358—132no—
198#358—132no—
199#357—131no—
200#357—131no—
201#357—132no—
202#346—132no—
203C4×C16—132no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13#48612yes—
207C22×C13C22×D811yescharacteristic
208C2×D13—81no—
209C2×D13—81no—
210C2×D13—81no—
211C4×C13—22no—
212C4×C13—22no—
213C4×C13—82no—
214C4×C13—81no—
215C4×C13—81no—
216C4×C13#48612yes—
217C4×C13C2×#12411yescharacteristic
218C4×C13C22×SD1611yescharacteristic
219Dic13—82no—
220Dic13—81no—
221C2×#41—261no—
222C22×Q8—261no—
223#137—524no—
224#135—262no—
225#135—262no—
226C2×Q16—132no—
227C2×Q16—131no—
228C2×Q16—262no—
229C2×Q16—262no—
230C2×Q16—261no—
231C2×Q16—262no—
232C2×SD16—261no—
233C2×SD16—262no—
234C2×D8—131no—
235C2×M16C22⋊D1311yescharacteristic
236C22×C8C22×D1311yescharacteristic
237C4⋊Q8—22no—
238C4⋊Q8—41no—
239C4⋊Q8—262no—
240#125—22no—
241#125—41no—
242#124—262no—
243#123—522no—
244C22⋊Q8—42no—
245C22⋊Q8—521no—
246C22⋊Q8—521no—
247#117—21no—
248#117C22⋊D1311yescharacteristic
249C2×C4⋊C4—21no—
250M32—262no—
251C2×C16—131no—
252C2×C16—132no—
253C2×C16—131no—
254C2×C16—262no—
255#107—21no—
256#107—22no—
257#107C22×D1312yes—
258#107C22×D1311yescharacteristic
259#107C22×D1311yescharacteristic
260#106—21no—
261#106—22no—
262#97C22⋊D1312yes—
263C4×C8C22×D1312yes—
264C2×C13—22no—
265C2×C13C2×#48611yescharacteristic
266C2×C13#341611yescharacteristic
267C2×C13#341711yescharacteristic
268D13—161no—
269#41—522no—
270#41—522no—
271C2×Q8—42no—
272C2×Q8—262no—
273C2×Q8—261no—
274C2×Q8—521no—
275C2×Q8—522no—
276C2×Q8—522no—
277C2×D4—261no—
278C2×D4—521no—
279C22×C4—41no—
280C22×C4—521no—
281C22×C4—521no—
282C22×C4C2×C22⋊D1311yescharacteristic
283Q16—262no—
284Q16—262no—
285Q16—261no—
286Q16—261no—
287Q16—524no—
288Q16—522no—
289SD16—524no—
290SD16—522no—
291D8—261no—
292D8—261no—
293M16#610614yes—
294C2×C8#613112yes—
295C2×C8#613112yes—
296C2×C8C2×C22⋊D1312yes—
297C2×C8C2×C22⋊D1311yescharacteristic
298C2×C8C23×D1311yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—522no—
307C4⋊C4—522no—
308C4⋊C4#610411yescharacteristic
309C4⋊C4#610411yescharacteristic
310C22⋊C4—41no—
311C22⋊C4—522no—
312C22⋊C4—522no—
313C22⋊C4#610412yes—
314C42—41no—
315C42C2×C22⋊D1312yes—
316C16—261no—
317C16—261no—
318C16—262no—
319C13#3370311yescharacteristic, complemented, Sylow
320C23—521no—
321C23C2×#610411yescharacteristic
322Q8—162no—
323Q8—522no—
324Q8—521no—
325Q8—521no—
326Q8—522no—
327Q8—1042no—
328D4—521no—
329D4—521no—
330D4—1042no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—161no—
335C2×C4—522no—
336C2×C4—521no—
337C2×C4—1042no—
338C2×C4—1042no—
339C2×C4C2×#610412yes—
340C2×C4C2×#610412yes—
341C2×C4C2×#610411yescharacteristic
342C2×C4C2×#610612yes—
343C2×C4#8820112yes—
344C2×C4C22×C22⋊D1311yescharacteristic
345C8C2×#610614yes—
346C8#8820112yes—
347C8C2×#613111yescharacteristic
348C8C2×#613111yescharacteristic
349C22—21no—
350C22—21no—
351C22—1041no—
352C22—1041no—
353C22—1041no—
354C22#1171874912yes—
355C22C22×#610411yescharacteristic
356C4—22no—
357C4—22no—
358C4—82no—
359C4—81no—
360C4—81no—
361C4—1041no—
362C4—1042no—
363C4#1171874912yes—
364C4C22×#610611yescharacteristic
365C4C2×#8820111yescharacteristic
366C2—22no—
367C2—2081no—
368C2C2×#1171874911yescharacteristic
369C2#1312798311yescharacteristic
370C2#1312798711yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3164C2
socleC22×C13C22×D8
prime radicalC2×#88158C22
hypercenter#3164D13
hypocenterC13#33703
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3164

Complements

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

NH ≅ G/Ntype
2. #13117083C2semidirect
3. #13117075C2semidirect
4. #13117070C2semidirect
5. #13117065C2semidirect
6. #13116555C2semidirect
9. C2×#11718084C2semidirect
10. #13116433C2semidirect
11. C13×#3164C2semidirect
135. #3164D13semidirect
319. C13#33703semidirect

Maximal subgroups

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

subgroupindex
#131253302
#131170832
#131170752
#131170702
#131170652
#131165552
#131165462
#131165412
C2×#117180842
#131164332
C13×#31642
#3370313