Finite Group Databasebeta

← #15848253

Subgroups — #15848253

Order 3328.

622 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125982C211yesmaximal, characteristic
2#13124641C211yesmaximal, characteristic
3C2×#11718692C211yesmaximal, characteristic
4#13114266C214yesmaximal, complemented
5#13114218C214yesmaximal, complemented
6#13113607C211yesmaximal, characteristic
7#13113507C211yesmaximal, characteristic
8#13113491C211yesmaximal, characteristic
9C13×#2982C211yesmaximal, characteristic
10C2×C4×Q8×C13C2211yescharacteristic
11C22×#6107—21no—
12#11719175C2211yescharacteristic
13C2×#88123C2211yescharacteristic
14C8×Q8×C13—22no—
15C8×Q8×C13C2214yes—
16C13×#431—22no—
17C13×#431C2211yescharacteristic
18C13×#431C2211yescharacteristic
19#11718886—21no—
20#11718692—22no—
21#11718692C2214yes—
22#11718683—22no—
23#11718682C2212yes—
24#11718681C2212yes—
25C2×#88050—21no—
26#11718625—21no—
27#11718585C2211yescharacteristic
28C2×C4⋊#1055C2211yescharacteristic
29#11718512—22no—
30#11718382—22no—
31#11718342C2212yes—
32#11718341C2212yes—
33#11718078C2214yes—
34#11718074C2212yes—
35#11718073C2212yes—
36#11718049C2214yes—
37C22×Q8×C13D411yescharacteristic
38C22×Dic26—21no—
39C4×Q8×C13—21no—
40C4×Q8×C13—21no—
41C4×Q8×C13D412yes—
42C4×Q8×C13C2312yes—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4D411yescharacteristic
45C2×C42×C13—21no—
46C2×C42×C13C2311yescharacteristic
47C2×#6107—24no—
48C2×#6107—44no—
49#88180—21no—
50C2×C4⋊Dic13—21no—
51C2×C4⋊Dic13—21no—
52#88178—21no—
53#88178—21no—
54C2×#6099—21no—
55C22×#1055—21no—
56#88124—21no—
57#88123—21no—
58#88123—21no—
59#88123—21no—
60#88123C2312yes—
61#88123C2311yescharacteristic
62#88123C2311yescharacteristic
63C4×Dic26—21no—
64C4×Dic26—21no—
65C13×C4⋊C8—24no—
66C13×C4⋊C8D412yes—
67C13×C4⋊C8C2312yes—
68C13×C22⋊C8—21no—
69C13×C22⋊C8D412yes—
70C4×C8×C13—24no—
71C4×C8×C13—21no—
72C4×C8×C13C2312yes—
73#88075—22no—
74#88075—22no—
75#88057—24no—
76#88056—24no—
77#88050—24no—
78#88048—22no—
79#88047—22no—
80C4⋊#1055—21no—
81C4⋊#1055—21no—
82C4⋊#1055C2312yes—
83C4⋊#1055C2312yes—
84#19402—131nomaximal, Sylow
85C2×Q8×C13—21no—
86C2×Q8×C13—22no—
87C2×Q8×C13SD1614yes—
88C2×Q8×C13C2×D412yes—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13#4111yescharacteristic
94C22×Dic13—41no—
95C2×Dic26—21no—
96C2×Dic26—22no—
97C2×Dic26—21no—
98C2×Dic26—42no—
99C2×Dic26—42no—
100C2×Dic26—41no—
101C2×C8×C13—22no—
102C2×C8×C13C2×D414yes—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4C2×D412yes—
107C42×C13—22no—
108C42×C13—22no—
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13#4111yescharacteristic
112C42×C13C2411yescharacteristic
113C22⋊Dic13—41no—
114#6107—48no—
115C4⋊Dic13—21no—
116C4⋊Dic13—21no—
117C4⋊Dic13—21no—
118C4⋊Dic13—22no—
119C4⋊Dic13—21no—
120C4⋊Dic13—22no—
121C4⋊Dic13—41no—
122C4⋊Dic13—41no—
123#6101—41no—
124#6101—41no—
125C4×Dic13—41no—
126#6099—42no—
127C2×#1055—22no—
128C2×#1055—22no—
129C2×#1055—42no—
130#3229—131no—
131#3078—131no—
132C2×#462—131no—
133#2982D1311yescharacteristic
134#1680—134no—
135#1672—134no—
136#1570—131no—
137#1546—131no—
138#1542—131no—
139C23×C13#12111yescharacteristic
140Q8×C13—22no—
141Q8×C13—24no—
142Q8×C13C2×SD1614yes—
143C2×C4×C13—22no—
144C2×C4×C13—24no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—41no—
148C2×C4×C13—81no—
149C2×C4×C13#12111yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13C2×SD1612yes—
153C2×C4×C13#13512yes—
154C2×C4×C13C22×D411yescharacteristic
155C2×C4×C13C22×D411yescharacteristic
156C2×C4×C13C2×#4111yescharacteristic
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—42no—
160C2×Dic13—82no—
161Dic26—42no—
162Dic26—42no—
163Dic26—42no—
164Dic26—82no—
165Dic26—81no—
166C8×C13—24no—
167C8×C13—42no—
168#1055—42no—
169#1055—42no—
170C22×Q16—261no—
171#533—131no—
172C2×C4⋊Q8—131no—
173C2×C4×Q8C2×D1311yescharacteristic
174#498—132no—
175#487—132no—
176#483—262no—
177#479—262no—
178#477—132no—
179#475—132no—
180#475—262no—
181#462—134no—
182#462—262no—
183C8×Q8—22no—
184C8×Q8C2×D1314yes—
185#431—22no—
186#431C2×D1311yescharacteristic
187#431C2×D1311yescharacteristic
188#428—261no—
189#423—131no—
190C2×C4⋊C8—131no—
191#419—261no—
192C2×#103—261no—
193#334—134no—
194#333—132no—
195#332—132no—
196#332—134no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13#46512yes—
200C22×C13C2×#12111yescharacteristic
201C4×C13—21no—
202C4×C13—24no—
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—42no—
206C4×C13#46512yes—
207C4×C13C22×SD1611yescharacteristic
208C4×C13C2×#13511yescharacteristic
209C4×C13#57812yes—
210Dic13—81no—
211Dic13—82no—
212Dic13—81no—
213C22×Q8—261no—
214C22×Q8D5211yescharacteristic
215C2×Q16—264no—
216C2×Q16—524no—
217C2×M16—261no—
218C22×C8—261no—
219C4⋊Q8—132no—
220C4⋊Q8—131no—
221C4⋊Q8—131no—
222C4⋊Q8—261no—
223C4⋊Q8—261no—
224C4⋊Q8—261no—
225#125—261no—
226C22⋊Q8—261no—
227C22⋊Q8—261no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—261no—
231C4×Q8—261no—
232C4×Q8D5212yes—
233C4×Q8C22×D1312yes—
234#117—261no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—261no—
238C2×C4⋊C4D5211yescharacteristic
239C2×C42—21no—
240C2×C42C22×D1311yescharacteristic
241#107—262no—
242#106—264no—
243#106—262no—
244C4⋊C8—24no—
245C4⋊C8—132no—
246C4⋊C8—132no—
247C4⋊C8—261no—
248C4⋊C8—261no—
249C4⋊C8C22⋊D1312yes—
250C4⋊C8C22×D1312yes—
251#103—262no—
252#103—262no—
253#103—264no—
254#103—264no—
255C22⋊C8—21no—
256C22⋊C8C22⋊D1312yes—
257C4×C8—24no—
258C4×C8—21no—
259C4×C8C22×D1312yes—
260C2×C13—22no—
261C2×C13#304411yescharacteristic
262C2×C13C2×#46511yescharacteristic
263C2×C13#306911yescharacteristic
264C2×Q8—22no—
265C2×Q8—21no—
266C2×Q8—262no—
267C2×Q8—261no—
268C2×Q8—261no—
269C2×Q8—521no—
270C2×Q8—522no—
271C2×Q8—522no—
272C2×Q8#609514yes—
273C2×Q8C2×D5212yes—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—521no—
277C22×C4C2×D5211yescharacteristic
278C22×C4#612711yescharacteristic
279C22×C4C2×C22⋊D1311yescharacteristic
280Q16—528no—
281M16—522no—
282C2×C8—22no—
283C2×C8—262no—
284C2×C8—262no—
285C2×C8—522no—
286C2×C8C2×C22⋊D1314yes—
287C4⋊C4—22no—
288C4⋊C4—21no—
289C4⋊C4—22no—
290C4⋊C4—261no—
291C4⋊C4—261no—
292C4⋊C4—262no—
293C4⋊C4—261no—
294C4⋊C4—262no—
295C4⋊C4—261no—
296C4⋊C4—521no—
297C4⋊C4—521no—
298C4⋊C4—521no—
299C4⋊C4—521no—
300C4⋊C4C2×D5212yes—
301C22⋊C4—521no—
302C42—22no—
303C42—22no—
304C42—521no—
305C42C2×D5211yescharacteristic
306C42#612711yescharacteristic
307C42C2×C22⋊D1311yescharacteristic
308C42C23×D1311yescharacteristic
309C13#1940211yescharacteristic, complemented, Sylow
310C23#8818411yescharacteristic
311Q8—22no—
312Q8—24no—
313Q8—522no—
314Q8—522no—
315Q8—522no—
316Q8—1041no—
317Q8—1042no—
318Q8C2×#609514yes—
319C2×C4—22no—
320C2×C4—24no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—522no—
328C2×C4—1042no—
329C2×C4C2×#609512yes—
330C2×C4#8815812yes—
331C2×C4#8818411yescharacteristic
332C2×C4#8818411yescharacteristic
333C2×C4#8818411yescharacteristic
334C2×C4C22×D5211yescharacteristic
335C2×C4C2×#612711yescharacteristic
336C2×C4C22×C22⋊D1311yescharacteristic
337C8—24no—
338C8—42no—
339C8—522no—
340C8—522no—
341C22—21no—
342C22—21no—
343C22#1171877512yes—
344C22C2×#8818411yescharacteristic
345C4—21no—
346C4—24no—
347C4—21no—
348C4—21no—
349C4—42no—
350C4—1041no—
351C4—1042no—
352C4—1041no—
353C4#1171877512yes—
354C4C22×#609511yescharacteristic
355C4C2×#8815811yescharacteristic
356C4#1171954312yes—
357C2—22no—
358C2#1312436611yescharacteristic
359C2C2×#1171877511yescharacteristic
360C2#1312457311yescharacteristic
subgroupG/H
centerC22C2×#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#2982C2
socleC22×C13C2×#121
prime radicalC23×C13#121
hypercenter#2982D13
hypocenterC13#19402
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
4. #13114266C2semidirect
5. #13114218C2semidirect
309. C13#19402semidirect

Maximal subgroups

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

subgroupindex
#131259822
#131246412
C2×#117186922
#131142662
#131142182
#131136072
#131135072
#131134912
C13×#29822
#1940213