Finite Group Databasebeta

← #15758847

Subgroups — #15758847

Order 3328.

446 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124641C211yesmaximal, characteristic
2#13113399C211yesmaximal, characteristic
3#13113334C211yesmaximal, characteristic
4#13113231C211yesmaximal, characteristic
5#13112739C211yesmaximal, characteristic
6#13112694C211yesmaximal, characteristic
7C13×#2356C211yesmaximal, characteristic
8C2×C4×Q8×C13C2211yescharacteristic
9#11719175C2211yescharacteristic
10C13×#391—21no—
11C13×#387—22no—
12C13×#383—21no—
13C13×#382C2211yescharacteristic
14C4×C13×C4⋊C4—21no—
15C4×C13×C4⋊C4C2211yescharacteristic
16C13×#376—21no—
17#11718886—21no—
18#11718683—22no—
19#11718682C412yescomplemented
20#11718681C412yescomplemented
21#11718625—21no—
22#11718586C2211yescharacteristic
23#11718586C2211yescharacteristic
24#11718585C2211yescharacteristic
25Q8⋊#1055—22no—
26#11718044—22no—
27#11718044—21no—
28#11718044—21no—
29C22×Q8×C13D411yescharacteristic
30C4×Q8×C13—21no—
31C4×Q8×C13—21no—
32C4×Q8×C13C2×C412yes—
33C4×Q8×C13D412yes—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C42×C13—21no—
39C2×C42×C13—22no—
40C2×C42×C13—21no—
41C2×C42×C13C2311yescharacteristic
42#88180—21no—
43#88178—21no—
44#88178—21no—
45C2×#6099—21no—
46#88124—21no—
47#88123C2×C411yescharacteristic
48#88123C2×C411yescharacteristic
49C4×Dic26—21no—
50C4×Dic26—21no—
51C13×#95—22no—
52C13×#95—22no—
53C13×#95—22no—
54C13×#95—21no—
55C13×#95D411yescharacteristic
56C13×#95D411yescharacteristic
57C13×#95D412yes—
58#88075—22no—
59#88075—22no—
60C22⋊#1055—21no—
61C22⋊#1055—21no—
62#88048—22no—
63#88047—22no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055C2×C412yes—
68C4×#1055—21no—
69C4×#1055—21no—
70#9178—131nomaximal, Sylow
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13—21no—
74C2×Q8×C13—21no—
75C2×Q8×C13—21no—
76C2×Q8×C13C22⋊C412yes—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—22no—
81C22×C4×C13—21no—
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C2×Dic26—21no—
86C2×Dic26—21no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4C22⋊C412yes—
94C42×C13—22no—
95C42×C13—22no—
96C42×C13—44no—
97C42×C13—41no—
98C42×C13—41no—
99C42×C13C22×C411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13#4111yescharacteristic
102C42×C13#4111yescharacteristic
103C22⋊Dic13—41no—
104C4⋊Dic13—21no—
105C4⋊Dic13—21no—
106C4⋊Dic13—21no—
107C4⋊Dic13—21no—
108#6101—41no—
109#6101—41no—
110C4×Dic13—41no—
111#6099—41no—
112#6099—41no—
113C2×#1055—22no—
114C2×#1055—41no—
115C2×#1055—41no—
116#3078—131no—
117#2356D1311yescharacteristic
118#1518—131no—
119#1503—131no—
120#1479—131no—
121#1303—131no—
122#1286—131no—
123C23×C13#12011yescharacteristic
124Q8×C13—22no—
125Q8×C13—22no—
126Q8×C13—41no—
127Q8×C13—41no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—42no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—42no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—42no—
142C2×C4×C13—41no—
143C2×C4×C13—42no—
144C2×C4×C13C2×C22⋊C411yescharacteristic
145C2×C4×C13C4×D411yescharacteristic
146C2×C4×C13C4×D411yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12311yescharacteristic
150C2×C4×C13#13511yescharacteristic
151C2×C4×C13#13511yescharacteristic
152C2×C4×C13#13711yescharacteristic
153C2×C4×C13#13711yescharacteristic
154C2×Dic13—41no—
155C2×Dic13—41no—
156Dic26—81no—
157Dic26—81no—
158#1055—42no—
159#1055—81no—
160#1055—81no—
161#533—131no—
162C2×C4×Q8C2×D1311yescharacteristic
163#479—262no—
164#477—132no—
165#475—132no—
166#431—131no—
167#431—131no—
168#428—261no—
169#423—131no—
170#419—261no—
171#391—21no—
172#387—22no—
173#383—21no—
174#382C2×D1311yescharacteristic
175C4×C4⋊C4—21no—
176C4×C4⋊C4C2×D1311yescharacteristic
177#376—21no—
178#328—261no—
179#328—261no—
180#328—262no—
181Q8⋊C8—262no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13#38611yescharacteristic
185C22×C13#45211yescharacteristic
186C22×C13#45211yescharacteristic
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—42no—
192C4×C13—42no—
193C4×C13—42no—
194C4×C13—81no—
195C4×C13—82no—
196C4×C13#41611yescharacteristic
197C4×C13#41911yescharacteristic
198C4×C13#48511yescharacteristic
199C4×C13#48511yescharacteristic
200Dic13—81no—
201Dic13—81no—
202C22×Q8C22⋊D1311yescharacteristic
203C2×M16—261no—
204C4⋊Q8—131no—
205C4⋊Q8—131no—
206#125—261no—
207C22⋊Q8—261no—
208C22⋊Q8—261no—
209C4×Q8—21no—
210C4×Q8—21no—
211C4×Q8—261no—
212C4×Q8—261no—
213C4×Q8C4×D1312yes—
214C4×Q8D5212yes—
215#117—261no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C22⋊D1311yescharacteristic
220C2×C42—21no—
221C2×C42—22no—
222C2×C42—21no—
223C2×C42C22×D1311yescharacteristic
224#107—262no—
225#106—262no—
226C4⋊C8—132no—
227C4⋊C8—261no—
228C4⋊C8—261no—
229C4⋊C8—261no—
230#103—262no—
231#103—262no—
232C22⋊C8—261no—
233C22⋊C8—261no—
234C4×C8—261no—
235C4×C8—261no—
236#95—22no—
237#95—22no—
238#95—22no—
239#95—21no—
240#95C22⋊D1311yescharacteristic
241#95C22⋊D1311yescharacteristic
242#95C22⋊D1312yes—
243C2×C13—21no—
244C2×C13—21no—
245C2×C13#187311yescharacteristic
246C2×C13#190511yescharacteristic
247C2×C13#190611yescharacteristic
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—261no—
254C2×Q8—261no—
255C2×Q8#610312yes—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4C2×C22⋊D1311yescharacteristic
262C22×C4C2×C22⋊D1311yescharacteristic
263C22×C4C2×C22⋊D1311yescharacteristic
264M16—521no—
265M16—521no—
266C2×C8—262no—
267C2×C8—521no—
268C2×C8—521no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—42no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—521no—
280C4⋊C4—521no—
281C4⋊C4#610312yes—
282C22⋊C4—521no—
283C42—22no—
284C42—22no—
285C42—44no—
286C42—41no—
287C42—41no—
288C42—521no—
289C42C2×C4×D1311yescharacteristic
290C42C2×D5211yescharacteristic
291C42#612711yescharacteristic
292C42#612711yescharacteristic
293C13#917811yescharacteristic, complemented, Sylow
294C23#8820711yescharacteristic
295Q8—22no—
296Q8—22no—
297Q8—41no—
298Q8—41no—
299Q8—1041no—
300Q8—1041no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4C2×#610311yescharacteristic
320C2×C4C4×C22⋊D1311yescharacteristic
321C2×C4C4×C22⋊D1311yescharacteristic
322C2×C4#8818311yescharacteristic
323C2×C4#8818411yescharacteristic
324C2×C4#8818411yescharacteristic
325C2×C4#8820411yescharacteristic
326C2×C4#8820411yescharacteristic
327C2×C4#8820511yescharacteristic
328C2×C4#8820511yescharacteristic
329C8—522no—
330C8—1041no—
331C8—1041no—
332C22—21no—
333C22—21no—
334C22#1171887411yescharacteristic
335C22#1171890011yescharacteristic
336C22#1171890011yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—42no—
343C4—42no—
344C4—81no—
345C4—82no—
346C4—1041no—
347C4—1041no—
348C4#1171865711yescharacteristic
349C4#1171865711yescharacteristic
350C4#1171866311yescharacteristic
351C4#1171866511yescharacteristic
352C2—21no—
353C2—21no—
354C2#1311514811yescharacteristic
355C2#1311533011yescharacteristic
356C2#1311533711yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2356C2
socleC22×C13#386
prime radicalC23×C13#120
cosocleC2×C42×C13C23
hypercenter#2356D13
hypocenterC13#9178
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2356

Complements

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

NH ≅ G/Ntype
19. #11718682C4semidirect
20. #11718681C4semidirect
293. C13#9178semidirect

Maximal subgroups

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

subgroupindex
#131246412
#131133992
#131133342
#131132312
#131127392
#131126942
C13×#23562
#917813