Finite Group Databasebeta

← #15762104

Subgroups — #15762104

Order 3328.

422 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88059C211yesmaximal, characteristic, complemented
2#13113431C211yesmaximal, characteristic, complemented
3#13113428C211yesmaximal, characteristic
4#13113257C211yesmaximal, characteristic, complemented
5#13113253C211yesmaximal, characteristic
6C8×#6099C211yesmaximal, characteristic, complemented
7C13×#3167C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C13×#532C2211yescharacteristic
10C13×#498C411yescharacteristic
11C13×#492C411yescharacteristic
12C13×#487C411yescharacteristic
13C13×#486C411yescharacteristic
14C13×#465—21no—
15C13×#465—21no—
16C4×C13×SD16—21no—
17C4×C13×SD16—21no—
18C2×C4×C8×C13C2211yescharacteristic
19C2×#88059—21no—
20#11718586C2211yescharacteristic
21C4×#6099C2211yescharacteristic
22C4×#6099C2211yescharacteristic
23C4×#6099C2211yescharacteristic
24#11718144—21no—
25#11718135—22no—
26#11718132—22no—
27Q8⋊#1055—22no—
28D4⋊#1055—22no—
29#11718046—21no—
30C8×#1055—21no—
31C2×C13×#41—21no—
32C2×C13×SD16—21no—
33C2×C13×SD16—21no—
34C22×C8×C13D411yescharacteristic
35C22×C8×C13D411yescharacteristic
36C13×C4⋊Q8C2×C411yescharacteristic
37C13×C4⋊Q8C2×C411yescharacteristic
38C13×C4⋊Q8C2×C411yescharacteristic
39C13×#127C2×C411yescharacteristic
40C13×#125—21no—
41C13×#124—21no—
42C13×C22⋊Q8—21no—
43C13×C22⋊Q8—21no—
44C13×#121—21no—
45C13×#121—21no—
46C4×Q8×C13—21no—
47C4×Q8×C13—21no—
48C4×D4×C13—21no—
49C4×D4×C13—21no—
50C13×#117—21no—
51C2×C42×C13C2311yescharacteristic
52C2×#6099—21no—
53C2×#6099—21no—
54C2×#6099—21no—
55C13×#106—21no—
56C13×#106—21no—
57C13×#103—21no—
58C13×#103—21no—
59C13×#102—21no—
60C13×#102—21no—
61C4×C8×C13C2×C411yescharacteristic
62C4×C8×C13C2×C411yescharacteristic
63C4×C8×C13D411yescharacteristic
64C4×C8×C13D411yescharacteristic
65C22⋊#1055—21no—
66#88059—24no—
67C4⋊#1055D412yes—
68#88043—21no—
69#88043—21no—
70#88043D412yes—
71C4×#1055—21no—
72C4×#1055—21no—
73C4×#1055—21no—
74C4×#1055—21no—
75#9723—131nomaximal, Sylow
76C13×#41—82no—
77C2×Q8×C13—21no—
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×D4×C13—21no—
81C2×D4×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13#4111yescharacteristic
87C22×C4×C13#4111yescharacteristic
88C13×SD16—42no—
89C13×SD16—42no—
90C2×C8×C13—22no—
91C2×C8×C13—41no—
92C2×C8×C13C22⋊C411yescharacteristic
93C2×C8×C13C22⋊C411yescharacteristic
94C2×C8×C13C22⋊C411yescharacteristic
95C2×C8×C13C22⋊C411yescharacteristic
96C13×C4⋊C4—21no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—41no—
107C42×C13—41no—
108C42×C13C22×C411yescharacteristic
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13C2×D411yescharacteristic
112#6099—24no—
113#6099—22no—
114#6099—22no—
115#6099—41no—
116#6099—41no—
117C2×#1055—22no—
118C2×#1055—22no—
119C2×#1055—41no—
120C2×#1055—41no—
121#3167D1311yescharacteristic
122C4×#108—131no—
123#1526—131no—
124#1525—131no—
125#1485—131no—
126#1484—131no—
127C8×M16—131no—
128C23×C13—41no—
129C23×C13#12411yescharacteristic
130Q8×C13—41no—
131Q8×C13—41no—
132Q8×C13—42no—
133Q8×C13—81no—
134D4×C13—41no—
135D4×C13—41no—
136D4×C13—42no—
137D4×C13—81no—
138D4×C13—82no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—82no—
147C2×C4×C13C2×C22⋊C411yescharacteristic
148C2×C4×C13C4×D411yescharacteristic
149C2×C4×C13C4×D411yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12711yescharacteristic
153C8×C13—21no—
154C8×C13—21no—
155C8×C13—21no—
156C8×C13#10412yes—
157#1055—24no—
158#1055—42no—
159#1055—42no—
160#1055—42no—
161#533C2×D1311yescharacteristic
162#532C2×D1311yescharacteristic
163#498Dic1311yescharacteristic
164#492Dic1311yescharacteristic
165#487Dic1311yescharacteristic
166#486Dic1311yescharacteristic
167#465—21no—
168#465—21no—
169C4×SD16—21no—
170C4×SD16—21no—
171#431—131no—
172C2×#108—261no—
173C4×M16—131no—
174C4×M16—131no—
175C4×M16—131no—
176C2×C4×C8C2×D1311yescharacteristic
177#341—261no—
178#330—262no—
179#329—262no—
180Q8⋊C8—262no—
181D4⋊C8—262no—
182#322—261no—
183C82—261no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13—81no—
190C22×C13#39011yescharacteristic
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—81no—
195C4×C13—81no—
196C4×C13—81no—
197C4×C13C2×#10411yescharacteristic
198C4×C13#42111yescharacteristic
199C4×C13#44312yes—
200C4×C13#47112yes—
201C2×#41—21no—
202C2×SD16—21no—
203C2×SD16—21no—
204C2×M16—261no—
205C2×M16—261no—
206C2×M16—261no—
207C22×C8C22⋊D1311yescharacteristic
208C22×C8C22⋊D1311yescharacteristic
209C4⋊Q8C2×Dic1311yescharacteristic
210C4⋊Q8C2×Dic1311yescharacteristic
211C4⋊Q8C2×Dic1311yescharacteristic
212#127C2×Dic1311yescharacteristic
213#125—21no—
214#124—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217#121—21no—
218#121—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×D4—21no—
222C4×D4—21no—
223#117—21no—
224C2×C42C22×D1311yescharacteristic
225#108—264no—
226#106—21no—
227#106—21no—
228C4⋊C8—132no—
229#103—21no—
230#103—21no—
231#102—21no—
232#102—21no—
233C22⋊C8—261no—
234#97—132no—
235#97—261no—
236#97—261no—
237C4×C8—261no—
238C4×C8—261no—
239C4×C8—261no—
240C4×C8—261no—
241C4×C8C2×Dic1311yescharacteristic
242C4×C8C2×Dic1311yescharacteristic
243C4×C8C22⋊D1311yescharacteristic
244C4×C8C22⋊D1311yescharacteristic
245C2×C13—41no—
246C2×C13—161no—
247C2×C13#197411yescharacteristic
248C2×C13#197711yescharacteristic
249C2×C13#198011yescharacteristic
250#41—82no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C22×C4—41no—
259C22×C4#612911yescharacteristic
260C22×C4#612911yescharacteristic
261C22×C4C2×C22⋊D1311yescharacteristic
262SD16—42no—
263SD16—42no—
264M16—264no—
265M16—262no—
266M16—262no—
267M16—521no—
268M16—521no—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—262no—
272C2×C8—262no—
273C2×C8—521no—
274C2×C8—521no—
275C2×C8C22⋊Dic1311yescharacteristic
276C2×C8C22⋊Dic1311yescharacteristic
277C2×C8C22⋊Dic1311yescharacteristic
278C2×C8C22⋊Dic1311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C42—41no—
291C42D4×D1311yescharacteristic
292C42D4×D1311yescharacteristic
293C42C22×Dic1311yescharacteristic
294C42C2×C22⋊D1311yescharacteristic
295C13#972311yescharacteristic, complemented, Sylow
296C23—41no—
297C23#8819011yescharacteristic
298Q8—42no—
299Q8—41no—
300Q8—41no—
301Q8—81no—
302D4—42no—
303D4—41no—
304D4—41no—
305D4—81no—
306D4—82no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—82no—
315C2×C4D4×Dic1311yescharacteristic
316C2×C4D4×Dic1311yescharacteristic
317C2×C4#8819211yescharacteristic
318C2×C4#8819211yescharacteristic
319C2×C4#8819411yescharacteristic
320C2×C4C2×C22⋊Dic1311yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8—264no—
325C8—522no—
326C8—522no—
327C8—522no—
328C8#8807712yes—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#1171888211yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4#1171883812yes—
343C4#1171885712yes—
344C4C2×#8807711yescharacteristic
345C4#1171889711yescharacteristic
346C2—41no—
347C2—161no—
348C2#1311572511yescharacteristic
349C2#1311574111yescharacteristic
350C2#1311575611yescharacteristic
subgroupG/H
centerC2×C4#88192
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3167C2
socleC22×C13#390
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#3167D13
hypocenterC13#9723
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. C4×#88059C2semidirect
2. #13113431C2semidirect
4. #13113257C2semidirect
6. C8×#6099C2semidirect
295. C13#9723semidirect

Maximal subgroups

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

subgroupindex
C4×#880592
#131134312
#131134282
#131132572
#131132532
C8×#60992
C13×#31672
#972313