Finite Group Databasebeta

← #15782086

Subgroups — #15782086

Order 3328.

446 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718849C211yesmaximal, characteristic
2C2×#11718082C211yesmaximal, characteristic, complemented
3C2×#11718156C211yesmaximal, characteristic, complemented
4C2×#11718099C211yesmaximal, characteristic
5#13114862C211yesmaximal, characteristic
6#13112928C211yesmaximal, characteristic, complemented
7C2×C13×#358C211yesmaximal, characteristic, complemented
8C22×C13×Q16C2211yescharacteristic
9C2×#88200—21no—
10C22×C8×D13C2211yescharacteristic
11C22×C13×C16C2211yescharacteristic
12C2×C13×#107C2211yescharacteristic
13C2×#88075—21no—
14#11718849—22no—
15#11718849—22no—
16C2×#88058C2211yescharacteristic
17C2×#88058C2211yescharacteristic
18C22×#6090C2211yescharacteristic
19#11718648—21no—
20C13×#358—22no—
21#11718156—22no—
22#11718121—21no—
23#11718099—22no—
24#11718082—22no—
25C22×Q8×C13—21no—
26C22×C4×D13D411yescharacteristic
27C2×C13×Q16—21no—
28C2×C13×Q16—21no—
29C2×C13×Q16—21no—
30C2×C13×Q16—21no—
31C2×C13×Q16—21no—
32C2×C13×Q16D412yes—
33C22×C8×C13C2311yescharacteristic
34C2×C13×C4⋊C4—21no—
35#88200—24no—
36#88200—42no—
37C2×#6103—41no—
38C2×#6103—41no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×#6101—41no—
42C22×#1055D411yescharacteristic
43C2×C8×D13—21no—
44C2×C8×D13—21no—
45C2×C8×D13—21no—
46C2×C8×D13—21no—
47C2×C8×D13—21no—
48C2×C8×D13—21no—
49C2×C13×C16—21no—
50C2×C13×C16—21no—
51C2×C13×C16—21no—
52C13×#107—21no—
53C13×#107—21no—
54#88075—24no—
55#88071—41no—
56#88058—21no—
57#88058—21no—
58#88058—21no—
59#88058D412yes—
60C2×#6090—21no—
61C2×#6090—21no—
62C2×#6090D412yes—
63#13382—131nomaximal, Sylow
64C23×D13D811yescharacteristic
65C2×Q8×C13—22no—
66C2×Q8×C13—41no—
67C2×Q8×C13—41no—
68C2×Q8×C13—41no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13C2×D411yescharacteristic
74C22×Dic13—41no—
75C22×Dic13—41no—
76C22×Dic13D811yescharacteristic
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×C4×D13—21no—
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×C4×D13—21no—
83C13×Q16—22no—
84C13×Q16—22no—
85C13×Q16—41no—
86C13×Q16—41no—
87C2×C8×C13C2×D411yescharacteristic
88C2×C8×C13C2×D411yescharacteristic
89C2×C8×C13C2×D411yescharacteristic
90C2×C8×C13#4111yescharacteristic
91C2×C8×C13#4111yescharacteristic
92C2×C8×C13#4111yescharacteristic
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95#6103—44no—
96#6103—82no—
97C4⋊Dic13—22no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101#6101—44no—
102C2×#1055—21no—
103C2×#1055—21no—
104C2×#1055—21no—
105C8×D13—41no—
106C8×D13—41no—
107C8×D13—41no—
108C8×D13—41no—
109C13×C16—41no—
110#6090—22no—
111C2×#467—131no—
112C2×#367—131no—
113C2×#358—131no—
114C2×#358D1311yescharacteristic, complemented
115C2×C22⋊C16—131no—
116#1808—131no—
117#1380—131no—
118C23×C13C2×D811yescharacteristic
119C22×D13—21no—
120C22×D13—21no—
121C22×D13—21no—
122C22×D13—21no—
123C22×D13—21no—
124C22×D13—21no—
125C22×D13SD3212yes—
126Q8×C13—42no—
127Q8×C13—42no—
128Q8×C13—81no—
129Q8×C13—81no—
130C2×C4×C13—42no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13—81no—
136C2×C4×C13#12011yescharacteristic
137C2×C4×C13#12111yescharacteristic
138C2×C4×C13#12311yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C13#13711yescharacteristic
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—42no—
146C2×Dic13—81no—
147C2×Dic13—81no—
148C2×Dic13—81no—
149C2×Dic13—81no—
150C2×Dic13—81no—
151C4×D13—41no—
152C4×D13—41no—
153C4×D13—41no—
154C4×D13—41no—
155C8×C13#12111yescharacteristic
156C8×C13#12111yescharacteristic
157C8×C13#12311yescharacteristic
158C8×C13#12411yescharacteristic
159#1055—41no—
160C22×Q16C2×D1311yescharacteristic
161C23×C8—131no—
162C2×C22⋊Q8—261no—
163C22×C16—131no—
164C22×C16C2×D1311yescharacteristic
165#467—262no—
166#467—262no—
167C2×#107—131no—
168C2×#107—131no—
169C2×#107C2×D1311yescharacteristic
170C2×#103—261no—
171#380—261no—
172#367—262no—
173#358—22no—
174#358—262no—
175C22⋊C16—262no—
176#340—261no—
177C22×C13#44711yescharacteristic
178C22×C13#46611yescharacteristic
179C22×C13#48011yescharacteristic
180C22×C13C2×SD3211yescharacteristic
181C22×C13#50811yescharacteristic
182C22×C13#51011yescharacteristic
183C22×C13#51011yescharacteristic
184C2×D13—22no—
185C2×D13—22no—
186C2×D13—22no—
187C2×D13—41no—
188C2×D13—41no—
189C2×D13—41no—
190C2×D13—41no—
191C4×C13—82no—
192C4×C13—161no—
193C4×C13#39411yescharacteristic
194C4×C13#45211yescharacteristic
195C4×C13#46811yescharacteristic
196C4×C13#48211yescharacteristic
197Dic13—41no—
198Dic13—82no—
199Dic13—161no—
200C22×Q8—21no—
201C23×C4—131no—
202C2×Q16—21no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16C22⋊D1312yes—
208C22×C8—131no—
209C22×C8—261no—
210C22×C8—261no—
211C22×C8—261no—
212C22×C8—261no—
213C22×C8—261no—
214C22×C8—261no—
215C22×C8C22×D1311yescharacteristic
216C22⋊Q8—264no—
217C22⋊Q8—522no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—521no—
222C2×C22⋊C4—521no—
223C2×C22⋊C4—521no—
224C2×C16—21no—
225C2×C16—21no—
226C2×C16—21no—
227C2×C16—132no—
228C2×C16—261no—
229C2×C16—261no—
230#107—21no—
231#107—21no—
232#107—132no—
233#107—261no—
234#107—261no—
235#107—261no—
236#103—264no—
237#95—521no—
238C2×C13#203311yescharacteristic
239C2×C13#218511yescharacteristic
240C2×C13#218911yescharacteristic
241C2×C13#221711yescharacteristic
242C2×C13#221911yescharacteristic
243C2×C13#223511yescharacteristic
244C2×C13#223711yescharacteristic
245D13—42no—
246C24—131no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—131no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—521no—
263C22×C4—521no—
264C22×C4D4×D1311yescharacteristic
265Q16—22no—
266Q16—22no—
267Q16—41no—
268Q16—41no—
269C2×C8—261no—
270C2×C8—261no—
271C2×C8—261no—
272C2×C8—521no—
273C2×C8—521no—
274C2×C8—521no—
275C2×C8—521no—
276C2×C8#612711yescharacteristic
277C2×C8#612711yescharacteristic
278C2×C8D4×D1311yescharacteristic
279C2×C8D4×D1311yescharacteristic
280C2×C8#612911yescharacteristic
281C2×C8C2×C22⋊D1311yescharacteristic
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—262no—
285C4⋊C4—524no—
286C4⋊C4—521no—
287C4⋊C4—521no—
288C4⋊C4—521no—
289C22⋊C4—524no—
290C22⋊C4—1042no—
291C16—41no—
292C16—262no—
293C13#1338211yescharacteristic, complemented, Sylow
294C23—132no—
295C23—261no—
296C23—261no—
297C23—261no—
298C23—261no—
299C23—261no—
300C23—261no—
301C23D8×D1311yescharacteristic
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306C2×C4—42no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—522no—
320C2×C4—1041no—
321C2×C4—1041no—
322C2×C4—1041no—
323C2×C4—1041no—
324C2×C4—1041no—
325C2×C4#8813711yescharacteristic
326C2×C4#8813811yescharacteristic
327C2×C4#8816511yescharacteristic
328C2×C4#8816911yescharacteristic
329C2×C4#8817011yescharacteristic
330C2×C4#8819111yescharacteristic
331C8—521no—
332C8#8813811yescharacteristic
333C8#8813911yescharacteristic
334C8#8818311yescharacteristic
335C8#8819311yescharacteristic
336C22—262no—
337C22—262no—
338C22—262no—
339C22—521no—
340C22—521no—
341C22—521no—
342C22—521no—
343C22#1171843511yescharacteristic
344C22#1171843611yescharacteristic
345C22D13×SD3211yescharacteristic
346C22#1171857611yescharacteristic
347C22#1171857911yescharacteristic
348C22#1171858011yescharacteristic
349C22#1171881711yescharacteristic
350C4—82no—
351C4—161no—
352C4—521no—
353C4—1042no—
354C4—2081no—
355C4#1171844011yescharacteristic
356C4#1171844111yescharacteristic
357C4#1171862011yescharacteristic
358C4#1171883411yescharacteristic
359C2—522no—
360C2#1311601611yescharacteristic
361C2#1311675111yescharacteristic
362C2#1311677511yescharacteristic
363C2#1311693511yescharacteristic
364C2#1311694311yescharacteristic
365C2#1311703211yescharacteristic
366C2#1311704311yescharacteristic
subgroupG/H
centerC23D8×D13
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC2×C13×#358C2
socleC23×C13C2×D8
prime radicalC23×D13D8
hypercenterC2×#358D13
hypocenterC13#13382
LCSG ▷ C22×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#11718082C2semidirect
3. C2×#11718156C2semidirect
6. #13112928C2semidirect
7. C2×C13×#358C2semidirect
114. C2×#358D13semidirect
293. C13#13382semidirect

Maximal subgroups

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

subgroupindex
C2×#117188492
C2×#117180822
C2×#117181562
C2×#117180992
#131148622
#131129282
C2×C13×#3582
#1338213