Finite Group Databasebeta

← #15756792

Subgroups — #15756792

Order 3328.

454 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123876C211yesmaximal, characteristic
2#13115630C211yesmaximal, characteristic
3C4×#88063C211yesmaximal, characteristic
4#13113589C211yesmaximal, characteristic, complemented
5#13113588C211yesmaximal, characteristic, complemented
6#13112673C211yesmaximal, characteristic, complemented
7C13×#1278C211yesmaximal, characteristic, complemented
8C2×C4×D52C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C4×C13×M16C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C2×#88063C411yescharacteristic
13C2×#88063C411yescharacteristic
14C2×#88060—22no—
15#11718586C2211yescharacteristic
16C2×C4⋊#1055C2211yescharacteristic
17C4×#6099C2211yescharacteristic
18#11718499—21no—
19#11718499—21no—
20#11718387—22no—
21#11718349—21no—
22#11718349—21no—
23#11718146C411yescharacteristic
24#11718146C411yescharacteristic
25#11718072—21no—
26#11718071—21no—
27#11718050—21no—
28#11718049—21no—
29C22×D52C2×C411yescharacteristic
30C22×C4×D13D412yes—
31C2×C13×M16C2×C411yescharacteristic
32C2×C13×M16C2×C411yescharacteristic
33C22×C8×C13—21no—
34C2×C42×C13C2311yescharacteristic
35C2×#6103Q812yes—
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6099C2×C411yescharacteristic
38C2×#6099C2×C411yescharacteristic
39C22×#1055—21no—
40C2×#6094—22no—
41C2×#6094—22no—
42C4×D52—21no—
43C4×D52—21no—
44C4×D52—21no—
45C4×D52—21no—
46C13×C4⋊C8D411yescharacteristic
47C13×C4⋊C8D411yescharacteristic
48C13×C22⋊C8—21no—
49C13×#97—21no—
50C4×C8×C13—21no—
51C4×C8×C13—21no—
52C4×C8×C13—21no—
53C4×C8×C13—21no—
54C22⋊#1055—21no—
55#88063—22no—
56#88063—22no—
57#88060—22no—
58#88060—22no—
59#88060—44no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055D411yescharacteristic
63C4⋊#1055D411yescharacteristic
64#88043—21no—
65C4×#1055—21no—
66C4×#1055—21no—
67#8837—131nomaximal, Sylow
68C23×D13C4⋊C412yes—
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×Q811yescharacteristic
72C22×Dic13C4⋊C412yes—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52—21no—
78C2×D52—21no—
79C2×C4×D13—22no—
80C2×C4×D13—22no—
81C2×C4×D13—42no—
82C2×C4×D13—42no—
83C13×M16—21no—
84C13×M16—21no—
85C13×M16—21no—
86C13×M16M1612yescomplemented
87C2×C8×C13—21no—
88C2×C8×C13—22no—
89C2×C8×C13—21no—
90C2×C8×C13—21no—
91C2×C8×C13—21no—
92C2×C8×C13—41no—
93C2×C8×C13—41no—
94C42×C13C2×D411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13#4111yescharacteristic
97C42×C13#4111yescharacteristic
98#6103—22no—
99#6103—22no—
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102#6099—21no—
103#6099—21no—
104#6099—21no—
105#6099M1612yescomplemented
106C2×#1055—21no—
107C2×#1055—21no—
108C2×#1055—21no—
109C2×#1055—21no—
110C2×#1055—42no—
111C2×#1055—41no—
112#6094—82no—
113#6094—82no—
114#2975—131no—
115#1954—131no—
116C4×#100—131no—
117#1565—131no—
118#1565—131no—
119#1278—131no—
120#1278D1311yescharacteristic, complemented
121C23×C13C2×C4⋊C411yescharacteristic
122C22×D13—22no—
123C22×D13—22no—
124C22×D13—22no—
125C22×D13—42no—
126C22×D13—42no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—41no—
130C2×C4×C13C4×D411yescharacteristic
131C2×C4×C13C4×D411yescharacteristic
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13C22⋊Q811yescharacteristic
134C2×C4×C13C22⋊Q811yescharacteristic
135C2×C4×C13#12311yescharacteristic
136C2×C4×C13C2×M1611yescharacteristic
137C2×C4×C13C2×M1611yescharacteristic
138C2×C4×C13#13111yescharacteristic
139C2×C4×C13#13111yescharacteristic
140C2×Dic13—22no—
141C2×Dic13—42no—
142D52—41no—
143D52—41no—
144D52—41no—
145D52—41no—
146C4×D13—42no—
147C4×D13—42no—
148C4×D13—82no—
149C8×C13—22no—
150C8×C13—42no—
151C8×C13—41no—
152C8×C13—41no—
153C8×C13—41no—
154#1055—22no—
155#1055—41no—
156#1055—41no—
157#1055—41no—
158#1055—81no—
159C2×C4×D4—131no—
160#436—261no—
161#436—261no—
162#436—261no—
163#436—261no—
164#431—131no—
165#431C2×D1311yescharacteristic
166C2×C4⋊C8—131no—
167C2×#100—131no—
168C2×#100—131no—
169#407—262no—
170C2×C22⋊C8—262no—
171C4×M16—131no—
172C4×M16C2×D1311yescharacteristic
173C2×C4×C8C2×D1311yescharacteristic
174#343—131no—
175#343—131no—
176#335—261no—
177#335—261no—
178#334—261no—
179#334—261no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13#38511yescharacteristic
183C22×C13#42311yescharacteristic
184C22×C13#42411yescharacteristic
185C2×D13—44no—
186C2×D13—42no—
187C2×D13—42no—
188C2×D13—42no—
189C2×D13—82no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13#43511yescharacteristic
194C4×C13#43511yescharacteristic
195C4×C13#43611yescharacteristic
196C4×C13#43611yescharacteristic
197C4×C13#45311yescharacteristic
198C4×C13#45511yescharacteristic
199Dic13—42no—
200C22×D4—131no—
201C23×C4—132no—
202C2×M16—131no—
203C2×M16—131no—
204C2×M16—262no—
205C2×M16—262no—
206C2×M16C4×D1311yescharacteristic
207C2×M16C4×D1311yescharacteristic
208C22×C8—21no—
209C22×C8—261no—
210C4×D4—261no—
211C4×D4—261no—
212C4×D4—261no—
213C4×D4—261no—
214C2×C4⋊C4—131no—
215C2×C22⋊C4—132no—
216C2×C42C22×D1311yescharacteristic
217C4⋊C8—131no—
218C4⋊C8—131no—
219C4⋊C8—261no—
220C4⋊C8—261no—
221C4⋊C8D5211yescharacteristic
222C4⋊C8D5211yescharacteristic
223#100—262no—
224#100—262no—
225C22⋊C8—21no—
226C22⋊C8—262no—
227C22⋊C8—262no—
228C22⋊C8—261no—
229C22⋊C8—524no—
230#97—21no—
231#97—261no—
232C4×C8—21no—
233C4×C8—21no—
234C4×C8—21no—
235C4×C8—21no—
236C4×C8—261no—
237C4×C8—261no—
238C2×C13—21no—
239C2×C13—21no—
240C2×C13#185111yescharacteristic
241C2×C13#185611yescharacteristic
242C2×C13#185811yescharacteristic
243D13—82no—
244C24—132no—
245C2×D4—261no—
246C2×D4—261no—
247C2×D4—261no—
248C2×D4—261no—
249C2×D4—261no—
250C2×D4—261no—
251C22×C4—132no—
252C22×C4—262no—
253C22×C4—262no—
254C22×C4—522no—
255C22×C4—522no—
256C22×C4C2×C4×D1311yescharacteristic
257C22×C4D4×D1311yescharacteristic
258C22×C4Q8×D1311yescharacteristic
259M16—21no—
260M16—21no—
261M16—21no—
262M16—132no—
263M16—261no—
264M16—261no—
265M16—261no—
266M16—1042no—
267M16—1042no—
268M16#609412yescomplemented
269C2×C8—21no—
270C2×C8—22no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—261no—
277C2×C8—261no—
278C2×C8—261no—
279C2×C8—261no—
280C2×C8—522no—
281C2×C8—521no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C22⋊C4—262no—
285C22⋊C4—262no—
286C42C2×D5211yescharacteristic
287C42#612711yescharacteristic
288C42D4×D1311yescharacteristic
289C42#612911yescharacteristic
290C13#883711yescharacteristic, complemented, Sylow
291C23—262no—
292C23—262no—
293C23—262no—
294C23—522no—
295C23—522no—
296C23C4⋊C4×D1311yescharacteristic
297D4—521no—
298D4—521no—
299D4—521no—
300D4—521no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—262no—
305C2×C4—522no—
306C2×C4—522no—
307C2×C4—522no—
308C2×C4—1042no—
309C2×C4C4×D5211yescharacteristic
310C2×C4#8813511yescharacteristic
311C2×C4#8813611yescharacteristic
312C2×C4#8813711yescharacteristic
313C2×C4#8815011yescharacteristic
314C2×C4#8815111yescharacteristic
315C2×C4C2×#609411yescharacteristic
316C2×C4#8815511yescharacteristic
317C2×C4M16×D1311yescharacteristic
318C2×C4#8816111yescharacteristic
319C8—22no—
320C8—42no—
321C8—41no—
322C8—41no—
323C8—41no—
324C8—262no—
325C8—521no—
326C8—521no—
327C8—521no—
328C8—1041no—
329C22—21no—
330C22—21no—
331C22—524no—
332C22—522no—
333C22—522no—
334C22—522no—
335C22—1042no—
336C22#1171832911yescharacteristic
337C22#1171849811yescharacteristic
338C22#1171850011yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—522no—
343C4#1171834911yescharacteristic
344C4#1171836711yescharacteristic
345C4#1171839011yescharacteristic
346C4#1171839111yescharacteristic
347C4#1171848311yescharacteristic
348C4#1171848611yescharacteristic
349C2—21no—
350C2—21no—
351C2—1042no—
352C2#1311502011yescharacteristic
353C2#1311504711yescharacteristic
354C2#1311505711yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1278C2
socleC22×C13#385
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1278D13
hypocenterC13#8837
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
4. #13113589C2semidirect
5. #13113588C2semidirect
6. #13112673C2semidirect
7. C13×#1278C2semidirect
86. C13×M16M16semidirect
105. #6099M16semidirect
120. #1278D13semidirect
268. M16#6094semidirect
290. C13#8837semidirect

Maximal subgroups

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

subgroupindex
#131238762
#131156302
C4×#880632
#131135892
#131135882
#131126732
C13×#12782
#883713