Finite Group Databasebeta

← #15755797

Subgroups — #15755797

Order 3328.

462 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88161C211yesmaximal, characteristic
2#13113582C211yesmaximal, characteristic, complemented
3C2×#11718071C211yesmaximal, characteristic, complemented
4#13113224C211yesmaximal, characteristic
5#13113221C211yesmaximal, characteristic
6#13112687C211yesmaximal, characteristic, complemented
7C13×#1283C211yesmaximal, characteristic, complemented
8C2×#88161C411yescharacteristic
9C2×#88161C411yescharacteristic
10C4×#6127C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C4×C13×M16C2211yescharacteristic
14#11718783C411yescharacteristic
15#11718783C411yescharacteristic
16#11718586C2211yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4×#1055C2211yescharacteristic
19#11718369—21no—
20#11718369—21no—
21C4×#6094—21no—
22C4×C8×D13—21no—
23#11718076—21no—
24#11718075—21no—
25#11718072—21no—
26#11718071—21no—
27#11718071—21no—
28#11718071—21no—
29#11718051—21no—
30#11718048—21no—
31C2×#6127C2×C411yescharacteristic
32C2×C13×M16C2×C411yescharacteristic
33C2×C13×M16C2×C411yescharacteristic
34C22×C8×C13—21no—
35C2×C42×C13C2311yescharacteristic
36C4×C22⋊D13—21no—
37C4×C22⋊D13—21no—
38#88180C2×C411yescharacteristic
39C22×#1055—21no—
40C22×#1055C2×C411yescharacteristic
41C22×#1055C2×C411yescharacteristic
42#88161—22no—
43#88161—22no—
44#88161—22no—
45#88161C814yescomplemented
46C2×#6094—21no—
47C2×#6094—21no—
48C2×C8×D13—21no—
49C2×C8×D13—21no—
50C4×D52D411yescharacteristic
51C4×D52Q811yescharacteristic
52#88126—21no—
53C42×D13—21no—
54C4×Dic26D411yescharacteristic
55C4×Dic26Q811yescharacteristic
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8—21no—
59C13×C22⋊C8—21no—
60C13×#97—21no—
61C4×C8×C13—21no—
62C4×C8×C13—21no—
63C22⋊#1055—21no—
64#88055—21no—
65#88055—21no—
66C8×Dic13—21no—
67C8×Dic13—21no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4×#1055—21no—
72C4×#1055D411yescharacteristic
73C4×#1055D411yescharacteristic
74C4×#1055D411yescharacteristic
75C4×#1055D411yescharacteristic
76#8605—131nomaximal, Sylow
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13#4111yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C2×C22⋊D13—21no—
81#6127—21no—
82#6127—21no—
83#6127C2×C812yes—
84#6127M1612yes—
85C2×D52C4⋊C411yescharacteristic
86C2×C4×D13—21no—
87C2×C4×D13—21no—
88C2×C4×D13—21no—
89C2×Dic26C4⋊C411yescharacteristic
90C13×M16—21no—
91C13×M16—21no—
92C13×M16C2×C812yes—
93C13×M16M1612yes—
94C2×C8×C13—21no—
95C2×C8×C13—21no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—81no—
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13C2×D411yescharacteristic
102C42×C13C2×Q811yescharacteristic
103C22⋊Dic13—21no—
104#6103—21no—
105#6103—21no—
106C4⋊Dic13C4⋊C411yescharacteristic
107C4⋊Dic13C4⋊C411yescharacteristic
108#6101—21no—
109#6101—21no—
110C4×Dic13—21no—
111C4×Dic13—21no—
112C4×Dic13—21no—
113C2×#1055—21no—
114C2×#1055—21no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055—81no—
118C2×#1055C22⋊C411yescharacteristic
119C2×#1055C22⋊C411yescharacteristic
120C2×#1055C22⋊C411yescharacteristic
121C2×#1055C22⋊C411yescharacteristic
122C2×#1055C2×C812yes—
123C2×#1055M1612yes—
124#6094—24no—
125#6094—24no—
126C8×D13—24no—
127C8×D13—24no—
128C4×#131—131no—
129#1564—131no—
130C2×#335—131no—
131#1477—131no—
132#1477—131no—
133#1283—131no—
134#1283D1311yescharacteristic, complemented
135C23×C13#11711yescharacteristic
136C22×D13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—41no—
140C2×C4×C13C2×C22⋊C411yescharacteristic
141C2×C4×C13C2×C4⋊C411yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13#12111yescharacteristic
144C2×C4×C13C22⋊Q811yescharacteristic
145C2×C4×C13C22⋊Q811yescharacteristic
146C2×C4×C13C22×C811yescharacteristic
147C2×C4×C13C2×M1611yescharacteristic
148C2×C4×C13C2×M1611yescharacteristic
149C2×C4×C13C2×M1611yescharacteristic
150C22⋊D13—22no—
151C22⋊D13—22no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155D52—21no—
156D52C4⋊C812yes—
157C4×D13—22no—
158C4×D13—22no—
159C4×D13—42no—
160C4×D13—41no—
161C4×D13—41no—
162Dic26—21no—
163Dic26C4⋊C812yes—
164C8×C13—22no—
165C8×C13—22no—
166C8×C13—81no—
167C8×C13—81no—
168#1055—21no—
169#1055—21no—
170#1055—81no—
171#1055—81no—
172#1055C22⋊C812yes—
173#1055C22⋊C812yes—
174C2×#131—131no—
175C2×#131—131no—
176C4×#41—131no—
177#431—131no—
178#431C2×D1311yescharacteristic
179C2×C4⋊C8—131no—
180C2×C4⋊C8C2×D1311yescharacteristic
181#405—131no—
182#405—131no—
183#405—261no—
184#405—261no—
185C4×M16—261no—
186C4×M16C2×D1311yescharacteristic
187C2×C4×C8—131no—
188C2×C4×C8—261no—
189#335—261no—
190#335—261no—
191#335—261no—
192#334—261no—
193Q8⋊C8—261no—
194Q8⋊C8—261no—
195D4⋊C8—261no—
196D4⋊C8—261no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13#38011yescharacteristic
200C22×C13#43111yescharacteristic
201C22×C13#43211yescharacteristic
202C2×D13—22no—
203C2×D13—41no—
204C2×D13—41no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—21no—
208C4×C13C2×C22⋊C811yescharacteristic
209C4×C13#40711yescharacteristic
210C4×C13C2×C4⋊C811yescharacteristic
211C4×C13#42311yescharacteristic
212C4×C13#47211yescharacteristic
213C4×C13#47311yescharacteristic
214Dic13—22no—
215Dic13—41no—
216Dic13—41no—
217C2×#41—131no—
218#131—134no—
219#131—262no—
220#131—262no—
221#131—262no—
222C2×M16—261no—
223C2×M16—261no—
224C2×M16C4×D1311yescharacteristic
225C2×M16C4×D1311yescharacteristic
226C22×C8—21no—
227C22×C8—131no—
228C22×C8—131no—
229C22×C8—261no—
230C22×C8—261no—
231C22×C8—261no—
232C4×Q8—131no—
233C4×Q8—131no—
234C4×D4—131no—
235C4×D4—131no—
236C4×D4—261no—
237C4×D4—261no—
238#117—131no—
239#117—261no—
240C2×C42—261no—
241C2×C42C22×D1311yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—261no—
246C4⋊C8—261no—
247C4⋊C8—261no—
248C22⋊C8—21no—
249C22⋊C8—261no—
250#97—21no—
251#97—261no—
252#97—261no—
253C4×C8—21no—
254C4×C8—21no—
255C4×C8—131no—
256C4×C8—131no—
257C4×C8—131no—
258C4×C8—131no—
259C4×C8—261no—
260C4×C8—261no—
261C4×C8—261no—
262C2×C13—21no—
263C2×C13—21no—
264C2×C13#179711yescharacteristic
265C2×C13#181411yescharacteristic
266C2×C13#181611yescharacteristic
267D13—42no—
268#41—132no—
269#41—132no—
270#41—261no—
271#41—261no—
272C2×Q8—131no—
273C2×D4—131no—
274C2×D4—261no—
275C22×C4—261no—
276C22×C4—261no—
277C22×C4—261no—
278C22×C4C2×C4×D1311yescharacteristic
279C22×C4#612711yescharacteristic
280C22×C4#612711yescharacteristic
281M16—21no—
282M16—21no—
283M16—264no—
284M16—264no—
285M16C8×D1312yes—
286M16#609412yes—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—81no—
292C2×C8—131no—
293C2×C8—131no—
294C2×C8—132no—
295C2×C8—132no—
296C2×C8—131no—
297C2×C8—131no—
298C2×C8—264no—
299C2×C8—264no—
300C2×C8—261no—
301C2×C8—261no—
302C2×C8—521no—
303C2×C8—521no—
304C2×C8—1041no—
305C4⋊C4—131no—
306C4⋊C4—131no—
307C4⋊C4—261no—
308C4⋊C4—261no—
309C22⋊C4—261no—
310C22⋊C4—261no—
311C22⋊C4—261no—
312C42—261no—
313C42—261no—
314C42—261no—
315C42D4×D1311yescharacteristic
316C42D4×D1311yescharacteristic
317C42D4×D1311yescharacteristic
318C42Q8×D1311yescharacteristic
319C13#860511yescharacteristic, complemented, Sylow
320C23—261no—
321C23#8812611yescharacteristic
322Q8—132no—
323Q8—261no—
324D4—132no—
325D4—262no—
326D4—262no—
327D4—261no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—261no—
332C2×C4—262no—
333C2×C4—262no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—522no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4C22⋊C4×D1311yescharacteristic
340C2×C4#8813811yescharacteristic
341C2×C4#8813811yescharacteristic
342C2×C4C4⋊C4×D1311yescharacteristic
343C2×C4#8815011yescharacteristic
344C2×C4#8815011yescharacteristic
345C2×C4C2×C8×D1311yescharacteristic
346C2×C4C2×#609411yescharacteristic
347C2×C4M16×D1311yescharacteristic
348C2×C4M16×D1311yescharacteristic
349C8—22no—
350C8—22no—
351C8—81no—
352C8—81no—
353C8—132no—
354C8—132no—
355C8—261no—
356C8—261no—
357C8—1041no—
358C8—1041no—
359C22—21no—
360C22—21no—
361C22—262no—
362C22—521no—
363C22—521no—
364C22#1171832811yescharacteristic
365C22#1171834611yescharacteristic
366C22#1171836611yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—262no—
371C4—521no—
372C4—521no—
373C4D13×C22⋊C811yescharacteristic
374C4#1171838711yescharacteristic
375C4#1171841011yescharacteristic
376C4#1171841611yescharacteristic
377C4D13×C4⋊C811yescharacteristic
378C4#1171849811yescharacteristic
379C2—21no—
380C2—21no—
381C2—522no—
382C2#1311481511yescharacteristic
383C2#1311488911yescharacteristic
384C2#1311489911yescharacteristic
subgroupG/H
centerC2×C4#88138
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1283C2
socleC22×C13#380
prime radicalC2×#6127C2×C4
cosocleC2×C42×C13C23
hypercenter#1283D13
hypocenterC13#8605
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
2. #13113582C2semidirect
3. C2×#11718071C2semidirect
6. #13112687C2semidirect
7. C13×#1283C2semidirect
45. #88161C8semidirect
134. #1283D13semidirect
319. C13#8605semidirect

Maximal subgroups

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

subgroupindex
C4×#881612
#131135822
C2×#117180712
#131132242
#131132212
#131126872
C13×#12832
#860513