Finite Group Databasebeta

← #15765533

Subgroups — #15765533

Order 3328.

510 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
1C2×#11718342C211yesmaximal, characteristic
2C2×#11718682C211yesmaximal, characteristic
3C2×#11718681C211yesmaximal, characteristic
4C2×#11718073C211yesmaximal, characteristic
5C2×#11718074C211yesmaximal, characteristic
6#13112671C211yesmaximal, characteristic
7C13×#1984C211yesmaximal, characteristic
8C2×C4×Q8×C13C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C2×#88075—21no—
14C2×#88075—21no—
15C2×#88056—22no—
16#11718682—22no—
17#11718682—22no—
18#11718681—22no—
19#11718681—22no—
20C2×#88048—21no—
21C2×#88047—21no—
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24#11718342—22no—
25#11718342—22no—
26C13×#336—22no—
27#11718074—22no—
28#11718073—22no—
29C22×Q8×C13D411yescharacteristic
30C22×Dic26—21no—
31C22×Dic26—21no—
32C22×C8×C13—21no—
33C22×C8×C13D412yes—
34C4×Q8×C13—21no—
35C4×Q8×C13—21no—
36C4×Q8×C13—21no—
37C4×Q8×C13—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C42×C13—21no—
41C2×C42×C13C2311yescharacteristic
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13—21no—
46C22×#1055—21no—
47C22×#1055—21no—
48#88123—21no—
49#88123—21no—
50#88123—21no—
51#88123—21no—
52#88123—21no—
53#88123—21no—
54#88123D412yes—
55#88123D412yes—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C4×C8×C13—21no—
59C4×C8×C13—21no—
60#88075—24no—
61#88075—24no—
62#88056—28no—
63#88048—24no—
64#88047—24no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055D412yes—
68C4⋊#1055D412yes—
69#10277—131nomaximal, Sylow
70C2×Q8×C13—21no—
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13—21no—
74C2×Q8×C13—21no—
75C2×Q8×C13Q1612yes—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C22×Dic13—41no—
82C22×Dic13—41no—
83C2×Dic26—22no—
84C2×Dic26—22no—
85C2×Dic26—42no—
86C2×Dic26—42no—
87C2×Dic26—41no—
88C2×Dic26—41no—
89C2×Dic26—82no—
90C2×C8×C13—22no—
91C2×C8×C13—22no—
92C2×C8×C13—22no—
93C2×C8×C13—41no—
94C2×C8×C13—42no—
95C13×C4⋊C4—21no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—41no—
99C42×C13—41no—
100C42×C13—41no—
101C42×C13C2×D411yescharacteristic
102C42×C13C2×D411yescharacteristic
103C42×C13C2×D411yescharacteristic
104C42×C13C2×D411yescharacteristic
105C4⋊Dic13—22no—
106C4⋊Dic13—22no—
107C4⋊Dic13—22no—
108C4⋊Dic13—22no—
109C4⋊Dic13—41no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112C4⋊Dic13—41no—
113C2×#1055—22no—
114C2×#1055—22no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055—41no—
118C2×#1055—41no—
119C2×#487—131no—
120C2×#477—131no—
121C2×#475—131no—
122#1984D1311yescharacteristic
123C2×#333—131no—
124C2×#332—131no—
125#1277—131no—
126C23×C13#12111yescharacteristic
127Q8×C13—22no—
128Q8×C13—22no—
129Q8×C13—41no—
130Q8×C13—41no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—42no—
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12011yescharacteristic
139C2×C4×C13#12011yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13#12111yescharacteristic
142C2×C4×C13#12711yescharacteristic
143C2×C4×C13C2×Q1611yescharacteristic
144C2×C4×C13#13511yescharacteristic
145C2×C4×C13#13512yes—
146C2×C4×C13#13711yescharacteristic
147C2×C4×C13#13711yescharacteristic
148C2×C4×C13#13712yes—
149C2×Dic13—42no—
150C2×Dic13—42no—
151C2×Dic13—82no—
152C2×Dic13—82no—
153Dic26—44no—
154Dic26—82no—
155Dic26—81no—
156Dic26—81no—
157Dic26—82no—
158C8×C13—42no—
159C8×C13—81no—
160#1055—42no—
161#1055—42no—
162C2×C4⋊Q8—131no—
163C2×C4⋊Q8—131no—
164C2×C4×Q8C2×D1311yescharacteristic
165#487—262no—
166#487—262no—
167#477—262no—
168#477—262no—
169#475—262no—
170#475—262no—
171C2×#107—261no—
172C2×#106—261no—
173C2×C4⋊C8—131no—
174C2×C4⋊C8—131no—
175C2×C4⋊C8C2×D1311yescharacteristic
176C2×#103—261no—
177C2×#103—261no—
178C2×#103—262no—
179C2×C4×C8C2×D1311yescharacteristic
180#336—22no—
181#333—262no—
182#332—262no—
183C22×C13#39211yescharacteristic
184C22×C13#46412yes—
185C22×C13#46711yescharacteristic
186C22×C13#47011yescharacteristic
187C22×C13#47112yes—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—42no—
191C4×C13—81no—
192C4×C13#45111yescharacteristic
193C4×C13#45111yescharacteristic
194C4×C13#45212yes—
195C4×C13#45211yescharacteristic
196C4×C13#45211yescharacteristic
197C4×C13#49511yescharacteristic
198C4×C13#49711yescharacteristic
199Dic13—82no—
200Dic13—82no—
201C22×Q8—261no—
202C22×Q8—261no—
203C22×Q8D5211yescharacteristic
204C22×C8—21no—
205C22×C8—261no—
206C22×C8—261no—
207C22×C8C22⋊D1312yes—
208C4⋊Q8—132no—
209C4⋊Q8—132no—
210C4⋊Q8—261no—
211C4⋊Q8—261no—
212C4⋊Q8—261no—
213C4⋊Q8—261no—
214C4⋊Q8—261no—
215C4⋊Q8—261no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×Q8—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4—261no—
223C2×C4⋊C4—261no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4D5211yescharacteristic
226C2×C42—21no—
227C2×C42C22×D1311yescharacteristic
228#107—264no—
229#106—264no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—132no—
233C4⋊C8—132no—
234C4⋊C8—261no—
235C4⋊C8—261no—
236#103—268no—
237#103—264no—
238#103—264no—
239C4×C8—21no—
240C4×C8—21no—
241C2×C13#168412yes—
242C2×C13#170412yes—
243C2×C13#200111yescharacteristic
244C2×C13#201511yescharacteristic
245C2×C13#201911yescharacteristic
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—262no—
252C2×Q8—262no—
253C2×Q8—521no—
254C2×Q8—521no—
255C2×Q8—522no—
256C2×Q8—522no—
257C2×Q8—1042no—
258C2×Q8Dic5212yes—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—521no—
262C22×C4—521no—
263C22×C4C2×D5211yescharacteristic
264C22×C4#612711yescharacteristic
265C22×C4C2×C22⋊D1311yescharacteristic
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—41no—
270C2×C8—42no—
271C2×C8—262no—
272C2×C8—262no—
273C2×C8—521no—
274C2×C8—521no—
275C2×C8—521no—
276C2×C8—521no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—262no—
282C4⋊C4—262no—
283C4⋊C4—262no—
284C4⋊C4—262no—
285C4⋊C4—521no—
286C4⋊C4—521no—
287C4⋊C4—521no—
288C4⋊C4—521no—
289C42—41no—
290C42—41no—
291C42D4×D1311yescharacteristic
292C42D4×D1311yescharacteristic
293C42D4×D1311yescharacteristic
294C42D4×D1311yescharacteristic
295C13#1027711yescharacteristic, complemented, Sylow
296C23#8818411yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—41no—
300Q8—41no—
301Q8—524no—
302Q8—1042no—
303Q8—1042no—
304Q8—1041no—
305Q8—1041no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—522no—
313C2×C4—522no—
314C2×C4—1042no—
315C2×C4—1042no—
316C2×C4#8813611yescharacteristic
317C2×C4#8813611yescharacteristic
318C2×C4#8813811yescharacteristic
319C2×C4#8813811yescharacteristic
320C2×C4#8815811yescharacteristic
321C2×C4C2×Dic5211yescharacteristic
322C2×C4#8816311yescharacteristic
323C2×C4#8816311yescharacteristic
324C2×C4#8819111yescharacteristic
325C2×C4#8819411yescharacteristic
326C2×C4#8819612yes—
327C2×C4#8820412yes—
328C8—42no—
329C8—81no—
330C8—522no—
331C8—522no—
332C22#1171862111yescharacteristic
333C22#1171868912yes—
334C22#1171877711yescharacteristic
335C22#1171879811yescharacteristic
336C22#1171880212yes—
337C4—21no—
338C4—21no—
339C4—42no—
340C4—81no—
341C4—1042no—
342C4—1042no—
343C4#1171839411yescharacteristic
344C4#1171839411yescharacteristic
345C4#1171840011yescharacteristic
346C4#1171840011yescharacteristic
347C4#1171870812yes—
348C4#1171872011yescharacteristic
349C4#1171874711yescharacteristic
350C2#1311429412yes—
351C2#1311441812yes—
352C2#1311584611yescharacteristic
353C2#1311592911yescharacteristic
354C2#1311595111yescharacteristic
subgroupG/H
centerC23#88184
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1984C2
socle, prime radicalC23×C13#121
hypercenter#1984D13
hypocenterC13#10277
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
295. C13#10277semidirect

Maximal subgroups

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

subgroupindex
C2×#117183422
C2×#117186822
C2×#117186812
C2×#117180732
C2×#117180742
#131126712
C13×#19842
#1027713