Finite Group Databasebeta

← #15765543

Subgroups — #15765543

Order 3328.

510 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
1C2×#11718739C211yesmaximal, characteristic
2C2×#11718511C211yesmaximal, characteristic
3C2×#11718752C211yesmaximal, characteristic
4#13115771C211yesmaximal, characteristic
5C2×#11718073C211yesmaximal, characteristic
6#13112670C211yesmaximal, characteristic
7C2×C13×#333C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C2×C4×Dic26C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×#88058—21no—
14C2×#88056—21no—
15#11718752—22no—
16#11718752—22no—
17#11718739—22no—
18#11718739—22no—
19C2×#88050—21no—
20C2×#88047—21no—
21C2×#88047—22no—
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4×#1055C2211yescharacteristic
24#11718511—22no—
25#11718511—22no—
26C13×#333—22no—
27#11718142—22no—
28#11718073—22no—
29C22×Q8×C13—21no—
30C22×Dic26—21no—
31C22×Dic26D411yescharacteristic
32C22×C8×C13—21no—
33C22×C8×C13—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8D412yes—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C42×C13C2311yescharacteristic
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13D411yescharacteristic
44C2×#6101—21no—
45C2×C4×Dic13—21no—
46C22×#1055—21no—
47C22×#1055D412yes—
48#88123—21no—
49#88123—21no—
50#88123—21no—
51#88123D412yes—
52C4×Dic26—21no—
53C4×Dic26—21no—
54C4×Dic26—21no—
55C4×Dic26—21no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8—21no—
59C13×C4⋊C8D412yes—
60#88058—24no—
61#88056—24no—
62#88050—24no—
63#88047—28no—
64#88047—24no—
65C4⋊#1055—21no—
66C4⋊#1055D412yes—
67C4×#1055—21no—
68C4×#1055—21no—
69#10279—131nomaximal, Sylow
70C2×Q8×C13—22no—
71C2×Q8×C13—41no—
72C2×Q8×C13—82no—
73C22×C4×C13—41no—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13#4111yescharacteristic
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—41no—
80C2×Dic26—21no—
81C2×Dic26—21no—
82C2×Dic26—21no—
83C2×Dic26—21no—
84C2×Dic26—21no—
85C2×Dic26—22no—
86C2×Dic26—41no—
87C2×Dic26—82no—
88C2×Dic26Q1612yes—
89C2×C8×C13—22no—
90C2×C8×C13—41no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C2×C8×C13—42no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C42×C13C2×D411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13C2×D411yescharacteristic
102C4⋊Dic13—21no—
103C4⋊Dic13—21no—
104C4⋊Dic13—22no—
105C4⋊Dic13—22no—
106C4⋊Dic13—41no—
107C4⋊Dic13—41no—
108#6101—41no—
109#6101—41no—
110C4×Dic13—41no—
111C4×Dic13—41no—
112C2×#1055—22no—
113C2×#1055—22no—
114C2×#1055—22no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055Q1614yes—
118C2×#500—131no—
119C2×#477—131no—
120C2×#477—131no—
121#1984—131no—
122C2×#333—131no—
123C2×#333D1311yescharacteristic
124#1277—131no—
125C23×C13#12111yescharacteristic
126Q8×C13—82no—
127Q8×C13—82no—
128C2×C4×C13—22no—
129C2×C4×C13—42no—
130C2×C4×C13—82no—
131C2×C4×C13#12011yescharacteristic
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12011yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12711yescharacteristic
137C2×C4×C13C2×Q1611yescharacteristic
138C2×C4×C13C2×Q1612yes—
139C2×C4×C13#13511yescharacteristic
140C2×C4×C13#13711yescharacteristic
141C2×C4×C13#13711yescharacteristic
142C2×C4×C13#13712yes—
143C2×Dic13—22no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13—82no—
150Dic26—22no—
151Dic26—22no—
152Dic26—41no—
153Dic26—41no—
154Dic26—82no—
155Dic26—82no—
156C8×C13—42no—
157C8×C13—81no—
158#1055—24no—
159#1055—42no—
160C2×C4⋊Q8—131no—
161C2×C4⋊Q8C2×D1311yescharacteristic
162C2×C4×Q8—131no—
163#500—262no—
164#500—262no—
165#477—262no—
166#477—262no—
167#477—262no—
168#477—262no—
169C2×#107—261no—
170C2×#107—262no—
171C2×#107—261no—
172C2×C4⋊C8—131no—
173C2×C4⋊C8C2×D1311yescharacteristic
174C2×C4⋊C8C2×D1311yescharacteristic
175C2×#103—261no—
176C2×#103—261no—
177C2×C4×C8—131no—
178#336—262no—
179#333—22no—
180#333—262no—
181C22×C13#39211yescharacteristic
182C22×C13#46212yes—
183C22×C13#46711yescharacteristic
184C22×C13#47011yescharacteristic
185C22×C13#47212yes—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—82no—
189C4×C13#45111yescharacteristic
190C4×C13#45112yes—
191C4×C13#45111yescharacteristic
192C4×C13#45211yescharacteristic
193C4×C13#45211yescharacteristic
194C4×C13#49411yescharacteristic
195C4×C13#49711yescharacteristic
196Dic13—42no—
197Dic13—82no—
198Dic13—81no—
199C22×Q8—21no—
200C22×Q8—131no—
201C22×Q8—261no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—132no—
205C22×C8—261no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—132no—
210C4⋊Q8—261no—
211C4⋊Q8—261no—
212C4⋊Q8—261no—
213C4⋊Q8D5212yes—
214C4×Q8—261no—
215C4×Q8—261no—
216C4×Q8—261no—
217C4×Q8—261no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—131no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4—261no—
223C2×C4⋊C4—261no—
224C2×C42—261no—
225C2×C42C22×D1311yescharacteristic
226#107—264no—
227#107—268no—
228#107—264no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—132no—
233C4⋊C8—261no—
234C4⋊C8C22⋊D1312yes—
235#103—264no—
236#103—264no—
237C4×C8—261no—
238C4×C8—261no—
239C2×C13#167612yes—
240C2×C13#169612yes—
241C2×C13#200111yescharacteristic
242C2×C13#201611yescharacteristic
243C2×C13#201811yescharacteristic
244C2×Q8—22no—
245C2×Q8—41no—
246C2×Q8—82no—
247C2×Q8—132no—
248C2×Q8—261no—
249C2×Q8—261no—
250C2×Q8—262no—
251C2×Q8—261no—
252C2×Q8—261no—
253C2×Q8—261no—
254C2×Q8—521no—
255C2×Q8—1042no—
256C22×C4—41no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—521no—
260C22×C4#612711yescharacteristic
261C22×C4D4×D1311yescharacteristic
262C22×C4D4×D1311yescharacteristic
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—42no—
267C2×C8—41no—
268C2×C8—134no—
269C2×C8—262no—
270C2×C8—262no—
271C2×C8—262no—
272C2×C8—521no—
273C2×C8—521no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—261no—
279C4⋊C4—262no—
280C4⋊C4—262no—
281C4⋊C4—261no—
282C4⋊C4—521no—
283C4⋊C4—521no—
284C4⋊C4—521no—
285C4⋊C4—521no—
286C42—521no—
287C42—521no—
288C42C2×D5211yescharacteristic
289C42D4×D1311yescharacteristic
290C42D4×D1311yescharacteristic
291C42C2×C22⋊D1311yescharacteristic
292C13#1027911yescharacteristic, complemented, Sylow
293C23#8813811yescharacteristic
294Q8—82no—
295Q8—82no—
296Q8—262no—
297Q8—262no—
298Q8—521no—
299Q8—521no—
300Q8—1042no—
301Q8—1042no—
302C2×C4—22no—
303C2×C4—42no—
304C2×C4—82no—
305C2×C4—262no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—522no—
309C2×C4—521no—
310C2×C4—522no—
311C2×C4—1042no—
312C2×C4#8813611yescharacteristic
313C2×C4#8813611yescharacteristic
314C2×C4#8813811yescharacteristic
315C2×C4#8816912yes—
316C2×C4#8816911yescharacteristic
317C2×C4#8817011yescharacteristic
318C2×C4Q16×D1312yes—
319C2×C4Q16×D1311yescharacteristic
320C2×C4#8817211yescharacteristic
321C2×C4#8818411yescharacteristic
322C2×C4#8819111yescharacteristic
323C2×C4#8819411yescharacteristic
324C8—42no—
325C8—81no—
326C8—264no—
327C8—522no—
328C22#1171841012yes—
329C22#1171845412yes—
330C22#1171847411yescharacteristic
331C22#1171847711yescharacteristic
332C22#1171862111yescharacteristic
333C4—21no—
334C4—21no—
335C4—82no—
336C4—522no—
337C4—1041no—
338C4—1042no—
339C4#1171846912yes—
340C4#1171846911yescharacteristic
341C4#1171847111yescharacteristic
342C4#1171882811yescharacteristic
343C4#1171883411yescharacteristic
344C4#1171884211yescharacteristic
345C4#1171884711yescharacteristic
346C2#1311423912yes—
347C2#1311436312yes—
348C2#1311584511yescharacteristic
349C2#1311593711yescharacteristic
350C2#1311594411yescharacteristic
subgroupG/H
centerC23#88138
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#333C2
socle, prime radicalC23×C13#121
hypercenterC2×#333D13
hypocenterC13#10279
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
292. C13#10279semidirect

Maximal subgroups

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

subgroupindex
C2×#117187392
C2×#117185112
C2×#117187522
#131157712
C2×#117180732
#131126702
C2×C13×#3332
#1027913