Finite Group Databasebeta

← #15763008

Subgroups — #15763008

Order 3328.

484 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
1#13123212C211yesmaximal, characteristic
2#13114690C211yesmaximal, characteristic
3#97×Dic13C211yesmaximal, characteristic
4#13112718C211yesmaximal, characteristic
5#13112718C211yesmaximal, characteristic
6#13112717C211yesmaximal, characteristic
7C13×#1295C211yesmaximal, characteristic
8C2×#88142C411yescharacteristic
9C2×#88142C411yescharacteristic
10C2×C13×#97C2211yescharacteristic
11C2×C13×#97C2211yescharacteristic
12C13×#382C2211yescharacteristic
13C2×#88055—21no—
14C2×#88054—21no—
15C2×C8×Dic13—21no—
16#11718638C411yescharacteristic
17#11718638C411yescharacteristic
18#11718597C2211yescharacteristic
19C42×Dic13C2211yescharacteristic
20C2×#88043C2211yescharacteristic
21C2×#88043C2211yescharacteristic
22#11718307—21no—
23#11718307—21no—
24#11718307—21no—
25#11718307—21no—
26#11718142—21no—
27C22×Dic26—21no—
28C22×Dic26—21no—
29C22×C8×C13—21no—
30C22×C8×C13—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C42×C13C2311yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C22×#1055—21no—
45C22×#1055—21no—
46#88142—42no—
47#88142—42no—
48C13×#97—21no—
49C13×#97—21no—
50C13×#97—21no—
51C13×#97Q812yescomplemented
52C13×#95—21no—
53C13×#95—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88055—24no—
61#88054—24no—
62C8×Dic13—24no—
63#88043—21no—
64#88043—21no—
65#88043—21no—
66#88043Q812yescomplemented
67#9890—131nomaximal, Sylow
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13C22⋊C411yescharacteristic
76C22×Dic13C22⋊C411yescharacteristic
77C22×Dic13C22⋊C411yescharacteristic
78C22×Dic13C22⋊C411yescharacteristic
79C2×Dic26—42no—
80C2×Dic26—42no—
81C2×Dic26—42no—
82C2×Dic26—42no—
83C2×Dic26—42no—
84C2×Dic26—42no—
85C2×C8×C13—22no—
86C2×C8×C13—22no—
87C2×C8×C13—22no—
88C2×C8×C13—22no—
89C2×C8×C13—41no—
90C2×C8×C13—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C42×C13C2×Q811yescharacteristic
94C42×C13C2×Q811yescharacteristic
95C42×C13#4111yescharacteristic
96C42×C13#4111yescharacteristic
97C4⋊Dic13—41no—
98C4⋊Dic13—41no—
99#6101—42no—
100#6101—42no—
101C4×Dic13—22no—
102C4×Dic13—22no—
103C4×Dic13—22no—
104C4×Dic13—22no—
105C4×Dic13—22no—
106C4×Dic13—41no—
107C2×#1055—22no—
108C2×#1055—22no—
109C2×#1055—22no—
110C2×#1055—22no—
111C2×#1055—41no—
112C2×#1055—41no—
113#2862—131no—
114#1767—131no—
115C4×#97—131no—
116#1295—131no—
117#1295—131no—
118#1295—131no—
119#1295D1311yescharacteristic
120C23×C13C2×C22⋊C411yescharacteristic
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13C4×Q811yescharacteristic
134C2×C4×C13C4×Q811yescharacteristic
135C2×C4×C13C22⋊Q811yescharacteristic
136C2×C4×C13C22⋊Q811yescharacteristic
137C2×C4×C13#12411yescharacteristic
138C2×C4×C13C4⋊Q811yescharacteristic
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13#10012yes—
153C2×Dic13#10112yes—
154C2×Dic13#10412yes—
155C2×Dic13#10412yes—
156C2×Dic13#10412yes—
157Dic26—84no—
158Dic26—84no—
159C8×C13—24no—
160C8×C13—42no—
161#1055—24no—
162#1055—42no—
163C2×C4⋊Q8—131no—
164C2×C4⋊Q8—131no—
165C2×C4⋊C8—261no—
166C2×#97—131no—
167C2×#97—131no—
168C2×#97—261no—
169C2×#97C2×D1311yescharacteristic
170C2×#97C2×D1311yescharacteristic
171C2×C4×C8—261no—
172#391—261no—
173#391—261no—
174#391—261no—
175#391—261no—
176#382—131no—
177#382—131no—
178#382—131no—
179#382C2×D1311yescharacteristic
180C43—131no—
181#336—261no—
182C22×C13#39111yescharacteristic
183C22×C13C2×#10011yescharacteristic
184C22×C13C2×#10111yescharacteristic
185C22×C13C2×#10411yescharacteristic
186C22×C13C2×#10411yescharacteristic
187C22×C13C2×#10411yescharacteristic
188C22×C13#42111yescharacteristic
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—81no—
196C4×C13—81no—
197Dic13—22no—
198Dic13—22no—
199Dic13—41no—
200Dic13—81no—
201Dic13—81no—
202Dic13#32914yes—
203C22×Q8—261no—
204C22×Q8—261no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—261no—
208C22×C8—261no—
209C4⋊Q8—522no—
210C4⋊Q8—522no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4C4×D1311yescharacteristic
216C2×C4⋊C4C4×D1311yescharacteristic
217C2×C42—131no—
218C2×C42—131no—
219C2×C42—131no—
220C2×C42—131no—
221C2×C42—131no—
222C2×C42—131no—
223C2×C42C22×D1311yescharacteristic
224C4⋊C8—264no—
225#97—21no—
226#97—21no—
227#97—21no—
228#97—132no—
229#97—264no—
230#97—261no—
231#97—261no—
232#97—261no—
233#97Dic2612yescomplemented
234C4×C8—264no—
235#95—21no—
236#95—21no—
237#95—261no—
238#95—261no—
239#95—261no—
240#95—261no—
241#95—261no—
242#95—261no—
243C2×C13C2×#32911yescharacteristic
244C2×C13#152611yescharacteristic
245C2×C13#152711yescharacteristic
246C2×C13#153111yescharacteristic
247C2×C13#198611yescharacteristic
248C2×C13#199411yescharacteristic
249C2×C13#199711yescharacteristic
250C2×Q8—522no—
251C2×Q8—522no—
252C2×Q8—522no—
253C2×Q8—522no—
254C2×Q8—522no—
255C2×Q8—522no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—131no—
259C22×C4—131no—
260C22×C4—131no—
261C22×C4—131no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4C2×C4×D1311yescharacteristic
265C22×C4D4×D1311yescharacteristic
266C22×C4D4×D1311yescharacteristic
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—262no—
274C2×C8—262no—
275C2×C8—262no—
276C2×C8—262no—
277C2×C8—521no—
278C2×C8—521no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—521no—
282C4⋊C4—521no—
283C4⋊C4—522no—
284C4⋊C4—522no—
285C42—262no—
286C42—262no—
287C42—262no—
288C42—262no—
289C42—262no—
290C42—521no—
291C42C2×Dic2611yescharacteristic
292C42#612711yescharacteristic
293C42#612911yescharacteristic
294C42Q8×D1311yescharacteristic
295C13#989011yescharacteristic, complemented, Sylow
296C23C22⋊C4×D1311yescharacteristic
297Q8—1044no—
298Q8—1044no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—132no—
312C2×C4—132no—
313C2×C4—132no—
314C2×C4—132no—
315C2×C4—132no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4C4×Dic2611yescharacteristic
330C2×C4#8813211yescharacteristic
331C2×C4#8813911yescharacteristic
332C2×C4#8814111yescharacteristic
333C2×C4#8814211yescharacteristic
334C2×C4#8815011yescharacteristic
335C8—24no—
336C8—42no—
337C8—264no—
338C8—522no—
339C22#1171830711yescharacteristic
340C22D13×#10011yescharacteristic
341C22D13×#10111yescharacteristic
342C22D13×#10411yescharacteristic
343C22D13×#10411yescharacteristic
344C22D13×#10411yescharacteristic
345C22#1171848211yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—81no—
353C4—81no—
354C4—134no—
355C4—262no—
356C4—262no—
357C4—521no—
358C4—1041no—
359C4—1041no—
360C2D13×#32911yescharacteristic
361C2#1311342911yescharacteristic
362C2#1311343211yescharacteristic
363C2#1311344911yescharacteristic
364C2#1311577811yescharacteristic
365C2#1311581111yescharacteristic
366C2#1311582311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1295C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1295D13
hypocenterC13#9890
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
51. C13×#97Q8semidirect
66. #88043Q8semidirect
233. #97Dic26semidirect
295. C13#9890semidirect

Maximal subgroups

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

subgroupindex
#131232122
#131146902
#97×Dic132
#131127182
#131127172
C13×#12952
#989013