Finite Group Databasebeta

← #15755597

Subgroups — #15755597

Order 3328.

570 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114816C211yesmaximal, characteristic
2#13114816C211yesmaximal, characteristic
3C2×#11718120C212yesmaximal
4#13112679C212yesmaximal
5C2×C13×#387C211yesmaximal, characteristic
6C22×C13×C4⋊C4C411yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C22×C42×C13C2211yescharacteristic
9C13×#387—21no—
10C13×#387—21no—
11C13×#387—21no—
12C13×#387—21no—
13C2×C13×#95C411yescharacteristic
14C2×C13×#95C411yescharacteristic
15C2×C13×#95C411yescharacteristic
16C2×C13×#95C2211yescharacteristic
17C2×C22⋊#1055C2212yes—
18C2×C22⋊#1055C2212yes—
19C2×C4⋊#1055—21no—
20C2×C4⋊#1055—21no—
21#11718120—24no—
22#11718116—21no—
23#11718116—21no—
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13C2×C411yescharacteristic
30C23×C4×C13C2311yescharacteristic
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—42no—
38C2×C13×C4⋊C4D412yes—
39C2×C13×C4⋊C4Q812yes—
40C2×C42×C13—42no—
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C22×#1055—22no—
46C22×#1055—22no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C22⋊#1055—22no—
56C22⋊#1055—22no—
57C22⋊#1055—22no—
58C22⋊#1055—22no—
59C4⋊#1055—42no—
60C4⋊#1055—42no—
61#8562—131nomaximal, Sylow
62C24×C13C22×C411yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—22no—
76C22×C4×C13—22no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C22⋊C411yescharacteristic
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C4⋊C412yes—
92C22×C4×C13C4⋊C412yes—
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×Q811yescharacteristic
97C22×C4×C13#4111yescharacteristic
98C22×C4×C13#4111yescharacteristic
99C13×C4⋊C4—22no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—42no—
104C13×C4⋊C4—42no—
105C42×C13—22no—
106C42×C13—22no—
107C42×C13—41no—
108C42×C13—41no—
109C2×#1055—42no—
110C2×#1055—42no—
111C2×#1055—42no—
112C2×#1055—42no—
113C2×#1055—42no—
114C2×#1055—42no—
115C2×#387D1311yescharacteristic
116#1797—131no—
117#1797—131no—
118C2×#324—132no—
119#1280—132no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13C2×C22⋊C411yescharacteristic
125C23×C13C2×C4⋊C411yescharacteristic
126C23×C13#11711yescharacteristic
127C23×C13#13112yes—
128C23×C13#13112yes—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—24no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—44no—
151C2×C4×C13—44no—
152C2×C4×C13—42no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—82no—
166C2×C4×C13—82no—
167C2×C4×C13#9912yes—
168C2×C4×C13#10112yes—
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13#12111yescharacteristic
171C2×C4×C13C22⋊Q811yescharacteristic
172C2×C4×C13C22⋊Q811yescharacteristic
173#1055—82no—
174#1055—82no—
175C22×C4⋊C4Dic1311yescharacteristic
176C22×C4⋊C4C2×D1311yescharacteristic
177C22×C42C2×D1311yescharacteristic
178C2×C4⋊C8—261no—
179C2×C4⋊C8—261no—
180C2×C22⋊C8—132no—
181C2×C22⋊C8—132no—
182#387—21no—
183#387—21no—
184#387—21no—
185#387—21no—
186C2×#95Dic1311yescharacteristic
187C2×#95Dic1311yescharacteristic
188C2×#95Dic1311yescharacteristic
189C2×#95C2×D1311yescharacteristic
190#336—261no—
191#336—261no—
192#324—264no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—22no—
198C22×C13—22no—
199C22×C13—22no—
200C22×C13—22no—
201C22×C13#38011yescharacteristic
202C22×C13#40811yescharacteristic
203C22×C13#40811yescharacteristic
204C22×C13C2×#9911yescharacteristic
205C22×C13#41011yescharacteristic
206C22×C13C2×#10111yescharacteristic
207C22×C13#41311yescharacteristic
208C22×C13#42412yes—
209C22×C13#43312yes—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—22no—
215C4×C13—22no—
216C4×C13—42no—
217C4×C13—42no—
218C4×C13—41no—
219C4×C13—41no—
220C4×C13—81no—
221C4×C13—81no—
222C23×C4C2×Dic1311yescharacteristic
223C23×C4C2×Dic1311yescharacteristic
224C23×C4C2×Dic1311yescharacteristic
225C23×C4C2×Dic1311yescharacteristic
226C23×C4C2×Dic1311yescharacteristic
227C23×C4C2×Dic1311yescharacteristic
228C23×C4C22×D1311yescharacteristic
229C22×C8—262no—
230C22×C8—262no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—42no—
238C2×C4⋊C4Dic2612yes—
239C2×C4⋊C4D5212yes—
240C2×C42—42no—
241C2×C42C22⋊D1311yescharacteristic
242C2×C42C22⋊D1311yescharacteristic
243C2×C42C22⋊D1311yescharacteristic
244C2×C42C22⋊D1311yescharacteristic
245C4⋊C8—522no—
246C4⋊C8—522no—
247C22⋊C8—262no—
248C22⋊C8—262no—
249C22⋊C8—262no—
250C22⋊C8—262no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259C2×C13—22no—
260C2×C13—22no—
261C2×C13#146811yescharacteristic
262C2×C13#147011yescharacteristic
263C2×C13#147211yescharacteristic
264C2×C13#147311yescharacteristic
265C2×C13#179811yescharacteristic
266C2×C13#179911yescharacteristic
267C2×C13#180111yescharacteristic
268C24C22×Dic1311yescharacteristic
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4C4⋊Dic1312yes—
294C22×C4C4⋊Dic1312yes—
295C22×C4C22⋊Dic1311yescharacteristic
296C22×C4C22⋊Dic1311yescharacteristic
297C22×C4C22⋊Dic1311yescharacteristic
298C22×C4C22⋊Dic1311yescharacteristic
299C22×C4C2×Dic2611yescharacteristic
300C22×C4C2×D5211yescharacteristic
301C22×C4#612711yescharacteristic
302C22×C4#612711yescharacteristic
303C22×C4C2×C22⋊D1311yescharacteristic
304C22×C4C2×C22⋊D1311yescharacteristic
305C2×C8—522no—
306C2×C8—522no—
307C2×C8—522no—
308C2×C8—522no—
309C2×C8—522no—
310C2×C8—522no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—42no—
316C4⋊C4—42no—
317C42—22no—
318C42—22no—
319C42—41no—
320C42—41no—
321C13#856211yescharacteristic, complemented, Sylow
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23C2×C4⋊Dic1311yescharacteristic
327C23#8818011yescharacteristic
328C23#8820212yes—
329C23#8820212yes—
330C23C2×C22⋊Dic1311yescharacteristic
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4#8807412yes—
370C2×C4#8807612yes—
371C2×C4#8817811yescharacteristic
372C2×C4#8817811yescharacteristic
373C2×C4#8818411yescharacteristic
374C2×C4#8818411yescharacteristic
375C8—1042no—
376C8—1042no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22#1171866012yes—
386C22#1171866112yes—
387C22#1171887311yescharacteristic
388C22C2×#8807411yescharacteristic
389C22C2×#8807611yescharacteristic
390C22#1171889511yescharacteristic
391C22#1171889511yescharacteristic
392C22#1171889811yescharacteristic
393C22#1171890111yescharacteristic
394C4—22no—
395C4—22no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—42no—
403C4—42no—
404C4—81no—
405C4—81no—
406C2—22no—
407C2—22no—
408C2#1311318411yescharacteristic
409C2#1311319211yescharacteristic
410C2#1311320011yescharacteristic
411C2#1311320511yescharacteristic
412C2#1311482011yescharacteristic
413C2#1311482411yescharacteristic
414C2#1311483211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#387C2
socleC23×C13C2×C22⋊C4
cosocleC23×C4×C13C23
hypercenterC2×#387D13
hypocenterC13#8562
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
321. C13#8562semidirect

Maximal subgroups

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

subgroupindex
#131148162
C2×#117181202
#131126792
C2×C13×#3872
#856213