Finite Group Databasebeta

← #15759353

Subgroups — #15759353

Order 3328.

524 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718383C211yesmaximal, characteristic
2#13117715C211yesmaximal, characteristic
3#13115820C211yesmaximal, characteristic
4#13114924C211yesmaximal, characteristic
5#13113407C211yesmaximal, characteristic
6#13112683C211yesmaximal, characteristic
7C13×#1289C211yesmaximal, characteristic
8C22×C4⋊Dic13C2211yescharacteristic
9C2×#88178C2211yescharacteristic
10C2×C13×C22⋊C8C2211yescharacteristic
11C13×#380C2211yescharacteristic
12C13×#380C2211yescharacteristic
13C4×C22⋊Dic13C2211yescharacteristic
14C2×C22⋊#1055C2211yescharacteristic
15C2×#88058C412yescomplemented
16C2×#88056C412yescomplemented
17C4⋊C4×Dic13—21no—
18#11718634—21no—
19#11718603—21no—
20C22⋊C4×Dic13—21no—
21#11718383—22no—
22#11718383—21no—
23#11718383—21no—
24#11718314—22no—
25#11718121—22no—
26#11718119—21no—
27#11718119—21no—
28#11718044—22no—
29C23×C4×C13C2311yescharacteristic
30C23×Dic13—21no—
31C22×Dic26C2×C411yescharacteristic
32C22×C8×C13C2×C412yes—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13D411yescharacteristic
39C2×C22⋊Dic13D411yescharacteristic
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13C2×C411yescharacteristic
44C2×C4⋊Dic13C2×C412yes—
45C2×C4⋊Dic13D412yes—
46C2×C4⋊Dic13D411yescharacteristic
47C2×C4⋊Dic13D411yescharacteristic
48#88178—21no—
49#88178—21no—
50#88178—21no—
51#88178—21no—
52C2×#6101—21no—
53C2×#6101—22no—
54C2×C4×Dic13—21no—
55C2×C4×Dic13—22no—
56C22×#1055—21no—
57C13×C22⋊C8—21no—
58C13×C22⋊C8—21no—
59C13×#95—21no—
60C13×#95D412yes—
61#88071—22no—
62#88071—22no—
63#88071—21no—
64C22⋊#1055—21no—
65C22⋊#1055—21no—
66#88058—22no—
67#88058—22no—
68#88056—22no—
69#88056—22no—
70#9257—131nomaximal, Sylow
71C24×C13C2×D411yescharacteristic
72C22×C4×C13—22no—
73C22×C4×C13—42no—
74C22×C4×C13—41no—
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—22no—
85C22×Dic13—22no—
86C22×Dic13—21no—
87C22×Dic13—21no—
88C22×Dic13—21no—
89C22×Dic13—82no—
90C2×Dic26—21no—
91C2×Dic26—21no—
92C2×Dic26—42no—
93C2×C8×C13—22no—
94C2×C8×C13—42no—
95C13×C4⋊C4—42no—
96C13×C4⋊C4—42no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C22⋊Dic13—21no—
102C22⋊Dic13—21no—
103C22⋊Dic13—21no—
104C22⋊Dic13—41no—
105C22⋊Dic13—41no—
106C22⋊Dic13Q1612yes—
107C4⋊Dic13—22no—
108C4⋊Dic13—22no—
109C4⋊Dic13—21no—
110C4⋊Dic13—21no—
111C4⋊Dic13—21no—
112C4⋊Dic13—21no—
113C4⋊Dic13C22⋊C412yes—
114C4⋊Dic13C22⋊C412yes—
115#6101—41no—
116#6101—41no—
117#6101—82no—
118C4×Dic13—42no—
119C4×Dic13—82no—
120C2×#1055—42no—
121C2×#1055—41no—
122C2×#484—131no—
123#2345—131no—
124#1996—131no—
125#1824—131no—
126#1520—131no—
127#1289D1311yescharacteristic
128#1282—131no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13C4×D411yescharacteristic
132C23×C13#12011yescharacteristic
133C23×C13#12111yescharacteristic
134C23×C13C2×Q1611yescharacteristic
135C23×C13#13511yescharacteristic
136C23×C13#13711yescharacteristic
137C23×C13#13711yescharacteristic
138C2×C4×C13—22no—
139C2×C4×C13—22no—
140C2×C4×C13—22no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—42no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13C2×C22⋊C411yescharacteristic
151C2×C4×C13C4×D411yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13#12311yescharacteristic
154C2×Dic13—22no—
155C2×Dic13—22no—
156C2×Dic13—22no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—42no—
160C2×Dic13—42no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13—82no—
167C2×Dic13—82no—
168C2×Dic13—81no—
169C2×Dic13—81no—
170Dic26—42no—
171Dic26—81no—
172C8×C13—42no—
173#1055—81no—
174C2×C22⋊Q8—131no—
175C22×C4⋊C4—131no—
176#484—262no—
177#484—261no—
178#484—261no—
179C2×#107—132no—
180C2×#103—132no—
181C2×C22⋊C8—131no—
182C2×C22⋊C8C2×D1311yescharacteristic
183#389—261no—
184#387—262no—
185#380—261no—
186#380C2×D1311yescharacteristic
187#380C2×D1311yescharacteristic
188C4×C4⋊C4—261no—
189C4×C22⋊C4—131no—
190C4×C22⋊C4—261no—
191#342—261no—
192#342—261no—
193#340—262no—
194#328—262no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13#38611yescharacteristic
206C22×C13C4×Q1611yescharacteristic
207C22×C13#44111yescharacteristic
208C22×C13#45111yescharacteristic
209C22×C13#45211yescharacteristic
210C22×C13#46211yescharacteristic
211C22×C13#46411yescharacteristic
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—82no—
216C4×C13—161no—
217C4×C13#41012yes—
218Dic13—42no—
219Dic13—42no—
220Dic13—42no—
221Dic13—81no—
222Dic13—81no—
223Dic13—81no—
224C22×Q8—131no—
225C23×C4—261no—
226C23×C4C22×D1311yescharacteristic
227C22×C8—261no—
228C22×C8C4×D1312yes—
229C22⋊Q8—261no—
230C22⋊Q8—261no—
231C22⋊Q8—261no—
232C22⋊Q8—261no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—132no—
236C2×C4⋊C4—132no—
237C2×C4⋊C4—131no—
238C2×C4⋊C4—131no—
239C2×C4⋊C4—131no—
240C2×C4⋊C4—261no—
241C2×C4⋊C4—261no—
242C2×C4⋊C4—261no—
243C2×C4⋊C4—261no—
244C2×C4⋊C4—262no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—131no—
248C2×C22⋊C4—131no—
249C2×C22⋊C4—261no—
250C2×C42—261no—
251C2×C42—262no—
252#107—262no—
253#107—262no—
254#103—262no—
255#103—262no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—261no—
259C22⋊C8—261no—
260#95—21no—
261#95—262no—
262#95—262no—
263#95—261no—
264#95D5212yes—
265C2×C13—21no—
266C2×C13—21no—
267C2×C13—21no—
268C2×C13—21no—
269C2×C13—21no—
270C2×C13—21no—
271C2×C13#187811yescharacteristic
272C2×C13#189911yescharacteristic
273C2×C13#190411yescharacteristic
274C24D4×D1311yescharacteristic
275C2×Q8—261no—
276C2×Q8—261no—
277C2×Q8—522no—
278C22×C4—22no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4—262no—
285C22×C4—262no—
286C22×C4—261no—
287C22×C4—261no—
288C22×C4—261no—
289C22×C4—1042no—
290C22×C4C2×C4×D1311yescharacteristic
291C22×C4C2×D5211yescharacteristic
292C22×C4#612711yescharacteristic
293C22×C4D4×D1311yescharacteristic
294C22×C4D4×D1311yescharacteristic
295C22×C4#613111yescharacteristic
296C2×C8—22no—
297C2×C8—42no—
298C2×C8—522no—
299C2×C8—521no—
300C4⋊C4—42no—
301C4⋊C4—42no—
302C4⋊C4—132no—
303C4⋊C4—132no—
304C4⋊C4—262no—
305C4⋊C4—261no—
306C4⋊C4—261no—
307C4⋊C4—262no—
308C4⋊C4—261no—
309C4⋊C4—261no—
310C4⋊C4—521no—
311C4⋊C4—521no—
312C4⋊C4—1042no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—132no—
318C22⋊C4—261no—
319C22⋊C4—261no—
320C22⋊C4—261no—
321C22⋊C4—521no—
322C22⋊C4—521no—
323C42—522no—
324C42—1042no—
325C13#925711yescharacteristic, complemented, Sylow
326C23—41no—
327C23—41no—
328C23#8813611yescharacteristic
329C23#8813811yescharacteristic
330C23#8814711yescharacteristic
331C23#8816611yescharacteristic
332C23#8816911yescharacteristic
333C23#8816911yescharacteristic
334C23Q16×D1311yescharacteristic
335Q8—522no—
336Q8—1041no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—262no—
350C2×C4—262no—
351C2×C4—262no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—522no—
355C2×C4—522no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—1042no—
362C2×C4—1042no—
363C2×C4—1041no—
364C2×C4—1041no—
365C2×C4C4×D5211yescharacteristic
366C2×C4C22⋊C4×D1311yescharacteristic
367C2×C4#8814811yescharacteristic
368C2×C4#8814911yescharacteristic
369C8—42no—
370C8—1041no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22#1171832611yescharacteristic
382C22#1171842811yescharacteristic
383C22#1171844411yescharacteristic
384C22#1171845411yescharacteristic
385C22#1171846911yescharacteristic
386C22#1171851411yescharacteristic
387C22#1171853411yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—82no—
392C4—161no—
393C4—522no—
394C4—522no—
395C4—522no—
396C4—1041no—
397C4—1041no—
398C4—1041no—
399C4#1171840112yes—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2#1311517811yescharacteristic
407C2#1311529311yescharacteristic
408C2#1311532411yescharacteristic
subgroupG/H
centerC22#11718326
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1289C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#1289D13
hypocenterC13#9257
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
15. C2×#88058C4semidirect
16. C2×#88056C4semidirect
325. C13#9257semidirect

Maximal subgroups

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

subgroupindex
C2×#117183832
#131177152
#131158202
#131149242
#131134072
#131126832
C13×#12892
#925713