Finite Group Databasebeta

← #15763442

Subgroups — #15763442

Order 3328.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#11718704C211yesmaximal, characteristic
2#13119322C211yesmaximal, characteristic
3#13115822C211yesmaximal, characteristic
4#13114923C211yesmaximal, characteristic
5#13113408C211yesmaximal, characteristic
6#13112683C211yesmaximal, characteristic
7C13×#3189C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×C13×C22⋊Q8C2211yescharacteristic
10C22×C4⋊Dic13C2211yescharacteristic
11C13×#484—21no—
12C13×#484—21no—
13C13×#467—22no—
14C13×#451—21no—
15C13×#451—21no—
16C2×C13×C22⋊C8C2211yescharacteristic
17#11718891—21no—
18C2×#88075—21no—
19#11718873C2211yescharacteristic
20C4×C22⋊Dic13C2211yescharacteristic
21C2×C22⋊#1055C2211yescharacteristic
22#11718704—22no—
23#11718704—22no—
24#11718647—22no—
25#11718638—21no—
26C2×#88048—21no—
27#11718604—22no—
28#11718143—22no—
29#11718130—22no—
30#11718118—22no—
31C22×Q8×C13D411yescharacteristic
32C22×Q8×C13D411yescharacteristic
33C23×C4×C13C2311yescharacteristic
34C23×Dic13—21no—
35C2×C13×Q16—22no—
36C22×C8×C13D412yes—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×C22⋊Q8—21no—
44C13×C22⋊Q8—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C22⋊Dic13—21no—
52C2×C22⋊Dic13D412yes—
53C2×C4⋊Dic13—21no—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13—21no—
56C2×C4⋊Dic13—21no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13D412yes—
60C2×C4×Dic13—21no—
61C22×#1055—21no—
62C13×#107—22no—
63C13×#103—22no—
64C13×#103—22no—
65C13×C22⋊C8—21no—
66C13×C22⋊C8—21no—
67#88075—24no—
68#88071—24no—
69#88071—24no—
70#88071—21no—
71#88071—21no—
72C22⋊#1055—21no—
73C22⋊#1055D412yes—
74#88048—24no—
75#9961—131nomaximal, Sylow
76C24×C13C2×D411yescharacteristic
77C2×Q8×C13—21no—
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—42no—
82C2×Q8×C13—42no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—42no—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13#4111yescharacteristic
94C22×Dic13—22no—
95C22×Dic13—22no—
96C22×Dic13—41no—
97C22×Dic13—41no—
98C22×Dic13—42no—
99C22×Dic13—42no—
100C22×Dic13—41no—
101C13×Q16—82no—
102C2×C8×C13—22no—
103C2×C8×C13—42no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—41no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C22⋊Dic13—22no—
117C22⋊Dic13—22no—
118C22⋊Dic13—42no—
119C4⋊Dic13—22no—
120C4⋊Dic13—22no—
121C4⋊Dic13—41no—
122C4⋊Dic13—41no—
123C4⋊Dic13—42no—
124C4×Dic13—42no—
125C2×#1055—22no—
126C2×#1055—42no—
127#3189D1311yescharacteristic
128C2×#483—131no—
129#2503—131no—
130#1996—131no—
131#1823—131no—
132#1520—131no—
133#1282—131no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13#12011yescharacteristic
137C23×C13#12111yescharacteristic
138C23×C13#12711yescharacteristic
139C23×C13#13512yes—
140C23×C13#13712yes—
141Q8×C13—42no—
142Q8×C13—42no—
143Q8×C13—42no—
144Q8×C13—81no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—81no—
158C2×C4×C13—81no—
159C2×C4×C13#12011yescharacteristic
160C2×C4×C13#12011yescharacteristic
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×Dic13—42no—
164C2×Dic13—42no—
165C2×Dic13—42no—
166C2×Dic13—42no—
167C2×Dic13—44no—
168C2×Dic13—82no—
169C2×Dic13—81no—
170C2×Dic13—81no—
171C2×Dic13—81no—
172C2×Dic13—81no—
173C2×Dic13—81no—
174C8×C13—42no—
175#1055—42no—
176C2×C22⋊Q8C2×D1311yescharacteristic
177C2×C22⋊Q8C2×D1311yescharacteristic
178C22×C4⋊C4—131no—
179#484—21no—
180#484—21no—
181#483—262no—
182#483—262no—
183#467—22no—
184#451—21no—
185#451—21no—
186C2×#106—261no—
187C2×#103—261no—
188C2×C22⋊C8—131no—
189C2×C22⋊C8C2×D1311yescharacteristic
190#400—262no—
191#391—261no—
192#382—261no—
193#381—262no—
194#380—131no—
195C4×C22⋊C4—131no—
196#342—262no—
197#340—262no—
198#328—262no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—42no—
206C22×C13—42no—
207C22×C13#39211yescharacteristic
208C22×C13#45212yes—
209C22×C13#46412yes—
210C22×C13#49511yescharacteristic
211C22×C13#49711yescharacteristic
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—81no—
216C4×C13—81no—
217C4×C13—81no—
218C4×C13—81no—
219C4×C13#45812yes—
220Dic13—82no—
221Dic13—82no—
222Dic13—161no—
223C22×Q8C22⋊D1311yescharacteristic
224C22×Q8C22⋊D1311yescharacteristic
225C23×C4—261no—
226C23×C4C22×D1311yescharacteristic
227C2×Q16—22no—
228C22×C8—261no—
229C22×C8C22⋊D1312yes—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—132no—
241C2×C4⋊C4—261no—
242C2×C4⋊C4—261no—
243C2×C4⋊C4—261no—
244C2×C4⋊C4—261no—
245C2×C4⋊C4—261no—
246C2×C4⋊C4—261no—
247C2×C4⋊C4C22⋊D1311yescharacteristic
248C2×C4⋊C4C22⋊D1311yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—132no—
252C2×C22⋊C4—261no—
253C2×C42—261no—
254#107—22no—
255#106—264no—
256#103—22no—
257#103—22no—
258#103—264no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—132no—
262C22⋊C8—261no—
263#95—264no—
264#95—264no—
265#95—261no—
266#95—261no—
267C2×C13—22no—
268C2×C13—21no—
269C2×C13—22no—
270C2×C13—21no—
271C2×C13#200911yescharacteristic
272C2×C13#201511yescharacteristic
273C2×C13#202211yescharacteristic
274C24D4×D1311yescharacteristic
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—42no—
280C2×Q8—42no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—262no—
287C22×C4—262no—
288C22×C4—522no—
289C22×C4—522no—
290C22×C4—521no—
291C22×C4—521no—
292C22×C4—521no—
293C22×C4D4×D1311yescharacteristic
294C22×C4D4×D1311yescharacteristic
295C22×C4#612911yescharacteristic
296C22×C4C2×C22⋊D1311yescharacteristic
297C22×C4C2×C22⋊D1311yescharacteristic
298C22×C4C2×C22⋊D1311yescharacteristic
299Q16—82no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—262no—
303C2×C8—522no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—262no—
313C4⋊C4—262no—
314C4⋊C4—522no—
315C4⋊C4—521no—
316C4⋊C4—521no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—262no—
322C22⋊C4—262no—
323C22⋊C4—522no—
324C42—522no—
325C13#996111yescharacteristic, complemented, Sylow
326C23—41no—
327C23—41no—
328C23#8817212yes—
329C23#8817312yes—
330C23#8819111yescharacteristic
331C23#8819311yescharacteristic
332C23#8819411yescharacteristic
333Q8—42no—
334Q8—42no—
335Q8—42no—
336Q8—81no—
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—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—522no—
352C2×C4—522no—
353C2×C4—522no—
354C2×C4—524no—
355C2×C4—522no—
356C2×C4—1042no—
357C2×C4—1041no—
358C2×C4—1041no—
359C2×C4—1041no—
360C2×C4—1041no—
361C2×C4—1041no—
362C2×C4#8819111yescharacteristic
363C2×C4#8819211yescharacteristic
364C2×C4#8819311yescharacteristic
365C2×C4#8820711yescharacteristic
366C8—42no—
367C8—522no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22#1171884612yes—
377C22#1171884812yes—
378C22#1171885111yescharacteristic
379C22#1171885211yescharacteristic
380C22#1171888411yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—1042no—
389C4—1042no—
390C4—2081no—
391C4#1171890412yes—
392C2—22no—
393C2—21no—
394C2—22no—
395C2—21no—
396C2#1311589311yescharacteristic
397C2#1311592711yescharacteristic
398C2#1311596511yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#3189C2
socleC22×C13#392
prime radicalC24×C13C2×D4
hypercenter#3189D13
hypocenterC13#9961
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
325. C13#9961semidirect

Maximal subgroups

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

subgroupindex
C2×#117187042
#131193222
#131158222
#131149232
#131134082
#131126832
C13×#31892
#996113