Finite Group Databasebeta

← #15760987

Subgroups — #15760987

Order 3328.

482 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 99 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
1#13124780C211yesmaximal, characteristic
2#13114936C211yesmaximal, characteristic
3#13114911C211yesmaximal, characteristic
4#13113369C211yesmaximal, characteristic
5#13112744C211yesmaximal, characteristic
6#13112689C211yesmaximal, characteristic
7C13×#2332C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×#88180C2211yescharacteristic
10C13×#391—21no—
11C13×#388—21no—
12C13×#388—21no—
13C13×#387—21no—
14C13×#387—21no—
15C13×#381C2211yescharacteristic
16C4×C13×C4⋊C4—21no—
17C4×C13×C22⋊C4C2211yescharacteristic
18#11718886—21no—
19#11718872C2211yescharacteristic
20#11718868C2211yescharacteristic
21#11718868C2211yescharacteristic
22#11718706—22no—
23#11718705C412yescomplemented
24#11718704C412yescomplemented
25#11718625—21no—
26#11718130—22no—
27#11718119—21no—
28#11718119—21no—
29#11718115—21no—
30#11718115—21no—
31C22×Q8×C13D411yescharacteristic
32C23×C4×C13C2311yescharacteristic
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8—21no—
35C13×C22⋊Q8C2×C412yes—
36C13×C22⋊Q8D412yes—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4D411yescharacteristic
44C2×C13×C22⋊C4D411yescharacteristic
45C2×C42×C13—21no—
46C2×C42×C13—21no—
47C2×C42×C13D411yescharacteristic
48C2×C42×C13D411yescharacteristic
49C2×C22⋊Dic13—21no—
50C2×C22⋊Dic13—21no—
51#88180—21no—
52#88180—21no—
53#88180—21no—
54#88180—21no—
55C2×C4⋊Dic13C2×C411yescharacteristic
56C2×C4⋊Dic13C2×C411yescharacteristic
57C2×C4×Dic13—21no—
58C2×#6099—21no—
59C2×#6099—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95—21no—
64C13×#95—21no—
65C13×#95—21no—
66C13×#95—21no—
67#88075—22no—
68#88075—22no—
69#88071—21no—
70#88071—21no—
71C22⋊#1055—21no—
72C22⋊#1055—21no—
73C22⋊#1055—21no—
74C22⋊#1055C2×C412yes—
75#88048—22no—
76#88047—22no—
77#9526—131nomaximal, Sylow
78C24×C13C2×D411yescharacteristic
79C2×Q8×C13—21no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×Q8×C13C22⋊C412yes—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13C22×C411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13#4111yescharacteristic
96C22×C4×C13#4111yescharacteristic
97C22×Dic13—21no—
98C22×Dic13—21no—
99C22×Dic13—41no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—42no—
104C13×C4⋊C4—81no—
105C13×C4⋊C4C22⋊C412yes—
106C13×C22⋊C4—22no—
107C13×C22⋊C4—22no—
108C13×C22⋊C4—42no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—41no—
111C42×C13—41no—
112C42×C13—41no—
113C42×C13—42no—
114C42×C13—81no—
115C22⋊Dic13—41no—
116C22⋊Dic13—41no—
117C22⋊Dic13—41no—
118C22⋊Dic13—41no—
119C4⋊Dic13—21no—
120C4⋊Dic13—21no—
121C4⋊Dic13—21no—
122C4⋊Dic13—21no—
123C4×Dic13—41no—
124C4×Dic13—41no—
125#6099—41no—
126#6099—41no—
127#6099—41no—
128#6099—41no—
129C2×#1055—22no—
130C2×#1055—41no—
131#3095—131no—
132#2332D1311yescharacteristic
133#1826—131no—
134#1820—131no—
135#1511—131no—
136#1306—131no—
137#1284—131no—
138C23×C13—21no—
139C23×C13—21no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13C4×D411yescharacteristic
143C23×C13#12011yescharacteristic
144C23×C13#12111yescharacteristic
145Q8×C13—42no—
146Q8×C13—81no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
153C2×C4×C13—22no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
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—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13C2×C22⋊C411yescharacteristic
174C2×C4×C13C4×D411yescharacteristic
175C2×C4×C13#12111yescharacteristic
176C2×C4×C13#12311yescharacteristic
177C2×Dic13—41no—
178C2×Dic13—41no—
179C2×Dic13—81no—
180C2×Dic13—81no—
181C2×Dic13—81no—
182C2×Dic13—81no—
183C2×Dic13—81no—
184#1055—42no—
185#1055—81no—
186C2×C22⋊Q8C2×D1311yescharacteristic
187C2×#117—131no—
188#485—262no—
189#484—132no—
190#483—132no—
191#428—261no—
192#419—261no—
193#407—131no—
194#407—131no—
195#391—21no—
196#388—21no—
197#388—21no—
198#387—21no—
199#387—21no—
200#381—131no—
201#381C2×D1311yescharacteristic
202C4×C4⋊C4—21no—
203C4×C22⋊C4C2×D1311yescharacteristic
204#342—261no—
205#342—261no—
206#339—261no—
207#339—261no—
208#328—262no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13#38611yescharacteristic
220C22×C13#45811yescharacteristic
221C22×C13#45811yescharacteristic
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—21no—
226C4×C13—42no—
227C4×C13—42no—
228C4×C13—42no—
229C4×C13—81no—
230C4×C13—81no—
231C4×C13—81no—
232Dic13—81no—
233Dic13—81no—
234Dic13—161no—
235C22×Q8C22⋊D1311yescharacteristic
236C23×C4C22×D1311yescharacteristic
237C2×M16—261no—
238C2×M16—261no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C22⋊Q8C4×D1312yes—
242C22⋊Q8D5212yes—
243#117—261no—
244#117—261no—
245#117—261no—
246#117—261no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—131no—
251C2×C4⋊C4—131no—
252C2×C4⋊C4C22⋊D1311yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—261no—
256C2×C22⋊C4—261no—
257C2×C22⋊C4C22⋊D1311yescharacteristic
258C2×C22⋊C4C22⋊D1311yescharacteristic
259C2×C42—21no—
260C2×C42—21no—
261C2×C42—261no—
262C2×C42C22⋊D1311yescharacteristic
263C2×C42C22⋊D1311yescharacteristic
264#107—262no—
265#106—262no—
266#103—262no—
267#103—262no—
268C22⋊C8—132no—
269C22⋊C8—261no—
270C22⋊C8—261no—
271C22⋊C8—261no—
272#95—21no—
273#95—21no—
274#95—21no—
275#95—21no—
276#95—21no—
277#95—21no—
278#95—21no—
279#95—261no—
280#95—261no—
281C2×C13—21no—
282C2×C13—21no—
283C2×C13—41no—
284C2×C13—41no—
285C2×C13#189011yescharacteristic
286C2×C13#190511yescharacteristic
287C2×C13#190611yescharacteristic
288C24C2×C22⋊D1311yescharacteristic
289C2×Q8—21no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8#610312yes—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—261no—
302C22×C4—261no—
303C22×C4—521no—
304C22×C4C2×C4×D1311yescharacteristic
305C22×C4C2×D5211yescharacteristic
306C22×C4#612711yescharacteristic
307C22×C4#612711yescharacteristic
308C22×C4C2×C22⋊D1311yescharacteristic
309C22×C4C2×C22⋊D1311yescharacteristic
310M16—521no—
311M16—521no—
312M16—521no—
313M16—521no—
314C2×C8—262no—
315C2×C8—521no—
316C4⋊C4—22no—
317C4⋊C4—21no—
318C4⋊C4—22no—
319C4⋊C4—42no—
320C4⋊C4—81no—
321C4⋊C4—261no—
322C4⋊C4—261no—
323C4⋊C4—261no—
324C4⋊C4—261no—
325C4⋊C4#610312yes—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—42no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—521no—
332C22⋊C4—521no—
333C22⋊C4—521no—
334C22⋊C4—521no—
335C42—41no—
336C42—41no—
337C42—42no—
338C42—81no—
339C42—521no—
340C42—521no—
341C13#952611yescharacteristic, complemented, Sylow
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23C4×C22⋊D1311yescharacteristic
347C23#8818411yescharacteristic
348C23#8820711yescharacteristic
349Q8—42no—
350Q8—81no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—521no—
378C2×C4—521no—
379C2×C4—1041no—
380C2×C4—1041no—
381C2×C4—1041no—
382C2×C4—1041no—
383C2×C4—1041no—
384C2×C4C2×#610311yescharacteristic
385C2×C4C4×C22⋊D1311yescharacteristic
386C2×C4#8818311yescharacteristic
387C2×C4#8818411yescharacteristic
388C8—522no—
389C8—1041no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22#1171887411yescharacteristic
401C22#1171890411yescharacteristic
402C22#1171890411yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—42no—
408C4—42no—
409C4—42no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4—1041no—
414C4—1041no—
415C4—2081no—
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2#1311524911yescharacteristic
421C2#1311533011yescharacteristic
422C2#1311533711yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2332C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2332D13
hypocenterC13#9526
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2332

Complements

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

NH ≅ G/Ntype
23. #11718705C4semidirect
24. #11718704C4semidirect
341. C13#9526semidirect

Maximal subgroups

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

subgroupindex
#131247802
#131149362
#131149112
#131133692
#131127442
#131126892
C13×#23322
#952613