Finite Group Databasebeta

← #15763374

Subgroups — #15763374

Order 3328.

610 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 109 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#13125589C211yesmaximal, characteristic
2C2×#11718629C211yesmaximal, characteristic
3#13115672C211yesmaximal, characteristic
4#13114926C211yesmaximal, characteristic, complemented
5#13113408C211yesmaximal, characteristic, complemented
6#13112684C211yesmaximal, characteristic, complemented
7C13×#2502C211yesmaximal, characteristic, complemented
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C2×#88184C2211yescharacteristic
11C13×#398—22no—
12C13×#391—21no—
13C13×#385—22no—
14C13×#384—21no—
15C4×C13×C22⋊C4C2211yescharacteristic
16#11718888—21no—
17#11718873C2211yescharacteristic
18C2×C22⋊#1055C2211yescharacteristic
19C2×C22⋊#1055C2211yescharacteristic
20#11718709—22no—
21#11718707—21no—
22#11718704—21no—
23#11718629—22no—
24#11718629—21no—
25#11718629—22no—
26C2×#88049—21no—
27C2×#88048—21no—
28C2×#88046—22no—
29#11718130—22no—
30#11718121—22no—
31C22×Q8×C13D411yescharacteristic
32C23×C4×C13—21no—
33C23×C4×C13C2311yescharacteristic
34C22×C22⋊D13—21no—
35C22×D52D411yescharacteristic
36C13×C22⋊Q8—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—24no—
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C13×C4⋊C4D412yes—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4D412yes—
51C2×C42×C13—21no—
52C2×C22⋊Dic13—21no—
53C2×#6106—22no—
54#88184—21no—
55#88184—21no—
56#88184—21no—
57#88184—21no—
58C2×#6103—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13D411yescharacteristic
61C22×#1055—21no—
62C22×#1055D412yes—
63C13×#95—24no—
64C13×#95—21no—
65#88075—22no—
66#88071—21no—
67C22⋊#1055—21no—
68C22⋊#1055—21no—
69C22⋊#1055—21no—
70C22⋊#1055D412yes—
71#88049—22no—
72#88049—24no—
73#88048—22no—
74#88048—24no—
75#88046—44no—
76#9951—131nomaximal, Sylow
77C24×C13C2×D411yescharacteristic
78C23×D13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—42no—
82C22×C4×C13—22no—
83C22×C4×C13—21no—
84C22×C4×C13—22no—
85C22×C4×C13—21no—
86C22×C4×C13—42no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—82no—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13#4111yescharacteristic
96C2×C22⋊D13—41no—
97C2×C22⋊D13—41no—
98C2×C22⋊D13—42no—
99C2×C22⋊D13—42no—
100C22×Dic13—21no—
101C22×Dic13—41no—
102C2×D52—21no—
103C2×D52—21no—
104C2×D52—42no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—84no—
114C13×C22⋊C4—22no—
115C13×C22⋊C4—41no—
116C13×C22⋊C4—41no—
117C13×C22⋊C4SD1614yescomplemented
118C42×C13—42no—
119C22⋊Dic13—42no—
120#6106—82no—
121#6103—41no—
122#6103—41no—
123C4⋊Dic13—21no—
124C4⋊Dic13—21no—
125C4⋊Dic13—42no—
126C2×#1055—22no—
127C2×#1055—22no—
128C2×#1055—42no—
129C2×#1055—42no—
130#3187—131no—
131C2×#481—131no—
132#2502D1311yescharacteristic, complemented
133#1964—131no—
134#1824—131no—
135#1520—131no—
136#1282—131no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13#12011yescharacteristic
140C23×C13#12111yescharacteristic
141C23×C13#12711yescharacteristic
142C23×C13C2×SD1612yes—
143C23×C13#13712yes—
144C22×D13—41no—
145C22×D13—42no—
146C22×D13—81no—
147C22×D13—81no—
148Q8×C13—42no—
149Q8×C13—81no—
150C2×C4×C13—22no—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
153C2×C4×C13—24no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—44no—
161C2×C4×C13—42no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—42no—
165C2×C4×C13—82no—
166C2×C4×C13—82no—
167C2×C4×C13#12011yescharacteristic
168C2×C4×C13#12011yescharacteristic
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13#12111yescharacteristic
171C22⋊D13—82no—
172C22⋊D13—81no—
173C22⋊D13—81no—
174C2×Dic13—41no—
175C2×Dic13—42no—
176C2×Dic13—81no—
177C2×Dic13—81no—
178C2×Dic13—81no—
179D52—42no—
180D52—42no—
181#1055—42no—
182#1055—42no—
183C2×C22⋊Q8C2×D1311yescharacteristic
184C2×#121—131no—
185C22×C4⋊C4C2×D1311yescharacteristic
186#483—261no—
187#481—262no—
188#481—262no—
189#481—261no—
190#465—262no—
191#450—261no—
192#448—261no—
193C2×#106—261no—
194C2×#102—261no—
195C2×#99—262no—
196C2×C22⋊C8—131no—
197C2×C22⋊C8—131no—
198#398—22no—
199#391—21no—
200#385—22no—
201#384—21no—
202#380—131no—
203C4×C22⋊C4C2×D1311yescharacteristic
204#340—262no—
205#328—262no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—42no—
213C22×C13—42no—
214C22×C13#39211yescharacteristic
215C22×C13#44812yes—
216C22×C13#46112yes—
217C22×C13#49211yescharacteristic
218C22×C13#49711yescharacteristic
219C2×D13—81no—
220C2×D13—81no—
221C2×D13—81no—
222C2×D13—162no—
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—21no—
226C4×C13—44no—
227C4×C13—81no—
228C4×C13—82no—
229C4×C13—81no—
230C4×C13#45812yes—
231Dic13—81no—
232Dic13—161no—
233C22×Q8C22⋊D1311yescharacteristic
234C22×D4—131no—
235C22×D4—261no—
236C23×C4—21no—
237C23×C4C22×D1311yescharacteristic
238C2×SD16—262no—
239C22×C8—132no—
240C22×C8—261no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245#121—261no—
246#121—261no—
247#121—261no—
248#121—261no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—131no—
257C2×C4⋊C4—261no—
258C2×C4⋊C4C22⋊D1312yes—
259C2×C4⋊C4C22⋊D1311yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—261no—
262C2×C22⋊C4—261no—
263C2×C22⋊C4C22⋊D1312yes—
264C2×C42—21no—
265#106—264no—
266#106—262no—
267#103—262no—
268#102—264no—
269#102—262no—
270#99—524no—
271C22⋊C8—132no—
272C22⋊C8—261no—
273C22⋊C8—261no—
274C22⋊C8—261no—
275#95—24no—
276#95—21no—
277#95—261no—
278C2×C13—21no—
279C2×C13—22no—
280C2×C13—22no—
281C2×C13—21no—
282C2×C13#200811yescharacteristic
283C2×C13#201311yescharacteristic
284C2×C13#202211yescharacteristic
285D13—161no—
286C24—261no—
287C24C2×C22⋊D1311yescharacteristic
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—42no—
291C2×D4—261no—
292C2×D4—261no—
293C2×D4—522no—
294C2×D4—521no—
295C2×D4—522no—
296C2×D4—522no—
297C2×D4—521no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—42no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—82no—
306C22×C4—261no—
307C22×C4—521no—
308C22×C4D4×D1311yescharacteristic
309C22×C4D4×D1311yescharacteristic
310C22×C4D4×D1311yescharacteristic
311C22×C4#612911yescharacteristic
312C22×C4C2×C22⋊D1311yescharacteristic
313C22×C4C2×C22⋊D1311yescharacteristic
314SD16—1042no—
315C2×C8—262no—
316C2×C8—262no—
317C2×C8—522no—
318C2×C8—522no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—84no—
328C4⋊C4—261no—
329C4⋊C4—261no—
330C4⋊C4—522no—
331C22⋊C4—22no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—521no—
335C22⋊C4—521no—
336C22⋊C4—522no—
337C22⋊C4#610614yescomplemented
338C42—42no—
339C13#995111yescharacteristic, complemented, Sylow
340C23—41no—
341C23—41no—
342C23—521no—
343C23—522no—
344C23—1041no—
345C23—1041no—
346C23#8819211yescharacteristic
347C23#8819411yescharacteristic
348C23C2×#610612yes—
349C23#8819612yes—
350C23#8820711yescharacteristic
351Q8—42no—
352Q8—81no—
353D4—522no—
354D4—522no—
355D4—1041no—
356D4—1041no—
357D4—1042no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—44no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—522no—
376C2×C4—521no—
377C2×C4—1041no—
378C2×C4—1041no—
379C2×C4—1041no—
380C2×C4#8819111yescharacteristic
381C2×C4#8819111yescharacteristic
382C2×C4#8819311yescharacteristic
383C2×C4#8819311yescharacteristic
384C8—522no—
385C8—522no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—42no—
393C22—42no—
394C22—1041no—
395C22—1041no—
396C22—1041no—
397C22—2082no—
398C22#1171874412yes—
399C22#1171874611yescharacteristic
400C22#1171874711yescharacteristic
401C22#1171888411yescharacteristic
402C22#1171888812yes—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—44no—
407C4—81no—
408C4—81no—
409C4—82no—
410C4—1041no—
411C4—2081no—
412C4#1171871412yes—
413C2—22no—
414C2—21no—
415C2—22no—
416C2—21no—
417C2—2081no—
418C2#1311588911yescharacteristic
419C2#1311591911yescharacteristic
420C2#1311596411yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2502C2
socleC22×C13#392
prime radicalC2×#88184C22
hypercenter#2502D13
hypocenterC13#9951
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2502

Complements

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

NH ≅ G/Ntype
4. #13114926C2semidirect
5. #13113408C2semidirect
6. #13112684C2semidirect
7. C13×#2502C2semidirect
117. C13×C22⋊C4SD16semidirect
132. #2502D13semidirect
337. C22⋊C4#6106semidirect
339. C13#9951semidirect

Maximal subgroups

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

subgroupindex
#131255892
C2×#117186292
#131156722
#131149262
#131134082
#131126842
C13×#25022
#995113