Finite Group Databasebeta

← #15763430

Subgroups — #15763430

Order 3328.

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

normal subgroups only

This group has 568 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#13125608C211yesmaximal, characteristic
2C2×#11718631C211yesmaximal, characteristic
3#13115821C211yesmaximal, characteristic
4#13114926C211yesmaximal, characteristic
5#13113408C211yesmaximal, characteristic
6#13112684C211yesmaximal, characteristic
7C13×#2502C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C2×#88178C2211yescharacteristic
11C13×#398—22no—
12C13×#391—21no—
13C13×#385—22no—
14C13×#384—21no—
15C4×C13×C22⋊C4C2211yescharacteristic
16#11718889—21no—
17#11718873C2211yescharacteristic
18C2×C22⋊#1055C2211yescharacteristic
19C2×C22⋊#1055C2211yescharacteristic
20#11718712—22no—
21#11718711—21no—
22#11718705—21no—
23#11718631—22no—
24#11718631—21no—
25#11718631—22no—
26C2×#88050—21no—
27C2×#88047—21no—
28#11718130—22no—
29#11718121—22no—
30#11718119—22no—
31C22×Q8×C13D411yescharacteristic
32C23×C4×C13—21no—
33C23×C4×C13C2311yescharacteristic
34C22×Dic26D411yescharacteristic
35C13×C22⋊Q8—21no—
36C13×C22⋊Q8—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C2×C13×C4⋊C4—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—24no—
46C2×C13×C4⋊C4D411yescharacteristic
47C2×C13×C4⋊C4D412yes—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4D412yes—
50C2×C42×C13—21no—
51C2×C22⋊Dic13—21no—
52C2×C22⋊Dic13—21no—
53C2×#6107—22no—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13D411yescharacteristic
56#88178—21no—
57#88178—21no—
58#88178—21no—
59#88178—21no—
60C2×#6101—21no—
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#88050—22no—
72#88050—24no—
73#88047—22no—
74#88047—24no—
75#9959—131nomaximal, Sylow
76C24×C13C2×D411yescharacteristic
77C2×Q8×C13—21no—
78C2×Q8×C13—21no—
79C2×Q8×C13—42no—
80C22×C4×C13—22no—
81C22×C4×C13—21no—
82C22×C4×C13—22no—
83C22×C4×C13—21no—
84C22×C4×C13—42no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13—82no—
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—21no—
95C22×Dic13—21no—
96C22×Dic13—41no—
97C2×Dic26—21no—
98C2×Dic26—21no—
99C2×Dic26—42no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—84no—
109C13×C22⋊C4—22no—
110C13×C22⋊C4—41no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4Q1614yescomplemented
113C42×C13—42no—
114C22⋊Dic13—41no—
115C22⋊Dic13—41no—
116C22⋊Dic13—42no—
117#6107—82no—
118C4⋊Dic13—21no—
119C4⋊Dic13—21no—
120C4⋊Dic13—42no—
121#6101—41no—
122#6101—41no—
123C2×#1055—22no—
124C2×#1055—22no—
125C2×#1055—42no—
126C2×#1055—42no—
127#3189—131no—
128C2×#484—131no—
129#2502D1311yescharacteristic
130#1996—131no—
131#1824—131no—
132#1520—131no—
133#1282—131no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13#12011yescharacteristic
137C23×C13#12111yescharacteristic
138C23×C13#12711yescharacteristic
139C23×C13C2×Q1612yes—
140C23×C13#13712yes—
141Q8×C13—42no—
142Q8×C13—81no—
143C2×C4×C13—22no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—24no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—44no—
154C2×C4×C13—42no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—82no—
159C2×C4×C13—82no—
160C2×C4×C13#12011yescharacteristic
161C2×C4×C13#12011yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13—81no—
167C2×Dic13—81no—
168C2×Dic13—81no—
169C2×Dic13—81no—
170C2×Dic13—81no—
171Dic26—42no—
172Dic26—42no—
173#1055—42no—
174#1055—42no—
175C2×C22⋊Q8—131no—
176C2×C22⋊Q8C2×D1311yescharacteristic
177C22×C4⋊C4C2×D1311yescharacteristic
178#484—262no—
179#484—261no—
180#484—262no—
181#484—261no—
182#467—262no—
183#451—261no—
184#451—261no—
185C2×#107—261no—
186C2×#103—261no—
187C2×C22⋊C8—131no—
188C2×C22⋊C8—131no—
189#398—22no—
190#391—21no—
191#385—22no—
192#384—21no—
193#380—131no—
194C4×C22⋊C4C2×D1311yescharacteristic
195#342—262no—
196#340—262no—
197#328—262no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—42no—
205C22×C13—42no—
206C22×C13#39211yescharacteristic
207C22×C13#45112yes—
208C22×C13#46212yes—
209C22×C13#49411yescharacteristic
210C22×C13#49711yescharacteristic
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—44no—
215C4×C13—81no—
216C4×C13—82no—
217C4×C13—81no—
218C4×C13#45812yes—
219Dic13—81no—
220Dic13—81no—
221Dic13—161no—
222C22×Q8—131no—
223C22×Q8C22⋊D1311yescharacteristic
224C23×C4—21no—
225C23×C4C22×D1311yescharacteristic
226C2×Q16—262no—
227C22×C8—132no—
228C22×C8—261no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C22⋊Q8—261no—
234C22⋊Q8—261no—
235C22⋊Q8—261no—
236C22⋊Q8—261no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—131no—
245C2×C4⋊C4—261no—
246C2×C4⋊C4—261no—
247C2×C4⋊C4C22⋊D1312yes—
248C2×C4⋊C4C22⋊D1311yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—261no—
251C2×C22⋊C4—261no—
252C2×C22⋊C4C22⋊D1312yes—
253C2×C42—21no—
254#107—264no—
255#107—262no—
256#103—264no—
257#103—262no—
258#103—262no—
259C22⋊C8—132no—
260C22⋊C8—261no—
261C22⋊C8—261no—
262C22⋊C8—261no—
263#95—24no—
264#95—21no—
265#95—261no—
266C2×C13—21no—
267C2×C13—22no—
268C2×C13—22no—
269C2×C13—21no—
270C2×C13#200811yescharacteristic
271C2×C13#201611yescharacteristic
272C2×C13#202211yescharacteristic
273C24C2×C22⋊D1311yescharacteristic
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—42no—
277C2×Q8—261no—
278C2×Q8—261no—
279C2×Q8—522no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—82no—
288C22×C4—261no—
289C22×C4—261no—
290C22×C4—521no—
291C22×C4D4×D1311yescharacteristic
292C22×C4D4×D1311yescharacteristic
293C22×C4D4×D1311yescharacteristic
294C22×C4#612911yescharacteristic
295C22×C4C2×C22⋊D1311yescharacteristic
296C22×C4C2×C22⋊D1311yescharacteristic
297Q16—1042no—
298C2×C8—262no—
299C2×C8—262no—
300C2×C8—522no—
301C2×C8—522no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—84no—
311C4⋊C4—261no—
312C4⋊C4—261no—
313C4⋊C4—522no—
314C4⋊C4—521no—
315C4⋊C4—521no—
316C22⋊C4—22no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—521no—
320C22⋊C4—521no—
321C22⋊C4—522no—
322C22⋊C4#610714yescomplemented
323C42—42no—
324C13#995911yescharacteristic, complemented, Sylow
325C23—41no—
326C23—41no—
327C23#8819211yescharacteristic
328C23#8819411yescharacteristic
329C23#8819612yes—
330C23C2×#610712yes—
331C23#8820711yescharacteristic
332Q8—42no—
333Q8—81no—
334Q8—522no—
335Q8—522no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—44no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—1041no—
356C2×C4—1041no—
357C2×C4—1041no—
358C2×C4—1041no—
359C2×C4—1041no—
360C2×C4#8819111yescharacteristic
361C2×C4#8819111yescharacteristic
362C2×C4#8819311yescharacteristic
363C2×C4#8819311yescharacteristic
364C8—522no—
365C8—522no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22#1171874711yescharacteristic
375C22#1171875112yes—
376C22#1171875311yescharacteristic
377C22#1171888411yescharacteristic
378C22#1171888912yes—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—44no—
383C4—81no—
384C4—81no—
385C4—82no—
386C4—1041no—
387C4—1041no—
388C4—2081no—
389C4#1171871412yes—
390C2—22no—
391C2—21no—
392C2—22no—
393C2—21no—
394C2#1311588911yescharacteristic
395C2#1311593611yescharacteristic
396C2#1311596411yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2502C2
socleC22×C13#392
prime radicalC24×C13C2×D4
hypercenter#2502D13
hypocenterC13#9959
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
112. C13×C22⋊C4Q16semidirect
322. C22⋊C4#6107semidirect
324. C13#9959semidirect

Maximal subgroups

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

subgroupindex
#131256082
C2×#117186312
#131158212
#131149262
#131134082
#131126842
C13×#25022
#995913