Finite Group Databasebeta

← #15758976

Subgroups — #15758976

Order 3328.

516 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 105 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#13120652C211yesmaximal, characteristic
2#13117438C211yesmaximal, characteristic
3#13113409C211yesmaximal, characteristic
4#13113407C211yesmaximal, characteristic
5C2×#11718061C211yesmaximal, characteristic
6#13112703C211yesmaximal, characteristic
7C13×#1289C211yesmaximal, characteristic
8C2×#88178C2211yescharacteristic
9C22×#6101C2211yescharacteristic
10C2×C13×C22⋊C8C2211yescharacteristic
11C13×#380C2211yescharacteristic
12C13×#380C2211yescharacteristic
13#11718873C2211yescharacteristic
14C2×C22⋊#1055C2211yescharacteristic
15#11718644—22no—
16#11718639—22no—
17#11718611—21no—
18#11718604—21no—
19#11718604—21no—
20C22⋊C4×Dic13—21no—
21#11718320C412yescomplemented
22#11718317C412yescomplemented
23#11718316—22no—
24#11718061—22no—
25#11718059—22no—
26#11718044—22no—
27C23×C4×C13C2311yescharacteristic
28C23×Dic13D411yescharacteristic
29C23×Dic13D411yescharacteristic
30C22×Dic26C2×C411yescharacteristic
31C22×C8×C13—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—22no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41#88178—21no—
42#88178—21no—
43#88178—21no—
44#88178—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×#6101—21no—
48C2×#6101—21no—
49C2×#6101—21no—
50C2×#6101C2×C412yes—
51C2×#6101D412yes—
52C2×C4×Dic13—22no—
53C22×#1055—21no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×#95C2×C412yes—
57C13×#95D412yes—
58#88071—22no—
59#88071—24no—
60#88071—22no—
61#88071—22no—
62#88071—22no—
63#88071D412yes—
64C22⋊#1055—21no—
65C22⋊#1055—21no—
66#9202—131nomaximal, Sylow
67C24×C13C2×D411yescharacteristic
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—81no—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13#4111yescharacteristic
76C22×C4×C13#4111yescharacteristic
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—21no—
87C22×Dic13—22no—
88C22×Dic13—81no—
89C22×Dic13C22⋊C412yes—
90C22×Dic13C22⋊C412yes—
91C2×Dic26—21no—
92C2×Dic26—21no—
93C2×Dic26—81no—
94C2×C8×C13—41no—
95C2×C8×C13—81no—
96C13×C4⋊C4—81no—
97C13×C4⋊C4—81no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C22⋊Dic13—41no—
103C22⋊Dic13—41no—
104C22⋊Dic13—41no—
105C22⋊Dic13—41no—
106C4⋊Dic13—21no—
107C4⋊Dic13—21no—
108C4⋊Dic13—82no—
109C4⋊Dic13—81no—
110#6101—22no—
111#6101—22no—
112#6101—22no—
113#6101—22no—
114#6101—41no—
115#6101—41no—
116C4×Dic13—82no—
117C2×#1055—41no—
118C2×#1055—81no—
119#2627—131no—
120#2313—131no—
121#1520—131no—
122#1520—131no—
123C2×#324—131no—
124#1289—131no—
125#1289D1311yescharacteristic
126C23×C13—41no—
127C23×C13—41no—
128C23×C13C2×C22⋊C411yescharacteristic
129C23×C13#12011yescharacteristic
130C23×C13#12311yescharacteristic
131C23×C13#13511yescharacteristic
132C23×C13#13511yescharacteristic
133C23×C13#13711yescharacteristic
134C23×C13#13711yescharacteristic
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13C4×D411yescharacteristic
148C2×C4×C13C4×D411yescharacteristic
149C2×C4×C13#12111yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×Dic13—22no—
152C2×Dic13—22no—
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—42no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C2×Dic13—41no—
166C2×Dic13—41no—
167C2×Dic13—42no—
168C2×Dic13—81no—
169Dic26—81no—
170Dic26—81no—
171C8×C13—81no—
172#1055—81no—
173C2×C22⋊Q8—131no—
174C22×C4⋊C4—131no—
175C2×C22⋊C8—131no—
176C2×C22⋊C8C2×D1311yescharacteristic
177#400—132no—
178#398—262no—
179#395—132no—
180#387—262no—
181#387—262no—
182#385—261no—
183#381—261no—
184#381—261no—
185#380—131no—
186#380C2×D1311yescharacteristic
187#380C2×D1311yescharacteristic
188C4×C22⋊C4—261no—
189#328—262no—
190#328—262no—
191#324—262no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13#38611yescharacteristic
203C22×C13#41611yescharacteristic
204C22×C13#41911yescharacteristic
205C22×C13#45211yescharacteristic
206C22×C13#45211yescharacteristic
207C22×C13#48511yescharacteristic
208C22×C13#48511yescharacteristic
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—82no—
214C4×C13—82no—
215Dic13—42no—
216Dic13—42no—
217Dic13—82no—
218Dic13—81no—
219Dic13—81no—
220C22×Q8—131no—
221C23×C4—131no—
222C23×C4—131no—
223C23×C4C22×D1311yescharacteristic
224C22×C8—21no—
225C22×C8—261no—
226C22⋊Q8—261no—
227C22⋊Q8—261no—
228C22⋊Q8—261no—
229C22⋊Q8—261no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—132no—
233C2×C4⋊C4—132no—
234C2×C4⋊C4—131no—
235C2×C4⋊C4—261no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—261no—
238C2×C4⋊C4—261no—
239C2×C4⋊C4—261no—
240C2×C4⋊C4—262no—
241C2×C4⋊C4—261no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—261no—
245C2×C22⋊C4—261no—
246C2×C42—262no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—261no—
250C22⋊C8—261no—
251#95—132no—
252#95—262no—
253#95—262no—
254#95—262no—
255#95—262no—
256#95—264no—
257#95C4×D1312yes—
258#95D5212yes—
259C2×C13—21no—
260C2×C13—21no—
261C2×C13—21no—
262C2×C13—21no—
263C2×C13—21no—
264C2×C13—21no—
265C2×C13#187311yescharacteristic
266C2×C13#191211yescharacteristic
267C2×C13#191311yescharacteristic
268C24D4×D1311yescharacteristic
269C2×Q8—261no—
270C2×Q8—261no—
271C2×Q8—1041no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—81no—
275C22×C4—132no—
276C22×C4—132no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4—261no—
286C22×C4—261no—
287C22×C4—262no—
288C22×C4—1041no—
289C22×C4C2×C4×D1311yescharacteristic
290C22×C4C2×D5211yescharacteristic
291C22×C4#612711yescharacteristic
292C22×C4D4×D1311yescharacteristic
293C22×C4D4×D1311yescharacteristic
294C22×C4#613111yescharacteristic
295C2×C8—41no—
296C2×C8—81no—
297C2×C8—521no—
298C2×C8—1041no—
299C4⋊C4—81no—
300C4⋊C4—81no—
301C4⋊C4—262no—
302C4⋊C4—262no—
303C4⋊C4—262no—
304C4⋊C4—262no—
305C4⋊C4—261no—
306C4⋊C4—261no—
307C4⋊C4—521no—
308C4⋊C4—521no—
309C4⋊C4—1041no—
310C4⋊C4—1042no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—521no—
316C22⋊C4—521no—
317C22⋊C4—521no—
318C22⋊C4—521no—
319C42—1042no—
320C13#920211yescharacteristic, complemented, Sylow
321C23—41no—
322C23—41no—
323C23C22⋊C4×D1311yescharacteristic
324C23#8813611yescharacteristic
325C23#8814811yescharacteristic
326C23#8816611yescharacteristic
327C23#8816911yescharacteristic
328C23#8817011yescharacteristic
329C23#8817211yescharacteristic
330Q8—1041no—
331Q8—1041no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—262no—
345C2×C4—262no—
346C2×C4—262no—
347C2×C4—262no—
348C2×C4—522no—
349C2×C4—521no—
350C2×C4—521no—
351C2×C4—521no—
352C2×C4—521no—
353C2×C4—522no—
354C2×C4—522no—
355C2×C4—522no—
356C2×C4—522no—
357C2×C4—522no—
358C2×C4—522no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—1041no—
362C2×C4C4×D5211yescharacteristic
363C2×C4#8813811yescharacteristic
364C2×C4#8814711yescharacteristic
365C2×C4#8814911yescharacteristic
366C8—81no—
367C8—1041no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1171832611yescharacteristic
379C22#1171843311yescharacteristic
380C22#1171844411yescharacteristic
381C22#1171846311yescharacteristic
382C22#1171847111yescharacteristic
383C22#1171852811yescharacteristic
384C22#1171854911yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—82no—
391C4—522no—
392C4—522no—
393C4—1042no—
394C4—1041no—
395C4—1041no—
396C2—21no—
397C2—21no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2#1311514711yescharacteristic
403C2#1311537211yescharacteristic
404C2#1311537711yescharacteristic
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#9202
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
21. #11718320C4semidirect
22. #11718317C4semidirect
320. C13#9202semidirect

Maximal subgroups

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

subgroupindex
#131206522
#131174382
#131134092
#131134072
C2×#117180612
#131127032
C13×#12892
#920213