Finite Group Databasebeta

← #15778090

Subgroups — #15778090

Order 3328.

564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 123 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#13117548C211yesmaximal, characteristic
2C2×#11718065C212yesmaximal
3C4×#88074C211yesmaximal, characteristic
4#13112960C212yesmaximal
5C4×C13×#99C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88190C2211yescharacteristic
8C2×C4×Dic26C411yescharacteristic, complemented
9C2×C13×#99C2212yes—
10C4×C13×C22⋊C4—21no—
11#11718882C2211yescharacteristic
12C2×#88074C2212yes—
13#11718871—21no—
14#11718871—21no—
15C4×C22⋊Dic13—21no—
16#11718637C411yescharacteristic, complemented
17#11718635C411yescharacteristic, complemented
18#11718605—21no—
19#11718605—21no—
20#11718593C411yescharacteristic, complemented
21C13×#342—21no—
22#11718118—21no—
23#11718065C418yescomplemented
24C22×D4×C13C2311yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C22×Dic26C2×C411yescharacteristic
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C42×C13—41no—
35C2×C42×C13C2×C411yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—22no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—21no—
41#88190—22no—
42#88190C2×C414yes—
43C2×C4⋊Dic13C2×C411yescharacteristic
44C2×#6101—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×C4×Dic13—21no—
48C2×C4×Dic13—41no—
49C2×C4×Dic13C2×C411yescharacteristic
50C2×C4×Dic13C2×C411yescharacteristic
51C4×Dic26—41no—
52C4×Dic26—41no—
53C13×#99—22no—
54C13×#99C2×C414yes—
55C13×#95—41no—
56#88074—22no—
57#88074C2×C414yes—
58#88071—21no—
59#88071—21no—
60#88071—21no—
61#88071—21no—
62#88071—41no—
63#12627—131nomaximal, Sylow
64C24×C13C2×D411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C2×D4×C13—41no—
67C2×D4×C13—41no—
68C2×D4×C13C22×C412yes—
69C2×D4×C13#4112yes—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—42no—
75C22×C4×C13—81no—
76C22×C4×C13—81no—
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22×C411yescharacteristic
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—42no—
87C2×Dic26—21no—
88C2×Dic26—41no—
89C2×Dic26—41no—
90C2×Dic26C4212yescomplemented
91C13×C4⋊C4—41no—
92C13×C22⋊C4—24no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—42no—
96C42×C13—21no—
97C42×C13—21no—
98C42×C13—82no—
99C22⋊Dic13—24no—
100C22⋊Dic13—24no—
101C22⋊Dic13—24no—
102C22⋊Dic13—42no—
103C22⋊Dic13—81no—
104C22⋊Dic13—81no—
105C4⋊Dic13—41no—
106#6101—41no—
107#6101—41no—
108#6101—81no—
109#6101—81no—
110C4×Dic13—21no—
111C4×Dic13—42no—
112C4×Dic13—41no—
113C4×Dic13—82no—
114C4×Dic13C4212yescomplemented
115#2326—131no—
116C2×#354—132no—
117C4×#99—131no—
118C4×#99D1311yescharacteristic
119#1393—132no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13C2×C22⋊C411yescharacteristic
129C23×C13C4×D412yes—
130C23×C13C4×D412yes—
131D4×C13—42no—
132D4×C13—42no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—44no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13—82no—
148C2×C4×C13—82no—
149C2×C4×C13#9911yescharacteristic
150C2×C4×C13#9911yescharacteristic
151C2×C4×C13C2×C4211yescharacteristic
152C2×C4×C13#11711yescharacteristic
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—44no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13—82no—
167C2×Dic13—82no—
168Dic26—42no—
169Dic26—42no—
170C2×#124—131no—
171C2×C4×Q8—131no—
172C2×C4×D4C2×D1311yescharacteristic
173C2×#99—132no—
174C2×#99C2×D1312yes—
175#391—131no—
176#390—131no—
177#388—261no—
178#388—261no—
179#385—261no—
180#385—261no—
181#384—131no—
182C4×C22⋊C4—21no—
183C4×C22⋊C4—261no—
184#376—131no—
185#354—138no—
186#342—21no—
187#342—261no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—22no—
191C22×C13—22no—
192C22×C13—42no—
193C22×C13—42no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13C4×C22⋊C411yescharacteristic
201C22×C13C2×#9911yescharacteristic
202C22×C13#41011yescharacteristic
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—41no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—84no—
211Dic13—42no—
212Dic13—42no—
213Dic13—81no—
214Dic13—84no—
215Dic13—81no—
216C22×Q8—131no—
217C22×D4C22×D1311yescharacteristic
218C23×C4D5211yescharacteristic
219C23×C4C22⋊D1311yescharacteristic
220#124—134no—
221#124—262no—
222C4×Q8—521no—
223C4×Q8—521no—
224C4×D4—41no—
225C4×D4—41no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4—261no—
228C2×C4⋊C4—261no—
229C2×C4⋊C4—261no—
230C2×C4⋊C4C4×D1311yescharacteristic
231C2×C22⋊C4—22no—
232C2×C22⋊C4—261no—
233C2×C22⋊C4—261no—
234C2×C22⋊C4—262no—
235C2×C22⋊C4—261no—
236C2×C22⋊C4—261no—
237C2×C22⋊C4D5211yescharacteristic
238C2×C22⋊C4C22⋊D1311yescharacteristic
239C2×C42—41no—
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—261no—
243C2×C42—521no—
244C2×C42C4×D1311yescharacteristic
245#99—22no—
246#99—134no—
247#99—262no—
248#99C4×D1314yes—
249#95—41no—
250#95—261no—
251#95—261no—
252#95—261no—
253#95—261no—
254#95—521no—
255C2×C13—21no—
256C2×C13—21no—
257C2×C13—42no—
258C2×C13—42no—
259C2×C13C4×#9911yescharacteristic
260C2×C13#212711yescharacteristic
261C2×C13#212911yescharacteristic
262C24C2×D5211yescharacteristic
263C24C2×C22⋊D1311yescharacteristic
264C2×Q8—132no—
265C2×Q8—261no—
266C2×Q8—521no—
267C2×Q8—521no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4C2×C4×D1312yes—
271C2×D4#612712yes—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—42no—
277C22×C4—81no—
278C22×C4—81no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4—522no—
284C22×C4#610311yescharacteristic
285C22×C4#610311yescharacteristic
286C22×C4#610311yescharacteristic
287C22×C4#610311yescharacteristic
288C22×C4C2×C4×D1311yescharacteristic
289C4⋊C4—41no—
290C4⋊C4—521no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C4⋊C4—1041no—
294C4⋊C4—1041no—
295C22⋊C4—24no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—42no—
299C22⋊C4—264no—
300C22⋊C4—264no—
301C22⋊C4—264no—
302C22⋊C4—522no—
303C22⋊C4—1041no—
304C22⋊C4—1041no—
305C42—21no—
306C42—21no—
307C42—82no—
308C42—132no—
309C42—261no—
310C42—521no—
311C42—522no—
312C42—1042no—
313C13#1262711yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23C4×D5212yes—
323C23C2×#610311yescharacteristic
324C23C4×C22⋊D1312yes—
325Q8—522no—
326Q8—522no—
327D4—42no—
328D4—42no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—44no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—262no—
346C2×C4—262no—
347C2×C4—521no—
348C2×C4—521no—
349C2×C4—521no—
350C2×C4—521no—
351C2×C4—524no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—521no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4—1042no—
359C2×C4—1042no—
360C2×C4#8804611yescharacteristic
361C2×C4#8804611yescharacteristic
362C2×C4C42×D1311yescharacteristic
363C2×C4#8812611yescharacteristic
364C22—21no—
365C22—21no—
366C22—22no—
367C22—22no—
368C22—42no—
369C22—42no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22—81no—
376C22C4×#610311yescharacteristic
377C22C2×#8804611yescharacteristic
378C22#1171866711yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—84no—
387C4—522no—
388C4—522no—
389C4—1041no—
390C4—1044no—
391C4—1041no—
392C2—21no—
393C2—21no—
394C2—42no—
395C2—42no—
396C2C4×#8804611yescharacteristic
397C2#1311650311yescharacteristic
398C2#1311651011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC2×C4×C13C2×C42
FrattiniC22×D4C22×D13
FittingC4×C13×#99C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenterC4×#99D13
hypocenterC13#12627
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
8. C2×C4×Dic26C4semidirect
16. #11718637C4semidirect
17. #11718635C4semidirect
20. #11718593C4semidirect
23. #11718065C4semidirect
90. C2×Dic26C42semidirect
114. C4×Dic13C42semidirect
313. C13#12627semidirect

Maximal subgroups

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

subgroupindex
#131175482
C2×#117180652
C4×#880742
#131129602
C4×C13×#992
#1262713