Finite Group Databasebeta

← #15778064

Subgroups — #15778064

Order 3328.

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

normal subgroups only

This group has 548 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#13117501C211yesmaximal, characteristic
2C2×#11718068C212yesmaximal
3C4×#88074C211yesmaximal, characteristic
4#13112955C212yesmaximal
5C4×C13×#100C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88189C2211yescharacteristic
8C22×#6101C411yescharacteristic, complemented
9C2×C13×#100C2212yes—
10C4×C13×M16—21no—
11#11718881C2211yescharacteristic
12C2×#88074C2212yes—
13#11718871—21no—
14C4×C22⋊Dic13—21no—
15C4×C22⋊Dic13C411yescharacteristic, complemented
16#11718633—21no—
17#11718607C411yescharacteristic, complemented
18#11718606—21no—
19#11718604C411yescharacteristic, complemented
20#11718594—21no—
21C13×#343—21no—
22#11718118—21no—
23#11718068C418yescomplemented
24C22×D4×C13C2311yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C23×Dic13C2×C411yescharacteristic
29C2×C13×M16—22no—
30C4×D4×C13—41no—
31C4×D4×C13—41no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C22⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—22no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13C2×C411yescharacteristic
40C2×C22⋊Dic13C2×C411yescharacteristic
41#88189—22no—
42#88189C2×C414yes—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×#6101—41no—
48C2×#6101—41no—
49C2×C4×Dic13—21no—
50C2×C4×Dic13—41no—
51C13×#100—22no—
52C13×#100C2×C414yes—
53C13×#97—41no—
54C4×C8×C13—41no—
55#88074—22no—
56#88074C2×C414yes—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88071—21no—
61#88071—21no—
62#88071—41no—
63#12621—131nomaximal, Sylow
64C24×C13C22×C411yescharacteristic
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—81no—
75C22×C4×C13—81no—
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—41no—
87C22×Dic13—41no—
88C22×Dic13—42no—
89C22×Dic13—41no—
90C22×Dic13—81no—
91C22×Dic13C4212yescomplemented
92C13×M16—24no—
93C13×M16—42no—
94C2×C8×C13—42no—
95C13×C4⋊C4—41no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C42×C13—21no—
99C42×C13—21no—
100C22⋊Dic13—21no—
101C22⋊Dic13—24no—
102C22⋊Dic13—24no—
103C22⋊Dic13—42no—
104C22⋊Dic13—41no—
105C22⋊Dic13—81no—
106C22⋊Dic13C4212yescomplemented
107#6101—24no—
108#6101—42no—
109#6101—41no—
110#6101—41no—
111#6101—81no—
112C4×Dic13—81no—
113C4×Dic13—82no—
114#2322—131no—
115C2×#352—132no—
116C4×#100D1311yescharacteristic
117C4×#99—131no—
118#1390—132no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13C2×C4211yescharacteristic
128C23×C13C2×C22⋊C411yescharacteristic
129C23×C13#11711yescharacteristic
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—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13#9911yescharacteristic
147C2×C4×C13#9911yescharacteristic
148C2×C4×C13C4×D412yes—
149C2×Dic13—22no—
150C2×Dic13—22no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—42no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—42no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—44no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—82no—
165C2×Dic13—82no—
166C2×Dic13—82no—
167C8×C13—44no—
168C2×#123—131no—
169C2×C4×D4C2×D1311yescharacteristic
170C22×C4⋊C4—131no—
171C2×#100C2×D1312yes—
172C2×#99—132no—
173C4×M16—21no—
174#389—261no—
175#388—261no—
176#387—261no—
177#386—131no—
178#385—131no—
179#385—261no—
180#381—131no—
181C4×C22⋊C4—131no—
182C4×C22⋊C4—261no—
183#352—138no—
184#343—21no—
185#342—261no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—22no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—42no—
194C22×C13—42no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—81no—
200C22×C13C4×C22⋊C411yescharacteristic
201C22×C13C2×#9911yescharacteristic
202C22×C13#41011yescharacteristic
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—22no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13—41no—
209Dic13—42no—
210Dic13—42no—
211Dic13—81no—
212Dic13—84no—
213Dic13—81no—
214C22×D4C22×D1311yescharacteristic
215C23×C4—131no—
216C23×C4—131no—
217C23×C4C4×D1311yescharacteristic
218C23×C4D5211yescharacteristic
219C2×M16—22no—
220#123—134no—
221#123—262no—
222C4×D4—41no—
223C4×D4—41no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4—261no—
226C2×C4⋊C4—261no—
227C2×C4⋊C4—261no—
228C2×C4⋊C4—521no—
229C2×C4⋊C4—521no—
230C2×C4⋊C4C22⋊D1311yescharacteristic
231C2×C22⋊C4—131no—
232C2×C22⋊C4—131no—
233C2×C22⋊C4—261no—
234C2×C22⋊C4—262no—
235C2×C22⋊C4—261no—
236C2×C22⋊C4C4×D1311yescharacteristic
237C2×C22⋊C4D5211yescharacteristic
238C2×C42—261no—
239C2×C42—521no—
240C2×C42C22⋊D1311yescharacteristic
241#100—22no—
242#100C4×D1314yes—
243#99—134no—
244#99—262no—
245#97—41no—
246C4×C8—41no—
247#95—261no—
248#95—261no—
249#95—261no—
250#95—261no—
251#95—261no—
252#95—521no—
253C2×C13—21no—
254C2×C13—21no—
255C2×C13—42no—
256C2×C13—41no—
257C2×C13—41no—
258C2×C13C4×#9911yescharacteristic
259C2×C13#212111yescharacteristic
260C2×C13#212311yescharacteristic
261C24C2×C4×D1311yescharacteristic
262C24C2×D5211yescharacteristic
263C2×D4—41no—
264C2×D4—41no—
265C2×D4C2×C4×D1312yes—
266C2×D4#612712yes—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—81no—
272C22×C4—81no—
273C22×C4—132no—
274C22×C4—261no—
275C22×C4—261no—
276C22×C4—261no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—521no—
280C22×C4—521no—
281C22×C4—522no—
282C22×C4—521no—
283C22×C4—1041no—
284C22×C4#610311yescharacteristic
285C22×C4#610311yescharacteristic
286C22×C4#610311yescharacteristic
287C22×C4#610311yescharacteristic
288C22×C4C2×C22⋊D1311yescharacteristic
289M16—24no—
290M16—42no—
291C2×C8—42no—
292C4⋊C4—41no—
293C4⋊C4—264no—
294C4⋊C4—522no—
295C4⋊C4—521no—
296C4⋊C4—521no—
297C4⋊C4—1041no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—132no—
301C22⋊C4—261no—
302C22⋊C4—264no—
303C22⋊C4—264no—
304C22⋊C4—522no—
305C22⋊C4—521no—
306C22⋊C4—1041no—
307C42—21no—
308C42—21no—
309C42—1041no—
310C42—1042no—
311C13#1262111yescharacteristic, complemented, Sylow
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23C42×D1311yescharacteristic
321C23#8812611yescharacteristic
322C23C4×D5212yes—
323C23C2×#610311yescharacteristic
324D4—42no—
325D4—42no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—262no—
340C2×C4—262no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4—522no—
344C2×C4—521no—
345C2×C4—521no—
346C2×C4—522no—
347C2×C4—521no—
348C2×C4—524no—
349C2×C4—521no—
350C2×C4—521no—
351C2×C4—521no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—1042no—
355C2×C4—1042no—
356C2×C4—1042no—
357C2×C4#8804611yescharacteristic
358C2×C4#8804611yescharacteristic
359C2×C4C4×C22⋊D1312yes—
360C8—44no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—42no—
369C22—42no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22C4×#610311yescharacteristic
376C22C2×#8804611yescharacteristic
377C22#1171866711yescharacteristic
378C4—22no—
379C4—21no—
380C4—21no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—522no—
385C4—522no—
386C4—1041no—
387C4—1044no—
388C4—1041no—
389C2—21no—
390C2—21no—
391C2—42no—
392C2—41no—
393C2—41no—
394C2C4×#8804611yescharacteristic
395C2#1311648311yescharacteristic
396C2#1311649111yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC23×C13C2×C42
FrattiniC22×D4C22×D13
FittingC4×C13×#100C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenterC4×#100D13
hypocenterC13#12621
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
8. C22×#6101C4semidirect
15. C4×C22⋊Dic13C4semidirect
17. #11718607C4semidirect
19. #11718604C4semidirect
23. #11718068C4semidirect
91. C22×Dic13C42semidirect
106. C22⋊Dic13C42semidirect
311. C13#12621semidirect

Maximal subgroups

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

subgroupindex
#131175012
C2×#117180682
C4×#880742
#131129552
C4×C13×#1002
#1262113