Finite Group Databasebeta

← #15758766

Subgroups — #15758766

Order 3328.

436 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 95 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#13124962C211yesmaximal, characteristic
2#13123923C211yesmaximal, characteristic
3#13114669C211yesmaximal, characteristic
4#13113451C211yesmaximal, characteristic
5#13112736C211yesmaximal, characteristic
6#13112692C211yesmaximal, characteristic
7C13×#1503C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C4×Dic26C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C4×C13×C4⋊C4C2211yescharacteristic
12#11718755C411yescharacteristic, complemented
13#11718755C411yescharacteristic, complemented
14#11718751C411yescharacteristic, complemented
15#11718751C411yescharacteristic, complemented
16#11718711—21no—
17#11718704—21no—
18#11718691—21no—
19#11718691—21no—
20C2×#88050—21no—
21#11718587C2211yescharacteristic
22#11718587C2211yescharacteristic
23C2×#88043C2211yescharacteristic
24#11718489—22no—
25#11718380—21no—
26#11718379—21no—
27#11718340—21no—
28C8×Dic26—21no—
29C13×#328—21no—
30C13×#328—21no—
31#11718135—22no—
32#11718121—21no—
33C22×Dic26D411yescharacteristic
34C13×C4⋊Q8C2×C411yescharacteristic
35C13×C4⋊Q8C2×C411yescharacteristic
36C13×#125—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C4×Q8×C13—21no—
40C4×Q8×C13—21no—
41C13×#117—21no—
42C2×C13×C4⋊C4—21no—
43C2×C42×C13—21no—
44C2×C42×C13C2311yescharacteristic
45C2×#6107—21no—
46C2×#6107—21no—
47C2×C4⋊Dic13D411yescharacteristic
48C2×#6101—21no—
49C2×C4×Dic13—21no—
50C22×#1055—21no—
51C4×Dic26—21no—
52C4×Dic26—21no—
53C4×Dic26C2×C411yescharacteristic
54C4×Dic26C2×C411yescharacteristic
55C4×Dic26D411yescharacteristic
56C4×Dic26D411yescharacteristic
57C13×C4⋊C8—21no—
58C13×C22⋊C8D411yescharacteristic
59C13×C22⋊C8D411yescharacteristic
60C4×C8×C13—21no—
61C13×#95—21no—
62#88075—21no—
63#88075—21no—
64C22⋊#1055—21no—
65C22⋊#1055—21no—
66#88055—22no—
67#88054—22no—
68#88054—22no—
69C8×Dic13—22no—
70#88050—24no—
71#88050—21no—
72#88050—21no—
73#88048—21no—
74#88048—21no—
75C4⋊#1055—21no—
76C4⋊#1055C2×C411yescharacteristic
77C4⋊#1055C2×C411yescharacteristic
78#88043—21no—
79#88043—21no—
80#88043—21no—
81#88043D412yes—
82#9166—131nomaximal, Sylow
83C2×Q8×C13—21no—
84C2×Q8×C13—21no—
85C22×C4×C13—41no—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13#4111yescharacteristic
89C22×Dic13—21no—
90C22×Dic13—21no—
91C2×Dic26—22no—
92C2×Dic26—21no—
93C2×Dic26—41no—
94C2×Dic26C22⋊C411yescharacteristic
95C2×Dic26C22⋊C411yescharacteristic
96C2×C8×C13—21no—
97C2×C8×C13—21no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C22⋊C4—41no—
107C42×C13—41no—
108C42×C13—81no—
109C42×C13C22×C411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13C2×D411yescharacteristic
112C42×C13#4111yescharacteristic
113#6107—42no—
114#6107—42no—
115C4⋊Dic13—21no—
116C4⋊Dic13C22⋊C411yescharacteristic
117C4⋊Dic13C22⋊C411yescharacteristic
118#6101—21no—
119#6101—21no—
120#6101—21no—
121#6101—21no—
122C4×Dic13—21no—
123C4×Dic13—21no—
124C4×Dic13—21no—
125C4×Dic13—21no—
126C2×#1055—22no—
127C2×#1055—21no—
128C2×#1055—21no—
129C2×#1055—22no—
130C2×#1055—41no—
131C2×#1055—41no—
132#3113—131no—
133#2984—131no—
134#1763—131no—
135#1531—131no—
136#1503D1311yescharacteristic
137#1302—131no—
138#1285—131no—
139C23×C13#12111yescharacteristic
140Q8×C13—41no—
141Q8×C13—41no—
142Q8×C13—81no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—41no—
148C2×C4×C13—42no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—81no—
152C2×C4×C13—81no—
153C2×C4×C13C2×C22⋊C411yescharacteristic
154C2×C4×C13C4×D411yescharacteristic
155C2×C4×C13C4×D411yescharacteristic
156C2×C4×C13#12011yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12311yescharacteristic
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—42no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166Dic26—21no—
167Dic26—21no—
168Dic26—21no—
169Dic26—42no—
170Dic26#10412yes—
171C8×C13—41no—
172C8×C13—41no—
173#1055—42no—
174#1055—42no—
175#1055—41no—
176#1055—41no—
177#533C2×D1311yescharacteristic
178C2×C4×Q8—131no—
179#483—261no—
180#475—131no—
181#475—131no—
182#462—131no—
183#462—131no—
184#451—261no—
185#446—261no—
186#446—262no—
187C8×Q8—261no—
188#441—261no—
189#441—261no—
190#432—131no—
191#432—131no—
192#432—261no—
193#431—261no—
194#431C2×D1311yescharacteristic
195C2×#103—261no—
196C2×#97—131no—
197C4×C4⋊C4C2×D1311yescharacteristic
198#340—261no—
199#330—262no—
200#328—21no—
201#328—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13#38611yescharacteristic
205C22×C13#47111yescharacteristic
206C22×C13#47311yescharacteristic
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—82no—
213C4×C13—81no—
214C4×C13—81no—
215C4×C13C2×#10411yescharacteristic
216C4×C13#42111yescharacteristic
217Dic13—22no—
218Dic13—41no—
219Dic13—41no—
220Dic13—41no—
221C22×Q8—131no—
222C2×Q16—261no—
223C2×Q16—261no—
224C22×C8—261no—
225C4⋊Q8C4×D1311yescharacteristic
226C4⋊Q8C4×D1311yescharacteristic
227#125—21no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×Q8—131no—
233C4×Q8—131no—
234C4×Q8—131no—
235C4×Q8—131no—
236C4×Q8—261no—
237C4×Q8—261no—
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—131no—
241C2×C4⋊C4—261no—
242C2×C42—21no—
243C2×C42—261no—
244C2×C42C22×D1311yescharacteristic
245#106—261no—
246#106—261no—
247C4⋊C8—21no—
248C4⋊C8—131no—
249C4⋊C8—131no—
250C4⋊C8—262no—
251C4⋊C8—262no—
252C4⋊C8—261no—
253#103—261no—
254#103—261no—
255#103—264no—
256#103—261no—
257#103—261no—
258C22⋊C8—261no—
259C22⋊C8—261no—
260C22⋊C8C22⋊D1311yescharacteristic
261C22⋊C8C22⋊D1311yescharacteristic
262#97—132no—
263#97—262no—
264#97—261no—
265#97—261no—
266#97—261no—
267C4×C8—21no—
268C4×C8—262no—
269#95—21no—
270C2×C13—21no—
271C2×C13—21no—
272C2×C13#187111yescharacteristic
273C2×C13#190511yescharacteristic
274C2×C13#190811yescharacteristic
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—131no—
278C2×Q8—131no—
279C2×Q8—262no—
280C2×Q8—261no—
281C2×Q8—521no—
282C22×C4—41no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4D4×D1311yescharacteristic
286C22×C4#612911yescharacteristic
287C22×C4C2×C22⋊D1311yescharacteristic
288Q16—522no—
289Q16—522no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—262no—
293C2×C8—261no—
294C2×C8—261no—
295C2×C8—262no—
296C2×C8—521no—
297C2×C8—521no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—131no—
307C4⋊C4—131no—
308C4⋊C4—261no—
309C4⋊C4—261no—
310C4⋊C4—261no—
311C4⋊C4—261no—
312C4⋊C4—261no—
313C22⋊C4—41no—
314C42—41no—
315C42—81no—
316C42—261no—
317C42—261no—
318C42—261no—
319C42—261no—
320C42C2×C4×D1311yescharacteristic
321C42#612711yescharacteristic
322C42D4×D1311yescharacteristic
323C42D4×D1311yescharacteristic
324C13#916611yescharacteristic, complemented, Sylow
325C23#8819211yescharacteristic
326Q8—41no—
327Q8—41no—
328Q8—81no—
329Q8—132no—
330Q8—261no—
331Q8—261no—
332Q8—261no—
333Q8—522no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—522no—
349C2×C4—521no—
350C2×C4—521no—
351C2×C4C22⋊C4×D1311yescharacteristic
352C2×C4#8813511yescharacteristic
353C2×C4#8813711yescharacteristic
354C2×C4#8813811yescharacteristic
355C2×C4C4×C22⋊D1311yescharacteristic
356C2×C4#8819111yescharacteristic
357C8—41no—
358C8—41no—
359C8—522no—
360C8—522no—
361C8—521no—
362C8—521no—
363C22—21no—
364C22—21no—
365C22#1171861711yescharacteristic
366C22#1171883811yescharacteristic
367C22#1171885311yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—82no—
374C4—81no—
375C4—81no—
376C4—262no—
377C4—521no—
378C4—521no—
379C4—521no—
380C4D13×#10411yescharacteristic
381C4#1171848211yescharacteristic
382C2—21no—
383C2—21no—
384C2#1311513511yescharacteristic
385C2#1311533311yescharacteristic
386C2#1311535411yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1503C2
socleC22×C13#386
prime radicalC23×C13#121
cosocleC2×C42×C13C23
hypercenter#1503D13
hypocenterC13#9166
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
12. #11718755C4semidirect
13. #11718755C4semidirect
14. #11718751C4semidirect
15. #11718751C4semidirect
324. C13#9166semidirect

Maximal subgroups

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

subgroupindex
#131249622
#131239232
#131146692
#131134512
#131127362
#131126922
C13×#15032
#916613