Finite Group Databasebeta

← #15773204

Subgroups — #15773204

Order 3328.

592 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#11718118C211yesmaximal, characteristic
2C2×#11718117C211yesmaximal, characteristic
3#13112860C212yesmaximal, complemented
4#13112857C212yesmaximal, complemented
5C13×#2626C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic, complemented
7C22×C13×C22⋊C4C2211yescharacteristic
8C22×C22⋊Dic13—21no—
9C13×#399C411yescharacteristic, complemented
10C13×#399C2211yescharacteristic
11C13×#396—21no—
12C13×#396—21no—
13C13×#393C411yescharacteristic, complemented
14C13×#393C2211yescharacteristic
15C13×#385—21no—
16C13×#380C411yescharacteristic, complemented
17C13×#379—21no—
18C2×C22⋊#1055—21no—
19#11718118—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C25×C13D411yescharacteristic
24C22×Q8×C13C2×C411yescharacteristic, complemented
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×Dic13—41no—
28C13×C22⋊Q8—41no—
29C13×C22⋊Q8—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—41no—
42C2×C13×C22⋊C4—41no—
43C2×C13×C22⋊C4C2×C411yescharacteristic
44C2×C13×C22⋊C4D411yescharacteristic
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C13×C22⋊C4C2311yescharacteristic
47C2×C22⋊Dic13—24no—
48C2×C22⋊Dic13—22no—
49C2×C22⋊Dic13—41no—
50C2×C22⋊Dic13—42no—
51C22×#1055—41no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95C2×C411yescharacteristic, complemented
55C13×#95C2×C411yescharacteristic, complemented
56C22⋊#1055—22no—
57C22⋊#1055—41no—
58#11716—131nomaximal, Sylow
59C24×C13—21no—
60C24×C13—21no—
61C24×C13—22no—
62C24×C13—81no—
63C24×C13—81no—
64C24×C13C22⋊C411yescharacteristic
65C24×C13C22⋊C411yescharacteristic
66C24×C13SD1612yes—
67C24×C13Q1612yes—
68C24×C13C2×D411yescharacteristic
69C2×Q8×C13—41no—
70C2×Q8×C13—81no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—81no—
80C22×C4×C13—81no—
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×Dic13—44no—
86C22×Dic13—42no—
87C22×Dic13—82no—
88C22×Dic13—82no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—81no—
92C13×C4⋊C4—81no—
93C13×C4⋊C4—81no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—81no—
102C13×C22⋊C4—81no—
103C13×C22⋊C4—81no—
104C13×C22⋊C4—81no—
105C22⋊Dic13—24no—
106C22⋊Dic13—44no—
107C22⋊Dic13—42no—
108C2×#1055—42no—
109C2×#1055—82no—
110#2626D1311yescharacteristic
111C2×#342—131no—
112C2×#323—131no—
113#1352—132no—
114#1351—132no—
115C23×C13—22no—
116C23×C13—22no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—22no—
120C23×C13—22no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—42no—
126C23×C13—42no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—81no—
132C23×C13—81no—
133C23×C13—82no—
134C23×C13—82no—
135C23×C13—84no—
136C23×C13#9911yescharacteristic
137C23×C13#9911yescharacteristic
138C23×C13#10312yes—
139C23×C13#10312yes—
140C23×C13#10412yes—
141C23×C13C2×C22⋊C411yescharacteristic
142C23×C13C2×SD1611yescharacteristic
143C23×C13C2×Q1611yescharacteristic
144Q8×C13—82no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—42no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C2×C4×C13—81no—
169C2×Dic13—44no—
170C2×Dic13—88no—
171C2×Dic13—82no—
172C2×Dic13—82no—
173#1055—82no—
174C2×C22⋊Q8Dic1311yescharacteristic, complemented
175C22×C22⋊C4—261no—
176C22×C22⋊C4C2×D1311yescharacteristic
177C2×C22⋊C8—261no—
178#399Dic1311yescharacteristic, complemented
179#399C2×D1311yescharacteristic
180#396—21no—
181#396—21no—
182#393Dic1311yescharacteristic, complemented
183#393C2×D1311yescharacteristic
184#385—21no—
185#380Dic1311yescharacteristic, complemented
186#379—21no—
187#342—132no—
188#342—261no—
189#323—132no—
190#323—261no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—22no—
199C22×C13—21no—
200C22×C13—42no—
201C22×C13—42no—
202C22×C13—42no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—44no—
206C22×C13—44no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13—82no—
214C22×C13—82no—
215C22×C13#32812yes—
216C22×C13#32812yes—
217C22×C13C2×#9911yescharacteristic
218C22×C13C2×#10311yescharacteristic
219C22×C13C2×#10411yescharacteristic
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—41no—
224C4×C13—81no—
225C4×C13—81no—
226C4×C13—81no—
227C4×C13—81no—
228Dic13—84no—
229C25C22⋊D1311yescharacteristic
230C22×Q8C2×Dic1311yescharacteristic, complemented
231C23×C4—521no—
232C23×C4C2×Dic1311yescharacteristic
233C23×C4C22⋊D1311yescharacteristic
234C22×C8—521no—
235C22⋊Q8—41no—
236C22⋊Q8—41no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C2×Dic1311yescharacteristic, complemented
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—41no—
249C2×C22⋊C4—41no—
250C2×C22⋊C4—264no—
251C2×C22⋊C4—262no—
252C2×C22⋊C4—521no—
253C2×C22⋊C4—522no—
254C2×C22⋊C4C2×Dic1311yescharacteristic
255C2×C22⋊C4C22⋊D1311yescharacteristic
256C2×C22⋊C4C22⋊D1311yescharacteristic
257C2×C22⋊C4C22×D1311yescharacteristic
258C22⋊C8—262no—
259C22⋊C8—521no—
260#95—21no—
261#95—21no—
262#95C2×Dic1311yescharacteristic, complemented
263#95C2×Dic1311yescharacteristic, complemented
264C2×C13—21no—
265C2×C13—22no—
266C2×C13—21no—
267C2×C13—22no—
268C2×C13—41no—
269C2×C13—42no—
270C2×C13—41no—
271C2×C13C2×#32811yescharacteristic
272C2×C13#212111yescharacteristic
273C2×C13#212711yescharacteristic
274C24—21no—
275C24—21no—
276C24—22no—
277C24—81no—
278C24—81no—
279C24#610612yes—
280C24#610712yes—
281C24C22⋊Dic1311yescharacteristic
282C24C22⋊Dic1311yescharacteristic
283C24C2×C22⋊D1311yescharacteristic
284C2×Q8—41no—
285C2×Q8—81no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—81no—
295C22×C4—81no—
296C22×C4—522no—
297C22×C4—524no—
298C22×C4—1042no—
299C22×C4—1042no—
300C22×C4C22⋊Dic1311yescharacteristic
301C22×C4C22⋊Dic1311yescharacteristic
302C22×C4C22×Dic1311yescharacteristic
303C22×C4C2×C22⋊D1311yescharacteristic
304C2×C8—522no—
305C2×C8—1042no—
306C4⋊C4—41no—
307C4⋊C4—42no—
308C4⋊C4—81no—
309C4⋊C4—81no—
310C4⋊C4—81no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—42no—
318C22⋊C4—81no—
319C22⋊C4—81no—
320C22⋊C4—81no—
321C22⋊C4—81no—
322C22⋊C4—264no—
323C22⋊C4—524no—
324C22⋊C4—522no—
325C13#1171611yescharacteristic, complemented, Sylow
326C23—21no—
327C23—21no—
328C23—22no—
329C23—22no—
330C23—21no—
331C23—21no—
332C23—22no—
333C23—22no—
334C23—41no—
335C23—41no—
336C23—42no—
337C23—42no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—81no—
343C23—81no—
344C23—82no—
345C23—82no—
346C23—84no—
347C23#8807411yescharacteristic
348C23#8807411yescharacteristic
349C23#8807512yes—
350C23#8807512yes—
351C23#8807712yes—
352C23C2×#610611yescharacteristic
353C23C2×#610711yescharacteristic
354C23C2×C22⋊Dic1311yescharacteristic
355Q8—82no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—524no—
381C2×C4—1048no—
382C2×C4—1042no—
383C2×C4—1042no—
384C8—1042no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—22no—
393C22—21no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22—41no—
398C22—41no—
399C22—44no—
400C22—44no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—81no—
406C22—81no—
407C22—82no—
408C22—82no—
409C22#1171813012yes—
410C22#1171813012yes—
411C22C2×#8807411yescharacteristic
412C22C2×#8807511yescharacteristic
413C22C2×#8807711yescharacteristic
414C4—41no—
415C4—41no—
416C4—41no—
417C4—41no—
418C4—81no—
419C4—81no—
420C4—81no—
421C4—81no—
422C4—1044no—
423C2—21no—
424C2—21no—
425C2—22no—
426C2—22no—
427C2—41no—
428C2—42no—
429C2—41no—
430C2C2×#1171813011yescharacteristic
431C2#1311648211yescharacteristic
432C2#1311650511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2626C2
socleC22×C13C2×#99
prime radicalC25×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2626D13
hypocenterC13#11716
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2626

Complements

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

NH ≅ G/Ntype
3. #13112860C2semidirect
4. #13112857C2semidirect
6. C2×C13×C22⋊Q8C4semidirect
9. C13×#399C4semidirect
13. C13×#393C4semidirect
16. C13×#380C4semidirect
24. C22×Q8×C13C2×C4semidirect
34. C2×C13×C4⋊C4C2×C4semidirect
54. C13×#95C2×C4semidirect
55. C13×#95C2×C4semidirect
174. C2×C22⋊Q8Dic13semidirect
178. #399Dic13semidirect
182. #393Dic13semidirect
185. #380Dic13semidirect
230. C22×Q8C2×Dic13semidirect
241. C2×C4⋊C4C2×Dic13semidirect
262. #95C2×Dic13semidirect
263. #95C2×Dic13semidirect
325. C13#11716semidirect

Maximal subgroups

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

subgroupindex
C2×#117181182
C2×#117181172
#131128602
#131128572
C13×#26262
#1171613