Finite Group Databasebeta

← #16780653

Subgroups — #16780653

Order 3328.

628 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 124 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#13130563C211yesmaximal, characteristic
2C2×#11718241C212yesmaximal
3#13130012C211yesmaximal, characteristic
4#13129709C212yesmaximal
5#13117366C211yesmaximal, characteristic
6C2×#88151C2211yescharacteristic
7C2×#88141C411yescharacteristic, complemented
8C2×C42×D13C2211yescharacteristic
9C2×(C2×#261)⋊C4—21no—
10C2×(C2×#261)⋊C4—21no—
11C2×(C2×#261)⋊C4C2212yes—
12C2×#88111C2212yes—
13C2×#88110—21no—
14C13×#389C411yescharacteristic, complemented
15#11718650—21no—
16#11718648C2211yescharacteristic
17C4⋊C4×Dic13—21no—
18C4⋊C4×Dic13C411yescharacteristic, complemented
19#11718590C411yescharacteristic, complemented
20#11718327—21no—
21#11718315—21no—
22#11718290—21no—
23#11718241C418yescomplemented
24C23×#261—22no—
25C22×C4×D13D411yescharacteristic
26C22×C4×D13D411yescharacteristic
27C22×C4×D13C2311yescharacteristic
28C22×Dic26C2×C411yescharacteristic
29C22×#1057—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C42×C13C2×C411yescharacteristic
34C2×#6103—21no—
35C2×#6103—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×#6101—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44#88151—22no—
45#88151C2×C414yes—
46#88141—42no—
47C42×D13—42no—
48(C2×#261)⋊C4—22no—
49(C2×#261)⋊C4—42no—
50(C2×#261)⋊C4—42no—
51(C2×#261)⋊C4C2×C414yes—
52#88111—22no—
53#88111C2×C414yes—
54#88110—42no—
55C13×#95—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#8217—131nomaximal, Sylow
61C23×D13C2×D411yescharacteristic
62C22×#261—24no—
63C22×#261—42no—
64C22×#261—42no—
65C22×#261—42no—
66C22×#261—42no—
67C22×#261—42no—
68C22×#261—42no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13C22⋊C411yescharacteristic
77C22×Dic13C22⋊C411yescharacteristic
78C22×Dic13C2×D411yescharacteristic
79C2×C4×D13—21no—
80C2×C4×D13—22no—
81C2×C4×D13—21no—
82C2×C4×D13—22no—
83C2×C4×D13—41no—
84C2×C4×D13—41no—
85C2×C4×D13—41no—
86C2×C4×D13—41no—
87C2×C4×D13—41no—
88C2×C4×D13C22×C412yes—
89C2×C4×D13#4112yes—
90C2×Dic26—21no—
91C2×Dic26—41no—
92C2×Dic26—41no—
93C2×Dic26C4212yes—
94C2×#1057—24no—
95C2×#1057—42no—
96C2×#1057—42no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—42no—
100C13×C4⋊C4C4212yes—
101C42×C13—41no—
102#6103—24no—
103#6103—41no—
104#6103—41no—
105C4⋊Dic13—24no—
106C4⋊Dic13—41no—
107#6101—42no—
108C4×Dic13—22no—
109C4×Dic13—22no—
110C4×Dic13—41no—
111C4×Dic13—42no—
112C4×Dic13—42no—
113C4×C22⋊Q8—131no—
114#1749—131no—
115C2×#328—132no—
116#1434—131no—
117#1294—132no—
118C23×C13C2×C22⋊C411yescharacteristic
119C22×D13—21no—
120C22×D13—21no—
121C22×D13—21no—
122C22×D13—21no—
123C22×D13C4×D412yes—
124C22×D13AGL(1,ℤ/8)11yescharacteristic
125C22×D13#13712yes—
126C22×D13#13711yescharacteristic
127C2×#261—44no—
128C2×#261—44no—
129C2×#261—44no—
130C2×#261—82no—
131C2×#261—82no—
132C2×#261—82no—
133C2×#261—82no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—22no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13C2×C4211yescharacteristic
149C2×C4×C13#11711yescharacteristic
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—22no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13#9912yes—
164C2×Dic13C4×D412yes—
165C4×D13—42no—
166C4×D13—42no—
167C4×D13—44no—
168C4×D13—42no—
169C4×D13—42no—
170Dic26—42no—
171Dic26—42no—
172#1057—44no—
173C2×C22⋊Q8—131no—
174C2×C4×Q8—131no—
175C22×C42—131no—
176C2×C22⋊C8—132no—
177C2×#97—261no—
178#391—131no—
179#389#26111yescharacteristic, complemented
180#387—261no—
181#385—261no—
182#380—131no—
183C4×C4⋊C4—131no—
184C4×C4⋊C4—261no—
185C4×C22⋊C4—261no—
186C2×#95—132no—
187C2×#95—261no—
188C2×#95—261no—
189#336—261no—
190#328—138no—
191C22×C13C4×C22⋊C411yescharacteristic
192C22×C13C2×#9911yescharacteristic
193C22×C13#41011yescharacteristic
194C22×C13#41711yescharacteristic
195C22×C13#41911yescharacteristic
196C22×C13#42111yescharacteristic
197C22×C13#42111yescharacteristic
198C2×D13—22no—
199C2×D13—22no—
200C2×D13—22no—
201C2×D13—21no—
202C2×D13—21no—
203C2×D13—21no—
204C2×D13—21no—
205C2×D13—22no—
206C2×D13#44012yes—
207C2×D13#44112yes—
208#261—84no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—42no—
212C4×C13—41no—
213C4×C13—41no—
214C4×C13—81no—
215Dic13—22no—
216Dic13—22no—
217Dic13—42no—
218Dic13—41no—
219Dic13—81no—
220C22×Q8—131no—
221C23×C4—131no—
222C23×C4—131no—
223C23×C4—131no—
224C23×C4—262no—
225C22×C8—262no—
226C22⋊Q8—134no—
227C22⋊Q8—262no—
228C4×Q8—522no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—131no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4—261no—
233C2×C4⋊C4C2×#26111yescharacteristic
234C2×C4⋊C4C2×#26111yescharacteristic
235C2×C22⋊C4—261no—
236C2×C22⋊C4—261no—
237C2×C42—131no—
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—261no—
241C2×C42—261no—
242C2×C42—522no—
243C2×C42C2×#26111yescharacteristic
244C22⋊C8—134no—
245C22⋊C8—262no—
246#97—522no—
247#95—21no—
248#95—134no—
249#95—261no—
250#95—261no—
251#95—262no—
252#95—261no—
253#95—261no—
254#95—522no—
255#95—522no—
256C2×C13#151111yescharacteristic
257C2×C13#151211yescharacteristic
258C2×C13#151311yescharacteristic
259C2×C13#151511yescharacteristic
260C2×C13C4×#9911yescharacteristic
261C2×C13#175911yescharacteristic
262C2×C13#176311yescharacteristic
263D13—22no—
264D13—22no—
265C24—131no—
266C2×Q8—132no—
267C2×Q8—261no—
268C2×Q8—521no—
269C2×Q8—521no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—132no—
275C22×C4—132no—
276C22×C4—131no—
277C22×C4—262no—
278C22×C4—261no—
279C22×C4—262no—
280C22×C4—261no—
281C22×C4—261no—
282C22×C4—264no—
283C22×C4—261no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4—521no—
287C22×C4—521no—
288C22×C4—521no—
289C22×C4—522no—
290C22×C4—522no—
291C22×C4—522no—
292C22×C4—522no—
293C22×C4—522no—
294C22×C4—522no—
295C22×C4C22⋊#26111yescharacteristic
296C22×C4C22⋊#26111yescharacteristic
297C22×C4C22×#26111yescharacteristic
298C2×C8—264no—
299C2×C8—522no—
300C2×C8—522no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—264no—
305C4⋊C4—521no—
306C4⋊C4—522no—
307C4⋊C4C4×#26112yes—
308C22⋊C4—264no—
309C22⋊C4—521no—
310C22⋊C4—521no—
311C42—41no—
312C42—262no—
313C42—262no—
314C42—521no—
315C42—522no—
316C42—522no—
317C13#821711yescharacteristic, complemented, Sylow
318C23—132no—
319C23—132no—
320C23—131no—
321C23—131no—
322C23—261no—
323C23—261no—
324C23—261no—
325C23—261no—
326C23C2×C22⋊#26111yescharacteristic
327Q8—522no—
328Q8—522no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—132no—
344C2×C4—132no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—262no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—522no—
354C2×C4—522no—
355C2×C4—524no—
356C2×C4—522no—
357C2×C4—522no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—524no—
361C2×C4—524no—
362C2×C4—524no—
363C2×C4—521no—
364C2×C4—521no—
365C2×C4—521no—
366C2×C4—1042no—
367C2×C4—1042no—
368C2×C4—1042no—
369C2×C4—1042no—
370C2×C4C2×C4×#26111yescharacteristic
371C2×C4#8823711yescharacteristic
372C8—524no—
373C22—132no—
374C22—132no—
375C22—262no—
376C22—261no—
377C22—261no—
378C22—261no—
379C22—261no—
380C22—262no—
381C22—262no—
382C22—262no—
383C22C4×C22⋊#26111yescharacteristic
384C22#1171914011yescharacteristic
385C22D13⋊#9911yescharacteristic
386C22#1171915311yescharacteristic
387C22#1171915611yescharacteristic
388C22#1171916411yescharacteristic
389C22#1171916611yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—42no—
395C4—81no—
396C4—262no—
397C4—262no—
398C4—521no—
399C4—522no—
400C4—1044no—
401C4—1041no—
402C2—262no—
403C2—262no—
404C2#1313024511yescharacteristic
405C2#1313025011yescharacteristic
406C2#1313025211yescharacteristic
407C2#1313025911yescharacteristic
408C2#1313058111yescharacteristic
409C2#1313059911yescharacteristic
410C2#1313060811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#389C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC22×C4×D13C23
hypercenter#389#261
hypocenterC13#8217
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
7. C2×#88141C4semidirect
14. C13×#389C4semidirect
18. C4⋊C4×Dic13C4semidirect
19. #11718590C4semidirect
23. #11718241C4semidirect
179. #389#261semidirect
317. C13#8217semidirect

Maximal subgroups

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

subgroupindex
#131305632
C2×#117182412
#131300122
#131297092
#131173662
#821713