Finite Group Databasebeta

← #15779976

Subgroups — #15779976

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88066C211yesmaximal, characteristic
2C2×#11718154C211yesmaximal, characteristic, complemented
3C2×#11718083C211yesmaximal, characteristic, complemented
4#13115702C211yesmaximal, characteristic, complemented
5#13112927C211yesmaximal, characteristic, complemented
6#13112914C211yesmaximal, characteristic, complemented
7C2×C4×C13×D8C211yesmaximal, characteristic, complemented
8C22×C13×D8C2211yescharacteristic
9C2×C4×D4×C13—21no—
10C22×D104C2211yescharacteristic
11C4×C13×D8—22no—
12C4×C13×D8—22no—
13C2×C13×#107C2211yescharacteristic
14C2×C13×#102—21no—
15C2×C4×C8×C13C2211yescharacteristic
16C2×#88066—22no—
17C2×#88066—22no—
18C2×#88066C414yescomplemented
19C2×#88061—21no—
20C2×#88058C2211yescharacteristic
21C22×#6090C2211yescharacteristic
22C22×#6090C2211yescharacteristic
23#11718600—21no—
24#11718154—22no—
25#11718083—22no—
26C22×D4×C13—21no—
27C23×C4×C13—41no—
28C22×D52—21no—
29C2×C13×D8—21no—
30C2×C13×D8—21no—
31C2×C13×D8—21no—
32C2×C13×D8C2×C412yes—
33C2×C13×D8D412yes—
34C2×C13×D8D412yes—
35C22×C8×C13D411yescharacteristic
36C22×C8×C13C2311yescharacteristic
37C4×D4×C13—24no—
38C4×D4×C13—42no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C22⋊C4—41no—
41C2×C42×C13D411yescharacteristic
42C2×#6103—41no—
43C2×#6103—41no—
44C2×C4⋊Dic13—21no—
45C2×D104—21no—
46C2×D104—21no—
47C2×D104—21no—
48C2×D104—21no—
49C2×D104—21no—
50C2×D104C2×C412yescomplemented
51C13×#107—21no—
52C13×#107D412yes—
53C13×#102—24no—
54C4×C8×C13—21no—
55C4×C8×C13—21no—
56#88066—28no—
57#88061—42no—
58#88058—21no—
59#88058—21no—
60C2×#6090—21no—
61C2×#6090—21no—
62C2×#6090—21no—
63C2×#6090—21no—
64C2×#6090—21no—
65C2×#6090C2×C412yescomplemented
66#13012—131nomaximal, Sylow
67C24×C13—41no—
68C23×D13—41no—
69C2×D4×C13—22no—
70C2×D4×C13—22no—
71C2×D4×C13—22no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C22×C4×C13—44no—
76C22×C4×C13—41no—
77C22×C4×C13—82no—
78C22×C4×C13—82no—
79C22×C4×C13D811yescharacteristic
80C22×C4×C13D811yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×Dic13—41no—
83C2×D52—22no—
84C2×D52—41no—
85C2×D52—41no—
86C2×D52—41no—
87C2×D52—41no—
88C2×D52—41no—
89C13×D8—22no—
90C13×D8—22no—
91C13×D8—22no—
92C13×D8C22⋊C414yescomplemented
93C2×C8×C13—21no—
94C2×C8×C13—21no—
95C2×C8×C13—21no—
96C2×C8×C13C22×C411yescharacteristic
97C2×C8×C13C2×D411yescharacteristic
98C2×C8×C13C2×D411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13#4111yescharacteristic
101C2×C8×C13#4111yescharacteristic
102C13×C4⋊C4—22no—
103C13×C4⋊C4—41no—
104C13×C22⋊C4—44no—
105C42×C13—21no—
106C42×C13—21no—
107#6103—82no—
108#6103—82no—
109C4⋊Dic13—41no—
110C4⋊Dic13—41no—
111D104—22no—
112D104—22no—
113D104—41no—
114D104—41no—
115#6090—22no—
116#6090—41no—
117C22×D16—131no—
118C2×C4×D8D1311yescharacteristic, complemented
119C2×#357—131no—
120C2×#357—131no—
121#1970—131no—
122#1380—131no—
123#1374—131no—
124C23×C13—42no—
125C23×C13—42no—
126C23×C13—42no—
127C23×C13—81no—
128C23×C13—81no—
129C23×C13—81no—
130C23×C13—81no—
131C23×C13C2×D811yescharacteristic
132C22×D13—42no—
133C22×D13—81no—
134C22×D13—81no—
135C22×D13—81no—
136C22×D13—81no—
137C22×D13—81no—
138C22×D13—81no—
139D4×C13—24no—
140D4×C13—42no—
141D4×C13—42no—
142D4×C13—42no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—42no—
149C2×C4×C13—88no—
150C2×C4×C13—81no—
151C2×C4×C13—81no—
152C2×C4×C13D1612yescomplemented
153C2×C4×C13C4×D411yescharacteristic
154C2×C4×C13#12011yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13#13511yescharacteristic
157C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
159C2×Dic13—81no—
160C2×Dic13—81no—
161C2×Dic13—81no—
162D52—42no—
163D52—42no—
164D52—81no—
165D52—81no—
166C8×C13—41no—
167C8×C13C2×C22⋊C411yescharacteristic
168C8×C13C4×D411yescharacteristic
169C8×C13#12111yescharacteristic
170C8×C13#12311yescharacteristic
171C22×D8—131no—
172C22×D8C2×D1311yescharacteristic
173C2×C4×D4—21no—
174C2×D16—134no—
175C2×D16—262no—
176C2×D16—262no—
177C22×C16—131no—
178C22×C16—131no—
179C4×D8—22no—
180C4×D8—22no—
181C2×#107—131no—
182C2×#107C2×D1311yescharacteristic
183C2×#102—21no—
184C2×#102—261no—
185C2×C4×C8C2×D1311yescharacteristic
186#390—261no—
187#357—262no—
188#357—262no—
189C22×C13—44no—
190C22×C13—82no—
191C22×C13—82no—
192C22×C13—82no—
193C22×C13—82no—
194C22×C13—82no—
195C22×C13—82no—
196C22×C13C4×D811yescharacteristic
197C22×C13#44711yescharacteristic
198C22×C13#45911yescharacteristic
199C22×C13C2×D1611yescharacteristic
200C22×C13#50811yescharacteristic
201C22×C13#50911yescharacteristic
202C22×C13#50911yescharacteristic
203C2×D13—82no—
204C2×D13—82no—
205C2×D13—82no—
206C2×D13—161no—
207C2×D13—161no—
208C2×D13—161no—
209C2×D13—161no—
210C4×C13—22no—
211C4×C13—41no—
212C4×C13—82no—
213C4×C13#38611yescharacteristic
214C4×C13#44211yescharacteristic
215C4×C13#44911yescharacteristic
216C4×C13#46311yescharacteristic
217Dic13—161no—
218C22×D4—21no—
219C22×D4—261no—
220C23×C4—41no—
221C2×D8—21no—
222C2×D8—21no—
223C2×D8—21no—
224C2×D8—132no—
225C2×D8—261no—
226C2×D8—261no—
227C2×D8—261no—
228C2×D8—261no—
229C2×D8—261no—
230C2×D8C4×D1312yes—
231C2×D8D5212yes—
232C2×D8C22⋊D1312yes—
233C22×C8C22⋊D1311yescharacteristic
234C22×C8C22×D1311yescharacteristic
235C4×D4—24no—
236C4×D4—42no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—261no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4—521no—
241C2×C22⋊C4—521no—
242C2×C42C22⋊D1311yescharacteristic
243D16—268no—
244C2×C16—132no—
245C2×C16—261no—
246C2×C16—261no—
247C2×C16—261no—
248C2×C16—261no—
249C2×C16—261no—
250#107—21no—
251#107—261no—
252#107—261no—
253#107C22⋊D1312yes—
254#102—24no—
255#102—522no—
256C4×C8—21no—
257C4×C8—21no—
258C2×C13—84no—
259C2×C13#187911yescharacteristic
260C2×C13C4×D1611yescharacteristic
261C2×C13#217711yescharacteristic
262C2×C13#218411yescharacteristic
263C2×C13#218611yescharacteristic
264C2×C13#220611yescharacteristic
265C2×C13#221011yescharacteristic
266D13—162no—
267C24—41no—
268C24—521no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—262no—
276C2×D4—521no—
277C2×D4—521no—
278C2×D4—521no—
279C2×D4—521no—
280C2×D4—521no—
281C22×C4—44no—
282C22×C4—41no—
283C22×C4—82no—
284C22×C4—82no—
285C22×C4—521no—
286C22×C4#610411yescharacteristic
287C22×C4#610411yescharacteristic
288C22×C4C2×C22⋊D1311yescharacteristic
289D8—22no—
290D8—22no—
291D8—22no—
292D8—262no—
293D8—262no—
294D8—521no—
295D8—521no—
296D8#610314yescomplemented
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8C2×C4×D1311yescharacteristic
301C2×C8C2×D5211yescharacteristic
302C2×C8#612711yescharacteristic
303C2×C8#612711yescharacteristic
304C2×C8C2×C22⋊D1311yescharacteristic
305C2×C8C2×C22⋊D1311yescharacteristic
306C4⋊C4—22no—
307C4⋊C4—41no—
308C4⋊C4—521no—
309C4⋊C4—521no—
310C22⋊C4—44no—
311C22⋊C4—1042no—
312C22⋊C4—1042no—
313C42—21no—
314C42—21no—
315C16—262no—
316C16—521no—
317C13#1301211yescharacteristic, complemented, Sylow
318C23—42no—
319C23—42no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—522no—
326C23—1041no—
327C23—1041no—
328C23—1041no—
329C23—1041no—
330C23—1041no—
331C23—1041no—
332C23C2×#610411yescharacteristic
333D4—24no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—522no—
338D4—522no—
339D4—1041no—
340D4—1041no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—88no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—1041no—
351C2×C4—1041no—
352C2×C4—1041no—
353C2×C4#8806612yescomplemented
354C2×C4C4×C22⋊D1311yescharacteristic
355C2×C4#8818411yescharacteristic
356C2×C4#8818611yescharacteristic
357C2×C4#8820311yescharacteristic
358C2×C4#8820411yescharacteristic
359C2×C4#8820711yescharacteristic
360C8—41no—
361C8C2×#610311yescharacteristic
362C8C4×C22⋊D1311yescharacteristic
363C8#8818311yescharacteristic
364C8#8818411yescharacteristic
365C22—44no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—1042no—
373C22—1042no—
374C22—1042no—
375C22—2081no—
376C22—2081no—
377C22—2081no—
378C22—2081no—
379C22C4×#610411yescharacteristic
380C22#1171867611yescharacteristic
381C22C2×#8806611yescharacteristic
382C22#1171880811yescharacteristic
383C22#1171885411yescharacteristic
384C22#1171885511yescharacteristic
385C22#1171887811yescharacteristic
386C4—22no—
387C4—41no—
388C4—82no—
389C4—2081no—
390C4#1171867511yescharacteristic
391C4#1171867711yescharacteristic
392C4#1171887411yescharacteristic
393C4#1171889911yescharacteristic
394C2—84no—
395C2—2082no—
396C2#1311518411yescharacteristic
397C2C4×#8806611yescharacteristic
398C2#1311671011yescharacteristic
399C2#1311674811yescharacteristic
400C2#1311675911yescharacteristic
401C2#1311687111yescharacteristic
402C2#1311689111yescharacteristic
subgroupG/H
centerC23C2×#6104
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C4×C13×D8C2
socleC23×C13C2×D8
prime radicalC22×#88066C2
cosocleC22×C8×C13C23
hypercenterC2×C4×D8D13
hypocenterC13#13012
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
2. C2×#11718154C2semidirect
3. C2×#11718083C2semidirect
4. #13115702C2semidirect
5. #13112927C2semidirect
6. #13112914C2semidirect
7. C2×C4×C13×D8C2semidirect
18. C2×#88066C4semidirect
50. C2×D104C2×C4semidirect
65. C2×#6090C2×C4semidirect
92. C13×D8C22⋊C4semidirect
118. C2×C4×D8D13semidirect
152. C2×C4×C13D16semidirect
296. D8#6103semidirect
317. C13#13012semidirect
353. C2×C4#88066semidirect

Maximal subgroups

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

subgroupindex
C22×#880662
C2×#117181542
C2×#117180832
#131157022
#131129272
#131129142
C2×C4×C13×D82
#1301213