Finite Group Databasebeta

← #15756161

Subgroups — #15756161

Order 3328.

430 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123548C211yesmaximal, characteristic
2#13115007C211yesmaximal, characteristic, complemented
3C2×#11718072C211yesmaximal, characteristic, complemented
4#13113513C211yesmaximal, characteristic
5#13112711C211yesmaximal, characteristic, complemented
6#13112710C211yesmaximal, characteristic, complemented
7C13×#1547C211yesmaximal, characteristic
8C13×#532C2211yescharacteristic
9C2×#88202—21no—
10C13×#423C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12#11718895—21no—
13C2×#88062—21no—
14C2×#88062—21no—
15#11718673—21no—
16#11718673C412yes—
17D4×#1055—21no—
18D4×#1055C412yes—
19#11718585C2211yescharacteristic
20#11718585C2211yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4×#1055C2211yescharacteristic
23C13×#332—21no—
24C13×#331—21no—
25#11718139—21no—
26#11718136—21no—
27#11718072—21no—
28#11718072—21no—
29C2×C13×#41—21no—
30C2×C13×M16—21no—
31C22×C8×C13—21no—
32C13×C4⋊Q8D411yescharacteristic
33C13×#127D411yescharacteristic
34C13×#124—21no—
35C13×#121—21no—
36C13×#121Q812yes—
37C4×D4×C13—21no—
38C4×D4×C13C2×C412yes—
39C2×C42×C13C2311yescharacteristic
40#88202—42no—
41#88202—42no—
42C2×#6099—21no—
43C2×#6099—22no—
44C2×#6099—21no—
45C22×#1055—22no—
46C22×#1055—21no—
47C22×#1055D411yescharacteristic
48C22×#1055D411yescharacteristic
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C22⋊#1055—22no—
54C22⋊#1055—22no—
55#88062—42no—
56#88062—42no—
57C4⋊#1055—21no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055C2×C412yes—
63C4×#1055C2×C411yescharacteristic
64C4×#1055C2×C411yescharacteristic
65C4×#1055D411yescharacteristic
66C4×#1055D411yescharacteristic
67#8682—131nomaximal, Sylow
68C13×#41—41no—
69C13×#41—41no—
70C13×#41—41no—
71C13×#41—41no—
72C2×Q8×C13—21no—
73C2×D4×C13—22no—
74C2×D4×C13—21no—
75C2×D4×C13—21no—
76C2×D4×C13C4⋊C412yes—
77C22×C4×C13—22no—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×Q811yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C13×M16—41no—
82C13×M16—41no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C2×C8×C13—81no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4C4⋊C412yes—
88C13×C22⋊C4—22no—
89C13×C22⋊C4—22no—
90C42×C13C22×C411yescharacteristic
91C42×C13C2×D411yescharacteristic
92C42×C13C2×D411yescharacteristic
93C42×C13#4111yescharacteristic
94#6099—41no—
95#6099—41no—
96#6099—44no—
97#6099—41no—
98#6099—41no—
99C2×#1055—21no—
100C2×#1055—21no—
101C2×#1055—22no—
102C2×#1055—44no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—81no—
106C2×#1055C22⋊C411yescharacteristic
107C2×#1055C22⋊C411yescharacteristic
108C2×#1055C22⋊C411yescharacteristic
109C2×#1055C22⋊C411yescharacteristic
110C2×#1055D812yes—
111C2×#1055SD1612yes—
112#2931—131no—
113#1848—131no—
114C2×#334—131no—
115#1547—131no—
116#1547D1311yescharacteristic
117#1292—131no—
118#1292—131no—
119C23×C13—22no—
120C23×C13C22⋊Q811yescharacteristic
121Q8×C13—41no—
122Q8×C13—41no—
123D4×C13—42no—
124D4×C13—42no—
125D4×C13—42no—
126D4×C13—41no—
127D4×C13—41no—
128D4×C13—41no—
129D4×C13—41no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—22no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13C2×C22⋊C411yescharacteristic
137C2×C4×C13C2×C4⋊C411yescharacteristic
138C2×C4×C13#11711yescharacteristic
139C2×C4×C13#12111yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13C22⋊Q811yescharacteristic
142C2×C4×C13C2×D811yescharacteristic
143C2×C4×C13C2×SD1611yescharacteristic
144C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C13#13711yescharacteristic
146C8×C13—81no—
147C8×C13—81no—
148#1055—21no—
149#1055—21no—
150#1055—42no—
151#1055—81no—
152#1055—81no—
153#1055#10212yes—
154#1055#10212yes—
155C2×#131—261no—
156#532C2×D1311yescharacteristic
157#436—132no—
158#436—261no—
159C8×D4—132no—
160C8×D4—261no—
161C2×#108—261no—
162C2×#108—261no—
163#423—131no—
164#423—131no—
165#423C2×D1311yescharacteristic
166C2×C4⋊C8—131no—
167C2×C4⋊C8C2×D1311yescharacteristic
168#408—261no—
169C2×C4×C8—131no—
170#334—261no—
171#334—261no—
172#332—21no—
173#332—261no—
174#331—21no—
175#331—261no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—42no—
179C22×C13—42no—
180C22×C13—42no—
181C22×C13#38011yescharacteristic
182C22×C13#47411yescharacteristic
183C22×C13#47611yescharacteristic
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—42no—
188C4×C13C2×#10211yescharacteristic
189C4×C13#41711yescharacteristic
190C4×C13#45911yescharacteristic
191C4×C13#46111yescharacteristic
192C4×C13#47111yescharacteristic
193C4×C13#47111yescharacteristic
194C2×#41—21no—
195#131—522no—
196#131—522no—
197C2×M16—21no—
198C2×M16—262no—
199C2×M16—261no—
200C2×M16—261no—
201C22×C8—21no—
202C22×C8—131no—
203C22×C8—131no—
204C22×C8—262no—
205C22×C8—261no—
206C4⋊Q8C22⋊D1311yescharacteristic
207#127C22⋊D1311yescharacteristic
208#124—21no—
209#121—21no—
210#121Dic2612yes—
211C4×D4—21no—
212C4×D4C4×D1312yes—
213C2×C42C22×D1311yescharacteristic
214#108—522no—
215#108—522no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—132no—
221C4⋊C8—261no—
222C4⋊C8—261no—
223C4⋊C8—261no—
224C4⋊C8—261no—
225C4⋊C8—261no—
226C22⋊C8—262no—
227C22⋊C8—262no—
228C4×C8—131no—
229C4×C8—131no—
230C4×C8—131no—
231C4×C8—131no—
232C2×C13—21no—
233C2×C13—21no—
234C2×C13—82no—
235C2×C13#180211yescharacteristic
236C2×C13#181311yescharacteristic
237C2×C13#181511yescharacteristic
238#41—41no—
239#41—41no—
240#41—41no—
241#41—41no—
242C2×Q8—21no—
243C2×D4—22no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4#610112yes—
247C22×C4—22no—
248C22×C4C2×Dic2611yescharacteristic
249C22×C4D4×D1311yescharacteristic
250C22×C4#612911yescharacteristic
251M16—41no—
252M16—41no—
253M16—524no—
254M16—521no—
255M16—521no—
256M16—521no—
257M16—521no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—81no—
261C2×C8—131no—
262C2×C8—131no—
263C2×C8—132no—
264C2×C8—132no—
265C2×C8—131no—
266C2×C8—131no—
267C2×C8—261no—
268C2×C8—261no—
269C2×C8—262no—
270C2×C8—524no—
271C2×C8—521no—
272C2×C8—521no—
273C2×C8—1041no—
274C4⋊C4—21no—
275C4⋊C4#610112yes—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C42C2×C4×D1311yescharacteristic
279C42D4×D1311yescharacteristic
280C42#612911yescharacteristic
281C42C2×C22⋊D1311yescharacteristic
282C13#868211yescharacteristic, complemented, Sylow
283C23—22no—
284C23#8813211yescharacteristic
285Q8—41no—
286Q8—41no—
287D4—42no—
288D4—42no—
289D4—42no—
290D4—41no—
291D4—41no—
292D4—41no—
293D4—41no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4#8813111yescharacteristic
301C2×C4#8813211yescharacteristic
302C2×C4C22⋊C4×D1311yescharacteristic
303C2×C4D8×D1311yescharacteristic
304C2×C4#8816511yescharacteristic
305C2×C4SD16×D1311yescharacteristic
306C2×C4#8816911yescharacteristic
307C2×C4C2×#610111yescharacteristic
308C2×C4#8819311yescharacteristic
309C2×C4#8819311yescharacteristic
310C8—81no—
311C8—81no—
312C8—132no—
313C8—132no—
314C8—261no—
315C8—261no—
316C8—522no—
317C8—1041no—
318C8—1041no—
319C22—21no—
320C22—21no—
321C22—42no—
322C22—42no—
323C22—42no—
324C22#1171842011yescharacteristic
325C22#1171842211yescharacteristic
326C22#1171860311yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—42no—
331C4D13×#10211yescharacteristic
332C4#1171843211yescharacteristic
333C4#1171881111yescharacteristic
334C4#1171882311yescharacteristic
335C4#1171886111yescharacteristic
336C4#1171886411yescharacteristic
337C2—21no—
338C2—21no—
339C2—82no—
340C2#1311483411yescharacteristic
341C2#1311488411yescharacteristic
342C2#1311489311yescharacteristic
subgroupG/H
centerC22#11718603
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1547C2
socleC22×C13#380
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#1547D13
hypocenterC13#8682
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
2. #13115007C2semidirect
3. C2×#11718072C2semidirect
5. #13112711C2semidirect
6. #13112710C2semidirect
282. C13#8682semidirect

Maximal subgroups

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

subgroupindex
#131235482
#131150072
C2×#117180722
#131135132
#131127112
#131127102
C13×#15472
#868213