Finite Group Databasebeta

← #15758334

Subgroups — #15758334

Order 3328.

480 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123916C211yesmaximal, characteristic
2C2×#11718691C211yesmaximal, characteristic
3#13113232C211yesmaximal, characteristic
4#13113160C211yesmaximal, characteristic
5#13112680C211yesmaximal, characteristic
6#13112666C211yesmaximal, characteristic
7C13×#1479C211yesmaximal, characteristic
8C2×C4×Q8×C13C2211yescharacteristic
9C22×#6107C411yescharacteristic
10C2×C4×Dic26C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#431C2211yescharacteristic
13C2×#88075C411yescharacteristic
14#11718691—22no—
15#11718691—22no—
16C2×#88050C411yescharacteristic
17C2×#88048C411yescharacteristic
18#11718586C2211yescharacteristic
19#11718586C2211yescharacteristic
20C2×#88043C2211yescharacteristic
21#11718491—22no—
22#11718379—22no—
23C8×Dic26—22no—
24C13×Q8⋊C8—22no—
25#11718120—22no—
26#11718048—22no—
27C22×Q8×C13C2×C411yescharacteristic
28C22×Dic26C2×C411yescharacteristic
29C4×Q8×C13—21no—
30C4×Q8×C13—21no—
31C4×Q8×C13—21no—
32C4×Q8×C13—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C42×C13—21no—
36C2×C42×C13C2311yescharacteristic
37C2×#6107—22no—
38C2×#6107—22no—
39C2×#6107C814yescomplemented
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×C4×Dic13—21no—
43C22×#1055C2×C411yescharacteristic
44C22×#1055C2×C411yescharacteristic
45C4×Dic26—21no—
46C4×Dic26—21no—
47C4×Dic26D412yes—
48C4×Dic26D412yes—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C22⋊C8—21no—
52C13×C22⋊C8—21no—
53C4×C8×C13—21no—
54C4×C8×C13D412yes—
55#88075—22no—
56C22⋊#1055—21no—
57C22⋊#1055D412yes—
58#88054—24no—
59C8×Dic13—24no—
60#88050—22no—
61#88048—22no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64#88043—21no—
65#88043—21no—
66C4×#1055—21no—
67C4×#1055—21no—
68#9088—131nomaximal, Sylow
69C2×Q8×C13—21no—
70C2×Q8×C13—21no—
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13—21no—
74C2×Q8×C13C2×C812yes—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×Dic13—21no—
81C22×Dic13—21no—
82C2×Dic26—21no—
83C2×Dic26—21no—
84C2×Dic26—21no—
85C2×Dic26C22⋊C412yes—
86C2×Dic26C2×C812yes—
87C2×Dic26M1612yes—
88C2×C8×C13—22no—
89C2×C8×C13—41no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C42×C13—41no—
95C42×C13—41no—
96C42×C13C2×D411yescharacteristic
97C42×C13C2×D411yescharacteristic
98C42×C13C2×D411yescharacteristic
99C42×C13#4111yescharacteristic
100#6107—28no—
101C4⋊Dic13—21no—
102C4⋊Dic13C22⋊C412yes—
103#6101—22no—
104#6101—22no—
105C4×Dic13—22no—
106C4×Dic13—22no—
107C2×#1055—21no—
108C2×#1055—21no—
109C2×#1055—21no—
110C2×#1055—22no—
111C2×#1055—21no—
112C2×#1055—21no—
113C2×#1055—41no—
114C2×#1055C2×C812yes—
115#2982—131no—
116C2×#441—131no—
117#1479—131no—
118#1479D1311yescharacteristic
119#1461—131no—
120#1281—131no—
121#1275—131no—
122C23×C13C4×D411yescharacteristic
123Q8×C13—22no—
124Q8×C13—22no—
125Q8×C13—41no—
126Q8×C13—41no—
127C2×C4×C13—22no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—81no—
134C2×C4×C13C2×C22⋊C411yescharacteristic
135C2×C4×C13C4×D411yescharacteristic
136C2×C4×C13#12011yescharacteristic
137C2×C4×C13#12111yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13#12311yescharacteristic
140C2×C4×C13C22×C811yescharacteristic
141C2×C4×C13C2×M1611yescharacteristic
142C2×C4×C13#13111yescharacteristic
143C2×C4×C13#13111yescharacteristic
144C2×Dic13—22no—
145C2×Dic13—22no—
146C2×Dic13—22no—
147C2×Dic13—22no—
148C2×Dic13—81no—
149Dic26—22no—
150Dic26—22no—
151Dic26—22no—
152Dic26C22⋊C814yes—
153C8×C13—42no—
154C8×C13—81no—
155#1055—22no—
156#1055—42no—
157#1055—41no—
158#1055—81no—
159C22×Q16—131no—
160C2×C4×Q8—131no—
161C2×C4×Q8C2×D1311yescharacteristic
162C8×Q8—262no—
163C8×Q8—262no—
164#441—262no—
165#441—262no—
166#431—131no—
167#431—131no—
168#431—262no—
169#431C2×D1311yescharacteristic
170#431C2×D1311yescharacteristic
171C2×#106—131no—
172C2×#103—131no—
173C2×#103—131no—
174C2×#97—131no—
175Q8⋊C8—22no—
176Q8⋊C8—262no—
177#324—262no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13#38611yescharacteristic
181C22×C13C8×D411yescharacteristic
182C22×C13#43511yescharacteristic
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—42no—
188C4×C13—81no—
189C4×C13C2×C22⋊C811yescharacteristic
190C4×C13#40811yescharacteristic
191C4×C13C8×D411yescharacteristic
192C4×C13#43511yescharacteristic
193Dic13—24no—
194Dic13—42no—
195C22×Q8—131no—
196C22×Q8C4×D1311yescharacteristic
197C2×Q16—134no—
198C2×Q16—262no—
199C2×Q16—262no—
200C22×C8—131no—
201C22×C8—131no—
202C4×Q8—21no—
203C4×Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206C4×Q8—132no—
207C4×Q8—132no—
208C4×Q8—261no—
209C4×Q8—261no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4C4×D1311yescharacteristic
214C2×C42—21no—
215C2×C42—261no—
216C2×C42C22×D1311yescharacteristic
217#106—262no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—264no—
221C4⋊C8—261no—
222C4⋊C8—261no—
223#103—262no—
224#103—262no—
225C22⋊C8—21no—
226C22⋊C8—21no—
227C22⋊C8—132no—
228C22⋊C8—261no—
229#97—261no—
230#97—261no—
231C4×C8—21no—
232C4×C8—264no—
233C4×C8—261no—
234C4×C8—261no—
235C4×C8C22⋊D1312yes—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13#186911yescharacteristic
239C2×C13#190211yescharacteristic
240C2×C13#190511yescharacteristic
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—132no—
247C2×Q8—132no—
248C2×Q8—132no—
249C2×Q8—261no—
250C2×Q8—261no—
251C2×Q8—261no—
252C2×Q8C8×D1312yes—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4C2×C4×D1311yescharacteristic
258C22×C4D4×D1311yescharacteristic
259C22×C4#612911yescharacteristic
260Q16—268no—
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—132no—
264C2×C8—261no—
265C2×C8—261no—
266C2×C8—261no—
267C2×C8—261no—
268C2×C8—261no—
269C2×C8—262no—
270C2×C8—521no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—132no—
276C4⋊C4—262no—
277C4⋊C4—261no—
278C4⋊C4—262no—
279C42—41no—
280C42—41no—
281C42—262no—
282C42—262no—
283C42#612711yescharacteristic
284C42D4×D1311yescharacteristic
285C42D4×D1311yescharacteristic
286C42C2×C22⋊D1311yescharacteristic
287C13#908811yescharacteristic, complemented, Sylow
288C23#8813511yescharacteristic
289Q8—22no—
290Q8—22no—
291Q8—41no—
292Q8—41no—
293Q8—134no—
294Q8—262no—
295Q8—262no—
296Q8—262no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—81no—
304C2×C4—262no—
305C2×C4—262no—
306C2×C4—262no—
307C2×C4—262no—
308C2×C4—1041no—
309C2×C4C22⋊C4×D1311yescharacteristic
310C2×C4#8813711yescharacteristic
311C2×C4#8813811yescharacteristic
312C2×C4C2×C8×D1311yescharacteristic
313C2×C4#8815511yescharacteristic
314C2×C4M16×D1311yescharacteristic
315C2×C4#8816111yescharacteristic
316C2×C4C4×C22⋊D1311yescharacteristic
317C2×C4#8819111yescharacteristic
318C2×C4#8819211yescharacteristic
319C8—42no—
320C8—81no—
321C8—262no—
322C8—522no—
323C8—521no—
324C8—1041no—
325C22—21no—
326C22—21no—
327C22#1171838611yescharacteristic
328C22#1171838911yescharacteristic
329C22#1171861711yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—81no—
336C4—264no—
337C4—522no—
338C4D13×C22⋊C811yescharacteristic
339C4#1171838811yescharacteristic
340C4C8×C22⋊D1311yescharacteristic
341C4#1171878811yescharacteristic
342C2—21no—
343C2—21no—
344C2#1311512511yescharacteristic
345C2#1311530611yescharacteristic
346C2#1311532711yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1479C2
socleC22×C13#386
prime radicalC23×C13C4×D4
cosocleC2×C42×C13C23
hypercenter#1479D13
hypocenterC13#9088
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
39. C2×#6107C8semidirect
287. C13#9088semidirect

Maximal subgroups

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

subgroupindex
#131239162
C2×#117186912
#131132322
#131131602
#131126802
#131126662
C13×#14792
#908813