Finite Group Databasebeta

← #15754577

Subgroups — #15754577

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88076C211yesmaximal, characteristic
2#13113438C212yesmaximal
3#13113283C212yesmaximal
4#13113180C211yesmaximal, characteristic
5C2×C13×#557C211yesmaximal, characteristic
6C13×#557—24no—
7C13×#557—24no—
8C2×C13×C4⋊Q8—21no—
9C2×C13×C4⋊Q8C411yescharacteristic
10C2×C13×#125—21no—
11C2×C13×#125—21no—
12C2×C13×#125C411yescharacteristic
13C2×C13×#125C2211yescharacteristic
14C2×C4×Q8×C13—21no—
15C2×C4×Q8×C13C411yescharacteristic
16C2×C4×Q8×C13C411yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C2×#88076—21no—
20#11718587C2212yes—
21C4×#6099C2212yes—
22#11718135—24no—
23Q8⋊#1055—24no—
24#11718122—21no—
25#11718120—21no—
26#11718120—21no—
27C22×Q8×C13—21no—
28C22×Q8×C13C2×C411yescharacteristic
29C22×Q8×C13D411yescharacteristic
30C13×C4⋊Q8—28no—
31C13×C4⋊Q8—22no—
32C13×C4⋊Q8—22no—
33C13×#125—28no—
34C13×#125—28no—
35C13×#125—22no—
36C13×#125—22no—
37C13×#125—22no—
38C13×#125D414yes—
39C4×Q8×C13—28no—
40C4×Q8×C13—22no—
41C4×Q8×C13—22no—
42C4×Q8×C13—22no—
43C4×Q8×C13—22no—
44C4×Q8×C13—22no—
45C4×Q8×C13—22no—
46C4×Q8×C13—22no—
47C4×Q8×C13D414yes—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4C2×C411yescharacteristic
57C2×C13×C4⋊C4C2×C411yescharacteristic
58C2×C13×C4⋊C4C2×C411yescharacteristic
59C2×C13×C4⋊C4D411yescharacteristic
60C2×C13×C4⋊C4D411yescharacteristic
61C2×C13×C4⋊C4D411yescharacteristic
62C2×C42×C13—21no—
63C2×C42×C13—21no—
64C2×C42×C13—21no—
65C2×C42×C13C2×C411yescharacteristic
66C2×C42×C13C2×C411yescharacteristic
67C2×C42×C13C2311yescharacteristic
68C2×#6099—22no—
69#88076—24no—
70C22⋊#1055—22no—
71C4⋊#1055—22no—
72#88043—22no—
73#88043—22no—
74C4×#1055—22no—
75#8374—131nomaximal, Sylow
76C2×Q8×C13—24no—
77C2×Q8×C13—24no—
78C2×Q8×C13—22no—
79C2×Q8×C13—21no—
80C2×Q8×C13—22no—
81C2×Q8×C13—41no—
82C2×Q8×C13—42no—
83C2×Q8×C13—42no—
84C2×Q8×C13C22⋊C412yes—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C22⋊C411yescharacteristic
92C22×C4×C13C22⋊C411yescharacteristic
93C22×C4×C13C22×C411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C13×C4⋊C4—24no—
97C13×C4⋊C4—24no—
98C13×C4⋊C4—24no—
99C13×C4⋊C4—24no—
100C13×C4⋊C4—24no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—24no—
105C13×C4⋊C4—24no—
106C13×C4⋊C4—24no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4C22⋊C412yes—
111C13×C4⋊C4C22⋊C412yes—
112C13×C4⋊C4C22⋊C412yes—
113C42×C13—24no—
114C42×C13—24no—
115C42×C13—21no—
116C42×C13—21no—
117C42×C13—21no—
118C42×C13—21no—
119C42×C13—24no—
120C42×C13C2×D412yes—
121C42×C13C2×D412yes—
122#6099—24no—
123#6099—42no—
124C2×#1055—42no—
125C2×#1055—42no—
126C2×#557D1311yescharacteristic
127C4×#101—131no—
128#1528—132no—
129#1491—132no—
130#1467—131no—
131C23×C13C2×C22⋊C411yescharacteristic
132Q8×C13—24no—
133Q8×C13—22no—
134Q8×C13—44no—
135Q8×C13—48no—
136Q8×C13#10114yescomplemented
137C2×C4×C13—24no—
138C2×C4×C13—22no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—22no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—22no—
147C2×C4×C13—21no—
148C2×C4×C13—22no—
149C2×C4×C13—22no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—41no—
153C2×C4×C13—42no—
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#10412yes—
161C2×C4×C13C2×C22⋊C411yescharacteristic
162C2×C4×C13C2×C22⋊C411yescharacteristic
163C2×C4×C13#12012yes—
164C2×C4×C13#12012yes—
165#1055—44no—
166#1055—82no—
167#557—24no—
168#557—24no—
169C2×C4⋊Q8—21no—
170C2×C4⋊Q8Dic1311yescharacteristic
171C2×#125—21no—
172C2×#125—21no—
173C2×#125Dic1311yescharacteristic
174C2×#125C2×D1311yescharacteristic
175C2×C4×Q8—21no—
176C2×C4×Q8Dic1311yescharacteristic
177C2×C4×Q8Dic1311yescharacteristic
178C2×C4×Q8C2×D1311yescharacteristic
179C2×C4×Q8C2×D1311yescharacteristic
180#432—132no—
181C2×#101—261no—
182C4×M16—132no—
183#343—261no—
184#330—264no—
185Q8⋊C8—264no—
186#324—261no—
187#324—261no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13#37911yescharacteristic
191C22×C13C2×#10411yescharacteristic
192C22×C13#42111yescharacteristic
193C4×C13—22no—
194C4×C13—24no—
195C4×C13—21no—
196C4×C13—22no—
197C4×C13—22no—
198C4×C13—41no—
199C4×C13—41no—
200C4×C13—42no—
201C4×C13—41no—
202C4×C13—42no—
203C4×C13—42no—
204C4×C13C2×#10112yes—
205C22×Q8—21no—
206C22×Q8C2×Dic1311yescharacteristic
207C22×Q8C22⋊D1311yescharacteristic
208C2×M16—262no—
209C4⋊Q8—28no—
210C4⋊Q8—22no—
211C4⋊Q8—22no—
212#125—28no—
213#125—28no—
214#125—22no—
215#125—22no—
216#125—22no—
217#125C22⋊D1314yes—
218C4×Q8—28no—
219C4×Q8—22no—
220C4×Q8—22no—
221C4×Q8—22no—
222C4×Q8—22no—
223C4×Q8—22no—
224C4×Q8—22no—
225C4×Q8—22no—
226C4×Q8C22⋊D1314yes—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C2×Dic1311yescharacteristic
236C2×C4⋊C4C2×Dic1311yescharacteristic
237C2×C4⋊C4C2×Dic1311yescharacteristic
238C2×C4⋊C4C22⋊D1311yescharacteristic
239C2×C4⋊C4C22⋊D1311yescharacteristic
240C2×C4⋊C4C22⋊D1311yescharacteristic
241C2×C42—21no—
242C2×C42—21no—
243C2×C42—21no—
244C2×C42C2×Dic1311yescharacteristic
245C2×C42C2×Dic1311yescharacteristic
246C2×C42C22×D1311yescharacteristic
247C4⋊C8—262no—
248#101—264no—
249C22⋊C8—262no—
250#97—262no—
251#97—262no—
252C4×C8—262no—
253C2×C13—21no—
254C2×C13—21no—
255C2×C13#178411yescharacteristic
256C2×C13#178911yescharacteristic
257C2×C13#179611yescharacteristic
258C2×Q8—24no—
259C2×Q8—24no—
260C2×Q8—22no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8C22⋊Dic1312yes—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4C22⋊Dic1311yescharacteristic
272C22×C4C22⋊Dic1311yescharacteristic
273C22×C4C22⋊Dic1311yescharacteristic
274C22×C4C22⋊Dic1311yescharacteristic
275C22×C4C22×Dic1311yescharacteristic
276C22×C4C2×C22⋊D1311yescharacteristic
277C22×C4C2×C22⋊D1311yescharacteristic
278M16—264no—
279M16—522no—
280C2×C8—522no—
281C2×C8—522no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—24no—
286C4⋊C4—24no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—24no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4C22⋊Dic1312yes—
297C4⋊C4C22⋊Dic1312yes—
298C4⋊C4C22⋊Dic1312yes—
299C42—24no—
300C42—24no—
301C42—21no—
302C42—21no—
303C42—21no—
304C42—21no—
305C42—24no—
306C42C2×C22⋊D1312yes—
307C42C2×C22⋊D1312yes—
308C13#837411yescharacteristic, complemented, Sylow
309C23C2×C22⋊Dic1311yescharacteristic
310Q8—24no—
311Q8—22no—
312Q8—44no—
313Q8—48no—
314Q8#8807614yescomplemented
315C2×C4—24no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4#8807712yes—
339C2×C4C2×C22⋊Dic1311yescharacteristic
340C2×C4C2×C22⋊Dic1311yescharacteristic
341C2×C4#8820712yes—
342C2×C4#8820712yes—
343C8—524no—
344C8—1042no—
345C22—21no—
346C22—21no—
347C22C2×#8807711yescharacteristic
348C22#1171889711yescharacteristic
349C22#1171890811yescharacteristic
350C4—24no—
351C4—21no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—42no—
357C4—42no—
358C4—41no—
359C4—41no—
360C4—42no—
361C4C2×#8807612yes—
362C2—21no—
363C2—21no—
364C2#1311476011yescharacteristic
365C2#1311478011yescharacteristic
366C2#1311481111yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#557C2
socleC22×C13#379
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenterC2×#557D13
hypocenterC13#8374
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
136. Q8×C13#101semidirect
308. C13#8374semidirect
314. Q8#88076semidirect

Maximal subgroups

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

subgroupindex
C4×#880762
#131134382
#131132832
#131131802
C2×C13×#5572
#837413