Finite Group Databasebeta

← #15828747

Subgroups — #15828747

Order 3328.

1162 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719277C211yesmaximal, characteristic
2#13123916C212yesmaximal, complemented
3#13113160C211yesmaximal, characteristic, complemented
4#13113158C214yesmaximal, complemented
5#13113149C214yesmaximal
6#13113148C212yesmaximal
7C13×#1461C211yesmaximal, characteristic, complemented
8C22×Q8×D13C411yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C2×Q8×Dic13C411yescharacteristic
11#11719277—24no—
12#11719277—24no—
13C2×#88146C411yescharacteristic
14C2×#88146C2212yes—
15C2×#88141C411yescharacteristic
16C2×#88141C2212yes—
17C2×#88126C412yes—
18C2×#88126C2211yescharacteristic
19C2×C4×Dic26C412yes—
20C2×C4×Dic26C2211yescharacteristic
21C13×#431C2212yes—
22#11718586C2212yes—
23#11718491—24no—
24#11718379C2218yes—
25C8×Dic26—24no—
26C13×#324C2214yes—
27#11718120C2214yes—
28#11718061C2214yes—
29#11718060C2214yes—
30C22×Q8×C13C2×C411yescharacteristic
31C2×Q8×D13—24no—
32C2×Q8×D13—24no—
33C2×Q8×D13C818yescomplemented
34C22×C4×D13C2×C412yes—
35C22×C4×D13C2×C411yescharacteristic
36C22×Dic26C2×C412yes—
37C22×Dic26C2×C411yescharacteristic
38C4×Q8×C13—22no—
39C4×Q8×C13—22no—
40C2×C13×C4⋊C4C2×C411yescharacteristic
41C2×C13×C4⋊C4C2312yes—
42C2×C42×C13C2×C412yes—
43C2×C42×C13C2311yescharacteristic
44Q8×Dic13—24no—
45C2×#6103C2×C411yescharacteristic
46C2×#6103C2×C412yes—
47C2×#6103C2311yescharacteristic
48C2×C4⋊Dic13C2×C412yes—
49C2×C4⋊Dic13C2×C411yescharacteristic
50C2×#6101C2×C411yescharacteristic
51C2×#6101C2×C412yes—
52C2×#6101C2×C412yes—
53C2×#6101C2311yescharacteristic
54C2×C4×Dic13C2×C412yes—
55C2×C4×Dic13C2×C412yes—
56C2×C4×Dic13C2×C412yes—
57C2×C4×Dic13C2×C411yescharacteristic
58C2×C4×Dic13C2312yes—
59#88146—24no—
60#88146—28no—
61#88141—24no—
62#88141—28no—
63#88126—22no—
64#88126—22no—
65#88126—24no—
66#88126—24no—
67C4×Dic26—24no—
68C4×Dic26—24no—
69C4×Dic26D414yes—
70C4×Dic26D414yes—
71C13×C4⋊C8—22no—
72C13×C22⋊C8C2314yes—
73C4×C8×C13—22no—
74C22⋊#1055C2314yes—
75#88054—28no—
76C8×Dic13—28no—
77C4⋊#1055—22no—
78C4×#1055—22no—
79#17352—131nomaximal, Sylow
80C23×D13C22×C411yescharacteristic
81C2×Q8×C13—22no—
82C2×Q8×C13—22no—
83C2×Q8×C13C2×C814yes—
84C22×C4×C13C22×C412yes—
85C22×C4×C13C22×C412yes—
86C22×C4×C13C22×C411yescharacteristic
87C22×C4×C13C22×C411yescharacteristic
88C22×C4×C13C2411yescharacteristic
89C22×Dic13C22×C411yescharacteristic
90C22×Dic13C22×C411yescharacteristic
91C22×Dic13C22×C411yescharacteristic
92C22×Dic13C22×C412yes—
93C22×Dic13C22×C412yes—
94Q8×D13—232no—
95C2×C4×D13—22no—
96C2×C4×D13—22no—
97C2×C4×D13—24no—
98C2×C4×D13—24no—
99C2×C4×D13C2×C814yes—
100C2×C4×D13C2×C818yes—
101C2×Dic26—24no—
102C2×Dic26—24no—
103C2×Dic26C22⋊C414yes—
104C2×Dic26C2×C818yes—
105C2×Dic26C2×C814yes—
106C2×Dic26M1614yes—
107C2×C8×C13—24no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—24no—
110C42×C13—22no—
111C42×C13—22no—
112C42×C13C2×D412yes—
113C42×C13C2×D412yes—
114#6103—21no—
115#6103—21no—
116#6103—22no—
117#6103—24no—
118C4⋊Dic13—24no—
119C4⋊Dic13C22⋊C414yes—
120#6101—21no—
121#6101—21no—
122#6101—22no—
123#6101—24no—
124#6101C22⋊C414yes—
125#6101C22⋊C414yes—
126C4×Dic13—22no—
127C4×Dic13—24no—
128C4×Dic13—24no—
129C4×Dic13—24no—
130C4×Dic13C2×D418yes—
131C2×#1055—24no—
132C2×#519—131no—
133#2982—132no—
134#1461—134no—
135#1461—131no—
136#1461D1311yescharacteristic, complemented
137#1458—132no—
138#1458—134no—
139C23×C13C23×C411yescharacteristic
140C22×D13—21no—
141C22×D13—21no—
142C22×D13—41no—
143C22×D13—41no—
144C22×D13C22×C812yes—
145Q8×C13—28no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—22no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—42no—
152C2×C4×C13C2×C22⋊C411yescharacteristic
153C2×C4×C13C2×C22⋊C411yescharacteristic
154C2×C4×C13C2×C22⋊C412yes—
155C2×C4×C13C22×C814yes—
156C2×C4×C13C22×C812yes—
157C2×C4×C13C2×M1612yes—
158C2×C4×C13C22×D412yes—
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—42no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13C2×C22⋊C414yes—
167C2×Dic13C2×C22⋊C414yes—
168C2×Dic13C22×C812yes—
169C2×Dic13C22×C814yes—
170C2×Dic13C2×M1614yes—
171C4×D13—28no—
172C4×D13—216no—
173Dic26—216no—
174Dic26C22⋊C8116yes—
175C8×C13—44no—
176#1055—44no—
177C23×Q8—131no—
178#519—264no—
179#519—264no—
180C2×C4×Q8—131no—
181C2×C4×Q8—131no—
182C2×C4×Q8—132no—
183C2×C4×Q8—132no—
184C2×C4×Q8—131no—
185C2×C4×Q8C2×D1311yescharacteristic
186C2×#117—131no—
187C2×#117—132no—
188C2×#117—132no—
189C2×#117—131no—
190C8×Q8—264no—
191C8×Q8—264no—
192#431—132no—
193#431—138no—
194#431C2×D1312yes—
195#324—134no—
196#324—134no—
197#324C2×D1314yes—
198#323—134no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13C22×C22⋊C411yescharacteristic
202C22×C13C23×C811yescharacteristic
203C22×C13C22×M1611yescharacteristic
204C2×D13—22no—
205C2×D13—42no—
206C2×D13—41no—
207C2×D13—41no—
208C2×D13—42no—
209C4×C13—24no—
210C4×C13—22no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—42no—
214C4×C13C2×C22⋊C814yes—
215Dic13—22no—
216Dic13—24no—
217Dic13—41no—
218Dic13—41no—
219Dic13C2×C22⋊C818yes—
220C22×Q8—138no—
221C22×Q8—131no—
222C22×Q8—132no—
223C22×Q8—264no—
224C22×Q8—264no—
225C22×Q8C4×D1311yescharacteristic
226C23×C4—132no—
227C23×C4—131no—
228C4×Q8—22no—
229C4×Q8—22no—
230C4×Q8—134no—
231C4×Q8—134no—
232C4×Q8—264no—
233C4×Q8—264no—
234C4×Q8—268no—
235C4×Q8—264no—
236C4×Q8—264no—
237#117—264no—
238#117—264no—
239#117—268no—
240#117—264no—
241#117—262no—
242#117—262no—
243C2×C4⋊C4—132no—
244C2×C4⋊C4—131no—
245C2×C4⋊C4—132no—
246C2×C4⋊C4—131no—
247C2×C4⋊C4—132no—
248C2×C4⋊C4—131no—
249C2×C4⋊C4C4×D1311yescharacteristic
250C2×C4⋊C4C22×D1312yes—
251C2×C22⋊C4—132no—
252C2×C22⋊C4—131no—
253C2×C22⋊C4—131no—
254C2×C42—132no—
255C2×C42—132no—
256C2×C42—132no—
257C2×C42—132no—
258C2×C42—131no—
259C2×C42C4×D1312yes—
260C2×C42C22×D1311yescharacteristic
261C4⋊C8—22no—
262C4⋊C8—268no—
263C4⋊C8—262no—
264C22⋊C8—134no—
265C22⋊C8C22×D1314yes—
266C4×C8—22no—
267C4×C8—268no—
268C4×C8—262no—
269C2×C13—21no—
270C2×C13—21no—
271C2×C13C22×C22⋊C811yescharacteristic
272C2×C13#288411yescharacteristic
273C2×C13#288911yescharacteristic
274D13—42no—
275C24—131no—
276C2×Q8—22no—
277C2×Q8—22no—
278C2×Q8—134no—
279C2×Q8—134no—
280C2×Q8—138no—
281C2×Q8—134no—
282C2×Q8—264no—
283C2×Q8—264no—
284C2×Q8—2632no—
285C2×Q8C8×D1314yes—
286C22×C4—132no—
287C22×C4—131no—
288C22×C4—132no—
289C22×C4—138no—
290C22×C4—134no—
291C22×C4—131no—
292C22×C4—131no—
293C22×C4—264no—
294C22×C4—264no—
295C22×C4—262no—
296C22×C4—262no—
297C22×C4C2×C4×D1312yes—
298C22×C4C2×C4×D1312yes—
299C22×C4C2×C4×D1311yescharacteristic
300C22×C4C2×C4×D1311yescharacteristic
301C22×C4C23×D1311yescharacteristic
302C2×C8—24no—
303C2×C8—264no—
304C4⋊C4—22no—
305C4⋊C4—24no—
306C4⋊C4—134no—
307C4⋊C4—134no—
308C4⋊C4—134no—
309C4⋊C4—264no—
310C4⋊C4—264no—
311C4⋊C4—261no—
312C4⋊C4—261no—
313C4⋊C4—262no—
314C22⋊C4—264no—
315C22⋊C4—261no—
316C22⋊C4—261no—
317C22⋊C4—262no—
318C42—22no—
319C42—22no—
320C42—138no—
321C42—264no—
322C42—264no—
323C42—264no—
324C42—262no—
325C42D4×D1312yes—
326C42D4×D1312yes—
327C13#1735211yescharacteristic, complemented, Sylow
328C23—132no—
329C23—261no—
330C23—261no—
331C23—521no—
332C23—521no—
333C23C22×C4×D1311yescharacteristic
334Q8—28no—
335Q8—1316no—
336Q8—2616no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—134no—
344C2×C4—134no—
345C2×C4—134no—
346C2×C4—132no—
347C2×C4—134no—
348C2×C4—2616no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—268no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—522no—
355C2×C4—521no—
356C2×C4—521no—
357C2×C4C22⋊C4×D1311yescharacteristic
358C2×C4C22⋊C4×D1311yescharacteristic
359C2×C4C22⋊C4×D1312yes—
360C2×C4C2×C8×D1314yes—
361C2×C4C2×C8×D1312yes—
362C2×C4M16×D1312yes—
363C2×C4C2×D4×D1312yes—
364C8—44no—
365C8—524no—
366C22—21no—
367C22—21no—
368C22—262no—
369C22—522no—
370C22—522no—
371C22—521no—
372C22—521no—
373C22C2×C22⋊C4×D1311yescharacteristic
374C22C22×C8×D1311yescharacteristic
375C22C2×M16×D1311yescharacteristic
376C4—24no—
377C4—22no—
378C4—21no—
379C4—21no—
380C4—42no—
381C4—138no—
382C4—262no—
383C4—264no—
384C4—521no—
385C4—521no—
386C4D13×C22⋊C814yes—
387C2—21no—
388C2—21no—
389C2—522no—
390C2C2×D13×C22⋊C811yescharacteristic
391C2#1312329811yescharacteristic
392C2#1312331611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC22×C13C23×C8
FrattiniC22×C4C23×D13
FittingC13×#1461C2
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenter#1461D13
hypocenterC13#17352
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #13123916C2semidirect
3. #13113160C2semidirect
4. #13113158C2semidirect
7. C13×#1461C2semidirect
33. C2×Q8×D13C8semidirect
136. #1461D13semidirect
327. C13#17352semidirect

Maximal subgroups

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

subgroupindex
C2×#117192772
#131239162
#131131602
#131131582
#131131492
#131131482
C13×#14612
#1735213