Finite Group Databasebeta

← #15755587

Subgroups — #15755587

Order 3328.

682 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718310C211yesmaximal, characteristic
2#13114814C212yesmaximal
3C2×#11718061C212yesmaximal
4#13112679C211yesmaximal, characteristic
5C13×#1280C211yesmaximal, characteristic
6C22×#6101C411yescharacteristic
7C22×#6101C2211yescharacteristic
8C22×C4×Dic13C411yescharacteristic
9C22×C4×Dic13C411yescharacteristic
10C22×C4×Dic13C2211yescharacteristic
11C2×C13×C22⋊C8C2212yes—
12C2×C13×#95C2211yescharacteristic
13C2×#88071C411yescharacteristic
14C2×C22⋊#1055C2212yes—
15C2×#88054—22no—
16#11718310—22no—
17#11718310—22no—
18#11718142—22no—
19#11718061—24no—
20C23×C4×C13C2×C411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13C2311yescharacteristic
23C23×Dic13C2×C411yescharacteristic
24C23×Dic13C2×C411yescharacteristic
25C23×Dic13C2×C411yescharacteristic
26C23×Dic13C2×C411yescharacteristic
27C22×C8×C13—22no—
28C2×#6101—22no—
29C2×#6101—22no—
30C2×#6101—22no—
31C2×#6101—22no—
32C2×#6101C814yescomplemented
33C2×#6101D412yes—
34C2×#6101Q812yes—
35C2×C4×Dic13—22no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13—22no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13—42no—
42C2×C4×Dic13—42no—
43C2×C4×Dic13D412yes—
44C2×C4×Dic13D412yes—
45C22×#1055—22no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—22no—
48C13×#95—22no—
49#88071—22no—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52#88054—44no—
53#8560—131nomaximal, Sylow
54C24×C13C22×C411yescharacteristic
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13C2×C812yes—
66C22×C4×C13M1612yes—
67C22×C4×C13C2×D412yes—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×Q811yescharacteristic
70C22×C4×C13#4112yes—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—22no—
78C22×Dic13—22no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—41no—
82C22×Dic13—41no—
83C22×Dic13—41no—
84C22×Dic13—41no—
85C22×Dic13C22⋊C412yes—
86C22×Dic13C22⋊C411yescharacteristic
87C22×Dic13C22⋊C411yescharacteristic
88C22×Dic13C4⋊C412yes—
89C22×Dic13C4⋊C412yes—
90C22×Dic13C2×C812yes—
91C22×Dic13C2×C812yes—
92C22×Dic13M1612yes—
93C22×Dic13M1612yes—
94C2×C8×C13—42no—
95C2×C8×C13—42no—
96C2×C8×C13—42no—
97#6101—24no—
98#6101—24no—
99#6101—28no—
100C4×Dic13—24no—
101C4×Dic13—24no—
102C4×Dic13—24no—
103C4×Dic13—42no—
104C4×Dic13—42no—
105C4×Dic13—42no—
106C2×#1055—42no—
107C2×#1055—42no—
108C2×#1055—42no—
109C2×C4×C4⋊C4—131no—
110#1797—132no—
111C2×#324—132no—
112#1280—131no—
113#1280D1311yescharacteristic
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13C2×C22⋊C411yescharacteristic
119C23×C13C2×C4⋊C411yescharacteristic
120C23×C13#11711yescharacteristic
121C23×C13C22×C811yescharacteristic
122C23×C13C2×M1611yescharacteristic
123C23×C13C2×M1611yescharacteristic
124C23×C13C2×M1611yescharacteristic
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13#12112yes—
141C2×C4×C13C22⋊Q812yes—
142C2×Dic13—24no—
143C2×Dic13—24no—
144C2×Dic13—22no—
145C2×Dic13—22no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—22no—
149C2×Dic13—22no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—22no—
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—22no—
156C2×Dic13—22no—
157C2×Dic13—42no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—42no—
163C2×Dic13C22⋊C814yes—
164C2×Dic13#9912yes—
165C2×Dic13#10112yes—
166C2×Dic13C4⋊C814yescomplemented
167C8×C13—82no—
168#1055—82no—
169C22×C4⋊C4—131no—
170C22×C4⋊C4—131no—
171C22×C42—131no—
172C22×C42—131no—
173C22×C42—131no—
174C2×C4⋊C8—262no—
175C2×C22⋊C8—132no—
176C2×C22⋊C8C2×D1312yes—
177C4×C4⋊C4—262no—
178C4×C4⋊C4—262no—
179C2×#95—131no—
180C2×#95C2×D1311yescharacteristic
181#336—262no—
182#324—264no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13#38011yescharacteristic
196C22×C13C2×C22⋊C811yescharacteristic
197C22×C13#40711yescharacteristic
198C22×C13C2×#9911yescharacteristic
199C22×C13#41011yescharacteristic
200C22×C13C2×#10111yescharacteristic
201C22×C13#41311yescharacteristic
202C22×C13C2×C4⋊C811yescharacteristic
203C22×C13#42311yescharacteristic
204C22×C13#43111yescharacteristic
205C22×C13#43211yescharacteristic
206C4×C13—22no—
207C4×C13—22no—
208C4×C13—42no—
209C4×C13—42no—
210Dic13—24no—
211Dic13—24no—
212Dic13—22no—
213Dic13—22no—
214Dic13—42no—
215C23×C4—131no—
216C23×C4—131no—
217C23×C4—131no—
218C23×C4—131no—
219C23×C4C4×D1311yescharacteristic
220C23×C4C4×D1311yescharacteristic
221C23×C4C22×D1311yescharacteristic
222C22×C8—22no—
223C22×C8—262no—
224C2×C4⋊C4—134no—
225C2×C4⋊C4—132no—
226C2×C4⋊C4—132no—
227C2×C4⋊C4—262no—
228C2×C4⋊C4—262no—
229C2×C4⋊C4—262no—
230C2×C4⋊C4—262no—
231C2×C42—132no—
232C2×C42—132no—
233C2×C42—261no—
234C2×C42—261no—
235C2×C42—262no—
236C2×C42—262no—
237C2×C42—261no—
238C2×C42—261no—
239C2×C42—522no—
240C2×C42—522no—
241C4⋊C8—524no—
242C22⋊C8—22no—
243C22⋊C8—22no—
244C22⋊C8—262no—
245C22⋊C8—262no—
246#95—22no—
247#95—262no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13—21no—
251C2×C13—21no—
252C2×C13#145911yescharacteristic
253C2×C13#146111yescharacteristic
254C2×C13#146311yescharacteristic
255C2×C13#146411yescharacteristic
256C2×C13#179711yescharacteristic
257C2×C13#179911yescharacteristic
258C2×C13#180111yescharacteristic
259C24C2×C4×D1311yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—132no—
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—132no—
274C22×C4—132no—
275C22×C4—132no—
276C22×C4—132no—
277C22×C4—132no—
278C22×C4—132no—
279C22×C4—262no—
280C22×C4—262no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4—261no—
286C22×C4—261no—
287C22×C4—261no—
288C22×C4—261no—
289C22×C4—521no—
290C22×C4—521no—
291C22×C4—521no—
292C22×C4—521no—
293C22×C4C8×D1312yes—
294C22×C4#609412yes—
295C22×C4#612712yes—
296C22×C4D4×D1312yes—
297C22×C4D4×D1311yescharacteristic
298C22×C4Q8×D1311yescharacteristic
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—522no—
303C2×C8—522no—
304C2×C8—522no—
305C4⋊C4—268no—
306C4⋊C4—264no—
307C4⋊C4—264no—
308C42—264no—
309C42—264no—
310C42—264no—
311C42—522no—
312C42—522no—
313C42—522no—
314C13#856011yescharacteristic, complemented, Sylow
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23#8812611yescharacteristic
320C23C22⋊C4×D1311yescharacteristic
321C23C4⋊C4×D1311yescharacteristic
322C23C2×C8×D1311yescharacteristic
323C23C2×#609411yescharacteristic
324C23M16×D1311yescharacteristic
325C23M16×D1311yescharacteristic
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—132no—
342C2×C4—132no—
343C2×C4—134no—
344C2×C4—134no—
345C2×C4—264no—
346C2×C4—264no—
347C2×C4—262no—
348C2×C4—261no—
349C2×C4—262no—
350C2×C4—261no—
351C2×C4—262no—
352C2×C4—262no—
353C2×C4—262no—
354C2×C4—262no—
355C2×C4—262no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—262no—
359C2×C4—262no—
360C2×C4—522no—
361C2×C4—522no—
362C2×C4—522no—
363C2×C4—521no—
364C2×C4—521no—
365C2×C4—522no—
366C2×C4#8813812yes—
367C2×C4#8815012yes—
368C8—82no—
369C8—1042no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22#1171832811yescharacteristic
383C22#1171834611yescharacteristic
384C22#1171836611yescharacteristic
385C22D13×C22⋊C811yescharacteristic
386C22#1171838711yescharacteristic
387C22#1171840111yescharacteristic
388C22D13×#9911yescharacteristic
389C22#1171840611yescharacteristic
390C22D13×#10111yescharacteristic
391C22D13×C4⋊C811yescharacteristic
392C22#1171849811yescharacteristic
393C4—22no—
394C4—22no—
395C4—42no—
396C4—42no—
397C4—264no—
398C4—262no—
399C4—262no—
400C4—264no—
401C4—522no—
402C2—21no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2#1311315111yescharacteristic
407C2#1311315811yescharacteristic
408C2#1311316411yescharacteristic
409C2#1311316711yescharacteristic
410C2#1311481511yescharacteristic
411C2#1311482311yescharacteristic
412C2#1311483111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC23×C13C22×C8
FrattiniC23×C4C22×D13
FittingC13×#1280C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC23×C4×C13C23
hypercenter#1280D13
hypocenterC13#8560
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
32. C2×#6101C8semidirect
166. C2×Dic13C4⋊C8semidirect
314. C13#8560semidirect

Maximal subgroups

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

subgroupindex
C2×#117183102
#131148142
C2×#117180612
#131126792
C13×#12802
#856013