Finite Group Databasebeta

← #15755586

Subgroups — #15755586

Order 3328.

682 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic13C211yesmaximal, characteristic
2#13114814C212yesmaximal
3C2×#11718120C211yesmaximal, characteristic
4#13112678C212yesmaximal
5C2×C13×#324C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C22×C4⋊Dic13C411yescharacteristic
8C22×C4×Dic13C411yescharacteristic
9C22×C4×Dic13C411yescharacteristic
10C22×C4×Dic13C2211yescharacteristic
11C2×C13×C22⋊C8C2212yes—
12C2×#88071C411yescharacteristic
13C2×#88071C2211yescharacteristic
14C2×C22⋊#1055C2212yes—
15C2×#88054—22no—
16C4⋊C4×Dic13—22no—
17C4⋊C4×Dic13—22no—
18C13×#324—22no—
19#11718142—22no—
20#11718120—22no—
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13C2×C411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C23×Dic13C2×C411yescharacteristic
25C23×Dic13C2×C411yescharacteristic
26C23×Dic13C2×C411yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C22×C8×C13—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4D412yes—
32C2×C13×C4⋊C4Q812yes—
33C2×C4⋊Dic13—22no—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13C814yescomplemented
36C2×C4×Dic13—22no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13—22no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13—21no—
42C2×C4×Dic13—42no—
43C2×C4×Dic13—42no—
44C2×C4×Dic13D412yes—
45C2×C4×Dic13D412yes—
46C22×#1055—22no—
47C13×C22⋊C8—22no—
48C13×C22⋊C8—22no—
49#88071—22no—
50#88071—22no—
51C22⋊#1055—22no—
52C22⋊#1055—22no—
53#88054—44no—
54#8560—131nomaximal, Sylow
55C24×C13C22×C411yescharacteristic
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13C4⋊C412yes—
67C22×C4×C13C4⋊C412yes—
68C22×C4×C13C2×C812yes—
69C22×C4×C13M1612yes—
70C22×C4×C13C2×D412yes—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×Q811yescharacteristic
73C22×C4×C13#4112yes—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—22no—
77C22×Dic13—22no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—41no—
83C22×Dic13—41no—
84C22×Dic13—41no—
85C22×Dic13—41no—
86C22×Dic13—41no—
87C22×Dic13—41no—
88C22×Dic13C22⋊C412yes—
89C22×Dic13C22⋊C411yescharacteristic
90C22×Dic13C22⋊C411yescharacteristic
91C22×Dic13C2×C812yes—
92C22×Dic13C2×C812yes—
93C22×Dic13M1612yes—
94C22×Dic13M1612yes—
95C2×C8×C13—42no—
96C2×C8×C13—42no—
97C2×C8×C13—42no—
98C13×C4⋊C4—24no—
99C13×C4⋊C4—24no—
100C4⋊Dic13—28no—
101C4×Dic13—24no—
102C4×Dic13—24no—
103C4×Dic13—24no—
104C4×Dic13—42no—
105C4×Dic13—42no—
106C4×Dic13—42no—
107C2×#1055—42no—
108C2×#1055—42no—
109C2×#1055—42no—
110C2×C4×C4⋊C4—131no—
111#1797—132no—
112C2×#324—131no—
113C2×#324D1311yescharacteristic
114#1280—132no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13C2×C22⋊C411yescharacteristic
120C23×C13C2×C4⋊C411yescharacteristic
121C23×C13#11711yescharacteristic
122C23×C13C22×C811yescharacteristic
123C23×C13C2×M1611yescharacteristic
124C23×C13C2×M1611yescharacteristic
125C23×C13C2×M1611yescharacteristic
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—42no—
142C2×C4×C13C4⋊C814yescomplemented
143C2×C4×C13#12112yes—
144C2×C4×C13C22⋊Q812yes—
145C2×Dic13—24no—
146C2×Dic13—24no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—22no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—22no—
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—42no—
156C2×Dic13—42no—
157C2×Dic13—42no—
158C2×Dic13—42no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C2×Dic13C22⋊C814yes—
166C2×Dic13#9912yes—
167C2×Dic13#10112yes—
168C8×C13—82no—
169#1055—82no—
170C22×C4⋊C4—131no—
171C22×C4⋊C4C2×D1311yescharacteristic
172C22×C42—131no—
173C22×C42—131no—
174C22×C42—131no—
175C2×C4⋊C8—262no—
176C2×C22⋊C8—132no—
177C2×C22⋊C8C2×D1312yes—
178C4×C4⋊C4—262no—
179C4×C4⋊C4—262no—
180C2×#95—131no—
181C2×#95—131no—
182#336—262no—
183#324—22no—
184#324—262no—
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—21no—
196C22×C13—21no—
197C22×C13#38011yescharacteristic
198C22×C13C2×C22⋊C811yescharacteristic
199C22×C13#40711yescharacteristic
200C22×C13C2×#9911yescharacteristic
201C22×C13#41011yescharacteristic
202C22×C13C2×#10111yescharacteristic
203C22×C13#41311yescharacteristic
204C22×C13C2×C4⋊C811yescharacteristic
205C22×C13#42311yescharacteristic
206C22×C13#43111yescharacteristic
207C22×C13#43211yescharacteristic
208C4×C13—24no—
209C4×C13—22no—
210C4×C13—22no—
211C4×C13—42no—
212Dic13—24no—
213Dic13—22no—
214Dic13—22no—
215Dic13—42no—
216Dic13—42no—
217C23×C4—131no—
218C23×C4—131no—
219C23×C4—131no—
220C23×C4—131no—
221C23×C4C4×D1311yescharacteristic
222C23×C4C4×D1311yescharacteristic
223C23×C4C22×D1311yescharacteristic
224C22×C8—22no—
225C22×C8—262no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—134no—
229C2×C4⋊C4—262no—
230C2×C4⋊C4—262no—
231C2×C4⋊C4Dic2612yes—
232C2×C4⋊C4C22⋊D1312yes—
233C2×C42—132no—
234C2×C42—132no—
235C2×C42—261no—
236C2×C42—261no—
237C2×C42—262no—
238C2×C42—262no—
239C2×C42—261no—
240C2×C42—261no—
241C2×C42—522no—
242C2×C42—522no—
243C4⋊C8—524no—
244C22⋊C8—22no—
245C22⋊C8—22no—
246C22⋊C8—262no—
247C22⋊C8—262no—
248#95—262no—
249#95—262no—
250C2×C13—21no—
251C2×C13—21no—
252C2×C13—21no—
253C2×C13—21no—
254C2×C13#145911yescharacteristic
255C2×C13#146111yescharacteristic
256C2×C13#146311yescharacteristic
257C2×C13#146411yescharacteristic
258C2×C13#179711yescharacteristic
259C2×C13#179911yescharacteristic
260C2×C13#180111yescharacteristic
261C24C2×C4×D1311yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—132no—
273C22×C4—131no—
274C22×C4—131no—
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—521no—
288C22×C4—521no—
289C22×C4—521no—
290C22×C4—521no—
291C22×C4—521no—
292C22×C4—521no—
293C22×C4C8×D1312yes—
294C22×C4#609412yes—
295C22×C4#610112yes—
296C22×C4#610112yes—
297C22×C4C2×Dic2611yescharacteristic
298C22×C4D4×D1312yes—
299C22×C4#612912yes—
300C22×C4C2×C22⋊D1311yescharacteristic
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—522no—
305C2×C8—522no—
306C2×C8—522no—
307C4⋊C4—24no—
308C4⋊C4—24no—
309C4⋊C4—268no—
310C42—264no—
311C42—264no—
312C42—264no—
313C42—522no—
314C42—522no—
315C42—522no—
316C13#856011yescharacteristic, complemented, Sylow
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23#8813111yescharacteristic
322C23C22⋊C4×D1311yescharacteristic
323C23C2×C8×D1311yescharacteristic
324C23C2×#609411yescharacteristic
325C23M16×D1311yescharacteristic
326C23M16×D1311yescharacteristic
327C23C2×#610111yescharacteristic
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—132no—
345C2×C4—132no—
346C2×C4—134no—
347C2×C4—264no—
348C2×C4—264no—
349C2×C4—262no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—262no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—262no—
356C2×C4—262no—
357C2×C4—522no—
358C2×C4—522no—
359C2×C4—522no—
360C2×C4—522no—
361C2×C4—521no—
362C2×C4—521no—
363C2×C4—521no—
364C2×C4—521no—
365C2×C4—522no—
366C2×C4—522no—
367C2×C4#8805414yescomplemented
368C2×C4#8813212yes—
369C2×C4#8819312yes—
370C8—82no—
371C8—1042no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22#1171837911yescharacteristic
385C22#1171838011yescharacteristic
386C22D13×C22⋊C811yescharacteristic
387C22#1171838711yescharacteristic
388C22#1171840111yescharacteristic
389C22D13×#9911yescharacteristic
390C22D13×#10111yescharacteristic
391C22#1171841211yescharacteristic
392C22#1171860311yescharacteristic
393C22C2×#8805411yescharacteristic
394C22#1171877911yescharacteristic
395C4—24no—
396C4—22no—
397C4—22no—
398C4—42no—
399C4—264no—
400C4—262no—
401C4—262no—
402C4—522no—
403C4—522no—
404C2—21no—
405C2—21no—
406C2—21no—
407C2—21no—
408C2#1311315311yescharacteristic
409C2#1311315811yescharacteristic
410C2#1311316411yescharacteristic
411C2#1311316911yescharacteristic
412C2#1311481411yescharacteristic
413C2#1311482211yescharacteristic
414C2#1311483011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC23×C13C22×C8
FrattiniC23×C4C22×D13
FittingC2×C13×#324C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC23×C4×C13C23
hypercenterC2×#324D13
hypocenterC13#8560
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
35. C2×C4⋊Dic13C8semidirect
142. C2×C4×C13C4⋊C8semidirect
316. C13#8560semidirect
367. C2×C4#88054semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic132
#131148142
C2×#117181202
#131126782
C2×C13×#3242
#856013