Finite Group Databasebeta

← #15755585

Subgroups — #15755585

Order 3328.

682 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6101C211yesmaximal, characteristic
2#13114816C211yesmaximal, characteristic
3C2×#11718061C212yesmaximal
4#13112678C212yesmaximal
5C13×#1797C211yesmaximal, characteristic
6C22×C42×C13C2211yescharacteristic
7C22×#6101C411yescharacteristic
8C22×#6101C2211yescharacteristic
9C22×C4×Dic13C411yescharacteristic
10C22×C4×Dic13C411yescharacteristic
11C2×C13×C4⋊C8—21no—
12C2×C13×C22⋊C8C2212yes—
13C2×#88071C411yescharacteristic
14C2×#88071C2211yescharacteristic
15C2×C22⋊#1055C2212yes—
16C4×#6101—21no—
17C4×#6101—21no—
18C4×#6101—21no—
19C4×#6101—21no—
20C2×C4⋊#1055—21no—
21C13×#336—21no—
22#11718116—21no—
23#11718061—24no—
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C23×Dic13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C23×Dic13C2×C411yescharacteristic
31C22×C8×C13—22no—
32C2×C42×C13—42no—
33C2×C42×C13D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—22no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101C814yescomplemented
45C2×#6101D412yes—
46C2×#6101Q812yes—
47C2×C4×Dic13—21no—
48C2×C4×Dic13—21no—
49C2×C4×Dic13—22no—
50C2×C4×Dic13—22no—
51C2×C4×Dic13—21no—
52C2×C4×Dic13—21no—
53C2×C4×Dic13—42no—
54C22×#1055—22no—
55C13×C4⋊C8—42no—
56C13×C22⋊C8—22no—
57C13×C22⋊C8—22no—
58#88071—21no—
59#88071—21no—
60#88071—21no—
61#88071—21no—
62C22⋊#1055—22no—
63C22⋊#1055—22no—
64C4⋊#1055—42no—
65#8560—131nomaximal, Sylow
66C24×C13C22×C411yescharacteristic
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C2×C812yes—
80C22×C4×C13M1612yes—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×Q811yescharacteristic
85C22×C4×C13#4111yescharacteristic
86C22×C4×C13#4111yescharacteristic
87C22×Dic13—21no—
88C22×Dic13—21no—
89C22×Dic13—21no—
90C22×Dic13—21no—
91C22×Dic13—21no—
92C22×Dic13—21no—
93C22×Dic13—21no—
94C22×Dic13—21no—
95C22×Dic13—21no—
96C22×Dic13—21no—
97C22×Dic13—41no—
98C22×Dic13—41no—
99C22×Dic13—41no—
100C22×Dic13—41no—
101C22×Dic13—41no—
102C22×Dic13—41no—
103C22×Dic13C4⋊C412yes—
104C22×Dic13C4⋊C412yes—
105C22×Dic13C2×C812yes—
106C22×Dic13C2×C812yes—
107C22×Dic13M1612yes—
108C22×Dic13M1612yes—
109C2×C8×C13—42no—
110C2×C8×C13—42no—
111C2×C8×C13—42no—
112C42×C13—22no—
113C42×C13—22no—
114C42×C13—41no—
115C42×C13—41no—
116#6101—24no—
117#6101—24no—
118#6101—22no—
119#6101—22no—
120#6101—22no—
121#6101—22no—
122C4×Dic13—24no—
123C4×Dic13—24no—
124C4×Dic13—42no—
125C4×Dic13—42no—
126C2×#1055—42no—
127C2×#1055—42no—
128C2×#1055—42no—
129C2×C4×C4⋊C4—131no—
130#1797—131no—
131#1797D1311yescharacteristic
132C2×#324—132no—
133#1280—132no—
134C23×C13—21no—
135C23×C13—21no—
136C23×C13—21no—
137C23×C13—21no—
138C23×C13C2×C22⋊C411yescharacteristic
139C23×C13C2×C4⋊C411yescharacteristic
140C23×C13#11711yescharacteristic
141C23×C13C22×C811yescharacteristic
142C23×C13C2×M1611yescharacteristic
143C23×C13C2×M1611yescharacteristic
144C23×C13C2×M1611yescharacteristic
145C2×C4×C13—24no—
146C2×C4×C13—24no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13C22⋊C812yes—
166C2×C4×C13C22⋊C812yes—
167C2×C4×C13#9912yes—
168C2×C4×C13#10112yes—
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13#12111yescharacteristic
171C2×C4×C13C22⋊Q811yescharacteristic
172C2×C4×C13C22⋊Q811yescharacteristic
173C2×Dic13—22no—
174C2×Dic13—22no—
175C2×Dic13—22no—
176C2×Dic13—22no—
177C2×Dic13—22no—
178C2×Dic13—22no—
179C2×Dic13—22no—
180C2×Dic13—22no—
181C2×Dic13—22no—
182C2×Dic13—42no—
183C2×Dic13—42no—
184C2×Dic13—42no—
185C2×Dic13—41no—
186C2×Dic13—41no—
187C2×Dic13—41no—
188C2×Dic13—41no—
189C2×Dic13—41no—
190C2×Dic13—41no—
191C2×Dic13—42no—
192C2×Dic13—42no—
193C2×Dic13—42no—
194C2×Dic13C4⋊C814yescomplemented
195C8×C13—82no—
196#1055—82no—
197C22×C4⋊C4—131no—
198C22×C4⋊C4—131no—
199C22×C42—131no—
200C22×C42—131no—
201C22×C42C2×D1311yescharacteristic
202C2×C4⋊C8—21no—
203C2×C4⋊C8—261no—
204C2×C22⋊C8—132no—
205C2×C22⋊C8C2×D1312yes—
206C4×C4⋊C4—261no—
207C4×C4⋊C4—261no—
208C4×C4⋊C4—261no—
209C4×C4⋊C4—261no—
210C2×#95—131no—
211C2×#95—131no—
212#336—21no—
213#336—261no—
214#324—264no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13#38011yescharacteristic
228C22×C13C2×C22⋊C811yescharacteristic
229C22×C13#40711yescharacteristic
230C22×C13C2×#9911yescharacteristic
231C22×C13#41011yescharacteristic
232C22×C13C2×#10111yescharacteristic
233C22×C13#41311yescharacteristic
234C22×C13C2×C4⋊C811yescharacteristic
235C22×C13#42311yescharacteristic
236C22×C13#43111yescharacteristic
237C22×C13#43211yescharacteristic
238C4×C13—21no—
239C4×C13—21no—
240C4×C13—21no—
241C4×C13—21no—
242C4×C13—22no—
243C4×C13—22no—
244C4×C13—22no—
245C4×C13—22no—
246Dic13—24no—
247Dic13—42no—
248Dic13—42no—
249Dic13—42no—
250C23×C4—131no—
251C23×C4—131no—
252C23×C4—131no—
253C23×C4—131no—
254C23×C4C4×D1311yescharacteristic
255C23×C4C4×D1311yescharacteristic
256C23×C4C22×D1311yescharacteristic
257C22×C8—22no—
258C22×C8—262no—
259C2×C4⋊C4—134no—
260C2×C4⋊C4—132no—
261C2×C4⋊C4—132no—
262C2×C4⋊C4—262no—
263C2×C4⋊C4—261no—
264C2×C4⋊C4—261no—
265C2×C4⋊C4—261no—
266C2×C4⋊C4—261no—
267C2×C4⋊C4—261no—
268C2×C4⋊C4—261no—
269C2×C42—42no—
270C2×C42—262no—
271C2×C42—262no—
272C2×C42—261no—
273C2×C42—261no—
274C2×C42—261no—
275C2×C42—261no—
276C2×C42—522no—
277C2×C42D5211yescharacteristic
278C2×C42D5211yescharacteristic
279C2×C42C22⋊D1311yescharacteristic
280C2×C42C22⋊D1311yescharacteristic
281C4⋊C8—42no—
282C4⋊C8—522no—
283C22⋊C8—22no—
284C22⋊C8—22no—
285C22⋊C8—262no—
286C22⋊C8—262no—
287#95—261no—
288#95—261no—
289#95—261no—
290#95—261no—
291C2×C13—21no—
292C2×C13—21no—
293C2×C13—21no—
294C2×C13—21no—
295C2×C13#145911yescharacteristic
296C2×C13#146111yescharacteristic
297C2×C13#146311yescharacteristic
298C2×C13#146411yescharacteristic
299C2×C13#179711yescharacteristic
300C2×C13#179911yescharacteristic
301C2×C13#180111yescharacteristic
302C24C2×C4×D1311yescharacteristic
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—132no—
312C22×C4—132no—
313C22×C4—132no—
314C22×C4—132no—
315C22×C4—132no—
316C22×C4—132no—
317C22×C4—261no—
318C22×C4—261no—
319C22×C4—261no—
320C22×C4—261no—
321C22×C4—261no—
322C22×C4—261no—
323C22×C4—261no—
324C22×C4—261no—
325C22×C4—261no—
326C22×C4—261no—
327C22×C4—521no—
328C22×C4—521no—
329C22×C4—521no—
330C22×C4—521no—
331C22×C4—521no—
332C22×C4—521no—
333C22×C4C8×D1312yes—
334C22×C4#609412yes—
335C22×C4#610311yescharacteristic
336C22×C4#610311yescharacteristic
337C22×C4#610311yescharacteristic
338C22×C4#610311yescharacteristic
339C22×C4C2×D5211yescharacteristic
340C22×C4D4×D1311yescharacteristic
341C22×C4#612911yescharacteristic
342C22×C4Q8×D1311yescharacteristic
343C22×C4#613111yescharacteristic
344C22×C4C2×C22⋊D1311yescharacteristic
345C2×C8—42no—
346C2×C8—42no—
347C2×C8—42no—
348C2×C8—522no—
349C2×C8—522no—
350C2×C8—522no—
351C4⋊C4—262no—
352C4⋊C4—262no—
353C4⋊C4—262no—
354C4⋊C4—262no—
355C4⋊C4—264no—
356C4⋊C4—264no—
357C42—22no—
358C42—22no—
359C42—41no—
360C42—41no—
361C42—264no—
362C42—264no—
363C42—522no—
364C42—522no—
365C13#856011yescharacteristic, complemented, Sylow
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23C4⋊C4×D1311yescharacteristic
371C23#8814611yescharacteristic
372C23C2×C8×D1311yescharacteristic
373C23C2×#609411yescharacteristic
374C23M16×D1311yescharacteristic
375C23M16×D1311yescharacteristic
376C23C2×#610311yescharacteristic
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—134no—
398C2×C4—262no—
399C2×C4—262no—
400C2×C4—262no—
401C2×C4—262no—
402C2×C4—262no—
403C2×C4—262no—
404C2×C4—262no—
405C2×C4—262no—
406C2×C4—262no—
407C2×C4—522no—
408C2×C4—522no—
409C2×C4—522no—
410C2×C4—521no—
411C2×C4—521no—
412C2×C4—521no—
413C2×C4—521no—
414C2×C4—521no—
415C2×C4—521no—
416C2×C4—522no—
417C2×C4—522no—
418C2×C4—522no—
419C2×C4#8804612yes—
420C2×C4#8806012yes—
421C2×C4#8806012yes—
422C2×C4#8806412yes—
423C2×C4#8814911yescharacteristic
424C2×C4#8815111yescharacteristic
425C2×C4#8819211yescharacteristic
426C2×C4#8820011yescharacteristic
427C8—82no—
428C8—1042no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22D13×C4⋊C811yescharacteristic
442C22#1171849411yescharacteristic
443C22#1171849611yescharacteristic
444C22#1171849811yescharacteristic
445C22C2×#8804611yescharacteristic
446C22#1171864811yescharacteristic
447C22#1171866711yescharacteristic
448C22C2×#8806011yescharacteristic
449C22#1171878711yescharacteristic
450C22#1171879311yescharacteristic
451C22C2×#8806411yescharacteristic
452C4—22no—
453C4—22no—
454C4—22no—
455C4—22no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—264no—
461C4—522no—
462C4—522no—
463C4—522no—
464C2—21no—
465C2—21no—
466C2—21no—
467C2—21no—
468C2#1311315211yescharacteristic
469C2#1311315911yescharacteristic
470C2#1311316511yescharacteristic
471C2#1311316811yescharacteristic
472C2#1311481311yescharacteristic
473C2#1311482111yescharacteristic
474C2#1311482911yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC23×C13C22×C8
FrattiniC23×C4C22×D13
FittingC13×#1797C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC23×C4×C13C23
hypercenter#1797D13
hypocenterC13#8560
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
44. C2×#6101C8semidirect
194. C2×Dic13C4⋊C8semidirect
365. C13#8560semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#61012
#131148162
C2×#117180612
#131126782
C13×#17972
#856013