Finite Group Databasebeta

← #15865828

Subgroups — #15865828

Order 3328.

906 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718366C211yesmaximal, characteristic, complemented
2C2×#11718658C211yesmaximal, characteristic, complemented
3#13117273C211yesmaximal, characteristic
4#13115447C211yesmaximal, characteristic, complemented
5#13115440C211yesmaximal, characteristic, complemented
6#13115398C211yesmaximal, characteristic, complemented
7#13115391C211yesmaximal, characteristic, complemented
8#13115131C211yesmaximal, characteristic
9#13115126C211yesmaximal, characteristic
10#13115018C211yesmaximal, characteristic, complemented
11#13115013C211yesmaximal, characteristic, complemented
12#13114696C211yesmaximal, characteristic, complemented
13C4×#88060C211yesmaximal, characteristic, complemented
14#13114587C211yesmaximal, characteristic, complemented
15C13×#1750C211yesmaximal, characteristic, complemented
16C2×C13×#117C2211yescharacteristic
17C2×C4×C22⋊D13C2211yescharacteristic
18C22×#6099C2211yescharacteristic
19C23×#1055C2211yescharacteristic
20C2×C42×D13C2211yescharacteristic
21C2×C13×C22⋊C8C2211yescharacteristic
22C2×C13×C22⋊C8C2211yescharacteristic
23C2×C13×#97C2211yescharacteristic
24C2×C4×C8×C13C2211yescharacteristic
25C4×C22⋊Dic13C2211yescharacteristic
26C2×#88060C2211yescharacteristic
27C2×#88060C2211yescharacteristic
28C2×#88060C2211yescharacteristic
29C2×#88060C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33C2×#88054C2211yescharacteristic
34#11718658—24no—
35#11718650C411yescharacteristic
36#11718650C411yescharacteristic
37#11718639C411yescharacteristic
38#11718639C411yescharacteristic
39#11718617C411yescharacteristic
40#11718617C411yescharacteristic
41#11718605C411yescharacteristic
42#11718605C411yescharacteristic
43C4×#6103C2211yescharacteristic
44#11718593C2211yescharacteristic
45C4×#6101C2211yescharacteristic
46C2×#88043C2211yescharacteristic
47C2×#88043C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718366—24no—
51C13×#336C2211yescharacteristic
52C13×#336C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13C2×C411yescharacteristic
63C22×C4×D13C2×C411yescharacteristic
64C22×C4×D13C2×C411yescharacteristic
65C22×C4×D13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C13×#117—22no—
71C13×#117—22no—
72C2×C13×C4⋊C4C2×C411yescharacteristic
73C2×C13×C4⋊C4C2×C411yescharacteristic
74C2×C13×C22⋊C4C2×C411yescharacteristic
75C2×C13×C22⋊C4C2×C411yescharacteristic
76C2×C42×C13C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×C22⋊Dic13C2×C411yescharacteristic
79C2×C22⋊Dic13C2×C411yescharacteristic
80C2×C22⋊Dic13C2×C411yescharacteristic
81C4×C22⋊D13—22no—
82C4×C22⋊D13—22no—
83C2×#6103C2×C411yescharacteristic
84C2×#6103C2×C411yescharacteristic
85C2×#6103C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×#6101C2×C411yescharacteristic
89C2×C4×Dic13C2×C411yescharacteristic
90C2×C4×Dic13C2×C411yescharacteristic
91C2×C4×Dic13C2311yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C2×#6099—22no—
95C2×#6099—22no—
96C2×#6099—22no—
97C22×#1055—22no—
98C22×#1055—22no—
99C22×#1055—22no—
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C42×D13—22no—
105C42×D13—22no—
106C13×C22⋊C8—22no—
107C13×C22⋊C8—22no—
108C13×#97—22no—
109C4×C8×C13—22no—
110#88071C2×C411yescharacteristic
111#88071C2×C411yescharacteristic
112#88071C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115#88071C2×C411yescharacteristic
116#88071C2×C411yescharacteristic
117#88071C2×C411yescharacteristic
118#88071C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120#88060—22no—
121#88060—22no—
122#88060—22no—
123#88060—22no—
124#88054—22no—
125#88054—22no—
126#88054—22no—
127#88054—22no—
128#88043—22no—
129#88043D414yescomplemented
130C4×#1055—22no—
131C4×#1055—22no—
132#21112—131nomaximal, Sylow
133C24×C13C22×C411yescharacteristic
134C23×D13C22×C411yescharacteristic
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C22×C411yescharacteristic
142C22×C4×C13C22×C411yescharacteristic
143C22×C4×C13C22×C411yescharacteristic
144C22×C4×C13#4112yes—
145C22×C4×C13#4112yes—
146C22×C4×C13C2411yescharacteristic
147C2×C22⋊D13—22no—
148C2×C22⋊D13—22no—
149C2×C22⋊D13—41no—
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C22×Dic13C22×C411yescharacteristic
153C22×Dic13C22×C411yescharacteristic
154C22×Dic13C22×C411yescharacteristic
155C22×Dic13C22×C411yescharacteristic
156C22×Dic13C22×C411yescharacteristic
157C2×C4×D13—22no—
158C2×C4×D13—22no—
159C2×C4×D13—22no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C4×D13—22no—
167C2×C4×D13—41no—
168C2×C4×D13—41no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—21no—
180C2×C8×C13—21no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C22⋊C4—22no—
184C13×C22⋊C4—22no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13C2×D412yes—
188C42×C13#4112yes—
189C22⋊Dic13—22no—
190C22⋊Dic13—22no—
191C22⋊Dic13—41no—
192#6103—22no—
193#6103—22no—
194#6103—41no—
195#6101—22no—
196#6101—22no—
197#6101—41no—
198C4×Dic13—22no—
199C4×Dic13—22no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13—21no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13—21no—
206#6099—28no—
207C2×#1055—28no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055C2×D412yes—
217C2×#1055C2×D412yes—
218C2×#1055#4112yes—
219C2×#1055#4112yes—
220C2×#432—131no—
221C2×#405—131no—
222#2290—131no—
223#1924—131no—
224#1923—131no—
225#1917—131no—
226#1916—131no—
227#1870—131no—
228#1869—131no—
229#1851—131no—
230#1850—131no—
231#1768—131no—
232#1750D1311yescharacteristic, complemented
233C4×C22⋊C8—131no—
234#1746—131no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13#11712yes—
242C23×C13C23×C411yescharacteristic
243C22×D13—21no—
244C22×D13—21no—
245C22×D13—21no—
246C22×D13—21no—
247C22×D13—21no—
248C22×D13—21no—
249C22×D13#13112yes—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13#11712yes—
267C2×C4×C13C4×D412yes—
268C2×C4×C13C4×D412yes—
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C22⋊D13—44no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—21no—
284C2×Dic13—21no—
285C2×Dic13—21no—
286C2×Dic13—21no—
287C2×Dic13—21no—
288C2×Dic13—21no—
289C2×Dic13—21no—
290C2×Dic13—21no—
291C2×Dic13—21no—
292C2×Dic13—21no—
293C2×Dic13—21no—
294C2×Dic13—21no—
295C2×Dic13—21no—
296C2×Dic13#13112yes—
297C4×D13—44no—
298C4×D13—44no—
299C4×D13—41no—
300C4×D13—41no—
301C4×D13—41no—
302C4×D13—41no—
303C8×C13—41no—
304C8×C13—41no—
305C8×C13—41no—
306C8×C13—41no—
307#1055—22no—
308#1055—22no—
309#1055—22no—
310#1055—22no—
311C22×M16—131no—
312C23×C8—131no—
313C2×C4×D4—131no—
314C2×#117C2×D1311yescharacteristic
315C22×C42—131no—
316#432—264no—
317C2×C4⋊C8—131no—
318C2×C4⋊C8—131no—
319C2×C4⋊C8—131no—
320C2×C4⋊C8—131no—
321C2×C22⋊C8—131no—
322C2×C22⋊C8—131no—
323C2×C22⋊C8—131no—
324C2×C22⋊C8—131no—
325C2×C22⋊C8C2×D1311yescharacteristic
326C2×C22⋊C8C2×D1311yescharacteristic
327#405—264no—
328C2×#97—131no—
329C2×#97—131no—
330C2×#97C2×D1311yescharacteristic
331C2×C4×C8—131no—
332C2×C4×C8—131no—
333C2×C4×C8C2×D1311yescharacteristic
334#388—131no—
335#388—131no—
336#387—131no—
337#387—131no—
338#386—131no—
339#386—131no—
340#385—131no—
341#385—131no—
342C4×C4⋊C4—131no—
343C4×C22⋊C4—131no—
344C4×C22⋊C4—131no—
345#376—131no—
346#336—131no—
347#336—131no—
348#336—131no—
349#336—131no—
350#336—131no—
351#336—131no—
352#336—131no—
353#336—131no—
354#336C2×D1311yescharacteristic
355#336C2×D1311yescharacteristic
356C22×C13—22no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—41no—
363C22×C13C2×#11711yescharacteristic
364C22×C13C2×C4×D411yescharacteristic
365C22×C13C4×#4111yescharacteristic
366C22×C13C2×#13111yescharacteristic
367C22×C13C2×#13111yescharacteristic
368C22×C13#56811yescharacteristic
369C22×C13#56811yescharacteristic
370C2×D13—22no—
371C2×D13—22no—
372C2×D13—22no—
373C2×D13—41no—
374C2×D13—41no—
375C2×D13—41no—
376C2×D13—41no—
377C4×C13—22no—
378C4×C13—22no—
379C4×C13—22no—
380C4×C13—41no—
381C4×C13—41no—
382C4×C13#52511yescharacteristic
383C4×C13#52511yescharacteristic
384C4×C13#52911yescharacteristic
385C4×C13#52911yescharacteristic
386Dic13—22no—
387Dic13—41no—
388Dic13—41no—
389Dic13—41no—
390Dic13—41no—
391Dic13—41no—
392Dic13—41no—
393C22×D4—131no—
394C23×C4—131no—
395C23×C4—131no—
396C23×C4—131no—
397C23×C4C22×D1311yescharacteristic
398C2×M16—262no—
399C2×M16—262no—
400C2×M16—262no—
401C22×C8—131no—
402C22×C8—131no—
403C22×C8—131no—
404C22×C8—131no—
405C22×C8—262no—
406C22×C8—262no—
407C22×C8—262no—
408C22×C8C22×D1311yescharacteristic
409C22×C8C22×D1311yescharacteristic
410C22×C8C22×D1311yescharacteristic
411C22×C8C22×D1311yescharacteristic
412C4×D4—262no—
413C4×D4—262no—
414#117—22no—
415#117—22no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—131no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4C4×D1311yescharacteristic
420C2×C4⋊C4C4×D1311yescharacteristic
421C2×C22⋊C4—131no—
422C2×C22⋊C4—131no—
423C2×C22⋊C4—131no—
424C2×C22⋊C4—131no—
425C2×C22⋊C4—131no—
426C2×C22⋊C4—131no—
427C2×C22⋊C4C4×D1311yescharacteristic
428C2×C22⋊C4C4×D1311yescharacteristic
429C2×C42—131no—
430C2×C42—131no—
431C2×C42—131no—
432C2×C42—131no—
433C2×C42—131no—
434C2×C42—262no—
435C2×C42—262no—
436C2×C42C22×D1311yescharacteristic
437C2×C42C22×D1311yescharacteristic
438C4⋊C8—262no—
439C4⋊C8—262no—
440C4⋊C8—262no—
441C4⋊C8—262no—
442C22⋊C8—22no—
443C22⋊C8—22no—
444C22⋊C8—262no—
445C22⋊C8—262no—
446C22⋊C8—262no—
447C22⋊C8—262no—
448#97—22no—
449#97—134no—
450#97—262no—
451C4×C8—22no—
452C4×C8—262no—
453C4×C8—262no—
454#95—131no—
455#95—131no—
456#95—131no—
457#95—131no—
458#95—131no—
459#95—131no—
460#95—131no—
461#95—131no—
462#95—131no—
463#95—131no—
464C2×C13—42no—
465C2×C13#229011yescharacteristic
466C2×C13#292411yescharacteristic
467C2×C13#292511yescharacteristic
468C2×C13#293311yescharacteristic
469C2×C13#293311yescharacteristic
470C2×C13#296611yescharacteristic
471C2×C13#296711yescharacteristic
472D13—42no—
473C24—131no—
474C24C2×C4×D1311yescharacteristic
475C2×D4—262no—
476C2×D4—262no—
477C2×D4—521no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—131no—
485C22×C4—131no—
486C22×C4—131no—
487C22×C4—131no—
488C22×C4—131no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—261no—
494C22×C4—261no—
495C22×C4—261no—
496C22×C4—261no—
497C22×C4—261no—
498C22×C4—261no—
499C22×C4—521no—
500C22×C4—521no—
501C22×C4C2×C4×D1311yescharacteristic
502C22×C4C2×C4×D1311yescharacteristic
503C22×C4C2×C4×D1311yescharacteristic
504C22×C4C2×C4×D1311yescharacteristic
505C22×C4C2×C4×D1311yescharacteristic
506C22×C4#612712yes—
507C22×C4#612712yes—
508C22×C4C23×D1311yescharacteristic
509M16—268no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—132no—
523C2×C8—132no—
524C2×C8—132no—
525C2×C8—132no—
526C2×C8—268no—
527C2×C8—261no—
528C2×C8—261no—
529C2×C8—261no—
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8—261no—
534C2×C8—261no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—262no—
538C4⋊C4—262no—
539C4⋊C4—521no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—262no—
543C22⋊C4—262no—
544C22⋊C4—262no—
545C22⋊C4—262no—
546C22⋊C4—521no—
547C22⋊C4—521no—
548C42—21no—
549C42—21no—
550C42—262no—
551C42—262no—
552C42—261no—
553C42—261no—
554C42—261no—
555C42—261no—
556C42—261no—
557C42—261no—
558C42D4×D1312yes—
559C42#612912yes—
560C13#2111211yescharacteristic, complemented, Sylow
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—132no—
568C23—261no—
569C23—261no—
570C23—261no—
571C23—261no—
572C23—261no—
573C23—261no—
574C23#8812612yes—
575C23C22×C4×D1311yescharacteristic
576D4—524no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—132no—
594C2×C4—261no—
595C2×C4—261no—
596C2×C4—261no—
597C2×C4—261no—
598C2×C4—261no—
599C2×C4—261no—
600C2×C4—261no—
601C2×C4—261no—
602C2×C4—261no—
603C2×C4—261no—
604C2×C4—261no—
605C2×C4—261no—
606C2×C4—261no—
607C2×C4—261no—
608C2×C4—261no—
609C2×C4—261no—
610C2×C4—261no—
611C2×C4—261no—
612C2×C4—261no—
613C2×C4—261no—
614C2×C4—524no—
615C2×C4—524no—
616C2×C4—521no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4#8812612yes—
621C2×C4#8813512yes—
622C2×C4#8813512yes—
623C2×C4C2×#612711yescharacteristic
624C2×C4C2×#612711yescharacteristic
625C2×C4C2×D4×D1311yescharacteristic
626C2×C4C2×#612911yescharacteristic
627C2×C4#41×D1311yescharacteristic
628C2×C4#41×D1311yescharacteristic
629C8—41no—
630C8—41no—
631C8—41no—
632C8—41no—
633C8—262no—
634C8—262no—
635C8—262no—
636C8—262no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—262no—
645C22—262no—
646C22—262no—
647C22—521no—
648C22—521no—
649C22—521no—
650C22—521no—
651C22C2×#8812611yescharacteristic
652C22C2×#8813511yescharacteristic
653C22#1171922711yescharacteristic
654C22D13×#13111yescharacteristic
655C22D13×#13111yescharacteristic
656C22#1171945511yescharacteristic
657C22#1171945511yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—41no—
662C4—41no—
663C4—262no—
664C4—521no—
665C4—521no—
666C4—521no—
667C4—521no—
668C4—521no—
669C4—521no—
670C4#1171924311yescharacteristic
671C4#1171924311yescharacteristic
672C4#1171925211yescharacteristic
673C4#1171925211yescharacteristic
674C2—42no—
675C2—522no—
676C2#1311727511yescharacteristic
677C2#1312349111yescharacteristic
678C2#1312350011yescharacteristic
679C2#1312356611yescharacteristic
680C2#1312356611yescharacteristic
681C2#1312380911yescharacteristic
682C2#1312381911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1750C2
prime radicalC22×C22⋊D13C2×C4
cosocleC22×C4×C13C24
hypercenter#1750D13
hypocenterC13#21112
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
1. C2×#11718366C2semidirect
2. C2×#11718658C2semidirect
4. #13115447C2semidirect
5. #13115440C2semidirect
6. #13115398C2semidirect
7. #13115391C2semidirect
10. #13115018C2semidirect
11. #13115013C2semidirect
12. #13114696C2semidirect
13. C4×#88060C2semidirect
14. #13114587C2semidirect
15. C13×#1750C2semidirect
129. #88043D4semidirect
232. #1750D13semidirect
560. C13#21112semidirect

Maximal subgroups

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

subgroupindex
C2×#117183662
C2×#117186582
#131172732
#131154472
#131154402
#131153982
#131153912
#131151312
#131151262
#131150182
#131150132
#131146962
C4×#880602
#131145872
C13×#17502
#2111213