Finite Group Databasebeta

← #16799040

Subgroups — #16799040

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719067C211yesmaximal, characteristic
2C2×#11719067C211yesmaximal, characteristic
3C2×#11719129C211yesmaximal, characteristic
4C2×#11719062C211yesmaximal, characteristic
5#13130938C211yesmaximal, characteristic, complemented
6#13130938C211yesmaximal, characteristic, complemented
7#13130937C211yesmaximal, characteristic, complemented
8#13130936C211yesmaximal, characteristic, complemented
9#13130935C211yesmaximal, characteristic, complemented
10#13130935C211yesmaximal, characteristic, complemented
11#13130934C211yesmaximal, characteristic, complemented
12#13130933C211yesmaximal, characteristic, complemented
13#13130502C211yesmaximal, characteristic
14C2×#11718290C211yesmaximal, characteristic
15#13117315C211yesmaximal, characteristic
16C22×#6122C2211yescharacteristic
17C22×#6122C2211yescharacteristic
18C23×#1057C2211yescharacteristic
19C23×#1057C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C2×#88131C2211yescharacteristic
22C2×#88131C2211yescharacteristic
23#11719129—24no—
24C2×#88112C2211yescharacteristic
25C2×#88112C2211yescharacteristic
26C2×#88112C2211yescharacteristic
27C2×#88112C2211yescharacteristic
28C2×#88112C2211yescharacteristic
29C2×#88112C2211yescharacteristic
30C2×#88110C2211yescharacteristic
31C2×#88110C2211yescharacteristic
32C2×C4⋊#1057C2211yescharacteristic
33C2×C4⋊#1057C2211yescharacteristic
34C2×C4⋊#1057C2211yescharacteristic
35C2×C4⋊#1057C2211yescharacteristic
36C2×C4⋊#1057C2211yescharacteristic
37C2×C4⋊#1057C2211yescharacteristic
38C2×C4×#1057C2211yescharacteristic
39C2×C4×#1057C2211yescharacteristic
40#11719067—24no—
41#11719067—24no—
42#11719062—24no—
43C13×#385C411yescharacteristic
44#11718871C411yescharacteristic
45C4⋊C4×Dic13C2211yescharacteristic
46C4⋊C4×Dic13C2211yescharacteristic
47#11718633C411yescharacteristic
48#11718633C411yescharacteristic
49#11718611C411yescharacteristic
50#11718607C411yescharacteristic
51#11718310C2211yescharacteristic
52#11718310C2211yescharacteristic
53#11718308C411yescharacteristic
54#11718308C411yescharacteristic
55#11718290C2211yescharacteristic
56#11718290C2211yescharacteristic
57#11718290C2211yescharacteristic
58#11718290C2211yescharacteristic
59#11718290C2211yescharacteristic
60#11718290C2211yescharacteristic
61#11718290C2211yescharacteristic
62#11718290C2211yescharacteristic
63C23×C4×C13C2×C411yescharacteristic
64C23×Dic13C2×C411yescharacteristic
65C23×Dic13C2311yescharacteristic
66C2×#6122—22no—
67C2×#6122—22no—
68C2×#6122—22no—
69C2×#6122—22no—
70C2×#6122—22no—
71C2×#6122D414yes—
72C22×#1057—22no—
73C22×#1057—22no—
74C22×#1057—22no—
75C22×#1057—22no—
76C22×#1057—22no—
77C22×#1057Q814yes—
78C22×#1057C2311yescharacteristic
79C22×#1057C2311yescharacteristic
80C22×#1057C2311yescharacteristic
81C22×#1057C2311yescharacteristic
82C22×#1057C2311yescharacteristic
83C22×#1057C2311yescharacteristic
84C22×#1057C2311yescharacteristic
85C22×#1057C2311yescharacteristic
86C2×C13×C4⋊C4C2×C411yescharacteristic
87C2×C13×C4⋊C4C2×C411yescharacteristic
88C2×C13×C22⋊C4C2×C411yescharacteristic
89C2×C13×C22⋊C4C2×C411yescharacteristic
90C2×C22⋊Dic13C2×C411yescharacteristic
91C2×C22⋊Dic13C2×C411yescharacteristic
92C2×C4⋊Dic13C2×C411yescharacteristic
93C2×C4⋊Dic13C2×C411yescharacteristic
94C2×#6101C2×C411yescharacteristic
95C2×#6101C2×C411yescharacteristic
96C2×#6101C2×C411yescharacteristic
97C2×#6101C2×C411yescharacteristic
98C2×#6101C2×C411yescharacteristic
99C2×#6101C2×C411yescharacteristic
100C2×#6101C2×C411yescharacteristic
101C2×#6101C2×C411yescharacteristic
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13C2×C411yescharacteristic
105C2×C4×Dic13C2×C411yescharacteristic
106C2×C4×Dic13C2311yescharacteristic
107C2×C4×Dic13C2311yescharacteristic
108C2×C4×Dic13C2311yescharacteristic
109C2×C4×Dic13C2311yescharacteristic
110C2×C4×Dic13C2311yescharacteristic
111C2×C4×Dic13C2311yescharacteristic
112#88131—22no—
113#88131—22no—
114#88131D414yes—
115#88131Q814yes—
116#88112—22no—
117#88112—22no—
118#88112—22no—
119#88112—22no—
120#88112—22no—
121#88112—22no—
122#88110—22no—
123#88110—22no—
124C4⋊#1057—22no—
125C4⋊#1057—22no—
126C4⋊#1057—22no—
127C4⋊#1057—22no—
128C4⋊#1057—22no—
129C4⋊#1057—22no—
130C4×#1057—22no—
131C4×#1057—22no—
132C13×#95C2×C411yescharacteristic
133C13×#95C2×C411yescharacteristic
134#88071C2×C411yescharacteristic
135#88071C2×C411yescharacteristic
136#88071C2×C411yescharacteristic
137#88071C2×C411yescharacteristic
138#88071C2×C411yescharacteristic
139#88071C2×C411yescharacteristic
140#21148—131nomaximal, Sylow
141C24×C13C22×C411yescharacteristic
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—41no—
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C22×C411yescharacteristic
147C22×C4×C13C22×C411yescharacteristic
148C22×C4×C13C22×C411yescharacteristic
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C22×C411yescharacteristic
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—41no—
154C22×Dic13C22×C411yescharacteristic
155C22×Dic13C22×C411yescharacteristic
156C22×Dic13C22×C411yescharacteristic
157C22×Dic13C22×C411yescharacteristic
158C22×Dic13C22×C411yescharacteristic
159C22×Dic13C22×C411yescharacteristic
160C22×Dic13C22×C411yescharacteristic
161C22×Dic13C2×D412yes—
162C22×Dic13C2×D412yes—
163C22×Dic13C2×Q812yes—
164C22×Dic13C2×Q812yes—
165C22×Dic13#4112yes—
166C22×Dic13#4112yes—
167C22×Dic13C2411yescharacteristic
168#6122—28no—
169#6122—44no—
170C2×#1057—28no—
171C2×#1057—21no—
172C2×#1057—21no—
173C2×#1057—21no—
174C2×#1057—21no—
175C2×#1057—21no—
176C2×#1057—21no—
177C2×#1057—21no—
178C2×#1057—21no—
179C2×#1057—21no—
180C2×#1057—21no—
181C2×#1057—21no—
182C2×#1057—21no—
183C2×#1057—21no—
184C2×#1057—21no—
185C2×#1057—21no—
186C2×#1057—21no—
187C2×#1057—21no—
188C2×#1057—21no—
189C2×#1057—21no—
190C2×#1057—21no—
191C2×#1057—44no—
192C2×#1057C2×D412yes—
193C2×#1057C2×D412yes—
194C2×#1057C2×Q812yes—
195C2×#1057C2×Q812yes—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—41no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4C4⋊C414yes—
200C22⋊Dic13—22no—
201C22⋊Dic13C4⋊C414yes—
202C4⋊Dic13—22no—
203C4⋊Dic13—41no—
204#6101—22no—
205#6101—22no—
206#6101—22no—
207#6101—22no—
208#6101—41no—
209#6101—41no—
210#6101C4⋊C414yes—
211#6101C4⋊C414yes—
212C4×Dic13—22no—
213C4×Dic13—22no—
214C4×Dic13—21no—
215C4×Dic13—21no—
216C4×Dic13—21no—
217C4×Dic13—21no—
218C4×Dic13—21no—
219C4×Dic13—21no—
220C4×Dic13—21no—
221C4×Dic13—21no—
222C4×Dic13C2×D412yes—
223C4×Dic13C2×D412yes—
224C4×Dic13C2×Q812yes—
225C4×Dic13C2×Q812yes—
226C2×#424—131no—
227C2×#424—131no—
228C2×#423—131no—
229C2×#405—131no—
230#2296—131no—
231#1940—131no—
232#1940—131no—
233#1940—131no—
234#1940—131no—
235#1939—131no—
236#1939—131no—
237#1939—131no—
238#1939—131no—
239#1729—131no—
240C2×#336—131no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13C2×C4⋊C412yes—
246C23×C13C4×D412yes—
247C23×C13C4×Q812yes—
248C23×C13C23×C411yescharacteristic
249C2×C4×C13—21no—
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—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—44no—
265C2×C4×C13C2×C4⋊C412yes—
266C2×C4×C13C2×C4⋊C412yes—
267C2×C4×C13#13112yes—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—44no—
284C2×Dic13C2×C4⋊C412yes—
285C2×Dic13C2×C4⋊C412yes—
286C2×Dic13C2×C4⋊C412yes—
287C2×Dic13C4×D412yes—
288C2×Dic13C4×Q812yes—
289C2×Dic13#12114yes—
290C2×Dic13C22⋊Q814yes—
291C2×Dic13#12514yes—
292C2×Dic13C4⋊Q814yes—
293C2×Dic13#13112yes—
294C2×Dic13C22×D411yescharacteristic
295C2×Dic13C22×D411yescharacteristic
296C2×Dic13C22×Q811yescharacteristic
297C2×Dic13C22×Q811yescharacteristic
298C2×Dic13C2×#4111yescharacteristic
299C2×Dic13C2×#4111yescharacteristic
300#1057—22no—
301#1057—22no—
302#1057—22no—
303#1057—22no—
304#1057—41no—
305#1057—41no—
306#1057—41no—
307#1057—41no—
308C22×M16—131no—
309C22×M16—131no—
310C23×C8—131no—
311C23×C8—131no—
312C2×#117—131no—
313C2×#117—131no—
314C22×C42—131no—
315#424—264no—
316#424—264no—
317#423—264no—
318C2×C4⋊C8—131no—
319C2×C4⋊C8—131no—
320C2×C4⋊C8—131no—
321C2×C4⋊C8—131no—
322C2×C4⋊C8—131no—
323C2×C4⋊C8—131no—
324C2×C4⋊C8—131no—
325C2×C4⋊C8—131no—
326C2×C4⋊C8—131no—
327C2×C4⋊C8—131no—
328C2×C4⋊C8—131no—
329C2×C4⋊C8—131no—
330#405—264no—
331C2×#97—131no—
332C2×#97—131no—
333C2×C4×C8—131no—
334C2×C4×C8—131no—
335#389—131no—
336#389—131no—
337#389—131no—
338#389—131no—
339#385—131no—
340#385—131no—
341#385—131no—
342#385#26111yescharacteristic
343C4×C4⋊C4—131no—
344C4×C4⋊C4—131no—
345C4×C4⋊C4—131no—
346C4×C4⋊C4—131no—
347#336—131no—
348#336—131no—
349#336—131no—
350#336—131no—
351#336—131no—
352#336—131no—
353#336—131no—
354#336—131no—
355C22×C13—22no—
356C22×C13—22no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—22no—
360C22×C13—22no—
361C22×C13#38914yes—
362C22×C13C22×C4⋊C411yescharacteristic
363C22×C13C2×C4×D411yescharacteristic
364C22×C13C2×C4×Q811yescharacteristic
365C22×C13C2×#13111yescharacteristic
366C22×C13C2×#13111yescharacteristic
367C22×C13#56811yescharacteristic
368C22×C13#56811yescharacteristic
369C4×C13—22no—
370C4×C13—22no—
371C4×C13—22no—
372C4×C13—41no—
373C4×C13—41no—
374C4×C13—41no—
375Dic13—22no—
376Dic13—22no—
377Dic13—22no—
378Dic13—41no—
379Dic13—41no—
380Dic13—41no—
381Dic13#38914yes—
382Dic13C2×#12111yescharacteristic
383Dic13C2×C22⋊Q811yescharacteristic
384Dic13C2×#12511yescharacteristic
385Dic13C2×C4⋊Q811yescharacteristic
386C23×C4—131no—
387C23×C4—131no—
388C23×C4C2×#26111yescharacteristic
389C2×M16—134no—
390C2×M16—262no—
391C2×M16—262no—
392C2×M16—262no—
393C2×M16—262no—
394C2×M16—262no—
395C22×C8—131no—
396C22×C8—131no—
397C22×C8—134no—
398C22×C8—131no—
399C22×C8—131no—
400C22×C8—131no—
401C22×C8—131no—
402C22×C8—131no—
403C22×C8—131no—
404C22×C8—262no—
405C22×C8—262no—
406C22×C8—262no—
407C22×C8—262no—
408C22×C8—262no—
409#117—134no—
410#117—134no—
411#117—262no—
412#117—262no—
413C2×C4⋊C4—131no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—131no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4—131no—
420C2×C4⋊C4—131no—
421C2×C4⋊C4—131no—
422C2×C4⋊C4—131no—
423C2×C4⋊C4C2×#26111yescharacteristic
424C2×C4⋊C4C2×#26111yescharacteristic
425C2×C22⋊C4—131no—
426C2×C22⋊C4—131no—
427C2×C22⋊C4C2×#26111yescharacteristic
428C2×C22⋊C4C2×#26111yescharacteristic
429C2×C42—131no—
430C2×C42—131no—
431C2×C42—131no—
432C2×C42—131no—
433C2×C42—131no—
434C2×C42—131no—
435C2×C42—131no—
436C2×C42—131no—
437C2×C42—262no—
438C2×C42—262no—
439C4⋊C8—262no—
440C4⋊C8—262no—
441C4⋊C8—262no—
442C4⋊C8—262no—
443C4⋊C8—262no—
444C4⋊C8—262no—
445C4⋊C8—262no—
446C4⋊C8—262no—
447C4⋊C8—262no—
448C4⋊C8—262no—
449C4⋊C8—262no—
450C4⋊C8—262no—
451#97—262no—
452#97—262no—
453C4×C8—262no—
454C4×C8—262no—
455#95—131no—
456#95—131no—
457#95—131no—
458#95—131no—
459#95—131no—
460#95—131no—
461#95C2×#26111yescharacteristic
462#95C2×#26111yescharacteristic
463C2×C13—24no—
464C2×C13C2×#38911yescharacteristic
465C2×C13#290611yescharacteristic
466C2×C13#290611yescharacteristic
467C2×C13#293311yescharacteristic
468C2×C13#293311yescharacteristic
469C2×C13#296011yescharacteristic
470C2×C13#296111yescharacteristic
471C24C22×#26111yescharacteristic
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—41no—
475C22×C4—132no—
476C22×C4—132no—
477C22×C4—132no—
478C22×C4—132no—
479C22×C4—132no—
480C22×C4—132no—
481C22×C4—131no—
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—521no—
492C22×C4C22×#26111yescharacteristic
493C22×C4C22×#26111yescharacteristic
494C22×C4C22×#26111yescharacteristic
495C22×C4C22×#26111yescharacteristic
496C22×C4C22×#26111yescharacteristic
497C22×C4C22×#26111yescharacteristic
498M16—268no—
499M16—524no—
500C2×C8—132no—
501C2×C8—132no—
502C2×C8—132no—
503C2×C8—132no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—268no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—261no—
524C2×C8—261no—
525C2×C8—524no—
526C4⋊C4—22no—
527C4⋊C4—41no—
528C4⋊C4—134no—
529C4⋊C4—134no—
530C4⋊C4—262no—
531C4⋊C4—262no—
532C4⋊C4—262no—
533C4⋊C4—262no—
534C4⋊C4—262no—
535C4⋊C4—521no—
536C4⋊C4—521no—
537C4⋊C4—521no—
538C22⋊C4—22no—
539C22⋊C4—134no—
540C22⋊C4—262no—
541C22⋊C4C4⋊#26114yes—
542C42—132no—
543C42—132no—
544C42—132no—
545C42—132no—
546C42—261no—
547C42—261no—
548C42—261no—
549C42—261no—
550C42—261no—
551C42—262no—
552C42—261no—
553C42—262no—
554C42—261no—
555C42—261no—
556C13#2114811yescharacteristic, complemented, Sylow
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23C2×C4⋊#26112yes—
562C23D4×#26112yes—
563C23Q8×#26112yes—
564C23C23×#26111yescharacteristic
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—44no—
581C2×C4—134no—
582C2×C4—134no—
583C2×C4—134no—
584C2×C4—134no—
585C2×C4—131no—
586C2×C4—131no—
587C2×C4—132no—
588C2×C4—131no—
589C2×C4—131no—
590C2×C4—132no—
591C2×C4—131no—
592C2×C4—131no—
593C2×C4—132no—
594C2×C4—132no—
595C2×C4—132no—
596C2×C4—132no—
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—524no—
613C2×C4C2×C4⋊#26112yes—
614C2×C4C2×C4⋊#26112yes—
615C2×C4#8823812yes—
616C8—262no—
617C8—262no—
618C8—262no—
619C8—262no—
620C8—521no—
621C8—521no—
622C8—521no—
623C8—521no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22#1171908314yes—
631C22C22×C4⋊#26111yescharacteristic
632C22C2×#8823811yescharacteristic
633C22#1171962111yescharacteristic
634C22C2×D4×#26111yescharacteristic
635C22C2×Q8×#26111yescharacteristic
636C22D13⋊#13111yescharacteristic
637C22#1171962911yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—131no—
645C4—131no—
646C4—131no—
647C4—131no—
648C4—134no—
649C4—262no—
650C4—262no—
651C4—262no—
652C4—521no—
653C4—521no—
654C4—521no—
655C2—24no—
656C2C2×#1171908311yescharacteristic
657C2#1313148111yescharacteristic
658C2#1313148311yescharacteristic
659C2#1313156811yescharacteristic
660C2#1313157011yescharacteristic
661C2#1313162411yescharacteristic
662C2#1313162711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC13×#385C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenter#385#261
hypocenterC13#21148
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
5. #13130938C2semidirect
6. #13130938C2semidirect
7. #13130937C2semidirect
8. #13130936C2semidirect
9. #13130935C2semidirect
10. #13130935C2semidirect
11. #13130934C2semidirect
12. #13130933C2semidirect
556. C13#21148semidirect

Maximal subgroups

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

subgroupindex
C2×#117190672
C2×#117191292
C2×#117190622
#131309382
#131309372
#131309362
#131309352
#131309342
#131309332
#131305022
C2×#117182902
#131173152
#2114813