Finite Group Databasebeta

← #29699566

Subgroups — #29699566

Order 15616.

762 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448284C211yesmaximal, characteristic
2#21446435C211yesmaximal, characteristic, complemented
3#21446429C211yesmaximal, characteristic, complemented
4#21446384C211yesmaximal, characteristic, complemented
5#21446375C211yesmaximal, characteristic, complemented
6#21446112C211yesmaximal, characteristic
7#21445961C211yesmaximal, characteristic, complemented
8#21445888C211yesmaximal, characteristic, complemented
9#21445801C211yesmaximal, characteristic, complemented
10#21445600C211yesmaximal, characteristic, complemented
11#21445598C211yesmaximal, characteristic, complemented
12#21445587C211yesmaximal, characteristic, complemented
13#21445566C211yesmaximal, characteristic, complemented
14#21445517C211yesmaximal, characteristic, complemented
15C61×#1870C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C2×#14519736C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C2×#14519706C2211yescharacteristic
20C2×#14519706C2211yescharacteristic
21C2×C22⋊#92418C2211yescharacteristic
22C2×C22⋊#92418C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24C2×#14519687C2211yescharacteristic
25C2×#14519687C2211yescharacteristic
26C2×#14519687C2211yescharacteristic
27C2×C8×Dic61C2211yescharacteristic
28#16839665C411yescharacteristic
29#16839665C411yescharacteristic
30#16839661C411yescharacteristic
31#16839661C411yescharacteristic
32#16839655C411yescharacteristic
33#16839655C411yescharacteristic
34#16839655C411yescharacteristic
35#16839655C411yescharacteristic
36C4×C4⋊Dic61C2211yescharacteristic
37C4×C22⋊Dic61C2211yescharacteristic
38C4×C22⋊Dic61C2211yescharacteristic
39C42×Dic61C2211yescharacteristic
40#16839517C2211yescharacteristic
41#16839517C2211yescharacteristic
42#16839516C2211yescharacteristic
43#16839516C2211yescharacteristic
44#16839516C2211yescharacteristic
45#16839516C2211yescharacteristic
46#16839516C2211yescharacteristic
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C22×M16×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×#92418—22no—
60C22×#92418—22no—
61C22×#92418—41no—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519736—41no—
67#14519736—41no—
68#14519736—41no—
69#14519736—41no—
70C2×C4⋊Dic61C2×C411yescharacteristic
71C2×C4⋊Dic61C2×C411yescharacteristic
72C2×C4⋊Dic61C2×C411yescharacteristic
73C2×C4⋊Dic61C2×C411yescharacteristic
74C2×C4⋊Dic61C2×C411yescharacteristic
75C2×C4⋊Dic61C2×C411yescharacteristic
76C2×C22⋊Dic61C2×C411yescharacteristic
77C2×C22⋊Dic61C2×C411yescharacteristic
78C2×C22⋊Dic61C2×C411yescharacteristic
79C2×C22⋊Dic61C2×C411yescharacteristic
80C2×C22⋊Dic61C2×C411yescharacteristic
81C2×C22⋊Dic61C2×C411yescharacteristic
82C2×C22⋊Dic61C2×C411yescharacteristic
83C2×C22⋊Dic61C2×C411yescharacteristic
84C2×C4×Dic61C2×C411yescharacteristic
85C2×C4×Dic61C2×C411yescharacteristic
86C2×C4×Dic61C2×C411yescharacteristic
87C2×C4×Dic61C2×C411yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89C2×C4×Dic61C2311yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92#14519706—41no—
93#14519706—41no—
94C22⋊#92418—22no—
95C22⋊#92418—22no—
96C22⋊#92418—41no—
97#14519687—22no—
98#14519687—22no—
99#14519687—41no—
100C8×Dic61—41no—
101#14519684C2×C411yescharacteristic
102#14519684C2×C411yescharacteristic
103#14519684C2×C411yescharacteristic
104#14519684C2×C411yescharacteristic
105#14519684C2×C411yescharacteristic
106#14519684C2×C411yescharacteristic
107C22×D4×C61C2×C411yescharacteristic
108C23×C4×C61C2311yescharacteristic
109C23×C4×C61C2311yescharacteristic
110C2×M16×C61—22no—
111C2×M16×C61—22no—
112C2×M16×C61—41no—
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117C4×D4×C61—22no—
118C4×D4×C61—22no—
119C2×C4⋊C4×C61C2×C411yescharacteristic
120C2×C22⋊C4×C61C2×C411yescharacteristic
121C2×C22⋊C4×C61C2×C411yescharacteristic
122C2×C42×C61C2311yescharacteristic
123C22⋊C8×C61—22no—
124C22⋊C8×C61—22no—
125C22⋊C8×C61—41no—
126C24×C61C22×C411yescharacteristic
127C24×C61C22×C411yescharacteristic
128C2×D4×C61—22no—
129C2×D4×C61—22no—
130C2×D4×C61—41no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61#4112yes—
146C22×C4×C61#4112yes—
147C22×C4×C61C2411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156M16×C61—44no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61#4112yes—
169C4⋊C4×C61—22no—
170C22⋊C4×C61—22no—
171C22⋊C4×C61—22no—
172C42×C61—21no—
173C42×C61—21no—
174C22⋊Dic61—41no—
175C22⋊Dic61—41no—
176C22⋊Dic61—41no—
177C22⋊Dic61—41no—
178C22⋊Dic61—41no—
179C22⋊Dic61—41no—
180C22⋊Dic61—41no—
181C22⋊Dic61—41no—
182C4⋊Dic61—22no—
183C4⋊Dic61—41no—
184C4⋊Dic61—41no—
185C4⋊Dic61—41no—
186C4⋊Dic61—41no—
187C4⋊Dic61—41no—
188C4×Dic61—22no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—41no—
198C4×Dic61—41no—
199C4×Dic61—41no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—44no—
212C2×#92418#4112yes—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61#11712yes—
227C23×C61C23×C411yescharacteristic
228D4×C61—44no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61#11712yes—
248C2×C4×C61#13112yes—
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61H(5,𝔽2)11yescharacteristic
254C2×C4×C61H(5,𝔽2)11yescharacteristic
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C8×C61—22no—
280C8×C61—41no—
281C8×C61—41no—
282C8×C61—41no—
283#92418—22no—
284#92418—41no—
285#92418—41no—
286#92418—41no—
287#22790—611nomaximal, Sylow
288C22×C61—22no—
289C22×C61—22no—
290C22×C61—22no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61C2×#11711yescharacteristic
303C22×C61C4×#4111yescharacteristic
304C22×C61#51811yescharacteristic
305C22×C61C2×#13111yescharacteristic
306C22×C61#56811yescharacteristic
307C22×C61#56811yescharacteristic
308C22×C61#56811yescharacteristic
309C4×C61—22no—
310C4×C61—22no—
311C4×C61—41no—
312C4×C61—41no—
313C4×C61#55111yescharacteristic
314C4×C61#55111yescharacteristic
315C4×C61#55311yescharacteristic
316C4×C61#55311yescharacteristic
317Dic61—41no—
318Dic61—41no—
319Dic61—41no—
320Dic61—41no—
321Dic61—41no—
322Dic61—41no—
323Dic61—41no—
324Dic61—41no—
325#2293—611no—
326#1924—611no—
327#1924—611no—
328#1917—611no—
329#1916—611no—
330#1870D6111yescharacteristic
331#1869—611no—
332#1839—611no—
333#1818—611no—
334#1798—611no—
335#1753—611no—
336#1752—611no—
337#1750—611no—
338#1745—611no—
339#1729—611no—
340C2×C61—42no—
341C2×C61—81no—
342C2×C61#235311yescharacteristic
343C2×C61#292311yescharacteristic
344C2×C61#292411yescharacteristic
345C2×C61#296711yescharacteristic
346C2×C61#296911yescharacteristic
347C2×C61#298011yescharacteristic
348C2×C61#298111yescharacteristic
349C22×M16C2×D6111yescharacteristic
350C23×C8—611no—
351C2×C4×D4C2×D6111yescharacteristic
352C2×#117—611no—
353C2×#117—611no—
354C2×C4⋊C8—611no—
355C2×C4⋊C8—611no—
356C2×C22⋊C8—611no—
357C2×C22⋊C8—611no—
358C2×C22⋊C8—611no—
359C2×C22⋊C8C2×D6111yescharacteristic
360C2×C22⋊C8C2×D6111yescharacteristic
361C2×C22⋊C8C2×D6111yescharacteristic
362C2×#97—611no—
363C2×#97—611no—
364C2×#97—611no—
365C2×C4×C8—611no—
366#390—611no—
367#390—611no—
368#389—611no—
369#389—611no—
370#388—611no—
371#388—611no—
372#388—611no—
373#388—611no—
374C4×C4⋊C4—611no—
375C4×C22⋊C4—611no—
376C4×C22⋊C4—611no—
377C43—611no—
378#336—611no—
379#336—611no—
380#336—611no—
381#336—611no—
382#336—611no—
383#336—611no—
384#336—611no—
385#336—611no—
386#336—611no—
387#336—611no—
388#336—611no—
389#336—611no—
390#336C2×D6111yescharacteristic
391#336C2×D6111yescharacteristic
392C61#2279011yescharacteristic, complemented, Sylow
393C22×D4C4×D6111yescharacteristic
394C23×C4C22×D6111yescharacteristic
395C23×C4C22×D6111yescharacteristic
396C2×M16—22no—
397C2×M16—22no—
398C2×M16—41no—
399C22×C8—611no—
400C22×C8—611no—
401C22×C8—611no—
402C22×C8—611no—
403C22×C8—1222no—
404C22×C8—1222no—
405C22×C8—2441no—
406C22×C8C22×D6111yescharacteristic
407C22×C8C22×D6111yescharacteristic
408C22×C8C22×D6111yescharacteristic
409C22×C8C22×D6111yescharacteristic
410C4×D4—22no—
411C4×D4—22no—
412#117—2441no—
413#117—2441no—
414#117—2441no—
415#117—2441no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4C4×D6111yescharacteristic
423C2×C22⋊C4—611no—
424C2×C22⋊C4—611no—
425C2×C22⋊C4—611no—
426C2×C22⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4—611no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—611no—
431C2×C22⋊C4C4×D6111yescharacteristic
432C2×C22⋊C4C4×D6111yescharacteristic
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42C22×D6111yescharacteristic
442C4⋊C8—2441no—
443C4⋊C8—2441no—
444C22⋊C8—22no—
445C22⋊C8—22no—
446C22⋊C8—41no—
447C22⋊C8—1222no—
448C22⋊C8—1222no—
449C22⋊C8—2441no—
450#97—1222no—
451#97—1222no—
452#97—2441no—
453C4×C8—2441no—
454#95—611no—
455#95—611no—
456#95—611no—
457#95—611no—
458#95—611no—
459#95—611no—
460C24C2×C4×D6111yescharacteristic
461C24C2×C4×D6111yescharacteristic
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—41no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4C2×C4×D6111yescharacteristic
484C22×C4C2×C4×D6111yescharacteristic
485C22×C4C2×C4×D6111yescharacteristic
486C22×C4C2×C4×D6111yescharacteristic
487C22×C4#1175822412yes—
488C22×C4#1175822412yes—
489C22×C4C23×D6111yescharacteristic
490M16—44no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—612no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—2444no—
515C2×C8#1175822412yes—
516C4⋊C4—22no—
517C4⋊C4—1222no—
518C4⋊C4—2441no—
519C4⋊C4—2441no—
520C4⋊C4—2441no—
521C4⋊C4—2441no—
522C4⋊C4—2441no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—2441no—
526C22⋊C4—2441no—
527C22⋊C4—2441no—
528C22⋊C4—2441no—
529C22⋊C4—2441no—
530C22⋊C4—2441no—
531C22⋊C4—2441no—
532C22⋊C4—2441no—
533C42—21no—
534C42—21no—
535C42—1221no—
536C42—1221no—
537C42—1221no—
538C42—1221no—
539C42—1221no—
540C42—1221no—
541C42—1221no—
542C42—1221no—
543C42—1222no—
544C42—2441no—
545C42—2441no—
546C42—2441no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23#1451973312yes—
561C23C22×C4×D6111yescharacteristic
562D4—44no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4#1451973312yes—
606C2×C4#1451978512yes—
607C2×C4#41×D6111yescharacteristic
608C2×C4C2×#1175822411yescharacteristic
609C2×C4C2×#1175822411yescharacteristic
610C2×C4C2×#1175822411yescharacteristic
611C2×C4#1451982211yescharacteristic
612C2×C4#1451982311yescharacteristic
613C8—22no—
614C8—41no—
615C8—41no—
616C8—41no—
617C8—1222no—
618C8—2441no—
619C8—2441no—
620C8—2441no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#1451973311yescharacteristic
636C22C4×#1175822411yescharacteristic
637C22#1684023411yescharacteristic
638C22C2×#1451978511yescharacteristic
639C22#1684052711yescharacteristic
640C22#1684052711yescharacteristic
641C22#1684052811yescharacteristic
642C4—22no—
643C4—22no—
644C4—41no—
645C4—41no—
646C4—2441no—
647C4—2441no—
648C4—2441no—
649C4—2441no—
650C4—2441no—
651C4—2441no—
652C4—2441no—
653C4—2441no—
654C4#1684043511yescharacteristic
655C4#1684044311yescharacteristic
656C4#1684045511yescharacteristic
657C4#1684046411yescharacteristic
658C2—42no—
659C2—81no—
660C2#2144875711yescharacteristic
661C2#2145446611yescharacteristic
662C2#2145447911yescharacteristic
663C2#2145480111yescharacteristic
664C2#2145482611yescharacteristic
665C2#2145488711yescharacteristic
666C2#2145489611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1870C2
prime radicalC22×D4×C61C2×C4
cosocleC22×C4×C61C24
hypercenter#1870D61
hypocenterC61#22790
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #21446435C2semidirect
3. #21446429C2semidirect
4. #21446384C2semidirect
5. #21446375C2semidirect
7. #21445961C2semidirect
8. #21445888C2semidirect
9. #21445801C2semidirect
10. #21445600C2semidirect
11. #21445598C2semidirect
12. #21445587C2semidirect
13. #21445566C2semidirect
14. #21445517C2semidirect
392. C61#22790semidirect

Maximal subgroups

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

subgroupindex
#214482842
#214464352
#214464292
#214463842
#214463752
#214461122
#214459612
#214458882
#214458012
#214456002
#214455982
#214455872
#214455662
#214455172
C61×#18702
#2279061