Finite Group Databasebeta

← #29700084

Subgroups — #29700084

Order 15616.

732 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
1#21448278C211yesmaximal, characteristic
2#21446615C211yesmaximal, characteristic
3#21446615C211yesmaximal, characteristic
4#21446430C211yesmaximal, characteristic, complemented
5#21446429C211yesmaximal, characteristic, complemented
6#21446423C211yesmaximal, characteristic, complemented
7#21446422C211yesmaximal, characteristic, complemented
8#21445934C211yesmaximal, characteristic, complemented
9#21445889C211yesmaximal, characteristic, complemented
10#21445692C211yesmaximal, characteristic, complemented
11#21445690C211yesmaximal, characteristic, complemented
12#21445671C211yesmaximal, characteristic, complemented
13#21445585C211yesmaximal, characteristic, complemented
14#21445584C211yesmaximal, characteristic, complemented
15C61×#1818C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊D61C2211yescharacteristic
17C2×#14519734C2211yescharacteristic
18C2×#14519706C2211yescharacteristic
19C2×#14519706C2211yescharacteristic
20C2×#14519706C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×C22⋊#92418C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24C2×#14519689C2211yescharacteristic
25C2×#14519689C2211yescharacteristic
26C2×#14519689C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519688C2211yescharacteristic
29C2×#14519687C2211yescharacteristic
30C2×#14519687C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic
33C2×C8×Dic61C2211yescharacteristic
34#16839662C411yescharacteristic
35#16839662C411yescharacteristic
36#16839657C411yescharacteristic
37#16839657C411yescharacteristic
38#16839656C411yescharacteristic
39#16839656C411yescharacteristic
40#16839652C411yescharacteristic
41#16839652C411yescharacteristic
42C4×#11758196C2211yescharacteristic
43C4×#11758198C2211yescharacteristic
44C4×C22⋊Dic61C2211yescharacteristic
45C42×Dic61C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#117×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C61×#336C2211yescharacteristic
56C61×#336C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×C22⋊D61C2×C411yescharacteristic
60C22×C4×D61C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C4×C22⋊D61—22no—
66C4×C22⋊D61—22no—
67#14519734—41no—
68#14519734—41no—
69C2×#11758196C2×C411yescharacteristic
70C2×#11758196C2×C411yescharacteristic
71C2×#11758196C2×C411yescharacteristic
72C2×#11758196C2×C411yescharacteristic
73C2×#11758196C2×C411yescharacteristic
74C2×C22⋊Dic61C2×C411yescharacteristic
75C2×C22⋊Dic61C2×C411yescharacteristic
76C2×C22⋊Dic61C2×C411yescharacteristic
77C2×#11758198C2×C411yescharacteristic
78C2×#11758198C2×C411yescharacteristic
79C2×#11758198C2×C411yescharacteristic
80C2×#11758198C2×C411yescharacteristic
81C2×#11758198C2×C411yescharacteristic
82C2×C4×Dic61C2×C411yescharacteristic
83C2×C4×Dic61C2×C411yescharacteristic
84C2×C4×Dic61C2×C411yescharacteristic
85C2×C4×Dic61C2×C411yescharacteristic
86C2×C4×Dic61C2311yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89#14519706—22no—
90#14519706—22no—
91#14519706—22no—
92#14519706—22no—
93C22⋊#92418—22no—
94C22⋊#92418—22no—
95#14519689—22no—
96#14519689—22no—
97#14519689—41no—
98#14519689—41no—
99#14519688—41no—
100#14519687—22no—
101#14519687—22no—
102#14519687—41no—
103C4×#92418—41no—
104C8×Dic61—41no—
105#14519684C2×C411yescharacteristic
106#14519684C2×C411yescharacteristic
107#14519684C2×C411yescharacteristic
108#14519684C2×C411yescharacteristic
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111C23×C4×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116#117×C61—41no—
117#117×C61—41no—
118C2×C4⋊C4×C61C2×C411yescharacteristic
119C2×C4⋊C4×C61C2×C411yescharacteristic
120C2×C22⋊C4×C61C2×C411yescharacteristic
121C2×C22⋊C4×C61C2×C411yescharacteristic
122C2×C42×C61C2311yescharacteristic
123C2×C42×C61C2311yescharacteristic
124C22⋊C8×C61—41no—
125C22⋊C8×C61—41no—
126C24×C61C22×C411yescharacteristic
127C23×D61C22×C411yescharacteristic
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C2411yescharacteristic
140C2×C22⋊D61—22no—
141C2×C22⋊D61—41no—
142C2×C22⋊D61—41no—
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C8×C61—21no—
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—
168C4⋊C4×C61—41no—
169C4⋊C4×C61—41no—
170C22⋊C4×C61—41no—
171C22⋊C4×C61—41no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61—21no—
176C22⋊Dic61—22no—
177C22⋊Dic61—22no—
178C22⋊Dic61—41no—
179#11758198—22no—
180#11758198—22no—
181#11758198—41no—
182#11758198—41no—
183#11758198—41no—
184#11758196—22no—
185#11758196—41no—
186#11758196—41no—
187#11758196—41no—
188#11758196—41no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—22no—
194C4×Dic61—41no—
195C4×Dic61—41no—
196C4×Dic61—41no—
197C4×Dic61#4112yes—
198C4×Dic61#4112yes—
199C2×#92418—21no—
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#4112yes—
210C2×#92418#4112yes—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61C23×C411yescharacteristic
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61H(5,𝔽2)11yescharacteristic
250C2×C4×C61H(5,𝔽2)11yescharacteristic
251C22⋊D61—44no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
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#11712yes—
271C2×Dic61#11712yes—
272C2×Dic61#13112yes—
273C4×D61—41no—
274C4×D61—41no—
275C4×D61—41no—
276C4×D61—41no—
277C8×C61—41no—
278C8×C61—41no—
279C8×C61—41no—
280C8×C61—41no—
281#92418—22no—
282#92418—22no—
283#92418—41no—
284#92418—41no—
285#22838—611nomaximal, Sylow
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61C2×#11711yescharacteristic
294C22×C61C4×#4111yescharacteristic
295C22×C61#51811yescharacteristic
296C22×C61C2×#13111yescharacteristic
297C22×C61#56811yescharacteristic
298C22×C61#56811yescharacteristic
299C22×C61#56811yescharacteristic
300C2×D61—41no—
301C2×D61—41no—
302C2×D61—41no—
303C2×D61—41no—
304C2×D61—41no—
305C2×D61—41no—
306C2×D61—41no—
307C4×C61—41no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—41no—
312C4×C61#55311yescharacteristic
313C4×C61#55311yescharacteristic
314C4×C61#55911yescharacteristic
315C4×C61#55911yescharacteristic
316Dic61—22no—
317Dic61—22no—
318Dic61—22no—
319Dic61—41no—
320Dic61—41no—
321Dic61—41no—
322Dic61—41no—
323#2293—611no—
324#1955—611no—
325#1955—611no—
326#1924—611no—
327#1924—611no—
328#1923—611no—
329#1923—611no—
330#1831—611no—
331#1818—611no—
332#1818D6111yescharacteristic, complemented
333#1771—611no—
334#1771—611no—
335#1767—611no—
336#1750—611no—
337#1750—611no—
338C2×C61—81no—
339C2×C61#235711yescharacteristic
340C2×C61#292111yescharacteristic
341C2×C61#292511yescharacteristic
342C2×C61#296711yescharacteristic
343C2×C61#296811yescharacteristic
344C2×C61#298011yescharacteristic
345C2×C61#298111yescharacteristic
346D61—81no—
347C2×C4×D4—611no—
348C2×#117—611no—
349C2×#117C2×D6111yescharacteristic
350C2×C4⋊C8—611no—
351C2×C4⋊C8—611no—
352C2×C4⋊C8—611no—
353C2×C4⋊C8—611no—
354C2×C22⋊C8—611no—
355C2×C22⋊C8—611no—
356C2×C22⋊C8—611no—
357C2×C22⋊C8—611no—
358C2×C22⋊C8—611no—
359C2×C22⋊C8—611no—
360C2×C22⋊C8C2×D6111yescharacteristic
361C2×C22⋊C8C2×D6111yescharacteristic
362C2×#97—611no—
363C2×#97—611no—
364C2×#97—611no—
365C2×#97—611no—
366C2×C4×C8—611no—
367C2×C4×C8—611no—
368#390—611no—
369#390—611no—
370#389—611no—
371#389—611no—
372#388—611no—
373#388—611no—
374#388—611no—
375#388—611no—
376C4×C4⋊C4—611no—
377C4×C22⋊C4—611no—
378C4×C22⋊C4—611no—
379C43—611no—
380#336—611no—
381#336—611no—
382#336—611no—
383#336—611no—
384#336—611no—
385#336—611no—
386#336C2×D6111yescharacteristic
387#336C2×D6111yescharacteristic
388#336C2×D6111yescharacteristic
389#336C2×D6111yescharacteristic
390C61#2283811yescharacteristic, complemented, Sylow
391C22×D4—611no—
392C23×C4—611no—
393C23×C4C22×D6111yescharacteristic
394C22×C8—611no—
395C22×C8—611no—
396C22×C8—611no—
397C22×C8—611no—
398C22×C8C22×D6111yescharacteristic
399C22×C8C22×D6111yescharacteristic
400C22×C8C22×D6111yescharacteristic
401C22×C8C22×D6111yescharacteristic
402C4×D4—1222no—
403C4×D4—1222no—
404#117—41no—
405#117—41no—
406#117—2441no—
407#117—2441no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4C4×D6111yescharacteristic
414C2×C4⋊C4C4×D6111yescharacteristic
415C2×C22⋊C4—611no—
416C2×C22⋊C4—611no—
417C2×C22⋊C4—611no—
418C2×C22⋊C4—611no—
419C2×C22⋊C4—611no—
420C2×C22⋊C4—611no—
421C2×C22⋊C4—611no—
422C2×C22⋊C4—611no—
423C2×C22⋊C4C4×D6111yescharacteristic
424C2×C22⋊C4C4×D6111yescharacteristic
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42C22×D6111yescharacteristic
433C2×C42C22×D6111yescharacteristic
434C4⋊C8—1222no—
435C4⋊C8—1222no—
436C4⋊C8—1222no—
437C4⋊C8—1222no—
438C22⋊C8—41no—
439C22⋊C8—41no—
440C22⋊C8—1222no—
441C22⋊C8—1222no—
442C22⋊C8—1222no—
443C22⋊C8—1222no—
444C22⋊C8—2441no—
445C22⋊C8—2441no—
446#97—1222no—
447#97—1222no—
448#97—2441no—
449#97—2441no—
450C4×C8—2441no—
451C4×C8—2441no—
452#95—611no—
453#95—611no—
454#95—611no—
455#95—611no—
456#95—611no—
457#95—611no—
458C24—611no—
459C24C2×C4×D6111yescharacteristic
460C2×D4—1222no—
461C2×D4—2441no—
462C2×D4—2441no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4C2×C4×D6111yescharacteristic
483C22×C4C2×C4×D6111yescharacteristic
484C22×C4C2×C4×D6111yescharacteristic
485C22×C4C2×C4×D6111yescharacteristic
486C22×C4C2×C4×D6111yescharacteristic
487C22×C4C23×D6111yescharacteristic
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
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—612no—
501C2×C8—612no—
502C2×C8—1221no—
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—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—1222no—
515C4⋊C4—2441no—
516C4⋊C4—2441no—
517C4⋊C4—2441no—
518C4⋊C4—2441no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—1222no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—2441no—
526C22⋊C4—2441no—
527C22⋊C4—2441no—
528C22⋊C4—2441no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—612no—
534C42—612no—
535C42—1222no—
536C42—1221no—
537C42—1221no—
538C42—1221no—
539C42—1221no—
540C42—2441no—
541C42—2441no—
542C42—2441no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—1221no—
551C23—1221no—
552C23—1221no—
553C23—1221no—
554C23—1221no—
555C23—1221no—
556C23—1221no—
557C23C22×C4×D6111yescharacteristic
558D4—2444no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
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—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—612no—
579C2×C4—612no—
580C2×C4—612no—
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—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4#41×D6111yescharacteristic
604C2×C4#41×D6111yescharacteristic
605C2×C4#41×D6111yescharacteristic
606C2×C4#41×D6111yescharacteristic
607C2×C4#1451982211yescharacteristic
608C2×C4#1451982211yescharacteristic
609C8—41no—
610C8—41no—
611C8—41no—
612C8—41no—
613C8—1222no—
614C8—1222no—
615C8—2441no—
616C8—2441no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—2441no—
625C22—2441no—
626C22—2441no—
627C22—2441no—
628C22—2441no—
629C22—2441no—
630C22—2441no—
631C22#117×D6111yescharacteristic
632C22#1684023011yescharacteristic
633C22#1684023511yescharacteristic
634C22#131×D6111yescharacteristic
635C22#1684052711yescharacteristic
636C22#1684052711yescharacteristic
637C22#1684052711yescharacteristic
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—1222no—
644C4—1222no—
645C4—1222no—
646C4—2441no—
647C4—2441no—
648C4—2441no—
649C4—2441no—
650C4#1684045711yescharacteristic
651C4#1684045711yescharacteristic
652C4#1684049611yescharacteristic
653C4#1684049611yescharacteristic
654C2—81no—
655C2—4881no—
656C2#2144878711yescharacteristic
657C2#2145445311yescharacteristic
658C2#2145448211yescharacteristic
659C2#2145480211yescharacteristic
660C2#2145481111yescharacteristic
661C2#2145488811yescharacteristic
662C2#2145489211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1818C2
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1818D61
hypocenterC61#22838
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1818

Complements

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

NH ≅ G/Ntype
4. #21446430C2semidirect
5. #21446429C2semidirect
6. #21446423C2semidirect
7. #21446422C2semidirect
8. #21445934C2semidirect
9. #21445889C2semidirect
10. #21445692C2semidirect
11. #21445690C2semidirect
12. #21445671C2semidirect
13. #21445585C2semidirect
14. #21445584C2semidirect
15. C61×#1818C2semidirect
332. #1818D61semidirect
390. C61#22838semidirect

Maximal subgroups

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

subgroupindex
#214482782
#214466152
#214464302
#214464292
#214464232
#214464222
#214459342
#214458892
#214456922
#214456902
#214456712
#214455852
#214455842
C61×#18182
#2283861