Finite Group Databasebeta

← #29690308

Subgroups — #29690308

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839727C211yesmaximal, characteristic
2#21448412C211yesmaximal, characteristic
3#21448408C211yesmaximal, characteristic
4#21446020C211yesmaximal, characteristic, complemented
5#21446017C211yesmaximal, characteristic, complemented
6#21446017C211yesmaximal, characteristic, complemented
7#21446016C211yesmaximal, characteristic, complemented
8#21446013C211yesmaximal, characteristic, complemented
9#21446008C211yesmaximal, characteristic, complemented
10#21446007C211yesmaximal, characteristic, complemented
11#21445851C211yesmaximal, characteristic, complemented
12#21445849C211yesmaximal, characteristic, complemented
13#21445847C211yesmaximal, characteristic, complemented
14#21445841C211yesmaximal, characteristic, complemented
15C61×#1853C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×#14519711C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26C2×#14519709C2211yescharacteristic
27C2×#14519708C2211yescharacteristic
28#16839727C418yescomplemented
29C2×C22⋊#92418C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32#16839667—21no—
33#16839666—21no—
34#16839663—21no—
35#16839662—21no—
36#16839641—21no—
37#16839641—21no—
38#16839640—21no—
39#16839638—21no—
40#16839622C2211yescharacteristic
41#16839619C2211yescharacteristic
42#16839619C2211yescharacteristic
43#16839619C2211yescharacteristic
44#16839619C2211yescharacteristic
45#16839619C2211yescharacteristic
46#16839619C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×#106×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C2×#11758222—41no—
61C2×#11758222—41no—
62C2×#11758222—41no—
63C2×#11758222—41no—
64C2×#11758222C2×C414yes—
65C2×#11758222Q814yes—
66C22×Dic122D411yescharacteristic
67C22×D244D411yescharacteristic
68C22×C22⋊D61D411yescharacteristic
69C22×C22⋊D61D411yescharacteristic
70C22×C4×D61—21no—
71C22×C4×D61C2311yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C2×#11758189—41no—
74C2×#11758189—41no—
75C2×#11758189C2×C414yescomplemented
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C2×C8×D61—41no—
79C2×C8×D61—41no—
80C2×C8×D61C2×C414yescomplemented
81#14519736—41no—
82#14519736—41no—
83#14519735—41no—
84#14519735—41no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C4⋊C4×D61—41no—
91C4⋊C4×D61—41no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103#14519711—41no—
104#14519710—41no—
105#14519710—41no—
106#14519710—41no—
107#14519709—41no—
108#14519708—41no—
109C22⋊#92418C2×C414yescomplemented
110#14519689C2×C414yescomplemented
111#14519689C2×C414yescomplemented
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C23×C4×C61—21no—
120C23×C4×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61—41no—
125C2×C4⋊C4×C61—41no—
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131#106×C61—41no—
132#106×C61—41no—
133C22⋊C8×C61C2×C414yescomplemented
134#95×C61—21no—
135C24×C61C2×D411yescharacteristic
136C23×D61C2×D411yescharacteristic
137C23×D61C2×D411yescharacteristic
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—42no—
147C22×C4×C61—81no—
148C22×C4×C61—81no—
149C22×C4×C61C22×C412yes—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×Q812yes—
152C22×C4×C61C2411yescharacteristic
153C2×C22⋊D61—41no—
154C2×C22⋊D61—41no—
155C2×C22⋊D61—41no—
156C2×C22⋊D61—41no—
157C2×C22⋊D61C4⋊C414yes—
158C2×C22⋊D61C4⋊C414yes—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165#11758222—44no—
166#11758222—44no—
167#11758222—44no—
168#11758222—44no—
169C2×D244—41no—
170C2×D244—41no—
171C2×D244C4⋊C414yes—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—42no—
181C2×C4×D61—81no—
182C2×C4×D61—81no—
183C2×C4×D61C22×C412yes—
184C2×C4×D61C22×C412yes—
185C2×C4×D61C2×Q812yes—
186C2×C4×D61C2×Q812yes—
187C2×Dic122—41no—
188C2×Dic122—41no—
189C2×Dic122C4⋊C414yes—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61C22×C412yes—
195C2×C8×C61C22×C412yes—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—42no—
205C22⋊C4×C61—81no—
206C22⋊Dic61—42no—
207C22⋊Dic61—81no—
208#11758198—42no—
209#11758198—81no—
210#11758198—81no—
211#11758198—81no—
212#11758198—81no—
213#11758198—81no—
214#11758198—81no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223#11758196—42no—
224C4×Dic61—42no—
225C4×Dic61—42no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418C22×C412yes—
231C2×#92418C22×C412yes—
232#11758189—44no—
233C8×D61—44no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61C2×C4⋊C412yes—
241C23×C61C22×D411yescharacteristic
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61C2×C4⋊C412yes—
255C22×D61C2×C4⋊C412yes—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—84no—
275C2×C4×C61C2×C4⋊C412yes—
276C2×C4×C61C23×C411yescharacteristic
277C2×C4×C61C22×Q811yescharacteristic
278C2×C4×C61H(5,𝔽2)11yescharacteristic
279C2×C4×C61H(5,𝔽2)11yescharacteristic
280C2×C4×C61H(5,𝔽2)11yescharacteristic
281C2×C4×C61H(5,𝔽2)11yescharacteristic
282C22⋊D61—44no—
283C22⋊D61—44no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61C2×C4⋊C412yes—
301C2×Dic61C2×C4⋊C412yes—
302D244—44no—
303C4×D61—22no—
304C4×D61—22no—
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—22no—
308C4×D61—22no—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—84no—
312Dic122—44no—
313C8×C61—22no—
314C8×C61—22no—
315#92418—22no—
316#92418—22no—
317#21945—611nomaximal, Sylow
318C22×C61—22no—
319C22×C61—22no—
320C22×C61—22no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61C22×C4⋊C411yescharacteristic
326C22×C61#53411yescharacteristic
327C22×C61#53411yescharacteristic
328C22×C61#57611yescharacteristic
329C22×C61#57711yescharacteristic
330C22×C61#57711yescharacteristic
331C22×C61#57811yescharacteristic
332C2×D61—22no—
333C2×D61—22no—
334C2×D61—22no—
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—41no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—41no—
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C4×C61—22no—
347C4×C61—81no—
348C4×C61—81no—
349C4×C61—81no—
350C4×C61—81no—
351C4×C61#51811yescharacteristic
352C4×C61#51811yescharacteristic
353C4×C61#54311yescharacteristic
354C4×C61#54311yescharacteristic
355Dic61—22no—
356Dic61—22no—
357Dic61—81no—
358Dic61—81no—
359Dic61—81no—
360Dic61—81no—
361C2×#408—611no—
362#2311—611no—
363#2311—611no—
364#1854—611no—
365#1854—611no—
366#1854—611no—
367#1854—611no—
368#1853—611no—
369#1853D6111yescharacteristic, complemented
370#1852—611no—
371#1852—611no—
372#1809—611no—
373#1809—611no—
374#1808—611no—
375#1807—611no—
376C2×C61—42no—
377C2×C61#231511yescharacteristic
378C2×C61#291211yescharacteristic
379C2×C61#291311yescharacteristic
380C2×C61#319811yescharacteristic
381C2×C61#319811yescharacteristic
382C2×C61#320111yescharacteristic
383C2×C61#320111yescharacteristic
384D61—42no—
385D61—42no—
386C22×#41—611no—
387C22×M16—611no—
388C23×C8—611no—
389C2×#117—611no—
390C2×#117—611no—
391C22×C4⋊C4—611no—
392C22×C4⋊C4C2×D6111yescharacteristic
393C2×#107—611no—
394C2×#107—611no—
395C2×#107—611no—
396C2×#107—611no—
397C2×#106—611no—
398C2×#106—611no—
399C2×#106C2×D6111yescharacteristic
400C2×#106C2×D6111yescharacteristic
401#408—618no—
402C2×C22⋊C8—611no—
403C2×C22⋊C8—611no—
404C2×C22⋊C8—611no—
405C2×C22⋊C8C2×D6111yescharacteristic
406#391—1221no—
407#391—1221no—
408#390—1221no—
409#390—1221no—
410#386—1221no—
411#386—1221no—
412#386—1221no—
413#386—1221no—
414#380—611no—
415#380—611no—
416#380—611no—
417#380—611no—
418#380—611no—
419#380—611no—
420#380—611no—
421#380C2×D6111yescharacteristic
422#340—611no—
423#340—611no—
424#340—611no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340C2×D6111yescharacteristic
429#340C2×D6111yescharacteristic
430C61#2194511yescharacteristic, complemented, Sylow
431C2×#41—614no—
432C2×#41—614no—
433C2×#41—2441no—
434C2×#41—2441no—
435C2×#41—2441no—
436C2×#41—2441no—
437C22×Q8—611no—
438C22×D4—611no—
439C22×D4—611no—
440C22×D4—611no—
441C23×C4—21no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—1221no—
445C23×C4C22×D6111yescharacteristic
446C2×M16—614no—
447C2×M16—2441no—
448C2×M16—2441no—
449C22×C8—611no—
450C22×C8—611no—
451C22×C8—614no—
452C22×C8—2441no—
453C22×C8—2441no—
454C22×C8C22×D6111yescharacteristic
455C22×C8C22×D6111yescharacteristic
456#117—2441no—
457#117—2441no—
458#117—2441no—
459#117—2441no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4—611no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—1221no—
468C2×C4⋊C4—2441no—
469C2×C4⋊C4—2441no—
470C2×C4⋊C4C22×D6111yescharacteristic
471C2×C4⋊C4C22×D6111yescharacteristic
472C2×C4⋊C4C22×D6111yescharacteristic
473C2×C4⋊C4C22×D6111yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—1221no—
476C2×C22⋊C4—1221no—
477C2×C22⋊C4—1221no—
478C2×C22⋊C4—1221no—
479C2×C22⋊C4—1221no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C42—1221no—
485C2×C42—1221no—
486#107—2441no—
487#107—2441no—
488#107—2441no—
489#107—2441no—
490#106—41no—
491#106—41no—
492#106—2441no—
493#106—2441no—
494C22⋊C8—614no—
495C22⋊C8—614no—
496C22⋊C8—614no—
497C22⋊C8C4×D6114yescomplemented
498#95—21no—
499#95—1221no—
500#95—1221no—
501#95—1221no—
502#95—1221no—
503#95—1221no—
504#95—1221no—
505#95—1221no—
506C24—611no—
507C24—611no—
508C24D4×D6111yescharacteristic
509#41—2444no—
510#41—2444no—
511#41—2444no—
512#41—2444no—
513C2×Q8—614no—
514C2×Q8—2441no—
515C2×Q8—2441no—
516C2×D4—614no—
517C2×D4—614no—
518C2×D4—614no—
519C2×D4—2441no—
520C2×D4—2441no—
521C2×D4—2441no—
522C2×D4—2441no—
523C2×D4—2441no—
524C2×D4—2441no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—612no—
539C22×C4—612no—
540C22×C4—612no—
541C22×C4—612no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—4881no—
555C22×C4—4881no—
556C22×C4—2442no—
557C22×C4C2×C4×D6112yes—
558C22×C4D4×D6111yescharacteristic
559C22×C4Q8×D6112yes—
560C22×C4C23×D6111yescharacteristic
561M16—2444no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—612no—
567C2×C8—612no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—2444no—
573C2×C8C2×C4×D6112yes—
574C2×C8C2×C4×D6112yes—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—1221no—
585C4⋊C4—1221no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—2442no—
593C22⋊C4—81no—
594C22⋊C4—4881no—
595C22⋊C4—4881no—
596C22⋊C4—4881no—
597C22⋊C4—4881no—
598C22⋊C4—4881no—
599C22⋊C4—4881no—
600C22⋊C4—4881no—
601C22⋊C4—2442no—
602C22⋊C4—2442no—
603C42—2442no—
604C42—2442no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—612no—
612C23—612no—
613C23—1221no—
614C23—1221no—
615C23—1221no—
616C23—1221no—
617C23—1221no—
618C23—1221no—
619C23—1221no—
620C23—1221no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23—1221no—
625C23C4⋊C4×D6112yes—
626C23C2×D4×D6111yescharacteristic
627Q8—2444no—
628D4—2444no—
629D4—2444no—
630D4—2444no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—612no—
651C2×C4—612no—
652C2×C4—1221no—
653C2×C4—1221no—
654C2×C4—1221no—
655C2×C4—1221no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—4884no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4C4⋊C4×D6112yes—
678C2×C4C22×C4×D6111yescharacteristic
679C2×C4C2×Q8×D6111yescharacteristic
680C2×C4#1451982211yescharacteristic
681C2×C4#1451982211yescharacteristic
682C2×C4#1451982311yescharacteristic
683C2×C4#1451982311yescharacteristic
684C8—22no—
685C8—22no—
686C8—1222no—
687C8—1222no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—1222no—
696C22—1222no—
697C22—1222no—
698C22—1222no—
699C22—1222no—
700C22—1222no—
701C22—2441no—
702C22—2441no—
703C22—2441no—
704C22—2441no—
705C22—2441no—
706C22—2441no—
707C22—2441no—
708C22—2441no—
709C22C2×C4⋊C4×D6111yescharacteristic
710C22#1684032211yescharacteristic
711C22#1684032311yescharacteristic
712C22#1684056611yescharacteristic
713C22#1684056811yescharacteristic
714C22#1684056811yescharacteristic
715C22#1684057811yescharacteristic
716C4—22no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4—81no—
721C4—1222no—
722C4—1222no—
723C4—4881no—
724C4—4881no—
725C4—4881no—
726C4—4881no—
727C4#1684023411yescharacteristic
728C4#1684023411yescharacteristic
729C4#1684038711yescharacteristic
730C4#1684038711yescharacteristic
731C2—42no—
732C2—2442no—
733C2—2442no—
734C2#2144843011yescharacteristic
735C2#2145441011yescharacteristic
736C2#2145441811yescharacteristic
737C2#2145667511yescharacteristic
738C2#2145667611yescharacteristic
739C2#2145669711yescharacteristic
740C2#2145670811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1853C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1853D61
hypocenterC61#21945
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
4. #21446020C2semidirect
5. #21446017C2semidirect
6. #21446017C2semidirect
7. #21446016C2semidirect
8. #21446013C2semidirect
9. #21446008C2semidirect
10. #21446007C2semidirect
11. #21445851C2semidirect
12. #21445849C2semidirect
13. #21445847C2semidirect
14. #21445841C2semidirect
15. C61×#1853C2semidirect
28. #16839727C4semidirect
75. C2×#11758189C2×C4semidirect
80. C2×C8×D61C2×C4semidirect
109. C22⋊#92418C2×C4semidirect
110. #14519689C2×C4semidirect
111. #14519689C2×C4semidirect
133. C22⋊C8×C61C2×C4semidirect
369. #1853D61semidirect
430. C61#21945semidirect
497. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397272
#214484122
#214484082
#214460202
#214460172
#214460162
#214460132
#214460082
#214460072
#214458512
#214458492
#214458472
#214458412
C61×#18532
#2194561