Finite Group Databasebeta

← #29697148

Subgroups — #29697148

Order 15616.

1218 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#102×D61C211yesmaximal, characteristic
2#21448684C211yesmaximal, characteristic, complemented
3D4×#11758198C211yesmaximal, characteristic
4#21446502C211yesmaximal, characteristic, complemented
5#21446500C211yesmaximal, characteristic, complemented
6#21446439C211yesmaximal, characteristic, complemented
7#21446437C211yesmaximal, characteristic, complemented
8#21446066C211yesmaximal, characteristic, complemented
9#21446064C211yesmaximal, characteristic, complemented
10#21445904C211yesmaximal, characteristic, complemented
11#21445847C211yesmaximal, characteristic, complemented
12#21445748C211yesmaximal, characteristic
13#102×Dic61C211yesmaximal, characteristic, complemented
14C8×#11758198C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×#14519734—21no—
20C2×C4⋊C4×D61C2211yescharacteristic
21C22×#11758198—21no—
22C2×#14519710C2211yescharacteristic, complemented
23C2×#14519710C2211yescharacteristic, complemented
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30#102×D61C418yescomplemented
31C2×#14519689C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic, complemented
33#16839664C2211yescharacteristic
34#16839663C2211yescharacteristic
35#16839660C2211yescharacteristic, complemented
36#16839658C2211yescharacteristic, complemented
37#16839646—21no—
38#16839644—21no—
39#16839641—21no—
40#16839639—21no—
41#16839624—21no—
42#16839619C2211yescharacteristic
43#16839619C2211yescharacteristic
44#16839617—21no—
45C4⋊C4×Dic61C2211yescharacteristic, complemented
46C4×#11758198C2211yescharacteristic
47#16839525C2211yescharacteristic, complemented
48#16839525C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C2×C4×D4×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×C4×C8×C61C2211yescharacteristic, complemented
57C4×C4⋊C4×C61C2211yescharacteristic, complemented
58C61×#340C2211yescharacteristic, complemented
59C61×#340C2211yescharacteristic, complemented
60C24×D61—21no—
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C2×D4×D61—22no—
64C2×D4×D61—22no—
65C2×D4×D61—22no—
66C2×D4×D61—41no—
67C2×D4×D61—41no—
68C2×D4×D61C2×C414yes—
69C23×Dic61—21no—
70C22×C4×D61—21no—
71C22×C4×D61C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C2×C8×D61—41no—
75C2×C8×D61—41no—
76C2×C8×D61C2×C414yescomplemented
77D4×Dic61—22no—
78D4×Dic61—41no—
79#14519734—44no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C4⋊C4×D61—22no—
87C4⋊C4×D61C2×C414yescomplemented
88C2×C22⋊Dic61—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—44no—
96C2×#11758198D411yescharacteristic
97C2×#11758198D411yescharacteristic
98C2×C4×Dic61—21no—
99C2×C4×Dic61C2311yescharacteristic
100#14519710—41no—
101#14519710—41no—
102#14519699—41no—
103#14519699C2×C414yescomplemented
104#14519698—22no—
105#14519698C2×C414yes—
106#14519697—41no—
107#14519697C2×C414yescomplemented
108#14519689—22no—
109C8×Dic61—41no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684D411yescharacteristic
116#14519684D411yescharacteristic
117C22×D4×C61C2311yescharacteristic
118C23×C4×C61—21no—
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C4×D4×C61—22no—
122C4×D4×C61—41no—
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C22⋊C4×C61—21no—
127C2×C42×C61—21no—
128C2×C42×C61C2311yescharacteristic
129#102×C61—22no—
130#102×C61C2×C414yes—
131C4×C8×C61—41no—
132#95×C61—21no—
133C24×C61—21no—
134C23×D61—21no—
135C23×D61—24no—
136C23×D61—42no—
137C23×D61—42no—
138C23×D61—42no—
139C23×D61—42no—
140C23×D61—81no—
141C23×D61—81no—
142C23×D61C2×D411yescharacteristic
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61C22×C412yes—
147C2×D4×C61#4112yes—
148C2×D4×C61#4112yes—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—42no—
153C22×C4×C61—42no—
154C22×C4×C61—81no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2411yescharacteristic
158C2×C22⋊D61—24no—
159C2×C22⋊D61—42no—
160C2×C22⋊D61—42no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—42no—
165C22×Dic61—42no—
166C22×Dic61—81no—
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170D4×D61—28no—
171D4×D61—44no—
172D4×D61—44no—
173D4×D61—44no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244C22×C412yes—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—24no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61C22×C412yes—
188C2×C4×D61#4112yes—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61C22×C412yes—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61C22×C412yes—
201C22⋊C4×C61—42no—
202C42×C61—21no—
203C42×C61—21no—
204C42×C61—42no—
205C22⋊Dic61—42no—
206#11758198—22no—
207#11758198—42no—
208#11758198—42no—
209#11758198—42no—
210#11758198—42no—
211#11758198—81no—
212#11758198—81no—
213#11758198D814yes—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61C22×C412yes—
220#11758196—24no—
221#11758196—42no—
222#11758196—42no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—42no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418C22×C412yes—
232C8×D61—44no—
233C23×C61—22no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61C22×D411yescharacteristic
241C22×D61—21no—
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—22no—
246C22×D61—48no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—48no—
254C22×D61—84no—
255C22×D61—84no—
256C22×D61—84no—
257C22×D61—84no—
258C22×D61—84no—
259C22×D61C4×D412yes—
260C22×D61C2×D812yes—
261C22×D61#13512yes—
262D4×C61—22no—
263D4×C61—22no—
264D4×C61—22no—
265D4×C61#11714yescomplemented
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—22no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—84no—
281C2×C4×C61C2×D812yes—
282C2×C4×C61C23×C411yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61H(5,𝔽2)11yescharacteristic
287C2×C4×C61H(5,𝔽2)11yescharacteristic
288C22⋊D61—48no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—22no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—84no—
306C2×Dic61C4×D412yes—
307C2×Dic61C2×D812yes—
308D244—22no—
309D244—22no—
310D244—41no—
311D244—41no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—48no—
317C8×C61—22no—
318C8×C61—41no—
319#92418—22no—
320#92418—41no—
321#22570—611nomaximal, Sylow
322C22×C61—24no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61—42no—
326C22×C61—42no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61C2×C4×D411yescharacteristic
330C22×C61#54611yescharacteristic
331C22×C61#54611yescharacteristic
332C22×C61C22×D811yescharacteristic
333C22×C61C2×#13511yescharacteristic
334C22×C61#57711yescharacteristic
335C22×C61#57711yescharacteristic
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—816no—
346C2×D61—81no—
347C2×D61—81no—
348C2×D61—81no—
349C2×D61—81no—
350C2×D61C4×D814yes—
351C4×C61—22no—
352C4×C61—42no—
353C4×C61—41no—
354C4×C61—81no—
355C4×C61—81no—
356C4×C61C2×#11711yescharacteristic
357C4×C61#51811yescharacteristic
358C4×C61#55111yescharacteristic
359C4×C61#55111yescharacteristic
360Dic61—22no—
361Dic61—22no—
362Dic61—42no—
363Dic61—41no—
364Dic61—81no—
365Dic61—81no—
366C22×#102—611no—
367#2344—611no—
368D4×C22⋊C4—611no—
369#1934—611no—
370#1934—611no—
371#1925—611no—
372#1925—611no—
373#1862—611no—
374#1862—611no—
375#1823—611no—
376#1808—611no—
377#1786—611no—
378C4×#102—611no—
379C4×#102D6111yescharacteristic, complemented
380C8×C22⋊C4—611no—
381C2×C61—44no—
382C2×C61#234211yescharacteristic
383C2×C61C2×C4×D811yescharacteristic
384C2×C61#294911yescharacteristic
385C2×C61#329411yescharacteristic
386C2×C61#329411yescharacteristic
387C2×C61#329611yescharacteristic
388C2×C61#329611yescharacteristic
389D61—24no—
390D61—82no—
391C23×D4—611no—
392C23×C8—611no—
393C2×C4×D4—611no—
394C2×C4×D4C2×D6111yescharacteristic
395C2×#117—1221no—
396C22×C4⋊C4—611no—
397C22×C22⋊C4—1221no—
398C2×#107—611no—
399C2×#107—611no—
400C2×#102—611no—
401C2×#102—611no—
402C2×#102—611no—
403C2×#102—618no—
404C2×#102—611no—
405C2×#102—611no—
406C2×#102—611no—
407C2×#102C2×D6111yescharacteristic
408C2×#102C2×D6111yescharacteristic
409C2×C22⋊C8—611no—
410C2×C4×C8—611no—
411C2×C4×C8C2×D6111yescharacteristic, complemented
412#390—611no—
413#390—611no—
414#389—611no—
415#389—611no—
416#387—1221no—
417#387—1221no—
418#386—1221no—
419#386—1221no—
420#381—1221no—
421#380—611no—
422#380—611no—
423#379—1221no—
424C4×C4⋊C4—611no—
425C4×C4⋊C4C2×D6111yescharacteristic, complemented
426C4×C22⋊C4—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340C2×D6111yescharacteristic, complemented
432#340C2×D6111yescharacteristic, complemented
433#336—611no—
434#336—611no—
435C61#2257011yescharacteristic, complemented, Sylow
436C25—1221no—
437C22×D4—614no—
438C22×D4—611no—
439C22×D4—1222no—
440C22×D4—1221no—
441C22×D4—1222no—
442C22×D4—1222no—
443C22×D4—2441no—
444C22×D4—2441no—
445C22×D4C22×D6111yescharacteristic
446C23×C4—21no—
447C23×C4—611no—
448C23×C4—1221no—
449C23×C4—1221no—
450C22×C8—611no—
451C22×C8—614no—
452C22×C8—611no—
453C22×C8—2441no—
454C22×C8—2441no—
455C22×C8C22×D6111yescharacteristic
456C22×C8C22×D6111yescharacteristic
457C4×D4—22no—
458C4×D4—41no—
459C4×D4—1222no—
460C4×D4—2441no—
461#117—2444no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—614no—
464C2×C4⋊C4—611no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—1222no—
467C2×C4⋊C4—1221no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4C22×D6111yescharacteristic
471C2×C4⋊C4C22×D6111yescharacteristic
472C2×C4⋊C4C22×D6111yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—611no—
475C2×C22⋊C4—611no—
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—2444no—
484C2×C42—21no—
485C2×C42—611no—
486C2×C42—1221no—
487C2×C42C22×D6111yescharacteristic
488#107—2441no—
489#107—2441no—
490#102—22no—
491#102—614no—
492#102—614no—
493#102—614no—
494#102—1222no—
495#102—2441no—
496#102—2441no—
497#102C4×D6114yes—
498C22⋊C8—1222no—
499C4×C8—41no—
500C4×C8—2441no—
501#95—21no—
502#95—611no—
503#95—611no—
504#95—1221no—
505#95—1221no—
506#95—1221no—
507#95—1221no—
508#95—1221no—
509C24—21no—
510C24—611no—
511C24—1224no—
512C24—1221no—
513C24—4881no—
514C24—4881no—
515C24—2442no—
516C24—2442no—
517C24—2442no—
518C24—2442no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—612no—
523C2×D4—1224no—
524C2×D4—1228no—
525C2×D4—1221no—
526C2×D4—1221no—
527C2×D4—1221no—
528C2×D4—1221no—
529C2×D4—1221no—
530C2×D4—2444no—
531C2×D4—2444no—
532C2×D4—2444no—
533C2×D4—2442no—
534C2×D4—2442no—
535C2×D4C2×C4×D6112yes—
536C2×D4#1175822212yes—
537C2×D4#1175822212yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—612no—
547C22×C4—612no—
548C22×C4—611no—
549C22×C4—1224no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—4881no—
558C22×C4—2442no—
559C22×C4—2442no—
560C22×C4—2442no—
561C22×C4—2442no—
562C22×C4D4×D6111yescharacteristic
563C22×C4D4×D6111yescharacteristic
564C22×C4C23×D6111yescharacteristic
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—612no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—2444no—
577C2×C8C2×C4×D6112yes—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—612no—
584C4⋊C4—1224no—
585C4⋊C4—1221no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—2442no—
591C4⋊C4—2442no—
592C4⋊C4C2×C4×D6112yes—
593C22⋊C4—42no—
594C22⋊C4—614no—
595C22⋊C4—1222no—
596C22⋊C4—4881no—
597C22⋊C4—4881no—
598C22⋊C4—2442no—
599C22⋊C4—2442no—
600C22⋊C4—2442no—
601C22⋊C4—2442no—
602C22⋊C4—2442no—
603C42—21no—
604C42—21no—
605C42—42no—
606C42—1221no—
607C42—1221no—
608C42—2442no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—612no—
617C23—612no—
618C23—612no—
619C23—1221no—
620C23—1221no—
621C23—1221no—
622C23—1221no—
623C23—1222no—
624C23—4884no—
625C23—4884no—
626C23—4884no—
627C23—4884no—
628C23—4884no—
629C23—2448no—
630C23—2448no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23C2×D4×D6111yescharacteristic
638D4—22no—
639D4—22no—
640D4—22no—
641D4—1222no—
642D4—1222no—
643D4—2448no—
644D4—2441no—
645D4—2441no—
646D4#1451973414yescomplemented
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4—612no—
663C2×C4—612no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—4884no—
677C2×C4—2448no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4D8×D6112yes—
687C2×C4C22×C4×D6111yescharacteristic
688C2×C4#41×D6111yescharacteristic
689C2×C4C2×#1175822211yescharacteristic
690C2×C4C2×#1175822211yescharacteristic
691C2×C4#1451982211yescharacteristic
692C2×C4#1451982311yescharacteristic
693C8—22no—
694C8—41no—
695C8—1222no—
696C8—2441no—
697C22—24no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—614no—
705C22—1222no—
706C22—1222no—
707C22—1222no—
708C22—1222no—
709C22—1222no—
710C22—1222no—
711C22—48816no—
712C22—4881no—
713C22—4881no—
714C22—4881no—
715C22—4881no—
716C22—2442no—
717C22—2442no—
718C22—2442no—
719C22C4×D4×D6111yescharacteristic
720C22#1684040211yescharacteristic
721C22#1684040811yescharacteristic
722C22C2×D8×D6111yescharacteristic
723C22#135×D6111yescharacteristic
724C22#1684056811yescharacteristic
725C22#1684056911yescharacteristic
726C4—22no—
727C4—42no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—1222no—
732C4—1222no—
733C4—4881no—
734C4—4881no—
735C4—2442no—
736C4—2441no—
737C4C2×#1451973411yescharacteristic
738C4#1684023411yescharacteristic
739C4#1684043611yescharacteristic
740C4#1684044111yescharacteristic
741C2—44no—
742C2—1224no—
743C2—4882no—
744C2#2144866211yescharacteristic
745C2C4×D8×D6111yescharacteristic
746C2#2145467311yescharacteristic
747C2#2145762811yescharacteristic
748C2#2145763411yescharacteristic
749C2#2145765511yescharacteristic
750C2#2145765911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#102×C61C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenterC4×#102D61
hypocenterC61#22570
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #21448684C2semidirect
4. #21446502C2semidirect
5. #21446500C2semidirect
6. #21446439C2semidirect
7. #21446437C2semidirect
8. #21446066C2semidirect
9. #21446064C2semidirect
10. #21445904C2semidirect
11. #21445847C2semidirect
13. #102×Dic61C2semidirect
14. C8×#11758198C2semidirect
15. C4×#102×C61C2semidirect
22. C2×#14519710C22semidirect
23. C2×#14519710C22semidirect
30. #102×D61C4semidirect
32. C2×C8×Dic61C22semidirect
35. #16839660C22semidirect
36. #16839658C22semidirect
45. C4⋊C4×Dic61C22semidirect
47. #16839525C22semidirect
48. #16839525C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839517C22semidirect
52. #16839516C22semidirect
56. C2×C4×C8×C61C22semidirect
57. C4×C4⋊C4×C61C22semidirect
58. C61×#340C22semidirect
59. C61×#340C22semidirect
76. C2×C8×D61C2×C4semidirect
87. C4⋊C4×D61C2×C4semidirect
103. #14519699C2×C4semidirect
107. #14519697C2×C4semidirect
265. D4×C61#117semidirect
379. C4×#102D61semidirect
411. C2×C4×C8C2×D61semidirect
425. C4×C4⋊C4C2×D61semidirect
431. #340C2×D61semidirect
432. #340C2×D61semidirect
435. C61#22570semidirect
646. D4#14519734semidirect

Maximal subgroups

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

subgroupindex
C2×#102×D612
#214486842
D4×#117581982
#214465022
#214465002
#214464392
#214464372
#214460662
#214460642
#214459042
#214458472
#214457482
#102×Dic612
C8×#117581982
C4×#102×C612
#2257061