Finite Group Databasebeta

← #29700435

Subgroups — #29700435

Order 15616.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839901C211yesmaximal, characteristic
2C2×#16839865C211yesmaximal, characteristic, complemented
3#21448857C211yesmaximal, characteristic
4Q8×C22⋊Dic61C211yesmaximal, characteristic, complemented
5#21446670C211yesmaximal, characteristic, complemented
6#21446506C211yesmaximal, characteristic, complemented
7#21446463C211yesmaximal, characteristic, complemented
8#21446257C211yesmaximal, characteristic
9#21446172C211yesmaximal, characteristic, complemented
10#21446150C211yesmaximal, characteristic, complemented
11#21446085C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#103×Dic61C211yesmaximal, characteristic, complemented
14#21445600C211yesmaximal, characteristic, complemented
15C2×C61×#419C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22#16839901C418yescomplemented
23#16839865—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33#16839669—21no—
34#16839669—21no—
35#16839669C2211yescharacteristic
36#16839669C2211yescharacteristic
37#16839663C2211yescharacteristic
38#16839662—21no—
39#16839658C2211yescharacteristic
40#16839653—21no—
41#16839638—21no—
42#16839622—21no—
43#16839622C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45C4×#11758198—21no—
46C4×C22⋊Dic61—21no—
47C4×C22⋊Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C23×Q8×C61C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C2×#117×C61C2211yescharacteristic
57C61×#419—24no—
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C22×C4×D61—21no—
65C2×#11758201—22no—
66C2×#11758201—22no—
67C2×#11758201—41no—
68C2×#11758201—41no—
69C2×#11758201C2×C414yes—
70C2×#11758201C2×C414yes—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519751—22no—
74#14519751C2×C414yes—
75Q8×Dic61—22no—
76Q8×Dic61—22no—
77Q8×Dic61—41no—
78Q8×Dic61—41no—
79#14519739—22no—
80#14519739—41no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61D411yescharacteristic
89C2×C22⋊Dic61D411yescharacteristic
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61C2311yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99#14519710—22no—
100#14519708—41no—
101#14519701C2×C414yescomplemented
102#14519701C2×C414yescomplemented
103#14519699—22no—
104#14519699—41no—
105C22⋊#92418C2×C414yescomplemented
106#14519687—22no—
107C8×Dic61—41no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684D411yescharacteristic
116#14519684D411yescharacteristic
117C22×Q8×C61—21no—
118C22×Q8×C61—22no—
119C22×Q8×C61—22no—
120C22×Q8×C61—22no—
121C22×Q8×C61—41no—
122C22×Q8×C61—41no—
123C22×Q8×C61C2×C414yescomplemented
124C22×Q8×C61C2311yescharacteristic
125C22×Q8×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C23×C4×C61C2311yescharacteristic
128C2×M16×C61—22no—
129C2×M16×C61—22no—
130C2×M16×C61—41no—
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133#117×C61—22no—
134#117×C61—41no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C42×C61—21no—
139#103×C61—22no—
140#103×C61—22no—
141#103×C61—22no—
142#103×C61D414yescomplemented
143C24×C61C2×D411yescharacteristic
144C23×D61—21no—
145C2×Q8×C61—24no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—28no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—42no—
156C2×Q8×C61—42no—
157C2×Q8×C61—44no—
158C2×Q8×C61—44no—
159C2×Q8×C61—44no—
160C2×Q8×C61C22×C412yes—
161C2×Q8×C61C22×C412yes—
162C2×Q8×C61C2×D412yes—
163C2×Q8×C61#4112yes—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—24no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61C22×C412yes—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61#4112yes—
178C22×C4×C61C2411yescharacteristic
179C2×C22⋊D61—24no—
180C2×C22⋊D61—81no—
181C2×C22⋊D61—81no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244C22×C412yes—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—81no—
198M16×C61—44no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61C2×D412yes—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61C2×D412yes—
209C22⋊C4×C61—42no—
210C42×C61—42no—
211C22⋊Dic61—22no—
212C22⋊Dic61—41no—
213C22⋊Dic61—42no—
214#11758201—28no—
215#11758201—44no—
216#11758198—24no—
217#11758198—42no—
218#11758198—42no—
219#11758198—81no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—42no—
226C4⋊Dic61—42no—
227C4⋊Dic61C22×C412yes—
228#11758196—81no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—42no—
234C4×Dic61—42no—
235C4×Dic61—81no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418C22×C412yes—
241C2×#92418C22×C412yes—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61C4×D412yes—
249C23×C61C22×D411yescharacteristic
250C22×D61—22no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257Q8×C61—22no—
258Q8×C61—22no—
259Q8×C61—22no—
260Q8×C61—22no—
261Q8×C61—22no—
262Q8×C61—48no—
263Q8×C61—41no—
264Q8×C61—41no—
265Q8×C61C4×D414yes—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—21no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—48no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61C4×D412yes—
286C2×C4×C61C23×C411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C61H(5,𝔽2)11yescharacteristic
292C22⋊D61—84no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—22no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61#13712yes—
314D244—22no—
315D244—22no—
316D244—41no—
317D244—41no—
318C4×D61—84no—
319C8×C61—22no—
320C8×C61—41no—
321#92418—22no—
322#92418—22no—
323#22865—611nomaximal, Sylow
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61C2×C4×D411yescharacteristic
332C22×C61D4211yescharacteristic
333C22×C61#54611yescharacteristic
334C22×C61C2×#13711yescharacteristic
335C22×C61#57511yescharacteristic
336C22×C61#57711yescharacteristic
337C22×C61#57711yescharacteristic
338C2×D61—42no—
339C2×D61—42no—
340C2×D61—42no—
341C2×D61—81no—
342C2×D61—81no—
343C2×D61—81no—
344C2×D61—81no—
345C4×C61—22no—
346C4×C61—24no—
347C4×C61—42no—
348C4×C61—42no—
349C4×C61—81no—
350C4×C61C2×C4×D411yescharacteristic
351C4×C61#51811yescharacteristic
352C4×C61#54611yescharacteristic
353C4×C61#55111yescharacteristic
354Dic61—22no—
355Dic61—42no—
356Dic61—41no—
357Dic61—41no—
358Dic61—41no—
359Dic61—81no—
360Dic61—81no—
361C2×#448—611no—
362C2×#440—611no—
363C2×#419D6111yescharacteristic, complemented
364#2363—611no—
365Q8×C22⋊C4—611no—
366#1968—611no—
367#1935—611no—
368#1928—611no—
369#1895—611no—
370#1880—611no—
371#1877—611no—
372#1865—611no—
373#1854—611no—
374C4×#103—611no—
375#1753—611no—
376C2×C61—42no—
377C2×C61#235811yescharacteristic
378C2×C61C4×#13711yescharacteristic
379C2×C61#294911yescharacteristic
380C2×C61#327511yescharacteristic
381C2×C61#327811yescharacteristic
382C2×C61#332011yescharacteristic
383C2×C61#332111yescharacteristic
384D61—82no—
385C23×Q8C2×D6111yescharacteristic
386C22×SD16—611no—
387C22×SD16—611no—
388C22×M16C2×D6111yescharacteristic
389C2×#121—611no—
390C2×C4×Q8—611no—
391C2×C4×Q8—611no—
392C2×C4×D4—611no—
393C2×#117C2×D6111yescharacteristic
394#448—618no—
395#440—1224no—
396C2×#107—611no—
397C2×#106—611no—
398#419—24no—
399C2×#103—611no—
400C2×#103—611no—
401C2×#103C2×D6111yescharacteristic
402C2×#103C2×D6111yescharacteristic
403C2×#103C2×D6111yescharacteristic
404C2×#103C2×D6111yescharacteristic
405C2×#102—611no—
406C2×#102—611no—
407C2×C22⋊C8—611no—
408C2×#97—611no—
409C2×C4×C8—611no—
410#391—611no—
411#391—611no—
412#391—1221no—
413#391—1221no—
414#390—611no—
415#390—1221no—
416#389—611no—
417#388—1221no—
418#386—1221no—
419#380—611no—
420#380—1221no—
421C4×C4⋊C4—611no—
422C4×C22⋊C4—611no—
423C4×C22⋊C4—1221no—
424C4×C22⋊C4—1221no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340—611no—
429#336—611no—
430#336—611no—
431C61#2286511yescharacteristic, complemented, Sylow
432C22×Q8—21no—
433C22×Q8—22no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—41no—
437C22×Q8—41no—
438C22×Q8C4×D6114yescomplemented
439C22×Q8C22×D6111yescharacteristic
440C22×Q8C22×D6111yescharacteristic
441C22×D4—611no—
442C22×D4—1221no—
443C23×C4—21no—
444C23×C4—1221no—
445C23×C4C22×D6111yescharacteristic
446C2×SD16—614no—
447C2×SD16—614no—
448C2×SD16—1222no—
449C2×SD16—1222no—
450C2×SD16—2441no—
451C2×SD16—2441no—
452C2×M16—22no—
453C2×M16—22no—
454C2×M16—41no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8C22×D6111yescharacteristic
458C22×C8C22×D6111yescharacteristic
459#121—614no—
460#121—1222no—
461C4×Q8—1222no—
462C4×Q8—1222no—
463C4×Q8—2441no—
464C4×Q8—2441no—
465C4×D4—1222no—
466C4×D4—2441no—
467#117—22no—
468#117—41no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4C22×D6111yescharacteristic
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C42—21no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—1221no—
489C2×C42—1221no—
490C2×C42—1221no—
491#107—1222no—
492#106—2441no—
493#103—22no—
494#103—22no—
495#103—22no—
496#103—614no—
497#103—614no—
498#103C22⋊D6114yescomplemented
499#102—1222no—
500#102—2441no—
501C22⋊C8—614no—
502#97—1222no—
503C4×C8—2441no—
504#95—611no—
505#95—611no—
506#95—1221no—
507#95—1221no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513C24—1221no—
514C24D4×D6111yescharacteristic
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—24no—
520C2×Q8—28no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—44no—
528C2×Q8—44no—
529C2×Q8—44no—
530C2×Q8C2×C4×D6112yes—
531C2×Q8C2×C4×D6112yes—
532C2×Q8#1175822212yes—
533C2×Q8C2×C22⋊D6112yes—
534C2×D4—612no—
535C2×D4—1224no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1221no—
539C2×D4—1221no—
540C2×D4—1221no—
541C2×D4—4881no—
542C2×D4—4881no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—4881no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4C2×C4×D6112yes—
565C22×C4D4×D6111yescharacteristic
566C22×C4#1175822412yes—
567C22×C4C23×D6111yescharacteristic
568SD16—1228no—
569SD16—2444no—
570M16—44no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—612no—
577C2×C8—612no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8C2×C22⋊D6112yes—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—612no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—4881no—
593C4⋊C4—2442no—
594C4⋊C4—2442no—
595C4⋊C4C2×C22⋊D6112yes—
596C22⋊C4—42no—
597C22⋊C4—1222no—
598C22⋊C4—1224no—
599C22⋊C4—4881no—
600C22⋊C4—2442no—
601C22⋊C4—2442no—
602C22⋊C4—2441no—
603C22⋊C4—2442no—
604C42—42no—
605C42—1221no—
606C42—1221no—
607C42—1221no—
608C42—1221no—
609C42—4881no—
610C42—2442no—
611C42—2442no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—1222no—
619C23—2441no—
620C23—2441no—
621C23—2441no—
622C23—2441no—
623C23—2441no—
624C23—2441no—
625C23#1451973712yes—
626C23C2×D4×D6111yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—48no—
633Q8—41no—
634Q8—41no—
635Q8C4×C22⋊D6114yes—
636D4—1222no—
637D4—1222no—
638D4—4884no—
639D4—2441no—
640D4—2441no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—612no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1222no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—4884no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4#1451973712yes—
683C2×C4C22×C4×D6111yescharacteristic
684C2×C4C22×C22⋊D6111yescharacteristic
685C2×C4C2×#1175822411yescharacteristic
686C2×C4C2×#1175822211yescharacteristic
687C2×C4#1451982211yescharacteristic
688C2×C4#1451982211yescharacteristic
689C8—22no—
690C8—41no—
691C8—1222no—
692C8—1222no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—4881no—
701C22—4881no—
702C22—4881no—
703C22—4881no—
704C22—2442no—
705C22—2442no—
706C22—2442no—
707C22C2×#1451973711yescharacteristic
708C22D4×C22⋊D6111yescharacteristic
709C22#1684040211yescharacteristic
710C22#137×D6111yescharacteristic
711C22#1684056111yescharacteristic
712C22#1684057111yescharacteristic
713C22#1684057111yescharacteristic
714C4—22no—
715C4—24no—
716C4—42no—
717C4—42no—
718C4—81no—
719C4—1222no—
720C4—4881no—
721C4—4881no—
722C4—2441no—
723C4—2441no—
724C4—2442no—
725C4—2441no—
726C4C2×C4×C22⋊D6111yescharacteristic
727C4#1684023511yescharacteristic
728C4#1684040611yescharacteristic
729C4#1684043811yescharacteristic
730C2—42no—
731C2—4882no—
732C2#2144879811yescharacteristic
733C2#2145463411yescharacteristic
734C2#2145467411yescharacteristic
735C2#2145744411yescharacteristic
736C2#2145747911yescharacteristic
737C2#2145799111yescharacteristic
738C2#2145800611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#419C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
cosocleC22×C4×C61C24
hypercenterC2×#419D61
hypocenterC61#22865
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
2. C2×#16839865C2semidirect
4. Q8×C22⋊Dic61C2semidirect
5. #21446670C2semidirect
6. #21446506C2semidirect
7. #21446463C2semidirect
9. #21446172C2semidirect
10. #21446150C2semidirect
11. #21446085C2semidirect
12. #21446018C2semidirect
13. #103×Dic61C2semidirect
14. #21445600C2semidirect
15. C2×C61×#419C2semidirect
22. #16839901C4semidirect
101. #14519701C2×C4semidirect
102. #14519701C2×C4semidirect
105. C22⋊#92418C2×C4semidirect
123. C22×Q8×C61C2×C4semidirect
142. #103×C61D4semidirect
363. C2×#419D61semidirect
431. C61#22865semidirect
438. C22×Q8C4×D61semidirect
498. #103C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399012
C2×#168398652
#214488572
Q8×C22⋊Dic612
#214466702
#214465062
#214464632
#214462572
#214461722
#214461502
#214460852
#214460182
#103×Dic612
#214456002
C2×C61×#4192
#2286561