Finite Group Databasebeta

← #29700387

Subgroups — #29700387

Order 15616.

1134 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×#16839922C211yesmaximal, characteristic
2C2×#16839865C211yesmaximal, characteristic, complemented
3C2×#16839764C211yesmaximal, characteristic
4#21448828C211yesmaximal, characteristic, complemented
5#21448647C211yesmaximal, characteristic
6#21446677C211yesmaximal, characteristic, complemented
7#21446510C211yesmaximal, characteristic, complemented
8#21446458C211yesmaximal, characteristic, complemented
9#21446158C211yesmaximal, characteristic, complemented
10#21446150C211yesmaximal, characteristic, complemented
11#21446067C211yesmaximal, characteristic, complemented
12#21446006C211yesmaximal, characteristic, complemented
13#21445633C211yesmaximal, characteristic, complemented
14#21445600C211yesmaximal, characteristic, complemented
15C61×#1894C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×#14519739C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22C22×C4⋊Dic61C2211yescharacteristic
23#16839922C418yescomplemented
24#16839865—24no—
25C2×#14519710C2211yescharacteristic
26C2×#14519710C2211yescharacteristic
27#16839764—24no—
28C2×#14519702C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×#14519687C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839669C2211yescharacteristic
38#16839667C2211yescharacteristic
39#16839667C2211yescharacteristic
40#16839661—21no—
41#16839661C2211yescharacteristic
42#16839648—21no—
43#16839638—21no—
44#16839638—21no—
45#16839637—21no—
46#16839624—21no—
47C4⋊C4×Dic61C2211yescharacteristic
48C22⋊C4×Dic61—21no—
49C4×C22⋊Dic61C2211yescharacteristic
50#95×D61—21no—
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222C2×C414yes—
68C22×Dic122C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C22⋊D61—21no—
71C23×Dic61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C2×#11758202—41no—
76C2×#11758202—41no—
77C2×#11758202C2×C414yescomplemented
78C2×#11758201—22no—
79C2×#11758201—22no—
80C2×#11758201C2×C414yescomplemented
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83Q8×Dic61—22no—
84Q8×Dic61—41no—
85#14519739—22no—
86#14519739—22no—
87#14519739—41no—
88#14519739—41no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—41no—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C22⋊Dic61D411yescharacteristic
97C2×C22⋊Dic61D411yescharacteristic
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104#14519710—22no—
105#14519710—41no—
106#14519702—22no—
107#14519702—22no—
108#14519700C2×C414yescomplemented
109#14519699—22no—
110#14519699D414yes—
111#14519697C2×C414yescomplemented
112C22⋊#92418C2×C414yescomplemented
113#14519687—22no—
114C8×Dic61—41no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684D411yescharacteristic
124#14519684D411yescharacteristic
125C22×Q8×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C2×M16×C61—22no—
128C2×M16×C61—22no—
129C2×M16×C61—41no—
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22⋊Q8×C61—22no—
133C22⋊Q8×C61C2×C414yescomplemented
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140#103×C61—22no—
141#103×C61—41no—
142#95×C61—21no—
143C24×C61C2×D411yescharacteristic
144C23×D61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61C22×C412yes—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61#4112yes—
162C22×C4×C61C2411yescharacteristic
163C2×C22⋊D61—24no—
164C2×C22⋊D61—42no—
165C2×C22⋊D61—42no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—42no—
170C22×Dic61—42no—
171C22×Dic61—81no—
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176#11758222—28no—
177#11758222—44no—
178#11758222—44no—
179#11758222—44no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244C22×C412yes—
184C2×D244C2×D412yes—
185C2×D244#4112yes—
186C2×C4×D61—24no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—81no—
194C2×C4×D61—81no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122C22×C412yes—
201M16×C61—44no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61C2×D412yes—
208C4⋊C4×C61—24no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61C22×C412yes—
215C22⋊C4×C61—24no—
216C22⋊C4×C61—81no—
217C22⋊Dic61—22no—
218C22⋊Dic61—41no—
219#11758202—44no—
220#11758201—28no—
221#11758198—42no—
222#11758198—42no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—42no—
227C4⋊Dic61—42no—
228C4⋊Dic61—81no—
229C4⋊Dic61C2×D412yes—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—21no—
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—22no—
252C22×D61—22no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257Q8×C61—22no—
258Q8×C61—22no—
259Q8×C61—41no—
260Q8×C61—41no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
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×C61C4×D412yes—
280C2×C4×C61C23×C411yescharacteristic
281C2×C4×C61C22×D411yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61H(5,𝔽2)11yescharacteristic
285C2×C4×C61H(5,𝔽2)11yescharacteristic
286C22⋊D61—48no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—22no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—22no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—84no—
308C2×Dic61#13712yes—
309D244—22no—
310D244—22no—
311D244—22no—
312D244C4×D414yes—
313C4×D61—48no—
314C4×D61—84no—
315C4×D61—84no—
316Dic122—22no—
317Dic122—22no—
318Dic122—41no—
319Dic122—41no—
320C8×C61—22no—
321C8×C61—41no—
322#92418—22no—
323#92418—22no—
324#22862—611nomaximal, Sylow
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61C2×C4×D411yescharacteristic
333C22×C61D4211yescharacteristic
334C22×C61#54611yescharacteristic
335C22×C61C2×#13711yescharacteristic
336C22×C61#57511yescharacteristic
337C22×C61#57611yescharacteristic
338C22×C61#57811yescharacteristic
339C2×D61—24no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C4×C61—22no—
347C4×C61—42no—
348C4×C61—42no—
349C4×C61—81no—
350C4×C61—81no—
351C4×C61C2×C4×D411yescharacteristic
352C4×C61#51811yescharacteristic
353C4×C61#54611yescharacteristic
354C4×C61#55111yescharacteristic
355Dic61—22no—
356Dic61—42no—
357Dic61—41no—
358Dic61—42no—
359Dic61—41no—
360Dic61—41no—
361Dic61—81no—
362C2×#452—611no—
363C2×#440—611no—
364C2×#417—611no—
365#2360—611no—
366#2339—611no—
367#1969—611no—
368#1935—611no—
369#1928—611no—
370#1894D6111yescharacteristic, complemented
371#1878—611no—
372#1877—611no—
373#1862—611no—
374#1852—611no—
375C4×#102—611no—
376#1753—611no—
377C2×C61—42no—
378C2×C61#235811yescharacteristic
379C2×C61C4×#13711yescharacteristic
380C2×C61#295111yescharacteristic
381C2×C61#327311yescharacteristic
382C2×C61#327611yescharacteristic
383C2×C61#331411yescharacteristic
384C2×C61#331511yescharacteristic
385D61—44no—
386C22×#41—611no—
387C22×Q16—611no—
388C22×SD16—611no—
389C22×M16C2×D6111yescharacteristic
390C2×C22⋊Q8C2×D6111yescharacteristic
391C2×C4×Q8—611no—
392C2×C4×D4—611no—
393C2×C4×D4—611no—
394C22×C4⋊C4—611no—
395#452—618no—
396#440—1224no—
397C2×#107—611no—
398C2×#107—611no—
399#417—1224no—
400C2×#103—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×#103C2×D6111yescharacteristic
404C2×#103C2×D6111yescharacteristic
405C2×#102—611no—
406C2×#102—611no—
407C2×#102—611no—
408C2×C22⋊C8—611no—
409C2×#97—611no—
410C2×C4×C8—611no—
411#391—611no—
412#391—611no—
413#391—611no—
414#389—611no—
415#389—1221no—
416#387—1221no—
417#386—1221no—
418#386—1221no—
419#385—1221no—
420#381—1221no—
421#380C2×D6111yescharacteristic
422C4×C4⋊C4—611no—
423C4×C22⋊C4—611no—
424C4×C22⋊C4—1221no—
425C2×#95—1221no—
426#340—611no—
427#340—611no—
428#340C2×D6111yescharacteristic
429#340C2×D6111yescharacteristic
430#336—611no—
431#336—611no—
432C61#2286211yescharacteristic, complemented, Sylow
433C2×#41—614no—
434C2×#41—1222no—
435C2×#41—1222no—
436C2×#41—1222no—
437C2×#41—2441no—
438C2×#41—2441no—
439C22×Q8—611no—
440C22×Q8C22×D6111yescharacteristic
441C22×D4—611no—
442C22×D4—1221no—
443C23×C4—1221no—
444C23×C4—1221no—
445C23×C4—1221no—
446C23×C4—1221no—
447C23×C4C22×D6111yescharacteristic
448C2×Q16—614no—
449C2×Q16—2441no—
450C2×Q16—2441no—
451C2×SD16—614no—
452C2×SD16—1222no—
453C2×SD16—1222no—
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8C22×D6111yescharacteristic
460C22×C8C22×D6111yescharacteristic
461C22⋊Q8—22no—
462C22⋊Q8C4×D6114yescomplemented
463C4×Q8—1222no—
464C4×Q8—2441no—
465C4×D4—1222no—
466C4×D4—1222no—
467C4×D4—2441no—
468C4×D4—2441no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—1222no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—2441no—
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C4⋊C4C22×D6111yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—611no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—1221no—
489C2×C42—1221no—
490#107—1222no—
491#107—2441no—
492#103—22no—
493#103—41no—
494#103—614no—
495#103—1222no—
496#103—1222no—
497#102—614no—
498#102—614no—
499#102—1222no—
500C22⋊C8—614no—
501#97—1222no—
502C4×C8—2441no—
503#95—21no—
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—
513#95—1221no—
514C24—1221no—
515C24D4×D6111yescharacteristic
516#41—1228no—
517#41—2444no—
518#41—2444no—
519#41—2444no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—612no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8C2×C4×D6112yes—
532C2×D4—612no—
533C2×D4—612no—
534C2×D4—612no—
535C2×D4—1224no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1221no—
539C2×D4—2442no—
540C2×D4—2442no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1224no—
556C22×C4—1221no—
557C22×C4—4881no—
558C22×C4—4881no—
559C22×C4—4881no—
560C22×C4—2442no—
561C22×C4—2442no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4—2442no—
565C22×C4—2442no—
566C22×C4—2442no—
567C22×C4—2442no—
568C22×C4C2×C4×D6112yes—
569C22×C4D4×D6111yescharacteristic
570C22×C4#1175822412yes—
571C22×C4C23×D6111yescharacteristic
572Q16—2444no—
573SD16—1228no—
574M16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—612no—
581C2×C8—612no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8D4×D6112yes—
587C4⋊C4—21no—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—612no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—4881no—
598C4⋊C4—2442no—
599C4⋊C4—2442no—
600C4⋊C4C2×C4×D6112yes—
601C22⋊C4—24no—
602C22⋊C4—81no—
603C22⋊C4—1222no—
604C22⋊C4—2442no—
605C22⋊C4—2442no—
606C22⋊C4—2441no—
607C42—1221no—
608C42—1221no—
609C42—1221no—
610C42—1221no—
611C42—4881no—
612C42—2442no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—1222no—
620C23—1222no—
621C23—1222no—
622C23—2441no—
623C23—2441no—
624C23—2441no—
625C23—2441no—
626C23#1451973712yes—
627C23C2×D4×D6111yescharacteristic
628Q8—22no—
629Q8—22no—
630Q8—41no—
631Q8—41no—
632Q8—1222no—
633Q8—1222no—
634Q8—2441no—
635Q8—2441no—
636D4—614no—
637D4—1222no—
638D4—1222no—
639D4—1222no—
640D4—2448no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—612no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—1222no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1222no—
672C2×C4—1221no—
673C2×C4—4884no—
674C2×C4—4884no—
675C2×C4—4884no—
676C2×C4—2448no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4#1451973712yes—
685C2×C4C22×C4×D6111yescharacteristic
686C2×C4C2×D4×D6111yescharacteristic
687C2×C4#41×D6111yescharacteristic
688C2×C4C2×#1175822411yescharacteristic
689C2×C4#1451982211yescharacteristic
690C2×C4#1451982311yescharacteristic
691C8—22no—
692C8—41no—
693C8—1222no—
694C8—1222no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—1224no—
703C22—2442no—
704C22—2442no—
705C22—2442no—
706C22—2442no—
707C22—2442no—
708C22—2442no—
709C22C2×#1451973711yescharacteristic
710C22#1684039611yescharacteristic
711C22#1684040111yescharacteristic
712C22#137×D6111yescharacteristic
713C22#1684056111yescharacteristic
714C22#1684056611yescharacteristic
715C22#1684057811yescharacteristic
716C4—22no—
717C4—42no—
718C4—42no—
719C4—81no—
720C4—81no—
721C4—1222no—
722C4—4881no—
723C4—2441no—
724C4—2442no—
725C4—2441no—
726C4—2442no—
727C4—2441no—
728C4C4×D4×D6111yescharacteristic
729C4#1684023411yescharacteristic
730C4#1684039911yescharacteristic
731C4#1684043511yescharacteristic
732C2—42no—
733C2—2444no—
734C2#2144879911yescharacteristic
735C2#2145463411yescharacteristic
736C2#2145469011yescharacteristic
737C2#2145742711yescharacteristic
738C2#2145746211yescharacteristic
739C2#2145789511yescharacteristic
740C2#2145791011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1894C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1894D61
hypocenterC61#22862
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
2. C2×#16839865C2semidirect
4. #21448828C2semidirect
6. #21446677C2semidirect
7. #21446510C2semidirect
8. #21446458C2semidirect
9. #21446158C2semidirect
10. #21446150C2semidirect
11. #21446067C2semidirect
12. #21446006C2semidirect
13. #21445633C2semidirect
14. #21445600C2semidirect
15. C61×#1894C2semidirect
23. #16839922C4semidirect
77. C2×#11758202C2×C4semidirect
80. C2×#11758201C2×C4semidirect
108. #14519700C2×C4semidirect
111. #14519697C2×C4semidirect
112. C22⋊#92418C2×C4semidirect
133. C22⋊Q8×C61C2×C4semidirect
370. #1894D61semidirect
432. C61#22862semidirect
462. C22⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399222
C2×#168398652
C2×#168397642
#214488282
#214486472
#214466772
#214465102
#214464582
#214461582
#214461502
#214460672
#214460062
#214456332
#214456002
C61×#18942
#2286261