Finite Group Databasebeta

← #29700465

Subgroups — #29700465

Order 15616.

1106 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839924C211yesmaximal, characteristic
2C2×#16839866C211yesmaximal, characteristic, complemented
3#21448824C211yesmaximal, characteristic, complemented
4#21448660C211yesmaximal, characteristic
5#21446674C211yesmaximal, characteristic, complemented
6#21446513C211yesmaximal, characteristic, complemented
7#21446449C211yesmaximal, characteristic, complemented
8#21446252C211yesmaximal, characteristic, complemented
9#21446171C211yesmaximal, characteristic, complemented
10#21446158C211yesmaximal, characteristic, complemented
11#21446085C211yesmaximal, characteristic, complemented
12#21446012C211yesmaximal, characteristic, complemented
13#103×Dic61C211yesmaximal, characteristic, complemented
14#21445600C211yesmaximal, characteristic, complemented
15C2×C61×#417C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×#14519742C2211yescharacteristic
22#16839924C418yescomplemented
23#16839866—24no—
24C2×#14519708C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33#16839667C2211yescharacteristic
34#16839665—21no—
35#16839665—21no—
36#16839665C2211yescharacteristic
37#16839665C2211yescharacteristic
38#16839658C2211yescharacteristic
39#16839657—21no—
40#16839643—21no—
41#16839635—21no—
42#16839622—21no—
43#16839622C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45C4×C22⋊Dic61—21no—
46C4×C22⋊Dic61—21no—
47C4×C22⋊Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×#41×C61C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C61×#417—24no—
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C22×Dic122C2311yescharacteristic
63C2×#11758202—22no—
64C2×#11758202—22no—
65C2×#11758202C2×C414yescomplemented
66C2×#11758200—41no—
67C2×#11758200—41no—
68C2×#11758200C2×C414yescomplemented
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71#14519756—22no—
72#14519756C2×C414yes—
73Q8×Dic61—22no—
74Q8×Dic61—22no—
75Q8×Dic61—41no—
76Q8×Dic61—41no—
77#14519742—22no—
78#14519742—41no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61D411yescharacteristic
94C2×C22⋊Dic61D411yescharacteristic
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61C2311yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101#14519708—22no—
102#14519708—41no—
103#14519702—22no—
104#14519702—41no—
105#14519701C2×C414yescomplemented
106#14519698C2×C414yescomplemented
107C22⋊#92418C2×C414yes—
108#14519687—22no—
109C8×Dic61—41no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684D411yescharacteristic
116#14519684D411yescharacteristic
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—41no—
121C2×#41×C61—41no—
122C2×#41×C61C2×C414yes—
123C22×Q8×C61C2311yescharacteristic
124C22×D4×C61—21no—
125C22×D4×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C23×C4×C61—21no—
128C23×C4×C61C2311yescharacteristic
129C2×M16×C61—22no—
130C2×M16×C61—22no—
131C2×M16×C61—41no—
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C2×C4⋊C4×C61—22no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—41no—
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139#103×C61—22no—
140#103×C61D414yes—
141#102×C61—22no—
142#102×C61—22no—
143C24×C61—21no—
144C24×C61C2×D411yescharacteristic
145#41×C61—28no—
146#41×C61—44no—
147#41×C61—44no—
148#41×C61—44no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61C22×C412yes—
153C2×Q8×C61C2×D412yes—
154C2×Q8×C61#4112yes—
155C2×D4×C61—24no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61C22×C412yes—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—24no—
171C22×C4×C61—21no—
172C22×C4×C61—42no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61—81no—
177C22×C4×C61C22×C412yes—
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61#4112yes—
180C22×C4×C61C2411yescharacteristic
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122C22×C412yes—
195M16×C61—44no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61C2×D412yes—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—42no—
206C4⋊C4×C61C2×D412yes—
207C22⋊Dic61—24no—
208C22⋊Dic61—22no—
209C22⋊Dic61—41no—
210C22⋊Dic61—42no—
211C22⋊Dic61—42no—
212C22⋊Dic61—81no—
213C22⋊Dic61—81no—
214C22⋊Dic61—81no—
215#11758202—28no—
216#11758200—44no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—42no—
223C4⋊Dic61—42no—
224C4⋊Dic61C22×C412yes—
225#11758196—24no—
226#11758196—42no—
227#11758196—81no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—42no—
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×C61—22no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61C4×D412yes—
256C23×C61C22×D411yescharacteristic
257Q8×C61—22no—
258Q8×C61—22no—
259Q8×C61—22no—
260Q8×C61C4×D414yes—
261D4×C61—22no—
262D4×C61—22no—
263D4×C61—48no—
264D4×C61—41no—
265D4×C61—41no—
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—48no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—84no—
283C2×C4×C61C4×D412yes—
284C2×C4×C61C23×C411yescharacteristic
285C2×C4×C61C22×D411yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61H(5,𝔽2)11yescharacteristic
289C2×C4×C61H(5,𝔽2)11yescharacteristic
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—41no—
304C2×Dic61—41no—
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—
314Dic122—22no—
315Dic122—22no—
316Dic122—41no—
317Dic122—41no—
318C8×C61—22no—
319C8×C61—41no—
320#92418—22no—
321#92418—22no—
322#22867—611nomaximal, Sylow
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—81no—
334C22×C61—81no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61C2×C4×D411yescharacteristic
338C22×C61D4211yescharacteristic
339C22×C61#54611yescharacteristic
340C22×C61C2×#13711yescharacteristic
341C22×C61#57511yescharacteristic
342C22×C61#57711yescharacteristic
343C22×C61#57711yescharacteristic
344C4×C61—22no—
345C4×C61—24no—
346C4×C61—42no—
347C4×C61—81no—
348C4×C61C2×C4×D411yescharacteristic
349C4×C61#51811yescharacteristic
350C4×C61#54611yescharacteristic
351C4×C61#55111yescharacteristic
352Dic61—22no—
353Dic61—42no—
354Dic61—42no—
355Dic61—41no—
356Dic61—41no—
357Dic61—41no—
358Dic61—81no—
359Dic61—81no—
360C2×#452—611no—
361C2×#441—611no—
362C2×#417D6111yescharacteristic
363#2360—611no—
364#2341—611no—
365#1968—611no—
366#1936—611no—
367#1926—611no—
368#1894—611no—
369#1880—611no—
370#1878—611no—
371#1865—611no—
372#1853—611no—
373C4×#103—611no—
374#1753—611no—
375C2×C61—42no—
376C2×C61—82no—
377C2×C61#235811yescharacteristic
378C2×C61C4×#13711yescharacteristic
379C2×C61#295211yescharacteristic
380C2×C61#327511yescharacteristic
381C2×C61#327811yescharacteristic
382C2×C61#331611yescharacteristic
383C2×C61#331711yescharacteristic
384C22×#41C2×D6111yescharacteristic
385C22×Q16—611no—
386C22×SD16—611no—
387C22×M16C2×D6111yescharacteristic
388C2×C22⋊Q8—611no—
389C2×C4×Q8—611no—
390C2×C4×Q8—611no—
391C2×C4×Q8—611no—
392C22×C4⋊C4C2×D6111yescharacteristic
393#452—618no—
394#441—1224no—
395C2×#106—611no—
396C2×#106—611no—
397#417—24no—
398C2×#103—611no—
399C2×#103—611no—
400C2×#103—611no—
401C2×#103C2×D6111yescharacteristic
402C2×#103C2×D6111yescharacteristic
403C2×#102—611no—
404C2×#102C2×D6111yescharacteristic
405C2×#102C2×D6111yescharacteristic
406C2×C22⋊C8—611no—
407C2×#97—611no—
408C2×C4×C8—611no—
409#391—611no—
410#390—611no—
411#390—611no—
412#390—1221no—
413#390—1221no—
414#389—611no—
415#389—1221no—
416#387—1221no—
417#385—1221no—
418#380—611no—
419#380—1221no—
420C4×C4⋊C4—611no—
421C4×C22⋊C4—611no—
422C4×C22⋊C4—1221no—
423C4×C22⋊C4—1221no—
424#340—611no—
425#340—611no—
426#340—611no—
427#340—611no—
428#336—611no—
429#336—611no—
430C61#2286711yescharacteristic, complemented, Sylow
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—41no—
435C2×#41—41no—
436C2×#41C4×D6114yes—
437C22×Q8—611no—
438C22×Q8C22×D6111yescharacteristic
439C22×D4—21no—
440C22×D4C22×D6111yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4C22×D6111yescharacteristic
444C2×Q16—614no—
445C2×Q16—1222no—
446C2×Q16—1222no—
447C2×SD16—614no—
448C2×SD16—2441no—
449C2×SD16—2441no—
450C2×M16—22no—
451C2×M16—22no—
452C2×M16—41no—
453C22×C8—611no—
454C22×C8—611no—
455C22×C8C22×D6111yescharacteristic
456C22×C8C22×D6111yescharacteristic
457C22⋊Q8—614no—
458C22⋊Q8—1222no—
459C4×Q8—1222no—
460C4×Q8—1222no—
461C4×Q8—1222no—
462C4×Q8—2441no—
463C4×Q8—2441no—
464C4×Q8—2441no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C4⋊C4C22×D6111yescharacteristic
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×C22⋊C4—1221no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—1221no—
489C2×C42—1221no—
490C2×C42—1221no—
491C2×C42—1221no—
492#106—1222no—
493#106—2441no—
494#103—22no—
495#103—614no—
496#103—1222no—
497#103—2441no—
498#103C22⋊D6114yes—
499#102—22no—
500#102—22no—
501#102—614no—
502C22⋊C8—614no—
503#97—1222no—
504C4×C8—2441no—
505#95—611no—
506#95—611no—
507#95—1221no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512C24—21no—
513C24D4×D6111yescharacteristic
514#41—28no—
515#41—44no—
516#41—44no—
517#41—44no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—612no—
522C2×Q8—1221no—
523C2×Q8—1221no—
524C2×Q8—1221no—
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8C2×C4×D6112yes—
528C2×Q8#1175822212yes—
529C2×Q8C2×C22⋊D6112yes—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4C2×C4×D6112yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—21no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—81no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4C2×C4×D6112yes—
561C22×C4D4×D6111yescharacteristic
562C22×C4#1175822412yes—
563C22×C4C23×D6111yescharacteristic
564Q16—1228no—
565SD16—2444no—
566M16—44no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—612no—
573C2×C8—612no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8C2×C22⋊D6112yes—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—42no—
583C4⋊C4—612no—
584C4⋊C4—1221no—
585C4⋊C4—1224no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—4881no—
591C4⋊C4—2442no—
592C4⋊C4—2442no—
593C4⋊C4—2442no—
594C4⋊C4C2×C22⋊D6112yes—
595C22⋊C4—1222no—
596C22⋊C4—1224no—
597C22⋊C4—4881no—
598C22⋊C4—4881no—
599C22⋊C4—4881no—
600C22⋊C4—2442no—
601C22⋊C4—2441no—
602C22⋊C4—2442no—
603C42—1221no—
604C42—1221no—
605C42—1221no—
606C42—1221no—
607C42—4881no—
608C42—2442no—
609C42—2442no—
610C42—2442no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23#1451973712yes—
625C23C2×D4×D6111yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—1222no—
630Q8—1222no—
631Q8—2441no—
632Q8—2441no—
633Q8C4×C22⋊D6114yes—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—48no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—84no—
656C2×C4—612no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4#1451973712yes—
681C2×C4C22×C4×D6111yescharacteristic
682C2×C4C22×C22⋊D6111yescharacteristic
683C2×C4C2×#1175822411yescharacteristic
684C2×C4C2×#1175822211yescharacteristic
685C2×C4#1451982211yescharacteristic
686C2×C4#1451982211yescharacteristic
687C8—22no—
688C8—41no—
689C8—1222no—
690C8—1222no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22C2×#1451973711yescharacteristic
706C22D4×C22⋊D6111yescharacteristic
707C22#1684040211yescharacteristic
708C22#137×D6111yescharacteristic
709C22#1684055811yescharacteristic
710C22#1684057111yescharacteristic
711C22#1684057211yescharacteristic
712C4—22no—
713C4—24no—
714C4—42no—
715C4—81no—
716C4—1222no—
717C4—4881no—
718C4—4881no—
719C4—2441no—
720C4—2441no—
721C4—2441no—
722C4—2442no—
723C4—2442no—
724C4C2×C4×C22⋊D6111yescharacteristic
725C4#1684023511yescharacteristic
726C4#1684040611yescharacteristic
727C4#1684043811yescharacteristic
728C2—42no—
729C2—82no—
730C2#2144879811yescharacteristic
731C2#2145464311yescharacteristic
732C2#2145469811yescharacteristic
733C2#2145745011yescharacteristic
734C2#2145747911yescharacteristic
735C2#2145793111yescharacteristic
736C2#2145794611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#417D61
hypocenterC61#22867
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#16839866C2semidirect
3. #21448824C2semidirect
5. #21446674C2semidirect
6. #21446513C2semidirect
7. #21446449C2semidirect
8. #21446252C2semidirect
9. #21446171C2semidirect
10. #21446158C2semidirect
11. #21446085C2semidirect
12. #21446012C2semidirect
13. #103×Dic61C2semidirect
14. #21445600C2semidirect
22. #16839924C4semidirect
65. C2×#11758202C2×C4semidirect
68. C2×#11758200C2×C4semidirect
105. #14519701C2×C4semidirect
106. #14519698C2×C4semidirect
430. C61#22867semidirect

Maximal subgroups

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

subgroupindex
C2×#168399242
C2×#168398662
#214488242
#214486602
#214466742
#214465132
#214464492
#214462522
#214461712
#214461582
#214460852
#214460122
#103×Dic612
#214456002
C2×C61×#4172
#2286761