Finite Group Databasebeta

← #29700371

Subgroups — #29700371

Order 15616.

1090 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839924C211yesmaximal, characteristic
2C2×#16839867C211yesmaximal, characteristic, complemented
3C2×#16839758C211yesmaximal, characteristic
4#21448844C211yesmaximal, characteristic, complemented
5#21446699C211yesmaximal, characteristic, complemented
6#21446519C211yesmaximal, characteristic, complemented
7#21446443C211yesmaximal, characteristic, complemented
8#21446240C211yesmaximal, characteristic, complemented
9#21446177C211yesmaximal, characteristic, complemented
10#21446160C211yesmaximal, characteristic, complemented
11#21446073C211yesmaximal, characteristic, complemented
12#21446016C211yesmaximal, characteristic, complemented
13#21445649C211yesmaximal, characteristic, complemented
14#21445597C211yesmaximal, characteristic, complemented
15C61×#2341C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×#14519736C2211yescharacteristic
22#16839924C418yescomplemented
23#16839867—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26#16839758—24no—
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519688C2211yescharacteristic
37C2×#14519688C2211yescharacteristic
38#16839668C2211yescharacteristic
39#16839660C2211yescharacteristic
40#16839656—21no—
41#16839650—21no—
42#16839644—21no—
43C4×C4⋊Dic61C2211yescharacteristic
44#16839613—21no—
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51C22×#41×C61C2211yescharacteristic
52C2×C4×Q8×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C61×#390—21no—
55C61×#390—21no—
56C61×#390C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#380—21no—
59C61×#380C2211yescharacteristic
60C4×C22⋊C4×C61—21no—
61C4×C22⋊C4×C61C2211yescharacteristic
62C22×Dic122C2311yescharacteristic
63C2×#11758202—22no—
64C2×#11758202—22no—
65C2×#11758202C2×C414yes—
66C2×#11758200—41no—
67C2×#11758200—41no—
68C2×#11758200C2×C414yes—
69C22×#92418—22no—
70C22×#92418—22no—
71C22×#92418—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76#14519756—22no—
77#14519756C2×C414yes—
78C4×Dic122—22no—
79C4×Dic122—41no—
80#14519736—22no—
81#14519736—41no—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93#14519710—41no—
94#14519708—22no—
95#14519701—22no—
96#14519701C2×C414yes—
97#14519701D414yes—
98#14519700—22no—
99#14519700—41no—
100#14519698—22no—
101#14519698—22no—
102#14519698C2×C414yes—
103C22⋊#92418C2×C414yes—
104#14519688—22no—
105#14519688—41no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110C2×#41×C61—22no—
111C2×#41×C61—22no—
112C2×#41×C61—22no—
113C2×#41×C61—41no—
114C2×#41×C61—41no—
115C2×#41×C61C2×C414yes—
116C22×Q8×C61C2311yescharacteristic
117C22×D4×C61—21no—
118C22×D4×C61C2311yescharacteristic
119C23×C4×C61—21no—
120C23×C4×C61C2311yescharacteristic
121C4×Q8×C61—22no—
122C4×Q8×C61—22no—
123C4×Q8×C61—41no—
124C4×Q8×C61—41no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61D411yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C42×C61—21no—
137C2×C42×C61—21no—
138C2×C42×C61C2311yescharacteristic
139C2×C42×C61C2311yescharacteristic
140#95×C61—21no—
141#95×C61D411yescharacteristic
142#95×C61D411yescharacteristic
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—24no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—42no—
173C22×C4×C61—42no—
174C22×C4×C61C22×C412yes—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61#4112yes—
181C22×C4×C61C2411yescharacteristic
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122C22×C412yes—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—42no—
197C4⋊C4×C61—42no—
198C22⋊C4×C61—41no—
199C22⋊C4×C61—41no—
200C22⋊C4×C61—42no—
201C22⋊C4×C61—42no—
202C22⋊C4×C61—81no—
203C22⋊C4×C61—81no—
204C22⋊C4×C61—81no—
205C42×C61—21no—
206C42×C61—21no—
207C42×C61—21no—
208C42×C61—21no—
209C42×C61—42no—
210C42×C61—42no—
211C22⋊Dic61—24no—
212C22⋊Dic61—42no—
213#11758202—28no—
214#11758200—44no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61C22×C412yes—
220C4⋊Dic61C2×D412yes—
221#11758196—24no—
222#11758196—42no—
223#11758196—42no—
224C4×Dic61—42no—
225C4×Dic61—42no—
226C4×Dic61—42no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—44no—
237C2×#92418C22×C412yes—
238C2×#92418C22×C412yes—
239C2×#92418C2×D412yes—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—22no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61C4×D412yes—
254C23×C61C22×D411yescharacteristic
255Q8×C61—22no—
256Q8×C61—22no—
257Q8×C61—22no—
258Q8×C61C4×D414yes—
259D4×C61—22no—
260D4×C61—22no—
261D4×C61—48no—
262D4×C61—41no—
263D4×C61—41no—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—48no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61C4×D412yes—
293C2×C4×C61C23×C411yescharacteristic
294C2×C4×C61C22×D411yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61H(5,𝔽2)11yescharacteristic
298C2×C4×C61H(5,𝔽2)11yescharacteristic
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311Dic122—22no—
312Dic122—22no—
313Dic122—41no—
314Dic122—41no—
315#92418—22no—
316#92418—22no—
317#92418—22no—
318#92418—41no—
319#22861—611nomaximal, Sylow
320C22×C61—22no—
321C22×C61—22no—
322C22×C61—22no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—81no—
331C22×C61—81no—
332C22×C61—81no—
333C22×C61—81no—
334C22×C61C2×C4×D411yescharacteristic
335C22×C61D4211yescharacteristic
336C22×C61#54611yescharacteristic
337C22×C61#57511yescharacteristic
338C22×C61#57511yescharacteristic
339C22×C61#57711yescharacteristic
340C22×C61#57811yescharacteristic
341C4×C61—22no—
342C4×C61—24no—
343C4×C61—41no—
344C4×C61—41no—
345C4×C61—41no—
346C4×C61—41no—
347C4×C61—81no—
348C4×C61—81no—
349C4×C61C2×C4×D411yescharacteristic
350C4×C61#51811yescharacteristic
351C4×C61#54611yescharacteristic
352C4×C61#55111yescharacteristic
353Dic61—42no—
354Dic61—42no—
355Dic61—42no—
356Dic61—81no—
357C2×#452—611no—
358C2×#441—611no—
359C2×#416—611no—
360#2362—611no—
361#2341D6111yescharacteristic
362#1973—611no—
363#1936—611no—
364#1926—611no—
365#1892—611no—
366#1880—611no—
367#1878—611no—
368#1863—611no—
369#1854—611no—
370#1763—611no—
371#1752—611no—
372C2×C61—42no—
373C2×C61—82no—
374C2×C61#235811yescharacteristic
375C2×C61#294311yescharacteristic
376C2×C61#294711yescharacteristic
377C2×C61#326911yescharacteristic
378C2×C61#327111yescharacteristic
379C2×C61#331311yescharacteristic
380C2×C61#331711yescharacteristic
381C22×#41C2×D6111yescharacteristic
382C22×Q16—611no—
383C22×SD16—611no—
384C23×C8—611no—
385C2×C22⋊Q8—611no—
386C2×C4×Q8—611no—
387C2×C4×Q8C2×D6111yescharacteristic
388C2×C4×Q8C2×D6111yescharacteristic
389C2×#117—611no—
390#452—618no—
391#441—1224no—
392C2×#107—611no—
393C2×#106—611no—
394#416—1224no—
395C2×#103—611no—
396C2×#103—611no—
397C2×#103—611no—
398C2×#103—611no—
399C2×#103—611no—
400C2×#102—611no—
401C2×#102—611no—
402C2×#102—611no—
403C2×C22⋊C8—611no—
404C2×#97—611no—
405C2×#97—611no—
406#391—611no—
407#390—21no—
408#390—21no—
409#390C2×D6111yescharacteristic
410#390C2×D6111yescharacteristic
411#389—611no—
412#388—1221no—
413#388—1221no—
414#387—1221no—
415#380—21no—
416#380C2×D6111yescharacteristic
417C4×C4⋊C4—611no—
418C4×C4⋊C4—1221no—
419C4×C22⋊C4—21no—
420C4×C22⋊C4C2×D6111yescharacteristic
421#340—611no—
422#340—611no—
423#340—611no—
424#340—611no—
425#336—611no—
426#336—611no—
427C61#2286111yescharacteristic, complemented, Sylow
428C2×#41—22no—
429C2×#41—22no—
430C2×#41—22no—
431C2×#41—41no—
432C2×#41—41no—
433C2×#41C4×D6114yes—
434C22×Q8—611no—
435C22×Q8C22×D6111yescharacteristic
436C22×D4—21no—
437C22×D4C22×D6111yescharacteristic
438C23×C4—21no—
439C23×C4C22×D6111yescharacteristic
440C2×Q16—614no—
441C2×Q16—1222no—
442C2×Q16—1222no—
443C2×SD16—614no—
444C2×SD16—2441no—
445C2×SD16—2441no—
446C22×C8—611no—
447C22×C8—611no—
448C22×C8—611no—
449C22×C8—611no—
450C22×C8—1222no—
451C22×C8—1222no—
452C22×C8—2441no—
453C22⋊Q8—614no—
454C22⋊Q8—1222no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×Q8—41no—
458C4×Q8—41no—
459C4×Q8—1222no—
460C4×Q8—2441no—
461#117—1222no—
462#117—2441no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4C22×D6111yescharacteristic
472C2×C4⋊C4C22×D6111yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—1221no—
479C2×C22⋊C4—1221no—
480C2×C22⋊C4C22⋊D6111yescharacteristic
481C2×C22⋊C4C22⋊D6111yescharacteristic
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—1221no—
485C2×C42—1221no—
486C2×C42—1221no—
487C2×C42C22×D6111yescharacteristic
488C2×C42C22×D6111yescharacteristic
489#107—2441no—
490#106—1222no—
491#103—614no—
492#103—614no—
493#103—1222no—
494#103—1222no—
495#103—2441no—
496#102—614no—
497#102—1222no—
498#102—1222no—
499C22⋊C8—614no—
500#97—1222no—
501#97—2441no—
502#95—21no—
503#95—1221no—
504#95—1221no—
505#95—1221no—
506#95—1221no—
507#95C22⋊D6111yescharacteristic
508#95C22⋊D6111yescharacteristic
509C24—21no—
510C24C2×C22⋊D6111yescharacteristic
511#41—28no—
512#41—44no—
513#41—44no—
514#41—44no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—612no—
519C2×Q8—1221no—
520C2×Q8—1221no—
521C2×Q8—1221no—
522C2×Q8—1221no—
523C2×Q8—1221no—
524C2×Q8C2×C4×D6112yes—
525C2×Q8D4×D6112yes—
526C2×Q8#1175822412yes—
527C2×D4—24no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4C2×C4×D6112yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4C2×C4×D6112yes—
551C22×C4#1175822212yes—
552C22×C4C2×C22⋊D6111yescharacteristic
553C22×C4C2×C22⋊D6111yescharacteristic
554C22×C4C2×C22⋊D6111yescharacteristic
555C22×C4C2×C22⋊D6111yescharacteristic
556C22×C4C2×C22⋊D6111yescharacteristic
557C22×C4C23×D6111yescharacteristic
558Q16—1228no—
559SD16—2444no—
560C2×C8—612no—
561C2×C8—612no—
562C2×C8—612no—
563C2×C8—1221no—
564C2×C8—1221no—
565C2×C8—1221no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—2444no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—612no—
580C4⋊C4—612no—
581C4⋊C4—1221no—
582C4⋊C4—1221no—
583C4⋊C4—1224no—
584C4⋊C4—1221no—
585C4⋊C4—1221no—
586C4⋊C4—2442no—
587C4⋊C4—2442no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C22⋊C4—81no—
595C22⋊C4—1224no—
596C22⋊C4—2442no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—42no—
602C42—42no—
603C42—2442no—
604C42—2442no—
605C42—2442no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23C4×C22⋊D6112yes—
620C23C22×C22⋊D6111yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—22no—
624Q8—1222no—
625Q8—1222no—
626Q8—2441no—
627Q8—2441no—
628Q8#1451973714yes—
629D4—22no—
630D4—22no—
631D4—48no—
632D4—41no—
633D4—41no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—48no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
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×C4C4×C22⋊D6112yes—
675C2×C4C22×C4×D6111yescharacteristic
676C2×C4C2×D4×D6111yescharacteristic
677C2×C4C2×#1175822411yescharacteristic
678C2×C4C2×#1175822211yescharacteristic
679C2×C4#1451982211yescharacteristic
680C2×C4#1451982211yescharacteristic
681C8—1222no—
682C8—1222no—
683C8—1222no—
684C8—2441no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22C2×C4×C22⋊D6111yescharacteristic
700C22D4×C22⋊D6111yescharacteristic
701C22#1684040611yescharacteristic
702C22#1684056011yescharacteristic
703C22#1684056011yescharacteristic
704C22#1684057311yescharacteristic
705C22#1684057711yescharacteristic
706C4—22no—
707C4—24no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—81no—
713C4—81no—
714C4—4881no—
715C4—2442no—
716C4—2442no—
717C4—2442no—
718C4C2×#1451973711yescharacteristic
719C4#1684023511yescharacteristic
720C4#1684040211yescharacteristic
721C4#1684043811yescharacteristic
722C2—42no—
723C2—82no—
724C2#2144879811yescharacteristic
725C2#2145461711yescharacteristic
726C2#2145465811yescharacteristic
727C2#2145737511yescharacteristic
728C2#2145740011yescharacteristic
729C2#2145788511yescharacteristic
730C2#2145794511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2341C2
socleC23×C61C22×D4
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenter#2341D61
hypocenterC61#22861
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#16839867C2semidirect
4. #21448844C2semidirect
5. #21446699C2semidirect
6. #21446519C2semidirect
7. #21446443C2semidirect
8. #21446240C2semidirect
9. #21446177C2semidirect
10. #21446160C2semidirect
11. #21446073C2semidirect
12. #21446016C2semidirect
13. #21445649C2semidirect
14. #21445597C2semidirect
22. #16839924C4semidirect
427. C61#22861semidirect

Maximal subgroups

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

subgroupindex
C2×#168399242
C2×#168398672
C2×#168397582
#214488442
#214466992
#214465192
#214464432
#214462402
#214461772
#214461602
#214460732
#214460162
#214456492
#214455972
C61×#23412
#2286161