Finite Group Databasebeta

← #29727577

Subgroups — #29727577

Order 15616.

1052 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839970C211yesmaximal, characteristic, complemented
2C2×#16839918C211yesmaximal, characteristic
3C2×#16839854C211yesmaximal, characteristic, complemented
4#21449414C211yesmaximal, characteristic
5Q8×C22⋊Dic61C211yesmaximal, characteristic
6#21447210C211yesmaximal, characteristic, complemented
7#21447023C211yesmaximal, characteristic
8#21447019C211yesmaximal, characteristic
9#21446917C211yesmaximal, characteristic, complemented
10#21446681C211yesmaximal, characteristic, complemented
11#21446422C211yesmaximal, characteristic
12#21446162C211yesmaximal, characteristic, complemented
13#21446157C211yesmaximal, characteristic, complemented
14#21446075C211yesmaximal, characteristic, complemented
15C2×C61×#451C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C2×#14519775C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×Q8×Dic61C2211yescharacteristic
22C2×#14519742C2211yescharacteristic
23#16839970—24no—
24#16839918—24no—
25#16839854—24no—
26C2×#14519711C2211yescharacteristic
27C2×#14519710C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839693—21no—
38#16839685—21no—
39#16839669—21no—
40#16839669—21no—
41#16839669C2211yescharacteristic
42#16839669C2211yescharacteristic
43#16839669C2211yescharacteristic
44#16839661C2211yescharacteristic
45#16839658—21no—
46#16839650—21no—
47#16839622—21no—
48#16839622C2211yescharacteristic
49C4×C22⋊Dic61—21no—
50C4×C22⋊Dic61C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C23×Q8×C61C2211yescharacteristic
56C22×Q16×C61C2211yescharacteristic
57C22×Q16×C61C2211yescharacteristic
58C2×C22⋊Q8×C61C2211yescharacteristic
59C61×#451—24no—
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C2×#11758202—22no—
65C2×#11758202—22no—
66C2×#11758202—22no—
67C2×#11758202—22no—
68C2×#11758202—41no—
69C2×#11758202D414yes—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519775—22no—
73#14519775—41no—
74#14519756—22no—
75#14519756—41no—
76Q8×Dic61—22no—
77Q8×Dic61—22no—
78Q8×Dic61—41no—
79Q8×Dic61—41no—
80#14519742—22no—
81#14519742—41no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61D411yescharacteristic
95C2×C22⋊Dic61D411yescharacteristic
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61C2311yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101#14519711—41no—
102#14519710—22no—
103#14519706—22no—
104#14519702—22no—
105#14519702—22no—
106#14519701—22no—
107#14519701—22no—
108#14519701—22no—
109#14519701—41no—
110C22⋊#92418—22no—
111C8×Dic61—22no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684D411yescharacteristic
121#14519684D411yescharacteristic
122C22×Q8×C61—22no—
123C22×Q8×C61—22no—
124C22×Q8×C61—21no—
125C22×Q8×C61—22no—
126C22×Q8×C61—22no—
127C22×Q8×C61—41no—
128C22×Q8×C61—41no—
129C22×Q8×C61C2311yescharacteristic
130C22×Q8×C61C2311yescharacteristic
131C22×Q8×C61C2311yescharacteristic
132C23×C4×C61—21no—
133C23×C4×C61C2311yescharacteristic
134C2×Q16×C61—22no—
135C2×Q16×C61—22no—
136C2×Q16×C61—22no—
137C2×Q16×C61—22no—
138C2×Q16×C61—22no—
139C2×Q16×C61—41no—
140C22×C8×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C22⋊Q8×C61—22no—
143C22⋊Q8×C61—41no—
144C2×C4⋊C4×C61—21no—
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147#103×C61—22no—
148#103×C61D414yes—
149C22⋊C8×C61—22no—
150C24×C61C2×D411yescharacteristic
151C2×Q8×C61—24no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—42no—
167C2×Q8×C61—42no—
168C2×Q8×C61—44no—
169C2×Q8×C61—44no—
170C2×Q8×C61—44no—
171C2×Q8×C61—44no—
172C2×Q8×C61C2×D412yes—
173C2×Q8×C61C2×D412yes—
174C2×Q8×C61#4112yes—
175C2×Q8×C61#4112yes—
176C22×C4×C61—21no—
177C22×C4×C61—24no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—42no—
188C22×C4×C61—42no—
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2411yescharacteristic
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122C2×D412yes—
205Q16×C61—44no—
206Q16×C61—44no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61C2×D412yes—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—42no—
215C4⋊C4×C61C2×D412yes—
216C22⋊C4×C61—42no—
217C22⋊Dic61—41no—
218C22⋊Dic61—42no—
219C22⋊Dic61—42no—
220C22⋊Dic61Q1614yescomplemented
221#11758202—28no—
222#11758202—44no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—42no—
230C4⋊Dic61—42no—
231C4⋊Dic61—42no—
232#11758196—42no—
233#11758196—42no—
234#11758196—42no—
235#11758196—42no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—42no—
241C4×Dic61—42no—
242C4×Dic61—42no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418C2×D412yes—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61C2×Q1612yes—
256C23×C61C22×D411yescharacteristic
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×C61—41no—
266Q8×C61—41no—
267Q8×C61—41no—
268Q8×C61—41no—
269Q8×C61#12114yes—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—21no—
275C2×C4×C61—22no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—48no—
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×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—22no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61C2×Q1612yes—
319C2×Dic61C2×Q1612yes—
320Dic122—22no—
321Dic122—22no—
322Dic122—41no—
323Dic122—41no—
324C8×C61—22no—
325C8×C61—41no—
326#92418—22no—
327#92418—41no—
328#25161—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61#52511yescharacteristic
337C22×C61D4211yescharacteristic
338C22×C61D4211yescharacteristic
339C22×C61C22×Q1611yescharacteristic
340C22×C61#57511yescharacteristic
341C22×C61#57811yescharacteristic
342C22×C61#57811yescharacteristic
343C4×C61—24no—
344C4×C61—41no—
345C4×C61—42no—
346C4×C61—42no—
347C4×C61—81no—
348C4×C61C2×#12111yescharacteristic
349C4×C61#53811yescharacteristic
350C4×C61#54611yescharacteristic
351C4×C61#54611yescharacteristic
352Dic61—22no—
353Dic61—22no—
354Dic61—42no—
355Dic61—41no—
356Dic61—41no—
357Dic61—81no—
358Dic61—81no—
359Dic61—81no—
360C2×#462—611no—
361C2×#451—611no—
362C2×#451D6111yescharacteristic
363C2×C4×Q16—611no—
364#2429—611no—
365Q8×C22⋊C4—611no—
366#2068—611no—
367#2036—611no—
368#2036—611no—
369#2016—611no—
370#1969—611no—
371#1923—611no—
372#1878—611no—
373#1878—611no—
374#1863—611no—
375C2×C61—42no—
376C2×C61#242411yescharacteristic
377C2×C61#310411yescharacteristic
378C2×C61#312711yescharacteristic
379C2×C61#326911yescharacteristic
380C2×C61#327711yescharacteristic
381C2×C61D4×Q1611yescharacteristic
382C2×C61D4×Q1611yescharacteristic
383C23×Q8C2×D6111yescharacteristic
384C22×Q16—611no—
385C22×Q16—611no—
386C22×Q16C2×D6111yescharacteristic
387C22×Q16C2×D6111yescharacteristic
388C2×C4⋊Q8—611no—
389C2×C22⋊Q8—611no—
390C2×C22⋊Q8C2×D6111yescharacteristic
391C2×C4×Q8—611no—
392C2×C4×Q8—611no—
393C2×C4×Q8—611no—
394#462—1224no—
395#451—24no—
396#451—1224no—
397C4×Q16—1224no—
398C2×#107—611no—
399C2×#107—611no—
400C2×C4⋊C8—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×#103—611no—
404C2×#103—611no—
405C2×#103—611no—
406C2×#103—611no—
407C2×#103C2×D6111yescharacteristic
408C2×#103C2×D6111yescharacteristic
409C2×C22⋊C8—611no—
410C2×C22⋊C8C2×D6111yescharacteristic
411C2×C4×C8—611no—
412#398—1221no—
413#396—1221no—
414#391—611no—
415#391—611no—
416#391—611no—
417#391—1221no—
418#391—1221no—
419#389—611no—
420#389—1221no—
421#388—1221no—
422#380—611no—
423#380—1221no—
424C4×C22⋊C4—611no—
425C4×C22⋊C4—1221no—
426#340—611no—
427#340—611no—
428#336—611no—
429#336—611no—
430C61#2516111yescharacteristic, complemented, Sylow
431C22×Q8—22no—
432C22×Q8—22no—
433C22×Q8—21no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—41no—
437C22×Q8—41no—
438C22×Q8—611no—
439C22×Q8C22×D6111yescharacteristic
440C22×Q8C22×D6111yescharacteristic
441C22×Q8C22×D6111yescharacteristic
442C23×C4—21no—
443C23×C4C22×D6111yescharacteristic
444C2×Q16—22no—
445C2×Q16—22no—
446C2×Q16—22no—
447C2×Q16—22no—
448C2×Q16—22no—
449C2×Q16—41no—
450C2×Q16—614no—
451C2×Q16—1222no—
452C2×Q16—1222no—
453C2×Q16—1222no—
454C2×Q16—1222no—
455C2×Q16—2441no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8C22×D6111yescharacteristic
459C22×C8C22×D6111yescharacteristic
460C4⋊Q8—1222no—
461C4⋊Q8—2441no—
462C22⋊Q8—22no—
463C22⋊Q8—41no—
464C22⋊Q8—1222no—
465C22⋊Q8—2441no—
466C4×Q8—1222no—
467C4×Q8—1222no—
468C4×Q8—1222no—
469C4×Q8—2441no—
470C4×Q8—2441no—
471C4×Q8—2441no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C42—611no—
490C2×C42—611no—
491C2×C42—1221no—
492C2×C42—1221no—
493C2×C42—1221no—
494#107—1222no—
495#107—2441no—
496C4⋊C8—1222no—
497#103—22no—
498#103—1222no—
499#103—1222no—
500#103—1222no—
501#103—1222no—
502#103—1222no—
503#103—2441no—
504#103C22⋊D6114yes—
505C22⋊C8—22no—
506C22⋊C8—1222no—
507C4×C8—1222no—
508#95—611no—
509#95—611no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518C24D4×D6111yescharacteristic
519C2×Q8—24no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—42no—
535C2×Q8—42no—
536C2×Q8—44no—
537C2×Q8—44no—
538C2×Q8—44no—
539C2×Q8—44no—
540C2×Q8—612no—
541C2×Q8—1221no—
542C2×Q8—1221no—
543C2×Q8—1221no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×Q8D4×D6112yes—
547C2×Q8#1175822412yes—
548C2×Q8#1175822412yes—
549C2×Q8C2×C22⋊D6112yes—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4D4×D6111yescharacteristic
572C22×C4C23×D6111yescharacteristic
573Q16—44no—
574Q16—44no—
575Q16—1228no—
576Q16—2444no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—612no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8C2×C22⋊D6112yes—
589C4⋊C4—21no—
590C4⋊C4—42no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—2442no—
598C4⋊C4—2442no—
599C4⋊C4—2442no—
600C4⋊C4—2442no—
601C4⋊C4—2442no—
602C4⋊C4—2442no—
603C4⋊C4—2442no—
604C4⋊C4C2×C22⋊D6112yes—
605C22⋊C4—42no—
606C22⋊C4—614no—
607C22⋊C4—2441no—
608C22⋊C4—2442no—
609C22⋊C4—2442no—
610C42—1221no—
611C42—1221no—
612C42—1221no—
613C42—1221no—
614C42—2442no—
615C42—2442no—
616C42—2442no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23Q16×D6112yes—
624C23C2×D4×D6111yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—48no—
631Q8—41no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—1222no—
638Q8—1222no—
639Q8—2441no—
640Q8—2441no—
641Q8#1451974814yes—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—48no—
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—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—612no—
663C2×C4—612no—
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—1222no—
674C2×C4—1221no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
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×C4C2×D4×D6111yescharacteristic
687C2×C4C22×C22⋊D6111yescharacteristic
688C2×C4C2×#1175822411yescharacteristic
689C2×C4C2×#1175822411yescharacteristic
690C2×C4#1451982211yescharacteristic
691C2×C4#1451982211yescharacteristic
692C8—22no—
693C8—41no—
694C8—1222no—
695C8—2441no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22#1684026811yescharacteristic
704C22#1684039411yescharacteristic
705C22D4×C22⋊D6111yescharacteristic
706C22C2×Q16×D6111yescharacteristic
707C22#1684056111yescharacteristic
708C22#1684057511yescharacteristic
709C22#1684057811yescharacteristic
710C4—24no—
711C4—41no—
712C4—42no—
713C4—42no—
714C4—81no—
715C4—1222no—
716C4—1222no—
717C4—4881no—
718C4—4881no—
719C4—4881no—
720C4—2441no—
721C4—2442no—
722C4—2441no—
723C4C2×#1451974811yescharacteristic
724C4#1684034711yescharacteristic
725C4#1684039911yescharacteristic
726C4#1684040611yescharacteristic
727C2—42no—
728C2#2144935111yescharacteristic
729C2#2145585311yescharacteristic
730C2#2145611311yescharacteristic
731C2#2145736811yescharacteristic
732C2#2145747611yescharacteristic
733C2#2145756411yescharacteristic
734C2Q16×C22⋊D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#451C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenterC2×#451D61
hypocenterC61#25161
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×#16839970C2semidirect
3. C2×#16839854C2semidirect
6. #21447210C2semidirect
9. #21446917C2semidirect
10. #21446681C2semidirect
12. #21446162C2semidirect
13. #21446157C2semidirect
14. #21446075C2semidirect
220. C22⋊Dic61Q16semidirect
430. C61#25161semidirect

Maximal subgroups

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

subgroupindex
C2×#168399702
C2×#168399182
C2×#168398542
#214494142
Q8×C22⋊Dic612
#214472102
#214470232
#214470192
#214469172
#214466812
#214464222
#214461622
#214461572
#214460752
C2×C61×#4512
#2516161