Finite Group Databasebeta

← #29712970

Subgroups — #29712970

Order 15616.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840083C211yesmaximal, characteristic, complemented
2C2×#16839758C211yesmaximal, characteristic, complemented
3#21450116C211yesmaximal, characteristic, complemented
4#21447050C211yesmaximal, characteristic, complemented
5#21447050C211yesmaximal, characteristic, complemented
6#21447005C211yesmaximal, characteristic, complemented
7#21446998C211yesmaximal, characteristic, complemented
8#21446248C211yesmaximal, characteristic, complemented
9#21446112C211yesmaximal, characteristic, complemented
10#21446087C211yesmaximal, characteristic, complemented
11#21446073C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445759C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#550C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C2×#14519736C2211yescharacteristic
18#16840083—24no—
19C2×#14519710C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21#16839758—24no—
22C2×#14519701C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37#16839690—21no—
38#16839676—21no—
39#16839660C2211yescharacteristic
40#16839660C2211yescharacteristic
41#16839650—21no—
42#16839643—21no—
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic
45#16839622C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C22×#41×C61C2211yescharacteristic
51C22×#41×C61C2211yescharacteristic
52C61×#550—24no—
53C61×#550—24no—
54C2×#127×C61—21no—
55C2×#127×C61C2211yescharacteristic
56C2×#121×C61—21no—
57C2×#121×C61—21no—
58C2×#121×C61C2211yescharacteristic
59C2×#121×C61C2211yescharacteristic
60C2×C4×Q8×C61C2211yescharacteristic
61C2×C4×D4×C61—21no—
62C2×C4×D4×C61C2211yescharacteristic
63C22×#92418—22no—
64C22×#92418—41no—
65C22×#92418—41no—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519736—22no—
71#14519736—22no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C4×Dic61—21no—
83#14519710—22no—
84#14519708—22no—
85#14519701—22no—
86#14519701—22no—
87#14519701—22no—
88#14519701—22no—
89#14519698—22no—
90#14519698—22no—
91#14519698—22no—
92#14519698—22no—
93#14519698—41no—
94#14519698—41no—
95#14519698—41no—
96#14519698—41no—
97C22⋊#92418—22no—
98C22⋊#92418—41no—
99C22⋊#92418—41no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105C2×#41×C61—22no—
106C2×#41×C61—22no—
107C2×#41×C61—22no—
108C2×#41×C61—22no—
109C2×#41×C61—22no—
110C2×#41×C61—22no—
111C2×#41×C61—22no—
112C2×#41×C61—41no—
113C2×#41×C61—41no—
114C2×#41×C61—41no—
115C2×#41×C61—41no—
116C2×#41×C61D414yes—
117C22×Q8×C61C2311yescharacteristic
118C22×D4×C61—21no—
119C22×D4×C61—21no—
120C22×D4×C61—21no—
121C22×D4×C61—21no—
122C22×D4×C61—21no—
123C22×D4×C61—21no—
124C22×D4×C61D411yescharacteristic
125C22×D4×C61C2311yescharacteristic
126C22×D4×C61C2311yescharacteristic
127C23×C4×C61—21no—
128C23×C4×C61—21no—
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131#127×C61—28no—
132#127×C61—22no—
133#127×C61—22no—
134#121×C61—28no—
135#121×C61—28no—
136#121×C61—22no—
137#121×C61—22no—
138#121×C61—22no—
139#121×C61D414yes—
140C4×Q8×C61—22no—
141C4×Q8×C61—22no—
142C4×D4×C61—28no—
143C4×D4×C61—22no—
144C4×D4×C61—22no—
145C2×C4⋊C4×C61—21no—
146C2×C4⋊C4×C61D411yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61D411yescharacteristic
151C2×C22⋊C4×C61D411yescharacteristic
152C2×C42×C61—21no—
153C2×C42×C61C2311yescharacteristic
154C24×C61—21no—
155C24×C61—21no—
156C24×C61C2×D411yescharacteristic
157C24×C61C2×D411yescharacteristic
158#41×C61—28no—
159#41×C61—44no—
160#41×C61—44no—
161#41×C61—44no—
162#41×C61—44no—
163#41×C61—44no—
164#41×C61—44no—
165#41×C61—44no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61C2×D412yes—
170C2×Q8×C61#4112yes—
171C2×Q8×C61#4112yes—
172C2×D4×C61—24no—
173C2×D4×C61—24no—
174C2×D4×C61—22no—
175C2×D4×C61—24no—
176C2×D4×C61—24no—
177C2×D4×C61—24no—
178C2×D4×C61—24no—
179C2×D4×C61—22no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—41no—
191C2×D4×C61—42no—
192C2×D4×C61—42no—
193C2×D4×C61—42no—
194C2×D4×C61—42no—
195C2×D4×C61—42no—
196C2×D4×C61—42no—
197C2×D4×C61—81no—
198C2×D4×C61—81no—
199C2×D4×C61—81no—
200C2×D4×C61—81no—
201C2×D4×C61—81no—
202C2×D4×C61—81no—
203C2×D4×C61C2×D412yes—
204C2×D4×C61C2×D412yes—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—24no—
211C22×C4×C61—21no—
212C22×C4×C61—24no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—42no—
220C22×C4×C61—42no—
221C22×C4×C61—42no—
222C22×C4×C61—42no—
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D412yes—
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C4⋊C4×C61—24no—
235C4⋊C4×C61—22no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61C2×D412yes—
238C22⋊C4×C61—24no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—24no—
241C22⋊C4×C61—22no—
242C42×C61—24no—
243C42×C61—21no—
244C42×C61—21no—
245C22⋊Dic61—42no—
246C22⋊Dic61—42no—
247C22⋊Dic61—81no—
248C22⋊Dic61—81no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257#11758196—42no—
258#11758196—81no—
259C4×Dic61—42no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—44no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61#12012yes—
301C23×C61C22×D411yescharacteristic
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61#12314yes—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—44no—
311D4×C61—48no—
312D4×C61—48no—
313D4×C61—48no—
314D4×C61—41no—
315D4×C61—41no—
316D4×C61—41no—
317D4×C61—41no—
318D4×C61—84no—
319D4×C61—84no—
320D4×C61—84no—
321C2×C4×C61—21no—
322C2×C4×C61—22no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—21no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—21no—
333C2×C4×C61—22no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—48no—
340C2×C4×C61—48no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61#12012yes—
348C2×C4×C61#13512yes—
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C2×#4111yescharacteristic
352C2×C4×C61C2×#4111yescharacteristic
353C2×C4×C61H(5,𝔽2)11yescharacteristic
354C2×C4×C61H(5,𝔽2)11yescharacteristic
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367#92418—41no—
368#92418—41no—
369#92418—41no—
370#92418—41no—
371#24034—611nomaximal, Sylow
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—41no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61—81no—
398C22×C61—81no—
399C22×C61—81no—
400C22×C61C2×#12011yescharacteristic
401C22×C61#54611yescharacteristic
402C22×C61#54611yescharacteristic
403C22×C61C2×#13511yescharacteristic
404C22×C61#57511yescharacteristic
405C22×C61#57611yescharacteristic
406C22×C61#57711yescharacteristic
407C4×C61—22no—
408C4×C61—24no—
409C4×C61—22no—
410C4×C61—41no—
411C4×C61—41no—
412C4×C61—42no—
413C4×C61C2×#12311yescharacteristic
414C4×C61#53411yescharacteristic
415C4×C61#54611yescharacteristic
416C4×C61#54611yescharacteristic
417Dic61—81no—
418Dic61—81no—
419Dic61—81no—
420Dic61—81no—
421C2×#550D6111yescharacteristic
422C2×#482—611no—
423C2×#416—611no—
424#2485—611no—
425#2041—611no—
426#2041—611no—
427#2034—611no—
428#2033—611no—
429#1893—611no—
430#1869—611no—
431#1865—611no—
432#1863—611no—
433#1788—611no—
434#1788—611no—
435#1788—611no—
436C2×C61—42no—
437C2×C61—81no—
438C2×C61—82no—
439C2×C61—82no—
440C2×C61#240511yescharacteristic
441C2×C61#300211yescharacteristic
442C2×C61#301211yescharacteristic
443C2×C61#330411yescharacteristic
444C2×C61#330511yescharacteristic
445C2×C61#330911yescharacteristic
446C2×C61#331711yescharacteristic
447C22×#41C2×D6111yescharacteristic
448C22×#41C2×D6111yescharacteristic
449C23×C8—611no—
450#550—24no—
451#550—24no—
452C2×#127—21no—
453C2×#127C2×D6111yescharacteristic
454C2×#121—21no—
455C2×#121—21no—
456C2×#121C2×D6111yescharacteristic
457C2×#121C2×D6111yescharacteristic
458C2×C4×Q8C2×D6111yescharacteristic
459C2×C4×D4—21no—
460C2×C4×D4C2×D6111yescharacteristic
461C2×#117—611no—
462#482—1224no—
463C2×#107—611no—
464C2×#106—611no—
465#416—1224no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#103—611no—
469C2×#103—611no—
470C2×#102—611no—
471C2×#102—611no—
472C2×#102—611no—
473C2×#102—611no—
474C2×#102—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×C22⋊C8—611no—
479C2×C22⋊C8—611no—
480C2×C22⋊C8—611no—
481#397—1221no—
482#394—1221no—
483#389—611no—
484#389—611no—
485#388—1221no—
486#387—1221no—
487#380—611no—
488#380—611no—
489#380—611no—
490#340—611no—
491#340—611no—
492#336—611no—
493#336—611no—
494C61#2403411yescharacteristic, complemented, Sylow
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C22⋊D6114yes—
507C22×Q8C22×D6111yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4C22⋊D6111yescharacteristic
515C22×D4C22×D6111yescharacteristic
516C22×D4C22×D6111yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C22×D6111yescharacteristic
520C23×C4C22×D6111yescharacteristic
521C22×C8—611no—
522C22×C8—611no—
523C22×C8—611no—
524C22×C8—611no—
525C22×C8—1222no—
526C22×C8—2441no—
527C22×C8—2441no—
528#127—28no—
529#127—22no—
530#127—22no—
531#121—28no—
532#121—28no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121C22⋊D6114yes—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×D4—28no—
540C4×D4—22no—
541C4×D4—22no—
542#117—1222no—
543#117—1222no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—611no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4C22⋊D6111yescharacteristic
552C2×C4⋊C4C22×D6111yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4C22⋊D6111yescharacteristic
560C2×C22⋊C4C22⋊D6111yescharacteristic
561C2×C42—21no—
562C2×C42—1221no—
563C2×C42C22×D6111yescharacteristic
564#107—1222no—
565#106—1222no—
566#103—1222no—
567#103—1222no—
568#103—1222no—
569#103—1222no—
570#102—1222no—
571#102—1222no—
572#102—1222no—
573#102—1222no—
574#102—2441no—
575#102—2441no—
576#102—2441no—
577#102—2441no—
578C22⋊C8—1222no—
579C22⋊C8—2441no—
580C22⋊C8—2441no—
581#95—1221no—
582#95—1221no—
583#95—1221no—
584#95—1221no—
585#95—1221no—
586C24—21no—
587C24—21no—
588C24C2×C22⋊D6111yescharacteristic
589C24C2×C22⋊D6111yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8#1175822412yes—
602C2×Q8#1175822412yes—
603C2×Q8C2×C22⋊D6112yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—22no—
622C2×D4—41no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×C22⋊D6112yes—
636C2×D4C2×C22⋊D6112yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—24no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4C2×C22⋊D6111yescharacteristic
660C22×C4C2×C22⋊D6111yescharacteristic
661C22×C4C2×C22⋊D6112yes—
662C22×C4C2×C22⋊D6112yes—
663C22×C4C2×C22⋊D6111yescharacteristic
664C22×C4C2×C22⋊D6111yescharacteristic
665C22×C4C23×D6111yescharacteristic
666C2×C8—1221no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—2444no—
679C4⋊C4—24no—
680C4⋊C4—21no—
681C4⋊C4—22no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—4881no—
691C4⋊C4—2442no—
692C4⋊C4C2×C22⋊D6112yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—4881no—
698C22⋊C4—4881no—
699C22⋊C4—2442no—
700C22⋊C4—2442no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—2442no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23#1451974612yes—
733C23C22×C22⋊D6111yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8#1451975814yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4#1451974612yes—
792C2×C4#1451979712yes—
793C2×C4C22×C22⋊D6111yescharacteristic
794C2×C4C22×C22⋊D6111yescharacteristic
795C2×C4C2×#1175822411yescharacteristic
796C2×C4C2×#1175822411yescharacteristic
797C2×C4#1451982211yescharacteristic
798C2×C4#1451982211yescharacteristic
799C8—2441no—
800C8—2441no—
801C8—2441no—
802C8—2441no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—42no—
822C22—42no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22C2×#1451974611yescharacteristic
832C22#1684040611yescharacteristic
833C22#1684040611yescharacteristic
834C22C2×#1451979711yescharacteristic
835C22#1684056011yescharacteristic
836C22#1684056511yescharacteristic
837C22#1684057311yescharacteristic
838C4—22no—
839C4—24no—
840C4—22no—
841C4—41no—
842C4—42no—
843C4—41no—
844C4—4881no—
845C4—4881no—
846C4—4881no—
847C4—4881no—
848C4C2×#1451975811yescharacteristic
849C4#1684032111yescharacteristic
850C4#1684040611yescharacteristic
851C4#1684040611yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2#2144914211yescharacteristic
857C2#2145503711yescharacteristic
858C2#2145512311yescharacteristic
859C2#2145775811yescharacteristic
860C2#2145776911yescharacteristic
861C2#2145782511yescharacteristic
862C2#2145794511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#550C2
socleC23×C61C22×D4
hypercenterC2×#550D61
hypocenterC61#24034
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#16840083C2semidirect
2. C2×#16839758C2semidirect
3. #21450116C2semidirect
4. #21447050C2semidirect
5. #21447050C2semidirect
6. #21447005C2semidirect
7. #21446998C2semidirect
8. #21446248C2semidirect
9. #21446112C2semidirect
10. #21446087C2semidirect
11. #21446073C2semidirect
12. #21445759C2semidirect
13. #21445759C2semidirect
14. #21445759C2semidirect
494. C61#24034semidirect

Maximal subgroups

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

subgroupindex
C2×#168400832
C2×#168397582
#214501162
#214470502
#214470052
#214469982
#214462482
#214461122
#214460872
#214460732
#214457592
C2×C61×#5502
#2403461