Finite Group Databasebeta

← #29586767

Subgroups — #29586767

Order 15616.

1574 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519803C211yesmaximal, characteristic
2C22×#14519703C211yesmaximal, characteristic, complemented
3#21448407C211yesmaximal, characteristic, complemented
4C2×#16839665C211yesmaximal, characteristic, complemented
5C2×#16839530C211yesmaximal, characteristic, complemented
6C2×#16839521C211yesmaximal, characteristic, complemented
7C2×C61×#418C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C2×#14519803—22no—
10C2×#14519803—22no—
11C2×#14519803—22no—
12C2×#14519803—22no—
13C2×#14519803—22no—
14C2×#14519803C414yescomplemented
15C22×#11758200—21no—
16C22×#11758199—21no—
17C22×#11758194C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C22⋊Dic61—22no—
20C22×C4×Dic61C2211yescharacteristic
21C2×#14519703—22no—
22C2×#14519703—22no—
23C2×#14519703—22no—
24#16839668—21no—
25#16839665—22no—
26#16839665—22no—
27#16839664—21no—
28#16839639—22no—
29#16839619—22no—
30#16839530—22no—
31#16839521—22no—
32C23×D4×C61C2211yescharacteristic
33C22×M16×C61C2211yescharacteristic
34C2×#117×C61C2211yescharacteristic
35C61×#418—22no—
36C61×#418—22no—
37C2×#102×C61—22no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222C2×C412yes—
49C2×#11758222D412yes—
50C22×Dic122D411yescharacteristic
51C22×D244D411yescharacteristic
52C22×C22⋊D61—21no—
53C23×Dic61—21no—
54C23×Dic61D412yes—
55C22×C4×D61—21no—
56#14519803—28no—
57#14519803—28no—
58#14519803—28no—
59#14519803—28no—
60C2×#11758200—24no—
61C2×#11758200—24no—
62C2×#11758200—24no—
63C2×#11758199—24no—
64C2×#11758199—24no—
65C2×#11758199—24no—
66C2×#11758194—21no—
67C2×#11758194—21no—
68C2×#11758194—21no—
69C2×#11758194C2×C412yes—
70C2×#11758194D412yes—
71C2×#11758194D412yes—
72C22×#92418—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C22⋊Dic61—28no—
80C2×C22⋊Dic61—48no—
81C2×#11758198—24no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61D412yes—
88#14519703—28no—
89#14519684—24no—
90C25×C61—21no—
91C22×D4×C61—21no—
92C22×D4×C61—21no—
93C22×D4×C61—21no—
94C22×D4×C61—21no—
95C22×D4×C61—21no—
96C22×D4×C61—21no—
97C22×D4×C61—21no—
98C22×D4×C61—21no—
99C22×D4×C61—21no—
100C22×D4×C61—21no—
101C22×D4×C61—21no—
102C22×D4×C61C2×C412yes—
103C22×D4×C61D412yes—
104C22×D4×C61D412yes—
105C23×C4×C61C2311yescharacteristic
106C2×M16×C61—21no—
107C2×M16×C61—21no—
108C2×M16×C61—21no—
109C2×M16×C61—21no—
110C2×M16×C61—21no—
111C2×M16×C61D412yes—
112C22×C8×C61—21no—
113#117×C61—21no—
114#117×C61—21no—
115#117×C61—21no—
116#117×C61—21no—
117C2×C4⋊C4×C61D412yes—
118C2×C22⋊C4×C61—21no—
119C2×C42×C61—21no—
120#102×C61—28no—
121C24×C61—22no—
122C24×C61—22no—
123C24×C61—22no—
124C24×C61—44no—
125C24×C61—44no—
126C24×C61—41no—
127C24×C61—41no—
128C24×C61—41no—
129C24×C61—41no—
130C24×C61C2×D411yescharacteristic
131C23×D61—21no—
132C2×D4×C61—22no—
133C2×D4×C61—22no—
134C2×D4×C61—22no—
135C2×D4×C61—22no—
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61—22no—
139C2×D4×C61—22no—
140C2×D4×C61—22no—
141C2×D4×C61—22no—
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C2×D4×C61—22no—
147C2×D4×C61—41no—
148C2×D4×C61—41no—
149C2×D4×C61—41no—
150C2×D4×C61—41no—
151C2×D4×C61—41no—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C2×D4×C61—41no—
157C2×D4×C61—41no—
158C2×D4×C61—41no—
159C2×D4×C61C22⋊C414yescomplemented
160C22×C4×C61—22no—
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61#4111yescharacteristic
172C22×C4×C61#4111yescharacteristic
173C22×C4×C61#4111yescharacteristic
174C22×C4×C61#4111yescharacteristic
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—41no—
178C2×C22⋊D61—41no—
179C2×C22⋊D61—41no—
180C2×C22⋊D61—41no—
181C22×Dic61—24no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—42no—
188C22×Dic61—41no—
189C22×Dic61—41no—
190C22×Dic61—44no—
191#11758222—22no—
192#11758222—22no—
193#11758222—22no—
194#11758222—22no—
195#11758222—22no—
196#11758222—22no—
197#11758222—22no—
198#11758222—22no—
199#11758222—41no—
200#11758222—41no—
201#11758222—41no—
202#11758222—41no—
203#11758222—41no—
204#11758222—41no—
205#11758222—41no—
206#11758222—41no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244C22⋊C412yescomplemented
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—41no—
216C2×C4×D61—41no—
217C2×C4×D61—41no—
218C2×C4×D61—41no—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122C22⋊C412yescomplemented
225M16×C61—22no—
226M16×C61—22no—
227M16×C61—41no—
228M16×C61—41no—
229C2×C8×C61—22no—
230C2×C8×C61—41no—
231C2×C8×C61—41no—
232C4⋊C4×C61—22no—
233C4⋊C4×C61—22no—
234C22⋊C4×C61—41no—
235C22⋊C4×C61—41no—
236C42×C61—41no—
237C42×C61—41no—
238C22⋊Dic61—416no—
239#11758200—216no—
240#11758199—216no—
241#11758198—84no—
242C4⋊Dic61—41no—
243C4⋊Dic61—41no—
244C4⋊Dic61—41no—
245C4⋊Dic61—41no—
246C4×Dic61—22no—
247C4×Dic61—22no—
248C4×Dic61—41no—
249C4×Dic61—41no—
250#11758194—22no—
251#11758194—22no—
252#11758194—22no—
253#11758194C22⋊C414yescomplemented
254C2×#92418—22no—
255C2×#92418—22no—
256C2×#92418—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—24no—
260C23×C61—44no—
261C23×C61—48no—
262C23×C61—44no—
263C23×C61—48no—
264C23×C61—42no—
265C23×C61—42no—
266C23×C61—42no—
267C23×C61—42no—
268C23×C61—42no—
269C23×C61—42no—
270C23×C61—84no—
271C23×C61—82no—
272C23×C61—82no—
273C23×C61—84no—
274C23×C61—82no—
275C23×C61—82no—
276C23×C61C4×D411yescharacteristic
277C23×C61#12011yescharacteristic
278C23×C61#12011yescharacteristic
279C23×C61#12111yescharacteristic
280C23×C61#12111yescharacteristic
281C23×C61#12111yescharacteristic
282C23×C61#12711yescharacteristic
283C22×D61—22no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—42no—
287C22×D61—42no—
288D4×C61—24no—
289D4×C61—24no—
290D4×C61—42no—
291D4×C61—42no—
292D4×C61—42no—
293D4×C61—42no—
294D4×C61—42no—
295D4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61C2×C22⋊C411yescharacteristic
300C2×C4×C61C2×C22⋊C411yescharacteristic
301C2×C4×C61C2×C22⋊C411yescharacteristic
302C2×C4×C61C4×D411yescharacteristic
303C2×C4×C61C4×D411yescharacteristic
304C2×C4×C61C4×D411yescharacteristic
305C2×C4×C61#12011yescharacteristic
306C2×C4×C61#12011yescharacteristic
307C2×C4×C61#12011yescharacteristic
308C2×C4×C61#12011yescharacteristic
309C2×C4×C61#12011yescharacteristic
310C2×C4×C61#12011yescharacteristic
311C2×C4×C61#12111yescharacteristic
312C2×C4×C61#12111yescharacteristic
313C2×C4×C61#12111yescharacteristic
314C2×C4×C61#12111yescharacteristic
315C2×C4×C61#12111yescharacteristic
316C2×C4×C61#12111yescharacteristic
317C2×C4×C61#12111yescharacteristic
318C2×C4×C61#12111yescharacteristic
319C2×C4×C61#12111yescharacteristic
320C2×C4×C61#12311yescharacteristic
321C2×C4×C61#12311yescharacteristic
322C2×C4×C61#12311yescharacteristic
323C2×C4×C61#12311yescharacteristic
324C2×C4×C61#12411yescharacteristic
325C2×C4×C61#12411yescharacteristic
326C2×C4×C61#12711yescharacteristic
327C22⋊D61—42no—
328C22⋊D61—42no—
329C22⋊D61—42no—
330C22⋊D61—42no—
331C2×Dic61—24no—
332C2×Dic61—22no—
333C2×Dic61—44no—
334C2×Dic61—42no—
335C2×Dic61—44no—
336C2×Dic61—42no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—44no—
340C2×Dic61—42no—
341C2×Dic61—44no—
342C2×Dic61—82no—
343D244—22no—
344D244—22no—
345D244—41no—
346D244—41no—
347C4×D61—42no—
348C4×D61—42no—
349C4×D61—42no—
350C4×D61—42no—
351Dic122—22no—
352Dic122—22no—
353Dic122—41no—
354Dic122—41no—
355C8×C61—42no—
356#92418—24no—
357#11016—611nomaximal, Sylow
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—48no—
367C22×C61—44no—
368C22×C61—84no—
369C22×C61—84no—
370C22×C61—84no—
371C22×C61—84no—
372C22×C61—82no—
373C22×C61—82no—
374C22×C61—84no—
375C22×C61#38611yescharacteristic
376C22×C61#38611yescharacteristic
377C22×C61#39011yescharacteristic
378C22×C61#39211yescharacteristic
379C22×C61#39211yescharacteristic
380C22×C61#39211yescharacteristic
381C22×C61#39411yescharacteristic
382C22×C61#45312yes—
383C22×C61#45412yes—
384C2×D61—44no—
385C2×D61—42no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—82no—
389C4×C61—82no—
390C4×C61#37911yescharacteristic
391C4×C61#38611yescharacteristic
392C4×C61#38611yescharacteristic
393C4×C61#39011yescharacteristic
394C4×C61#39211yescharacteristic
395C4×C61#39411yescharacteristic
396C4×C61#39411yescharacteristic
397C4×C61#39411yescharacteristic
398Dic61—44no—
399Dic61—42no—
400Dic61—82no—
401C22×AGL(1,ℤ/8)—611no—
402C22×#104—611no—
403C2×#418D6111yescharacteristic, complemented
404#2311—611no—
405C2×#390—611no—
406C2×#343—611no—
407C2×#339—611no—
408C2×C61—21no—
409C2×C61—21no—
410C2×C61—21no—
411C2×C61—21no—
412C2×C61—84no—
413C2×C61#143811yescharacteristic
414C2×C61#188312yes—
415C2×C61#200211yescharacteristic
416C2×C61#200311yescharacteristic
417C2×C61#200612yes—
418D61—82no—
419C22×#41—611no—
420C23×D4C2×D6111yescharacteristic
421C2×AGL(1,ℤ/8)—614no—
422C2×AGL(1,ℤ/8)—1222no—
423C2×AGL(1,ℤ/8)—1222no—
424C2×AGL(1,ℤ/8)—1222no—
425C2×AGL(1,ℤ/8)—1222no—
426C2×AGL(1,ℤ/8)—1222no—
427C22×SD16—1221no—
428C22×D8—1221no—
429C22×M16—611no—
430C22×M16C2×D6111yescharacteristic
431C2×#117C2×D6111yescharacteristic
432C22×C4⋊C4—611no—
433C22×C22⋊C4—1222no—
434C22×C42—611no—
435C2×#104—1222no—
436C2×#104—1222no—
437C2×#104—1222no—
438#418—22no—
439#418—22no—
440C2×#102—22no—
441#391—1221no—
442#390—1221no—
443#390—1222no—
444#390—1222no—
445#386—1222no—
446#380—1222no—
447#343—1222no—
448#339—1222no—
449C61#1101611yescharacteristic, complemented, Sylow
450C25—21no—
451C2×#41—612no—
452C2×#41—612no—
453C2×#41—1221no—
454C2×#41—1221no—
455C2×#41—1221no—
456C2×#41—1221no—
457C2×#41—1221no—
458C2×#41—1221no—
459C2×#41—1221no—
460C2×#41—1221no—
461C2×#41—1221no—
462C2×#41—1221no—
463C22×Q8—611no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—611no—
476C22×D4—1221no—
477C22×D4C4×D6112yes—
478C22×D4D24412yes—
479C22×D4C22⋊D6112yes—
480C23×C4—612no—
481C23×C4—1221no—
482C23×C4—1221no—
483C23×C4C22×D6111yescharacteristic
484AGL(1,ℤ/8)—1228no—
485AGL(1,ℤ/8)—1228no—
486AGL(1,ℤ/8)—1228no—
487AGL(1,ℤ/8)—1228no—
488C2×SD16—1224no—
489C2×SD16—1224no—
490C2×SD16—1224no—
491C2×D8—1224no—
492C2×D8—1224no—
493C2×D8—1224no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—612no—
500C2×M16—612no—
501C2×M16—612no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16—1221no—
505C2×M16C22⋊D6112yes—
506C22×C8—21no—
507C22×C8—1221no—
508#117—21no—
509#117—21no—
510#117—21no—
511#117—21no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4C22⋊D6112yes—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—1224no—
521C2×C22⋊C4—1228no—
522C2×C22⋊C4—2448no—
523C2×C42—21no—
524C2×C42—612no—
525C2×C42—1221no—
526C2×C42—1221no—
527C2×C42—1221no—
528C2×C42—1221no—
529C2×C42—1221no—
530#104—1228no—
531#102—28no—
532#95—1224no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—44no—
537C24—44no—
538C24—41no—
539C24—41no—
540C24—41no—
541C24—41no—
542C24—1221no—
543C24D4×D6111yescharacteristic
544#41—1222no—
545#41—1222no—
546#41—1222no—
547#41—1222no—
548#41—1222no—
549#41—1222no—
550#41—1222no—
551#41—1222no—
552#41—2441no—
553#41—2441no—
554#41—2441no—
555#41—2441no—
556#41—2441no—
557#41—2441no—
558#41—2441no—
559#41—2441no—
560C2×Q8—612no—
561C2×Q8—1221no—
562C2×Q8—1221no—
563C2×Q8—1221no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—612no—
594C2×D4—1222no—
595C2×D4—1222no—
596C2×D4—1221no—
597C2×D4—1221no—
598C2×D4—1221no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4—2441no—
602C2×D4—2441no—
603C2×D4—2441no—
604C2×D4—2441no—
605C2×D4#1175819814yescomplemented
606C22×C4—22no—
607C22×C4—1224no—
608C22×C4—1221no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—2444no—
616C22×C4—2442no—
617C22×C4—2441no—
618C22×C4—2441no—
619C22×C4—2441no—
620C22×C4—2441no—
621C22×C4—2441no—
622C22×C4—2441no—
623C22×C4C2×C4×D6111yescharacteristic
624C22×C4C2×D24411yescharacteristic
625C22×C4#1175822211yescharacteristic
626C22×C4#1175822211yescharacteristic
627C22×C4D4×D6111yescharacteristic
628C22×C4D4×D6111yescharacteristic
629C22×C4D4×D6111yescharacteristic
630C22×C4D4×D6111yescharacteristic
631C22×C4D4×D6111yescharacteristic
632C22×C4#1175822411yescharacteristic
633C22×C4#1175822411yescharacteristic
634C22×C4C2×C22⋊D6111yescharacteristic
635C22×C4C2×C22⋊D6111yescharacteristic
636C22×C4C2×C22⋊D6111yescharacteristic
637SD16—12216no—
638D8—12216no—
639M16—22no—
640M16—22no—
641M16—41no—
642M16—41no—
643M16—614no—
644M16—1222no—
645M16—1222no—
646M16—1222no—
647C2×C8—22no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—1222no—
651C2×C8—1222no—
652C2×C8—1222no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—2441no—
656C4⋊C4—2441no—
657C4⋊C4—2441no—
658C4⋊C4—2441no—
659C22⋊C4—41no—
660C22⋊C4—41no—
661C22⋊C4—4884no—
662C22⋊C4—24416no—
663C42—41no—
664C42—41no—
665C42—1222no—
666C42—1222no—
667C42—2441no—
668C42—2441no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—44no—
673C23—48no—
674C23—44no—
675C23—48no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—84no—
683C23—82no—
684C23—82no—
685C23—84no—
686C23—82no—
687C23—82no—
688C23—1222no—
689C23—2441no—
690C23—2441no—
691C23—2442no—
692C23—2442no—
693C23#1451973711yescharacteristic
694C23#1451974511yescharacteristic
695C23#1451974711yescharacteristic
696C23#1451974911yescharacteristic
697C23#1451975011yescharacteristic
698C23#1451975011yescharacteristic
699C23#1451977311yescharacteristic
700Q8—1222no—
701Q8—1222no—
702Q8—2441no—
703Q8—2441no—
704D4—24no—
705D4—24no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—1222no—
713D4—1222no—
714D4—2442no—
715D4—2442no—
716D4—2442no—
717D4—2442no—
718D4—2441no—
719D4—2441no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—1224no—
724C2×C4—1222no—
725C2×C4—4882no—
726C2×C4—2444no—
727C2×C4—2442no—
728C2×C4—2444no—
729C2×C4—2444no—
730C2×C4—2442no—
731C2×C4—2444no—
732C2×C4—2441no—
733C2×C4—2442no—
734C2×C4—2441no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4C22⋊C4×D6111yescharacteristic
740C2×C4C22⋊C4×D6111yescharacteristic
741C2×C4C2×#1175819811yescharacteristic
742C2×C4#1451973711yescharacteristic
743C2×C4C4×C22⋊D6111yescharacteristic
744C2×C4C4×C22⋊D6111yescharacteristic
745C2×C4#1451974511yescharacteristic
746C2×C4#1451974511yescharacteristic
747C2×C4#1451974511yescharacteristic
748C2×C4#1451974611yescharacteristic
749C2×C4#1451974711yescharacteristic
750C2×C4#1451974711yescharacteristic
751C2×C4#1451974811yescharacteristic
752C2×C4#1451974811yescharacteristic
753C2×C4#1451974911yescharacteristic
754C2×C4#1451974911yescharacteristic
755C2×C4#1451974911yescharacteristic
756C2×C4#1451975011yescharacteristic
757C2×C4#1451975011yescharacteristic
758C2×C4#1451975111yescharacteristic
759C2×C4#1451975111yescharacteristic
760C2×C4#1451975911yescharacteristic
761C2×C4#1451975911yescharacteristic
762C2×C4#1451976011yescharacteristic
763C2×C4#1451976111yescharacteristic
764C2×C4#1451976311yescharacteristic
765C2×C4#1451976311yescharacteristic
766C2×C4#1451977311yescharacteristic
767C8—42no—
768C8—1224no—
769C22—22no—
770C22—22no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—22no—
776C22—22no—
777C22—48no—
778C22—44no—
779C22—84no—
780C22—84no—
781C22—84no—
782C22—84no—
783C22—82no—
784C22—82no—
785C22—84no—
786C22—4881no—
787C22—4881no—
788C22—4882no—
789C22—2444no—
790C22—2442no—
791C22#1683963811yescharacteristic
792C22#1683963911yescharacteristic
793C22#1683966211yescharacteristic
794C22#1683967011yescharacteristic
795C22#1683967111yescharacteristic
796C22#1683967111yescharacteristic
797C22#1683967711yescharacteristic
798C22#1683992812yes—
799C22#1683993312yes—
800C4—82no—
801C4—4882no—
802C4—2444no—
803C4—2442no—
804C4#1683961711yescharacteristic
805C4#1683963811yescharacteristic
806C4#1683964111yescharacteristic
807C4#1683966211yescharacteristic
808C4#1683967011yescharacteristic
809C4#1683967711yescharacteristic
810C4#1683967811yescharacteristic
811C4#1683967811yescharacteristic
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—84no—
817C2—4882no—
818C2#2144405811yescharacteristic
819C2#2144619212yes—
820C2#2144683511yescharacteristic
821C2#2144684211yescharacteristic
822C2#2144685912yes—
subgroupG/H
centerC23#14519745
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#418C2
socleC23×C61#120
prime radicalC22×#14519803C2
cosocleC23×C4×C61C23
hypercenterC2×#418D61
hypocenterC61#11016
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C22×#14519703C2semidirect
3. #21448407C2semidirect
4. C2×#16839665C2semidirect
5. C2×#16839530C2semidirect
6. C2×#16839521C2semidirect
7. C2×C61×#418C2semidirect
14. C2×#14519803C4semidirect
159. C2×D4×C61C22⋊C4semidirect
212. C2×D244C22⋊C4semidirect
224. C2×Dic122C22⋊C4semidirect
253. #11758194C22⋊C4semidirect
403. C2×#418D61semidirect
449. C61#11016semidirect
605. C2×D4#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145198032
C22×#145197032
#214484072
C2×#168396652
C2×#168395302
C2×#168395212
C2×C61×#4182
#1101661