Finite Group Databasebeta

← #29586596

Subgroups — #29586596

Order 15616.

1334 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840340C211yesmaximal, characteristic
2C2×#16839779C211yesmaximal, characteristic, complemented
3C2×#16839744C211yesmaximal, characteristic, complemented
4C2×#16839735C211yesmaximal, characteristic, complemented
5#21445540C211yesmaximal, characteristic, complemented
6#21445539C211yesmaximal, characteristic, complemented
7C2×C61×#421C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10#16840340—22no—
11#16840340—22no—
12#16840340—22no—
13#16840340—22no—
14C2×#14519756—21no—
15C2×#14519753C412yescomplemented
16C2×#14519751—21no—
17C2×#14519749—22no—
18C2×#14519748C412yescomplemented
19C2×#14519736C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21#16839779—22no—
22#16839779—22no—
23C2×#14519704—22no—
24#16839744—22no—
25#16839744—22no—
26C2×#14519695—21no—
27C2×#14519693—21no—
28#16839735—22no—
29#16839735—22no—
30C2×#14519691—22no—
31#16839525—22no—
32#16839524—22no—
33C22×#41×C61C2211yescharacteristic
34C22×M16×C61C2211yescharacteristic
35C2×#117×C61C2211yescharacteristic
36C61×#421—22no—
37C61×#421—22no—
38C2×#104×C61—22no—
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×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C22×Dic122D411yescharacteristic
52C22×D244D411yescharacteristic
53C22×C22⋊D61—22no—
54C22×C22⋊D61D412yes—
55C23×Dic61—21no—
56C22×C4×D61C2×C412yes—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194—21no—
62C2×#11758194D412yescomplemented
63C22×#92418—21no—
64#14519756—24no—
65#14519756—24no—
66#14519753—24no—
67#14519753—24no—
68#14519751—24no—
69#14519751—24no—
70#14519749—28no—
71#14519749—28no—
72#14519748—24no—
73#14519748—24no—
74#14519736—21no—
75#14519736—21no—
76#14519736—21no—
77#14519736D412yescomplemented
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61C2×C412yes—
83C2×C4⋊Dic61D412yes—
84C2×C4⋊Dic61D412yes—
85C2×#11758196—22no—
86C2×C22⋊Dic61—22no—
87C2×C22⋊Dic61—21no—
88C2×#11758198—22no—
89C2×C4×Dic61—21no—
90#14519704—28no—
91#14519695—24no—
92#14519693—24no—
93#14519691—28no—
94C2×#41×C61—21no—
95C2×#41×C61—21no—
96C2×#41×C61—21no—
97C2×#41×C61—21no—
98C2×#41×C61—21no—
99C2×#41×C61—21no—
100C2×#41×C61—21no—
101C2×#41×C61—21no—
102C2×#41×C61—21no—
103C2×#41×C61—21no—
104C2×#41×C61D412yes—
105C2×#41×C61D412yes—
106C22×Q8×C61C2×C411yescharacteristic
107C22×D4×C61—21no—
108C22×D4×C61C2×C411yescharacteristic
109C23×C4×C61—21no—
110C23×C4×C61C2311yescharacteristic
111C2×M16×C61—21no—
112C2×M16×C61—21no—
113C2×M16×C61—21no—
114C2×M16×C61—21no—
115C2×M16×C61—21no—
116C2×M16×C61D412yescomplemented
117C22×C8×C61—21no—
118#117×C61—21no—
119#117×C61—21no—
120#117×C61—21no—
121#117×C61D412yescomplemented
122C2×C4⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C42×C61—21no—
125#104×C61—28no—
126C24×C61—21no—
127C24×C61C2×D411yescharacteristic
128C23×D61C22⋊C412yes—
129#41×C61—22no—
130#41×C61—22no—
131#41×C61—22no—
132#41×C61—22no—
133#41×C61—22no—
134#41×C61—22no—
135#41×C61—22no—
136#41×C61—22no—
137#41×C61—41no—
138#41×C61—41no—
139#41×C61—41no—
140#41×C61—41no—
141#41×C61—41no—
142#41×C61—41no—
143#41×C61—41no—
144#41×C61—41no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61C22⋊C412yes—
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—41no—
159C2×D4×C61—41no—
160C2×D4×C61—41no—
161C2×D4×C61—41no—
162C2×D4×C61C22⋊C412yes—
163C22×C4×C61—21no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—41no—
167C22×C4×C61—41no—
168C22×C4×C61—41no—
169C22×C4×C61—41no—
170C22×C4×C61—41no—
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61#4111yescharacteristic
182C22×C4×C61#4111yescharacteristic
183C22×C4×C61#4111yescharacteristic
184C22×C4×C61#4111yescharacteristic
185C2×C22⋊D61—22no—
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61—28no—
192C2×C22⋊D61—84no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—41no—
197C22×Dic61—82no—
198C22×Dic61C22⋊C412yes—
199#11758222—41no—
200#11758222—41no—
201#11758222—41no—
202#11758222—41no—
203#11758222—41no—
204#11758222—41no—
205#11758222—41no—
206#11758222—41no—
207#11758222—41no—
208#11758222—41no—
209#11758222—41no—
210#11758222—41no—
211#11758222—41no—
212#11758222—41no—
213#11758222—41no—
214#11758222—41no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×C4×D61—22no—
222C2×C4×D61—22no—
223C2×C4×D61—22no—
224C2×C4×D61—22no—
225C2×C4×D61—22no—
226C2×C4×D61—22no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233M16×C61—22no—
234M16×C61—22no—
235M16×C61—41no—
236M16×C61—41no—
237C2×C8×C61—22no—
238C2×C8×C61—41no—
239C2×C8×C61—41no—
240C4⋊C4×C61—22no—
241C4⋊C4×C61—41no—
242C22⋊C4×C61—22no—
243C22⋊C4×C61—41no—
244C42×C61—22no—
245C42×C61—41no—
246C22⋊Dic61—28no—
247C22⋊Dic61—22no—
248C22⋊Dic61—41no—
249#11758198—28no—
250C4⋊Dic61—22no—
251C4⋊Dic61—22no—
252C4⋊Dic61—22no—
253C4⋊Dic61—22no—
254C4⋊Dic61—41no—
255C4⋊Dic61C22⋊C414yes—
256#11758196—28no—
257C4×Dic61—22no—
258C4×Dic61—41no—
259#11758194—22no—
260#11758194—22no—
261#11758194—41no—
262#11758194—41no—
263C2×#92418—22no—
264C2×#92418—41no—
265C2×#92418—41no—
266C23×C61—22no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—42no—
270C23×C61—42no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61C2×C22⋊C411yescharacteristic
274C23×C61#12011yescharacteristic
275C23×C61#12011yescharacteristic
276C23×C61#12011yescharacteristic
277C23×C61#12111yescharacteristic
278C23×C61#12111yescharacteristic
279C23×C61#12311yescharacteristic
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—42no—
284C22×D61—42no—
285Q8×C61—22no—
286Q8×C61—22no—
287Q8×C61—41no—
288Q8×C61—41no—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—42no—
292D4×C61—42no—
293D4×C61—42no—
294D4×C61—42no—
295D4×C61—41no—
296D4×C61—41no—
297C2×C4×C61—22no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—81no—
306C2×C4×C61—81no—
307C2×C4×C61C2×C22⋊C411yescharacteristic
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C4×D411yescharacteristic
310C2×C4×C61C4×D411yescharacteristic
311C2×C4×C61C4×D411yescharacteristic
312C2×C4×C61C4×D411yescharacteristic
313C2×C4×C61#12011yescharacteristic
314C2×C4×C61#12011yescharacteristic
315C2×C4×C61#12011yescharacteristic
316C2×C4×C61#12011yescharacteristic
317C2×C4×C61#12011yescharacteristic
318C2×C4×C61#12111yescharacteristic
319C2×C4×C61#12111yescharacteristic
320C2×C4×C61#12111yescharacteristic
321C2×C4×C61#12111yescharacteristic
322C2×C4×C61#12111yescharacteristic
323C2×C4×C61#12111yescharacteristic
324C2×C4×C61#12111yescharacteristic
325C2×C4×C61#12111yescharacteristic
326C2×C4×C61#12111yescharacteristic
327C2×C4×C61#12111yescharacteristic
328C2×C4×C61#12311yescharacteristic
329C2×C4×C61#12311yescharacteristic
330C2×C4×C61#12311yescharacteristic
331C2×C4×C61#12411yescharacteristic
332C2×C4×C61#12411yescharacteristic
333C2×C4×C61#12711yescharacteristic
334C2×C4×C61#12711yescharacteristic
335C22⋊D61—42no—
336C22⋊D61—42no—
337C22⋊D61—42no—
338C22⋊D61—42no—
339C22⋊D61—88no—
340C2×Dic61—22no—
341C2×Dic61—24no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—44no—
345C2×Dic61—42no—
346C2×Dic61—82no—
347C2×Dic61—82no—
348C2×Dic61—81no—
349C2×Dic61—81no—
350D244—41no—
351D244—41no—
352D244—41no—
353D244—41no—
354C4×D61—42no—
355C4×D61—42no—
356C4×D61—42no—
357C4×D61—42no—
358Dic122—41no—
359Dic122—41no—
360Dic122—41no—
361Dic122—41no—
362C8×C61—42no—
363#92418—42no—
364#10986—611nomaximal, Sylow
365C22×C61—21no—
366C22×C61—21no—
367C22×C61—21no—
368C22×C61—21no—
369C22×C61—21no—
370C22×C61—21no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—82no—
379C22×C61—82no—
380C22×C61#37911yescharacteristic
381C22×C61#38611yescharacteristic
382C22×C61#38611yescharacteristic
383C22×C61#39211yescharacteristic
384C22×C61#39211yescharacteristic
385C22×C61#39411yescharacteristic
386C22×C61#39411yescharacteristic
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—82no—
391C2×D61—82no—
392C4×C61—42no—
393C4×C61—82no—
394C4×C61#38611yescharacteristic
395C4×C61#38611yescharacteristic
396C4×C61#39011yescharacteristic
397C4×C61#39011yescharacteristic
398C4×C61#39211yescharacteristic
399C4×C61#39211yescharacteristic
400C4×C61#39411yescharacteristic
401C4×C61#39411yescharacteristic
402Dic61—44no—
403Dic61—42no—
404Dic61—82no—
405C2×#537—611no—
406C2×#421—611no—
407C2×#421D6111yescharacteristic, complemented
408C2×#413—611no—
409C2×#410—611no—
410#1736—611no—
411#1736—611no—
412C2×C61—21no—
413C2×C61—21no—
414C2×C61—21no—
415C2×C61—21no—
416C2×C61—21no—
417C2×C61—21no—
418C2×C61—82no—
419C2×C61#143811yescharacteristic
420C2×C61#179511yescharacteristic
421C2×C61#179611yescharacteristic
422D61—82no—
423C22×#41—611no—
424C22×#41C2×D6111yescharacteristic
425C22×M16—611no—
426C22×M16C2×D6111yescharacteristic
427#537—1222no—
428#537—1222no—
429#537—1222no—
430#537—1222no—
431C2×C22⋊Q8—612no—
432C2×C22⋊Q8—1221no—
433C2×#121—612no—
434C2×#121—1221no—
435C2×#121—1222no—
436C2×#117—611no—
437C2×#117C2×D6111yescharacteristic
438C22×C4⋊C4—611no—
439#421—22no—
440#421—22no—
441#421—1222no—
442#421—1222no—
443C2×#104—22no—
444C2×#104—1222no—
445#413—1222no—
446#413—1222no—
447C2×#101—1221no—
448C2×#100—1221no—
449#410—1222no—
450#410—1222no—
451C2×#99—1222no—
452#340—1222no—
453#340—1222no—
454C61#1098611yescharacteristic, complemented, Sylow
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—1221no—
466C2×#41—1221no—
467C2×#41—1221no—
468C2×#41—1221no—
469C2×#41—1221no—
470C2×#41—1221no—
471C2×#41—1221no—
472C2×#41—1221no—
473C2×#41—1221no—
474C2×#41—1221no—
475C2×#41—1221no—
476C2×#41—1221no—
477C2×#41D24412yes—
478C2×#41C22⋊D6112yes—
479C22×Q8—611no—
480C22×Q8C4×D6111yescharacteristic
481C22×D4—21no—
482C22×D4—612no—
483C22×D4—611no—
484C22×D4—1222no—
485C22×D4C4×D6111yescharacteristic
486C23×C4—21no—
487C23×C4—612no—
488C23×C4—1221no—
489C23×C4C22×D6111yescharacteristic
490C2×M16—21no—
491C2×M16—21no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—612no—
496C2×M16—1221no—
497C2×M16—1221no—
498C2×M16—1221no—
499C2×M16—1221no—
500C2×M16—1221no—
501C2×M16C22⋊D6112yescomplemented
502C22×C8—21no—
503C22×C8—1221no—
504C22⋊Q8—1224no—
505C22⋊Q8—1224no—
506C22⋊Q8—1224no—
507C22⋊Q8—1224no—
508#121—1224no—
509#121—1224no—
510#121—1224no—
511#121—1228no—
512#121—1228no—
513#121—1224no—
514#117—21no—
515#117—21no—
516#117—21no—
517#117—612no—
518#117—1221no—
519#117—1221no—
520#117—1221no—
521#117C22⋊D6112yescomplemented
522C2×C4⋊C4—21no—
523C2×C4⋊C4—612no—
524C2×C4⋊C4—612no—
525C2×C4⋊C4—612no—
526C2×C4⋊C4—1222no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—1222no—
533C2×C22⋊C4—1222no—
534C2×C22⋊C4—1221no—
535C2×C42—21no—
536C2×C42—1221no—
537#104—28no—
538#104—1228no—
539#101—1224no—
540#100—1224no—
541#99—1228no—
542C24—21no—
543C24—612no—
544C24D4×D6111yescharacteristic
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—2441no—
562#41—2441no—
563#41—2441no—
564#41—2441no—
565#41—2441no—
566#41—2441no—
567#41—2441no—
568#41—2441no—
569#41—2441no—
570#41—2441no—
571#41—2441no—
572#41—2441no—
573#41—2441no—
574#41—2441no—
575#41—2441no—
576#41—2441no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—1221no—
583C2×Q8—1221no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8#1175819812yes—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—1228no—
601C2×D4—1222no—
602C2×D4—1222no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—4884no—
614C2×D4#1175819812yes—
615C22×C4—21no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—612no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—4882no—
634C22×C4—2441no—
635C22×C4C2×C4×D6111yescharacteristic
636C22×C4C2×D24411yescharacteristic
637C22×C4#1175822211yescharacteristic
638C22×C4#1175822211yescharacteristic
639C22×C4D4×D6111yescharacteristic
640C22×C4D4×D6111yescharacteristic
641C22×C4D4×D6111yescharacteristic
642C22×C4D4×D6111yescharacteristic
643C22×C4D4×D6111yescharacteristic
644C22×C4#1175822411yescharacteristic
645C22×C4#1175822411yescharacteristic
646C22×C4C2×C22⋊D6111yescharacteristic
647C22×C4C2×C22⋊D6111yescharacteristic
648C22×C4C2×C22⋊D6111yescharacteristic
649M16—22no—
650M16—22no—
651M16—41no—
652M16—41no—
653M16—1222no—
654M16—1222no—
655M16—2441no—
656M16—2441no—
657C2×C8—22no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—1222no—
661C2×C8—2441no—
662C2×C8—2441no—
663C4⋊C4—22no—
664C4⋊C4—41no—
665C4⋊C4—614no—
666C4⋊C4—1228no—
667C4⋊C4—1222no—
668C4⋊C4—1222no—
669C4⋊C4—1222no—
670C4⋊C4—1222no—
671C4⋊C4—2441no—
672C22⋊C4—22no—
673C22⋊C4—41no—
674C22⋊C4—1228no—
675C22⋊C4—1228no—
676C22⋊C4—1222no—
677C22⋊C4—2441no—
678C42—22no—
679C42—41no—
680C42—1222no—
681C42—2441no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23—41no—
688C23—41no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—2442no—
693C23—2442no—
694C23C22⋊C4×D6111yescharacteristic
695C23#1451974511yescharacteristic
696C23#1451974511yescharacteristic
697C23#1451974711yescharacteristic
698C23#1451974811yescharacteristic
699C23#1451975011yescharacteristic
700C23#1451975911yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—41no—
704Q8—41no—
705Q8—2441no—
706Q8—2441no—
707Q8—2441no—
708Q8—2441no—
709D4—22no—
710D4—22no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—41no—
716D4—41no—
717D4—4888no—
718D4—2442no—
719D4—2442no—
720D4—2442no—
721D4—2442no—
722D4—2441no—
723D4—2441no—
724D4—2441no—
725D4—2441no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—1224no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—4881no—
741C2×C4—4881no—
742C2×C4—4882no—
743C2×C4—4882no—
744C2×C4—2442no—
745C2×C4—2444no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4C22⋊C4×D6111yescharacteristic
751C2×C4C2×#1175819811yescharacteristic
752C2×C4#1451973711yescharacteristic
753C2×C4#1451973711yescharacteristic
754C2×C4C4×C22⋊D6111yescharacteristic
755C2×C4C4×C22⋊D6111yescharacteristic
756C2×C4#1451974511yescharacteristic
757C2×C4#1451974511yescharacteristic
758C2×C4#1451974611yescharacteristic
759C2×C4#1451974711yescharacteristic
760C2×C4#1451974711yescharacteristic
761C2×C4#1451974811yescharacteristic
762C2×C4#1451974911yescharacteristic
763C2×C4#1451974911yescharacteristic
764C2×C4#1451974911yescharacteristic
765C2×C4#1451974911yescharacteristic
766C2×C4#1451975011yescharacteristic
767C2×C4#1451975011yescharacteristic
768C2×C4#1451975011yescharacteristic
769C2×C4#1451975111yescharacteristic
770C2×C4#1451975111yescharacteristic
771C2×C4#1451975911yescharacteristic
772C2×C4#1451976011yescharacteristic
773C2×C4#1451976111yescharacteristic
774C2×C4#1451976311yescharacteristic
775C2×C4#1451976311yescharacteristic
776C2×C4#1451977311yescharacteristic
777C2×C4#1451977311yescharacteristic
778C8—42no—
779C8—2442no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—82no—
794C22—82no—
795C22—4882no—
796C22—4882no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22#1683961711yescharacteristic
801C22#1683963811yescharacteristic
802C22#1683963811yescharacteristic
803C22#1683967011yescharacteristic
804C22#1683967111yescharacteristic
805C22#1683967711yescharacteristic
806C22#1683967811yescharacteristic
807C4—42no—
808C4—82no—
809C4—4882no—
810C4—2444no—
811C4—2442no—
812C4#1683963911yescharacteristic
813C4#1683964111yescharacteristic
814C4#1683966211yescharacteristic
815C4#1683966211yescharacteristic
816C4#1683967011yescharacteristic
817C4#1683967111yescharacteristic
818C4#1683967711yescharacteristic
819C4#1683967811yescharacteristic
820C2—21no—
821C2—21no—
822C2—21no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—82no—
827C2—4882no—
828C2#2144405811yescharacteristic
829C2#2144578811yescharacteristic
830C2#2144579311yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#421C2
socleC22×C61#379
prime radicalC2×#16840340C2
cosocleC23×C4×C61C23
hypercenterC2×#421D61
hypocenterC61#10986
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#16839779C2semidirect
3. C2×#16839744C2semidirect
4. C2×#16839735C2semidirect
5. #21445540C2semidirect
6. #21445539C2semidirect
7. C2×C61×#421C2semidirect
15. C2×#14519753C4semidirect
18. C2×#14519748C4semidirect
62. C2×#11758194D4semidirect
77. #14519736D4semidirect
116. C2×M16×C61D4semidirect
121. #117×C61D4semidirect
407. C2×#421D61semidirect
454. C61#10986semidirect
501. C2×M16C22⋊D61semidirect
521. #117C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403402
C2×#168397792
C2×#168397442
C2×#168397352
#214455402
#214455392
C2×C61×#4212
#1098661