Finite Group Databasebeta

← #29586568

Subgroups — #29586568

Order 15616.

1382 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840308C211yesmaximal, characteristic
2C2×#16839779C211yesmaximal, characteristic, complemented
3C2×#16839735C211yesmaximal, characteristic, complemented
4#21454263C211yesmaximal, characteristic, complemented
5C2×#16839523C211yesmaximal, characteristic, complemented
6C2×#16839521C211yesmaximal, characteristic, complemented
7C2×C61×#421C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10#16840308—22no—
11#16840308—22no—
12#16840308—22no—
13#16840308—22no—
14C2×#14519775C411yescharacteristic, complemented
15C2×#14519773C411yescharacteristic, complemented
16C2×#14519766C411yescharacteristic, complemented
17C2×#14519764C411yescharacteristic, complemented
18C2×#14519749—22no—
19C2×C4×C22⋊D61—22no—
20C2×#14519736C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22#16839779—22no—
23#16839779—22no—
24C2×#14519704—22no—
25#16839735—22no—
26#16839735—22no—
27C2×#14519691—22no—
28#16839730—22no—
29#16839728—22no—
30#16839725—22no—
31#16839523—22no—
32#16839521—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×Dic122C2×C411yescharacteristic
52C22×D244C2×C411yescharacteristic
53C22×C22⋊D61—22no—
54C22×C22⋊D61D412yes—
55C23×Dic61—21no—
56C22×C4×D61D412yes—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194—21no—
62C2×#11758194D412yescomplemented
63C22×#92418—21no—
64#14519775—22no—
65#14519775—22no—
66#14519773—22no—
67#14519773—22no—
68#14519766—22no—
69#14519766—22no—
70#14519764—22no—
71#14519764—22no—
72#14519749—28no—
73#14519749—28no—
74C4×C22⋊D61—28no—
75C4×C22⋊D61—28no—
76#14519736—21no—
77#14519736—21no—
78#14519736—21no—
79#14519736D412yescomplemented
80C2×C4⋊Dic61—21no—
81C2×#11758196—22no—
82C2×C22⋊Dic61—22no—
83C2×C22⋊Dic61—21no—
84C2×#11758198—22no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2×C411yescharacteristic
91C2×C4×Dic61D412yes—
92C2×C4×Dic61D412yes—
93#14519704—28no—
94#14519691—28no—
95#14519689—28no—
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×C61—21no—
105C2×#41×C61—21no—
106C2×#41×C61D412yes—
107C2×#41×C61D412yes—
108C22×Q8×C61C2×C411yescharacteristic
109C22×D4×C61—21no—
110C22×D4×C61C2×C411yescharacteristic
111C23×C4×C61—21no—
112C23×C4×C61C2311yescharacteristic
113C2×M16×C61—21no—
114C2×M16×C61—21no—
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C2×M16×C61D412yescomplemented
119C22×C8×C61—21no—
120#117×C61—21no—
121#117×C61—21no—
122#117×C61—21no—
123#117×C61D412yescomplemented
124C2×C4⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C42×C61—21no—
127#104×C61—28no—
128C24×C61—21no—
129C24×C61C2×D411yescharacteristic
130C23×D61C22⋊C412yes—
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—22no—
138#41×C61—22no—
139#41×C61—41no—
140#41×C61—41no—
141#41×C61—41no—
142#41×C61—41no—
143#41×C61—41no—
144#41×C61—41no—
145#41×C61—41no—
146#41×C61—41no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61C22⋊C412yes—
153C2×D4×C61—22no—
154C2×D4×C61—22no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—41no—
161C2×D4×C61—41no—
162C2×D4×C61—41no—
163C2×D4×C61—41no—
164C2×D4×C61C22⋊C412yes—
165C22×C4×C61—21no—
166C22×C4×C61—22no—
167C22×C4×C61—22no—
168C22×C4×C61—41no—
169C22×C4×C61—41no—
170C22×C4×C61—41no—
171C22×C4×C61—41no—
172C22×C4×C61—41no—
173C22×C4×C61C22×C411yescharacteristic
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×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61#4111yescharacteristic
184C22×C4×C61#4111yescharacteristic
185C22×C4×C61#4111yescharacteristic
186C22×C4×C61#4111yescharacteristic
187C2×C22⋊D61—28no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61—22no—
194C2×C22⋊D61—48no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—44no—
200C22×Dic61—41no—
201C22×Dic61C22⋊C412yes—
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—
215#11758222—41no—
216#11758222—41no—
217#11758222—41no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×C4×D61—22no—
225C2×C4×D61—22no—
226C2×C4×D61—22no—
227C2×C4×D61—22no—
228C2×C4×D61—22no—
229C2×C4×D61—22no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236M16×C61—22no—
237M16×C61—22no—
238M16×C61—41no—
239M16×C61—41no—
240C2×C8×C61—22no—
241C2×C8×C61—41no—
242C2×C8×C61—41no—
243C4⋊C4×C61—22no—
244C4⋊C4×C61—41no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—41no—
247C42×C61—22no—
248C42×C61—41no—
249C22⋊Dic61—28no—
250C22⋊Dic61—22no—
251C22⋊Dic61—41no—
252#11758198—28no—
253C4⋊Dic61—22no—
254C4⋊Dic61—41no—
255#11758196—28no—
256C4×Dic61—21no—
257C4×Dic61—21no—
258C4×Dic61—22no—
259C4×Dic61—22no—
260C4×Dic61—22no—
261C4×Dic61—41no—
262C4×Dic61C22⋊C412yes—
263C4×Dic61C22⋊C412yes—
264#11758194—22no—
265#11758194—22no—
266#11758194—41no—
267#11758194—41no—
268C2×#92418—22no—
269C2×#92418—41no—
270C2×#92418—41no—
271C23×C61—22no—
272C23×C61—42no—
273C23×C61—44no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61C2×C22⋊C411yescharacteristic
277C23×C61#12011yescharacteristic
278C23×C61#12011yescharacteristic
279C23×C61#12011yescharacteristic
280C23×C61#12111yescharacteristic
281C23×C61#12111yescharacteristic
282C23×C61#12311yescharacteristic
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—44no—
287Q8×C61—22no—
288Q8×C61—22no—
289Q8×C61—41no—
290Q8×C61—41no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—42no—
294D4×C61—42no—
295D4×C61—42no—
296D4×C61—42no—
297D4×C61—41no—
298D4×C61—41no—
299C2×C4×C61—22no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—82no—
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C4×D411yescharacteristic
311C2×C4×C61C4×D411yescharacteristic
312C2×C4×C61C4×D411yescharacteristic
313C2×C4×C61C4×D411yescharacteristic
314C2×C4×C61#12011yescharacteristic
315C2×C4×C61#12011yescharacteristic
316C2×C4×C61#12011yescharacteristic
317C2×C4×C61#12011yescharacteristic
318C2×C4×C61#12011yescharacteristic
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#12111yescharacteristic
329C2×C4×C61#12311yescharacteristic
330C2×C4×C61#12311yescharacteristic
331C2×C4×C61#12311yescharacteristic
332C2×C4×C61#12411yescharacteristic
333C2×C4×C61#12411yescharacteristic
334C2×C4×C61#12711yescharacteristic
335C2×C4×C61#12711yescharacteristic
336C22⋊D61—416no—
337C22⋊D61—42no—
338C22⋊D61—42no—
339C22⋊D61—42no—
340C22⋊D61—42no—
341C2×Dic61—24no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—44no—
348C2×Dic61—44no—
349C2×Dic61—42no—
350C2×Dic61—42no—
351C2×Dic61—82no—
352D244—41no—
353D244—41no—
354D244—41no—
355D244—41no—
356C4×D61—42no—
357C4×D61—42no—
358C4×D61—42no—
359C4×D61—42no—
360Dic122—41no—
361Dic122—41no—
362Dic122—41no—
363Dic122—41no—
364C8×C61—42no—
365#92418—42no—
366#10979—611nomaximal, Sylow
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—44no—
375C22×C61—42no—
376C22×C61—82no—
377C22×C61—82no—
378C22×C61#37911yescharacteristic
379C22×C61#38611yescharacteristic
380C22×C61#38611yescharacteristic
381C22×C61#39211yescharacteristic
382C22×C61#39211yescharacteristic
383C22×C61#39411yescharacteristic
384C22×C61#39411yescharacteristic
385C2×D61—44no—
386C2×D61—44no—
387C2×D61—42no—
388C2×D61—82no—
389C4×C61—42no—
390C4×C61—82no—
391C4×C61#38611yescharacteristic
392C4×C61#38611yescharacteristic
393C4×C61#39011yescharacteristic
394C4×C61#39011yescharacteristic
395C4×C61#39211yescharacteristic
396C4×C61#39211yescharacteristic
397C4×C61#39411yescharacteristic
398C4×C61#39411yescharacteristic
399Dic61—24no—
400Dic61—42no—
401Dic61—42no—
402Dic61—82no—
403C2×#532—611no—
404C2×#421—611no—
405C2×#421D6111yescharacteristic, complemented
406C2×#410—611no—
407#2879—611no—
408C2×#339—611no—
409C2×#339—611no—
410C2×C61—21no—
411C2×C61—21no—
412C2×C61—21no—
413C2×C61—21no—
414C2×C61—21no—
415C2×C61—21no—
416C2×C61—82no—
417C2×C61#143811yescharacteristic
418C2×C61#188412yes—
419D61—82no—
420C22×#41—611no—
421C22×#41C2×D6111yescharacteristic
422C22×M16—611no—
423C22×M16C2×D6111yescharacteristic
424#532—1222no—
425#532—1222no—
426#532—1222no—
427#532—1222no—
428C2×C4⋊Q8—611no—
429C2×#127—611no—
430C2×#124—611no—
431C2×#124—611no—
432C2×#121—1222no—
433C2×C4×D4—1222no—
434C2×#117—611no—
435C2×#117C2×D6111yescharacteristic
436C22×C42—611no—
437#421—22no—
438#421—22no—
439#421—1222no—
440#421—1222no—
441C2×#104—22no—
442C2×#104—1222no—
443#410—1222no—
444#410—1222no—
445C2×#99—1222no—
446#408—1222no—
447#408—1222no—
448#407—1222no—
449#339—1222no—
450#339—1222no—
451C61#1097911yescharacteristic, complemented, Sylow
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—1221no—
463C2×#41—1221no—
464C2×#41—1221no—
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×#41D24412yes—
475C2×#41C22⋊D6112yes—
476C22×Q8—611no—
477C22×Q8C4×D6111yescharacteristic
478C22×D4—21no—
479C22×D4—612no—
480C22×D4—611no—
481C22×D4—1222no—
482C22×D4C4×D6111yescharacteristic
483C23×C4—21no—
484C23×C4—612no—
485C23×C4—1221no—
486C23×C4C22×D6111yescharacteristic
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—21no—
492C2×M16—612no—
493C2×M16—1221no—
494C2×M16—1221no—
495C2×M16—1221no—
496C2×M16—1221no—
497C2×M16—1221no—
498C2×M16C22⋊D6112yescomplemented
499C22×C8—21no—
500C22×C8—1221no—
501C4⋊Q8—1222no—
502C4⋊Q8—1222no—
503#127—1222no—
504#127—1222no—
505#124—1222no—
506#124—1222no—
507#124—1222no—
508#124—1222no—
509#121—1228no—
510#121—1228no—
511C4×D4—1228no—
512C4×D4—1228no—
513#117—21no—
514#117—21no—
515#117—21no—
516#117—612no—
517#117—1221no—
518#117—1221no—
519#117—1221no—
520#117C22⋊D6112yescomplemented
521C2×C4⋊C4—21no—
522C2×C4⋊C4—1222no—
523C2×C4⋊C4—1221no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—1222no—
526C2×C22⋊C4—1222no—
527C2×C22⋊C4—1221no—
528C2×C42—21no—
529C2×C42—611no—
530C2×C42—611no—
531C2×C42—612no—
532C2×C42—612no—
533C2×C42—1221no—
534C2×C42—1221no—
535C2×C42—1221no—
536C2×C42—1221no—
537#104—28no—
538#104—1228no—
539#99—1228no—
540C22⋊C8—1228no—
541C24—21no—
542C24—612no—
543C24D4×D6111yescharacteristic
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—2441no—
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—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—1221no—
582C2×Q8—1221no—
583C2×Q8—1221no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×Q8#1175819812yes—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—1228no—
600C2×D4—1222no—
601C2×D4—1222no—
602C2×D4—1222no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—2448no—
613C2×D4#1175819812yes—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—612no—
623C22×C4—1221no—
624C22×C4—1221no—
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—2444no—
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—1228no—
666C4⋊C4—1222no—
667C4⋊C4—2441no—
668C22⋊C4—22no—
669C22⋊C4—41no—
670C22⋊C4—1228no—
671C22⋊C4—1228no—
672C22⋊C4—1222no—
673C22⋊C4—2441no—
674C42—22no—
675C42—41no—
676C42—612no—
677C42—612no—
678C42—1221no—
679C42—1221no—
680C42—1222no—
681C42—1222no—
682C42—1222no—
683C42—2441no—
684C23—22no—
685C23—42no—
686C23—44no—
687C23—41no—
688C23—41no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—2444no—
693C23C22⋊C4×D6111yescharacteristic
694C23#1451974511yescharacteristic
695C23#1451974511yescharacteristic
696C23#1451974711yescharacteristic
697C23#1451974811yescharacteristic
698C23#1451975011yescharacteristic
699C23#1451975911yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—41no—
703Q8—41no—
704Q8—2441no—
705Q8—2441no—
706Q8—2441no—
707Q8—2441no—
708D4—22no—
709D4—22no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—41no—
715D4—41no—
716D4—24416no—
717D4—2442no—
718D4—2442no—
719D4—2442no—
720D4—2442no—
721D4—2441no—
722D4—2441no—
723D4—2441no—
724D4—2441no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—82no—
734C2×C4—1224no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—4882no—
741C2×C4—2444no—
742C2×C4—2444no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4C22⋊C4×D6111yescharacteristic
750C2×C4C2×#1175819811yescharacteristic
751C2×C4#1451973711yescharacteristic
752C2×C4#1451973711yescharacteristic
753C2×C4C4×C22⋊D6111yescharacteristic
754C2×C4C4×C22⋊D6111yescharacteristic
755C2×C4#1451974511yescharacteristic
756C2×C4#1451974511yescharacteristic
757C2×C4#1451974611yescharacteristic
758C2×C4#1451974711yescharacteristic
759C2×C4#1451974711yescharacteristic
760C2×C4#1451974811yescharacteristic
761C2×C4#1451974911yescharacteristic
762C2×C4#1451974911yescharacteristic
763C2×C4#1451974911yescharacteristic
764C2×C4#1451974911yescharacteristic
765C2×C4#1451975011yescharacteristic
766C2×C4#1451975011yescharacteristic
767C2×C4#1451975011yescharacteristic
768C2×C4#1451975111yescharacteristic
769C2×C4#1451975111yescharacteristic
770C2×C4#1451975911yescharacteristic
771C2×C4#1451976011yescharacteristic
772C2×C4#1451976111yescharacteristic
773C2×C4#1451976311yescharacteristic
774C2×C4#1451976311yescharacteristic
775C2×C4#1451977311yescharacteristic
776C2×C4#1451977311yescharacteristic
777C8—42no—
778C8—2442no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—44no—
787C22—42no—
788C22—82no—
789C22—82no—
790C22—4882no—
791C22—2444no—
792C22—2444no—
793C22—2442no—
794C22#1683961711yescharacteristic
795C22#1683963811yescharacteristic
796C22#1683963811yescharacteristic
797C22#1683967011yescharacteristic
798C22#1683967111yescharacteristic
799C22#1683967711yescharacteristic
800C22#1683967811yescharacteristic
801C4—42no—
802C4—82no—
803C4—1224no—
804C4—4882no—
805C4—2442no—
806C4—2442no—
807C4#1683963911yescharacteristic
808C4#1683964111yescharacteristic
809C4#1683966211yescharacteristic
810C4#1683966211yescharacteristic
811C4#1683967011yescharacteristic
812C4#1683967111yescharacteristic
813C4#1683967711yescharacteristic
814C4#1683967811yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—82no—
822C2—4882no—
823C2#2144405811yescharacteristic
824C2#2144619912yes—
subgroupG/H
centerC2×C4#14519745
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#421C2
socleC22×C61#386
prime radicalC2×#16840308C2
cosocleC23×C4×C61C23
hypercenterC2×#421D61
hypocenterC61#10979
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#16839779C2semidirect
3. C2×#16839735C2semidirect
4. #21454263C2semidirect
5. C2×#16839523C2semidirect
6. C2×#16839521C2semidirect
7. C2×C61×#421C2semidirect
14. C2×#14519775C4semidirect
15. C2×#14519773C4semidirect
16. C2×#14519766C4semidirect
17. C2×#14519764C4semidirect
62. C2×#11758194D4semidirect
79. #14519736D4semidirect
118. C2×M16×C61D4semidirect
123. #117×C61D4semidirect
405. C2×#421D61semidirect
451. C61#10979semidirect
498. C2×M16C22⋊D61semidirect
520. #117C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403082
C2×#168397792
C2×#168397352
#214542632
C2×#168395232
C2×#168395212
C2×C61×#4212
#1097961