Finite Group Databasebeta

← #29682048

Subgroups — #29682048

Order 15616.

1692 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×#16840528C211yesmaximal, characteristic, complemented
2#21459152C211yesmaximal, characteristic
3C2×#16839744C211yesmaximal, characteristic, complemented
4C2×#16839744C211yesmaximal, characteristic, complemented
5C2×#16839744C211yesmaximal, characteristic, complemented
6#21446370C214yesmaximal, complemented
7#21446365C214yesmaximal, complemented
8C2×#16839532C211yesmaximal, characteristic, complemented
9C2×C61×#344C211yesmaximal, characteristic, complemented
10C22×#11758222C2211yescharacteristic
11C22×#11758222C2211yescharacteristic
12#16840528—22no—
13#16840528—22no—
14#16840528—22no—
15#16840528C2214yes—
16C2×#14519785—22no—
17C2×#14519783—22no—
18C22×#11758194C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20C2×M16×D61—22no—
21#16840343—22no—
22#16840338—21no—
23#16840338C2212yes—
24#16840331—21no—
25#16840331C2212yes—
26#16840324C414yes—
27#16840312—22no—
28#16840274—22no—
29#16840274C414yes—
30#16839744—22no—
31#16839744—22no—
32#16839744—22no—
33#16839744—22no—
34#16839744—22no—
35#16839744C2214yes—
36C2×#14519695—21no—
37C2×#14519695C2212yescomplemented
38C2×#14519695C2212yescomplemented
39C2×#14519693—21no—
40C2×#14519693C2212yescomplemented
41C2×#14519693C2212yescomplemented
42#16839532C2214yescomplemented
43C22×M16×C61C2211yescharacteristic
44C22×M16×C61C2211yescharacteristic
45C2×#117×C61C2211yescharacteristic
46C61×#344C2214yescomplemented
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222—21no—
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—21no—
56C2×#11758222—21no—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222—21no—
62C2×#11758222—21no—
63C2×#11758222—21no—
64C2×#11758222—21no—
65C2×#11758222—21no—
66C2×#11758222—21no—
67C2×#11758222C2×C412yes—
68C2×#11758222D412yes—
69C2×#11758222D412yes—
70C2×#11758222C2312yes—
71C22×Dic122D411yescharacteristic
72C22×Dic122C2311yescharacteristic
73C22×D244D411yescharacteristic
74C22×D244C2311yescharacteristic
75C22×C22⋊D61C2×C412yes—
76C22×C22⋊D61C2×C412yes—
77C22×C4×D61C2×C412yes—
78C22×C4×D61D412yes—
79#14519785—28no—
80#14519785—28no—
81#14519783—28no—
82#14519783—28no—
83C2×#11758194—21no—
84C2×#11758194—21no—
85C2×#11758194—21no—
86C2×#11758194—21no—
87C2×#11758194—21no—
88C2×#11758194—21no—
89C2×#11758194—21no—
90C2×#11758194—21no—
91C2×#11758194D412yescomplemented
92C2×#11758194D412yescomplemented
93C2×#11758194C2312yes—
94C2×#11758194C2312yes—
95C2×#11758189—24no—
96M16×D61—28no—
97M16×D61—28no—
98C22×#92418—21no—
99C22×#92418—21no—
100C2×C8×D61—24no—
101#14519777—22no—
102#14519774—22no—
103#14519765—22no—
104#14519765—22no—
105#14519761—24no—
106#14519761C2×C418yes—
107#14519757—24no—
108#14519757—24no—
109#14519752—24no—
110#14519752—24no—
111#14519751—28no—
112#14519747—24no—
113#14519747C2×C418yes—
114C4×D244—28no—
115#14519695—24no—
116#14519695—24no—
117#14519695—24no—
118#14519693—24no—
119#14519693—24no—
120#14519693—24no—
121C23×C4×C61C2311yescharacteristic
122C2×M16×C61—21no—
123C2×M16×C61—21no—
124C2×M16×C61—21no—
125C2×M16×C61—21no—
126C2×M16×C61—21no—
127C2×M16×C61—21no—
128C2×M16×C61—21no—
129C2×M16×C61—21no—
130C2×M16×C61D412yescomplemented
131C2×M16×C61D412yescomplemented
132C2×M16×C61C2312yes—
133C2×M16×C61C2312yes—
134C22×C8×C61—21no—
135C22×C8×C61—21no—
136#117×C61—21no—
137#117×C61—21no—
138#117×C61C2×C412yes—
139#117×C61C2312yes—
140C2×C4⋊C4×C61—21no—
141C2×C22⋊C4×C61C2×C412yes—
142C2×C42×C61—21no—
143C24×C61C22×C411yescharacteristic
144C23×D61C22⋊C412yes—
145C23×D61C22×C412yes—
146C22×C4×C61—22no—
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61#4111yescharacteristic
157C22×C4×C61#4111yescharacteristic
158C22×C4×C61#4111yescharacteristic
159C22×C4×C61#4111yescharacteristic
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61C22⋊C414yes—
172C2×C22⋊D61C22×C414yes—
173C22×Dic61C22⋊C412yes—
174C22×Dic61C22×C412yes—
175#11758222—22no—
176#11758222—22no—
177#11758222—22no—
178#11758222—22no—
179#11758222—22no—
180#11758222—22no—
181#11758222—22no—
182#11758222—22no—
183#11758222—22no—
184#11758222—22no—
185#11758222—22no—
186#11758222—22no—
187#11758222—22no—
188#11758222—22no—
189#11758222—22no—
190#11758222—22no—
191#11758222—41no—
192#11758222—41no—
193#11758222—41no—
194#11758222—41no—
195#11758222—41no—
196#11758222—41no—
197#11758222—41no—
198#11758222—41no—
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×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—28no—
218C2×D244C22⋊C412yes—
219C2×D244C2×D412yes—
220C2×C4×D61—22no—
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×C4×D61—22no—
228C2×C4×D61—22no—
229C2×C4×D61—22no—
230C2×C4×D61C22⋊C414yes—
231C2×C4×D61C2×D414yes—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122C22⋊C412yes—
243C2×Dic122C2×D412yes—
244M16×C61—22no—
245M16×C61—22no—
246M16×C61—22no—
247M16×C61—22no—
248M16×C61—22no—
249M16×C61—41no—
250M16×C61—41no—
251M16×C61C2×D414yes—
252C2×C8×C61—22no—
253C2×C8×C61—22no—
254C2×C8×C61—22no—
255C2×C8×C61—22no—
256C2×C8×C61—41no—
257C2×C8×C61—41no—
258C4⋊C4×C61—22no—
259C4⋊C4×C61—22no—
260C22⋊C4×C61—22no—
261C22⋊C4×C61C22×C414yes—
262C42×C61—22no—
263C42×C61—22no—
264#11758198—28no—
265#11758198—28no—
266C4⋊Dic61—28no—
267#11758194—22no—
268#11758194—22no—
269#11758194—22no—
270#11758194—22no—
271#11758194—22no—
272#11758194—41no—
273#11758194—41no—
274#11758194C2×D414yes—
275C2×#92418—22no—
276C2×#92418—22no—
277C2×#92418—22no—
278C2×#92418—22no—
279C2×#92418—41no—
280C2×#92418—41no—
281#11758189—216no—
282C8×D61—216no—
283C23×C61—81no—
284C23×C61C2×C22⋊C411yescharacteristic
285C23×C61C2×C22⋊C411yescharacteristic
286C23×C61C4×D411yescharacteristic
287C23×C61C4×D411yescharacteristic
288C23×C61C4×D411yescharacteristic
289C23×C61C4×D411yescharacteristic
290C23×C61C23×C411yescharacteristic
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—82no—
297C22×D61—82no—
298C22×D61C2×C22⋊C414yes—
299C2×C4×C61—24no—
300C2×C4×C61—82no—
301C2×C4×C61C2×C22⋊C411yescharacteristic
302C2×C4×C61C2×C22⋊C411yescharacteristic
303C2×C4×C61C4×D411yescharacteristic
304C2×C4×C61C4×D411yescharacteristic
305C2×C4×C61C4×D411yescharacteristic
306C2×C4×C61C4×D411yescharacteristic
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#12311yescharacteristic
320C2×C4×C61#12311yescharacteristic
321C2×C4×C61#12311yescharacteristic
322C2×C4×C61#12311yescharacteristic
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C2×#4111yescharacteristic
328C2×C4×C61C2×#4111yescharacteristic
329C22⋊D61—24no—
330C22⋊D61—24no—
331C22⋊D61—24no—
332C22⋊D61—24no—
333C22⋊D61—42no—
334C22⋊D61—42no—
335C22⋊D61—42no—
336C22⋊D61—42no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61C2×C22⋊C414yes—
343D244—22no—
344D244—22no—
345D244—22no—
346D244—22no—
347D244—41no—
348D244—41no—
349D244—41no—
350D244—41no—
351D244—88no—
352C4×D61—24no—
353C4×D61—24no—
354C4×D61—24no—
355C4×D61—24no—
356C4×D61—42no—
357C4×D61—42no—
358C4×D61—42no—
359C4×D61—42no—
360Dic122—22no—
361Dic122—22no—
362Dic122—22no—
363Dic122—22no—
364Dic122—41no—
365Dic122—41no—
366Dic122—41no—
367Dic122—41no—
368C8×C61—24no—
369C8×C61—42no—
370#92418—24no—
371#92418—42no—
372#21017—611nomaximal, Sylow
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61#38611yescharacteristic
381C22×C61#38611yescharacteristic
382C22×C61#38611yescharacteristic
383C22×C61#38611yescharacteristic
384C22×C61C22×C22⋊C411yescharacteristic
385C22×C61C2×C4×D411yescharacteristic
386C22×C61C2×C4×D411yescharacteristic
387C2×D61—24no—
388C2×D61—44no—
389C2×D61—44no—
390C2×D61—44no—
391C2×D61—42no—
392C2×D61—82no—
393C2×D61—82no—
394C2×D61—82no—
395C4×C61—44no—
396C4×C61#38611yescharacteristic
397C4×C61#38611yescharacteristic
398C4×C61#38611yescharacteristic
399C4×C61#38611yescharacteristic
400C4×C61C2×#12011yescharacteristic
401C4×C61C2×#12111yescharacteristic
402C4×C61C2×#12111yescharacteristic
403C4×C61C2×#12311yescharacteristic
404Dic61—24no—
405Dic61—42no—
406C2×#568—611no—
407#3449—611no—
408C2×#413—611no—
409C2×#413—611no—
410C2×#413—611no—
411#1915—614no—
412#1914—614no—
413C2×#344—611no—
414C2×#344D6111yescharacteristic, complemented
415C2×C61—21no—
416C2×C61—21no—
417C2×C61—21no—
418C2×C61—21no—
419C2×C61—21no—
420C2×C61—21no—
421C2×C61—21no—
422C2×C61C2×#38611yescharacteristic
423D61—44no—
424D61—82no—
425C22×#41—611no—
426C22×#41—611no—
427#568—614no—
428#568—1222no—
429#568—1222no—
430#568—1222no—
431C2×#131—1222no—
432C2×#131—1222no—
433C22×M16—611no—
434C22×M16—611no—
435C22×M16—1222no—
436C22×M16C2×D6111yescharacteristic
437C22×M16C2×D6111yescharacteristic
438#537—1222no—
439#536—612no—
440#536—1221no—
441#535—612no—
442#535—1221no—
443#534—614no—
444#532—1222no—
445#525—614no—
446#525—1222no—
447C2×#117C2×D6111yescharacteristic
448#413—614no—
449#413—1222no—
450#413—1222no—
451#413—1222no—
452#413—1222no—
453#413—1222no—
454C2×#101—612no—
455C2×#101—612no—
456C2×#101—1221no—
457C2×#100—612no—
458C2×#100—612no—
459C2×#100—1221no—
460#344—614no—
461#344C2×D6114yescomplemented
462C61#2101711yescharacteristic, complemented, Sylow
463C2×#41—612no—
464C2×#41—612no—
465C2×#41—612no—
466C2×#41—612no—
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×#41—1221no—
478C2×#41—1221no—
479C2×#41—1221no—
480C2×#41—1221no—
481C2×#41—1221no—
482C2×#41—1221no—
483C2×#41—1221no—
484C2×#41—1221no—
485C2×#41—1221no—
486C2×#41—1221no—
487C22×Q8—611no—
488C22×Q8—611no—
489C22×D4—612no—
490C22×D4—612no—
491C22×D4—611no—
492C22×D4—611no—
493C23×C4—612no—
494C23×C4—612no—
495C23×C4C22×D6111yescharacteristic
496#131—1228no—
497#131—1228no—
498#131—1228no—
499#131—1228no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—612no—
509C2×M16—612no—
510C2×M16—612no—
511C2×M16—612no—
512C2×M16—1224no—
513C2×M16—1228no—
514C2×M16—1228no—
515C2×M16—1221no—
516C2×M16—1221no—
517C2×M16—1221no—
518C2×M16—1221no—
519C2×M16—1221no—
520C2×M16—1221no—
521C2×M16—1221no—
522C2×M16—1221no—
523C2×M16D24412yescomplemented
524C2×M16D24412yescomplemented
525C2×M16C22×D6112yes—
526C2×M16C22×D6112yes—
527C22×C8—21no—
528C22×C8—21no—
529C22×C8—1224no—
530C22×C8—1221no—
531C22×C8—1221no—
532C4⋊Q8—1222no—
533#127—1222no—
534#124—1222no—
535#124—1222no—
536#123—618no—
537#123—1224no—
538C22⋊Q8—1224no—
539C22⋊Q8—1224no—
540#121—1224no—
541#121—1224no—
542#121—1228no—
543#120—618no—
544#120—1224no—
545C4×D4—1228no—
546#117—21no—
547#117—21no—
548#117C4×D6112yes—
549#117C22×D6112yes—
550C2×C4⋊C4—21no—
551C2×C22⋊C4C4×D6112yes—
552C2×C42—21no—
553#101—1224no—
554#101—1224no—
555#101—1224no—
556#100—1224no—
557#100—1224no—
558#100—1224no—
559C24—612no—
560C24—612no—
561C24C2×C4×D6111yescharacteristic
562#41—1222no—
563#41—1222no—
564#41—1222no—
565#41—1222no—
566#41—1222no—
567#41—1222no—
568#41—1222no—
569#41—1222no—
570#41—1222no—
571#41—1222no—
572#41—1222no—
573#41—1222no—
574#41—1222no—
575#41—1222no—
576#41—1222no—
577#41—1222no—
578#41—2441no—
579#41—2441no—
580#41—2441no—
581#41—2441no—
582#41—2441no—
583#41—2441no—
584#41—2441no—
585#41—2441no—
586#41—2441no—
587#41—2441no—
588#41—2441no—
589#41—2441no—
590#41—2441no—
591#41—2441no—
592#41—2441no—
593#41—2441no—
594C2×Q8—612no—
595C2×Q8—612no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8—1221no—
600C2×Q8—1221no—
601C2×Q8—1221no—
602C2×Q8—1221no—
603C2×Q8—1221no—
604C2×Q8—1221no—
605C2×Q8—1221no—
606C2×D4—614no—
607C2×D4—614no—
608C2×D4—612no—
609C2×D4—612no—
610C2×D4—1228no—
611C2×D4—1222no—
612C2×D4—1222no—
613C2×D4—1222no—
614C2×D4—1222no—
615C2×D4—1222no—
616C2×D4—1222no—
617C2×D4—1222no—
618C2×D4—1222no—
619C2×D4—1222no—
620C2×D4—1222no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—1221no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C22×C4—22no—
632C22×C4—612no—
633C22×C4—614no—
634C22×C4—614no—
635C22×C4—612no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4C2×C4×D6111yescharacteristic
647C22×C4C2×D24411yescharacteristic
648C22×C4C2×D24411yescharacteristic
649C22×C4#1175822211yescharacteristic
650C22×C4#1175822211yescharacteristic
651C22×C4D4×D6111yescharacteristic
652C22×C4D4×D6111yescharacteristic
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4D4×D6111yescharacteristic
656C22×C4D4×D6111yescharacteristic
657C22×C4#1175822611yescharacteristic
658C22×C4#1175822611yescharacteristic
659C22×C4C23×D6111yescharacteristic
660M16—22no—
661M16—22no—
662M16—22no—
663M16—22no—
664M16—22no—
665M16—41no—
666M16—41no—
667M16—614no—
668M16—12216no—
669M16—1222no—
670M16—1222no—
671M16—1222no—
672M16—1222no—
673M16—1222no—
674M16—2441no—
675M16—2441no—
676M16C2×D24414yes—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—41no—
682C2×C8—41no—
683C2×C8—12216no—
684C2×C8—1222no—
685C2×C8—1222no—
686C2×C8—1222no—
687C2×C8—1222no—
688C2×C8—2441no—
689C2×C8—2441no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—1228no—
693C22⋊C4—22no—
694C22⋊C4—1228no—
695C22⋊C4—1228no—
696C22⋊C4C2×C4×D6114yes—
697C42—22no—
698C42—22no—
699C23—81no—
700C23—614no—
701C23—1222no—
702C23—1222no—
703C23—1222no—
704C23—1222no—
705C23—1222no—
706C23—4882no—
707C23—4882no—
708C23C22⋊C4×D6111yescharacteristic
709C23C22⋊C4×D6111yescharacteristic
710C23#1451973911yescharacteristic
711C23#1451973911yescharacteristic
712C23C4×D24411yescharacteristic
713C23C4×D24411yescharacteristic
714C23C22×C4×D6111yescharacteristic
715Q8—1222no—
716Q8—1222no—
717Q8—1222no—
718Q8—1222no—
719Q8—2441no—
720Q8—2441no—
721Q8—2441no—
722Q8—2441no—
723D4—1224no—
724D4—1224no—
725D4—1224no—
726D4—1224no—
727D4—1222no—
728D4—1222no—
729D4—1222no—
730D4—1222no—
731D4—4888no—
732D4—2442no—
733D4—2442no—
734D4—2442no—
735D4—2442no—
736D4—2441no—
737D4—2441no—
738D4—2441no—
739D4—2441no—
740C2×C4—24no—
741C2×C4—82no—
742C2×C4—614no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1224no—
746C2×C4—1224no—
747C2×C4—1224no—
748C2×C4—1224no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4C22⋊C4×D6111yescharacteristic
757C2×C4C22⋊C4×D6111yescharacteristic
758C2×C4#1451973911yescharacteristic
759C2×C4#1451973911yescharacteristic
760C2×C4C4×D24411yescharacteristic
761C2×C4C4×D24411yescharacteristic
762C2×C4#1451974711yescharacteristic
763C2×C4#1451974711yescharacteristic
764C2×C4#1451974711yescharacteristic
765C2×C4#1451974711yescharacteristic
766C2×C4#1451975011yescharacteristic
767C2×C4#1451975011yescharacteristic
768C2×C4#1451975011yescharacteristic
769C2×C4#1451975011yescharacteristic
770C2×C4#1451975211yescharacteristic
771C2×C4#1451975211yescharacteristic
772C2×C4#1451975211yescharacteristic
773C2×C4#1451975211yescharacteristic
774C2×C4#1451976211yescharacteristic
775C2×C4#1451976211yescharacteristic
776C2×C4#1451976211yescharacteristic
777C2×C4#1451976211yescharacteristic
778C2×C4C2×D4×D6111yescharacteristic
779C2×C4C2×D4×D6111yescharacteristic
780C2×C4C2×D4×D6111yescharacteristic
781C2×C4C22×D24411yescharacteristic
782C2×C4C2×#1175822211yescharacteristic
783C2×C4C2×#1175822611yescharacteristic
784C8—24no—
785C8—42no—
786C8—1224no—
787C8—2442no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—1224no—
796C22—4882no—
797C22—4882no—
798C22—4882no—
799C22—2444no—
800C22—2444no—
801C22—2444no—
802C22—2442no—
803C22#1683964011yescharacteristic
804C22#1683964011yescharacteristic
805C22#1683964011yescharacteristic
806C22#1683964011yescharacteristic
807C22C2×C22⋊C4×D6111yescharacteristic
808C22C2×#1451973911yescharacteristic
809C22C2×C4×D24411yescharacteristic
810C4—44no—
811C4—1224no—
812C4—2442no—
813C4#1683964011yescharacteristic
814C4#1683964011yescharacteristic
815C4#1683964011yescharacteristic
816C4#1683964011yescharacteristic
817C4C2×#1451974711yescharacteristic
818C4C2×#1451975011yescharacteristic
819C4C2×#1451975211yescharacteristic
820C4C2×#1451976211yescharacteristic
821C2—21no—
822C2—21no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—21no—
827C2—21no—
828C2—4882no—
829C2—2444no—
830C2C2×#1683964011yescharacteristic
subgroupG/H
centerC4#16839640
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#344C2
socleC2×C61C2×#386
prime radical#21459152C2
cosocleC22×C4×C61C24
hypercenterC2×#344D61
hypocenterC61#21017
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#16840528C2semidirect
3. C2×#16839744C2semidirect
4. C2×#16839744C2semidirect
5. C2×#16839744C2semidirect
6. #21446370C2semidirect
7. #21446365C2semidirect
8. C2×#16839532C2semidirect
9. C2×C61×#344C2semidirect
37. C2×#14519695C22semidirect
38. C2×#14519695C22semidirect
40. C2×#14519693C22semidirect
41. C2×#14519693C22semidirect
42. #16839532C22semidirect
46. C61×#344C22semidirect
91. C2×#11758194D4semidirect
92. C2×#11758194D4semidirect
130. C2×M16×C61D4semidirect
131. C2×M16×C61D4semidirect
414. C2×#344D61semidirect
461. #344C2×D61semidirect
462. C61#21017semidirect
523. C2×M16D244semidirect
524. C2×M16D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168405282
#214591522
C2×#168397442
#214463702
#214463652
C2×#168395322
C2×C61×#3442
#2101761