Finite Group Databasebeta

← #29681669

Subgroups — #29681669

Order 15616.

1700 conjugacy classes of subgroups.

The subgroup lattice has 822 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
4#21454263C211yesmaximal, characteristic, complemented
5#21454263C211yesmaximal, characteristic, complemented
6#21446236C218yesmaximal, complemented
7C2×#16839532C211yesmaximal, characteristic, complemented
8C2×C61×#344C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C22×#11758222C2211yescharacteristic
11#16840528—22no—
12#16840528—22no—
13#16840528—22no—
14#16840528C2214yes—
15C2×#14519785—22no—
16C2×#14519783—22no—
17C22×#11758194C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C2×M16×D61—22no—
20#16840343—22no—
21#16840338—21no—
22#16840338C412yes—
23#16840331—21no—
24#16840331C412yes—
25#16840324C414yes—
26#16840312—22no—
27#16840274—22no—
28#16840274C2214yes—
29#16839744—22no—
30#16839744C2214yes—
31C2×#14519695—21no—
32C2×#14519693—21no—
33#16839730—22no—
34#16839730—22no—
35#16839728—22no—
36#16839728—22no—
37#16839725C2214yescomplemented
38#16839725C2214yescomplemented
39#16839532C2214yescomplemented
40C22×M16×C61C2211yescharacteristic
41C22×M16×C61C2211yescharacteristic
42C2×#117×C61C2211yescharacteristic
43C61×#344C2214yescomplemented
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
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×#11758222C2×C412yes—
65C2×#11758222D412yes—
66C2×#11758222D412yes—
67C2×#11758222C2312yes—
68C22×Dic122C2×C411yescharacteristic
69C22×Dic122D411yescharacteristic
70C22×D244C2×C411yescharacteristic
71C22×D244D411yescharacteristic
72C22×C22⋊D61C2×C412yes—
73C22×C22⋊D61C2×C412yes—
74C22×C4×D61D412yes—
75C22×C4×D61C2312yes—
76#14519785—28no—
77#14519785—28no—
78#14519783—28no—
79#14519783—28no—
80C2×#11758194—21no—
81C2×#11758194—21no—
82C2×#11758194—21no—
83C2×#11758194—21no—
84C2×#11758194—21no—
85C2×#11758194—21no—
86C2×#11758194—21no—
87C2×#11758194—21no—
88C2×#11758194—21no—
89C2×#11758194D412yescomplemented
90C2×#11758194C2312yes—
91C2×#11758194C2312yes—
92C2×#11758189—24no—
93M16×D61—28no—
94M16×D61—28no—
95C22×#92418—21no—
96C22×#92418D412yescomplemented
97C2×C8×D61—24no—
98#14519777—22no—
99#14519774—22no—
100#14519765—22no—
101#14519765—22no—
102#14519761—24no—
103#14519761C2×C418yes—
104#14519757—24no—
105#14519757—24no—
106#14519752—24no—
107#14519752—24no—
108#14519751—28no—
109#14519747—24no—
110#14519747C2×C418yes—
111C4×D244—28no—
112#14519695—24no—
113#14519693—24no—
114#14519689—28no—
115#14519689—28no—
116C23×C4×C61C2311yescharacteristic
117C2×M16×C61—21no—
118C2×M16×C61—21no—
119C2×M16×C61—21no—
120C2×M16×C61—21no—
121C2×M16×C61—21no—
122C2×M16×C61—21no—
123C2×M16×C61—21no—
124C2×M16×C61—21no—
125C2×M16×C61—21no—
126C2×M16×C61D412yescomplemented
127C2×M16×C61C2312yes—
128C2×M16×C61C2312yes—
129C22×C8×C61—21no—
130C22×C8×C61D412yescomplemented
131#117×C61—21no—
132#117×C61—21no—
133#117×C61C2×C412yes—
134#117×C61C2312yes—
135C2×C4⋊C4×C61—21no—
136C2×C22⋊C4×C61C2×C412yes—
137C2×C42×C61—21no—
138C24×C61C22×C411yescharacteristic
139C23×D61C22⋊C412yes—
140C23×D61C22×C412yes—
141C22×C4×C61—22no—
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61#4111yescharacteristic
152C22×C4×C61#4111yescharacteristic
153C22×C4×C61#4111yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61C22⋊C414yes—
167C2×C22⋊D61C22×C414yes—
168C22×Dic61C22⋊C412yes—
169C22×Dic61C22×C412yes—
170#11758222—22no—
171#11758222—22no—
172#11758222—22no—
173#11758222—22no—
174#11758222—22no—
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—41no—
187#11758222—41no—
188#11758222—41no—
189#11758222—41no—
190#11758222—41no—
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—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—28no—
213C2×D244C22⋊C412yes—
214C2×D244C2×D412yes—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—22no—
222C2×C4×D61—22no—
223C2×C4×D61—22no—
224C2×C4×D61—22no—
225C2×C4×D61C22⋊C414yes—
226C2×C4×D61C2×D414yes—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122C22⋊C412yes—
238C2×Dic122C2×D412yes—
239M16×C61—22no—
240M16×C61—22no—
241M16×C61—22no—
242M16×C61—22no—
243M16×C61—22no—
244M16×C61—22no—
245M16×C61—41no—
246M16×C61—41no—
247C2×C8×C61—22no—
248C2×C8×C61—22no—
249C2×C8×C61—22no—
250C2×C8×C61—41no—
251C2×C8×C61—41no—
252C2×C8×C61C2×D414yes—
253C4⋊C4×C61—22no—
254C4⋊C4×C61—22no—
255C22⋊C4×C61—22no—
256C22⋊C4×C61C22×C414yes—
257C42×C61—22no—
258C42×C61—22no—
259#11758198—28no—
260#11758198—28no—
261C4⋊Dic61—28no—
262#11758194—22no—
263#11758194—22no—
264#11758194—22no—
265#11758194—22no—
266#11758194—22no—
267#11758194—22no—
268#11758194—41no—
269#11758194—41no—
270C2×#92418—22no—
271C2×#92418—22no—
272C2×#92418—22no—
273C2×#92418—41no—
274C2×#92418—41no—
275C2×#92418C2×D414yes—
276#11758189—216no—
277C8×D61—216no—
278C23×C61—81no—
279C23×C61C2×C22⋊C411yescharacteristic
280C23×C61C2×C22⋊C411yescharacteristic
281C23×C61C4×D411yescharacteristic
282C23×C61C4×D411yescharacteristic
283C23×C61C4×D411yescharacteristic
284C23×C61C4×D411yescharacteristic
285C23×C61C23×C411yescharacteristic
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—82no—
292C22×D61—82no—
293C22×D61C2×C22⋊C414yes—
294C2×C4×C61—24no—
295C2×C4×C61—82no—
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C4×D411yescharacteristic
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C4×D411yescharacteristic
301C2×C4×C61C4×D411yescharacteristic
302C2×C4×C61#12011yescharacteristic
303C2×C4×C61#12011yescharacteristic
304C2×C4×C61#12011yescharacteristic
305C2×C4×C61#12011yescharacteristic
306C2×C4×C61#12111yescharacteristic
307C2×C4×C61#12111yescharacteristic
308C2×C4×C61#12111yescharacteristic
309C2×C4×C61#12111yescharacteristic
310C2×C4×C61#12111yescharacteristic
311C2×C4×C61#12111yescharacteristic
312C2×C4×C61#12111yescharacteristic
313C2×C4×C61#12111yescharacteristic
314C2×C4×C61#12311yescharacteristic
315C2×C4×C61#12311yescharacteristic
316C2×C4×C61#12311yescharacteristic
317C2×C4×C61#12311yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C2×#4111yescharacteristic
323C2×C4×C61C2×#4111yescharacteristic
324C22⋊D61—24no—
325C22⋊D61—24no—
326C22⋊D61—24no—
327C22⋊D61—24no—
328C22⋊D61—42no—
329C22⋊D61—42no—
330C22⋊D61—42no—
331C22⋊D61—42no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61C2×C22⋊C414yes—
338D244—22no—
339D244—22no—
340D244—22no—
341D244—22no—
342D244—41no—
343D244—41no—
344D244—41no—
345D244—41no—
346D244—88no—
347C4×D61—24no—
348C4×D61—24no—
349C4×D61—24no—
350C4×D61—24no—
351C4×D61—42no—
352C4×D61—42no—
353C4×D61—42no—
354C4×D61—42no—
355Dic122—22no—
356Dic122—22no—
357Dic122—22no—
358Dic122—22no—
359Dic122—41no—
360Dic122—41no—
361Dic122—41no—
362Dic122—41no—
363C8×C61—24no—
364C8×C61—42no—
365#92418—24no—
366#92418—42no—
367#20964—611nomaximal, Sylow
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61#38611yescharacteristic
376C22×C61#38611yescharacteristic
377C22×C61#38611yescharacteristic
378C22×C61#38611yescharacteristic
379C22×C61C22×C22⋊C411yescharacteristic
380C22×C61C2×C4×D411yescharacteristic
381C22×C61C2×C4×D411yescharacteristic
382C2×D61—24no—
383C2×D61—44no—
384C2×D61—44no—
385C2×D61—44no—
386C2×D61—44no—
387C2×D61—44no—
388C2×D61—42no—
389C2×D61—82no—
390C4×C61—44no—
391C4×C61#38611yescharacteristic
392C4×C61#38611yescharacteristic
393C4×C61#38611yescharacteristic
394C4×C61#38611yescharacteristic
395C4×C61C2×#12011yescharacteristic
396C4×C61C2×#12111yescharacteristic
397C4×C61C2×#12111yescharacteristic
398C4×C61C2×#12311yescharacteristic
399Dic61—24no—
400Dic61—42no—
401C2×#568—611no—
402#3449—611no—
403C2×#413—611no—
404#2879—611no—
405#2879—611no—
406#1891—618no—
407C2×#344—611no—
408C2×#344D6111yescharacteristic, complemented
409C2×C61—21no—
410C2×C61—21no—
411C2×C61—21no—
412C2×C61—21no—
413C2×C61—21no—
414C2×C61—21no—
415C2×C61—21no—
416C2×C61C2×#38611yescharacteristic
417D61—44no—
418D61—82no—
419C22×#41—611no—
420C22×#41—611no—
421#568—614no—
422#568—1222no—
423#568—1222no—
424#568—1222no—
425C2×#131—1222no—
426C2×#131—1222no—
427C22×M16—611no—
428C22×M16—611no—
429C22×M16—1222no—
430C22×M16C2×D6111yescharacteristic
431C22×M16C2×D6111yescharacteristic
432#537—1222no—
433#536—612no—
434#536—1221no—
435#535—612no—
436#535—1221no—
437#534—614no—
438#532—1222no—
439#525—614no—
440#525—1222no—
441C2×#117C2×D6111yescharacteristic
442#413—614no—
443#413—1222no—
444C2×#101—1221no—
445C2×#100—1221no—
446#408—1222no—
447#408—1222no—
448#408—1222no—
449#408—1222no—
450#407—614no—
451#407—614no—
452#344—614no—
453#344C2×D6114yescomplemented
454C61#2096411yescharacteristic, complemented, Sylow
455C2×#41—612no—
456C2×#41—612no—
457C2×#41—612no—
458C2×#41—612no—
459C2×#41—1221no—
460C2×#41—1221no—
461C2×#41—1221no—
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×#41—1221no—
475C2×#41—1221no—
476C2×#41—1221no—
477C2×#41—1221no—
478C2×#41—1221no—
479C22×Q8—611no—
480C22×Q8—611no—
481C22×D4—612no—
482C22×D4—612no—
483C22×D4—611no—
484C22×D4—611no—
485C23×C4—612no—
486C23×C4—612no—
487C23×C4C22×D6111yescharacteristic
488#131—1228no—
489#131—1228no—
490#131—1228no—
491#131—1228no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—612no—
502C2×M16—612no—
503C2×M16—612no—
504C2×M16—1224no—
505C2×M16—1228no—
506C2×M16—1228no—
507C2×M16—1221no—
508C2×M16—1221no—
509C2×M16—1221no—
510C2×M16—1221no—
511C2×M16—1221no—
512C2×M16—1221no—
513C2×M16—1221no—
514C2×M16—1221no—
515C2×M16—1221no—
516C2×M16D24412yescomplemented
517C2×M16C22×D6112yes—
518C2×M16C22×D6112yes—
519C22×C8—21no—
520C22×C8—612no—
521C22×C8—1224no—
522C22×C8—1221no—
523C22×C8D24412yescomplemented
524C4⋊Q8—1222no—
525#127—1222no—
526#124—1222no—
527#124—1222no—
528#123—618no—
529#123—1224no—
530C22⋊Q8—1224no—
531C22⋊Q8—1224no—
532#121—1224no—
533#121—1224no—
534#121—1228no—
535#120—618no—
536#120—1224no—
537C4×D4—1228no—
538#117—21no—
539#117—21no—
540#117C4×D6112yes—
541#117C22×D6112yes—
542C2×C4⋊C4—21no—
543C2×C22⋊C4C4×D6112yes—
544C2×C42—21no—
545#101—1224no—
546#100—1224no—
547C22⋊C8—1228no—
548C22⋊C8—1228no—
549C24—612no—
550C24—612no—
551C24C2×C4×D6111yescharacteristic
552#41—1222no—
553#41—1222no—
554#41—1222no—
555#41—1222no—
556#41—1222no—
557#41—1222no—
558#41—1222no—
559#41—1222no—
560#41—1222no—
561#41—1222no—
562#41—1222no—
563#41—1222no—
564#41—1222no—
565#41—1222no—
566#41—1222no—
567#41—1222no—
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—
577#41—2441no—
578#41—2441no—
579#41—2441no—
580#41—2441no—
581#41—2441no—
582#41—2441no—
583#41—2441no—
584C2×Q8—612no—
585C2×Q8—612no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8—1221no—
590C2×Q8—1221no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×D4—614no—
597C2×D4—614no—
598C2×D4—612no—
599C2×D4—612no—
600C2×D4—1228no—
601C2×D4—1222no—
602C2×D4—1222no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—1222no—
608C2×D4—1222no—
609C2×D4—1222no—
610C2×D4—1222no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1221no—
621C22×C4—22no—
622C22×C4—612no—
623C22×C4—614no—
624C22×C4—614no—
625C22×C4—612no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4C2×C4×D6111yescharacteristic
637C22×C4C2×D24411yescharacteristic
638C22×C4C2×D24411yescharacteristic
639C22×C4#1175822211yescharacteristic
640C22×C4#1175822211yescharacteristic
641C22×C4D4×D6111yescharacteristic
642C22×C4D4×D6111yescharacteristic
643C22×C4D4×D6111yescharacteristic
644C22×C4D4×D6111yescharacteristic
645C22×C4D4×D6111yescharacteristic
646C22×C4D4×D6111yescharacteristic
647C22×C4#1175822611yescharacteristic
648C22×C4#1175822611yescharacteristic
649C22×C4C23×D6111yescharacteristic
650M16—22no—
651M16—22no—
652M16—22no—
653M16—22no—
654M16—22no—
655M16—22no—
656M16—41no—
657M16—41no—
658M16—12216no—
659M16—1222no—
660M16—1222no—
661M16—1222no—
662M16—1222no—
663M16—1222no—
664M16—1222no—
665M16—2441no—
666M16—2441no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—41no—
671C2×C8—41no—
672C2×C8—614no—
673C2×C8—12216no—
674C2×C8—1222no—
675C2×C8—1222no—
676C2×C8—1222no—
677C2×C8—2441no—
678C2×C8—2441no—
679C2×C8C2×D24414yes—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—1228no—
683C22⋊C4—22no—
684C22⋊C4—1228no—
685C22⋊C4—1228no—
686C22⋊C4C2×C4×D6114yes—
687C42—22no—
688C42—22no—
689C23—81no—
690C23—614no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23—1222no—
695C23—1222no—
696C23—4882no—
697C23—4882no—
698C23C22⋊C4×D6111yescharacteristic
699C23C22⋊C4×D6111yescharacteristic
700C23#1451973911yescharacteristic
701C23#1451973911yescharacteristic
702C23C4×D24411yescharacteristic
703C23C4×D24411yescharacteristic
704C23C22×C4×D6111yescharacteristic
705Q8—1222no—
706Q8—1222no—
707Q8—1222no—
708Q8—1222no—
709Q8—2441no—
710Q8—2441no—
711Q8—2441no—
712Q8—2441no—
713D4—1224no—
714D4—1224no—
715D4—1224no—
716D4—1224no—
717D4—1222no—
718D4—1222no—
719D4—1222no—
720D4—1222no—
721D4—4888no—
722D4—2442no—
723D4—2442no—
724D4—2442no—
725D4—2442no—
726D4—2441no—
727D4—2441no—
728D4—2441no—
729D4—2441no—
730C2×C4—24no—
731C2×C4—82no—
732C2×C4—614no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1224no—
736C2×C4—1224no—
737C2×C4—1224no—
738C2×C4—1224no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4C22⋊C4×D6111yescharacteristic
747C2×C4C22⋊C4×D6111yescharacteristic
748C2×C4#1451973911yescharacteristic
749C2×C4#1451973911yescharacteristic
750C2×C4C4×D24411yescharacteristic
751C2×C4C4×D24411yescharacteristic
752C2×C4#1451974711yescharacteristic
753C2×C4#1451974711yescharacteristic
754C2×C4#1451974711yescharacteristic
755C2×C4#1451974711yescharacteristic
756C2×C4#1451975011yescharacteristic
757C2×C4#1451975011yescharacteristic
758C2×C4#1451975011yescharacteristic
759C2×C4#1451975011yescharacteristic
760C2×C4#1451975211yescharacteristic
761C2×C4#1451975211yescharacteristic
762C2×C4#1451975211yescharacteristic
763C2×C4#1451975211yescharacteristic
764C2×C4#1451976211yescharacteristic
765C2×C4#1451976211yescharacteristic
766C2×C4#1451976211yescharacteristic
767C2×C4#1451976211yescharacteristic
768C2×C4C2×D4×D6111yescharacteristic
769C2×C4C2×D4×D6111yescharacteristic
770C2×C4C2×D4×D6111yescharacteristic
771C2×C4C22×D24411yescharacteristic
772C2×C4C2×#1175822211yescharacteristic
773C2×C4C2×#1175822611yescharacteristic
774C8—24no—
775C8—42no—
776C8—1224no—
777C8—2442no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—1224no—
786C22—4882no—
787C22—2444no—
788C22—2444no—
789C22—2444no—
790C22—2444no—
791C22—2444no—
792C22—2442no—
793C22#1683964011yescharacteristic
794C22#1683964011yescharacteristic
795C22#1683964011yescharacteristic
796C22#1683964011yescharacteristic
797C22C2×C22⋊C4×D6111yescharacteristic
798C22C2×#1451973911yescharacteristic
799C22C2×C4×D24411yescharacteristic
800C4—44no—
801C4—1224no—
802C4—2442no—
803C4#1683964011yescharacteristic
804C4#1683964011yescharacteristic
805C4#1683964011yescharacteristic
806C4#1683964011yescharacteristic
807C4C2×#1451974711yescharacteristic
808C4C2×#1451975011yescharacteristic
809C4C2×#1451975211yescharacteristic
810C4C2×#1451976211yescharacteristic
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—21no—
817C2—21no—
818C2—4882no—
819C2—2444no—
820C2C2×#1683964011yescharacteristic
subgroupG/H
centerC4C2×#14519747
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#344C2
socleC2×C61C2×#386
prime radical#21459152C2
cosocleC22×C4×C61C24
hypercenterC2×#344D61
hypocenterC61#20964
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. #21454263C2semidirect
5. #21454263C2semidirect
6. #21446236C2semidirect
7. C2×#16839532C2semidirect
8. C2×C61×#344C2semidirect
37. #16839725C22semidirect
38. #16839725C22semidirect
39. #16839532C22semidirect
43. C61×#344C22semidirect
89. C2×#11758194D4semidirect
96. C22×#92418D4semidirect
126. C2×M16×C61D4semidirect
130. C22×C8×C61D4semidirect
408. C2×#344D61semidirect
453. #344C2×D61semidirect
454. C61#20964semidirect
516. C2×M16D244semidirect
523. C22×C8D244semidirect

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
#214542632
#214462362
C2×#168395322
C2×C61×#3442
#2096461