Finite Group Databasebeta

← #29707857

Subgroups — #29707857

Order 15616.

1332 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840560C211yesmaximal, characteristic
2C2×#16839810C211yesmaximal, characteristic, complemented
3C2×#16839780C211yesmaximal, characteristic, complemented
4C2×#16839746C211yesmaximal, characteristic, complemented
5C2×#16839744C211yesmaximal, characteristic, complemented
6#21447097C214yesmaximal, complemented
7#21447090C214yesmaximal, complemented
8C2×#16839532C211yesmaximal, characteristic, complemented
9C61×#2896C211yesmaximal, characteristic, complemented
10C22×#11758222C2211yescharacteristic
11#16840560—22no—
12#16840560—22no—
13#16840560—22no—
14#16840560—22no—
15C2×#14519808C2212yes—
16C2×#14519807—21no—
17C2×#14519803C2212yes—
18C2×#14519802—21no—
19C2×#14519797—22no—
20C22×#11758194C2211yescharacteristic
21C22×#11758194C2211yescharacteristic
22C22×#11758194C2211yescharacteristic
23#16839810—22no—
24#16839810C2214yescomplemented
25C2×#14519712—22no—
26#16839780—22no—
27#16839780C2214yes—
28C2×#14519705—22no—
29#16839746—22no—
30#16839746—22no—
31#16839744—22no—
32#16839744C2214yes—
33C2×#14519696C2212yescomplemented
34C2×#14519695—21no—
35C2×#14519694C2212yescomplemented
36C2×#14519693—21no—
37#16839532C2214yescomplemented
38C22×#41×C61C2211yescharacteristic
39C22×M16×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C61×#419C2212yescomplemented
42C61×#418C2212yescomplemented
43C61×#417—22no—
44C61×#416—22no—
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×#11758222D412yes—
56C2×#11758222C2312yes—
57C22×Dic122D411yescharacteristic
58C22×D244D411yescharacteristic
59C22×C22⋊D61—21no—
60C22×C4×D61—21no—
61#14519808—24no—
62#14519808—24no—
63#14519807—24no—
64#14519807—24no—
65#14519803—24no—
66#14519803—24no—
67#14519802—24no—
68#14519802—24no—
69#14519797—28no—
70#14519797—28no—
71C2×#11758202—22no—
72C2×#11758200—22no—
73C2×#11758201—22no—
74C2×#11758199—22no—
75C2×#11758194—21no—
76C2×#11758194—21no—
77C2×#11758194—21no—
78C2×#11758194—21no—
79C2×#11758194—21no—
80C2×#11758194—21no—
81C2×#11758194—21no—
82C2×#11758194—21no—
83C2×#11758194—21no—
84C2×#11758194—21no—
85C2×#11758194—21no—
86C2×#11758194D412yes—
87C2×#11758194D412yes—
88C2×#11758194D412yes—
89C2×#11758194D412yes—
90C2×#11758194C2312yes—
91C2×#11758194C2312yes—
92C2×#11758194C2312yes—
93C22×#92418—21no—
94C22×#92418—21no—
95C22×#92418—21no—
96#14519712—28no—
97#14519705—28no—
98#14519696—24no—
99#14519695—24no—
100#14519694—24no—
101#14519693—24no—
102C2×#41×C61—21no—
103C2×#41×C61—21no—
104C2×#41×C61—21no—
105C2×#41×C61—21no—
106C2×#41×C61—21no—
107C2×#41×C61—21no—
108C2×#41×C61—21no—
109C2×#41×C61—21no—
110C2×#41×C61—21no—
111C2×#41×C61—21no—
112C2×#41×C61D412yes—
113C2×#41×C61D412yes—
114C22×Q8×C61C2311yescharacteristic
115C22×D4×C61—21no—
116C22×D4×C61C2311yescharacteristic
117C23×C4×C61—21no—
118C23×C4×C61C2311yescharacteristic
119C2×M16×C61—21no—
120C2×M16×C61—21no—
121C2×M16×C61—21no—
122C2×M16×C61—21no—
123C2×M16×C61—21no—
124C2×M16×C61C2312yes—
125C22×C8×C61—21no—
126#117×C61—21no—
127#117×C61—21no—
128#117×C61—21no—
129#117×C61C2312yes—
130C2×C4⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C42×C61—21no—
133#103×C61—24no—
134#102×C61—24no—
135C24×C61—21no—
136C24×C61#4111yescharacteristic
137C23×D61—21no—
138#41×C61—22no—
139#41×C61—22no—
140#41×C61—22no—
141#41×C61—22no—
142#41×C61—22no—
143#41×C61—22no—
144#41×C61—22no—
145#41×C61—22no—
146#41×C61—41no—
147#41×C61—41no—
148#41×C61—41no—
149#41×C61—41no—
150#41×C61—41no—
151#41×C61—41no—
152#41×C61—41no—
153#41×C61—41no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61C2×D412yes—
160C2×D4×C61—22no—
161C2×D4×C61—22no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—41no—
168C2×D4×C61—41no—
169C2×D4×C61—41no—
170C2×D4×C61—41no—
171C2×D4×C61C2×D412yes—
172C22×C4×C61—21no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—41no—
176C22×C4×C61—41no—
177C22×C4×C61—41no—
178C22×C4×C61—41no—
179C22×C4×C61—41no—
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61#4111yescharacteristic
189C22×C4×C61#4111yescharacteristic
190C22×C4×C61#4111yescharacteristic
191C22×C4×C61#4111yescharacteristic
192C22×C4×C61#4111yescharacteristic
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—22no—
195C2×C22⋊D61—22no—
196C2×C22⋊D61—41no—
197C2×C22⋊D61—41no—
198C2×C22⋊D61—41no—
199C2×C22⋊D61—41no—
200C22×Dic61—21no—
201#11758222—22no—
202#11758222—22no—
203#11758222—22no—
204#11758222—22no—
205#11758222—22no—
206#11758222—22no—
207#11758222—22no—
208#11758222—22no—
209#11758222—41no—
210#11758222—41no—
211#11758222—41no—
212#11758222—41no—
213#11758222—41no—
214#11758222—41no—
215#11758222—41no—
216#11758222—41no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244C2×D412yes—
223C2×C4×D61—22no—
224C2×C4×D61—22no—
225C2×C4×D61—41no—
226C2×C4×D61—41no—
227C2×C4×D61—41no—
228C2×C4×D61—41no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122C2×D412yes—
235M16×C61—22no—
236M16×C61—22no—
237M16×C61—41no—
238M16×C61—41no—
239C2×C8×C61—22no—
240C2×C8×C61—41no—
241C2×C8×C61—41no—
242C4⋊C4×C61—22no—
243C4⋊C4×C61—41no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—41no—
246C42×C61—22no—
247C42×C61—41no—
248#11758202—28no—
249#11758201—28no—
250#11758200—28no—
251#11758199—28no—
252#11758194—22no—
253#11758194—22no—
254#11758194—22no—
255#11758194—22no—
256#11758194—22no—
257#11758194—22no—
258#11758194—22no—
259#11758194—22no—
260#11758194—41no—
261#11758194—41no—
262#11758194C2×D414yes—
263#11758194C2×D414yes—
264C2×#92418—22no—
265C2×#92418—22no—
266C2×#92418—22no—
267C2×#92418—22no—
268C2×#92418—22no—
269C2×#92418—22no—
270C2×#92418—22no—
271C2×#92418—41no—
272C2×#92418—41no—
273C23×C61—22no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—81no—
277C23×C61—82no—
278C23×C61#12111yescharacteristic
279C23×C61#12111yescharacteristic
280C23×C61#12311yescharacteristic
281C23×C61#12311yescharacteristic
282C23×C61#12411yescharacteristic
283C23×C61#12411yescharacteristic
284C23×C61C2×#4111yescharacteristic
285C22×D61—22no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—82no—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61—41no—
292Q8×C61—41no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—42no—
296D4×C61—42no—
297D4×C61—42no—
298D4×C61—42no—
299D4×C61—41no—
300D4×C61—41no—
301C2×C4×C61—22no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—82no—
310C2×C4×C61#12011yescharacteristic
311C2×C4×C61#12011yescharacteristic
312C2×C4×C61#12011yescharacteristic
313C2×C4×C61#12011yescharacteristic
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#12111yescharacteristic
321C2×C4×C61#12111yescharacteristic
322C2×C4×C61#12111yescharacteristic
323C2×C4×C61#12111yescharacteristic
324C2×C4×C61#12311yescharacteristic
325C2×C4×C61#12311yescharacteristic
326C2×C4×C61#12311yescharacteristic
327C2×C4×C61#12311yescharacteristic
328C2×C4×C61#12311yescharacteristic
329C2×C4×C61#12311yescharacteristic
330C2×C4×C61#12411yescharacteristic
331C2×C4×C61#12411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C2×#4111yescharacteristic
337C2×C4×C61C2×#4111yescharacteristic
338C22⋊D61—42no—
339C22⋊D61—42no—
340C22⋊D61—42no—
341C22⋊D61—42no—
342C2×Dic61—22no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345D244—22no—
346D244—22no—
347D244—41no—
348D244—41no—
349C4×D61—42no—
350C4×D61—42no—
351C4×D61—42no—
352C4×D61—42no—
353Dic122—22no—
354Dic122—22no—
355Dic122—41no—
356Dic122—41no—
357C8×C61—42no—
358#92418—24no—
359#92418—24no—
360#92418—42no—
361#23525—611nomaximal, Sylow
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—42no—
370C22×C61—82no—
371C22×C61—82no—
372C22×C61—82no—
373C22×C61#39411yescharacteristic
374C22×C61#39411yescharacteristic
375C22×C61#39411yescharacteristic
376C22×C61#39411yescharacteristic
377C22×C61C2×#12111yescharacteristic
378C22×C61C2×#12311yescharacteristic
379C22×C61C2×#12411yescharacteristic
380C2×D61—42no—
381C2×D61—82no—
382C2×D61—82no—
383C2×D61—82no—
384C4×C61—42no—
385C4×C61—82no—
386C4×C61#39411yescharacteristic
387C4×C61#39411yescharacteristic
388C4×C61#39411yescharacteristic
389C4×C61#39411yescharacteristic
390C4×C61C2×#12011yescharacteristic
391C4×C61C2×#12111yescharacteristic
392C4×C61C2×#12111yescharacteristic
393C4×C61C2×#12311yescharacteristic
394Dic61—42no—
395C2×#575—611no—
396C2×#430—611no—
397C2×#421—611no—
398#2896D6111yescharacteristic, complemented
399C2×#413—611no—
400C2×#413—611no—
401#2049—614no—
402#2048—614no—
403C2×#344—611no—
404C2×C61—21no—
405C2×C61—21no—
406C2×C61—21no—
407C2×C61—21no—
408C2×C61—21no—
409C2×C61—21no—
410C2×C61—21no—
411C2×C61—82no—
412C2×C61C2×#39411yescharacteristic
413D61—82no—
414C22×#41—611no—
415C22×#41C2×D6111yescharacteristic
416#575—1222no—
417#575—1222no—
418#575—1222no—
419#575—1222no—
420C2×#137—612no—
421C2×#137—1221no—
422C2×AGL(1,ℤ/8)—612no—
423C2×AGL(1,ℤ/8)—1221no—
424C2×#135—1222no—
425C22×M16—611no—
426C22×M16—611no—
427C22×M16—611no—
428C22×M16C2×D6111yescharacteristic
429C2×#117C2×D6111yescharacteristic
430#430—614no—
431#430—1222no—
432C2×#108—1222no—
433#421—614no—
434#421—1222no—
435C2×#104—1222no—
436#419C2×D6112yescomplemented
437#418C2×D6112yescomplemented
438#417—22no—
439#416—22no—
440#413—614no—
441#413—1222no—
442#413—1222no—
443#413—1222no—
444C2×#101—612no—
445C2×#101—1221no—
446C2×#100—612no—
447C2×#100—1221no—
448#344—614no—
449C61#2352511yescharacteristic, complemented, Sylow
450C2×#41—21no—
451C2×#41—21no—
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—612no—
461C2×#41—612no—
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×#41C22⋊D6112yes—
473C2×#41C22⋊D6112yes—
474C22×Q8—611no—
475C22×Q8C22×D6111yescharacteristic
476C22×D4—21no—
477C22×D4—611no—
478C22×D4—1221no—
479C22×D4C22×D6111yescharacteristic
480C23×C4—21no—
481C23×C4—1221no—
482C23×C4C22×D6111yescharacteristic
483#137—1224no—
484#137—1224no—
485#137—1224no—
486#137—1224no—
487AGL(1,ℤ/8)—1224no—
488AGL(1,ℤ/8)—1224no—
489AGL(1,ℤ/8)—1224no—
490AGL(1,ℤ/8)—1224no—
491#135—1228no—
492#135—1228no—
493C2×Q16—1222no—
494C2×SD16—1222no—
495C2×SD16—1222no—
496C2×D8—1222no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—612no—
503C2×M16—612no—
504C2×M16—612no—
505C2×M16—612no—
506C2×M16—612no—
507C2×M16—612no—
508C2×M16—612no—
509C2×M16—1221no—
510C2×M16—1221no—
511C2×M16—1221no—
512C2×M16—1221no—
513C2×M16—1221no—
514C2×M16—1221no—
515C2×M16—1221no—
516C2×M16—1221no—
517C2×M16—1221no—
518C2×M16—1221no—
519C2×M16—1221no—
520C2×M16C22×D6112yes—
521C22×C8—21no—
522C22×C8—1221no—
523C22×C8—1221no—
524C22×C8—1221no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117C22×D6112yes—
529C2×C4⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C42—21no—
532#108—1228no—
533#104—1228no—
534#103—24no—
535#102—24no—
536#101—1224no—
537#101—1224no—
538#100—1224no—
539#100—1224no—
540C24—21no—
541C24—1221no—
542C24#1175822411yescharacteristic
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
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—2441no—
568#41—2441no—
569#41—2441no—
570#41—2441no—
571#41—2441no—
572#41—2441no—
573#41—2441no—
574#41—2441no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—612no—
581C2×Q8—1221no—
582C2×Q8—1221no—
583C2×Q8—1221no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8C2×C22⋊D6112yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—612no—
599C2×D4—1222no—
600C2×D4—1222no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—2441no—
607C2×D4—2441no—
608C2×D4—2441no—
609C2×D4—2441no—
610C2×D4C2×C22⋊D6112yes—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—1221no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—2441no—
623C22×C4—2441no—
624C22×C4—2441no—
625C22×C4—2441no—
626C22×C4#1175822211yescharacteristic
627C22×C4#1175822211yescharacteristic
628C22×C4#1175822211yescharacteristic
629C22×C4#1175822211yescharacteristic
630C22×C4D4×D6111yescharacteristic
631C22×C4D4×D6111yescharacteristic
632C22×C4D4×D6111yescharacteristic
633C22×C4D4×D6111yescharacteristic
634C22×C4D4×D6111yescharacteristic
635C22×C4D4×D6111yescharacteristic
636C22×C4#1175822411yescharacteristic
637C22×C4C2×C22⋊D6111yescharacteristic
638C22×C4C2×C22⋊D6111yescharacteristic
639C22×C4C23×D6111yescharacteristic
640Q16—1228no—
641SD16—1228no—
642SD16—1228no—
643D8—1228no—
644M16—22no—
645M16—22no—
646M16—41no—
647M16—41no—
648M16—614no—
649M16—614no—
650M16—1222no—
651M16—1222no—
652M16—1222no—
653M16—1222no—
654M16—1222no—
655M16—1222no—
656M16—1222no—
657M16—1222no—
658M16—2441no—
659M16—2441no—
660C2×C8—22no—
661C2×C8—41no—
662C2×C8—41no—
663C2×C8—1222no—
664C2×C8—1222no—
665C2×C8—1222no—
666C2×C8—1222no—
667C2×C8—1222no—
668C2×C8—1222no—
669C2×C8—1222no—
670C2×C8—2441no—
671C2×C8—2441no—
672C4⋊C4—22no—
673C4⋊C4—41no—
674C22⋊C4—22no—
675C22⋊C4—41no—
676C42—22no—
677C42—41no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—81no—
682C23—82no—
683C23—1222no—
684C23—4882no—
685C23—2441no—
686C23—2441no—
687C23#1451974911yescharacteristic
688C23#1451974911yescharacteristic
689C23#1451975911yescharacteristic
690C23#1451975911yescharacteristic
691C23#1451976311yescharacteristic
692C23#1451976311yescharacteristic
693C23C2×#1175822411yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—41no—
697Q8—41no—
698Q8—1222no—
699Q8—1222no—
700Q8—2441no—
701Q8—2441no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—41no—
709D4—41no—
710D4—1222no—
711D4—1222no—
712D4—2442no—
713D4—2442no—
714D4—2442no—
715D4—2442no—
716D4—2441no—
717D4—2441no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—82no—
727C2×C4—1222no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2442no—
733C2×C4—2442no—
734C2×C4#1451974511yescharacteristic
735C2×C4#1451974511yescharacteristic
736C2×C4#1451974511yescharacteristic
737C2×C4#1451974511yescharacteristic
738C2×C4#1451974911yescharacteristic
739C2×C4#1451974911yescharacteristic
740C2×C4#1451975011yescharacteristic
741C2×C4#1451975011yescharacteristic
742C2×C4#1451975011yescharacteristic
743C2×C4#1451975011yescharacteristic
744C2×C4#1451975011yescharacteristic
745C2×C4#1451975011yescharacteristic
746C2×C4#1451975011yescharacteristic
747C2×C4#1451975011yescharacteristic
748C2×C4#1451975911yescharacteristic
749C2×C4#1451975911yescharacteristic
750C2×C4#1451976011yescharacteristic
751C2×C4#1451976011yescharacteristic
752C2×C4#1451976011yescharacteristic
753C2×C4#1451976011yescharacteristic
754C2×C4#1451976311yescharacteristic
755C2×C4#1451976311yescharacteristic
756C2×C4C2×D4×D6111yescharacteristic
757C2×C4C2×D4×D6111yescharacteristic
758C2×C4C2×D4×D6111yescharacteristic
759C2×C4C22×C22⋊D6111yescharacteristic
760C2×C4C2×#1175822211yescharacteristic
761C2×C4C2×#1175822211yescharacteristic
762C8—42no—
763C8—1224no—
764C8—1224no—
765C8—2442no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—4882no—
778C22—4882no—
779C22—4882no—
780C22—2442no—
781C22#1683967711yescharacteristic
782C22#1683967711yescharacteristic
783C22#1683967711yescharacteristic
784C22#1683967711yescharacteristic
785C22C2×#1451974911yescharacteristic
786C22C2×#1451975911yescharacteristic
787C22C2×#1451976311yescharacteristic
788C4—42no—
789C4—82no—
790C4—2442no—
791C4#1683967711yescharacteristic
792C4#1683967711yescharacteristic
793C4#1683967711yescharacteristic
794C4#1683967711yescharacteristic
795C4C2×#1451974511yescharacteristic
796C4C2×#1451975011yescharacteristic
797C4C2×#1451975011yescharacteristic
798C4C2×#1451976011yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—82no—
807C2—4882no—
808C2C2×#1683967711yescharacteristic
subgroupG/H
centerC4#16839677
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2896C2
socleC2×C61C2×#394
prime radicalC2×#16840560C2
hypercenter#2896D61
hypocenterC61#23525
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
2. C2×#16839810C2semidirect
3. C2×#16839780C2semidirect
4. C2×#16839746C2semidirect
5. C2×#16839744C2semidirect
6. #21447097C2semidirect
7. #21447090C2semidirect
8. C2×#16839532C2semidirect
9. C61×#2896C2semidirect
24. #16839810C22semidirect
33. C2×#14519696C22semidirect
35. C2×#14519694C22semidirect
37. #16839532C22semidirect
41. C61×#419C22semidirect
42. C61×#418C22semidirect
398. #2896D61semidirect
436. #419C2×D61semidirect
437. #418C2×D61semidirect
449. C61#23525semidirect

Maximal subgroups

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

subgroupindex
C2×#168405602
C2×#168398102
C2×#168397802
C2×#168397462
C2×#168397442
#214470972
#214470902
C2×#168395322
C61×#28962
#2352561