Finite Group Databasebeta

← #29586601

Subgroups — #29586601

Order 15616.

1466 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840329C211yesmaximal, characteristic
2C2×#16839767C211yesmaximal, characteristic, complemented
3C2×#16839735C211yesmaximal, characteristic, complemented
4#21454263C211yesmaximal, characteristic, complemented
5C2×#16839519C211yesmaximal, characteristic, complemented
6C2×#16839518C211yesmaximal, characteristic, complemented
7C2×C61×#418C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10#16840329—22no—
11#16840329—22no—
12#16840329—22no—
13#16840329—22no—
14C2×#14519773C412yescomplemented
15C2×#14519764C412yescomplemented
16C2×#14519748—22no—
17C2×#14519746—22no—
18C2×#14519736C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20#16839767—22no—
21#16839767—22no—
22C2×#14519698—22no—
23#16839735—22no—
24#16839735—22no—
25C2×#14519691—22no—
26#16839730—22no—
27#16839728—22no—
28#16839725—22no—
29#16839519—22no—
30#16839518—22no—
31C23×D4×C61C2211yescharacteristic
32C22×M16×C61C2211yescharacteristic
33C2×#117×C61C2211yescharacteristic
34C61×#418—22no—
35C61×#418—22no—
36C2×#102×C61—22no—
37C2×#11758222—21no—
38C2×#11758222—21no—
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—
49C22×Dic122C2×C411yescharacteristic
50C22×D244C2×C411yescharacteristic
51C22×C22⋊D61—24no—
52C22×C22⋊D61D412yes—
53C22×C4×D61D412yes—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C22×#92418D412yescomplemented
61#14519773—24no—
62#14519773—24no—
63#14519764—24no—
64#14519764—24no—
65#14519748—28no—
66#14519748—28no—
67#14519746—28no—
68#14519746—28no—
69#14519736—21no—
70#14519736—21no—
71#14519736—21no—
72#14519736—21no—
73#14519736—21no—
74#14519736D412yes—
75#14519736D412yes—
76#14519736D412yescomplemented
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—24no—
81C2×C22⋊Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61C2×C412yes—
84#14519698—28no—
85#14519691—28no—
86#14519689—28no—
87C25×C61—21no—
88C22×D4×C61—21no—
89C22×D4×C61—21no—
90C22×D4×C61—21no—
91C22×D4×C61—21no—
92C22×D4×C61—21no—
93C22×D4×C61—21no—
94C22×D4×C61—21no—
95C22×D4×C61—21no—
96C22×D4×C61—21no—
97C22×D4×C61—21no—
98C22×D4×C61—21no—
99C22×D4×C61C2×C412yes—
100C22×D4×C61D412yes—
101C22×D4×C61D412yes—
102C23×C4×C61C2311yescharacteristic
103C2×M16×C61—21no—
104C2×M16×C61—21no—
105C2×M16×C61—21no—
106C2×M16×C61—21no—
107C2×M16×C61—21no—
108C2×M16×C61—21no—
109C22×C8×C61D412yescomplemented
110#117×C61—21no—
111#117×C61—21no—
112#117×C61—21no—
113#117×C61D412yescomplemented
114C2×C4⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C42×C61—21no—
117#102×C61—28no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—41no—
122C24×C61—41no—
123C24×C61—41no—
124C24×C61—41no—
125C24×C61—84no—
126C24×C61C2×D411yescharacteristic
127C23×D61C22⋊C412yes—
128C2×D4×C61—22no—
129C2×D4×C61—22no—
130C2×D4×C61—22no—
131C2×D4×C61—22no—
132C2×D4×C61—22no—
133C2×D4×C61—22no—
134C2×D4×C61—22no—
135C2×D4×C61—22no—
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61—22no—
139C2×D4×C61—22no—
140C2×D4×C61—22no—
141C2×D4×C61—22no—
142C2×D4×C61—22no—
143C2×D4×C61—41no—
144C2×D4×C61—41no—
145C2×D4×C61—41no—
146C2×D4×C61—41no—
147C2×D4×C61—41no—
148C2×D4×C61—41no—
149C2×D4×C61—41no—
150C2×D4×C61—41no—
151C2×D4×C61—41no—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61—41no—
155C2×D4×C61C22⋊C414yes—
156C22×C4×C61—41no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61#4111yescharacteristic
168C22×C4×C61#4111yescharacteristic
169C22×C4×C61#4111yescharacteristic
170C22×C4×C61#4111yescharacteristic
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—216no—
178C2×C22⋊D61—88no—
179C22×Dic61—22no—
180C22×Dic61—41no—
181C22×Dic61C22⋊C412yes—
182#11758222—41no—
183#11758222—41no—
184#11758222—41no—
185#11758222—41no—
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—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×C4×D61—22no—
205C2×C4×D61—22no—
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216M16×C61—41no—
217M16×C61—41no—
218M16×C61—41no—
219M16×C61—41no—
220C2×C8×C61—22no—
221C2×C8×C61—22no—
222C2×C8×C61—22no—
223C4⋊C4×C61—22no—
224C4⋊C4×C61—41no—
225C22⋊C4×C61—22no—
226C22⋊C4×C61—41no—
227C42×C61—22no—
228C42×C61—41no—
229C22⋊Dic61—216no—
230C22⋊Dic61—22no—
231C22⋊Dic61—22no—
232C22⋊Dic61—22no—
233C22⋊Dic61—41no—
234C4⋊Dic61—22no—
235C4⋊Dic61—22no—
236C4⋊Dic61—22no—
237C4⋊Dic61—41no—
238C4×Dic61—22no—
239C4×Dic61—22no—
240C4×Dic61—41no—
241C4×Dic61C22⋊C414yes—
242#11758194—41no—
243#11758194—41no—
244#11758194—41no—
245#11758194—41no—
246C2×#92418—22no—
247C2×#92418—22no—
248C2×#92418—22no—
249C23×C61—24no—
250C23×C61—42no—
251C23×C61—48no—
252C23×C61—42no—
253C23×C61—42no—
254C23×C61—42no—
255C23×C61—42no—
256C23×C61—42no—
257C23×C61—42no—
258C23×C61—84no—
259C23×C61—84no—
260C23×C61—84no—
261C23×C61—84no—
262C23×C61—84no—
263C23×C61—84no—
264C23×C61C2×C22⋊C411yescharacteristic
265C23×C61#12011yescharacteristic
266C23×C61#12011yescharacteristic
267C23×C61#12011yescharacteristic
268C23×C61#12111yescharacteristic
269C23×C61#12111yescharacteristic
270C23×C61#12311yescharacteristic
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—44no—
275D4×C61—24no—
276D4×C61—24no—
277D4×C61—42no—
278D4×C61—42no—
279D4×C61—42no—
280D4×C61—42no—
281D4×C61—42no—
282D4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—82no—
285C2×C4×C61C2×C22⋊C411yescharacteristic
286C2×C4×C61C2×C22⋊C411yescharacteristic
287C2×C4×C61C4×D411yescharacteristic
288C2×C4×C61C4×D411yescharacteristic
289C2×C4×C61C4×D411yescharacteristic
290C2×C4×C61C4×D411yescharacteristic
291C2×C4×C61#12011yescharacteristic
292C2×C4×C61#12011yescharacteristic
293C2×C4×C61#12011yescharacteristic
294C2×C4×C61#12011yescharacteristic
295C2×C4×C61#12011yescharacteristic
296C2×C4×C61#12111yescharacteristic
297C2×C4×C61#12111yescharacteristic
298C2×C4×C61#12111yescharacteristic
299C2×C4×C61#12111yescharacteristic
300C2×C4×C61#12111yescharacteristic
301C2×C4×C61#12111yescharacteristic
302C2×C4×C61#12111yescharacteristic
303C2×C4×C61#12111yescharacteristic
304C2×C4×C61#12111yescharacteristic
305C2×C4×C61#12111yescharacteristic
306C2×C4×C61#12311yescharacteristic
307C2×C4×C61#12311yescharacteristic
308C2×C4×C61#12311yescharacteristic
309C2×C4×C61#12411yescharacteristic
310C2×C4×C61#12411yescharacteristic
311C2×C4×C61#12711yescharacteristic
312C2×C4×C61#12711yescharacteristic
313C22⋊D61—42no—
314C22⋊D61—42no—
315C22⋊D61—42no—
316C22⋊D61—42no—
317C22⋊D61—816no—
318C2×Dic61—24no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—44no—
323C2×Dic61—42no—
324C2×Dic61—82no—
325D244—41no—
326D244—41no—
327D244—41no—
328D244—41no—
329C4×D61—42no—
330C4×D61—42no—
331C4×D61—42no—
332C4×D61—42no—
333Dic122—41no—
334Dic122—41no—
335Dic122—41no—
336Dic122—41no—
337C8×C61—42no—
338#92418—42no—
339#10987—611nomaximal, Sylow
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—48no—
348C22×C61—44no—
349C22×C61—84no—
350C22×C61—84no—
351C22×C61—84no—
352C22×C61—84no—
353C22×C61—84no—
354C22×C61—84no—
355C22×C61#37911yescharacteristic
356C22×C61#38611yescharacteristic
357C22×C61#38611yescharacteristic
358C22×C61#39211yescharacteristic
359C22×C61#39211yescharacteristic
360C22×C61#39411yescharacteristic
361C22×C61#39411yescharacteristic
362C2×D61—44no—
363C2×D61—44no—
364C2×D61—42no—
365C2×D61—82no—
366C4×C61—82no—
367C4×C61#38611yescharacteristic
368C4×C61#38611yescharacteristic
369C4×C61#39011yescharacteristic
370C4×C61#39011yescharacteristic
371C4×C61#39211yescharacteristic
372C4×C61#39211yescharacteristic
373C4×C61#39411yescharacteristic
374C4×C61#39411yescharacteristic
375Dic61—44no—
376Dic61—42no—
377Dic61—82no—
378C2×#535—611no—
379C2×#418—611no—
380C2×#418D6111yescharacteristic, complemented
381C2×#410—611no—
382#2879—611no—
383C2×H(3,ℤ/4)—611no—
384C2×H(3,ℤ/4)—611no—
385C2×C61—21no—
386C2×C61—21no—
387C2×C61—21no—
388C2×C61—21no—
389C2×C61—21no—
390C2×C61—21no—
391C2×C61—84no—
392C2×C61#143811yescharacteristic
393C2×C61#191012yes—
394D61—82no—
395C22×#41—611no—
396C23×D4C2×D6111yescharacteristic
397C22×M16—611no—
398C22×M16C2×D6111yescharacteristic
399#535—1222no—
400#535—1222no—
401#535—1222no—
402#535—1222no—
403C2×#127—612no—
404C2×#124—612no—
405C2×#121—1222no—
406C2×#120—1222no—
407C2×#117—611no—
408C2×#117—611no—
409C2×#117C2×D6111yescharacteristic
410#418—22no—
411#418—22no—
412#418—1222no—
413#418—1222no—
414C2×#102—22no—
415C2×#102—1222no—
416#410—1222no—
417#410—1222no—
418C2×#99—1222no—
419#408—1222no—
420#408—1222no—
421#407—1222no—
422H(3,ℤ/4)—1222no—
423H(3,ℤ/4)—1222no—
424C61#1098711yescharacteristic, complemented, Sylow
425C25—21no—
426C2×#41—1221no—
427C2×#41—1221no—
428C2×#41—1221no—
429C2×#41—1221no—
430C2×#41—1221no—
431C2×#41—1221no—
432C2×#41—1221no—
433C2×#41—1221no—
434C2×#41—1221no—
435C2×#41—1221no—
436C2×#41—1221no—
437C2×#41—1221no—
438C22×Q8—611no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—612no—
451C22×D4—611no—
452C22×D4—1224no—
453C22×D4C4×D6112yes—
454C22×D4D24412yes—
455C22×D4C22⋊D6112yes—
456C23×C4—612no—
457C23×C4C22×D6111yescharacteristic
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—1221no—
465C2×M16—1221no—
466C2×M16—1221no—
467C2×M16—1221no—
468C2×M16—1221no—
469C2×M16—1221no—
470C22×C8—612no—
471C22×C8C22⋊D6112yescomplemented
472#127—1224no—
473#127—1224no—
474#124—1224no—
475#124—1224no—
476#121—1228no—
477#121—1228no—
478#120—1228no—
479#120—1228no—
480#117—21no—
481#117—21no—
482#117—21no—
483#117—612no—
484#117—612no—
485#117—612no—
486#117—1221no—
487#117—1221no—
488#117—1221no—
489#117—1221no—
490#117—1221no—
491#117C22⋊D6112yescomplemented
492C2×C4⋊C4—21no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—1224no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C42—21no—
500C2×C42—612no—
501C2×C42—1221no—
502#102—28no—
503#102—1228no—
504#99—1228no—
505C22⋊C8—1228no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—41no—
510C24—41no—
511C24—41no—
512C24—41no—
513C24—84no—
514C24—612no—
515C24D4×D6111yescharacteristic
516#41—2441no—
517#41—2441no—
518#41—2441no—
519#41—2441no—
520#41—2441no—
521#41—2441no—
522#41—2441no—
523#41—2441no—
524#41—2441no—
525#41—2441no—
526#41—2441no—
527#41—2441no—
528#41—2441no—
529#41—2441no—
530#41—2441no—
531#41—2441no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—12216no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1221no—
578C2×D4—4888no—
579C2×D4#1175819814yes—
580C22×C4—41no—
581C22×C4—612no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—2441no—
590C22×C4C2×C4×D6111yescharacteristic
591C22×C4C2×D24411yescharacteristic
592C22×C4#1175822211yescharacteristic
593C22×C4#1175822211yescharacteristic
594C22×C4D4×D6111yescharacteristic
595C22×C4D4×D6111yescharacteristic
596C22×C4D4×D6111yescharacteristic
597C22×C4D4×D6111yescharacteristic
598C22×C4D4×D6111yescharacteristic
599C22×C4#1175822411yescharacteristic
600C22×C4#1175822411yescharacteristic
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C2×C22⋊D6111yescharacteristic
603C22×C4C2×C22⋊D6111yescharacteristic
604M16—41no—
605M16—41no—
606M16—41no—
607M16—41no—
608M16—2441no—
609M16—2441no—
610M16—2441no—
611M16—2441no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—1222no—
616C2×C8—1222no—
617C2×C8—1222no—
618C4⋊C4—22no—
619C4⋊C4—41no—
620C4⋊C4—1222no—
621C4⋊C4—1222no—
622C4⋊C4—1222no—
623C4⋊C4—2441no—
624C22⋊C4—22no—
625C22⋊C4—41no—
626C22⋊C4—12216no—
627C22⋊C4—1222no—
628C22⋊C4—1222no—
629C22⋊C4—1222no—
630C22⋊C4—2441no—
631C42—22no—
632C42—41no—
633C42—614no—
634C42—1222no—
635C42—1222no—
636C42—2441no—
637C23—24no—
638C23—42no—
639C23—48no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—1222no—
653C23—1222no—
654C23—1222no—
655C23—2444no—
656C23C22⋊C4×D6111yescharacteristic
657C23#1451974511yescharacteristic
658C23#1451974511yescharacteristic
659C23#1451974711yescharacteristic
660C23#1451974811yescharacteristic
661C23#1451975011yescharacteristic
662C23#1451975911yescharacteristic
663Q8—2441no—
664Q8—2441no—
665Q8—2441no—
666Q8—2441no—
667D4—24no—
668D4—24no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—48816no—
676D4—2442no—
677D4—2442no—
678D4—2442no—
679D4—2442no—
680D4—2441no—
681D4—2441no—
682D4—2441no—
683D4—2441no—
684C2×C4—42no—
685C2×C4—82no—
686C2×C4—1224no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—4882no—
691C2×C4—2442no—
692C2×C4—2444no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4C22⋊C4×D6111yescharacteristic
698C2×C4C2×#1175819811yescharacteristic
699C2×C4#1451973711yescharacteristic
700C2×C4#1451973711yescharacteristic
701C2×C4C4×C22⋊D6111yescharacteristic
702C2×C4C4×C22⋊D6111yescharacteristic
703C2×C4#1451974511yescharacteristic
704C2×C4#1451974511yescharacteristic
705C2×C4#1451974611yescharacteristic
706C2×C4#1451974711yescharacteristic
707C2×C4#1451974711yescharacteristic
708C2×C4#1451974811yescharacteristic
709C2×C4#1451974911yescharacteristic
710C2×C4#1451974911yescharacteristic
711C2×C4#1451974911yescharacteristic
712C2×C4#1451974911yescharacteristic
713C2×C4#1451975011yescharacteristic
714C2×C4#1451975011yescharacteristic
715C2×C4#1451975011yescharacteristic
716C2×C4#1451975111yescharacteristic
717C2×C4#1451975111yescharacteristic
718C2×C4#1451975911yescharacteristic
719C2×C4#1451976011yescharacteristic
720C2×C4#1451976111yescharacteristic
721C2×C4#1451976311yescharacteristic
722C2×C4#1451976311yescharacteristic
723C2×C4#1451977311yescharacteristic
724C2×C4#1451977311yescharacteristic
725C8—42no—
726C8—2442no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—48no—
735C22—44no—
736C22—84no—
737C22—84no—
738C22—84no—
739C22—84no—
740C22—84no—
741C22—84no—
742C22—4882no—
743C22—2444no—
744C22—2444no—
745C22—2442no—
746C22#1683961711yescharacteristic
747C22#1683963811yescharacteristic
748C22#1683963811yescharacteristic
749C22#1683967011yescharacteristic
750C22#1683967111yescharacteristic
751C22#1683967711yescharacteristic
752C22#1683967811yescharacteristic
753C4—82no—
754C4—4882no—
755C4—2444no—
756C4—2442no—
757C4#1683963911yescharacteristic
758C4#1683964111yescharacteristic
759C4#1683966211yescharacteristic
760C4#1683966211yescharacteristic
761C4#1683967011yescharacteristic
762C4#1683967111yescharacteristic
763C4#1683967711yescharacteristic
764C4#1683967811yescharacteristic
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—84no—
772C2—4882no—
773C2#2144405811yescharacteristic
774C2#2144634312yes—
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#418C2
socleC22×C61#386
prime radicalC2×#16840329C2
cosocleC23×C4×C61C23
hypercenterC2×#418D61
hypocenterC61#10987
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#16839767C2semidirect
3. C2×#16839735C2semidirect
4. #21454263C2semidirect
5. C2×#16839519C2semidirect
6. C2×#16839518C2semidirect
7. C2×C61×#418C2semidirect
14. C2×#14519773C4semidirect
15. C2×#14519764C4semidirect
60. C22×#92418D4semidirect
76. #14519736D4semidirect
109. C22×C8×C61D4semidirect
113. #117×C61D4semidirect
380. C2×#418D61semidirect
424. C61#10987semidirect
471. C22×C8C22⋊D61semidirect
491. #117C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403292
C2×#168397672
C2×#168397352
#214542632
C2×#168395192
C2×#168395182
C2×C61×#4182
#1098761