Finite Group Databasebeta

← #29682017

Subgroups — #29682017

Order 15616.

1732 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459152C211yesmaximal, characteristic
2#21459020C211yesmaximal, characteristic, complemented
3C2×#16839780C211yesmaximal, characteristic, complemented
4C2×#16839778C211yesmaximal, characteristic, complemented
5C2×#16839744C211yesmaximal, characteristic, complemented
6#21446355C214yesmaximal, complemented
7#21446350C214yesmaximal, complemented
8C2×#16839518C211yesmaximal, characteristic, complemented
9C2×C61×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
10C22×#11758222C2211yescharacteristic
11C22×#11758222C2211yescharacteristic
12C22×#11758194C2211yescharacteristic
13#16840343—22no—
14#16840338C412yescomplemented
15#16840338C2212yes—
16#16840331C412yescomplemented
17#16840331C2212yes—
18#16840324—22no—
19#16840312C414yescomplemented
20#16840274—22no—
21#16840274—22no—
22#16840243—22no—
23#16840242—22no—
24#16840239C2212yescomplemented
25#16840236C2212yescomplemented
26#16840235—22no—
27C4×#11758222—22no—
28#16840230—22no—
29C2×#14519736C2211yescharacteristic
30#117×D61—22no—
31#16839780—22no—
32#16839780C2214yes—
33#16839778—22no—
34#16839778C2214yes—
35C2×#14519705—22no—
36C2×#14519703—22no—
37#16839744—22no—
38#16839744—22no—
39C2×#14519695C2212yescomplemented
40C2×#14519693C2212yescomplemented
41#16839518C2214yescomplemented
42C22×M16×C61C2211yescharacteristic
43C2×#117×C61C2211yescharacteristic
44C2×#117×C61C2211yescharacteristic
45C61×H(3,ℤ/4)C2214yescomplemented
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×#11758222C2×C412yes—
66C2×#11758222C2×C412yescomplemented
67C2×#11758222D412yes—
68C2×#11758222D412yes—
69C2×#11758222C2312yes—
70C22×Dic122C2×C411yescharacteristic, complemented
71C22×Dic122C2311yescharacteristic
72C22×D244C2×C411yescharacteristic, complemented
73C22×D244C2311yescharacteristic
74C22×C22⋊D61—21no—
75C22×C22⋊D61D412yes—
76C22×C4×D61—21no—
77C22×C4×D61D412yes—
78C2×#11758194—21no—
79C2×#11758194—21no—
80C2×#11758194—21no—
81C2×#11758194—21no—
82C2×#11758194—21no—
83C2×#11758194C2312yes—
84C22×#92418—21no—
85#14519777C2×C414yescomplemented
86#14519774C2×C414yescomplemented
87#14519765C2×C414yescomplemented
88#14519765C2×C414yescomplemented
89#14519761—24no—
90#14519761—24no—
91#14519757—24no—
92#14519757—24no—
93#14519752—24no—
94#14519752—24no—
95#14519751—28no—
96#14519747—24no—
97#14519747—24no—
98C4×Dic122—24no—
99#14519742—24no—
100C4×D244—28no—
101C4×D244—24no—
102#14519739—24no—
103C4×C22⋊D61—28no—
104#14519737—28no—
105#14519736—21no—
106#14519736—21no—
107#14519736D412yescomplemented
108#14519736C2312yes—
109#14519735—24no—
110#14519734—24no—
111#14519733—24no—
112C2×C4⋊Dic61—21no—
113C4⋊C4×D61—24no—
114C2×C22⋊Dic61—21no—
115C22⋊C4×D61—24no—
116C2×C4×Dic61D412yescomplemented
117C42×D61—24no—
118#14519705—28no—
119#14519703—28no—
120#14519695—24no—
121#14519693—24no—
122C23×C4×C61C2311yescharacteristic
123C2×M16×C61—21no—
124C2×M16×C61—21no—
125C2×M16×C61—21no—
126C2×M16×C61—21no—
127C2×M16×C61—21no—
128C2×M16×C61C2312yes—
129C22×C8×C61—21no—
130#117×C61—21no—
131#117×C61—21no—
132#117×C61—21no—
133#117×C61—21no—
134#117×C61C2×C412yescomplemented
135#117×C61D412yescomplemented
136#117×C61C2312yes—
137#117×C61C2312yes—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C42×C61C2×C412yescomplemented
143C2×C42×C61D412yescomplemented
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146C23×D61C2×D412yes—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61#4111yescharacteristic
159C22×C4×C61#4111yescharacteristic
160C22×C4×C61#4111yescharacteristic
161C22×C4×C61#4111yescharacteristic
162C22×C4×C61C2411yescharacteristic
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—41no—
170C2×C22⋊D61—41no—
171C2×C22⋊D61—41no—
172C2×C22⋊D61—41no—
173C2×C22⋊D61C22⋊C414yes—
174C2×C22⋊D61C22⋊C414yes—
175C22×Dic61—21no—
176C22×Dic61—22no—
177C22×Dic61C2×D412yes—
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—22no—
192#11758222—22no—
193#11758222—22no—
194#11758222—22no—
195#11758222—22no—
196#11758222—22no—
197#11758222—22no—
198#11758222—22no—
199#11758222—22no—
200#11758222—22no—
201#11758222—22no—
202#11758222—41no—
203#11758222—41no—
204#11758222—41no—
205#11758222—41no—
206#11758222—41no—
207#11758222—41no—
208#11758222—41no—
209#11758222—41no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—28no—
220C2×D244C22×C412yes—
221C2×D244C22×C412yes—
222C2×D244C2×D412yes—
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—28no—
230C2×C4×D61—41no—
231C2×C4×D61—41no—
232C2×C4×D61—41no—
233C2×C4×D61—41no—
234C2×C4×D61C22⋊C414yes—
235C2×C4×D61C22⋊C414yes—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122C22×C412yes—
246C2×Dic122C22×C412yes—
247C2×Dic122C2×D412yes—
248M16×C61—22no—
249M16×C61—22no—
250M16×C61—41no—
251M16×C61—41no—
252C2×C8×C61—22no—
253C2×C8×C61—41no—
254C2×C8×C61—41no—
255C4⋊C4×C61—22no—
256C4⋊C4×C61—22no—
257C4⋊C4×C61—22no—
258C4⋊C4×C61—22no—
259C22⋊C4×C61—22no—
260C22⋊C4×C61—22no—
261C22⋊C4×C61—22no—
262C22⋊C4×C61—22no—
263C42×C61—22no—
264C42×C61—22no—
265C42×C61C22×C414yes—
266C42×C61C2×D414yes—
267C22⋊Dic61—22no—
268C22⋊Dic61—22no—
269#11758198—28no—
270#11758198—28no—
271#11758198—28no—
272C4⋊Dic61—22no—
273C4⋊Dic61—22no—
274C4⋊Dic61—28no—
275#11758196—28no—
276C4×Dic61—28no—
277C4×Dic61—22no—
278C4×Dic61C2×D414yes—
279#11758194—22no—
280#11758194—22no—
281#11758194—41no—
282#11758194—41no—
283C2×#92418—22no—
284C2×#92418—41no—
285C2×#92418—41no—
286C23×C61—81no—
287C23×C61C2×C22⋊C411yescharacteristic
288C23×C61C2×C22⋊C411yescharacteristic
289C23×C61#12011yescharacteristic
290C23×C61#12011yescharacteristic
291C23×C61#12311yescharacteristic
292C23×C61#12311yescharacteristic
293C23×C61C22×D411yescharacteristic
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—82no—
300C22×D61—82no—
301C22×D61C2×C22⋊C414yes—
302C2×C4×C61—24no—
303C2×C4×C61—24no—
304C2×C4×C61—82no—
305C2×C4×C61—82no—
306C2×C4×C61C2×C22⋊C411yescharacteristic
307C2×C4×C61C2×C22⋊C411yescharacteristic
308C2×C4×C61C4×D411yescharacteristic
309C2×C4×C61C4×D411yescharacteristic
310C2×C4×C61C4×D411yescharacteristic
311C2×C4×C61C4×D411yescharacteristic
312C2×C4×C61C4×D411yescharacteristic
313C2×C4×C61C4×D411yescharacteristic
314C2×C4×C61C4×D411yescharacteristic
315C2×C4×C61C4×D411yescharacteristic
316C2×C4×C61#12011yescharacteristic
317C2×C4×C61#12011yescharacteristic
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#12111yescharacteristic
325C2×C4×C61#12111yescharacteristic
326C2×C4×C61#12311yescharacteristic
327C2×C4×C61#12311yescharacteristic
328C2×C4×C61C23×C411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C2×#4111yescharacteristic
333C2×C4×C61C2×#4111yescharacteristic
334C22⋊D61—24no—
335C22⋊D61—24no—
336C22⋊D61—24no—
337C22⋊D61—24no—
338C22⋊D61—42no—
339C22⋊D61—42no—
340C22⋊D61—42no—
341C22⋊D61—42no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—24no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—82no—
349C2×Dic61C2×C22⋊C414yes—
350D244—22no—
351D244—22no—
352D244—22no—
353D244—22no—
354D244—22no—
355D244—22no—
356D244—41no—
357D244—41no—
358D244—88no—
359C4×D61—24no—
360C4×D61—24no—
361C4×D61—24no—
362C4×D61—24no—
363C4×D61—42no—
364C4×D61—42no—
365C4×D61—42no—
366C4×D61—42no—
367C4×D61—88no—
368Dic122—22no—
369Dic122—22no—
370Dic122—22no—
371Dic122—22no—
372Dic122—22no—
373Dic122—22no—
374Dic122—41no—
375Dic122—41no—
376C8×C61—42no—
377#92418—42no—
378#21012—611nomaximal, Sylow
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61#38611yescharacteristic
387C22×C61#38611yescharacteristic
388C22×C61#38611yescharacteristic
389C22×C61#38611yescharacteristic
390C22×C61C22×C22⋊C411yescharacteristic
391C22×C61C2×#12011yescharacteristic
392C22×C61C2×#12311yescharacteristic
393C2×D61—24no—
394C2×D61—44no—
395C2×D61—44no—
396C2×D61—44no—
397C2×D61—42no—
398C2×D61—82no—
399C2×D61—82no—
400C2×D61—82no—
401C4×C61—44no—
402C4×C61—44no—
403C4×C61#38611yescharacteristic
404C4×C61#38611yescharacteristic
405C4×C61#38611yescharacteristic
406C4×C61#38611yescharacteristic
407C4×C61C2×C4×D411yescharacteristic
408C4×C61C2×C4×D411yescharacteristic
409C4×C61C2×#12111yescharacteristic
410C4×C61C2×#12111yescharacteristic
411Dic61—24no—
412Dic61—44no—
413Dic61—42no—
414#3449—611no—
415#3428—611no—
416C2×#421—611no—
417C2×#421—611no—
418C2×#413—611no—
419#1912—614no—
420#1911—614no—
421C2×H(3,ℤ/4)—611no—
422C2×H(3,ℤ/4)D6111yescharacteristic, complemented
423C2×C61—21no—
424C2×C61—21no—
425C2×C61—21no—
426C2×C61—21no—
427C2×C61—21no—
428C2×C61—21no—
429C2×C61—21no—
430C2×C61C2×#38611yescharacteristic
431D61—44no—
432D61—82no—
433C22×#41—611no—
434C22×#41—611no—
435C22×M16—611no—
436C22×M16C2×D6111yescharacteristic
437#537—1222no—
438#536—612no—
439#536—612no—
440#535—612no—
441#535—612no—
442#534—1222no—
443#532—614no—
444#525—1222no—
445#525—1222no—
446#520—1222no—
447#520—1222no—
448#519—612no—
449#518—612no—
450#518—1222no—
451C4×#41—1222no—
452C4×#41—1222no—
453C2×#117—611no—
454C2×#117—1222no—
455C2×#117C2×D6111yescharacteristic
456C2×#117C2×D6111yescharacteristic
457#421—614no—
458#421—614no—
459#421—1222no—
460#421—1222no—
461C2×#104—1222no—
462C2×#104—1222no—
463#413—1222no—
464#413—1222no—
465C2×#101—612no—
466C2×#100—612no—
467H(3,ℤ/4)—614no—
468H(3,ℤ/4)C2×D6114yescomplemented
469C61#2101211yescharacteristic, complemented, Sylow
470C2×#41—612no—
471C2×#41—612no—
472C2×#41—612no—
473C2×#41—612no—
474C2×#41—612no—
475C2×#41—612no—
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—
487C2×#41—1221no—
488C2×#41—1221no—
489C2×#41—1221no—
490C2×#41—1221no—
491C2×#41—1221no—
492C2×#41—1221no—
493C2×#41—1221no—
494C22×Q8—611no—
495C22×Q8—611no—
496C22×D4—612no—
497C22×D4—611no—
498C22×D4—611no—
499C22×D4—1221no—
500C23×C4—612no—
501C23×C4—1221no—
502C23×C4C22×D6111yescharacteristic
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—612no—
509C2×M16—1221no—
510C2×M16—1221no—
511C2×M16—1221no—
512C2×M16—1221no—
513C2×M16—1221no—
514C2×M16C22×D6112yes—
515C22×C8—21no—
516C22×C8—1221no—
517C4⋊Q8—614no—
518#127—614no—
519#124—614no—
520#124—614no—
521#123—1224no—
522#123—1224no—
523C22⋊Q8—1224no—
524C22⋊Q8—1224no—
525#121—1224no—
526#121—1224no—
527#121—1228no—
528#120—1224no—
529#120—1224no—
530C4×Q8—1224no—
531C4×Q8—1224no—
532C4×D4—1228no—
533C4×D4—1224no—
534C4×D4—1228no—
535C4×D4—1228no—
536C4×D4—1224no—
537#117—21no—
538#117—21no—
539#117—21no—
540#117—21no—
541#117—612no—
542#117—612no—
543#117—1224no—
544#117—1224no—
545#117—1224no—
546#117—1221no—
547#117—1221no—
548#117C4×D6112yescomplemented
549#117D24412yescomplemented
550#117C22×D6112yes—
551#117C22×D6112yes—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—1224no—
555C2×C4⋊C4—1221no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—1224no—
559C2×C22⋊C4—1221no—
560C2×C42—612no—
561C2×C42—1224no—
562C2×C42C4×D6112yescomplemented
563C2×C42D24412yescomplemented
564#104—1228no—
565#104—1228no—
566#101—1224no—
567#100—1224no—
568C24—612no—
569C24—1221no—
570C24D4×D6111yescharacteristic
571#41—1222no—
572#41—1222no—
573#41—1222no—
574#41—1222no—
575#41—1222no—
576#41—1222no—
577#41—1222no—
578#41—1222no—
579#41—1222no—
580#41—1222no—
581#41—1222no—
582#41—1222no—
583#41—1222no—
584#41—1222no—
585#41—1222no—
586#41—1222no—
587#41—1222no—
588#41—1222no—
589#41—1222no—
590#41—1222no—
591#41—1222no—
592#41—1222no—
593#41—1222no—
594#41—1222no—
595#41—2441no—
596#41—2441no—
597#41—2441no—
598#41—2441no—
599#41—2441no—
600#41—2441no—
601#41—2441no—
602#41—2441no—
603C2×Q8—612no—
604C2×Q8—612no—
605C2×Q8—612no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1221no—
612C2×Q8—1221no—
613C2×Q8—1221no—
614C2×Q8—1221no—
615C2×D4—614no—
616C2×D4—614no—
617C2×D4—612no—
618C2×D4—612no—
619C2×D4—612no—
620C2×D4—1228no—
621C2×D4—1222no—
622C2×D4—1222no—
623C2×D4—1222no—
624C2×D4—1222no—
625C2×D4—1222no—
626C2×D4—1222no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—2441no—
637C2×D4—2441no—
638C2×D4—2441no—
639C2×D4—2441no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—612no—
643C22×C4—614no—
644C22×C4—614no—
645C22×C4—1228no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1221no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—2441no—
655C22×C4—2441no—
656C22×C4—2441no—
657C22×C4—2441no—
658C22×C4C2×C4×D6111yescharacteristic
659C22×C4C2×C4×D6111yescharacteristic
660C22×C4C2×D24411yescharacteristic
661C22×C4C2×D24411yescharacteristic
662C22×C4#1175822211yescharacteristic
663C22×C4#1175822211yescharacteristic
664C22×C4D4×D6111yescharacteristic
665C22×C4D4×D6111yescharacteristic
666C22×C4D4×D6111yescharacteristic
667C22×C4D4×D6111yescharacteristic
668C22×C4D4×D6111yescharacteristic
669C22×C4#1175822611yescharacteristic
670C22×C4#1175822611yescharacteristic
671C22×C4C23×D6111yescharacteristic
672M16—22no—
673M16—22no—
674M16—41no—
675M16—41no—
676M16—1222no—
677M16—1222no—
678M16—2441no—
679M16—2441no—
680C2×C8—22no—
681C2×C8—41no—
682C2×C8—41no—
683C2×C8—1222no—
684C2×C8—2441no—
685C2×C8—2441no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—1228no—
691C4⋊C4—1228no—
692C4⋊C4—1222no—
693C4⋊C4—1222no—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—1228no—
699C22⋊C4—1228no—
700C22⋊C4—1228no—
701C22⋊C4—1222no—
702C22⋊C4—1222no—
703C42—22no—
704C42—22no—
705C42—614no—
706C42—1228no—
707C42—1222no—
708C42C2×C4×D6114yes—
709C42C2×D24414yes—
710C23—81no—
711C23—614no—
712C23—1222no—
713C23—1222no—
714C23—1222no—
715C23—4882no—
716C23—4882no—
717C23—2441no—
718C23—2441no—
719C23C22⋊C4×D6111yescharacteristic
720C23C22⋊C4×D6111yescharacteristic
721C23#1451974711yescharacteristic
722C23#1451974711yescharacteristic
723C23#1451976211yescharacteristic
724C23#1451976211yescharacteristic
725C23C2×D4×D6111yescharacteristic
726Q8—1222no—
727Q8—1222no—
728Q8—1222no—
729Q8—1222no—
730Q8—1222no—
731Q8—1222no—
732Q8—2441no—
733Q8—2441no—
734D4—1224no—
735D4—1224no—
736D4—1224no—
737D4—1224no—
738D4—1222no—
739D4—1222no—
740D4—1222no—
741D4—1222no—
742D4—1222no—
743D4—1222no—
744D4—4888no—
745D4—2442no—
746D4—2442no—
747D4—2442no—
748D4—2442no—
749D4—2441no—
750D4—2441no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—82no—
754C2×C4—82no—
755C2×C4—614no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1224no—
759C2×C4—1224no—
760C2×C4—1224no—
761C2×C4—1224no—
762C2×C4—1222no—
763C2×C4—1224no—
764C2×C4—4888no—
765C2×C4—4882no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2442no—
769C2×C4—2442no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4C22⋊C4×D6111yescharacteristic
773C2×C4C22⋊C4×D6111yescharacteristic
774C2×C4#1451973911yescharacteristic
775C2×C4#1451973911yescharacteristic
776C2×C4#1451973911yescharacteristic
777C2×C4#1451973911yescharacteristic
778C2×C4C4×D24411yescharacteristic
779C2×C4C4×D24411yescharacteristic
780C2×C4C4×D24411yescharacteristic
781C2×C4C4×D24411yescharacteristic
782C2×C4#1451974711yescharacteristic
783C2×C4#1451974711yescharacteristic
784C2×C4#1451975011yescharacteristic
785C2×C4#1451975011yescharacteristic
786C2×C4#1451975011yescharacteristic
787C2×C4#1451975011yescharacteristic
788C2×C4#1451975211yescharacteristic
789C2×C4#1451975211yescharacteristic
790C2×C4#1451975211yescharacteristic
791C2×C4#1451975211yescharacteristic
792C2×C4#1451976211yescharacteristic
793C2×C4#1451976211yescharacteristic
794C2×C4C22×C4×D6111yescharacteristic
795C2×C4C2×D4×D6111yescharacteristic
796C2×C4C2×D4×D6111yescharacteristic
797C2×C4C22×D24411yescharacteristic
798C2×C4C2×#1175822211yescharacteristic
799C2×C4C2×#1175822611yescharacteristic
800C8—42no—
801C8—2442no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—1224no—
810C22—4882no—
811C22—4882no—
812C22—4882no—
813C22—2444no—
814C22—2444no—
815C22—2444no—
816C22—2442no—
817C22#1683964011yescharacteristic
818C22#1683964011yescharacteristic
819C22#1683964011yescharacteristic
820C22#1683964011yescharacteristic
821C22C2×C22⋊C4×D6111yescharacteristic
822C22C2×#1451974711yescharacteristic
823C22C2×#1451976211yescharacteristic
824C4—44no—
825C4—44no—
826C4—1224no—
827C4—2444no—
828C4—2442no—
829C4#1683964011yescharacteristic
830C4#1683964011yescharacteristic
831C4#1683964011yescharacteristic
832C4#1683964011yescharacteristic
833C4C2×#1451973911yescharacteristic
834C4C2×C4×D24411yescharacteristic
835C4C2×#1451975011yescharacteristic
836C4C2×#1451975211yescharacteristic
837C2—21no—
838C2—21no—
839C2—21no—
840C2—21no—
841C2—21no—
842C2—21no—
843C2—21no—
844C2—4882no—
845C2—2444no—
846C2C2×#1683964011yescharacteristic
subgroupG/H
centerC4#16839640
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×H(3,ℤ/4)C2
socleC2×C61C2×#386
prime radical#21459152C2
cosocleC22×C4×C61C24
hypercenterC2×H(3,ℤ/4)D61
hypocenterC61#21012
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. #21459020C2semidirect
3. C2×#16839780C2semidirect
4. C2×#16839778C2semidirect
5. C2×#16839744C2semidirect
6. #21446355C2semidirect
7. #21446350C2semidirect
8. C2×#16839518C2semidirect
9. C2×C61×H(3,ℤ/4)C2semidirect
14. #16840338C4semidirect
16. #16840331C4semidirect
19. #16840312C4semidirect
24. #16840239C22semidirect
25. #16840236C22semidirect
39. C2×#14519695C22semidirect
40. C2×#14519693C22semidirect
41. #16839518C22semidirect
45. C61×H(3,ℤ/4)C22semidirect
66. C2×#11758222C2×C4semidirect
70. C22×Dic122C2×C4semidirect
72. C22×D244C2×C4semidirect
85. #14519777C2×C4semidirect
86. #14519774C2×C4semidirect
87. #14519765C2×C4semidirect
88. #14519765C2×C4semidirect
107. #14519736D4semidirect
116. C2×C4×Dic61D4semidirect
134. #117×C61C2×C4semidirect
135. #117×C61D4semidirect
142. C2×C42×C61C2×C4semidirect
143. C2×C42×C61D4semidirect
422. C2×H(3,ℤ/4)D61semidirect
468. H(3,ℤ/4)C2×D61semidirect
469. C61#21012semidirect
548. #117C4×D61semidirect
549. #117D244semidirect
562. C2×C42C4×D61semidirect
563. C2×C42D244semidirect

Maximal subgroups

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

subgroupindex
#214591522
#214590202
C2×#168397802
C2×#168397782
C2×#168397442
#214463552
#214463502
C2×#168395182
C2×C61×H(3,ℤ/4)2
#2101261