Finite Group Databasebeta

← #29681778

Subgroups — #29681778

Order 15616.

1954 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840274C211yesmaximal, characteristic
2C2×#117×D61C211yesmaximal, characteristic, complemented
3C2×#16839780C211yesmaximal, characteristic, complemented
4C2×#16839778C211yesmaximal, characteristic, complemented
5C2×#16839725C211yesmaximal, characteristic, complemented
6#21446266C214yesmaximal, complemented
7#21446261C214yesmaximal, complemented
8#21445528C211yesmaximal, characteristic, complemented
9C61×#1733C211yesmaximal, characteristic, complemented
10C22×#11758222C2211yescharacteristic
11C23×C4×D61C2211yescharacteristic
12C22×#11758194C2211yescharacteristic
13#16840274—21no—
14#16840274—21no—
15#16840274—22no—
16#16840274C414yescomplemented
17#16840274C2212yes—
18#16840274C2212yes—
19C2×#14519761—21no—
20C2×#14519757C412yescomplemented
21C2×#14519752C412yescomplemented
22C2×#14519747—21no—
23C2×C4×D244—22no—
24C2×#14519736C2211yescharacteristic
25C2×#14519735—21no—
26C2×#14519734C2212yescomplemented
27C2×#14519733—21no—
28#117×D61—24no—
29#117×D61—24no—
30C2×C4⋊C4×D61—21no—
31C2×C22⋊C4×D61—21no—
32C2×C42×D61C2212yescomplemented
33#16839780—24no—
34#16839778—24no—
35C2×#14519705C2214yescomplemented
36C2×#14519703C2214yescomplemented
37#16839725—22no—
38#16839725C2212yescomplemented
39#16839725C2212yescomplemented
40C2×#14519689—22no—
41#16839521C2214yescomplemented
42C22×M16×C61C2211yescharacteristic
43C2×#117×C61C2211yescharacteristic
44C2×#117×C61C2211yescharacteristic
45C61×#339C2214yescomplemented
46C24×D61D411yescharacteristic
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—22no—
50C2×#11758222—22no—
51C2×#11758222—22no—
52C2×#11758222—22no—
53C2×#11758222C2×C412yescomplemented
54C2×#11758222C2312yes—
55C22×Dic122C2×C411yescharacteristic, complemented
56C22×D244—22no—
57C22×D244C2×C411yescharacteristic, complemented
58C22×C22⋊D61—21no—
59C23×Dic61D411yescharacteristic
60C22×C4×D61—22no—
61C22×C4×D61—22no—
62C22×C4×D61—22no—
63C22×C4×D61—22no—
64C22×C4×D61—22no—
65C22×C4×D61—21no—
66C22×C4×D61C2×C412yes—
67C22×C4×D61C2×C412yes—
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D412yes—
71C22×C4×D61D412yes—
72C22×C4×D61C2311yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C2×#11758194—21no—
75C2×#11758194—22no—
76C2×#11758194—22no—
77C2×#11758194C2312yes—
78C22×#92418—21no—
79#14519761—24no—
80#14519761—22no—
81#14519761—22no—
82#14519757—22no—
83#14519757—22no—
84#14519757C2×C414yes—
85#14519757C2×C414yescomplemented
86#14519752—22no—
87#14519752—22no—
88#14519752C2×C414yes—
89#14519752C2×C414yescomplemented
90#14519747—24no—
91#14519747—22no—
92#14519747—22no—
93C4×D244—24no—
94C4×D244—24no—
95C4×D244—24no—
96C4×D244—24no—
97#14519736—22no—
98#14519736D414yescomplemented
99#14519735—28no—
100#14519734—24no—
101#14519734—24no—
102#14519733—28no—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61—22no—
105C2×#11758196—22no—
106C4⋊C4×D61—28no—
107C2×C22⋊Dic61—21no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C22⋊C4×D61—28no—
112C2×C4×Dic61—22no—
113C2×C4×Dic61C2312yes—
114C42×D61—24no—
115C42×D61—24no—
116#14519705—28no—
117#14519703—28no—
118#14519689—24no—
119#14519689—24no—
120C23×C4×C61C2311yescharacteristic
121C2×M16×C61—21no—
122C2×M16×C61—22no—
123C2×M16×C61—22no—
124C2×M16×C61C2312yes—
125C22×C8×C61—21no—
126#117×C61—22no—
127#117×C61—21no—
128#117×C61—21no—
129#117×C61C2×C412yescomplemented
130#117×C61D414yescomplemented
131#117×C61C2312yes—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61C2×C412yescomplemented
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C42×C61—21no—
137C2×C42×C61C2312yes—
138C24×C61C2×D411yescharacteristic
139C23×D61—22no—
140C23×D61—22no—
141C23×D61—21no—
142C23×D61—44no—
143C23×D61C22⋊C412yes—
144C23×D61C22⋊C412yes—
145C23×D61C2×D411yescharacteristic
146C23×D61C2×D411yescharacteristic
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×D412yes—
155C22×C4×C61C2×D412yes—
156C22×C4×C61#4112yes—
157C22×C4×C61#4112yes—
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—42no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—21no—
166C22×Dic61—22no—
167C22×Dic61C22⋊C412yes—
168C22×Dic61C22⋊C412yes—
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171#11758222—24no—
172#11758222—24no—
173#11758222—22no—
174#11758222—22no—
175#11758222—22no—
176#11758222—22no—
177#11758222—42no—
178#11758222—42no—
179#11758222—42no—
180#11758222—42no—
181C2×D244—22no—
182C2×D244—22no—
183C2×D244—24no—
184C2×D244—24no—
185C2×D244—21no—
186C2×D244—48no—
187C2×D244C22×C412yes—
188C2×C4×D61—24no—
189C2×C4×D61—24no—
190C2×C4×D61—24no—
191C2×C4×D61—24no—
192C2×C4×D61—22no—
193C2×C4×D61—22no—
194C2×C4×D61—24no—
195C2×C4×D61—24no—
196C2×C4×D61—24no—
197C2×C4×D61—24no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—28no—
209C2×C4×D61—22no—
210C2×C4×D61—22no—
211C2×C4×D61—48no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C2×C4×D61C22⋊C412yes—
215C2×C4×D61C22⋊C412yes—
216C2×C4×D61C22⋊C412yes—
217C2×C4×D61C22⋊C412yes—
218C2×C4×D61C22×C412yes—
219C2×C4×D61C22×C412yes—
220C2×C4×D61C2×D412yes—
221C2×C4×D61C2×D412yes—
222C2×Dic122—22no—
223C2×Dic122—22no—
224C2×Dic122—21no—
225C2×Dic122C22×C412yes—
226M16×C61—22no—
227M16×C61—22no—
228M16×C61—42no—
229C2×C8×C61—22no—
230C2×C8×C61—42no—
231C4⋊C4×C61—22no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61C22×C414yes—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—24no—
236C22⋊C4×C61—22no—
237C42×C61—22no—
238C42×C61—22no—
239C42×C61—22no—
240C42×C61C2×D414yescomplemented
241C22⋊Dic61—24no—
242#11758198—28no—
243#11758198—24no—
244#11758198—24no—
245#11758198—24no—
246#11758198—24no—
247C4⋊Dic61—24no—
248C4⋊Dic61—24no—
249C4⋊Dic61—24no—
250#11758196—28no—
251C4×Dic61—28no—
252C4×Dic61—22no—
253C4×Dic61C2×D414yescomplemented
254#11758194—22no—
255#11758194—22no—
256#11758194—42no—
257C2×#92418—22no—
258C2×#92418—42no—
259C23×C61—42no—
260C23×C61C2×C22⋊C411yescharacteristic
261C23×C61C2×C22⋊C411yescharacteristic
262C23×C61#12012yes—
263C23×C61#12312yes—
264C23×C61C22×D411yescharacteristic
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—24no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—24no—
271C22×D61—24no—
272C22×D61—24no—
273C22×D61—24no—
274C22×D61—22no—
275C22×D61—42no—
276C22×D61—42no—
277C22×D61—42no—
278C22×D61—48no—
279C22×D61—48no—
280C22×D61—44no—
281C22×D61—42no—
282C22×D61C2×C22⋊C412yes—
283C22×D61C2×C22⋊C412yes—
284C2×C4×C61—24no—
285C2×C4×C61—24no—
286C2×C4×C61—44no—
287C2×C4×C61—44no—
288C2×C4×C61C2×C22⋊C411yescharacteristic
289C2×C4×C61C2×C22⋊C411yescharacteristic
290C2×C4×C61C4×D412yes—
291C2×C4×C61C4×D412yes—
292C2×C4×C61C4×D412yes—
293C2×C4×C61C4×D412yes—
294C2×C4×C61#12012yes—
295C2×C4×C61#12112yes—
296C2×C4×C61#12112yes—
297C2×C4×C61#12112yes—
298C2×C4×C61#12112yes—
299C2×C4×C61#12312yes—
300C2×C4×C61C23×C411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C22⋊D61—42no—
307C22⋊D61—42no—
308C22⋊D61—44no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—24no—
314C2×Dic61—24no—
315C2×Dic61—22no—
316C2×Dic61—24no—
317C2×Dic61—44no—
318C2×Dic61—42no—
319C2×Dic61C2×C22⋊C412yes—
320C2×Dic61C2×C22⋊C412yes—
321D244—22no—
322D244—22no—
323D244—48no—
324D244—48no—
325D244—42no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—24no—
335C4×D61—24no—
336C4×D61—24no—
337C4×D61—24no—
338C4×D61—416no—
339C4×D61—42no—
340C4×D61—42no—
341C4×D61—44no—
342Dic122—22no—
343Dic122—22no—
344Dic122—42no—
345C8×C61—42no—
346#92418—42no—
347#20979—611nomaximal, Sylow
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61#38612yes—
354C22×C61#38612yes—
355C22×C61C22×C22⋊C411yescharacteristic
356C22×C61C2×#12011yescharacteristic
357C22×C61C2×#12311yescharacteristic
358C2×D61—24no—
359C2×D61—24no—
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—48no—
366C2×D61—48no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—44no—
370C2×D61—42no—
371C2×D61—84no—
372C2×D61#42114yescomplemented
373C4×C61—44no—
374C4×C61—44no—
375C4×C61#38612yes—
376C4×C61#38612yes—
377C4×C61C2×C4×D411yescharacteristic
378C4×C61C2×C4×D411yescharacteristic
379C4×C61C2×#12111yescharacteristic
380C4×C61C2×#12111yescharacteristic
381Dic61—22no—
382Dic61—22no—
383Dic61—44no—
384Dic61—42no—
385C2×#525—611no—
386C22×#117—611no—
387C2×#421—611no—
388C2×#421—611no—
389C2×#407—611no—
390#1897—614no—
391#1896—614no—
392#1733—611no—
393#1733D6111yescharacteristic, complemented
394C2×C61—21no—
395C2×C61—21no—
396C2×C61—22no—
397C2×C61—22no—
398C2×C61C2×#38611yescharacteristic
399C2×C61C2×#42112yes—
400D61—24no—
401D61—42no—
402D61—82no—
403C22×#41—611no—
404C24×C4—611no—
405C22×M16—611no—
406C22×M16C2×D6111yescharacteristic
407#525—614no—
408#525—612no—
409#525—612no—
410#525—1221no—
411#525—1221no—
412#525—1222no—
413C2×#123—1221no—
414C2×C22⋊Q8—612no—
415C2×#121—612no—
416C2×#120—1221no—
417C2×C4×D4—1222no—
418C2×#117—611no—
419C2×#117—612no—
420C2×#117—1221no—
421C2×#117—1221no—
422C2×#117—1224no—
423C2×#117—1224no—
424C2×#117C2×D6111yescharacteristic
425C2×#117C2×D6111yescharacteristic
426C22×C4⋊C4—1221no—
427C22×C22⋊C4—1221no—
428C22×C42—612no—
429#421—1224no—
430#421—1224no—
431C2×#104—614no—
432C2×#104—614no—
433#407—612no—
434#407—612no—
435#407—1222no—
436C2×C22⋊C8—1222no—
437#339—614no—
438#339C2×D6114yescomplemented
439C61#2097911yescharacteristic, complemented, Sylow
440C25—611no—
441C2×#41—612no—
442C2×#41—612no—
443C2×#41—1221no—
444C2×#41—1221no—
445C2×#41—1222no—
446C2×#41—1222no—
447C2×#41—1222no—
448C2×#41—1222no—
449C22×Q8—611no—
450C22×D4—611no—
451C22×D4—1222no—
452C22×D4—1221no—
453C23×C4—611no—
454C23×C4—612no—
455C23×C4—612no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—612no—
459C23×C4—612no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—1222no—
463C23×C4—1222no—
464C23×C4—1222no—
465C23×C4—1222no—
466C23×C4—1222no—
467C23×C4—1221no—
468C23×C4C22×D6111yescharacteristic
469C2×M16—21no—
470C2×M16—22no—
471C2×M16—22no—
472C2×M16—612no—
473C2×M16—1221no—
474C2×M16—1222no—
475C2×M16—1222no—
476C2×M16C22×D6112yes—
477C22×C8—21no—
478C22×C8—1221no—
479#123—1222no—
480#123—1222no—
481#123—1224no—
482C22⋊Q8—614no—
483C22⋊Q8—614no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486#121—614no—
487#121—614no—
488#121—1222no—
489#121—1222no—
490#120—1222no—
491#120—1222no—
492#120—1224no—
493C4×D4—1224no—
494C4×D4—1224no—
495C4×D4—1224no—
496C4×D4—1224no—
497#117—22no—
498#117—21no—
499#117—21no—
500#117—614no—
501#117—1224no—
502#117—1228no—
503#117—1228no—
504#117—1222no—
505#117—1224no—
506#117C4×D6112yescomplemented
507#117D24414yescomplemented
508#117C22×D6112yes—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—1228no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1222no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4C4×D6112yescomplemented
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—1228no—
518C2×C22⋊C4—1222no—
519C2×C22⋊C4—1222no—
520C2×C22⋊C4—1222no—
521C2×C22⋊C4—1221no—
522C2×C42—21no—
523C2×C42—612no—
524C2×C42—1224no—
525C2×C42—1222no—
526C2×C42—1224no—
527C2×C42C22×D6112yes—
528#104—1228no—
529#104—1228no—
530C22⋊C8—1224no—
531C22⋊C8—1224no—
532C24—611no—
533C24—612no—
534C24—612no—
535C24—611no—
536C24—1222no—
537C24—1222no—
538C24—1221no—
539C24—2444no—
540C24D4×D6111yescharacteristic
541#41—1222no—
542#41—1222no—
543#41—1222no—
544#41—1222no—
545#41—1224no—
546#41—1224no—
547#41—2442no—
548#41—2442no—
549#41—2442no—
550#41—2442no—
551C2×Q8—612no—
552C2×Q8—1221no—
553C2×Q8—1222no—
554C2×Q8—1222no—
555C2×D4—612no—
556C2×D4—1224no—
557C2×D4—1224no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1221no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—2448no—
564C2×D4—2442no—
565C2×D4—2442no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—612no—
571C22×C4—612no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—612no—
575C22×C4—612no—
576C22×C4—612no—
577C22×C4—612no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—1228no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1224no—
592C22×C4—1224no—
593C22×C4—1224no—
594C22×C4—1224no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1224no—
598C22×C4—1224no—
599C22×C4—1224no—
600C22×C4—1224no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1221no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—2448no—
608C22×C4—2442no—
609C22×C4—2442no—
610C22×C4C2×C4×D6111yescharacteristic
611C22×C4C2×C4×D6111yescharacteristic
612C22×C4C2×D24412yes—
613C22×C4#1175822212yes—
614C22×C4D4×D6112yes—
615C22×C4D4×D6111yescharacteristic
616C22×C4D4×D6111yescharacteristic
617C22×C4D4×D6111yescharacteristic
618C22×C4#1175822612yes—
619C22×C4C23×D6111yescharacteristic
620M16—22no—
621M16—22no—
622M16—42no—
623M16—1222no—
624M16—1222no—
625M16—2442no—
626C2×C8—22no—
627C2×C8—42no—
628C2×C8—1222no—
629C2×C8—2442no—
630C4⋊C4—22no—
631C4⋊C4—24no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4—1228no—
635C4⋊C4—1224no—
636C4⋊C4C2×C4×D6114yes—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—24no—
640C22⋊C4—1224no—
641C22⋊C4—1224no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C22⋊C4—1228no—
645C22⋊C4—1224no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—614no—
650C42—1228no—
651C42—1222no—
652C42C2×D24414yescomplemented
653C23—42no—
654C23—612no—
655C23—612no—
656C23—1224no—
657C23—1224no—
658C23—1224no—
659C23—1221no—
660C23—1221no—
661C23—1221no—
662C23—1221no—
663C23—1224no—
664C23—1224no—
665C23—1222no—
666C23—2442no—
667C23—2442no—
668C23—2442no—
669C23—2444no—
670C23—2448no—
671C23—2448no—
672C23—2442no—
673C23C22⋊C4×D6111yescharacteristic
674C23C22⋊C4×D6111yescharacteristic
675C23#1451974712yes—
676C23#1451976212yes—
677C23C2×D4×D6111yescharacteristic
678Q8—1222no—
679Q8—1222no—
680Q8—2442no—
681D4—1222no—
682D4—1222no—
683D4—2448no—
684D4—2448no—
685D4—2442no—
686D4—2442no—
687D4—2444no—
688D4—2442no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1224no—
700C2×C4—1224no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1224no—
710C2×C4—1224no—
711C2×C4—1224no—
712C2×C4—1224no—
713C2×C4—1222no—
714C2×C4—1224no—
715C2×C4—24416no—
716C2×C4—2444no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2444no—
721C2×C4C22⋊C4×D6111yescharacteristic
722C2×C4C22⋊C4×D6111yescharacteristic
723C2×C4#1451973912yes—
724C2×C4#1451973912yes—
725C2×C4C4×D24412yes—
726C2×C4C4×D24412yes—
727C2×C4#1451974712yes—
728C2×C4#1451975012yes—
729C2×C4#1451975012yes—
730C2×C4#1451975212yes—
731C2×C4#1451975212yes—
732C2×C4#1451976212yes—
733C2×C4C22×C4×D6111yescharacteristic
734C2×C4C2×D4×D6111yescharacteristic
735C2×C4C2×D4×D6111yescharacteristic
736C2×C4C22×D24411yescharacteristic
737C2×C4C2×#1175822211yescharacteristic
738C2×C4C2×#1175822611yescharacteristic
739C8—42no—
740C8—2442no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—42no—
745C22—42no—
746C22—614no—
747C22—1224no—
748C22—1224no—
749C22—1222no—
750C22—1222no—
751C22—1222no—
752C22—1222no—
753C22—1222no—
754C22—4884no—
755C22—2448no—
756C22—2448no—
757C22—2442no—
758C22—2442no—
759C22—2444no—
760C22—2442no—
761C22#1683964012yes—
762C22#1683964012yes—
763C22C2×C22⋊C4×D6111yescharacteristic
764C22C2×#1451974711yescharacteristic
765C22C2×#1451976211yescharacteristic
766C4—44no—
767C4—44no—
768C4—1222no—
769C4—1222no—
770C4—2444no—
771C4—2442no—
772C4#1683964012yes—
773C4#1683964012yes—
774C4C2×#1451973911yescharacteristic
775C4C2×C4×D24411yescharacteristic
776C4C2×#1451975011yescharacteristic
777C4C2×#1451975211yescharacteristic
778C2—21no—
779C2—21no—
780C2—22no—
781C2—22no—
782C2—1224no—
783C2—4882no—
784C2—2442no—
785C2C2×#1683964011yescharacteristic
786C2#421×D6112yes—
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1733C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840274C2
cosocleC22×C4×C61C24
hypercenter#1733D61
hypocenterC61#20979
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
2. C2×#117×D61C2semidirect
3. C2×#16839780C2semidirect
4. C2×#16839778C2semidirect
5. C2×#16839725C2semidirect
6. #21446266C2semidirect
7. #21446261C2semidirect
8. #21445528C2semidirect
9. C61×#1733C2semidirect
16. #16840274C4semidirect
20. C2×#14519757C4semidirect
21. C2×#14519752C4semidirect
26. C2×#14519734C22semidirect
32. C2×C42×D61C22semidirect
35. C2×#14519705C22semidirect
36. C2×#14519703C22semidirect
38. #16839725C22semidirect
39. #16839725C22semidirect
41. #16839521C22semidirect
45. C61×#339C22semidirect
53. C2×#11758222C2×C4semidirect
55. C22×Dic122C2×C4semidirect
57. C22×D244C2×C4semidirect
85. #14519757C2×C4semidirect
89. #14519752C2×C4semidirect
98. #14519736D4semidirect
129. #117×C61C2×C4semidirect
130. #117×C61D4semidirect
133. C2×C4⋊C4×C61C2×C4semidirect
240. C42×C61C2×D4semidirect
253. C4×Dic61C2×D4semidirect
372. C2×D61#421semidirect
393. #1733D61semidirect
438. #339C2×D61semidirect
439. C61#20979semidirect
506. #117C4×D61semidirect
507. #117D244semidirect
514. C2×C4⋊C4C4×D61semidirect
652. C42C2×D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168402742
C2×#117×D612
C2×#168397802
C2×#168397782
C2×#168397252
#214462662
#214462612
#214455282
C61×#17332
#2097961