Finite Group Databasebeta

← #29646233

Subgroups — #29646233

Order 15616.

1290 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840413C211yesmaximal, characteristic
2#21454265C212yesmaximal, complemented
3#21444181C212yesmaximal, complemented
4#21444166C212yesmaximal, complemented
5#21444165C212yesmaximal, complemented
6#21444156C211yesmaximal, characteristic, complemented
7#21444149C211yesmaximal, characteristic, complemented
8#21444147C211yesmaximal, characteristic, complemented
9#21444136C211yesmaximal, characteristic, complemented
10#324×D61C211yesmaximal, characteristic, complemented
11C2×C61×#324C211yesmaximal, characteristic, complemented
12C22×#11758222C411yescharacteristic
13C22×#11758222C2211yescharacteristic
14C2×#14519783—22no—
15#16840413—22no—
16#16840413—22no—
17#16840413—22no—
18#16840413—22no—
19C2×#14519776C411yescharacteristic
20C2×#14519762C411yescharacteristic
21C2×#14519762C2211yescharacteristic
22C2×#14519760C411yescharacteristic
23C2×#14519760C2211yescharacteristic
24C2×#14519755C411yescharacteristic
25C2×#14519755C2211yescharacteristic
26C2×#14519752C411yescharacteristic
27C2×#14519751C411yescharacteristic
28C2×#14519739C2211yescharacteristic
29C2×C4×C22⋊D61C411yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31#16839728—22no—
32#16839727—22no—
33#16839727—22no—
34#16839726C2212yes—
35#16839724C2212yes—
36#16839724C2212yes—
37C22⋊C8×D61C2212yes—
38C22⋊C8×D61C2212yes—
39#16839488C2211yescharacteristic
40#16839488C2211yescharacteristic
41#16839488C2212yes—
42#16839487C2212yes—
43#16839487C2212yes—
44#16839485C2212yes—
45#16839485C2212yes—
46C22×C4⋊C4×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2212yes—
48C61×#324C2211yescharacteristic
49C61×#324C2211yescharacteristic
50C61×#324C2212yes—
51C2×#11758222—21no—
52C2×#11758222—21no—
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—44no—
56C2×#11758222—44no—
57C2×#11758222D412yes—
58C2×#11758222D412yes—
59C2×#11758222D412yes—
60C2×#11758222D412yes—
61C22×Dic122C2×C411yescharacteristic
62C22×Dic122C2×C411yescharacteristic
63C22×D244C2×C411yescharacteristic
64C22×D244C2×C411yescharacteristic
65C22×D244C2×C411yescharacteristic
66C22×C22⋊D61C2×C411yescharacteristic
67C22×C22⋊D61C2×C411yescharacteristic
68C22×C22⋊D61C2×C411yescharacteristic
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61C2×C411yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C22×C4×D61C2311yescharacteristic
74#14519783—48no—
75C2×#11758194—22no—
76C2×#11758189—22no—
77C2×#11758189—22no—
78C2×C8×D61—22no—
79C2×C8×D61—22no—
80#14519776—22no—
81#14519776—22no—
82#14519762—22no—
83#14519762—22no—
84#14519762—22no—
85#14519762—22no—
86#14519760—22no—
87#14519760—22no—
88#14519760—22no—
89#14519760—22no—
90#14519755—22no—
91#14519755—22no—
92#14519755—22no—
93#14519755—22no—
94#14519752—22no—
95#14519752—22no—
96#14519751—22no—
97#14519751—22no—
98#14519739—22no—
99#14519739—22no—
100C4×C22⋊D61—21no—
101C4×C22⋊D61—21no—
102C4×C22⋊D61—21no—
103C4×C22⋊D61—21no—
104C2×C4⋊Dic61C2×C411yescharacteristic
105C2×#11758196C2×C411yescharacteristic
106C2×#11758196C2×C411yescharacteristic
107C2×#11758196C2×C411yescharacteristic
108C2×#11758196C2×C411yescharacteristic
109C2×#11758196C2311yescharacteristic
110C4⋊C4×D61—22no—
111C4⋊C4×D61—22no—
112C2×C22⋊Dic61C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×#11758198C2×C411yescharacteristic
118C2×#11758198C2×C411yescharacteristic
119C2×#11758198C2311yescharacteristic
120C2×C4×Dic61C2×C411yescharacteristic
121C22⋊#92418—22no—
122C22⋊#92418C2312yes—
123C22⋊#92418C2312yes—
124#14519689—22no—
125#14519689—22no—
126#14519689—22no—
127#14519689—22no—
128C23×C4×C61C2×C411yescharacteristic
129C23×C4×C61C2×C411yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C22×C8×C61—22no—
132C2×C4⋊C4×C61—22no—
133C2×C4⋊C4×C61—22no—
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C4⋊C4×C61C2×C411yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C22⋊C8×C61—22no—
139C22⋊C8×C61C2312yes—
140C22⋊C8×C61C2312yes—
141C24×C61C22×C411yescharacteristic
142C23×D61C22×C411yescharacteristic
143C23×D61C22×C411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—22no—
150C22×C4×C61—42no—
151C22×C4×C61—41no—
152C22×C4×C61—42no—
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C2×D412yes—
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—24no—
162C2×C22⋊D61—21no—
163C2×C22⋊D61—21no—
164C2×C22⋊D61—42no—
165C2×C22⋊D61—42no—
166C2×C22⋊D61C22⋊C411yescharacteristic
167C2×C22⋊D61C22⋊C411yescharacteristic
168C2×C22⋊D61C22⋊C411yescharacteristic
169C2×C22⋊D61C22⋊C412yes—
170C2×C22⋊D61C22⋊C412yes—
171C2×C22⋊D61C22⋊C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177#11758222—28no—
178#11758222—44no—
179#11758222—44no—
180#11758222—44no—
181#11758222—44no—
182#11758222—44no—
183#11758222—44no—
184#11758222—44no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—42no—
190C2×D244—41no—
191C2×D244—42no—
192C2×D244C22⋊C412yes—
193C2×D244C22⋊C412yes—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—22no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—41no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61C2×D412yes—
207C2×C4×D61C2×D412yes—
208C2×C4×D61C2×D412yes—
209C2×C4×D61C2×D412yes—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—42no—
213C2×Dic122—42no—
214C2×Dic122C22⋊C412yes—
215C2×Dic122C22⋊C412yes—
216C2×C8×C61—22no—
217C2×C8×C61—22no—
218C2×C8×C61—44no—
219C4⋊C4×C61—22no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—22no—
223C22⋊Dic61—21no—
224C22⋊Dic61—21no—
225#11758198—21no—
226#11758198—21no—
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232#11758198—22no—
233C4⋊Dic61—22no—
234#11758196—22no—
235#11758196—22no—
236#11758196—22no—
237#11758196—21no—
238#11758196—21no—
239#11758196—22no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242#11758194—44no—
243C2×#92418—22no—
244C2×#92418—22no—
245#11758189—44no—
246#11758189—44no—
247C8×D61—44no—
248C8×D61—44no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—22no—
252C23×C61—41no—
253C23×C61C2×C22⋊C411yescharacteristic
254C23×C61C2×C22⋊C411yescharacteristic
255C23×C61C23×C411yescharacteristic
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—22no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61C2×C22⋊C412yes—
270C22×D61C2×C22⋊C411yescharacteristic
271C22×D61C2×C22⋊C411yescharacteristic
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—24no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61C2×C22⋊C412yes—
290C2×C4×C61#13112yescomplemented
291C2×C4×C61C22×D412yes—
292C22⋊D61—24no—
293C22⋊D61—22no—
294C22⋊D61—22no—
295C22⋊D61—22no—
296C22⋊D61—42no—
297C22⋊D61—42no—
298C22⋊D61—42no—
299C22⋊D61#9914yes—
300C2×Dic61—22no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61C2×C22⋊C411yescharacteristic
310C2×Dic61C2×C22⋊C412yes—
311C2×Dic61C2×C22⋊C411yescharacteristic
312D244—24no—
313D244—42no—
314D244—44no—
315D244—42no—
316D244—42no—
317C4×D61—24no—
318C4×D61—24no—
319C4×D61—42no—
320C4×D61—42no—
321C4×D61—42no—
322C4×D61—42no—
323C4×D61—42no—
324C4×D61—42no—
325C4×D61—42no—
326C4×D61—42no—
327Dic122—24no—
328Dic122—42no—
329Dic122—42no—
330Dic122—42no—
331C8×C61—42no—
332C8×C61—42no—
333#92418—42no—
334#92418—42no—
335#17416—611nomaximal, Sylow
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—21no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61C2×#9912yes—
346C22×C61C22×C22⋊C411yescharacteristic
347C22×C61C2×#13111yescharacteristic
348C22×C61#56811yescharacteristic
349C2×D61—21no—
350C2×D61—21no—
351C2×D61—21no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—21no—
355C2×D61—21no—
356C2×D61—22no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—41no—
360C2×D61—41no—
361C2×D61—41no—
362C2×D61—81no—
363C2×D61—81no—
364C2×D61—81no—
365C2×D61—81no—
366C2×D61C2×#9912yes—
367C4×C61—22no—
368C4×C61—22no—
369C4×C61—22no—
370C4×C61—41no—
371C4×C61—41no—
372C4×C61—41no—
373Dic61—22no—
374Dic61—21no—
375Dic61—41no—
376Dic61—41no—
377Dic61—41no—
378Dic61C2×#9912yes—
379C2×#547—611no—
380#2880—612no—
381#1472—612no—
382#1468—612no—
383#1468—612no—
384#1465—611no—
385#1463—611no—
386#1463—611no—
387#1459—611no—
388C2×#324—611no—
389C2×#324D6111yescharacteristic, complemented
390C2×C61—21no—
391C2×C61—21no—
392C2×C61—22no—
393C2×C61—41no—
394C2×C61#288011yescharacteristic
395C2×C61C22×#9911yescharacteristic
396C2×C61#288911yescharacteristic
397D61—22no—
398D61—41no—
399D61—42no—
400D61—81no—
401C22×#41—611no—
402C22×#41—611no—
403C2×#131—1222no—
404#547—1222no—
405#547—1222no—
406#547—1222no—
407#547—1222no—
408C2×C4⋊Q8—611no—
409C2×#123—611no—
410C2×#123—611no—
411C2×#123—611no—
412C2×#123—611no—
413C2×C22⋊Q8—611no—
414C2×C22⋊Q8—611no—
415C2×#121—611no—
416C2×#121—611no—
417C2×C4×D4—611no—
418C2×C4×D4—611no—
419C22×C4⋊C4—611no—
420C22×C4⋊C4C2×D6111yescharacteristic
421#408—1222no—
422#408—1222no—
423#408—1222no—
424#407—612no—
425#407—612no—
426#407—612no—
427C2×C22⋊C8—612no—
428C2×C22⋊C8—612no—
429C2×C22⋊C8C2×D6112yes—
430#324—611no—
431#324—611no—
432#324—612no—
433#324—612no—
434#324—612no—
435#324C2×D6111yescharacteristic
436#324C2×D6111yescharacteristic
437#324C2×D6112yes—
438#323—612no—
439#323—612no—
440C61#1741611yescharacteristic, complemented, Sylow
441C2×#41—612no—
442C2×#41—612no—
443C2×#41—612no—
444C2×#41—612no—
445C2×#41—1221no—
446C2×#41—1221no—
447C2×#41—1221no—
448C2×#41—1221no—
449C2×#41—2444no—
450C2×#41—2444no—
451C22×Q8—611no—
452C22×Q8—611no—
453C22×D4—611no—
454C22×D4—611no—
455C22×D4—611no—
456C22×D4—611no—
457C22×D4—611no—
458C22×D4—611no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4C4×D6111yescharacteristic
465C23×C4C4×D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467#131—2448no—
468C2×M16—1222no—
469C2×M16—1222no—
470C2×M16—1222no—
471C22×C8—22no—
472C22×C8—1222no—
473C22×C8—1222no—
474C4⋊Q8—1222no—
475C4⋊Q8—1222no—
476#123—1222no—
477#123—1222no—
478#123—1222no—
479#123—1222no—
480#123—1222no—
481#123—1222no—
482#123—1222no—
483#123—1222no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488#121—1222no—
489#121—1222no—
490#121—1222no—
491#121—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494C4×D4—1221no—
495C4×D4—1221no—
496C4×D4—1221no—
497C4×D4—1221no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—1222no—
507C2×C4⋊C4—1222no—
508C2×C4⋊C4C4×D6111yescharacteristic
509C2×C4⋊C4C4×D6111yescharacteristic
510C2×C4⋊C4C22×D6111yescharacteristic
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C22⋊C4—611no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4—611no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—611no—
519C2×C22⋊C4—611no—
520C2×C42—611no—
521C22⋊C8—22no—
522C22⋊C8—612no—
523C22⋊C8—612no—
524C22⋊C8—1222no—
525C22⋊C8—1222no—
526C22⋊C8—1222no—
527C22⋊C8—1222no—
528C22⋊C8—1222no—
529C22⋊C8C22×D6112yes—
530C22⋊C8C22×D6112yes—
531C24—611no—
532C24—611no—
533C24—611no—
534C24C2×C4×D6111yescharacteristic
535#41—1228no—
536#41—2444no—
537#41—2444no—
538#41—2444no—
539#41—2444no—
540#41—2444no—
541#41—2444no—
542#41—2444no—
543C2×Q8—612no—
544C2×Q8—612no—
545C2×Q8—1221no—
546C2×Q8—1221no—
547C2×Q8—2442no—
548C2×Q8—2442no—
549C2×D4—611no—
550C2×D4—611no—
551C2×D4—611no—
552C2×D4—611no—
553C2×D4—612no—
554C2×D4—612no—
555C2×D4—612no—
556C2×D4—612no—
557C2×D4—1222no—
558C2×D4—1221no—
559C2×D4—1221no—
560C2×D4—1224no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—1222no—
564C2×D4—2441no—
565C2×D4—2442no—
566C2×D4—2442no—
567C2×D4—2442no—
568C2×D4—2442no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—41no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—612no—
580C22×C4—612no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1222no—
593C22×C4—2441no—
594C22×C4—2442no—
595C22×C4—2442no—
596C22×C4—2442no—
597C22×C4—2442no—
598C22×C4C2×C4×D6111yescharacteristic
599C22×C4C2×C4×D6111yescharacteristic
600C22×C4C2×C4×D6111yescharacteristic
601C22×C4C2×C4×D6111yescharacteristic
602C22×C4C2×C4×D6111yescharacteristic
603C22×C4D4×D6112yes—
604C22×C4D4×D6112yes—
605C22×C4C23×D6111yescharacteristic
606M16—2444no—
607M16—2444no—
608M16—2444no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—44no—
612C2×C8—1222no—
613C2×C8—1222no—
614C2×C8—2444no—
615C2×C8—2444no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—1222no—
621C4⋊C4—1222no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1222no—
625C4⋊C4—1222no—
626C4⋊C4—1222no—
627C22⋊C4—1222no—
628C22⋊C4—1221no—
629C22⋊C4—1221no—
630C22⋊C4—1222no—
631C22⋊C4—1222no—
632C22⋊C4—1222no—
633C22⋊C4—1221no—
634C22⋊C4—1221no—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C42—1221no—
638C42—1221no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—41no—
643C23—611no—
644C23—612no—
645C23—611no—
646C23—1222no—
647C23—1221no—
648C23—1221no—
649C23—1221no—
650C23—1221no—
651C23—1221no—
652C23—1221no—
653C23—1221no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23C22⋊C4×D6111yescharacteristic
660C23C22⋊C4×D6111yescharacteristic
661C23C22×C4×D6111yescharacteristic
662Q8—1224no—
663Q8—2442no—
664Q8—2442no—
665Q8—2442no—
666D4—614no—
667D4—1224no—
668D4—1222no—
669D4—1222no—
670D4—1222no—
671D4—1224no—
672D4—2442no—
673D4—2444no—
674D4—2442no—
675D4—2442no—
676D4—2442no—
677D4—2442no—
678D4—2442no—
679C2×C4—21no—
680C2×C4—24no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—611no—
697C2×C4—611no—
698C2×C4—612no—
699C2×C4—1224no—
700C2×C4—1224no—
701C2×C4—1222no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4C22⋊C4×D6112yes—
719C2×C4#1451978312yescomplemented
720C2×C4C2×D4×D6112yes—
721C8—42no—
722C8—42no—
723C8—2442no—
724C8—2442no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—42no—
733C22—42no—
734C22—612no—
735C22—1221no—
736C22—1221no—
737C22—1221no—
738C22—1222no—
739C22—1222no—
740C22—1221no—
741C22—1222no—
742C22—1221no—
743C22—4881no—
744C22—4881no—
745C22—4881no—
746C22—4881no—
747C22—2442no—
748C22—2442no—
749C22—2441no—
750C22—2441no—
751C22—2441no—
752C22#99×D6112yes—
753C22C2×C22⋊C4×D6111yescharacteristic
754C22C2×#1451978311yescharacteristic
755C22#1684052811yescharacteristic
756C4—22no—
757C4—22no—
758C4—22no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—612no—
763C4—1221no—
764C4—1222no—
765C4—2441no—
766C4—2441no—
767C4—2441no—
768C2—21no—
769C2—21no—
770C2—22no—
771C2—41no—
772C2—1222no—
773C2—4881no—
774C2—2442no—
775C2—2441no—
776C2#2145426511yescharacteristic
777C2C2×#99×D6111yescharacteristic
778C2#2145429911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#324C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840413C2
cosocleC22×C4×C61C24
hypercenterC2×#324D61
hypocenterC61#17416
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #21454265C2semidirect
3. #21444181C2semidirect
4. #21444166C2semidirect
5. #21444165C2semidirect
6. #21444156C2semidirect
7. #21444149C2semidirect
8. #21444147C2semidirect
9. #21444136C2semidirect
10. #324×D61C2semidirect
11. C2×C61×#324C2semidirect
290. C2×C4×C61#131semidirect
389. C2×#324D61semidirect
440. C61#17416semidirect
719. C2×C4#14519783semidirect

Maximal subgroups

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

subgroupindex
C2×#168404132
#214542652
#214441812
#214441662
#214441652
#214441562
#214441492
#214441472
#214441362
#324×D612
C2×C61×#3242
#1741661