Finite Group Databasebeta

← #29828840

Subgroups — #29828840

Order 15616.

1436 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D61C211yesmaximal, characteristic
2C2×#16839971C211yesmaximal, characteristic, complemented
3C2×#16839970C211yesmaximal, characteristic, complemented
4C2×#16839919C211yesmaximal, characteristic
5C2×#16839916C211yesmaximal, characteristic
6#21454168C211yesmaximal, characteristic
7#21446163C211yesmaximal, characteristic, complemented
8#21446160C211yesmaximal, characteristic, complemented
9#21446159C211yesmaximal, characteristic, complemented
10#21446125C211yesmaximal, characteristic
11#21446123C211yesmaximal, characteristic
12#21445823C211yesmaximal, characteristic, complemented
13#21445822C211yesmaximal, characteristic, complemented
14#21445798C211yesmaximal, characteristic
15C61×#1878C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×Dic244C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C2×#14519775C2211yescharacteristic
21C2×#14519757C2211yescharacteristic
22C2×#14519753C2211yescharacteristic
23C2×Q8×Dic61C2211yescharacteristic
24C2×C4×Dic122—21no—
25C2×C4×Dic122C2211yescharacteristic
26C2×#14519742—21no—
27C2×#14519742C2211yescharacteristic
28C4×Q8×D61—24no—
29C4×Q8×D61—24no—
30C2×C4⋊C4×D61—21no—
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×C42×D61—21no—
33C2×C42×D61C2211yescharacteristic
34#16839971—24no—
35#16839970—24no—
36#16839919—24no—
37#16839916—24no—
38C2×#14519706C2211yescharacteristic
39C2×#14519706C2211yescharacteristic
40C2×#14519702C2211yescharacteristic
41C2×#14519702C2211yescharacteristic
42C2×#14519701C2211yescharacteristic
43C2×#14519701C2211yescharacteristic
44C2×#14519700C2211yescharacteristic
45C2×#14519700C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519689C2211yescharacteristic
48#16839668C2211yescharacteristic
49#16839659—21no—
50#16839659—21no—
51#16839631C2211yescharacteristic
52#16839621—21no—
53#16839621—21no—
54#16839525C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57#16839517C2211yescharacteristic
58C22×Q16×C61C2211yescharacteristic
59C2×C4×Q8×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C61×#391C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C61×#336C2211yescharacteristic
65C22×Dic122—21no—
66C22×Dic122C2311yescharacteristic
67C22×Dic122C2311yescharacteristic
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—22no—
71C2×Q8×D61—22no—
72C2×Q8×D61—22no—
73C2×Q8×D61D414yes—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61D411yescharacteristic
77C22×C4×D61D411yescharacteristic
78C22×C4×D61C2311yescharacteristic
79C2×Dic244—22no—
80C2×Dic244—22no—
81C2×Dic244—22no—
82C2×#11758202—22no—
83C2×#11758202—22no—
84C2×#11758202—22no—
85C2×#11758202—22no—
86C2×#11758202—22no—
87C2×#11758202—22no—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90#14519775—22no—
91#14519775—22no—
92#14519757—22no—
93#14519757—22no—
94#14519753—22no—
95#14519753—22no—
96Q8×Dic61—22no—
97Q8×Dic61D414yes—
98C4×Dic122—28no—
99C4×Dic122—22no—
100C4×Dic122—22no—
101#14519742—28no—
102#14519742—22no—
103#14519742D414yes—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61—21no—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196—21no—
114C2×#11758196—21no—
115C2×#11758196—21no—
116C4⋊C4×D61—28no—
117C4⋊C4×D61—22no—
118C4⋊C4×D61—22no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61—21no—
124C2×C4×Dic61D411yescharacteristic
125C2×C4×Dic61D411yescharacteristic
126C2×C4×Dic61C2311yescharacteristic
127C42×D61—28no—
128C42×D61—22no—
129C42×D61—22no—
130#14519706—22no—
131#14519706—22no—
132#14519702—22no—
133#14519702—22no—
134#14519701—22no—
135#14519701—22no—
136#14519700—22no—
137#14519700—22no—
138#14519689—22no—
139#14519689—22no—
140#14519684—21no—
141#14519684—21no—
142C22×Q8×C61C2311yescharacteristic
143C22×Q8×C61C2311yescharacteristic
144C2×Q16×C61—22no—
145C2×Q16×C61—22no—
146C2×Q16×C61—22no—
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C4×Q8×C61—22no—
150C4×Q8×C61—22no—
151C2×C4⋊C4×C61—21no—
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C42×C61—21no—
155C2×C42×C61C2311yescharacteristic
156#103×C61—22no—
157#103×C61—22no—
158#95×C61—21no—
159#95×C61—21no—
160C23×D61C2×D411yescharacteristic
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61C2×D412yes—
171C2×Q8×C61C2×D412yes—
172C2×Q8×C61#4112yes—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2411yescharacteristic
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187Q8×D61—28no—
188Q8×D61—28no—
189Q8×D61—28no—
190Q8×D61—28no—
191C2×C4×D61—24no—
192C2×C4×D61—24no—
193C2×C4×D61—24no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—24no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—41no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61Q1614yescomplemented
207C2×C4×D61C2×D412yes—
208C2×C4×D61#4112yes—
209C2×Dic122—24no—
210C2×Dic122—24no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—24no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122C2×D412yes—
222C2×Dic122C2×D412yes—
223C2×Dic122#4112yes—
224Q16×C61—44no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C2×D412yes—
236C42×C61—24no—
237C42×C61—21no—
238C42×C61—21no—
239#11758202—44no—
240#11758202—44no—
241#11758198—42no—
242#11758198—42no—
243C4⋊Dic61—21no—
244C4⋊Dic61—24no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—42no—
248C4⋊Dic61C2×D412yes—
249#11758196—24no—
250#11758196—24no—
251#11758196—24no—
252#11758196—42no—
253#11758196—42no—
254#11758196—42no—
255#11758196—42no—
256#11758196—42no—
257C4×Dic61—24no—
258C4×Dic61—24no—
259C4×Dic61—24no—
260C4×Dic61—22no—
261C4×Dic61—22no—
262C4×Dic61C2×D412yes—
263C4×Dic61C2×D412yes—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270Dic244—44no—
271C23×C61C22×D411yescharacteristic
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61#12112yes—
277C22×D61C2×Q1612yes—
278C22×D61#13712yes—
279Q8×C61—22no—
280Q8×C61—22no—
281Q8×C61—22no—
282Q8×C61—41no—
283Q8×C61—41no—
284Q8×C61—41no—
285Q8×C61—41no—
286Q8×C61#12114yes—
287C2×C4×C61—21no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—22no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61C2×Q1612yes—
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C22×D411yescharacteristic
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C2×#4111yescharacteristic
309C2×C4×C61C2×#4111yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×Dic61—21no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—21no—
315C2×Dic61—22no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—22no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61#12012yes—
328C2×Dic61#12012yes—
329C2×Dic61#12112yes—
330C2×Dic61C2×Q1612yes—
331C2×Dic61#13712yes—
332C4×D61—216no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—28no—
338C4×D61—44no—
339C4×D61—48no—
340Dic122—216no—
341Dic122—22no—
342Dic122—22no—
343Dic122—22no—
344Dic122—41no—
345Dic122—41no—
346Dic122—41no—
347Dic122—41no—
348Dic122#12114yes—
349C8×C61—41no—
350C8×C61—41no—
351#92418—41no—
352#92418—41no—
353#32906—611nomaximal, Sylow
354C22×C61C2×#12011yescharacteristic
355C22×C61C2×#12111yescharacteristic
356C22×C61#52511yescharacteristic
357C22×C61C22×Q1611yescharacteristic
358C22×C61C2×#13711yescharacteristic
359C22×C61C2×#13711yescharacteristic
360C22×C61#57511yescharacteristic
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61#46214yescomplemented
368C4×C61—24no—
369C4×C61—22no—
370C4×C61—41no—
371C4×C61—42no—
372C4×C61—81no—
373C4×C61—81no—
374C4×C61C2×#12111yescharacteristic
375C4×C61C2×#12111yescharacteristic
376C4×C61#52511yescharacteristic
377C4×C61#52511yescharacteristic
378Dic61—22no—
379Dic61—24no—
380Dic61—22no—
381Dic61—42no—
382Dic61—81no—
383Dic61—81no—
384Dic61#45114yescomplemented
385C22×C4×Q8—611no—
386C2×#462—611no—
387C2×#462—611no—
388C2×#451—611no—
389C2×#451—611no—
390#2857—611no—
391#1878—611no—
392#1878—611no—
393#1878—611no—
394#1878D6111yescharacteristic, complemented
395#1872—611no—
396#1872—611no—
397#1803—611no—
398#1803—611no—
399#1797—611no—
400C2×C61#284711yescharacteristic
401C2×C61C2×#45111yescharacteristic
402C2×C61#300711yescharacteristic
403C2×C61C2×#46211yescharacteristic
404C2×C61#303711yescharacteristic
405C2×C61#310411yescharacteristic
406C2×C61#311311yescharacteristic
407D61—24no—
408C23×Q8—611no—
409C22×Q16—611no—
410C22×Q16—611no—
411C22×Q16—611no—
412C22×Q16C2×D6111yescharacteristic
413C2×C4⋊Q8—611no—
414C2×C22⋊Q8—611no—
415C2×C22⋊Q8—611no—
416C2×C4×Q8—611no—
417C2×C4×Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×Q8—1221no—
420C2×C4×Q8—1221no—
421C2×C4×Q8—1224no—
422C2×C4×Q8—1224no—
423C2×C4×Q8C2×D6111yescharacteristic
424C22×C4⋊C4—611no—
425C22×C4⋊C4—1221no—
426C22×C42—611no—
427C22×C42—1221no—
428#462—1224no—
429#462—1224no—
430#451—1224no—
431#451—1224no—
432C2×C4⋊C8—611no—
433C2×C4⋊C8—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103C2×D6111yescharacteristic
441C2×#103C2×D6111yescharacteristic
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444#391—611no—
445#391C2×D6111yescharacteristic
446#389—1221no—
447#389—1221no—
448#384—611no—
449#380—1221no—
450#380—1221no—
451#340—611no—
452#340—611no—
453#340—611no—
454#340C2×D6111yescharacteristic
455#336—611no—
456#336C2×D6111yescharacteristic
457C61#3290611yescharacteristic, complemented, Sylow
458C22×Q8—614no—
459C22×Q8—611no—
460C22×Q8—611no—
461C22×Q8—1221no—
462C22×Q8—1222no—
463C22×Q8—1222no—
464C22×Q8—1222no—
465C22×Q8—1222no—
466C22×Q8—1222no—
467C22×Q8C22×D6111yescharacteristic
468C22×Q8C22×D6111yescharacteristic
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—1221no—
473C23×C4—1221no—
474C2×Q16—22no—
475C2×Q16—22no—
476C2×Q16—22no—
477C2×Q16—1222no—
478C2×Q16—1222no—
479C2×Q16—1222no—
480C2×Q16—1222no—
481C2×Q16—1222no—
482C2×Q16—1222no—
483C2×Q16—1222no—
484C2×Q16—1222no—
485C2×Q16—1222no—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8C22×D6111yescharacteristic
489C22×C8C22×D6111yescharacteristic
490C4⋊Q8—1222no—
491C4⋊Q8—1222no—
492C22⋊Q8—1222no—
493C22⋊Q8—1222no—
494C22⋊Q8—1222no—
495C22⋊Q8—1222no—
496C4×Q8—22no—
497C4×Q8—22no—
498C4×Q8—614no—
499C4×Q8—614no—
500C4×Q8—1222no—
501C4×Q8—1222no—
502C4×Q8—1228no—
503C4×Q8—1222no—
504C4×Q8—1222no—
505C4×Q8—1228no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4—1228no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1222no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4C22×D6111yescharacteristic
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C42—21no—
527C2×C42—611no—
528C2×C42—611no—
529C2×C42—611no—
530C2×C42—1222no—
531C2×C42—1222no—
532C2×C42—1228no—
533C2×C42—1221no—
534C2×C42—1221no—
535C2×C42—1221no—
536C2×C42C22×D6111yescharacteristic
537C4⋊C8—1222no—
538C4⋊C8—1222no—
539#103—22no—
540#103—22no—
541#103—1222no—
542#103—1222no—
543#103—1222no—
544#103—1222no—
545#103—1222no—
546#103—1222no—
547C22⋊C8—1222no—
548C22⋊C8—1222no—
549#95—21no—
550#95—21no—
551#95—1221no—
552#95—1221no—
553C24—611no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—612no—
564C2×Q8—612no—
565C2×Q8—612no—
566C2×Q8—1224no—
567C2×Q8—1224no—
568C2×Q8—1224no—
569C2×Q8—1228no—
570C2×Q8—1228no—
571C2×Q8—1228no—
572C2×Q8—1228no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—1221no—
576C2×Q8—1221no—
577C2×Q8—1221no—
578C2×Q8—1221no—
579C2×Q8—1221no—
580C2×Q8—1221no—
581C2×Q8—1221no—
582C2×Q8#1175822212yes—
583C2×Q8D4×D6112yes—
584C2×Q8D4×D6112yes—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—612no—
593C22×C4—612no—
594C22×C4—614no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1224no—
599C22×C4—1224no—
600C22×C4—1224no—
601C22×C4—1222no—
602C22×C4—1224no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—2441no—
612C22×C4—2442no—
613C22×C4—2442no—
614C22×C4D4×D6111yescharacteristic
615C22×C4D4×D6111yescharacteristic
616C22×C4C23×D6111yescharacteristic
617Q16—44no—
618Q16—2444no—
619Q16—2444no—
620Q16—2444no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—1221no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—612no—
638C4⋊C4—1224no—
639C4⋊C4—1224no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—2442no—
646C4⋊C4—2442no—
647C4⋊C4—2442no—
648C4⋊C4—2442no—
649C4⋊C4—2442no—
650C4⋊C4—2442no—
651C4⋊C4D4×D6112yes—
652C22⋊C4—2442no—
653C22⋊C4—2442no—
654C42—24no—
655C42—21no—
656C42—21no—
657C42—612no—
658C42—612no—
659C42—1222no—
660C42—1222no—
661C42—1224no—
662C42—1224no—
663C42—1224no—
664C23—612no—
665C23—612no—
666C23—612no—
667C23—1221no—
668C23—1221no—
669C23—1221no—
670C23—1221no—
671C23C2×D4×D6111yescharacteristic
672Q8—22no—
673Q8—22no—
674Q8—22no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—614no—
680Q8—12216no—
681Q8—1222no—
682Q8—1222no—
683Q8—1222no—
684Q8—2441no—
685Q8—2441no—
686Q8—2441no—
687Q8—2441no—
688Q8#1451975014yes—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—612no—
707C2×C4—612no—
708C2×C4—612no—
709C2×C4—612no—
710C2×C4—612no—
711C2×C4—1228no—
712C2×C4—12216no—
713C2×C4—1221no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1221no—
717C2×C4—1222no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—2444no—
726C2×C4—2448no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4Q16×D6112yes—
736C2×C4C2×D4×D6111yescharacteristic
737C2×C4C2×D4×D6111yescharacteristic
738C2×C4C2×D4×D6111yescharacteristic
739C2×C4#41×D6111yescharacteristic
740C2×C4#41×D6111yescharacteristic
741C2×C4C2×#1175822211yescharacteristic
742C8—41no—
743C8—41no—
744C8—2441no—
745C8—2441no—
746C22—614no—
747C22—1222no—
748C22—1222no—
749C22—1222no—
750C22—1222no—
751C22—1222no—
752C22—1222no—
753C22#120×D6111yescharacteristic
754C22#121×D6111yescharacteristic
755C22#1684027111yescharacteristic
756C22C2×Q16×D6111yescharacteristic
757C22#137×D6111yescharacteristic
758C22#137×D6111yescharacteristic
759C22#1684055911yescharacteristic
760C4—24no—
761C4—22no—
762C4—41no—
763C4—42no—
764C4—81no—
765C4—81no—
766C4—614no—
767C4—1222no—
768C4—1224no—
769C4—1222no—
770C4—4881no—
771C4—4881no—
772C4—2442no—
773C4#121×D6111yescharacteristic
774C4C2×#1451975011yescharacteristic
775C4#1684027011yescharacteristic
776C4#1684027111yescharacteristic
777C2—1224no—
778C2#2145410011yescharacteristic
779C2#451×D6111yescharacteristic
780C2#2145507611yescharacteristic
781C2#462×D6111yescharacteristic
782C2#2145528911yescharacteristic
783C2#2145585611yescharacteristic
784C2#2145594711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1878C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#1878D61
hypocenterC61#32906
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. C2×#16839971C2semidirect
3. C2×#16839970C2semidirect
7. #21446163C2semidirect
8. #21446160C2semidirect
9. #21446159C2semidirect
12. #21445823C2semidirect
13. #21445822C2semidirect
15. C61×#1878C2semidirect
206. C2×C4×D61Q16semidirect
367. C2×D61#462semidirect
384. Dic61#451semidirect
394. #1878D61semidirect
457. C61#32906semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D612
C2×#168399712
C2×#168399702
C2×#168399192
C2×#168399162
#214541682
#214461632
#214461602
#214461592
#214461252
#214461232
#214458232
#214458222
#214457982
C61×#18782
#3290661