Finite Group Databasebeta

← #29733129

Subgroups — #29733129

Order 15616.

1124 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840469C211yesmaximal, characteristic
2C2×#16840093C211yesmaximal, characteristic, complemented
3C2×#16840020C211yesmaximal, characteristic, complemented
4#21449248C211yesmaximal, characteristic
5#21447153C211yesmaximal, characteristic, complemented
6#21447016C211yesmaximal, characteristic, complemented
7#21446961C211yesmaximal, characteristic, complemented
8#21446829C211yesmaximal, characteristic, complemented
9#21446159C211yesmaximal, characteristic, complemented
10#21446129C211yesmaximal, characteristic, complemented
11#21446124C211yesmaximal, characteristic, complemented
12#21446090C211yesmaximal, characteristic, complemented
13#21446014C211yesmaximal, characteristic, complemented
14#21445539C211yesmaximal, characteristic, complemented
15C61×#1870C211yesmaximal, characteristic
16C22×Dic244C2211yescharacteristic
17#16840469—24no—
18#16840469—24no—
19C2×#14519777C2211yescharacteristic
20C2×#14519768—21no—
21C2×#14519756C2211yescharacteristic
22C2×#14519756C2211yescharacteristic
23C2×#14519756C2211yescharacteristic
24C2×#14519756C2211yescharacteristic
25C2×#14519754—21no—
26C2×#14519754—21no—
27C2×C4×Dic122C2211yescharacteristic
28C2×D4×Dic61—21no—
29C2×#14519736C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31C22×C4⋊Dic61C2211yescharacteristic
32#16840093—24no—
33#16840020—24no—
34C2×#14519709C2211yescharacteristic
35C2×#14519709C2211yescharacteristic
36C2×#14519709C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519702C2211yescharacteristic
40C2×#14519702C2211yescharacteristic
41C2×#14519702C2211yescharacteristic
42C2×#14519702C2211yescharacteristic
43#16839690—21no—
44#16839676—21no—
45#16839668C2211yescharacteristic
46#16839660C2211yescharacteristic
47#16839657—21no—
48#16839656—21no—
49#16839622C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839525C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C22×Dic122C2311yescharacteristic
66C23×Dic61—21no—
67C23×Dic61—21no—
68C2×Dic244—22no—
69C2×Dic244—22no—
70C2×Dic244—41no—
71#14519777—22no—
72#14519777—22no—
73#14519768—28no—
74#14519756—22no—
75#14519756—22no—
76#14519756—22no—
77#14519756—22no—
78#14519756—22no—
79#14519756—22no—
80#14519756—41no—
81#14519756D414yes—
82#14519754—28no—
83#14519754—28no—
84C4×Dic122—22no—
85C4×Dic122—22no—
86D4×Dic61—28no—
87#14519736—22no—
88#14519736—41no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—22no—
94C2×C4⋊Dic61—22no—
95C2×C4⋊Dic61D414yes—
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61—21no—
116#14519709—22no—
117#14519709—22no—
118#14519709—22no—
119#14519702—22no—
120#14519702—22no—
121#14519702—22no—
122#14519702—22no—
123#14519702—22no—
124#14519702—41no—
125#14519684—21no—
126#14519684—21no—
127#14519684—21no—
128#14519684—21no—
129C22×D4×C61D411yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C2×M16×C61—22no—
133C2×M16×C61—22no—
134C2×M16×C61—41no—
135C22×C8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C4×D4×C61—22no—
140C4×D4×C61—22no—
141C2×C4⋊C4×C61D411yescharacteristic
142C2×C22⋊C4×C61D411yescharacteristic
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C42×C61C2311yescharacteristic
145C22⋊C8×C61—22no—
146C22⋊C8×C61—22no—
147C22⋊C8×C61—41no—
148C24×C61C2×D411yescharacteristic
149C24×C61C2×D411yescharacteristic
150C2×D4×C61—22no—
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D412yes—
167C22×C4×C61C2×D412yes—
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2411yescharacteristic
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—24no—
176C22×Dic61—24no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—81no—
181C22×Dic61—81no—
182C22×Dic61—81no—
183C22×Dic61—81no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—24no—
196C2×Dic122—81no—
197C2×Dic122—81no—
198C2×Dic122C2×D412yes—
199M16×C61—44no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61#4112yes—
212C4⋊C4×C61—22no—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—22no—
215C42×C61—21no—
216C42×C61—21no—
217C22⋊Dic61—24no—
218C22⋊Dic61—24no—
219C22⋊Dic61—42no—
220C22⋊Dic61—42no—
221C22⋊Dic61—42no—
222C22⋊Dic61—42no—
223C4⋊Dic61—24no—
224C4⋊Dic61—24no—
225C4⋊Dic61—24no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61C2×D412yes—
235C4⋊Dic61C2×D412yes—
236C4⋊Dic61C2×D412yes—
237C4⋊Dic61#4112yes—
238#11758196—24no—
239#11758196—24no—
240#11758196—24no—
241#11758196—42no—
242#11758196—42no—
243#11758196—42no—
244C4×Dic61—24no—
245C4×Dic61—42no—
246Dic244—44no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61#12012yes—
260C23×C61#13712yes—
261C23×C61C22×D411yescharacteristic
262D4×C61—28no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61#12012yes—
282C2×C4×C61#13712yes—
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61H(5,𝔽2)11yescharacteristic
288C2×C4×C612−1+411yescharacteristic
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—84no—
314C2×Dic61—84no—
315Dic122—22no—
316Dic122—22no—
317Dic122—41no—
318Dic122—41no—
319Dic122—41no—
320Dic122—41no—
321Dic122—41no—
322Dic122—41no—
323Dic122—84no—
324C8×C61—22no—
325C8×C61—41no—
326C8×C61—41no—
327C8×C61—41no—
328#25561—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61C2×#12011yescharacteristic
344C22×C61#54611yescharacteristic
345C22×C61#54711yescharacteristic
346C22×C61C2×#13711yescharacteristic
347C22×C61C2×#13711yescharacteristic
348C22×C61#57711yescharacteristic
349C22×C61#57711yescharacteristic
350C4×C61—22no—
351C4×C61—22no—
352C4×C61—41no—
353C4×C61—41no—
354C4×C61#53211yescharacteristic
355C4×C61#53711yescharacteristic
356C4×C61#54611yescharacteristic
357C4×C61#54711yescharacteristic
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361Dic61—42no—
362Dic61—42no—
363Dic61—81no—
364Dic61—81no—
365Dic61—81no—
366C2×#554—611no—
367C2×#483—611no—
368C2×#470—611no—
369#2415—611no—
370#2058—611no—
371#2035—611no—
372#2024—611no—
373#2001—611no—
374#1878—611no—
375#1873—611no—
376#1872—611no—
377#1870D6111yescharacteristic
378#1865—611no—
379#1853—611no—
380#1736—611no—
381C2×C61—42no—
382C2×C61—42no—
383C2×C61#243011yescharacteristic
384C2×C61#300411yescharacteristic
385C2×C61#300911yescharacteristic
386C2×C61#331611yescharacteristic
387C2×C61#333111yescharacteristic
388C2×C61#334411yescharacteristic
389C2×C61#335611yescharacteristic
390C22×Q16—611no—
391C22×M16C2×D6111yescharacteristic
392#554—1224no—
393#554—1224no—
394C2×C4⋊Q8—611no—
395C2×#125—1221no—
396C2×C22⋊Q8—611no—
397C2×C22⋊Q8—611no—
398C2×C22⋊Q8—611no—
399C2×C22⋊Q8—611no—
400C2×C22⋊Q8—1221no—
401C2×C22⋊Q8—1221no—
402C2×C4×Q8—611no—
403C2×C4×D4—1221no—
404C2×C4×D4C2×D6111yescharacteristic
405C2×#117—611no—
406C22×C4⋊C4—611no—
407C22×C4⋊C4—611no—
408#483—1224no—
409#470—1224no—
410C2×#106—611no—
411C2×#106—611no—
412C2×#106—611no—
413C2×#103—611no—
414C2×#103—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#103—611no—
418C2×#103—611no—
419C2×C22⋊C8C2×D6111yescharacteristic
420C2×C22⋊C8C2×D6111yescharacteristic
421C2×C22⋊C8C2×D6111yescharacteristic
422#397—1221no—
423#394—1221no—
424#391—611no—
425#389—611no—
426#389—1221no—
427#388—1221no—
428#380—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435#336C2×D6111yescharacteristic
436#336C2×D6111yescharacteristic
437C61#2556111yescharacteristic, complemented, Sylow
438C22×Q8—611no—
439C22×Q8—611no—
440C22×Q8—1221no—
441C22×D4D24411yescharacteristic
442C23×C4—1221no—
443C23×C4—1221no—
444C23×C4C22×D6111yescharacteristic
445C23×C4C22×D6111yescharacteristic
446C2×Q16—1222no—
447C2×Q16—1222no—
448C2×Q16—2441no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—41no—
452C22×C8C22×D6111yescharacteristic
453C22×C8C22×D6111yescharacteristic
454C22×C8C22×D6111yescharacteristic
455C22×C8C22×D6111yescharacteristic
456C4⋊Q8—1222no—
457C4⋊Q8—1222no—
458#125—1228no—
459C22⋊Q8—614no—
460C22⋊Q8—1228no—
461C22⋊Q8—1228no—
462C22⋊Q8—1222no—
463C22⋊Q8—1222no—
464C22⋊Q8—1222no—
465C22⋊Q8—1222no—
466C22⋊Q8—1222no—
467C22⋊Q8—1222no—
468C22⋊Q8—2441no—
469C4×Q8—1222no—
470C4×Q8—1222no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—1228no—
474#117—1222no—
475#117—2441no—
476C2×C4⋊C4—614no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1222no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4D24411yescharacteristic
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4D24411yescharacteristic
503C2×C22⋊C4D24411yescharacteristic
504C2×C42—1221no—
505C2×C42—1221no—
506C2×C42C22×D6111yescharacteristic
507#106—1222no—
508#106—1222no—
509#106—1222no—
510#103—1222no—
511#103—1222no—
512#103—1222no—
513#103—1222no—
514#103—1222no—
515#103—2441no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C22⋊C8—41no—
519#95—1221no—
520#95—1221no—
521#95—1221no—
522#95—1221no—
523C24C2×D24411yescharacteristic
524C24C2×D24411yescharacteristic
525C2×Q8—612no—
526C2×Q8—1224no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×Q8—4881no—
539C2×Q8—4881no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—1224no—
554C22×C4—1224no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—4881no—
564C22×C4—4881no—
565C22×C4—4881no—
566C22×C4—4881no—
567C22×C4C2×D24411yescharacteristic
568C22×C4C2×D24411yescharacteristic
569C22×C4C2×D24411yescharacteristic
570C22×C4C2×D24411yescharacteristic
571C22×C4D4×D6112yes—
572C22×C4D4×D6112yes—
573C22×C4C23×D6111yescharacteristic
574Q16—2444no—
575M16—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8#1175822412yes—
588C4⋊C4—22no—
589C4⋊C4—612no—
590C4⋊C4—612no—
591C4⋊C4—612no—
592C4⋊C4—612no—
593C4⋊C4—1224no—
594C4⋊C4—1224no—
595C4⋊C4—1224no—
596C4⋊C4—1224no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1224no—
602C4⋊C4—1224no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—2442no—
608C4⋊C4—2442no—
609C4⋊C4—2442no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—1224no—
613C22⋊C4—1224no—
614C22⋊C4—2442no—
615C22⋊C4—2442no—
616C22⋊C4—2442no—
617C22⋊C4—2442no—
618C42—21no—
619C42—21no—
620C42—1224no—
621C42—2442no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23#1451974712yes—
635C23#1451981012yes—
636C23C22×D24411yescharacteristic
637Q8—1222no—
638Q8—1222no—
639Q8—4884no—
640Q8—2441no—
641Q8—2441no—
642Q8—2441no—
643Q8—2441no—
644Q8—2441no—
645Q8—2441no—
646D4—28no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—4884no—
671C2×C4—4884no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4#1451974712yes—
692C2×C4#1451981012yes—
693C2×C4C2×D4×D6111yescharacteristic
694C2×C4C2×D4×D6111yescharacteristic
695C2×C4#41×D6111yescharacteristic
696C2×C4C2×#1175822411yescharacteristic
697C2×C4#1451982211yescharacteristic
698C2×C4#1451982411yescharacteristic
699C8—22no—
700C8—41no—
701C8—41no—
702C8—41no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22C2×#1451974711yescharacteristic
718C22#1684040711yescharacteristic
719C22#1684041611yescharacteristic
720C22C2×#1451981011yescharacteristic
721C22C2×#1451981011yescharacteristic
722C22#1684057411yescharacteristic
723C22#1684057411yescharacteristic
724C4—22no—
725C4—22no—
726C4—41no—
727C4—41no—
728C4—4881no—
729C4—4881no—
730C4—4881no—
731C4—2442no—
732C4—2442no—
733C4—2442no—
734C4—2442no—
735C4—2442no—
736C4#1684030711yescharacteristic
737C4#1684033911yescharacteristic
738C4#1684039911yescharacteristic
739C4#1684041011yescharacteristic
740C2—42no—
741C2—42no—
742C2#2144942711yescharacteristic
743C2#2145505611yescharacteristic
744C2#2145509811yescharacteristic
745C2#2145793211yescharacteristic
746C2#2145813611yescharacteristic
747C2#2145827611yescharacteristic
748C2#2145843511yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1870C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenter#1870D61
hypocenterC61#25561
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#16840093C2semidirect
3. C2×#16840020C2semidirect
5. #21447153C2semidirect
6. #21447016C2semidirect
7. #21446961C2semidirect
8. #21446829C2semidirect
9. #21446159C2semidirect
10. #21446129C2semidirect
11. #21446124C2semidirect
12. #21446090C2semidirect
13. #21446014C2semidirect
14. #21445539C2semidirect
437. C61#25561semidirect

Maximal subgroups

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

subgroupindex
C2×#168404692
C2×#168400932
C2×#168400202
#214492482
#214471532
#214470162
#214469612
#214468292
#214461592
#214461292
#214461242
#214460902
#214460142
#214455392
C61×#18702
#2556161