Finite Group Databasebeta

← #29722319

Subgroups — #29722319

Order 15616.

1054 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840008C211yesmaximal, characteristic, complemented
2C2×#16839992C211yesmaximal, characteristic, complemented
3C2×#16839831C211yesmaximal, characteristic, complemented
4C2×#107×D61C211yesmaximal, characteristic, complemented
5#21449272C211yesmaximal, characteristic, complemented
6#21449261C211yesmaximal, characteristic
7#21447215C211yesmaximal, characteristic, complemented
8#21447208C211yesmaximal, characteristic, complemented
9#21447022C211yesmaximal, characteristic, complemented
10#21447001C211yesmaximal, characteristic, complemented
11#21446698C211yesmaximal, characteristic, complemented
12#21446555C211yesmaximal, characteristic, complemented
13#21446135C211yesmaximal, characteristic, complemented
14#21446125C211yesmaximal, characteristic, complemented
15C61×#1809C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×#14519757C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×#14519752C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519750—21no—
23C2×C4×C22⋊D61C2211yescharacteristic
24C2×C4⋊C4×D61C2211yescharacteristic
25C2×C4⋊C4×D61C2211yescharacteristic
26#16840008—24no—
27#16839992—24no—
28#16839831—24no—
29C2×#14519711C2211yescharacteristic
30C2×#14519710C2211yescharacteristic
31C2×#14519710C2211yescharacteristic
32#107×D61—24no—
33C2×#14519706C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519687C2211yescharacteristic
43#16839696—21no—
44#16839686—21no—
45#16839685—21no—
46#16839677—21no—
47#16839667C2211yescharacteristic
48#16839663C2211yescharacteristic
49#16839658C2211yescharacteristic
50#16839658C2211yescharacteristic
51#16839640—21no—
52#16839638—21no—
53#16839621—21no—
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C2×#107×C61C2211yescharacteristic
58C2×#106×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#380C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61D411yescharacteristic
68C22×C4×D61—21no—
69C22×C4×D61—21no—
70C22×C4×D61C2311yescharacteristic
71C2×#11758190—22no—
72C2×#11758190—22no—
73C2×#11758190—22no—
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C2×C8×D61—22no—
77C2×C8×D61—22no—
78C2×C8×D61D414yescomplemented
79#14519757—22no—
80#14519757—22no—
81#14519756—22no—
82#14519756—41no—
83#14519752—22no—
84#14519752—22no—
85#14519751—22no—
86#14519751—41no—
87#14519750—44no—
88C4×C22⋊D61—22no—
89C4×C22⋊D61—22no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196D411yescharacteristic
99C4⋊C4×D61—22no—
100C4⋊C4×D61—22no—
101C4⋊C4×D61—41no—
102C4⋊C4×D61—41no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61D411yescharacteristic
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112#14519711D414yescomplemented
113#14519710—22no—
114#14519710—22no—
115#14519706—22no—
116#14519702—22no—
117#14519700—22no—
118#14519700—41no—
119#14519699—22no—
120#14519697—22no—
121#14519697—41no—
122C22⋊#92418—22no—
123#14519689—22no—
124#14519687—22no—
125#14519684—21no—
126#14519684—21no—
127#14519684—21no—
128#14519684—21no—
129C23×C4×C61C2311yescharacteristic
130C2×M16×C61—22no—
131C2×M16×C61—22no—
132C2×M16×C61—22no—
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141#107×C61—22no—
142#106×C61—22no—
143#95×C61—21no—
144#95×C61—21no—
145C24×C61C2×D411yescharacteristic
146C23×D61—21no—
147C23×D61C2×D411yescharacteristic
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2411yescharacteristic
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61—42no—
165C2×C22⋊D61—81no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—42no—
179C2×D244—42no—
180C2×D244—42no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—81no—
190C2×C4×D61—81no—
191C2×C4×D61C2×D412yes—
192C2×C4×D61#4112yes—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199M16×C61—44no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61C2×D412yes—
204C2×C8×C61C2×D412yes—
205C2×C8×C61#4112yes—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—81no—
216C22⋊Dic61—22no—
217C22⋊Dic61—42no—
218#11758198—22no—
219#11758198—42no—
220#11758198—42no—
221#11758198—42no—
222#11758198—42no—
223#11758198—81no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—42no—
227C4⋊Dic61C2×D412yes—
228C4⋊Dic61C2×D412yes—
229#11758196—22no—
230#11758196—42no—
231#11758196—42no—
232#11758196—42no—
233#11758196—42no—
234#11758196—81no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418C2×D412yes—
243#11758190—44no—
244C8×D61—28no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61C22×D411yescharacteristic
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61#12112yes—
265C22×D61AGL(1,ℤ/8)12yes—
266C22×D61#13712yes—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C612−1+411yescharacteristic
292C22⋊D61—44no—
293C22⋊D61—84no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61#12112yes—
312D244—41no—
313D244—41no—
314D244—41no—
315D244—41no—
316D244—84no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—84no—
322C4×D61—84no—
323Dic122—41no—
324Dic122—41no—
325Dic122—41no—
326Dic122—41no—
327C8×C61—41no—
328C8×C61#12114yescomplemented
329#92418—22no—
330#92418—41no—
331#24787—611nomaximal, Sylow
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61C2×#12111yescharacteristic
340C22×C61D4211yescharacteristic
341C22×C61#54711yescharacteristic
342C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C61C2×#13711yescharacteristic
344C22×C61#57611yescharacteristic
345C22×C61#57811yescharacteristic
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61—81no—
355C2×D61—81no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61#46814yescomplemented
360C4×C61—41no—
361C4×C61—81no—
362C4×C61—81no—
363C4×C61—81no—
364C4×C61—81no—
365C4×C61C2×#12111yescharacteristic
366C4×C61#53711yescharacteristic
367C4×C61#54811yescharacteristic
368C4×C61#55311yescharacteristic
369Dic61—22no—
370Dic61—42no—
371Dic61—42no—
372Dic61—41no—
373Dic61—41no—
374Dic61—81no—
375C2×#468—611no—
376C2×#465—611no—
377C2×#435—611no—
378C22×#107—611no—
379#2417—611no—
380#2416—611no—
381#2068—611no—
382#2067—611no—
383#2036—611no—
384#2033—611no—
385#1973—611no—
386#1943—611no—
387#1874—611no—
388#1872—611no—
389#1809D6111yescharacteristic, complemented
390C2×C61—81no—
391C2×C61#241611yescharacteristic
392C2×C61C2×#46811yescharacteristic
393C2×C61#306111yescharacteristic
394C2×C61#326411yescharacteristic
395C2×C61#327011yescharacteristic
396C2×C61#334311yescharacteristic
397C2×C61#334611yescharacteristic
398D61—24no—
399D61—161no—
400C22×SD16—611no—
401C22×M16C2×D6111yescharacteristic
402C23×C8—611no—
403C2×C22⋊Q8—611no—
404C2×C22⋊Q8—611no—
405C2×#121—611no—
406C2×#121—611no—
407C2×#121—1221no—
408C2×C4×D4—611no—
409C22×C4⋊C4—611no—
410C22×C4⋊C4—611no—
411#468—1224no—
412#465—1224no—
413#435—1224no—
414C2×#107—611no—
415C2×#107—611no—
416C2×#107—611no—
417C2×#107—1224no—
418C2×#107C2×D6111yescharacteristic
419C2×#106C2×D6111yescharacteristic
420C2×C4⋊C8—611no—
421C2×#103—611no—
422C2×#103—611no—
423C2×#103—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#102—611no—
427C2×C22⋊C8—611no—
428C2×C22⋊C8—611no—
429C2×#97—611no—
430#398—1221no—
431#396—1221no—
432#396—1221no—
433#394—1221no—
434#391—611no—
435#390—611no—
436#389—611no—
437#389—611no—
438#386—1221no—
439#386—1221no—
440#380—1221no—
441#380C2×D6111yescharacteristic
442#380C2×D6111yescharacteristic
443#340—611no—
444#340—611no—
445#340C2×D6111yescharacteristic
446#340C2×D6111yescharacteristic
447C61#2478711yescharacteristic, complemented, Sylow
448C22×Q8—611no—
449C22×D4—611no—
450C22×D4—611no—
451C22×D4—1221no—
452C22×D4—1221no—
453C23×C4—611no—
454C23×C4—1221no—
455C23×C4—1221no—
456C23×C4C22×D6111yescharacteristic
457C2×SD16—1222no—
458C2×SD16—1222no—
459C2×SD16—1222no—
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—22no—
463C22×C8—611no—
464C22×C8—614no—
465C22×C8—611no—
466C22×C8—1222no—
467C22×C8—1222no—
468C22×C8C22×D6111yescharacteristic
469C22×C8C22×D6111yescharacteristic
470C22⋊Q8—1222no—
471C22⋊Q8—1222no—
472C22⋊Q8—1222no—
473C22⋊Q8—2441no—
474#121—1222no—
475#121—1222no—
476#121—1222no—
477#121—2444no—
478#121—2441no—
479C4×D4—1222no—
480C4×D4—1222no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—1222no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—2441no—
493C2×C4⋊C4—2441no—
494C2×C4⋊C4C22×D6111yescharacteristic
495C2×C4⋊C4C22×D6111yescharacteristic
496C2×C4⋊C4C22×D6111yescharacteristic
497C2×C4⋊C4C22×D6111yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—611no—
501C2×C22⋊C4—611no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C42—611no—
509#107—22no—
510#107—614no—
511#107—1222no—
512#107—1222no—
513#106—22no—
514C4⋊C8—1222no—
515#103—1222no—
516#103—1222no—
517#103—2441no—
518#102—1222no—
519#102—1222no—
520#102—2441no—
521C22⋊C8—1222no—
522C22⋊C8—1222no—
523#97—1222no—
524#95—21no—
525#95—21no—
526#95—1221no—
527#95—1221no—
528#95—1221no—
529#95—1221no—
530C24—611no—
531C24—1221no—
532C24D4×D6111yescharacteristic
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×Q8—1221no—
539C2×D4—1222no—
540C2×D4—1222no—
541C2×D4—1222no—
542C2×D4—1221no—
543C2×D4—1221no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—4881no—
549C2×D4—2442no—
550C2×D4—2442no—
551C2×D4—2442no—
552C2×D4—2442no—
553C2×D4—2442no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—611no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—4881no—
577C22×C4—4881no—
578C22×C4—2442no—
579C22×C4—2442no—
580C22×C4—2442no—
581C22×C4—2442no—
582C22×C4D4×D6111yescharacteristic
583C22×C4C23×D6111yescharacteristic
584SD16—2444no—
585M16—44no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—612no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1228no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8#1175822212yes—
597C2×C8D4×D6112yes—
598C2×C8D4×D6112yes—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—612no—
608C4⋊C4—612no—
609C4⋊C4—1222no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—4881no—
613C4⋊C4—2442no—
614C4⋊C4—2442no—
615C4⋊C4—2442no—
616C4⋊C4—2442no—
617C4⋊C4—2442no—
618C22⋊C4—42no—
619C22⋊C4—81no—
620C22⋊C4—1222no—
621C22⋊C4—1222no—
622C22⋊C4—4881no—
623C22⋊C4—2442no—
624C22⋊C4—2442no—
625C22⋊C4—2442no—
626C22⋊C4—2442no—
627C22⋊C4—2442no—
628C42—1221no—
629C42—1221no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—612no—
638C23—612no—
639C23—612no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—2441no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23C2×D4×D6111yescharacteristic
652Q8—2441no—
653Q8—2441no—
654Q8—2441no—
655Q8—2441no—
656D4—4884no—
657D4—4884no—
658D4—2444no—
659D4—2441no—
660D4—2441no—
661D4—2441no—
662D4—2441no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—612no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—4884no—
698C2×C4—4884no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4C2×D4×D6111yescharacteristic
707C2×C4C2×D4×D6111yescharacteristic
708C2×C4#41×D6111yescharacteristic
709C2×C4C2×#1175822211yescharacteristic
710C2×C4#1451982311yescharacteristic
711C2×C4#1451982511yescharacteristic
712C8—41no—
713C8—1222no—
714C8—2441no—
715C8#1451975014yescomplemented
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—614no—
724C22—1222no—
725C22—1222no—
726C22—1222no—
727C22—1222no—
728C22—1222no—
729C22—1222no—
730C22—4881no—
731C22—4881no—
732C22—4881no—
733C22—4881no—
734C22—4881no—
735C22—4881no—
736C22—4881no—
737C22#121×D6111yescharacteristic
738C22#1684039611yescharacteristic
739C22#1684041311yescharacteristic
740C22AGL(1,ℤ/8)×D6111yescharacteristic
741C22#137×D6111yescharacteristic
742C22#1684056611yescharacteristic
743C22#1684057811yescharacteristic
744C4—41no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4—1222no—
750C4—4881no—
751C4—2441no—
752C4—2441no—
753C4—2442no—
754C4—2442no—
755C4C2×#1451975011yescharacteristic
756C4#1684034211yescharacteristic
757C4#1684042211yescharacteristic
758C4#1684045611yescharacteristic
759C2—81no—
760C2—1224no—
761C2—9761no—
762C2#2144926111yescharacteristic
763C2#468×D6111yescharacteristic
764C2#2145548711yescharacteristic
765C2#2145730611yescharacteristic
766C2#2145739611yescharacteristic
767C2#2145826011yescharacteristic
768C2#2145830511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1809C2
socleC23×C61C22×D4
prime radical#21449261C2
hypercenter#1809D61
hypocenterC61#24787
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
1. C2×#16840008C2semidirect
2. C2×#16839992C2semidirect
3. C2×#16839831C2semidirect
4. C2×#107×D61C2semidirect
5. #21449272C2semidirect
7. #21447215C2semidirect
8. #21447208C2semidirect
9. #21447022C2semidirect
10. #21447001C2semidirect
11. #21446698C2semidirect
12. #21446555C2semidirect
13. #21446135C2semidirect
14. #21446125C2semidirect
15. C61×#1809C2semidirect
78. C2×C8×D61D4semidirect
112. #14519711D4semidirect
328. C8×C61#121semidirect
359. C2×D61#468semidirect
389. #1809D61semidirect
447. C61#24787semidirect
715. C8#14519750semidirect

Maximal subgroups

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

subgroupindex
C2×#168400082
C2×#168399922
C2×#168398312
C2×#107×D612
#214492722
#214492612
#214472152
#214472082
#214470222
#214470012
#214466982
#214465552
#214461352
#214461252
C61×#18092
#2478761