Finite Group Databasebeta

← #29722309

Subgroups — #29722309

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×#16840009C211yesmaximal, characteristic, complemented
2C2×#16839991C211yesmaximal, characteristic, complemented
3C2×#16839833C211yesmaximal, characteristic, complemented
4#21449264C211yesmaximal, characteristic, complemented
5#21449253C211yesmaximal, characteristic
6#21447209C211yesmaximal, characteristic, complemented
7#21447202C211yesmaximal, characteristic, complemented
8#21447024C211yesmaximal, characteristic, complemented
9#21447003C211yesmaximal, characteristic, complemented
10#21446698C211yesmaximal, characteristic, complemented
11#21446558C211yesmaximal, characteristic, complemented
12#21446136C211yesmaximal, characteristic, complemented
13#21446126C211yesmaximal, characteristic, complemented
14#21445853C211yesmaximal, characteristic, complemented
15C22×#107×C61C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×#14519757C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×#14519752C2211yescharacteristic
21C2×#14519751—21no—
22C2×#14519751C2211yescharacteristic
23C2×C4×C22⋊D61C2211yescharacteristic
24#16840009—24no—
25#16839991—24no—
26#16839833—24no—
27C2×#14519709C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519687C2211yescharacteristic
38#16839692—21no—
39#16839684—21no—
40#16839684—21no—
41#16839679—21no—
42#16839667C2211yescharacteristic
43#16839663C2211yescharacteristic
44#16839661C2211yescharacteristic
45#16839661C2211yescharacteristic
46#16839641—21no—
47#16839641—21no—
48#16839622—21no—
49#16839619C2211yescharacteristic
50#16839619C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C22×C4⋊C4×C61C2211yescharacteristic
58C2×#107×C61—24no—
59C2×#107×C61C2211yescharacteristic
60C2×#107×C61C2211yescharacteristic
61C2×#107×C61C2211yescharacteristic
62C2×#107×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61D411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C2×#11758190—22no—
70C2×#11758190—22no—
71C2×#11758190—22no—
72C2×#11758189—22no—
73C2×#11758189—22no—
74C2×#11758189—22no—
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519757—22no—
78#14519757—41no—
79#14519756—22no—
80#14519756—22no—
81#14519752—22no—
82#14519752—41no—
83#14519751—22no—
84#14519751—22no—
85#14519751—44no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—22no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196D411yescharacteristic
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61D411yescharacteristic
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198D411yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106#14519709—22no—
107#14519706—22no—
108#14519702—22no—
109#14519700—22no—
110#14519700—41no—
111#14519699—22no—
112#14519697—22no—
113#14519697—41no—
114C22⋊#92418—22no—
115#14519689—22no—
116#14519687—22no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123C23×C4×C61—21no—
124C23×C4×C61—21no—
125C23×C4×C61C2311yescharacteristic
126C22×C8×C61—22no—
127C22×C8×C61—22no—
128C22×C8×C61D414yescomplemented
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C2×C4⋊C4×C61—22no—
132C2×C4⋊C4×C61—22no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—41no—
136C2×C4⋊C4×C61—41no—
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141#107×C61—22no—
142#107×C61—22no—
143#107×C61—22no—
144#107×C61D414yescomplemented
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—42no—
157C22×C4×C61—42no—
158C22×C4×C61—42no—
159C22×C4×C61—42no—
160C22×C4×C61—81no—
161C22×C4×C61—81no—
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D412yes—
164C22×C4×C61#4112yes—
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—42no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—42no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—42no—
185C2×D244—42no—
186C2×D244—81no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—28no—
202C2×C8×C61C2×D412yes—
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—42no—
213C4⋊C4×C61—42no—
214C4⋊C4×C61C2×D412yes—
215C4⋊C4×C61C2×D412yes—
216C22⋊Dic61—22no—
217C22⋊Dic61—42no—
218#11758198—22no—
219#11758198—42no—
220#11758198—42no—
221#11758198—42no—
222#11758198—42no—
223#11758198—42no—
224#11758198—81no—
225#11758198—81no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—42no—
231C4⋊Dic61—42no—
232C4⋊Dic61—81no—
233#11758196—22no—
234#11758196—42no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243#11758190—44no—
244#11758189—44no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61#12112yes—
250C23×C61AGL(1,ℤ/8)12yes—
251C23×C61#13712yes—
252C23×C61C22×D411yescharacteristic
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
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—84no—
286C2×C4×C61—84no—
287C2×C4×C61#12112yes—
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C2×C4×C612−1+411yescharacteristic
294C22⋊D61—44no—
295C22⋊D61—84no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
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—41no—
314D244—41no—
315D244—41no—
316D244—41no—
317D244—41no—
318D244—84no—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—41no—
323Dic122—41no—
324Dic122—41no—
325Dic122—41no—
326Dic122—41no—
327C8×C61—22no—
328C8×C61#12114yescomplemented
329#92418—41no—
330#92418—41no—
331#24787—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61#46814yescomplemented
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—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—81no—
354C2×D61—81no—
355C2×D61—81no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C4×C61—22no—
361C4×C61—42no—
362C4×C61—42no—
363C4×C61—81no—
364C4×C61—81no—
365C4×C61C2×#12111yescharacteristic
366C4×C61#53711yescharacteristic
367C4×C61#54811yescharacteristic
368C4×C61#55311yescharacteristic
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372Dic61—81no—
373Dic61—81no—
374Dic61—81no—
375C2×#468—611no—
376C2×#465—611no—
377C2×#435—611no—
378C22×#107D6111yescharacteristic, complemented
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#1809—611no—
390C2×C61—24no—
391C2×C61#241611yescharacteristic
392C2×C61C2×#46811yescharacteristic
393C2×C61#306111yescharacteristic
394C2×C61#326411yescharacteristic
395C2×C61#327011yescharacteristic
396C2×C61#334311yescharacteristic
397C2×C61#334611yescharacteristic
398D61—81no—
399D61—161no—
400C22×SD16—611no—
401C22×M16—611no—
402C23×C8C2×D6111yescharacteristic
403C2×C22⋊Q8—611no—
404C2×C22⋊Q8—611no—
405C2×#121—611no—
406C2×#121—611no—
407C2×#121—1221no—
408C2×C4×D4—611no—
409C22×C4⋊C4C2×D6111yescharacteristic
410C22×C4⋊C4C2×D6111yescharacteristic
411#468—1224no—
412#465—1224no—
413#435—1224no—
414C2×#107—24no—
415C2×#107C2×D6111yescharacteristic
416C2×#107C2×D6111yescharacteristic
417C2×#107C2×D6111yescharacteristic
418C2×#107C2×D6111yescharacteristic
419C2×#106—611no—
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—611no—
441#380—611no—
442#380—1221no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447C61#2478711yescharacteristic, complemented, Sylow
448C22×Q8—611no—
449C22×D4—611no—
450C22×D4—611no—
451C22×D4—1221no—
452C22×D4—1221no—
453C23×C4—21no—
454C23×C4—21no—
455C23×C4—611no—
456C23×C4C22×D6111yescharacteristic
457C2×SD16—1222no—
458C2×SD16—1222no—
459C2×SD16—1222no—
460C2×M16—1222no—
461C2×M16—1222no—
462C2×M16—1222no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8D24414yescomplemented
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—2441no—
478#121—2444no—
479C4×D4—1222no—
480C4×D4—1222no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4—41no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4C22×D6111yescharacteristic
495C2×C4⋊C4C22×D6111yescharacteristic
496C2×C4⋊C4C22×D6111yescharacteristic
497C2×C4⋊C4C22×D6111yescharacteristic
498C2×C22⋊C4—611no—
499C2×C22⋊C4—611no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
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—22no—
511#107—22no—
512#107C22⋊D6114yescomplemented
513#106—1222no—
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—1221no—
525#95—1221no—
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—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—81no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4C2×D24412yes—
581C22×C4D4×D6111yescharacteristic
582C22×C4#1175822612yes—
583C22×C4C23×D6111yescharacteristic
584SD16—2444no—
585M16—2444no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—28no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8C2×D24412yes—
596C2×C8C2×D24412yes—
597C2×C8#1175822212yes—
598C2×C8C2×C22⋊D6112yes—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—1222no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—4881no—
613C4⋊C4—2442no—
614C4⋊C4—2442no—
615C4⋊C4—2442no—
616C4⋊C4C2×C22⋊D6112yes—
617C4⋊C4C2×C22⋊D6112yes—
618C22⋊C4—1222no—
619C22⋊C4—1222no—
620C22⋊C4—4881no—
621C22⋊C4—4881no—
622C22⋊C4—2442no—
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—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23#1451975212yes—
649C23#1451980112yes—
650C23#1451980912yes—
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—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
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—84no—
682C2×C4—84no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4#1451975212yes—
706C2×C4C22×C22⋊D6111yescharacteristic
707C2×C4C22×D24411yescharacteristic
708C2×C4C2×#1175822211yescharacteristic
709C2×C4C2×#1175822611yescharacteristic
710C2×C4#1451982211yescharacteristic
711C2×C4#1451982511yescharacteristic
712C8—22no—
713C8—2441no—
714C8—2441no—
715C8#1451975114yescomplemented
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—4881no—
723C22—4881no—
724C22—4881no—
725C22—4881no—
726C22—4881no—
727C22—4881no—
728C22—4881no—
729C22—2441no—
730C22—2441no—
731C22—2441no—
732C22—2441no—
733C22—2441no—
734C22—2441no—
735C22—2441no—
736C22#1684000914yescomplemented
737C22C2×#1451975211yescharacteristic
738C22D4×C22⋊D6111yescharacteristic
739C22#1684041311yescharacteristic
740C22C2×#1451980111yescharacteristic
741C22C2×#1451980911yescharacteristic
742C22#1684056311yescharacteristic
743C22#1684057511yescharacteristic
744C4—22no—
745C4—42no—
746C4—42no—
747C4—81no—
748C4—81no—
749C4—4881no—
750C4—4881no—
751C4—4881no—
752C4—2441no—
753C4—2441no—
754C4—2441no—
755C4C2×#1451975111yescharacteristic
756C4#1684034311yescharacteristic
757C4#1684042311yescharacteristic
758C4#1684046011yescharacteristic
759C2—24no—
760C2—9761no—
761C2—4881no—
762C2#2144925311yescharacteristic
763C2C2×#1684000911yescharacteristic
764C2#2145549111yescharacteristic
765C2#2145729911yescharacteristic
766C2#2145738911yescharacteristic
767C2#2145825511yescharacteristic
768C2#2145830011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#107×C61C2
socleC23×C61C22×D4
prime radical#21449253C2
hypercenterC22×#107D61
hypocenterC61#24787
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
1. C2×#16840009C2semidirect
2. C2×#16839991C2semidirect
3. C2×#16839833C2semidirect
4. #21449264C2semidirect
6. #21447209C2semidirect
7. #21447202C2semidirect
8. #21447024C2semidirect
9. #21447003C2semidirect
10. #21446698C2semidirect
11. #21446558C2semidirect
12. #21446136C2semidirect
13. #21446126C2semidirect
14. #21445853C2semidirect
15. C22×#107×C61C2semidirect
128. C22×C8×C61D4semidirect
144. #107×C61D4semidirect
328. C8×C61#121semidirect
338. C22×C61#468semidirect
378. C22×#107D61semidirect
447. C61#24787semidirect
467. C22×C8D244semidirect
512. #107C22⋊D61semidirect
715. C8#14519751semidirect
736. C22#16840009semidirect

Maximal subgroups

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

subgroupindex
C2×#168400092
C2×#168399912
C2×#168398332
#214492642
#214492532
#214472092
#214472022
#214470242
#214470032
#214466982
#214465582
#214461362
#214461262
#214458532
C22×#107×C612
#2478761