Finite Group Databasebeta

← #29722315

Subgroups — #29722315

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×#16839991C211yesmaximal, characteristic, complemented
3C22×#14519711C211yesmaximal, characteristic, complemented
4#21449270C211yesmaximal, characteristic, complemented
5#21449259C211yesmaximal, characteristic
6#21447213C211yesmaximal, characteristic, complemented
7#21447206C211yesmaximal, characteristic, complemented
8#21447023C211yesmaximal, characteristic, complemented
9#21447002C211yesmaximal, characteristic, complemented
10#21446700C211yesmaximal, characteristic, complemented
11#21446557C211yesmaximal, characteristic, complemented
12#21446134C211yesmaximal, characteristic, complemented
13#21446124C211yesmaximal, characteristic, complemented
14#21445852C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519749—21no—
22C22×C4⋊Dic61C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24#16840008—24no—
25#16839991—24no—
26C2×#14519711—24no—
27C2×#14519711C2211yescharacteristic
28C2×#14519711C2211yescharacteristic
29C2×#14519711C2211yescharacteristic
30C2×#14519711C2211yescharacteristic
31C2×#14519709C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38#16839695—21no—
39#16839685—21no—
40#16839684—21no—
41#16839678—21no—
42#16839668C2211yescharacteristic
43#16839664C2211yescharacteristic
44#16839660C2211yescharacteristic
45#16839660C2211yescharacteristic
46#16839642—21no—
47#16839639—21no—
48#16839622C2211yescharacteristic
49#16839622C2211yescharacteristic
50#16839620—21no—
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C23×C8×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C61×#435—24no—
59C2×C4⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×#97×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C22⋊D61—21no—
67C23×Dic61—21no—
68C23×Dic61—21no—
69C2×#11758190—22no—
70C2×#11758190—22no—
71C2×#11758190—22no—
72#14519756—22no—
73#14519756—22no—
74#14519756—22no—
75#14519756—41no—
76#14519751—22no—
77#14519751—22no—
78#14519751—22no—
79#14519751—41no—
80#14519749—44no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61—41no—
86C2×C4⋊Dic61—41no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105#14519711—22no—
106#14519711—22no—
107#14519711—22no—
108#14519711D414yescomplemented
109#14519709—22no—
110#14519702—22no—
111#14519702—22no—
112#14519702—41no—
113#14519699—22no—
114#14519699—22no—
115#14519699—41no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122C22×D4×C61D411yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C2×M16×C61—22no—
126C2×M16×C61—22no—
127C2×M16×C61—22no—
128C22×C8×C61—22no—
129C22×C8×C61—22no—
130C22×C8×C61D414yescomplemented
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C4×D4×C61—22no—
136C4×D4×C61—22no—
137C2×C4⋊C4×C61D411yescharacteristic
138C2×C22⋊C4×C61D411yescharacteristic
139C2×C22⋊C4×C61D411yescharacteristic
140C2×C42×C61C2311yescharacteristic
141C4⋊C8×C61—22no—
142C22⋊C8×C61—22no—
143C22⋊C8×C61—22no—
144#97×C61—22no—
145C24×C61C2×D411yescharacteristic
146C24×C61C2×D411yescharacteristic
147C23×D61—21no—
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61—22no—
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×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D412yes—
166C22×C4×C61#4112yes—
167C22×C4×C61C2411yescharacteristic
168C2×C22⋊D61—42no—
169C2×C22⋊D61—42no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—42no—
172C2×C22⋊D61—42no—
173C2×C22⋊D61—81no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—42no—
182C22×Dic61—42no—
183C22×Dic61—42no—
184C22×Dic61—42no—
185C22×Dic61—81no—
186C22×Dic61—81no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
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—28no—
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×C61C2×D412yes—
210C2×C8×C61C2×D412yes—
211C2×C8×C61C2×D412yes—
212C2×C8×C61#4112yes—
213C4⋊C4×C61—22no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—22no—
216C42×C61—21no—
217C42×C61—21no—
218C22⋊Dic61—42no—
219C22⋊Dic61—42no—
220C22⋊Dic61—42no—
221C22⋊Dic61—81no—
222#11758198—42no—
223#11758198—42no—
224#11758198—42no—
225#11758198—81no—
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⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—42no—
237C4⋊Dic61—42no—
238C4⋊Dic61C2×D412yes—
239C4⋊Dic61C2×D412yes—
240#11758196—42no—
241#11758196—42no—
242#11758196—42no—
243#11758196—81no—
244#11758190—44no—
245C23×C61—21no—
246C23×C61—21no—
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#12112yes—
257C23×C61AGL(1,ℤ/8)12yes—
258C23×C61#13712yes—
259C23×C61C22×D411yescharacteristic
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267D4×C61—44no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
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—84no—
295C22⋊D61—84no—
296C2×Dic61—22no—
297C2×Dic61—22no—
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—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—84no—
318C2×Dic61—84no—
319D244—41no—
320D244—41no—
321D244—41no—
322D244—41no—
323Dic122—41no—
324Dic122—41no—
325Dic122—41no—
326Dic122—41no—
327C8×C61—22no—
328C8×C61—41no—
329C8×C61—41no—
330C8×C61#12114yescomplemented
331#24787—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61#46814yescomplemented
346C22×C61C2×#12111yescharacteristic
347C22×C61D4211yescharacteristic
348C22×C61#54711yescharacteristic
349C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C61C2×#13711yescharacteristic
351C22×C61#57611yescharacteristic
352C22×C61#57811yescharacteristic
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—41no—
362C4×C61—41no—
363C4×C61—41no—
364C4×C61C2×#12111yescharacteristic
365C4×C61#53711yescharacteristic
366C4×C61#54811yescharacteristic
367C4×C61#55311yescharacteristic
368Dic61—42no—
369Dic61—42no—
370Dic61—81no—
371Dic61—81no—
372Dic61—81no—
373Dic61—81no—
374Dic61—81no—
375C2×#468—611no—
376C2×#465—611no—
377C2×#435D6111yescharacteristic, complemented
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#1809—611no—
390C2×C61—24no—
391C2×C61—81no—
392C2×C61#241611yescharacteristic
393C2×C61C2×#46811yescharacteristic
394C2×C61#306111yescharacteristic
395C2×C61#326411yescharacteristic
396C2×C61#327011yescharacteristic
397C2×C61#334311yescharacteristic
398C2×C61#334611yescharacteristic
399D61—161no—
400C22×SD16—611no—
401C22×M16C2×D6111yescharacteristic
402C23×C8C2×D6111yescharacteristic
403C2×C22⋊Q8—611no—
404C2×C22⋊Q8—611no—
405C2×#121—611no—
406C2×#121—611no—
407C2×#121—1221no—
408C2×C4×D4C2×D6111yescharacteristic
409C22×C4⋊C4—611no—
410C22×C4⋊C4—611no—
411#468—1224no—
412#465—1224no—
413#435—24no—
414C2×#107—611no—
415C2×#107—611no—
416C2×#107—611no—
417C2×#107—611no—
418C2×#107—1224no—
419C2×#106—611no—
420C2×C4⋊C8C2×D6111yescharacteristic
421C2×#103—611no—
422C2×#103—611no—
423C2×#103—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#102—611no—
427C2×C22⋊C8C2×D6111yescharacteristic
428C2×C22⋊C8C2×D6111yescharacteristic
429C2×#97C2×D6111yescharacteristic
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—1221no—
451C22×D4—1221no—
452C22×D4D24411yescharacteristic
453C23×C4—1221no—
454C23×C4—1221no—
455C23×C4C22×D6111yescharacteristic
456C23×C4C22×D6111yescharacteristic
457C2×SD16—1222no—
458C2×SD16—1222no—
459C2×SD16—1222no—
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—22no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8C22⋊D6114yescomplemented
466C22×C8C22×D6111yescharacteristic
467C22×C8C22×D6111yescharacteristic
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—22no—
480C4×D4—22no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—1222no—
488C2×C4⋊C4—1222no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—2441no—
496C2×C4⋊C4—2441no—
497C2×C4⋊C4D24411yescharacteristic
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
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⋊C4D24411yescharacteristic
507C2×C22⋊C4D24411yescharacteristic
508C2×C42C22×D6111yescharacteristic
509#107—614no—
510#107—1222no—
511#107—1222no—
512#107—1222no—
513#106—1222no—
514C4⋊C8—22no—
515#103—1222no—
516#103—1222no—
517#103—2441no—
518#102—1222no—
519#102—1222no—
520#102—2441no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523#97—22no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528#95—1221no—
529#95—1221no—
530C24—1221no—
531C24C2×D24411yescharacteristic
532C24C2×D24411yescharacteristic
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×Q8—1221no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
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—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—4881no—
572C22×C4—4881no—
573C22×C4—2442no—
574C22×C4—2442no—
575C22×C4—2442no—
576C22×C4—2442no—
577C22×C4C2×D24411yescharacteristic
578C22×C4C2×D24411yescharacteristic
579C22×C4C2×D24411yescharacteristic
580C22×C4C2×D24411yescharacteristic
581C22×C4#1175822212yes—
582C22×C4C2×C22⋊D6112yes—
583C22×C4C23×D6111yescharacteristic
584SD16—2444no—
585M16—44no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—28no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8D4×D6112yes—
596C2×C8#1175822412yes—
597C2×C8C2×C22⋊D6112yes—
598C2×C8C2×C22⋊D6112yes—
599C4⋊C4—22no—
600C4⋊C4—612no—
601C4⋊C4—612no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
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⋊C4—2442no—
617C4⋊C4—2442no—
618C22⋊C4—22no—
619C22⋊C4—22no—
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—21no—
629C42—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23#1451975112yes—
649C23#1451980512yes—
650C23#1451981012yes—
651C23C22×D24411yescharacteristic
652Q8—2441no—
653Q8—2441no—
654Q8—2441no—
655Q8—2441no—
656D4—44no—
657D4—4884no—
658D4—4884no—
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—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—4884no—
685C2×C4—4884no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
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#1451975112yes—
706C2×C4C2×D4×D6111yescharacteristic
707C2×C4C22×C22⋊D6111yescharacteristic
708C2×C4C2×#1175822411yescharacteristic
709C2×C4C2×#1175822211yescharacteristic
710C2×C4#1451982311yescharacteristic
711C2×C4#1451982411yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8#1451974914yescomplemented
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—4881no—
730C22—4881no—
731C22—4881no—
732C22—4881no—
733C22—4881no—
734C22—4881no—
735C22—4881no—
736C22#1684000814yescomplemented
737C22C2×#1451975111yescharacteristic
738C22D4×D24411yescharacteristic
739C22#1684041611yescharacteristic
740C22C2×#1451980511yescharacteristic
741C22C2×#1451981011yescharacteristic
742C22#1684056711yescharacteristic
743C22#1684057911yescharacteristic
744C4—22no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—4881no—
749C4—4881no—
750C4—4881no—
751C4—4881no—
752C4—4881no—
753C4—2442no—
754C4—2442no—
755C4C2×#1451974911yescharacteristic
756C4#1684034011yescharacteristic
757C4#1684042111yescharacteristic
758C4#1684045811yescharacteristic
759C2—24no—
760C2—81no—
761C2—9761no—
762C2#2144925911yescharacteristic
763C2C2×#1684000811yescharacteristic
764C2#2145548911yescharacteristic
765C2#2145730411yescharacteristic
766C2#2145739411yescharacteristic
767C2#2145826111yescharacteristic
768C2#2145830611yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radical#21449259C2
hypercenterC2×#435D61
hypocenterC61#24787
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16840008C2semidirect
2. C2×#16839991C2semidirect
3. C22×#14519711C2semidirect
4. #21449270C2semidirect
6. #21447213C2semidirect
7. #21447206C2semidirect
8. #21447023C2semidirect
9. #21447002C2semidirect
10. #21446700C2semidirect
11. #21446557C2semidirect
12. #21446134C2semidirect
13. #21446124C2semidirect
14. #21445852C2semidirect
15. C2×C61×#435C2semidirect
108. #14519711D4semidirect
130. C22×C8×C61D4semidirect
330. C8×C61#121semidirect
345. C22×C61#468semidirect
377. C2×#435D61semidirect
447. C61#24787semidirect
465. C22×C8C22⋊D61semidirect
715. C8#14519749semidirect
736. C22#16840008semidirect

Maximal subgroups

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

subgroupindex
C2×#168400082
C2×#168399912
C22×#145197112
#214492702
#214492592
#214472132
#214472062
#214470232
#214470022
#214467002
#214465572
#214461342
#214461242
#214458522
C2×C61×#4352
#2478761