Finite Group Databasebeta

← #29723708

Subgroups — #29723708

Order 15616.

1154 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840084C211yesmaximal, characteristic, complemented
2#21449169C211yesmaximal, characteristic
3#21448769C211yesmaximal, characteristic, complemented
4#21447345C211yesmaximal, characteristic, complemented
5#21447225C211yesmaximal, characteristic, complemented
6#21447007C211yesmaximal, characteristic, complemented
7#21446999C211yesmaximal, characteristic, complemented
8#21446449C211yesmaximal, characteristic, complemented
9#21446448C211yesmaximal, characteristic, complemented
10#21446138C211yesmaximal, characteristic, complemented
11#21446116C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#21445852C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C2×C61×#418C211yesmaximal, characteristic, complemented
16C2×#14519748C2211yescharacteristic
17C2×#14519748C2211yescharacteristic
18C2×#14519746—21no—
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×#14519735C2211yescharacteristic, complemented
21#16840084—24no—
22C2×#14519711C2211yescharacteristic, complemented
23C2×#14519710C2211yescharacteristic, complemented
24C2×#14519709C2211yescharacteristic, complemented
25C2×#14519708C2211yescharacteristic, complemented
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519689C2211yescharacteristic, complemented
32C2×#14519689C2211yescharacteristic, complemented
33#16839676—21no—
34#16839670—21no—
35#16839665C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839662—21no—
38#16839653—21no—
39#16839650—21no—
40#16839631C2211yescharacteristic, complemented
41#16839622C2211yescharacteristic
42#16839622C2211yescharacteristic
43#16839619C2211yescharacteristic, complemented
44#16839618—21no—
45C4⋊C4×Dic61C2211yescharacteristic, complemented
46C4×#11758196—21no—
47#16839525C2211yescharacteristic, complemented
48#16839525C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C23×D4×C61C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C2×#117×C61C2211yescharacteristic
56C61×#418—24no—
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C22×C22⋊D61—21no—
62C22×C22⋊D61—21no—
63C22×C22⋊D61D411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519748—22no—
68#14519748—22no—
69#14519748—41no—
70#14519748—41no—
71#14519746—44no—
72C4×C22⋊D61—22no—
73C4×C22⋊D61—22no—
74#14519735—22no—
75#14519735—41no—
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196D411yescharacteristic
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61D411yescharacteristic
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198D411yescharacteristic
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61C2311yescharacteristic
98#14519711—22no—
99#14519710—41no—
100#14519709—41no—
101#14519708—22no—
102#14519698—22no—
103#14519698—22no—
104#14519698—41no—
105#14519698—41no—
106C22⋊#92418—22no—
107#14519689—22no—
108#14519689—41no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113C25×C61—21no—
114C22×D4×C61—22no—
115C22×D4×C61—22no—
116C22×D4×C61—21no—
117C22×D4×C61—22no—
118C22×D4×C61—22no—
119C22×D4×C61—41no—
120C22×D4×C61—41no—
121C22×D4×C61C2311yescharacteristic
122C22×D4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C2×M16×C61—22no—
125C2×M16×C61—22no—
126C2×M16×C61—41no—
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129#117×C61—22no—
130#117×C61—41no—
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C22⋊C4×C61—21no—
134C2×C42×C61—21no—
135#102×C61—22no—
136#102×C61—22no—
137#102×C61—22no—
138#102×C61D414yescomplemented
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—42no—
142C24×C61—42no—
143C24×C61—42no—
144C24×C61—42no—
145C24×C61—42no—
146C24×C61—81no—
147C24×C61—81no—
148C24×C61C2×D411yescharacteristic
149C23×D61C2×D411yescharacteristic
150C2×D4×C61—28no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—44no—
162C2×D4×C61—44no—
163C2×D4×C61—42no—
164C2×D4×C61—42no—
165C2×D4×C61—44no—
166C2×D4×C61—42no—
167C2×D4×C61C2×D412yes—
168C2×D4×C61#4112yes—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61#4112yes—
177C22×C4×C61#4112yes—
178C22×C4×C61C2411yescharacteristic
179C2×C22⋊D61—22no—
180C2×C22⋊D61—22no—
181C2×C22⋊D61—41no—
182C2×C22⋊D61—42no—
183C2×C22⋊D61—42no—
184C2×C22⋊D61—42no—
185C2×C22⋊D61—42no—
186C2×C22⋊D61—81no—
187C2×C22⋊D61—81no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201M16×C61—44no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61C2×D412yes—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61C2×D412yes—
212C22⋊C4×C61—42no—
213C42×C61—42no—
214C22⋊Dic61—22no—
215C22⋊Dic61—42no—
216C22⋊Dic61—42no—
217C22⋊Dic61—42no—
218C22⋊Dic61—42no—
219C22⋊Dic61—42no—
220C22⋊Dic61—81no—
221C22⋊Dic61—81no—
222C22⋊Dic61—81no—
223#11758198—22no—
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—
234#11758196—22no—
235#11758196—42no—
236#11758196—81no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—42no—
240C4×Dic61—42no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—48no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—84no—
269C23×C61—84no—
270C23×C61—84no—
271C23×C61—84no—
272C23×C61—84no—
273C23×C61—84no—
274C23×C61#12312yes—
275C23×C61C22×D411yescharacteristic
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—22no—
286D4×C61—22no—
287D4×C61—48no—
288D4×C61—41no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61—41no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61#12312yes—
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61C2×#4111yescharacteristic
309C2×C4×C61H(5,𝔽2)11yescharacteristic
310C2×C4×C61H(5,𝔽2)11yescharacteristic
311C22⋊D61—44no—
312C22⋊D61—84no—
313C22⋊D61—84no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61AGL(1,ℤ/8)12yes—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C8×C61—22no—
340C8×C61—41no—
341#92418—41no—
342#92418—41no—
343#24890—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—816no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61C2×#12311yescharacteristic
367C22×C61D4211yescharacteristic
368C22×C61#54611yescharacteristic
369C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C61#57511yescharacteristic
371C22×C61#57611yescharacteristic
372C22×C61#57711yescharacteristic
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C4×C61—22no—
381C4×C61—42no—
382C4×C61—81no—
383C4×C61#52511yescharacteristic
384C4×C61#53811yescharacteristic
385C4×C61#54611yescharacteristic
386C4×C61#55111yescharacteristic
387Dic61—22no—
388Dic61—41no—
389Dic61—41no—
390Dic61—81no—
391Dic61—81no—
392Dic61—81no—
393Dic61—81no—
394C2×#482—611no—
395C2×#418D6111yescharacteristic, complemented
396#2408—611no—
397#2354—611no—
398#2093—611no—
399#2071—611no—
400#2034—611no—
401#2033—611no—
402#1926—611no—
403#1926—611no—
404#1875—611no—
405#1870—611no—
406#1854—611no—
407#1809—611no—
408#1786—611no—
409C2×C61—42no—
410C2×C61—82no—
411C2×C61—82no—
412C2×C61#241811yescharacteristic
413C2×C61#309411yescharacteristic
414C2×C61#309611yescharacteristic
415C2×C61#326711yescharacteristic
416C2×C61#327411yescharacteristic
417C2×C61#331911yescharacteristic
418C2×C61#332411yescharacteristic
419D61—81no—
420C23×D4C2×D6111yescharacteristic
421C22×M16C2×D6111yescharacteristic
422C2×#121—611no—
423C2×#121—611no—
424C2×#120—1221no—
425C2×C4×D4—611no—
426C2×#117—611no—
427C2×#117C2×D6111yescharacteristic
428#482—1224no—
429C2×#107—611no—
430C2×#107—611no—
431C2×#106—611no—
432C2×#106—611no—
433#418—24no—
434C2×#102—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102C2×D6111yescharacteristic
439C2×#102C2×D6111yescharacteristic
440C2×#102C2×D6111yescharacteristic
441C2×#102C2×D6111yescharacteristic
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445#394—1221no—
446#392—1221no—
447#390—611no—
448#390—611no—
449#390—1221no—
450#388—1221no—
451#388—1221no—
452#384—611no—
453#380—611no—
454#380—611no—
455#380—611no—
456#379—1221no—
457C4×C4⋊C4—611no—
458C4×C4⋊C4—1221no—
459#340—611no—
460#340—611no—
461#340—611no—
462#340—611no—
463#336—611no—
464#336—611no—
465C61#2489011yescharacteristic, complemented, Sylow
466C25—21no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—22no—
472C22×D4—41no—
473C22×D4—41no—
474C22×D4—611no—
475C22×D4—1221no—
476C22×D4—1221no—
477C22×D4C22×D6111yescharacteristic
478C22×D4C22×D6111yescharacteristic
479C23×C4—611no—
480C23×C4C22×D6111yescharacteristic
481C2×M16—22no—
482C2×M16—22no—
483C2×M16—41no—
484C22×C8—611no—
485C22×C8—611no—
486C22×C8C22×D6111yescharacteristic
487C22×C8C22×D6111yescharacteristic
488#121—1222no—
489#121—1222no—
490#121—2441no—
491#121—2441no—
492#120—2444no—
493C4×D4—1222no—
494C4×D4—1222no—
495#117—22no—
496#117—41no—
497#117—1222no—
498#117—2441no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—611no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C42—21no—
522C2×C42—611no—
523C2×C42—1221no—
524C2×C42—1221no—
525#107—1222no—
526#107—2441no—
527#106—1222no—
528#106—2441no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—1222no—
533#102—1222no—
534#102—2441no—
535#102—2441no—
536#102C22⋊D6114yescomplemented
537C22⋊C8—1222no—
538C22⋊C8—1222no—
539C22⋊C8—2441no—
540#95—1221no—
541#95—1221no—
542#95—1221no—
543#95—1221no—
544C24—21no—
545C24—21no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—81no—
552C24—81no—
553C24—611no—
554C24D4×D6111yescharacteristic
555C2×D4—28no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—4881no—
575C2×D4—4881no—
576C2×D4—2441no—
577C2×D4—2442no—
578C2×D4—2442no—
579C2×D4—2442no—
580C2×D4—2442no—
581C2×D4#1175822212yes—
582C2×D4C2×C22⋊D6112yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4#1175822212yes—
603C22×C4D4×D6111yescharacteristic
604C22×C4#1175822412yes—
605C22×C4C23×D6111yescharacteristic
606M16—44no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8C2×C22⋊D6112yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—1222no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—4881no—
632C4⋊C4—2442no—
633C4⋊C4C2×C22⋊D6112yes—
634C22⋊C4—42no—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C22⋊C4—4881no—
638C22⋊C4—4881no—
639C22⋊C4—4881no—
640C22⋊C4—4881no—
641C22⋊C4—2442no—
642C22⋊C4—2442no—
643C22⋊C4—2442no—
644C22⋊C4—2442no—
645C22⋊C4—2442no—
646C22⋊C4—2442no—
647C42—42no—
648C42—1221no—
649C42—1221no—
650C42—2442no—
651C42—2442no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—22no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23—1221no—
683C23—1221no—
684C23—1221no—
685C23—1221no—
686C23#1451975912yes—
687C23C2×D4×D6111yescharacteristic
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—48no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—4884no—
698D4—4884no—
699D4—2444no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—612no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
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×C4—2441no—
736C2×C4—2441no—
737C2×C4#1451975912yes—
738C2×C4C22×C22⋊D6111yescharacteristic
739C2×C4C2×#1175822411yescharacteristic
740C2×C4C2×#1175822211yescharacteristic
741C2×C4C2×#1175822211yescharacteristic
742C2×C4#1451982211yescharacteristic
743C2×C4#1451982211yescharacteristic
744C8—22no—
745C8—41no—
746C8—2441no—
747C8—2441no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—816no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—2441no—
771C22—2441no—
772C22—2441no—
773C22—2441no—
774C22—2441no—
775C22—2441no—
776C22—2441no—
777C22C2×#1451975911yescharacteristic
778C22D4×C22⋊D6111yescharacteristic
779C22#1684040211yescharacteristic
780C22AGL(1,ℤ/8)×D6111yescharacteristic
781C22#1684055811yescharacteristic
782C22#1684056611yescharacteristic
783C22#1684057211yescharacteristic
784C4—22no—
785C4—42no—
786C4—81no—
787C4—1222no—
788C4—4881no—
789C4—4881no—
790C4—4881no—
791C4—4881no—
792C4—2441no—
793C4—2441no—
794C4#1684027311yescharacteristic
795C4#1684035011yescharacteristic
796C4#1684040611yescharacteristic
797C4#1684043811yescharacteristic
798C2—42no—
799C2—82no—
800C2—82no—
801C2—4881no—
802C2#2144928111yescharacteristic
803C2#2145575711yescharacteristic
804C2#2145577511yescharacteristic
805C2#2145733811yescharacteristic
806C2#2145743311yescharacteristic
807C2#2145797611yescharacteristic
808C2#2145804611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#418C2
socleC23×C61C22×D4
prime radical#21449169C2
hypercenterC2×#418D61
hypocenterC61#24890
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. C2×#16840084C2semidirect
3. #21448769C2semidirect
4. #21447345C2semidirect
5. #21447225C2semidirect
6. #21447007C2semidirect
7. #21446999C2semidirect
8. #21446449C2semidirect
9. #21446448C2semidirect
10. #21446138C2semidirect
11. #21446116C2semidirect
12. #21446018C2semidirect
13. #21445852C2semidirect
14. #21445750C2semidirect
15. C2×C61×#418C2semidirect
20. C2×#14519735C22semidirect
22. C2×#14519711C22semidirect
23. C2×#14519710C22semidirect
24. C2×#14519709C22semidirect
25. C2×#14519708C22semidirect
31. C2×#14519689C22semidirect
32. C2×#14519689C22semidirect
40. #16839631C22semidirect
43. #16839619C22semidirect
45. C4⋊C4×Dic61C22semidirect
47. #16839525C22semidirect
48. #16839525C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839516C22semidirect
52. #16839516C22semidirect
138. #102×C61D4semidirect
395. C2×#418D61semidirect
465. C61#24890semidirect
536. #102C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400842
#214491692
#214487692
#214473452
#214472252
#214470072
#214469992
#214464492
#214464482
#214461382
#214461162
#214460182
#214458522
#214457502
C2×C61×#4182
#2489061