Finite Group Databasebeta

← #29700507

Subgroups — #29700507

Order 15616.

1398 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839895C211yesmaximal, characteristic
2C2×#16839842C211yesmaximal, characteristic, complemented
3C22×#14519699C211yesmaximal, characteristic, complemented
4#21448839C211yesmaximal, characteristic, complemented
5#21448639C211yesmaximal, characteristic, complemented
6#21446682C211yesmaximal, characteristic, complemented
7#21446503C211yesmaximal, characteristic, complemented
8#21446437C211yesmaximal, characteristic, complemented
9#21446165C211yesmaximal, characteristic, complemented
10#21446164C211yesmaximal, characteristic, complemented
11#21446067C211yesmaximal, characteristic, complemented
12#21446006C211yesmaximal, characteristic, complemented
13#21445633C211yesmaximal, characteristic, complemented
14C8×C22⋊Dic61C211yesmaximal, characteristic, complemented
15C61×#1893C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C2×D4×Dic61—21no—
20C2×D4×Dic61C2211yescharacteristic, complemented
21C2×#14519739C2211yescharacteristic
22C2×#14519739C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24C2×C22⋊C4×D61—21no—
25#16839895C418yescomplemented
26#16839842—24no—
27C2×#14519710C2211yescharacteristic, complemented
28C2×#14519710C2211yescharacteristic, complemented
29C2×#14519699—24no—
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic, complemented
38C2×C8×Dic61C2211yescharacteristic, complemented
39#16839665C2211yescharacteristic, complemented
40#16839663C2211yescharacteristic
41#16839663C2211yescharacteristic
42#16839661C2211yescharacteristic, complemented
43#16839655—21no—
44#16839642—21no—
45#16839640—21no—
46#16839640—21no—
47#16839637—21no—
48#16839617—21no—
49C4⋊C4×Dic61C2211yescharacteristic, complemented
50C4×C22⋊Dic61C2211yescharacteristic
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55C23×C8×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic, complemented
58C2×#102×C61C2211yescharacteristic, complemented
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—21no—
66C22×D244—22no—
67C22×D244—41no—
68C22×D244—41no—
69C22×D244C2×C414yescomplemented
70C22×D244C2311yescharacteristic
71C22×D244C2311yescharacteristic
72C23×Dic61—21no—
73C23×Dic61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C2×#11758199—22no—
77C2×#11758199—22no—
78C2×#11758199—41no—
79C2×#11758199—41no—
80C2×#11758199C2×C414yescomplemented
81C2×#11758199C2×C414yescomplemented
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84D4×Dic61—22no—
85D4×Dic61—41no—
86D4×Dic61—44no—
87#14519739—22no—
88#14519739—22no—
89#14519739—41no—
90#14519739—41no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61—41no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61D411yescharacteristic
101C2×C22⋊Dic61D411yescharacteristic
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C22⋊C4×D61—44no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61C2311yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112#14519710—22no—
113#14519710—41no—
114#14519699—22no—
115#14519699—22no—
116#14519699—22no—
117#14519699D414yescomplemented
118#14519697C2×C414yescomplemented
119#14519697C2×C414yescomplemented
120C22⋊#92418C2×C414yescomplemented
121C8×Dic61—22no—
122C8×Dic61—41no—
123#14519684—21no—
124#14519684—21no—
125#14519684D411yescharacteristic
126#14519684D411yescharacteristic
127C22×D4×C61—21no—
128C22×D4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C22×C8×C61—22no—
131C22×C8×C61—22no—
132C22×C8×C61—41no—
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135#121×C61—22no—
136#121×C61C2×C414yescomplemented
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142#102×C61—22no—
143#102×C61—41no—
144#95×C61—21no—
145C24×C61—21no—
146C24×C61C2×D411yescharacteristic
147C23×D61—21no—
148C23×D61—21no—
149C23×D61—24no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61—42no—
153C23×D61—42no—
154C23×D61—81no—
155C23×D61—81no—
156C2×D4×C61—24no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—42no—
163C2×D4×C61—42no—
164C2×D4×C61C22×C412yes—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61C22×C412yes—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61#4112yes—
175C22×C4×C61C2411yescharacteristic
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—42no—
179C22×Dic61—42no—
180C22×Dic61—42no—
181C22×Dic61—42no—
182C22×Dic61—81no—
183C22×Dic61—81no—
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—28no—
196C2×D244—24no—
197C2×D244—21no—
198C2×D244—44no—
199C2×D244—44no—
200C2×D244—44no—
201C2×D244—42no—
202C2×D244—42no—
203C2×D244C22×C412yes—
204C2×D244C22×C412yes—
205C2×D244C2×D412yes—
206C2×D244#4112yes—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61—81no—
212C2×C4×D61—81no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—44no—
219C2×C8×C61C2×D412yes—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61C22×C412yes—
226C22⋊C4×C61—24no—
227C22⋊C4×C61—42no—
228C22⋊Dic61—22no—
229C22⋊Dic61—42no—
230C22⋊Dic61—42no—
231C22⋊Dic61—81no—
232C22⋊Dic61D814yescomplemented
233#11758199—28no—
234#11758199—44no—
235#11758198—42no—
236#11758198—42no—
237#11758198—42no—
238#11758198—42no—
239#11758198—81no—
240#11758198—81no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—42no—
245C4⋊Dic61—42no—
246C4⋊Dic61C2×D412yes—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61—42no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418C22×C412yes—
257C2×#92418C22×C412yes—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—22no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61C4×D412yes—
270C23×C61C2×D812yes—
271C23×C61#13512yes—
272C23×C61C22×D411yescharacteristic
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—48no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—48no—
289C22×D61—84no—
290C22×D61—84no—
291C22×D61—84no—
292C22×D61—84no—
293C22×D61—84no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—48no—
297D4×C61—41no—
298D4×C61—41no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61C4×D412yes—
315C2×C4×C61C23×C411yescharacteristic
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61H(5,𝔽2)11yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—22no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—84no—
338C2×Dic61—84no—
339C2×Dic61C2×D812yes—
340C2×Dic61C2×D812yes—
341D244—22no—
342D244—22no—
343D244—22no—
344D244—22no—
345D244—22no—
346D244—48no—
347D244—41no—
348D244—41no—
349D244C4×D414yescomplemented
350C4×D61—84no—
351C4×D61—84no—
352C8×C61—22no—
353C8×C61—41no—
354#92418—22no—
355#92418—22no—
356#22870—611nomaximal, Sylow
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—22no—
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61C4×D814yescomplemented
371C22×C61C2×C4×D411yescharacteristic
372C22×C61D4211yescharacteristic
373C22×C61#54611yescharacteristic
374C22×C61C22×D811yescharacteristic
375C22×C61C2×#13511yescharacteristic
376C22×C61#57611yescharacteristic
377C22×C61#57711yescharacteristic
378C2×D61—24no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—816no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61—81no—
392C2×D61—81no—
393C4×C61—22no—
394C4×C61—42no—
395C4×C61—81no—
396C4×C61—81no—
397C4×C61C2×C4×D411yescharacteristic
398C4×C61#51811yescharacteristic
399C4×C61#54611yescharacteristic
400C4×C61#55111yescharacteristic
401Dic61—22no—
402Dic61—22no—
403Dic61—42no—
404Dic61—41no—
405Dic61—41no—
406Dic61—81no—
407C2×#447—611no—
408C2×C4×D8—611no—
409C22×#102—611no—
410#2361—611no—
411D4×C22⋊C4—611no—
412#1970—611no—
413#1934—611no—
414#1925—611no—
415#1893D6111yescharacteristic, complemented
416#1879—611no—
417#1879—611no—
418#1862—611no—
419#1852—611no—
420C4×#102—611no—
421C8×C22⋊C4—611no—
422C2×C61—24no—
423C2×C61—82no—
424C2×C61#235811yescharacteristic
425C2×C61C2×C4×D811yescharacteristic
426C2×C61#294611yescharacteristic
427C2×C61D4×D811yescharacteristic
428C2×C61#328211yescharacteristic
429C2×C61#329411yescharacteristic
430C2×C61#329711yescharacteristic
431D61—44no—
432D61—82no—
433C23×D4—611no—
434C22×D8—611no—
435C22×D8—611no—
436C23×C8C2×D6111yescharacteristic
437C2×#121C2×D6111yescharacteristic
438C2×C4×D4—611no—
439C2×C4×D4—611no—
440C2×C4×D4—611no—
441C2×C4×D4—1221no—
442C22×C4⋊C4—611no—
443C22×C22⋊C4—1221no—
444#447—618no—
445C4×D8—1224no—
446C2×#107—611no—
447C2×#107—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—1224no—
455C2×#102C2×D6111yescharacteristic, complemented
456C2×#102C2×D6111yescharacteristic, complemented
457C2×C22⋊C8—611no—
458C2×C4×C8—611no—
459C2×C4×C8—611no—
460#390—611no—
461#390—611no—
462#390—611no—
463#389—611no—
464#388—1221no—
465#386—1221no—
466#386—1221no—
467#386—1221no—
468#385—1221no—
469#380C2×D6111yescharacteristic
470#379—1221no—
471C4×C4⋊C4—611no—
472C4×C22⋊C4—611no—
473#340—611no—
474#340—611no—
475#340C2×D6111yescharacteristic, complemented
476#340C2×D6111yescharacteristic, complemented
477#336—611no—
478#336—611no—
479C61#2287011yescharacteristic, complemented, Sylow
480C25—1221no—
481C22×D4—21no—
482C22×D4—614no—
483C22×D4—611no—
484C22×D4—611no—
485C22×D4—1222no—
486C22×D4—1222no—
487C22×D4—1221no—
488C22×D4—1222no—
489C22×D4—2441no—
490C22×D4—2441no—
491C22×D4C22×D6111yescharacteristic
492C23×C4—1221no—
493C23×C4—1221no—
494C23×C4—1221no—
495C23×C4—1221no—
496C23×C4C22×D6111yescharacteristic
497C2×D8—614no—
498C2×D8—614no—
499C2×D8—1222no—
500C2×D8—1222no—
501C2×D8—2441no—
502C2×D8—2441no—
503C22×C8—22no—
504C22×C8—22no—
505C22×C8—41no—
506C22×C8—611no—
507C22×C8—611no—
508C22×C8C22×D6111yescharacteristic
509C22×C8C22×D6111yescharacteristic
510#121—22no—
511#121C4×D6114yescomplemented
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1222no—
515C4×D4—2441no—
516C4×D4—2441no—
517C4×D4—2441no—
518C4×D4—2444no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—1222no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—2441no—
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—2444no—
542C2×C42—611no—
543C2×C42—611no—
544C2×C42—1221no—
545#107—1222no—
546#107—2441no—
547#102—22no—
548#102—41no—
549#102—614no—
550#102—614no—
551#102—614no—
552#102—1222no—
553#102—1222no—
554#102—1222no—
555C22⋊C8—614no—
556C4×C8—1222no—
557C4×C8—2441no—
558#95—21no—
559#95—611no—
560#95—611no—
561#95—1221no—
562#95—1221no—
563C24—21no—
564C24—1221no—
565C24—1224no—
566C24—1221no—
567C24—4881no—
568C24—4881no—
569C24—2442no—
570C24—2442no—
571C24—2442no—
572C24—2442no—
573C24D4×D6111yescharacteristic
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—612no—
583C2×D4—612no—
584C2×D4—612no—
585C2×D4—612no—
586C2×D4—1228no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—1224no—
596C2×D4—2444no—
597C2×D4—2444no—
598C2×D4—2444no—
599C2×D4—2442no—
600C2×D4—2442no—
601C2×D4C2×C4×D6112yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—4881no—
616C22×C4—4881no—
617C22×C4—4881no—
618C22×C4—4881no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4C2×C4×D6112yes—
628C22×C4D4×D6111yescharacteristic
629C22×C4#1175822412yes—
630C22×C4C23×D6111yescharacteristic
631D8—1228no—
632D8—2444no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—44no—
639C2×C8—612no—
640C2×C8—612no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8D4×D6112yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—612no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—2442no—
656C4⋊C4—2442no—
657C4⋊C4C2×C4×D6112yes—
658C22⋊C4—24no—
659C22⋊C4—42no—
660C22⋊C4—614no—
661C22⋊C4—1222no—
662C22⋊C4—4881no—
663C22⋊C4—4881no—
664C22⋊C4—4881no—
665C22⋊C4—2442no—
666C22⋊C4—2442no—
667C22⋊C4—2442no—
668C22⋊C4—2442no—
669C22⋊C4—2442no—
670C22⋊C4—2442no—
671C42—1221no—
672C42—1221no—
673C42—1221no—
674C42—1221no—
675C42—2442no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—1222no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—4884no—
692C23—4884no—
693C23—4884no—
694C23—4884no—
695C23—4884no—
696C23—2448no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2448no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23#1451973712yes—
709C23D8×D6112yes—
710C23#1451979812yes—
711C23C2×D4×D6111yescharacteristic
712D4—22no—
713D4—22no—
714D4—48no—
715D4—41no—
716D4—41no—
717D4—614no—
718D4—1222no—
719D4—1222no—
720D4—1222no—
721D4—1222no—
722D4—1222no—
723D4—2448no—
724D4—2441no—
725D4—2441no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—612no—
742C2×C4—612no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1222no—
753C2×C4—1221no—
754C2×C4—4884no—
755C2×C4—4884no—
756C2×C4—4884no—
757C2×C4—4884no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4#1451973712yes—
764C2×C4C22×C4×D6111yescharacteristic
765C2×C4C2×D4×D6111yescharacteristic
766C2×C4#41×D6111yescharacteristic
767C2×C4C2×#1175822411yescharacteristic
768C2×C4#1451982211yescharacteristic
769C2×C4#1451982311yescharacteristic
770C8—22no—
771C8—41no—
772C8—1222no—
773C8—1222no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—1224no—
788C22—48816no—
789C22—4881no—
790C22—4881no—
791C22—4881no—
792C22—4881no—
793C22—2442no—
794C22—2442no—
795C22—2442no—
796C22—2442no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22#1683984214yescomplemented
803C22C2×#1451973711yescharacteristic
804C22#1684039611yescharacteristic
805C22#1684040111yescharacteristic
806C22C2×D8×D6111yescharacteristic
807C22C2×#1451979811yescharacteristic
808C22#1684056411yescharacteristic
809C22#1684056911yescharacteristic
810C4—22no—
811C4—42no—
812C4—81no—
813C4—81no—
814C4—1222no—
815C4—1222no—
816C4—4881no—
817C4—2441no—
818C4—2442no—
819C4—2441no—
820C4C4×D4×D6111yescharacteristic
821C4#1684023411yescharacteristic
822C4#1684039911yescharacteristic
823C4#1684043511yescharacteristic
824C2—24no—
825C2—82no—
826C2—4882no—
827C2—2444no—
828C2#2144879911yescharacteristic
829C2C2×#1683984211yescharacteristic
830C2#2145465411yescharacteristic
831C2#2145749311yescharacteristic
832C2#2145752311yescharacteristic
833C2#2145762711yescharacteristic
834C2#2145767511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1893C2
socleC23×C61C22×D4
prime radicalC2×#16839895C2
cosocleC22×C4×C61C24
hypercenter#1893D61
hypocenterC61#22870
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#16839842C2semidirect
3. C22×#14519699C2semidirect
4. #21448839C2semidirect
5. #21448639C2semidirect
6. #21446682C2semidirect
7. #21446503C2semidirect
8. #21446437C2semidirect
9. #21446165C2semidirect
10. #21446164C2semidirect
11. #21446067C2semidirect
12. #21446006C2semidirect
13. #21445633C2semidirect
14. C8×C22⋊Dic61C2semidirect
15. C61×#1893C2semidirect
20. C2×D4×Dic61C22semidirect
25. #16839895C4semidirect
27. C2×#14519710C22semidirect
28. C2×#14519710C22semidirect
37. C2×C8×Dic61C22semidirect
38. C2×C8×Dic61C22semidirect
39. #16839665C22semidirect
42. #16839661C22semidirect
49. C4⋊C4×Dic61C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839516C22semidirect
54. #16839516C22semidirect
57. C2×#102×C61C22semidirect
58. C2×#102×C61C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
69. C22×D244C2×C4semidirect
80. C2×#11758199C2×C4semidirect
81. C2×#11758199C2×C4semidirect
117. #14519699D4semidirect
118. #14519697C2×C4semidirect
119. #14519697C2×C4semidirect
120. C22⋊#92418C2×C4semidirect
136. #121×C61C2×C4semidirect
232. C22⋊Dic61D8semidirect
349. D244C4×D4semidirect
370. C22×C61C4×D8semidirect
415. #1893D61semidirect
455. C2×#102C2×D61semidirect
456. C2×#102C2×D61semidirect
475. #340C2×D61semidirect
476. #340C2×D61semidirect
479. C61#22870semidirect
511. #121C4×D61semidirect
802. C22#16839842semidirect

Maximal subgroups

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

subgroupindex
C2×#168398952
C2×#168398422
C22×#145196992
#214488392
#214486392
#214466822
#214465032
#214464372
#214461652
#214461642
#214460672
#214460062
#214456332
C8×C22⋊Dic612
C61×#18932
#2287061