Finite Group Databasebeta

← #29700482

Subgroups — #29700482

Order 15616.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839897C211yesmaximal, characteristic
2C2×#16839871C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4#21448859C211yesmaximal, characteristic, complemented
5D4×#11758198C211yesmaximal, characteristic, complemented
6#21446685C211yesmaximal, characteristic, complemented
7#21446517C211yesmaximal, characteristic, complemented
8#21446446C211yesmaximal, characteristic, complemented
9#21446256C211yesmaximal, characteristic, complemented
10#21446168C211yesmaximal, characteristic, complemented
11#21446167C211yesmaximal, characteristic, complemented
12#21446068C211yesmaximal, characteristic, complemented
13#21446021C211yesmaximal, characteristic, complemented
14#21445602C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×D488C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C2×#14519752C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic
22C2×#14519739C2211yescharacteristic, complemented
23C2×#14519735C2211yescharacteristic
24C22×#11758198—21no—
25#16839897C418yescomplemented
26#16839871—24no—
27C2×#14519711C2211yescharacteristic, complemented
28C2×#14519708C2211yescharacteristic, complemented
29#16839765—24no—
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic, complemented
32C2×#14519698C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic, complemented
36C2×#14519689C2211yescharacteristic
37C2×#14519687C2211yescharacteristic, complemented
38#16839664—21no—
39#16839664C2211yescharacteristic
40#16839664C2211yescharacteristic, complemented
41#16839663C2211yescharacteristic
42#16839661C2211yescharacteristic, complemented
43#16839654—21no—
44#16839641—21no—
45#16839640—21no—
46#16839639—21no—
47#16839619C2211yescharacteristic
48#16839617—21no—
49C4×#11758198—21no—
50C4×#11758198C2211yescharacteristic
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839517C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55C2×C4×D4×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×C4×C8×C61C2211yescharacteristic, complemented
59C4×C4⋊C4×C61C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×D244—21no—
64C22×D244C2311yescharacteristic
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61—41no—
71C2×D4×D61—41no—
72C2×D4×D61C2×C414yescomplemented
73C23×Dic61—21no—
74C22×C4×D61—21no—
75C22×C4×D61C2311yescharacteristic
76C2×D488—41no—
77C2×D488—41no—
78C2×D488C2×C414yescomplemented
79C2×#11758199—22no—
80C2×#11758199—22no—
81C2×#11758199C2×C414yes—
82C2×#11758189—22no—
83C2×#11758189—22no—
84C2×#11758189—41no—
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87#14519752—22no—
88#14519752C2×C414yescomplemented
89D4×Dic61—22no—
90D4×Dic61—41no—
91#14519739—22no—
92#14519739—41no—
93#14519735—22no—
94#14519735—41no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C22⋊Dic61—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—44no—
110C2×#11758198D411yescharacteristic
111C2×#11758198D411yescharacteristic
112C2×C4×Dic61—21no—
113C2×C4×Dic61C2311yescharacteristic
114#14519711—41no—
115#14519708—22no—
116#14519699—22no—
117#14519699—22no—
118#14519698—22no—
119#14519697—22no—
120#14519697—41no—
121#14519697C2×C414yescomplemented
122#14519689C2×C414yescomplemented
123#14519687—22no—
124#14519684—21no—
125#14519684—21no—
126#14519684D411yescharacteristic
127#14519684D411yescharacteristic
128C22×D4×C61C2311yescharacteristic
129C23×C4×C61—21no—
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C4×D4×C61—22no—
133C4×D4×C61—41no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C42×C61—21no—
139C2×C42×C61C2311yescharacteristic
140#102×C61C2×C414yescomplemented
141#102×C61D414yescomplemented
142C4×C8×C61—41no—
143#95×C61—21no—
144C24×C61—21no—
145C23×D61—21no—
146C23×D61—21no—
147C23×D61—24no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61—81no—
153C23×D61—81no—
154C23×D61C2×D411yescharacteristic
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61C22×C412yes—
159C2×D4×C61C2×D412yes—
160C2×D4×C61#4112yes—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—42no—
165C22×C4×C61—42no—
166C22×C4×C61—81no—
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2411yescharacteristic
170C2×C22⋊D61—24no—
171C2×C22⋊D61—42no—
172C2×C22⋊D61—42no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—42no—
176C22×Dic61—42no—
177C22×Dic61—81no—
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181D4×D61—28no—
182D4×D61—44no—
183D4×D61—44no—
184D4×D61—44no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—24no—
196C2×D244—81no—
197C2×D244—81no—
198C2×D244C22×C412yes—
199C2×D244C22×C412yes—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—81no—
207C2×C4×D61C22×C412yes—
208C2×C4×D61#4112yes—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61C22×C412yes—
214C2×C8×C61C2×D412yes—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61C22×C412yes—
220C4⋊C4×C61C2×D412yes—
221C22⋊C4×C61—42no—
222C42×C61—21no—
223C42×C61—21no—
224C42×C61—81no—
225C22⋊Dic61—42no—
226#11758199—28no—
227#11758198—22no—
228#11758198—24no—
229#11758198—41no—
230#11758198—42no—
231#11758198—42no—
232#11758198—42no—
233#11758198—42no—
234#11758198—42no—
235#11758198—42no—
236#11758198—81no—
237#11758198—81no—
238#11758198—81no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—81no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—42no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418C22×C412yes—
253D488—44no—
254#11758189—44no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61C22×D411yescharacteristic
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—48no—
272C22×D61—48no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—84no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—84no—
289C22×D61—84no—
290C22×D61C4×D412yes—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—22no—
294D4×C61C4×D414yes—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—84no—
310C2×C4×C61AGL(1,ℤ/8)12yes—
311C2×C4×C61C23×C411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C2×C4×C61H(5,𝔽2)11yescharacteristic
317C22⋊D61—48no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—84no—
333C2×Dic61C4×D412yes—
334D244—22no—
335D244—22no—
336D244—22no—
337D244—22no—
338D244—41no—
339D244—41no—
340D244—41no—
341D244—41no—
342D244—84no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—84no—
348C8×C61—22no—
349C8×C61—22no—
350#92418—22no—
351#92418—41no—
352#22868—611nomaximal, Sylow
353C22×C61—24no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61C2×C4×D411yescharacteristic
361C22×C61D4211yescharacteristic
362C22×C61#54611yescharacteristic
363C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
364C22×C61#57511yescharacteristic
365C22×C61#57611yescharacteristic
366C22×C61#57611yescharacteristic
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—816no—
381C2×D61—81no—
382C2×D61—81no—
383C2×D61—81no—
384C2×D61—81no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C4×C61—22no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61—41no—
393C4×C61—81no—
394C4×C61C2×C4×D411yescharacteristic
395C4×C61#51811yescharacteristic
396C4×C61#54611yescharacteristic
397C4×C61#55111yescharacteristic
398Dic61—22no—
399Dic61—41no—
400Dic61—41no—
401Dic61—81no—
402Dic61—81no—
403C2×#447—611no—
404C2×#442—611no—
405C2×#418—611no—
406#2363—611no—
407D4×C22⋊C4—611no—
408#1970—611no—
409#1936—611no—
410#1926—611no—
411#1895—611no—
412#1879—611no—
413#1879—611no—
414#1862—611no—
415#1854—611no—
416C4×#102D6111yescharacteristic, complemented
417#1753—611no—
418C2×C61—44no—
419C2×C61#235811yescharacteristic
420C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
421C2×C61#294811yescharacteristic
422C2×C61#327311yescharacteristic
423C2×C61#327411yescharacteristic
424C2×C61#331811yescharacteristic
425C2×C61#331911yescharacteristic
426D61—42no—
427D61—82no—
428D61—82no—
429C23×D4—611no—
430C22×D8—611no—
431C22×D8—611no—
432C22×M16—611no—
433C2×#121—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4C2×D6111yescharacteristic
437C2×#117—611no—
438C22×C22⋊C4—1221no—
439#447—618no—
440#442—1224no—
441C2×#107—611no—
442C2×#106—611no—
443#418—1224no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102C2×D6111yescharacteristic
451C2×#102C2×D6111yescharacteristic
452C2×C22⋊C8—611no—
453C2×#97—611no—
454C2×C4×C8C2×D6111yescharacteristic, complemented
455#390—611no—
456#390—611no—
457#390—611no—
458#390—1221no—
459#389—611no—
460#388—1221no—
461#386—1221no—
462#386—1221no—
463#386—1221no—
464#380—611no—
465#379—1221no—
466C4×C4⋊C4C2×D6111yescharacteristic, complemented
467C4×C22⋊C4—611no—
468C4×C22⋊C4—1221no—
469#340—611no—
470#340—611no—
471#340C2×D6111yescharacteristic, complemented
472#340C2×D6111yescharacteristic, complemented
473#336—611no—
474#336—611no—
475C61#2286811yescharacteristic, complemented, Sylow
476C25—1221no—
477C22×D4—614no—
478C22×D4—611no—
479C22×D4—611no—
480C22×D4—1221no—
481C22×D4—1222no—
482C22×D4—1221no—
483C22×D4—1222no—
484C22×D4—1222no—
485C22×D4—2441no—
486C22×D4—2441no—
487C22×D4C22×D6111yescharacteristic
488C23×C4—21no—
489C23×C4—611no—
490C23×C4—1221no—
491C23×C4—1221no—
492C2×D8—614no—
493C2×D8—614no—
494C2×D8—1222no—
495C2×D8—1222no—
496C2×D8—2441no—
497C2×D8—2441no—
498C2×M16—1222no—
499C2×M16—1222no—
500C2×M16—2441no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8C22×D6111yescharacteristic
504C22×C8C22×D6111yescharacteristic
505#121—614no—
506#121—1222no—
507C4×D4—22no—
508C4×D4—41no—
509C4×D4—1222no—
510C4×D4—1222no—
511C4×D4—2441no—
512C4×D4—2441no—
513#117—1222no—
514#117—2441no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—2444no—
536C2×C42—21no—
537C2×C42—611no—
538C2×C42—1221no—
539C2×C42C22×D6111yescharacteristic
540#107—2441no—
541#106—1222no—
542#102—614no—
543#102—1222no—
544#102—1222no—
545#102—1222no—
546#102—1222no—
547#102—2441no—
548#102C4×D6114yescomplemented
549#102D24414yescomplemented
550C22⋊C8—614no—
551#97—1222no—
552C4×C8—41no—
553#95—21no—
554#95—611no—
555#95—611no—
556#95—1221no—
557#95—1221no—
558C24—21no—
559C24—611no—
560C24—1224no—
561C24—1221no—
562C24—1221no—
563C24—4881no—
564C24—4881no—
565C24—2442no—
566C24—2442no—
567C24—2442no—
568C24—2442no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—612no—
573C2×D4—612no—
574C2×D4—1224no—
575C2×D4—1224no—
576C2×D4—1228no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—4881no—
588C2×D4—4881no—
589C2×D4—2444no—
590C2×D4—2444no—
591C2×D4—2444no—
592C2×D4—2442no—
593C2×D4—2442no—
594C2×D4C2×C4×D6112yes—
595C2×D4C2×D24412yes—
596C2×D4#1175822212yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—81no—
603C22×C4—611no—
604C22×C4—612no—
605C22×C4—612no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—4881no—
615C22×C4—4881no—
616C22×C4—2442no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4—2442no—
620C22×C4D4×D6111yescharacteristic
621C22×C4D4×D6111yescharacteristic
622C22×C4C23×D6111yescharacteristic
623D8—1228no—
624D8—2444no—
625M16—2444no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—612no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8C2×C4×D6112yes—
637C2×C8C2×D24412yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—4881no—
647C4⋊C4C2×C4×D6112yes—
648C4⋊C4C2×D24412yes—
649C22⋊C4—42no—
650C22⋊C4—1224no—
651C22⋊C4—1222no—
652C22⋊C4—4881no—
653C22⋊C4—4881no—
654C22⋊C4—4881no—
655C22⋊C4—2441no—
656C22⋊C4—2442no—
657C22⋊C4—2442no—
658C22⋊C4—2442no—
659C22⋊C4—2442no—
660C22⋊C4—2442no—
661C22⋊C4—2442no—
662C22⋊C4—2442no—
663C42—21no—
664C42—21no—
665C42—81no—
666C42—1221no—
667C42—1221no—
668C42—2442no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—612no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23—1221no—
683C23—1222no—
684C23—1222no—
685C23—4884no—
686C23—4884no—
687C23—4884no—
688C23—4884no—
689C23—4884no—
690C23—2448no—
691C23—2448no—
692C23—2441no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23—2441no—
704C23C2×D4×D6111yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—1222no—
709D4—1222no—
710D4—1222no—
711D4—1222no—
712D4—4884no—
713D4—2448no—
714D4—2441no—
715D4—2441no—
716D4—2441no—
717D4—2441no—
718D4C4×D24414yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—84no—
734C2×C4—612no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—4884no—
748C2×C4—4884no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4#1451980412yes—
756C2×C4C22×C4×D6111yescharacteristic
757C2×C4C22×D24411yescharacteristic
758C2×C4#41×D6111yescharacteristic
759C2×C4C2×#1175822211yescharacteristic
760C2×C4#1451982211yescharacteristic
761C2×C4#1451982311yescharacteristic
762C8—22no—
763C8—22no—
764C8—1222no—
765C8—2441no—
766C22—24no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—1222no—
774C22—1222no—
775C22—1222no—
776C22—48816no—
777C22—4881no—
778C22—4881no—
779C22—4881no—
780C22—4881no—
781C22—4881no—
782C22—4881no—
783C22—4881no—
784C22—4881no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22—2442no—
791C22—2441no—
792C22—2441no—
793C22—2441no—
794C22—2441no—
795C22C4×D4×D6111yescharacteristic
796C22D4×D24411yescharacteristic
797C22#1684040211yescharacteristic
798C22C2×#1451980411yescharacteristic
799C22#1684055911yescharacteristic
800C22#1684056311yescharacteristic
801C22#1684056411yescharacteristic
802C4—22no—
803C4—42no—
804C4—41no—
805C4—42no—
806C4—81no—
807C4—1222no—
808C4—4881no—
809C4—4881no—
810C4—2441no—
811C4—2441no—
812C4C2×C4×D24411yescharacteristic
813C4#1684023411yescharacteristic
814C4#1684040711yescharacteristic
815C4#1684043611yescharacteristic
816C2—44no—
817C2—4882no—
818C2—4882no—
819C2—2442no—
820C2#2144880111yescharacteristic
821C2C4×#1451980411yescharacteristic
822C2#2145466611yescharacteristic
823C2#2145742911yescharacteristic
824C2#2145744011yescharacteristic
825C2#2145795611yescharacteristic
826C2#2145797111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#102×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839897C2
cosocleC22×C4×C61C24
hypercenterC4×#102D61
hypocenterC61#22868
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×#16839871C2semidirect
3. C2×#16839765C2semidirect
4. #21448859C2semidirect
5. D4×#11758198C2semidirect
6. #21446685C2semidirect
7. #21446517C2semidirect
8. #21446446C2semidirect
9. #21446256C2semidirect
10. #21446168C2semidirect
11. #21446167C2semidirect
12. #21446068C2semidirect
13. #21446021C2semidirect
14. #21445602C2semidirect
15. C4×#102×C61C2semidirect
22. C2×#14519739C22semidirect
25. #16839897C4semidirect
27. C2×#14519711C22semidirect
28. C2×#14519708C22semidirect
31. C2×#14519699C22semidirect
35. C2×#14519697C22semidirect
37. C2×#14519687C22semidirect
40. #16839664C22semidirect
42. #16839661C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839517C22semidirect
54. #16839516C22semidirect
58. C2×C4×C8×C61C22semidirect
59. C4×C4⋊C4×C61C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
72. C2×D4×D61C2×C4semidirect
78. C2×D488C2×C4semidirect
88. #14519752C2×C4semidirect
121. #14519697C2×C4semidirect
122. #14519689C2×C4semidirect
140. #102×C61C2×C4semidirect
141. #102×C61D4semidirect
416. C4×#102D61semidirect
454. C2×C4×C8C2×D61semidirect
466. C4×C4⋊C4C2×D61semidirect
471. #340C2×D61semidirect
472. #340C2×D61semidirect
475. C61#22868semidirect
548. #102C4×D61semidirect
549. #102D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168398972
C2×#168398712
C2×#168397652
#214488592
D4×#117581982
#214466852
#214465172
#214464462
#214462562
#214461682
#214461672
#214460682
#214460212
#214456022
C4×#102×C612
#2286861