Finite Group Databasebeta

← #29700485

Subgroups — #29700485

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×#16839898C211yesmaximal, characteristic
2C2×#16839875C211yesmaximal, characteristic, complemented
3C2×#16839768C211yesmaximal, characteristic, complemented
4#21448855C211yesmaximal, characteristic, complemented
5C22⋊C4×D244C211yesmaximal, characteristic, complemented
6#21446685C211yesmaximal, characteristic, complemented
7#21446516C211yesmaximal, characteristic, complemented
8#21446447C211yesmaximal, characteristic, complemented
9#21446257C211yesmaximal, characteristic, complemented
10#21446166C211yesmaximal, characteristic, complemented
11#21446166C211yesmaximal, characteristic, complemented
12#21446069C211yesmaximal, characteristic, complemented
13#21446020C211yesmaximal, characteristic, complemented
14C4×#14519699C211yesmaximal, characteristic, complemented
15C61×#1753C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×D488C2211yescharacteristic
18C22×D488C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic, complemented
23C2×#14519736C2211yescharacteristic
24C2×C22⋊C4×D61—21no—
25#16839898C418yescomplemented
26#16839875—24no—
27C2×#14519711C2211yescharacteristic, complemented
28C2×#14519709C2211yescharacteristic, complemented
29#16839768—24no—
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic, complemented
37C2×#14519699C2211yescharacteristic, complemented
38#16839664C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839664C2211yescharacteristic, complemented
41#16839662—21no—
42#16839660C2211yescharacteristic, complemented
43#16839651—21no—
44#16839640—21no—
45#16839640—21no—
46#16839638—21no—
47#16839622C2211yescharacteristic
48#16839617—21no—
49C4×C4⋊Dic61C2211yescharacteristic, complemented
50#16839609—21no—
51#16839525C2211yescharacteristic, complemented
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55C22×M16×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic, complemented
58C2×C4×C8×C61C2211yescharacteristic, complemented
59C4×C22⋊C4×C61C2211yescharacteristic
60C61×#336C2211yescharacteristic, complemented
61C61×#336C2211yescharacteristic, 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
72C22×D244C2311yescharacteristic
73C22×C22⋊D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C2×D488—22no—
78C2×D488—22no—
79C2×D488—41no—
80C2×D488—41no—
81C2×D488C2×C414yes—
82C2×D488C2×C414yescomplemented
83#14519751—22no—
84#14519751C2×C414yescomplemented
85C4×D244—22no—
86C4×D244—22no—
87C4×D244—22no—
88C4×D244—41no—
89C4×D244—41no—
90C4×D244—41no—
91#14519736—22no—
92#14519736—41no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—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—21no—
110C2×#11758198—21no—
111C22⋊C4×D61—44no—
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114#14519711—41no—
115#14519709—22no—
116#14519699—22no—
117#14519699—22no—
118#14519699—22no—
119#14519699—22no—
120#14519699—41no—
121#14519699C2×C414yescomplemented
122#14519699C2×C414yescomplemented
123#14519699D414yescomplemented
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127C23×C4×C61C2311yescharacteristic
128C2×M16×C61—22no—
129C2×M16×C61—22no—
130C2×M16×C61—41no—
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C2×C42×C61C2311yescharacteristic
139C22⋊C8×C61C2×C414yescomplemented
140#97×C61—22no—
141C4×C8×C61—41no—
142#95×C61D411yescharacteristic
143#95×C61D411yescharacteristic
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146C23×D61—21no—
147C23×D61—21no—
148C23×D61—24no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61—42no—
153C23×D61—81no—
154C23×D61—81no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61#4112yes—
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—24no—
168C2×C22⋊D61—81no—
169C2×C22⋊D61—81no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—28no—
187C2×D244—24no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—44no—
191C2×D244—44no—
192C2×D244—44no—
193C2×D244—42no—
194C2×D244—42no—
195C2×D244C22×C412yes—
196C2×D244C22×C412yes—
197C2×D244C22×C412yes—
198C2×D244C2×D412yes—
199C2×D244#4112yes—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—81no—
207C2×C4×D61—81no—
208C2×C4×D61—81no—
209M16×C61—44no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61C22×C412yes—
220C2×C8×C61C22×C412yes—
221C2×C8×C61C2×D412yes—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—41no—
224C42×C61—21no—
225C42×C61—21no—
226C42×C61—21no—
227C42×C61—21no—
228C22⋊Dic61—42no—
229C22⋊Dic61—42no—
230#11758198—24no—
231#11758198—42no—
232#11758198—42no—
233#11758198—42no—
234#11758198—42no—
235#11758198—42no—
236#11758198—42no—
237#11758198—81no—
238#11758198—81no—
239#11758198—81no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61C22×C412yes—
249C4⋊Dic61C2×D412yes—
250#11758196—81no—
251C4×Dic61—42no—
252C4×Dic61—81no—
253D488—28no—
254D488—44no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61C4×D412yes—
262C23×C61C22×D411yescharacteristic
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—48no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—48no—
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—41no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—84no—
289C22×D61—84no—
290C22×D61—84no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61C4×D412yes—
309C2×C4×C61AGL(1,ℤ/8)12yes—
310C2×C4×C61C23×C411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C2×#4111yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61H(5,𝔽2)11yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C22⋊D61—84no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
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—
332D244—22no—
333D244—22no—
334D244—22no—
335D244—22no—
336D244—22no—
337D244—22no—
338D244—22no—
339D244—48no—
340D244—41no—
341D244—41no—
342D244—41no—
343D244—41no—
344D244C4×D414yes—
345C4×D61—84no—
346C4×D61—84no—
347C4×D61—84no—
348C8×C61—22no—
349C8×C61—22no—
350C8×C61—22no—
351C8×C61—41no—
352#22868—611nomaximal, Sylow
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
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—24no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
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—22no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61—41no—
394C4×C61C2×C4×D411yescharacteristic
395C4×C61#51811yescharacteristic
396C4×C61#54611yescharacteristic
397C4×C61#55111yescharacteristic
398Dic61—42no—
399Dic61—42no—
400Dic61—81no—
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×#102—611no—
417#1753D6111yescharacteristic, complemented
418C2×C61—42no—
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—44no—
427D61—82no—
428D61—82no—
429C23×D4—611no—
430C22×D8—611no—
431C22×D8—611no—
432C22×M16C2×D6111yescharacteristic
433C2×#121—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
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×#102—611no—
451C2×#102—611no—
452C2×C22⋊C8C2×D6111yescharacteristic
453C2×#97C2×D6111yescharacteristic, complemented
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⋊C4—611no—
467C4×C22⋊C4—1221no—
468C4×C22⋊C4C2×D6111yescharacteristic
469#340—611no—
470#340—611no—
471#340—611no—
472#340—611no—
473#336C2×D6111yescharacteristic, complemented
474#336C2×D6111yescharacteristic, complemented
475C61#2286811yescharacteristic, complemented, Sylow
476C25—1221no—
477C22×D4—614no—
478C22×D4—611no—
479C22×D4—611no—
480C22×D4—611no—
481C22×D4—1222no—
482C22×D4—1222no—
483C22×D4—1221no—
484C22×D4—1221no—
485C22×D4—1222no—
486C22×D4—2441no—
487C22×D4—2441no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4C22×D6111yescharacteristic
492C2×D8—614no—
493C2×D8—614no—
494C2×D8—1222no—
495C2×D8—1222no—
496C2×D8—2441no—
497C2×D8—2441no—
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—41no—
501C22×C8C22×D6111yescharacteristic
502C22×C8C22×D6111yescharacteristic
503C22×C8C22×D6111yescharacteristic
504C22×C8C22×D6111yescharacteristic
505#121—614no—
506#121—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4—2441no—
511C4×D4—2441no—
512C4×D4—2441no—
513#117—1222no—
514#117—2441no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
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—2444no—
534C2×C22⋊C4D24411yescharacteristic
535C2×C22⋊C4D24411yescharacteristic
536C2×C42—1221no—
537C2×C42—1221no—
538C2×C42C22×D6111yescharacteristic
539C2×C42C22×D6111yescharacteristic
540#107—2441no—
541#106—1222no—
542#102—614no—
543#102—614no—
544#102—614no—
545#102—1222no—
546#102—1222no—
547#102—1222no—
548#102—1222no—
549#102—2441no—
550C22⋊C8C4×D6114yescomplemented
551#97—22no—
552C4×C8—41no—
553#95—1221no—
554#95—1221no—
555#95—1221no—
556#95D24411yescharacteristic
557#95D24411yescharacteristic
558C24—1221no—
559C24—1224no—
560C24—1221no—
561C24—1221no—
562C24—4881no—
563C24—4881no—
564C24—2442no—
565C24—2442no—
566C24—2442no—
567C24—2442no—
568C24C2×D24411yescharacteristic
569C2×D4—612no—
570C2×D4—612no—
571C2×D4—612no—
572C2×D4—612no—
573C2×D4—612no—
574C2×D4—1228no—
575C2×D4—1224no—
576C2×D4—1221no—
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—1221no—
588C2×D4—1221no—
589C2×D4—1224no—
590C2×D4—4881no—
591C2×D4—4881no—
592C2×D4—2444no—
593C2×D4—2444no—
594C2×D4—2444no—
595C2×D4—2442no—
596C2×D4—2442no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—4881no—
607C22×C4—4881no—
608C22×C4—4881no—
609C22×C4—2442no—
610C22×C4—2442no—
611C22×C4—2442no—
612C22×C4—2442no—
613C22×C4—2442no—
614C22×C4—2442no—
615C22×C4C2×C4×D6112yes—
616C22×C4C2×D24411yescharacteristic
617C22×C4C2×D24411yescharacteristic
618C22×C4C2×D24411yescharacteristic
619C22×C4C2×D24411yescharacteristic
620C22×C4C2×D24411yescharacteristic
621C22×C4#1175822212yes—
622C22×C4C23×D6111yescharacteristic
623D8—1228no—
624D8—2444no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8C2×C4×D6112yes—
636C2×C8C2×C4×D6112yes—
637C2×C8D4×D6112yes—
638C4⋊C4—612no—
639C4⋊C4—612no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—4881no—
649C22⋊C4—22no—
650C22⋊C4—41no—
651C22⋊C4—1224no—
652C22⋊C4—4881no—
653C22⋊C4—4881no—
654C22⋊C4—4881no—
655C22⋊C4—2442no—
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—21no—
666C42—21no—
667C42—4881no—
668C42—2442no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23—1222no—
679C23—1222no—
680C23—4884no—
681C23—4884no—
682C23—4884no—
683C23—4884no—
684C23—4884no—
685C23—2448no—
686C23—2448no—
687C23—2441no—
688C23—2441no—
689C23—2441no—
690C23—2441no—
691C23—2441no—
692C23—2441no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23C4×D24412yes—
704C23C22×D24411yescharacteristic
705D4—614no—
706D4—1222no—
707D4—1222no—
708D4—1222no—
709D4—1222no—
710D4—1222no—
711D4—1222no—
712D4—1222no—
713D4—4884no—
714D4—2448no—
715D4—2441no—
716D4—2441no—
717D4—2441no—
718D4—2441no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—4884no—
739C2×C4—4884no—
740C2×C4—4884no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4C4×D24412yes—
755C2×C4#1451980512yes—
756C2×C4C22×C4×D6111yescharacteristic
757C2×C4C2×D4×D6111yescharacteristic
758C2×C4#41×D6111yescharacteristic
759C2×C4C2×#1175822211yescharacteristic
760C2×C4#1451982211yescharacteristic
761C2×C4#1451982311yescharacteristic
762C8—22no—
763C8—22no—
764C8—22no—
765C8—41no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—1224no—
774C22—48816no—
775C22—4881no—
776C22—4881no—
777C22—4881no—
778C22—4881no—
779C22—4881no—
780C22—4881no—
781C22—4881no—
782C22—4881no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22—2442no—
791C22—2442no—
792C22—2442no—
793C22—2442no—
794C22—2442no—
795C22C2×C4×D24411yescharacteristic
796C22D4×D24411yescharacteristic
797C22#1684040711yescharacteristic
798C22C2×#1451980511yescharacteristic
799C22#1684056211yescharacteristic
800C22#1684056711yescharacteristic
801C22#1684056711yescharacteristic
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—4881no—
808C4—4881no—
809C4—4881no—
810C4—2442no—
811C4—2442no—
812C4C4×D4×D6111yescharacteristic
813C4#1684023411yescharacteristic
814C4#1684040211yescharacteristic
815C4#1684043611yescharacteristic
816C2—42no—
817C2—4882no—
818C2—4882no—
819C2—2444no—
820C2#2144880111yescharacteristic
821C2C4×#1451980511yescharacteristic
822C2#2145467211yescharacteristic
823C2#2145743111yescharacteristic
824C2#2145744111yescharacteristic
825C2#2145796211yescharacteristic
826C2#2145797711yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1753C2
socleC23×C61C22×D4
prime radicalC2×#16839898C2
cosocleC22×C4×C61C24
hypercenter#1753D61
hypocenterC61#22868
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. C2×#16839875C2semidirect
3. C2×#16839768C2semidirect
4. #21448855C2semidirect
5. C22⋊C4×D244C2semidirect
6. #21446685C2semidirect
7. #21446516C2semidirect
8. #21446447C2semidirect
9. #21446257C2semidirect
10. #21446166C2semidirect
11. #21446166C2semidirect
12. #21446069C2semidirect
13. #21446020C2semidirect
14. C4×#14519699C2semidirect
15. C61×#1753C2semidirect
22. C2×C4×D244C22semidirect
25. #16839898C4semidirect
27. C2×#14519711C22semidirect
28. C2×#14519709C22semidirect
36. C2×#14519699C22semidirect
37. C2×#14519699C22semidirect
40. #16839664C22semidirect
42. #16839660C22semidirect
49. C4×C4⋊Dic61C22semidirect
51. #16839525C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
57. C2×#97×C61C22semidirect
58. C2×C4×C8×C61C22semidirect
60. C61×#336C22semidirect
61. C61×#336C22semidirect
69. C22×D244C2×C4semidirect
82. C2×D488C2×C4semidirect
84. #14519751C2×C4semidirect
121. #14519699C2×C4semidirect
122. #14519699C2×C4semidirect
123. #14519699D4semidirect
139. C22⋊C8×C61C2×C4semidirect
417. #1753D61semidirect
453. C2×#97C2×D61semidirect
454. C2×C4×C8C2×D61semidirect
473. #336C2×D61semidirect
474. #336C2×D61semidirect
475. C61#22868semidirect
550. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398982
C2×#168398752
C2×#168397682
#214488552
C22⋊C4×D2442
#214466852
#214465162
#214464472
#214462572
#214461662
#214460692
#214460202
C4×#145196992
C61×#17532
#2286861