Finite Group Databasebeta

← #29700481

Subgroups — #29700481

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×#16839895C211yesmaximal, characteristic
2C2×#16839872C211yesmaximal, characteristic, complemented
3C2×#16839766C211yesmaximal, characteristic, complemented
4C22⋊C4×D244C211yesmaximal, characteristic, complemented
5#21446684C211yesmaximal, characteristic, complemented
6#21446515C211yesmaximal, characteristic, complemented
7#21446446C211yesmaximal, characteristic, complemented
8#21446258C211yesmaximal, characteristic, complemented
9#21446170C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446065C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13C4×#14519697C211yesmaximal, characteristic, complemented
14#21445603C211yesmaximal, characteristic, complemented
15C61×#2363C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C22⋊C4×D61—21no—
23#16839895C418yescomplemented
24#16839872—24no—
25C2×#14519710C2211yescharacteristic, complemented
26C2×#14519708C2211yescharacteristic, complemented
27#16839766—24no—
28C2×#14519698C2211yescharacteristic, complemented
29C2×#14519698C2211yescharacteristic, complemented
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×#14519688C2211yescharacteristic, complemented
38C2×C4×#92418C2211yescharacteristic, complemented
39#16839664C2211yescharacteristic
40#16839664C2211yescharacteristic
41#16839640—21no—
42#16839640—21no—
43#16839622C2211yescharacteristic
44#16839617—21no—
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51C2×#121×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic, complemented
53C2×#117×C61C2211yescharacteristic
54C61×#390—21no—
55C61×#390C2211yescharacteristic, complemented
56C61×#389C2211yescharacteristic, complemented
57C61×#388—21no—
58C61×#386—21no—
59C4×C4⋊C4×C61C2211yescharacteristic, complemented
60C4×C22⋊C4×C61—21no—
61C4×C22⋊C4×C61C2211yescharacteristic
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×C4×D61—21no—
73C22×C4×D61—21no—
74C2×#11758199—22no—
75C2×#11758199—22no—
76C2×#11758199—41no—
77C2×#11758199—41no—
78C2×#11758199C2×C414yes—
79C2×#11758199C2×C414yescomplemented
80C2×#11758194—22no—
81C2×#11758194—22no—
82C2×#11758194—41no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C4×D244—22no—
88C4×D244—22no—
89C4×D244—41no—
90C4×D244—41no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C22⋊C4×D61—44no—
101#14519710—41no—
102#14519708—22no—
103#14519698—22no—
104#14519698—41no—
105#14519697—22no—
106#14519697—22no—
107#14519697—22no—
108#14519697C2×C414yescomplemented
109#14519697C2×C414yescomplemented
110#14519697D414yescomplemented
111C22⋊#92418C2×C414yescomplemented
112#14519688—22no—
113C4×#92418—41no—
114#14519684—21no—
115C22×D4×C61—21no—
116C22×D4×C61C2311yescharacteristic
117C23×C4×C61—21no—
118C23×C4×C61C2311yescharacteristic
119#121×C61—22no—
120#121×C61C2×C414yescomplemented
121C4×D4×C61—22no—
122C4×D4×C61—41no—
123#117×C61—22no—
124#117×C61—41no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61D411yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C42×C61—21no—
137C2×C42×C61—21no—
138C2×C42×C61C2311yescharacteristic
139C2×C42×C61C2311yescharacteristic
140#95×C61—21no—
141#95×C61—21no—
142#95×C61D411yescharacteristic
143#95×C61D411yescharacteristic
144C24×C61—21no—
145C24×C61C2×D411yescharacteristic
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—
155C2×D4×C61—24no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—81no—
162C2×D4×C61—81no—
163C2×D4×C61C22×C412yes—
164C22×C4×C61—21no—
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—42no—
172C22×C4×C61—42no—
173C22×C4×C61—81no—
174C22×C4×C61C22×C412yes—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61#4112yes—
181C22×C4×C61C2411yescharacteristic
182C22×Dic61—21no—
183C22×Dic61—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—28no—
192C2×D244—24no—
193C2×D244—21no—
194C2×D244—44no—
195C2×D244—44no—
196C2×D244—44no—
197C2×D244—42no—
198C2×D244—42no—
199C2×D244C22×C412yes—
200C2×D244C22×C412yes—
201C2×D244C2×D412yes—
202C2×D244#4112yes—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—81no—
208C2×C4×D61—81no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—81no—
214C4⋊C4×C61C22×C412yes—
215C4⋊C4×C61C2×D412yes—
216C22⋊C4×C61—24no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—41no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—81no—
223C42×C61—21no—
224C42×C61—21no—
225C42×C61—21no—
226C42×C61—21no—
227C42×C61—42no—
228C42×C61—81no—
229C22⋊Dic61—42no—
230#11758199—28no—
231#11758199—44no—
232#11758198—42no—
233#11758198—42no—
234#11758198—42no—
235#11758198—42no—
236#11758198—81no—
237#11758198—81no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242#11758194—44no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418C22×C412yes—
253C2×#92418C22×C412yes—
254C2×#92418C2×D412yes—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—22no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61C4×D412yes—
269C23×C61C22×D411yescharacteristic
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—48no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—48no—
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—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—41no—
294D4×C61—41no—
295D4×C61—84no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—22no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—84no—
323C2×C4×C61C4×D412yes—
324C2×C4×C61AGL(1,ℤ/8)12yes—
325C2×C4×C61C23×C411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C2×#4111yescharacteristic
328C2×C4×C61C2×#4111yescharacteristic
329C2×C4×C61H(5,𝔽2)11yescharacteristic
330C2×C4×C61H(5,𝔽2)11yescharacteristic
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337D244—22no—
338D244—22no—
339D244—22no—
340D244—22no—
341D244—22no—
342D244—48no—
343D244—41no—
344D244—41no—
345D244C4×D414yes—
346C4×D61—84no—
347C4×D61—84no—
348#92418—22no—
349#92418—22no—
350#92418—22no—
351#92418—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×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61C2×C4×D411yescharacteristic
368C22×C61D4211yescharacteristic
369C22×C61#54611yescharacteristic
370C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C61#57511yescharacteristic
372C22×C61#57611yescharacteristic
373C22×C61#57611yescharacteristic
374C2×D61—24no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—816no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C4×C61—22no—
390C4×C61—22no—
391C4×C61—42no—
392C4×C61—41no—
393C4×C61—42no—
394C4×C61—41no—
395C4×C61—41no—
396C4×C61—81no—
397C4×C61C2×C4×D411yescharacteristic
398C4×C61#51811yescharacteristic
399C4×C61#54611yescharacteristic
400C4×C61#55111yescharacteristic
401Dic61—81no—
402Dic61—81no—
403C2×#447—611no—
404C2×#442—611no—
405C2×#418—611no—
406#2363D6111yescharacteristic, complemented
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#1753—611no—
418C2×C61—42no—
419C2×C61—82no—
420C2×C61#235811yescharacteristic
421C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
422C2×C61#294811yescharacteristic
423C2×C61#327311yescharacteristic
424C2×C61#327411yescharacteristic
425C2×C61#331811yescharacteristic
426C2×C61#331911yescharacteristic
427D61—44no—
428D61—82no—
429C23×D4—611no—
430C22×D8—611no—
431C22×D8—611no—
432C22×M16—611no—
433C2×#121C2×D6111yescharacteristic
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4C2×D6111yescharacteristic, complemented
437C2×#117C2×D6111yescharacteristic
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⋊C8—611no—
453C2×#97—611no—
454C2×C4×C8—611no—
455#390—21no—
456#390—611no—
457#390—611no—
458#390C2×D6111yescharacteristic, complemented
459#389C2×D6111yescharacteristic, complemented
460#388—21no—
461#386—21no—
462#386—1221no—
463#386—1221no—
464#380—611no—
465#379—1221no—
466C4×C4⋊C4C2×D6111yescharacteristic, complemented
467C4×C22⋊C4—21no—
468C4×C22⋊C4C2×D6111yescharacteristic
469#340—611no—
470#340—611no—
471#340—611no—
472#340—611no—
473#336—611no—
474#336—611no—
475C61#2286811yescharacteristic, complemented, Sylow
476C25—1221no—
477C22×D4—21no—
478C22×D4—614no—
479C22×D4—611no—
480C22×D4—611no—
481C22×D4—1222no—
482C22×D4—1222no—
483C22×D4—1222no—
484C22×D4—1221no—
485C22×D4—2441no—
486C22×D4—2441no—
487C22×D4C22×D6111yescharacteristic
488C23×C4—21no—
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—1222no—
499C2×M16—1222no—
500C2×M16—2441no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—611no—
505#121—22no—
506#121C4×D6114yescomplemented
507C4×D4—22no—
508C4×D4—41no—
509C4×D4—1222no—
510C4×D4—1222no—
511C4×D4—2441no—
512C4×D4—2441no—
513#117—22no—
514#117—41no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
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⋊C4C22⋊D6111yescharacteristic
535C2×C22⋊C4C22⋊D6111yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
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⋊C8—614no—
551#97—1222no—
552C4×C8—2441no—
553#95—21no—
554#95—21no—
555#95—1221no—
556#95C22⋊D6111yescharacteristic
557#95C22⋊D6111yescharacteristic
558C24—21no—
559C24—1221no—
560C24—1224no—
561C24—1221no—
562C24—4881no—
563C24—4881no—
564C24—2442no—
565C24—2442no—
566C24—2442no—
567C24—2442no—
568C24C2×C22⋊D6111yescharacteristic
569C2×D4—24no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—81no—
576C2×D4—81no—
577C2×D4—612no—
578C2×D4—612no—
579C2×D4—612no—
580C2×D4—612no—
581C2×D4—1228no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1224no—
591C2×D4—2444no—
592C2×D4—2444no—
593C2×D4—2444no—
594C2×D4—2442no—
595C2×D4—2442no—
596C2×D4C2×C4×D6112yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—81no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—4881no—
610C22×C4—4881no—
611C22×C4—2442no—
612C22×C4—2442no—
613C22×C4—2442no—
614C22×C4—2442no—
615C22×C4C2×C4×D6112yes—
616C22×C4#1175822212yes—
617C22×C4C2×C22⋊D6111yescharacteristic
618C22×C4C2×C22⋊D6111yescharacteristic
619C22×C4C2×C22⋊D6111yescharacteristic
620C22×C4C2×C22⋊D6111yescharacteristic
621C22×C4C2×C22⋊D6111yescharacteristic
622C22×C4C23×D6111yescharacteristic
623D8—1228no—
624D8—2444no—
625M16—2444no—
626C2×C8—612no—
627C2×C8—612no—
628C2×C8—612no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—81no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4C2×C4×D6112yes—
648C4⋊C4D4×D6112yes—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—81no—
656C22⋊C4—4881no—
657C22⋊C4—4881no—
658C22⋊C4—2442no—
659C22⋊C4—2442no—
660C22⋊C4—2442no—
661C22⋊C4—2442no—
662C22⋊C4—2442no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—42no—
668C42—81no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—1222no—
683C23—1222no—
684C23—1222no—
685C23—1222no—
686C23—4884no—
687C23—4884no—
688C23—4884no—
689C23—4884no—
690C23—4884no—
691C23—2448no—
692C23—2448no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23C4×C22⋊D6112yes—
704C23C22×C22⋊D6111yescharacteristic
705D4—22no—
706D4—22no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—614no—
711D4—1222no—
712D4—1222no—
713D4—1222no—
714D4—1222no—
715D4—1222no—
716D4—2448no—
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—22no—
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—22no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—84no—
746C2×C4—4884no—
747C2×C4—4884no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4C4×C22⋊D6112yes—
755C2×C4#1451980212yes—
756C2×C4C22×C4×D6111yescharacteristic
757C2×C4C2×D4×D6111yescharacteristic
758C2×C4#41×D6111yescharacteristic
759C2×C4C2×#1175822211yescharacteristic
760C2×C4#1451982211yescharacteristic
761C2×C4#1451982311yescharacteristic
762C8—1222no—
763C8—1222no—
764C8—1222no—
765C8—2441no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—1224no—
781C22—48816no—
782C22—4881no—
783C22—4881no—
784C22—4881no—
785C22—4881no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22—2442no—
791C22—2442no—
792C22—2442no—
793C22—2442no—
794C22—2442no—
795C22C2×C4×C22⋊D6111yescharacteristic
796C22D4×C22⋊D6111yescharacteristic
797C22#1684040011yescharacteristic
798C22C2×#1451980211yescharacteristic
799C22#1684056011yescharacteristic
800C22#1684056511yescharacteristic
801C22#1684056511yescharacteristic
802C4—22no—
803C4—22no—
804C4—41no—
805C4—42no—
806C4—41no—
807C4—41no—
808C4—42no—
809C4—81no—
810C4—4881no—
811C4—4881no—
812C4C4×D4×D6111yescharacteristic
813C4#1684023411yescharacteristic
814C4#1684040811yescharacteristic
815C4#1684044111yescharacteristic
816C2—42no—
817C2—82no—
818C2—4882no—
819C2—2444no—
820C2#2144879611yescharacteristic
821C2C4×#1451980211yescharacteristic
822C2#2145466911yescharacteristic
823C2#2145742611yescharacteristic
824C2#2145743911yescharacteristic
825C2#2145795411yescharacteristic
826C2#2145796911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2363C2
socleC23×C61C22×D4
prime radicalC2×#16839895C2
cosocleC22×C4×C61C24
hypercenter#2363D61
hypocenterC61#22868
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. C2×#16839872C2semidirect
3. C2×#16839766C2semidirect
4. C22⋊C4×D244C2semidirect
5. #21446684C2semidirect
6. #21446515C2semidirect
7. #21446446C2semidirect
8. #21446258C2semidirect
9. #21446170C2semidirect
10. #21446167C2semidirect
11. #21446065C2semidirect
12. #21446018C2semidirect
13. C4×#14519697C2semidirect
14. #21445603C2semidirect
15. C61×#2363C2semidirect
23. #16839895C4semidirect
25. C2×#14519710C22semidirect
26. C2×#14519708C22semidirect
28. C2×#14519698C22semidirect
29. C2×#14519698C22semidirect
37. C2×#14519688C22semidirect
38. C2×C4×#92418C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839524C22semidirect
49. #16839517C22semidirect
50. #16839517C22semidirect
52. C2×C4×D4×C61C22semidirect
55. C61×#390C22semidirect
56. C61×#389C22semidirect
59. C4×C4⋊C4×C61C22semidirect
69. C22×D244C2×C4semidirect
79. C2×#11758199C2×C4semidirect
108. #14519697C2×C4semidirect
109. #14519697C2×C4semidirect
110. #14519697D4semidirect
111. C22⋊#92418C2×C4semidirect
120. #121×C61C2×C4semidirect
406. #2363D61semidirect
436. C2×C4×D4C2×D61semidirect
458. #390C2×D61semidirect
459. #389C2×D61semidirect
466. C4×C4⋊C4C2×D61semidirect
475. C61#22868semidirect
506. #121C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398952
C2×#168398722
C2×#168397662
C22⋊C4×D2442
#214466842
#214465152
#214464462
#214462582
#214461702
#214461672
#214460652
#214460182
C4×#145196972
#214456032
C61×#23632
#2286861