Finite Group Databasebeta

← #29700476

Subgroups — #29700476

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×#16839896C211yesmaximal, characteristic
2C2×#16839872C211yesmaximal, characteristic, complemented
3C2×#16839767C211yesmaximal, characteristic, complemented
4#21448855C211yesmaximal, characteristic, complemented
5#21446684C211yesmaximal, characteristic, complemented
6#21446519C211yesmaximal, characteristic, complemented
7#21446443C211yesmaximal, characteristic, complemented
8#21446255C211yesmaximal, characteristic, complemented
9#21446170C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446066C211yesmaximal, characteristic, complemented
12#21446016C211yesmaximal, characteristic, complemented
13C4×#14519698C211yesmaximal, characteristic, complemented
14#21445603C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic, complemented
21C2×#14519736C2211yescharacteristic
22#16839896C418yescomplemented
23#16839872—24no—
24C2×#14519710C2211yescharacteristic, complemented
25C2×#14519708C2211yescharacteristic, complemented
26#16839767—24no—
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519697C2211yescharacteristic, complemented
34C2×#14519697C2211yescharacteristic, complemented
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519688C2211yescharacteristic, complemented
37C2×C4×#92418C2211yescharacteristic, complemented
38#16839664C2211yescharacteristic, complemented
39#16839662—21no—
40#16839660C2211yescharacteristic, complemented
41#16839651—21no—
42#16839638—21no—
43C4×C4⋊Dic61C2211yescharacteristic, complemented
44#16839609—21no—
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51C23×D4×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C22×C22⋊C4×C61—21no—
55C61×#390C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C61×#386—21no—
58C61×#386—21no—
59C61×#380C2211yescharacteristic
60C61×#379—21no—
61C4×C22⋊C4×C61C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C22×C4×D61—21no—
65C2×#11758199—22no—
66C2×#11758199—22no—
67C2×#11758199—41no—
68C2×#11758199—41no—
69C2×#11758199C2×C414yes—
70C2×#11758199C2×C414yescomplemented
71C2×#11758194—22no—
72C2×#11758194—22no—
73C2×#11758194—41no—
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78#14519751—22no—
79#14519751C2×C414yescomplemented
80C4×D244—22no—
81C4×D244—41no—
82#14519736—22no—
83#14519736—41no—
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C2×C22⋊Dic61—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61—21no—
95#14519710—41no—
96#14519708—22no—
97#14519698—22no—
98#14519698—22no—
99#14519698—22no—
100#14519698C2×C414yescomplemented
101#14519698C2×C414yescomplemented
102#14519698D414yescomplemented
103#14519697—22no—
104#14519697—41no—
105C22⋊#92418C2×C414yescomplemented
106#14519688—22no—
107C4×#92418—41no—
108#14519684—21no—
109#14519684—21no—
110C25×C61—21no—
111C22×D4×C61—22no—
112C22×D4×C61—22no—
113C22×D4×C61—21no—
114C22×D4×C61—22no—
115C22×D4×C61—41no—
116C22×D4×C61—41no—
117C22×D4×C61C2×C414yescomplemented
118C22×D4×C61C2311yescharacteristic
119C22×D4×C61C2311yescharacteristic
120C23×C4×C61—21no—
121C23×C4×C61—21no—
122C23×C4×C61C2311yescharacteristic
123C4×D4×C61—22no—
124C4×D4×C61—22no—
125C4×D4×C61—41no—
126C4×D4×C61—41no—
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×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—44no—
137C2×C22⋊C4×C61D411yescharacteristic
138C2×C22⋊C4×C61D411yescharacteristic
139C2×C42×C61C2311yescharacteristic
140C2×C42×C61C2311yescharacteristic
141#95×C61—21no—
142#95×C61D411yescharacteristic
143#95×C61D411yescharacteristic
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—24no—
147C24×C61—42no—
148C24×C61—42no—
149C24×C61—42no—
150C24×C61—42no—
151C24×C61—81no—
152C24×C61—81no—
153C24×C61C2×D411yescharacteristic
154C23×D61—21no—
155C2×D4×C61—28no—
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—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—44no—
166C2×D4×C61—44no—
167C2×D4×C61—44no—
168C2×D4×C61—42no—
169C2×D4×C61—42no—
170C2×D4×C61C22×C412yes—
171C2×D4×C61C22×C412yes—
172C2×D4×C61C2×D412yes—
173C2×D4×C61#4112yes—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—42no—
181C22×C4×C61—42no—
182C22×C4×C61—42no—
183C22×C4×C61—42no—
184C22×C4×C61—81no—
185C22×C4×C61—81no—
186C22×C4×C61C22×C412yes—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61#4112yes—
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—24no—
195C2×C22⋊D61—81no—
196C2×C22⋊D61—81no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244C22×C412yes—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—81no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—41no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—81no—
221C22⋊C4×C61—81no—
222C42×C61—21no—
223C42×C61—21no—
224C42×C61—21no—
225C42×C61—21no—
226C22⋊Dic61—42no—
227#11758199—28no—
228#11758199—44no—
229#11758198—24no—
230#11758198—42no—
231#11758198—42no—
232#11758198—81no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61C22×C412yes—
238C4⋊Dic61C2×D412yes—
239#11758196—81no—
240C4×Dic61—42no—
241C4×Dic61—81no—
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—22no—
256C23×C61—21no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—22no—
265C23×C61—48no—
266C23×C61—48no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—84no—
278C23×C61—84no—
279C23×C61—84no—
280C23×C61—84no—
281C23×C61—84no—
282C23×C61C4×D412yes—
283C23×C61C22×D411yescharacteristic
284C22×D61—22no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—48no—
297D4×C61—41no—
298D4×C61—41no—
299D4×C61C4×D414yes—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
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—21no—
316C2×C4×C61—21no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—84no—
324C2×C4×C61—84no—
325C2×C4×C61C4×D412yes—
326C2×C4×C61AGL(1,ℤ/8)12yes—
327C2×C4×C61C23×C411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C2×C4×C61C2×#4111yescharacteristic
331C2×C4×C61H(5,𝔽2)11yescharacteristic
332C2×C4×C61H(5,𝔽2)11yescharacteristic
333C22⋊D61—84no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343D244—22no—
344D244—22no—
345D244—41no—
346D244—41no—
347C4×D61—84no—
348#92418—22no—
349#92418—22no—
350#92418—22no—
351#92418—41no—
352#22868—611nomaximal, Sylow
353C22×C61—22no—
354C22×C61—24no—
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—41no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—41no—
363C22×C61—42no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—816no—
371C22×C61—81no—
372C22×C61—81no—
373C22×C61—81no—
374C22×C61—81no—
375C22×C61C2×C4×D411yescharacteristic
376C22×C61D4211yescharacteristic
377C22×C61#54611yescharacteristic
378C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
379C22×C61#57511yescharacteristic
380C22×C61#57611yescharacteristic
381C22×C61#57611yescharacteristic
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
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×C61—81no—
395C4×C61—81no—
396C4×C61C2×C4×D411yescharacteristic
397C4×C61#51811yescharacteristic
398C4×C61#54611yescharacteristic
399C4×C61#55111yescharacteristic
400Dic61—42no—
401Dic61—42no—
402Dic61—81no—
403C2×#447—611no—
404C2×#442—611no—
405C2×#418—611no—
406#2363—611no—
407D4×C22⋊C4D6111yescharacteristic, complemented
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—44no—
420C2×C61—82no—
421C2×C61#235811yescharacteristic
422C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
423C2×C61#294811yescharacteristic
424C2×C61#327311yescharacteristic
425C2×C61#327411yescharacteristic
426C2×C61#331811yescharacteristic
427C2×C61#331911yescharacteristic
428D61—82no—
429C23×D4C2×D6111yescharacteristic
430C22×D8—611no—
431C22×D8—611no—
432C22×M16—611no—
433C2×#121—611no—
434C2×C4×D4—611no—
435C2×C4×D4C2×D6111yescharacteristic
436C2×C4×D4C2×D6111yescharacteristic
437C2×#117—611no—
438C22×C22⋊C4—21no—
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—611no—
456#390—1221no—
457#390C2×D6111yescharacteristic
458#390C2×D6111yescharacteristic
459#389—611no—
460#388—1221no—
461#386—21no—
462#386—21no—
463#386—1221no—
464#380C2×D6111yescharacteristic
465#379—21no—
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#336—611no—
474#336—611no—
475C61#2286811yescharacteristic, complemented, Sylow
476C25—21no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—21no—
481C22×D4—41no—
482C22×D4—41no—
483C22×D4—611no—
484C22×D4—1221no—
485C22×D4C4×D6114yescomplemented
486C22×D4C22×D6111yescharacteristic
487C22×D4C22×D6111yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
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—614no—
506#121—1222no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—41no—
510C4×D4—41no—
511C4×D4—1222no—
512C4×D4—2441no—
513#117—1222no—
514#117—2441no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—1221no—
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—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—44no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4C22⋊D6111yescharacteristic
535C2×C22⋊C4C22⋊D6111yescharacteristic
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⋊C8—614no—
551#97—1222no—
552C4×C8—2441no—
553#95—21no—
554#95—1221no—
555#95—1221no—
556#95C22⋊D6111yescharacteristic
557#95C22⋊D6111yescharacteristic
558C24—21no—
559C24—21no—
560C24—24no—
561C24—42no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—81no—
566C24—81no—
567C24—1221no—
568C24C2×C22⋊D6111yescharacteristic
569C2×D4—28no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—24no—
579C2×D4—44no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—612no—
585C2×D4—1224no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—4881no—
592C2×D4—4881no—
593C2×D4C2×C4×D6112yes—
594C2×D4C2×C4×D6112yes—
595C2×D4D4×D6112yes—
596C2×D4#1175822412yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—4881no—
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—612no—
643C4⋊C4—612no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—4881no—
649C22⋊C4—22no—
650C22⋊C4—41no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—81no—
657C22⋊C4—81no—
658C22⋊C4—1224no—
659C22⋊C4—4881no—
660C22⋊C4—2442no—
661C22⋊C4—2442no—
662C22⋊C4—2442no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—4881no—
668C42—2442no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—21no—
676C23—22no—
677C23—21no—
678C23—22no—
679C23—48no—
680C23—48no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23—84no—
696C23—1222no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23C4×C22⋊D6112yes—
704C23C22×C22⋊D6111yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—48no—
711D4—41no—
712D4—41no—
713D4—1222no—
714D4—1222no—
715D4—4884no—
716D4—2441no—
717D4—2441no—
718D4#1451973714yes—
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—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—4884no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4C4×C22⋊D6112yes—
755C2×C4#1451980312yes—
756C2×C4C22×C4×D6111yescharacteristic
757C2×C4C2×D4×D6111yescharacteristic
758C2×C4C2×#1175822411yescharacteristic
759C2×C4C2×#1175822211yescharacteristic
760C2×C4#1451982211yescharacteristic
761C2×C4#1451982211yescharacteristic
762C8—1222no—
763C8—1222no—
764C8—1222no—
765C8—2441no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—24no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—816no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—4881no—
789C22—4881no—
790C22—4881no—
791C22—4881no—
792C22—2442no—
793C22—2442no—
794C22—2442no—
795C22C2×C4×C22⋊D6111yescharacteristic
796C22D4×C22⋊D6111yescharacteristic
797C22#1684040611yescharacteristic
798C22C2×#1451980311yescharacteristic
799C22#1684056011yescharacteristic
800C22#1684056511yescharacteristic
801C22#1684056511yescharacteristic
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—81no—
808C4—81no—
809C4—4881no—
810C4—2442no—
811C4—2442no—
812C4C2×#1451973711yescharacteristic
813C4#1684023511yescharacteristic
814C4#1684040211yescharacteristic
815C4#1684043811yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—4882no—
820C2#2144879811yescharacteristic
821C2C4×#1451980311yescharacteristic
822C2#2145466911yescharacteristic
823C2#2145742611yescharacteristic
824C2#2145743511yescharacteristic
825C2#2145796011yescharacteristic
826C2#2145797511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingD4×C22⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839896C2
cosocleC22×C4×C61C24
hypercenterD4×C22⋊C4D61
hypocenterC61#22868
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16839872C2semidirect
3. C2×#16839767C2semidirect
4. #21448855C2semidirect
5. #21446684C2semidirect
6. #21446519C2semidirect
7. #21446443C2semidirect
8. #21446255C2semidirect
9. #21446170C2semidirect
10. #21446167C2semidirect
11. #21446066C2semidirect
12. #21446016C2semidirect
13. C4×#14519698C2semidirect
14. #21445603C2semidirect
15. D4×C22⋊C4×C61C2semidirect
20. C2×C4×D244C22semidirect
22. #16839896C4semidirect
24. C2×#14519710C22semidirect
25. C2×#14519708C22semidirect
33. C2×#14519697C22semidirect
34. C2×#14519697C22semidirect
36. C2×#14519688C22semidirect
37. C2×C4×#92418C22semidirect
38. #16839664C22semidirect
40. #16839660C22semidirect
43. C4×C4⋊Dic61C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839524C22semidirect
49. #16839517C22semidirect
50. #16839517C22semidirect
70. C2×#11758199C2×C4semidirect
79. #14519751C2×C4semidirect
100. #14519698C2×C4semidirect
101. #14519698C2×C4semidirect
102. #14519698D4semidirect
105. C22⋊#92418C2×C4semidirect
117. C22×D4×C61C2×C4semidirect
407. D4×C22⋊C4D61semidirect
475. C61#22868semidirect
485. C22×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398962
C2×#168398722
C2×#168397672
#214488552
#214466842
#214465192
#214464432
#214462552
#214461702
#214461672
#214460662
#214460162
C4×#145196982
#214456032
D4×C22⋊C4×C612
#2286861