Finite Group Databasebeta

← #29727506

Subgroups — #29727506

Order 15616.

1268 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839967C211yesmaximal, characteristic, complemented
2C2×#16839913C211yesmaximal, characteristic
3C2×#16839913C211yesmaximal, characteristic
4C2×C4×#11758200C211yesmaximal, characteristic, complemented
5#21449418C211yesmaximal, characteristic, complemented
6#21447193C211yesmaximal, characteristic, complemented
7#21447015C211yesmaximal, characteristic, complemented
8#21447015C211yesmaximal, characteristic, complemented
9#21446901C211yesmaximal, characteristic, complemented
10#21446672C211yesmaximal, characteristic, complemented
11#21446427C211yesmaximal, characteristic, complemented
12#21446177C211yesmaximal, characteristic, complemented
13#21446153C211yesmaximal, characteristic, complemented
14#21446080C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C61C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C2×#14519777C2211yescharacteristic, complemented
21C2×#14519756C2211yescharacteristic
22C2×#14519756C2211yescharacteristic
23C2×C4×Dic122C2211yescharacteristic, complemented
24#16839967—24no—
25#16839913—24no—
26#16839913—24no—
27C4×#11758200—24no—
28C2×#14519708C2211yescharacteristic, complemented
29C2×#14519708C2211yescharacteristic, complemented
30C2×C4⋊#92418C2211yescharacteristic, complemented
31C2×#14519700C2211yescharacteristic, complemented
32C2×#14519700C2211yescharacteristic, complemented
33C2×#14519700C2211yescharacteristic, complemented
34C2×#14519700C2211yescharacteristic, complemented
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic, complemented
42#16839696—21no—
43#16839685—21no—
44#16839668C2211yescharacteristic, complemented
45#16839660C2211yescharacteristic, complemented
46#16839659—21no—
47#16839655—21no—
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52C23×D4×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C22×C22⋊C4×C61—21no—
56C61×#390C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#386—21no—
59C61×#386—21no—
60C61×#380C2211yescharacteristic
61C61×#379—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×Dic122C2311yescharacteristic
65C2×#11758200—22no—
66C2×#11758200—22no—
67C2×#11758200—22no—
68C2×#11758200—22no—
69C2×#11758200—22no—
70C2×#11758200—22no—
71C2×#11758200—22no—
72C2×#11758200—22no—
73C2×#11758200—22no—
74C2×#11758200—41no—
75C2×#11758200—41no—
76C2×#11758200D414yes—
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81#14519777—22no—
82#14519777—41no—
83#14519756—22no—
84#14519756—22no—
85#14519756—41no—
86#14519756—41no—
87C4×Dic122—22no—
88C4×Dic122—41no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C4×Dic61—21no—
100#14519708—22no—
101#14519708—41no—
102C4⋊#92418—22no—
103#14519700—22no—
104#14519700—22no—
105#14519700—22no—
106#14519700—41no—
107#14519698—22no—
108#14519698—22no—
109#14519698—22no—
110#14519698D414yes—
111C22⋊#92418—22no—
112C22⋊#92418—22no—
113C4×#92418—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C25×C61—21no—
118C22×D4×C61—22no—
119C22×D4×C61—22no—
120C22×D4×C61—22no—
121C22×D4×C61—22no—
122C22×D4×C61—21no—
123C22×D4×C61—41no—
124C22×D4×C61—41no—
125C22×D4×C61C2311yescharacteristic
126C22×D4×C61C2311yescharacteristic
127C23×C4×C61—21no—
128C23×C4×C61—21no—
129C23×C4×C61C2311yescharacteristic
130C4×D4×C61—22no—
131C4×D4×C61—22no—
132C4×D4×C61—41no—
133C4×D4×C61—41no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—44no—
144C2×C22⋊C4×C61D411yescharacteristic
145C2×C22⋊C4×C61D411yescharacteristic
146C2×C42×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148#95×C61—21no—
149#95×C61D411yescharacteristic
150#95×C61D411yescharacteristic
151C24×C61—21no—
152C24×C61—24no—
153C24×C61—21no—
154C24×C61—42no—
155C24×C61—42no—
156C24×C61—42no—
157C24×C61—42no—
158C24×C61—81no—
159C24×C61—81no—
160C24×C61C2×D411yescharacteristic
161C2×D4×C61—24no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—44no—
173C2×D4×C61—44no—
174C2×D4×C61—44no—
175C2×D4×C61—44no—
176C2×D4×C61C2×D412yes—
177C2×D4×C61C2×D412yes—
178C2×D4×C61#4112yes—
179C2×D4×C61#4112yes—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—42no—
189C22×C4×C61—42no—
190C22×C4×C61—42no—
191C22×C4×C61—42no—
192C22×C4×C61—81no—
193C22×C4×C61—81no—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2411yescharacteristic
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122C2×D412yes—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C22⋊C4×C61—41no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—42no—
223C22⋊C4×C61—42no—
224C22⋊C4×C61—42no—
225C22⋊C4×C61—42no—
226C22⋊C4×C61—81no—
227C22⋊C4×C61—81no—
228C22⋊C4×C61SD1614yescomplemented
229C42×C61—21no—
230C42×C61—21no—
231C42×C61—21no—
232C42×C61—21no—
233C22⋊Dic61—42no—
234C22⋊Dic61—42no—
235#11758200—28no—
236#11758200—44no—
237#11758200—44no—
238#11758200—44no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—42no—
243C4⋊Dic61—42no—
244C4⋊Dic61C2×D412yes—
245#11758196—42no—
246#11758196—42no—
247#11758196—42no—
248#11758196—42no—
249C4×Dic61—42no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418C2×D412yes—
261C2×#92418C2×D412yes—
262C23×C61—21no—
263C23×C61—22no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—22no—
272C23×C61—48no—
273C23×C61—48no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—84no—
285C23×C61—84no—
286C23×C61—84no—
287C23×C61—84no—
288C23×C61—84no—
289C23×C61C2×SD1612yes—
290C23×C61C22×D411yescharacteristic
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×C61#12114yes—
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×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
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—41no—
323C2×C4×C61—84no—
324C2×C4×C61—84no—
325C2×C4×C61C2×SD1612yes—
326C2×C4×C61C2×SD1612yes—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C2×C4×C61C2×#4111yescharacteristic
331C2×C4×C61H(5,𝔽2)11yescharacteristic
332C2×C4×C61H(5,𝔽2)11yescharacteristic
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345Dic122—22no—
346Dic122—22no—
347Dic122—41no—
348Dic122—41no—
349Dic122—41no—
350Dic122—41no—
351Dic122—41no—
352Dic122—41no—
353#92418—22no—
354#92418—22no—
355#92418—41no—
356#92418—41no—
357#25156—611nomaximal, Sylow
358C22×C61—22no—
359C22×C61—24no—
360C22×C61—22no—
361C22×C61—22no—
362C22×C61—42no—
363C22×C61—41no—
364C22×C61—42no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—42no—
368C22×C61—41no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—816no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61#52511yescharacteristic
381C22×C61D4211yescharacteristic
382C22×C61D4211yescharacteristic
383C22×C61C22×SD1611yescharacteristic
384C22×C61#57511yescharacteristic
385C22×C61#57711yescharacteristic
386C22×C61#57711yescharacteristic
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—81no—
393C4×C61—81no—
394C4×C61C2×#12111yescharacteristic
395C4×C61#53811yescharacteristic
396C4×C61#54611yescharacteristic
397C4×C61#54611yescharacteristic
398Dic61—42no—
399Dic61—42no—
400Dic61—81no—
401Dic61—81no—
402C2×#461—611no—
403C2×#450—611no—
404C2×#450—611no—
405C2×C4×SD16—611no—
406#2429—611no—
407D4×C22⋊C4D6111yescharacteristic
408#2065—611no—
409#2035—611no—
410#2035—611no—
411#2013—611no—
412#1968—611no—
413#1923—611no—
414#1880—611no—
415#1877—611no—
416#1864—611no—
417C2×C61—42no—
418C2×C61—44no—
419C2×C61—82no—
420C2×C61#242411yescharacteristic
421C2×C61#310111yescharacteristic
422C2×C61#312311yescharacteristic
423C2×C61#326711yescharacteristic
424C2×C61#327511yescharacteristic
425C2×C61D4×SD1611yescharacteristic
426C2×C61D4×SD1611yescharacteristic
427C23×D4C2×D6111yescharacteristic
428C22×SD16—611no—
429C22×SD16—611no—
430C22×SD16—611no—
431C22×SD16—611no—
432C2×C4⋊Q8—611no—
433C2×C22⋊Q8—611no—
434C2×C22⋊Q8—611no—
435C2×C4×Q8—611no—
436C2×C4×D4C2×D6111yescharacteristic
437C2×C4×D4C2×D6111yescharacteristic
438C22×C22⋊C4—21no—
439#461—1224no—
440#450—1224no—
441#450—1224no—
442C4×SD16—1224no—
443C2×#106—611no—
444C2×#106—611no—
445C2×C4⋊C8—611no—
446C2×#103—611no—
447C2×#103—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×C22⋊C8—611no—
455C2×C22⋊C8—611no—
456C2×C4×C8—611no—
457#398—1221no—
458#396—1221no—
459#391—611no—
460#390C2×D6111yescharacteristic
461#390C2×D6111yescharacteristic
462#389—611no—
463#389—1221no—
464#388—1221no—
465#386—21no—
466#386—21no—
467#380C2×D6111yescharacteristic
468#379—21no—
469C4×C22⋊C4C2×D6111yescharacteristic
470#340—611no—
471#340—611no—
472#336—611no—
473#336—611no—
474C61#2515611yescharacteristic, complemented, Sylow
475C25—21no—
476C22×Q8—611no—
477C22×Q8—611no—
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—41no—
484C22×D4—41no—
485C22×D4C22×D6111yescharacteristic
486C22×D4C22×D6111yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C22×D6111yescharacteristic
490C2×SD16—614no—
491C2×SD16—1222no—
492C2×SD16—1222no—
493C2×SD16—1222no—
494C2×SD16—1222no—
495C2×SD16—1222no—
496C2×SD16—1222no—
497C2×SD16—1222no—
498C2×SD16—1222no—
499C2×SD16—1222no—
500C2×SD16—2441no—
501C2×SD16—2441no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—611no—
505C22×C8—611no—
506C4⋊Q8—1222no—
507C4⋊Q8—2441no—
508C22⋊Q8—1222no—
509C22⋊Q8—1222no—
510C22⋊Q8—2441no—
511C22⋊Q8—2441no—
512C4×Q8—1222no—
513C4×Q8—2441no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—41no—
517C4×D4—41no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—44no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4C22⋊D6111yescharacteristic
539C2×C22⋊C4C22⋊D6111yescharacteristic
540C2×C42—1221no—
541C2×C42C22×D6111yescharacteristic
542C2×C42C22×D6111yescharacteristic
543#106—1222no—
544#106—2441no—
545C4⋊C8—1222no—
546#103—1222no—
547#103—1222no—
548#103—1222no—
549#103—2441no—
550#102—614no—
551#102—1222no—
552#102—1222no—
553#102—1222no—
554C22⋊C8—1222no—
555C22⋊C8—1222no—
556C4×C8—1222no—
557#95—21no—
558#95—1221no—
559#95—1221no—
560#95—1221no—
561#95C22⋊D6111yescharacteristic
562#95C22⋊D6111yescharacteristic
563C24—21no—
564C24—24no—
565C24—21no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24C2×C22⋊D6111yescharacteristic
573C2×Q8—612no—
574C2×Q8—1221no—
575C2×Q8—1221no—
576C2×Q8—1221no—
577C2×Q8—1221no—
578C2×Q8—1221no—
579C2×Q8—1221no—
580C2×Q8—1221no—
581C2×Q8—1221no—
582C2×Q8—1221no—
583C2×Q8—1221no—
584C2×Q8—1221no—
585C2×D4—24no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4#1175822212yes—
601C2×D4#1175822212yes—
602C2×D4D4×D6112yes—
603C2×D4D4×D6112yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4C2×C22⋊D6111yescharacteristic
623C22×C4C2×C22⋊D6111yescharacteristic
624C22×C4C2×C22⋊D6111yescharacteristic
625C22×C4C2×C22⋊D6111yescharacteristic
626C22×C4C2×C22⋊D6111yescharacteristic
627C22×C4C23×D6111yescharacteristic
628SD16—1228no—
629SD16—2444no—
630SD16—2444no—
631SD16—2444no—
632C2×C8—612no—
633C2×C8—612no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—612no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—2442no—
653C4⋊C4—2442no—
654C4⋊C4—2442no—
655C4⋊C4—2442no—
656C4⋊C4—2442no—
657C4⋊C4—2442no—
658C22⋊C4—41no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—81no—
665C22⋊C4—81no—
666C22⋊C4—2442no—
667C22⋊C4—2442no—
668C22⋊C4#1175820014yescomplemented
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—2442no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—22no—
680C23—22no—
681C23—21no—
682C23—21no—
683C23—22no—
684C23—48no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23C2×#1175820012yes—
702C23C22×C22⋊D6111yescharacteristic
703Q8—1222no—
704Q8—1222no—
705Q8—2441no—
706Q8—2441no—
707Q8—2441no—
708Q8—2441no—
709Q8—2441no—
710Q8—2441no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4#1451975014yes—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
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—41no—
742C2×C4—41no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4C2×#1175820012yes—
758C2×C4C2×#1175820012yes—
759C2×C4C2×D4×D6111yescharacteristic
760C2×C4C2×D4×D6111yescharacteristic
761C2×C4C2×#1175822211yescharacteristic
762C2×C4C2×#1175822211yescharacteristic
763C2×C4#1451982211yescharacteristic
764C2×C4#1451982211yescharacteristic
765C8—1222no—
766C8—1222no—
767C8—2441no—
768C8—2441no—
769C22—22no—
770C22—22no—
771C22—24no—
772C22—22no—
773C22—41no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—41no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22#1684027311yescharacteristic
792C22D4×C22⋊D6111yescharacteristic
793C22D4×C22⋊D6111yescharacteristic
794C22C22×#1175820011yescharacteristic
795C22#1684056011yescharacteristic
796C22#1684057311yescharacteristic
797C22#1684057311yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—4881no—
806C4—4881no—
807C4—2442no—
808C4—2442no—
809C4C2×#1451975011yescharacteristic
810C4#1684035011yescharacteristic
811C4#1684040211yescharacteristic
812C4#1684040211yescharacteristic
813C2—42no—
814C2—44no—
815C2—82no—
816C2#2144935511yescharacteristic
817C2#2145582711yescharacteristic
818C2#2145607111yescharacteristic
819C2#2145734011yescharacteristic
820C2#2145744611yescharacteristic
821C2D4×#1175820011yescharacteristic
822C2D4×#1175820011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingD4×C22⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
hypercenterD4×C22⋊C4D61
hypocenterC61#25156
LCSG ▷ C22×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
1. C2×#16839967C2semidirect
4. C2×C4×#11758200C2semidirect
5. #21449418C2semidirect
6. #21447193C2semidirect
7. #21447015C2semidirect
8. #21447015C2semidirect
9. #21446901C2semidirect
10. #21446672C2semidirect
11. #21446427C2semidirect
12. #21446177C2semidirect
13. #21446153C2semidirect
14. #21446080C2semidirect
20. C2×#14519777C22semidirect
23. C2×C4×Dic122C22semidirect
28. C2×#14519708C22semidirect
29. C2×#14519708C22semidirect
30. C2×C4⋊#92418C22semidirect
31. C2×#14519700C22semidirect
32. C2×#14519700C22semidirect
33. C2×#14519700C22semidirect
34. C2×#14519700C22semidirect
41. C2×C4×#92418C22semidirect
44. #16839668C22semidirect
45. #16839660C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
228. C22⋊C4×C61SD16semidirect
474. C61#25156semidirect
668. C22⋊C4#11758200semidirect

Maximal subgroups

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

subgroupindex
C2×#168399672
C2×#168399132
C2×C4×#117582002
#214494182
#214471932
#214470152
#214469012
#214466722
#214464272
#214461772
#214461532
#214460802
D4×C22⋊C4×C612
#2515661