Finite Group Databasebeta

← #29647219

Subgroups — #29647219

Order 15616.

1102 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459856C211yesmaximal, characteristic
2#21454855C211yesmaximal, characteristic, complemented
3#21448177C211yesmaximal, characteristic, complemented
4#21444341C211yesmaximal, characteristic, complemented
5#21444340C211yesmaximal, characteristic, complemented
6#21444337C211yesmaximal, characteristic, complemented
7#21444329C211yesmaximal, characteristic, complemented
8#21444320C211yesmaximal, characteristic, complemented
9#21444316C211yesmaximal, characteristic, complemented
10#21444310C211yesmaximal, characteristic, complemented
11#21444307C211yesmaximal, characteristic, complemented
12#21444302C211yesmaximal, characteristic, complemented
13C2×#16839498C211yesmaximal, characteristic, complemented
14#328×D61C211yesmaximal, characteristic, complemented
15C61×#1504C211yesmaximal, characteristic, complemented
16#16840480C411yescharacteristic, complemented
17#16840471—21no—
18#16840454C411yescharacteristic, complemented
19#16840451C411yescharacteristic, complemented
20#16840443—21no—
21#16840441—21no—
22#16840425C411yescharacteristic, complemented
23#16840419C411yescharacteristic, complemented
24#16840418C411yescharacteristic, complemented
25#16840412C411yescharacteristic, complemented
26#16840411C411yescharacteristic, complemented
27#16840399—21no—
28#16840380—21no—
29#16840355—21no—
30#16840354—21no—
31#16840314C2211yescharacteristic
32#16840293C2211yescharacteristic
33#16840272C2211yescharacteristic
34C2×#14519756C2211yescharacteristic
35C22⋊Q8×D61C2211yescharacteristic
36#16840241—21no—
37C2×C4×C22⋊D61—21no—
38C2×C4×C22⋊D61C2211yescharacteristic
39#16839838—21no—
40#16839831—21no—
41#16839830—21no—
42#16839825—21no—
43#16839816C2211yescharacteristic
44#16839812C2211yescharacteristic
45#16839724C2211yescharacteristic
46C2×C22⋊#92418C2211yescharacteristic
47C22⋊C8×D61C2211yescharacteristic
48#16839613—21no—
49#16839613C2211yescharacteristic
50C4×C22⋊Dic61—21no—
51C4×C22⋊Dic61C2211yescharacteristic
52#16839609—21no—
53#16839609C2211yescharacteristic
54#16839607C2211yescharacteristic
55#95×D61C2211yescharacteristic
56#16839500C2211yescharacteristic
57#16839500C2211yescharacteristic
58#16839500C2211yescharacteristic
59#16839500C2211yescharacteristic
60#16839499C2211yescharacteristic
61#16839499C2211yescharacteristic
62#16839498C2211yescharacteristic
63#16839498C2211yescharacteristic
64#16839498C2211yescharacteristic
65#16839498C2211yescharacteristic
66#16839496C2211yescharacteristic
67#16839496C2211yescharacteristic
68C61×#525C2211yescharacteristic
69C61×#407C2211yescharacteristic
70C2×#95×C61C2211yescharacteristic
71C61×#328C2211yescharacteristic
72C61×#328C2211yescharacteristic
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758224—21no—
76C2×#11758224C2×C411yescharacteristic, complemented
77C22×Dic122C2×C411yescharacteristic, complemented
78C2×Q8×D61C2×C411yescharacteristic, complemented
79C22×C22⋊D61D411yescharacteristic
80C22×C4×D61—21no—
81C22×C4×D61C2311yescharacteristic
82C2×#11758189—21no—
83C22×#92418—21no—
84C2×C8×D61—21no—
85#14519776—21no—
86#14519776C2×C411yescharacteristic, complemented
87#14519775C2×C411yescharacteristic, complemented
88#14519772—21no—
89#14519771—21no—
90#14519770—21no—
91#14519770—21no—
92#14519770—21no—
93#14519769—21no—
94#14519768—21no—
95#14519768C2×C411yescharacteristic, complemented
96#14519767—21no—
97#14519764—21no—
98#14519764C2×C411yescharacteristic, complemented
99#14519763—21no—
100#14519763—21no—
101#14519761—21no—
102#14519760—21no—
103#14519759—21no—
104#14519759—21no—
105#14519759—21no—
106#14519758—21no—
107#14519758—21no—
108#14519758—21no—
109#14519757C2×C411yescharacteristic, complemented
110#14519757C2×C411yescharacteristic, complemented
111#14519756—21no—
112#14519756—21no—
113#14519756—21no—
114#14519756C2×C411yescharacteristic, complemented
115#14519756C2×C411yescharacteristic, complemented
116#14519756C2311yescharacteristic
117#14519756C2311yescharacteristic
118#14519755—21no—
119#14519755—21no—
120#14519754—21no—
121#14519754—21no—
122#14519754—21no—
123#14519754—21no—
124#14519754—21no—
125#14519753C2×C411yescharacteristic, complemented
126#14519749—21no—
127#14519749—21no—
128#14519748—21no—
129#14519748C2×C411yescharacteristic, complemented
130#14519745—21no—
131Q8×Dic61C2×C411yescharacteristic, complemented
132C4×Dic122—21no—
133#14519742—21no—
134#14519742C2×C411yescharacteristic, complemented
135#14519742C2×C411yescharacteristic, complemented
136D4×Dic61—21no—
137D4×Dic61—21no—
138D4×Dic61—21no—
139D4×Dic61C2×C411yescharacteristic, complemented
140C4×C22⋊D61—28no—
141C4×C22⋊D61—21no—
142C4×C22⋊D61C2×C411yescharacteristic
143C4×C22⋊D61C2×C411yescharacteristic
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61C2×C411yescharacteristic
146C4×C22⋊D61D411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150#14519737—21no—
151#14519737—21no—
152#14519735C2×C411yescharacteristic, complemented
153#14519734—21no—
154#14519733—21no—
155#14519733—21no—
156#14519733—21no—
157C2×C4⋊Dic61C2×C411yescharacteristic, complemented
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196—21no—
161C2×#11758196D411yescharacteristic
162C4⋊C4×D61—21no—
163C4⋊C4×D61C2×C411yescharacteristic, complemented
164C2×C22⋊Dic61—21no—
165C2×C22⋊Dic61—21no—
166C2×C22⋊Dic61D411yescharacteristic
167C2×#11758198—21no—
168C2×#11758198D411yescharacteristic
169C22⋊C4×D61—21no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61—21no—
173C2×C4×Dic61—21no—
174C2×C4×Dic61C2311yescharacteristic
175#14519706—21no—
176#14519706—21no—
177C22⋊#92418—21no—
178C22⋊#92418C2311yescharacteristic
179C22⋊#92418C2311yescharacteristic
180#14519689—21no—
181#14519689—21no—
182#14519687—21no—
183C8×Dic61—21no—
184#14519684—21no—
185#14519684—21no—
186#14519684C2311yescharacteristic
187#14519684C2311yescharacteristic
188C2×#41×C61C2×C411yescharacteristic, complemented
189C23×C4×C61—21no—
190C23×C4×C61C2311yescharacteristic
191C2×M16×C61—21no—
192#123×C61—21no—
193C22⋊Q8×C61C2×C411yescharacteristic, complemented
194C22⋊Q8×C61C2311yescharacteristic
195#121×C61C2×C411yescharacteristic, complemented
196#121×C61C2311yescharacteristic
197#120×C61—21no—
198C4×D4×C61—21no—
199C4×D4×C61—21no—
200#117×C61C2×C411yescharacteristic, complemented
201C22⋊C8×C61—21no—
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204#95×C61—21no—
205#95×C61C2311yescharacteristic
206#95×C61C2311yescharacteristic
207C24×C61C2×D411yescharacteristic
208C23×D61C2×D411yescharacteristic
209#41×C61—81no—
210C2×Q8×C61C22×C411yescharacteristic
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61C22×C411yescharacteristic
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—24no—
218C22×C4×C61—21no—
219C22×C4×C61—81no—
220C22×C4×C61—81no—
221C22×C4×C61—81no—
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2411yescharacteristic
228C2×C22⋊D61—24no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61C22⋊C411yescharacteristic
232C2×C22⋊D61C22⋊C411yescharacteristic
233C2×C22⋊D61C22⋊C411yescharacteristic
234C2×C22⋊D61C22⋊C411yescharacteristic
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244Q8×D61—81no—
245#11758224—44no—
246#11758224—81no—
247C2×C4×D61—21no—
248C2×C4×D61—24no—
249C2×C4×D61—21no—
250C2×C4×D61—81no—
251C2×C4×D61—81no—
252C2×C4×D61—81no—
253C2×C4×D61C22×C411yescharacteristic
254C2×C4×D61C22×C411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×Dic122—21no—
258C2×Dic122—21no—
259C2×Dic122—21no—
260C2×Dic122—81no—
261C2×Dic122C22×C411yescharacteristic
262C2×Dic122C22×C411yescharacteristic
263M16×C61—81no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61C22×C411yescharacteristic
269C4⋊C4×C61C22×C411yescharacteristic
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C42×C61—21no—
276C22⋊Dic61—24no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61C22⋊C411yescharacteristic
286C22⋊Dic61C22⋊C411yescharacteristic
287C22⋊Dic61C22⋊C411yescharacteristic
288C22⋊Dic61C22⋊C411yescharacteristic
289#11758198—24no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198C22⋊C411yescharacteristic
295#11758198C22⋊C411yescharacteristic
296#11758198C22⋊C411yescharacteristic
297#11758198C22⋊C411yescharacteristic
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61C22×C411yescharacteristic
304C4⋊Dic61C22×C411yescharacteristic
305#11758196—24no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196C22⋊C411yescharacteristic
319#11758196C22⋊C411yescharacteristic
320#11758196C22⋊C411yescharacteristic
321#11758196C22⋊C411yescharacteristic
322C4×Dic61—24no—
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61—21no—
326C4×Dic61—21no—
327C4×Dic61—81no—
328C4×Dic61—81no—
329C4×Dic61—81no—
330C4×Dic61C22×C411yescharacteristic
331C4×Dic61C22×C411yescharacteristic
332C4×Dic61C2×D411yescharacteristic
333C4×Dic61C2×D411yescharacteristic
334C2×#92418—21no—
335C2×#92418—21no—
336C2×#92418—81no—
337#11758189—81no—
338C8×D61—81no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—22no—
342C23×C61—21no—
343C23×C61—41no—
344C23×C61C2×C22⋊C411yescharacteristic
345C23×C61C2×C22⋊C411yescharacteristic
346C23×C61C22×D411yescharacteristic
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—22no—
350C22×D61—41no—
351C22×D61C2×C22⋊C411yescharacteristic
352C22×D61C2×C22⋊C411yescharacteristic
353Q8×C61—41no—
354D4×C61—41no—
355D4×C61—41no—
356D4×C61—41no—
357D4×C61—42no—
358D4×C61—81no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—81no—
375C2×C4×C61—84no—
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C23×C411yescharacteristic
379C2×C4×C61C22×D411yescharacteristic
380C22⋊D61—22no—
381C22⋊D61—22no—
382C22⋊D61—22no—
383C22⋊D61—42no—
384C22⋊D61—81no—
385C22⋊D61#10414yes—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—42no—
401C2×Dic61—42no—
402C2×Dic61—81no—
403C2×Dic61—81no—
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C2×C22⋊C411yescharacteristic
408C2×Dic61C2×C22⋊C411yescharacteristic
409C2×Dic61C2×C22⋊C411yescharacteristic
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—42no—
415C4×D61—81no—
416C4×D61—84no—
417Dic122—42no—
418Dic122—41no—
419Dic122—41no—
420Dic122—81no—
421Dic122—81no—
422C8×C61—41no—
423C8×C61—41no—
424#92418—41no—
425#92418—41no—
426#17548—611nomaximal, Sylow
427C22×C61—21no—
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—42no—
435C22×C61—42no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61C2×#10412yes—
440C22×C61C22×C22⋊C411yescharacteristic
441C22×C61#57711yescharacteristic
442C22×C61#57811yescharacteristic
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—42no—
449C2×D61—42no—
450C2×D61C2×#10412yes—
451C4×C61—21no—
452C4×C61—21no—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—42no—
456C4×C61—42no—
457C4×C61—41no—
458C4×C61—41no—
459C4×C61—41no—
460Dic61—21no—
461Dic61—21no—
462Dic61—21no—
463Dic61—21no—
464Dic61—21no—
465Dic61—42no—
466Dic61—42no—
467Dic61—41no—
468Dic61—41no—
469Dic61—41no—
470Dic61—41no—
471Dic61C2×#10412yes—
472#3520—611no—
473#2974—611no—
474#2275—611no—
475#1509—611no—
476#1508—611no—
477#1508—611no—
478#1506—611no—
479#1504—611no—
480#1504D6111yescharacteristic, complemented
481#1503—611no—
482#1501—611no—
483#1501—611no—
484#1500—611no—
485C2×#328—611no—
486C2×#328—611no—
487C2×C61—21no—
488C2×C61—21no—
489C2×C61—22no—
490C2×C61—41no—
491C2×C61—81no—
492C2×C61#288311yescharacteristic
493C2×C61#289811yescharacteristic
494C2×C61C22×#10411yescharacteristic
495D61—22no—
496D61—41no—
497#556—611no—
498#554—1221no—
499#552—611no—
500#552—611no—
501#551—1221no—
502#551—1221no—
503D4×Q8—611no—
504#548—611no—
505#548—611no—
506#547—611no—
507#547—611no—
508#546—1221no—
509#542—1221no—
510#539—1221no—
511#539—1221no—
512#533—611no—
513#529—611no—
514#525—611no—
515#525C2×D6111yescharacteristic
516C2×C22⋊Q8—611no—
517C2×C22⋊Q8—611no—
518#520—1221no—
519C2×C4×D4—611no—
520C2×C4×D4—1221no—
521#436—1221no—
522#435—1221no—
523#435—1221no—
524C8×D4—1221no—
525#432—611no—
526#431—611no—
527#407—611no—
528#407C2×D6111yescharacteristic
529C2×C22⋊C8—611no—
530C2×C22⋊C8—611no—
531C4×C4⋊C4—611no—
532C4×C4⋊C4—1221no—
533C4×C22⋊C4—611no—
534C4×C22⋊C4—611no—
535C4×C22⋊C4—1221no—
536C4×C22⋊C4—1221no—
537#376—611no—
538C2×#95—611no—
539C2×#95C2×D6111yescharacteristic
540#328—611no—
541#328—611no—
542#328—611no—
543#328—611no—
544#328—611no—
545#328—611no—
546#328—611no—
547#328—611no—
548#328—611no—
549#328—611no—
550#328C2×D6111yescharacteristic
551#328C2×D6111yescharacteristic
552#327—611no—
553#327—611no—
554#327C2×D6111yescharacteristic
555#327C2×D6111yescharacteristic
556C61#1754811yescharacteristic, complemented, Sylow
557C2×#41—611no—
558C2×#41—1221no—
559C2×#41C4×D6111yescharacteristic, complemented
560C22×Q8—611no—
561C22×Q8—611no—
562C22×D4—611no—
563C23×C4—21no—
564C23×C4—611no—
565C23×C4—1221no—
566C23×C4C22×D6111yescharacteristic
567C2×M16—21no—
568C2×M16—1221no—
569C22×C8—1221no—
570C22×C8—1221no—
571C4⋊Q8—611no—
572C4⋊Q8—611no—
573C4⋊Q8—1221no—
574#126—1221no—
575#126—1221no—
576#126—1221no—
577#126—1221no—
578#126—1221no—
579#125—611no—
580#125—1221no—
581#125—1221no—
582#125—1221no—
583#124—611no—
584#124—1221no—
585#124—1221no—
586#124—1221no—
587#123—21no—
588#123—1221no—
589#123—1221no—
590#123—1221no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596C22⋊Q8—611no—
597C22⋊Q8—611no—
598C22⋊Q8—611no—
599C22⋊Q8—611no—
600C22⋊Q8—611no—
601C22⋊Q8—611no—
602C22⋊Q8—611no—
603C22⋊Q8—1221no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8—1221no—
609C22⋊Q8—1221no—
610C22⋊Q8—1221no—
611C22⋊Q8—1221no—
612C22⋊Q8—1221no—
613C22⋊Q8C4×D6111yescharacteristic, complemented
614C22⋊Q8C22×D6111yescharacteristic
615#121—611no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121C4×D6111yescharacteristic, complemented
620#121C22×D6111yescharacteristic
621#120—21no—
622#120—1221no—
623C4×Q8—611no—
624C4×Q8—611no—
625C4×Q8—611no—
626C4×Q8—1221no—
627C4×Q8—1221no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—611no—
631C4×D4—611no—
632C4×D4—611no—
633C4×D4—611no—
634C4×D4—611no—
635C4×D4—611no—
636C4×D4—611no—
637C4×D4—611no—
638C4×D4—611no—
639C4×D4—1221no—
640C4×D4—1221no—
641C4×D4—1221no—
642C4×D4—1221no—
643C4×D4—1228no—
644C4×D4—1221no—
645C4×D4—1221no—
646#117—611no—
647#117—1221no—
648#117—1221no—
649#117—1221no—
650#117—1221no—
651#117C4×D6111yescharacteristic, complemented
652C2×C4⋊C4—611no—
653C2×C4⋊C4—611no—
654C2×C4⋊C4—611no—
655C2×C4⋊C4—1221no—
656C2×C4⋊C4—1221no—
657C2×C4⋊C4—1221no—
658C2×C4⋊C4—1221no—
659C2×C22⋊C4—611no—
660C2×C22⋊C4—611no—
661C2×C22⋊C4—1221no—
662C2×C22⋊C4—1221no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C42—611no—
666C2×C42—1221no—
667C2×C42—1221no—
668C2×C42—1221no—
669C2×C42—1221no—
670C4⋊C8—1221no—
671C4⋊C8—1221no—
672C22⋊C8—21no—
673C22⋊C8—611no—
674C22⋊C8—611no—
675C22⋊C8—1221no—
676C22⋊C8—1221no—
677C22⋊C8—1221no—
678C22⋊C8C22×D6111yescharacteristic
679C22⋊C8C22×D6111yescharacteristic
680#97—1221no—
681C4×C8—1221no—
682#95—21no—
683#95—611no—
684#95—611no—
685#95—1221no—
686#95—1221no—
687#95C22×D6111yescharacteristic
688#95C22×D6111yescharacteristic
689C24—611no—
690C24D4×D6111yescharacteristic
691#41—81no—
692#41—4881no—
693#41—2444no—
694C2×Q8—611no—
695C2×Q8—611no—
696C2×Q8—1221no—
697C2×Q8—1221no—
698C2×Q8—1221no—
699C2×Q8—4881no—
700C2×Q8—4881no—
701C2×Q8C2×C4×D6111yescharacteristic
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—611no—
706C2×D4—611no—
707C2×D4—611no—
708C2×D4—611no—
709C2×D4—1224no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4C2×C4×D6111yescharacteristic
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—21no—
717C22×C4—81no—
718C22×C4—81no—
719C22×C4—81no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—1221no—
728C22×C4—1224no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—4881no—
737C22×C4—4881no—
738C22×C4—4881no—
739C22×C4C2×C4×D6111yescharacteristic
740C22×C4C2×C4×D6111yescharacteristic
741C22×C4D4×D6111yescharacteristic
742C22×C4D4×D6111yescharacteristic
743C22×C4D4×D6111yescharacteristic
744C22×C4C23×D6111yescharacteristic
745M16—81no—
746M16—4881no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—1221no—
750C2×C8—1221no—
751C2×C8—4881no—
752C2×C8—4881no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—611no—
756C4⋊C4—611no—
757C4⋊C4—611no—
758C4⋊C4—611no—
759C4⋊C4—611no—
760C4⋊C4—611no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1224no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—1221no—
778C4⋊C4—1221no—
779C4⋊C4C2×C4×D6111yescharacteristic
780C4⋊C4C2×C4×D6111yescharacteristic
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—611no—
787C22⋊C4—611no—
788C22⋊C4—611no—
789C22⋊C4—611no—
790C22⋊C4—611no—
791C22⋊C4—611no—
792C22⋊C4—611no—
793C22⋊C4—611no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1224no—
799C22⋊C4—1221no—
800C22⋊C4—1221no—
801C22⋊C4—1221no—
802C22⋊C4—1221no—
803C22⋊C4—1224no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C42—21no—
809C42—611no—
810C42—611no—
811C42—611no—
812C42—611no—
813C42—1221no—
814C42—1221no—
815C42—1221no—
816C42—1221no—
817C42—1224no—
818C42—4881no—
819C42—4881no—
820C42—4881no—
821C23—22no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—611no—
827C23—611no—
828C23—1222no—
829C23—1221no—
830C23—1221no—
831C23—2441no—
832C23C22⋊C4×D6111yescharacteristic
833C23C22⋊C4×D6111yescharacteristic
834C23C2×D4×D6111yescharacteristic
835Q8—41no—
836Q8—4881no—
837Q8—4881no—
838Q8—2441no—
839Q8—2441no—
840Q8—2442no—
841D4—41no—
842D4—42no—
843D4—41no—
844D4—41no—
845D4—81no—
846D4—614no—
847D4—1222no—
848D4—1222no—
849D4—1222no—
850D4—4881no—
851D4—2442no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—81no—
868C2×C4—84no—
869C2×C4—611no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—611no—
874C2×C4—611no—
875C2×C4—1222no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—4881no—
885C2×C4—4884no—
886C2×C4—4881no—
887C2×C4—4881no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2442no—
893C2×C4—2442no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2442no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4C22⋊C4×D6111yescharacteristic
901C2×C4C22⋊C4×D6111yescharacteristic
902C2×C4C22×C4×D6111yescharacteristic
903C2×C4C2×D4×D6111yescharacteristic
904C8—41no—
905C8—41no—
906C8—2441no—
907C8—2441no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—612no—
921C22—1221no—
922C22—1221no—
923C22—1221no—
924C22—1221no—
925C22—1221no—
926C22—2442no—
927C22—2442no—
928C22#104×D6112yes—
929C22C2×C22⋊C4×D6111yescharacteristic
930C22#1684057211yescharacteristic
931C22#1684057811yescharacteristic
932C4—21no—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—42no—
937C4—42no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—612no—
942C4—1221no—
943C4—1221no—
944C4—1221no—
945C4—1221no—
946C4—1221no—
947C4—2442no—
948C4—2442no—
949C4—2441no—
950C4—2441no—
951C4—2441no—
952C4—2441no—
953C2—21no—
954C2—21no—
955C2—22no—
956C2—41no—
957C2—81no—
958C2—1222no—
959C2—2441no—
960C2#2145427711yescharacteristic
961C2#2145435011yescharacteristic
962C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1504C2
socleC22×C61C22×C22⋊C4
prime radical#21459856C2
cosocleC22×C4×C61C24
hypercenter#1504D61
hypocenterC61#17548
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #21454855C2semidirect
3. #21448177C2semidirect
4. #21444341C2semidirect
5. #21444340C2semidirect
6. #21444337C2semidirect
7. #21444329C2semidirect
8. #21444320C2semidirect
9. #21444316C2semidirect
10. #21444310C2semidirect
11. #21444307C2semidirect
12. #21444302C2semidirect
13. C2×#16839498C2semidirect
14. #328×D61C2semidirect
15. C61×#1504C2semidirect
16. #16840480C4semidirect
18. #16840454C4semidirect
19. #16840451C4semidirect
22. #16840425C4semidirect
23. #16840419C4semidirect
24. #16840418C4semidirect
25. #16840412C4semidirect
26. #16840411C4semidirect
76. C2×#11758224C2×C4semidirect
77. C22×Dic122C2×C4semidirect
78. C2×Q8×D61C2×C4semidirect
86. #14519776C2×C4semidirect
87. #14519775C2×C4semidirect
95. #14519768C2×C4semidirect
98. #14519764C2×C4semidirect
109. #14519757C2×C4semidirect
110. #14519757C2×C4semidirect
114. #14519756C2×C4semidirect
115. #14519756C2×C4semidirect
125. #14519753C2×C4semidirect
129. #14519748C2×C4semidirect
131. Q8×Dic61C2×C4semidirect
134. #14519742C2×C4semidirect
135. #14519742C2×C4semidirect
139. D4×Dic61C2×C4semidirect
152. #14519735C2×C4semidirect
157. C2×C4⋊Dic61C2×C4semidirect
163. C4⋊C4×D61C2×C4semidirect
188. C2×#41×C61C2×C4semidirect
193. C22⋊Q8×C61C2×C4semidirect
195. #121×C61C2×C4semidirect
200. #117×C61C2×C4semidirect
480. #1504D61semidirect
556. C61#17548semidirect
559. C2×#41C4×D61semidirect
613. C22⋊Q8C4×D61semidirect
619. #121C4×D61semidirect
651. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214598562
#214548552
#214481772
#214443412
#214443402
#214443372
#214443292
#214443202
#214443162
#214443102
#214443072
#214443022
C2×#168394982
#328×D612
C61×#15042
#1754861