Finite Group Databasebeta

← #29647821

Subgroups — #29647821

Order 15616.

1002 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459654C211yesmaximal, characteristic
2#21454847C211yesmaximal, characteristic, complemented
3#21448790C211yesmaximal, characteristic, complemented
4#21444374C211yesmaximal, characteristic, complemented
5#21444372C211yesmaximal, characteristic, complemented
6#21444358C211yesmaximal, characteristic, complemented
7#21444357C211yesmaximal, characteristic, complemented
8#21444350C211yesmaximal, characteristic, complemented
9#21444346C211yesmaximal, characteristic, complemented
10#21444342C211yesmaximal, characteristic, complemented
11#21444337C211yesmaximal, characteristic, complemented
12#21444333C211yesmaximal, characteristic, complemented
13#21444309C211yesmaximal, characteristic, complemented
14#21444307C211yesmaximal, characteristic, complemented
15C61×#1509C211yesmaximal, characteristic, complemented
16#16840465C411yescharacteristic, complemented
17#16840463—21no—
18#16840462C411yescharacteristic, complemented
19#16840456—21no—
20#16840453C411yescharacteristic, complemented
21#16840450C411yescharacteristic, complemented
22#16840437—21no—
23#16840436—21no—
24#16840424C411yescharacteristic, complemented
25#16840420C411yescharacteristic, complemented
26#16840407C411yescharacteristic, complemented
27#16840405C411yescharacteristic, complemented
28#16840356—21no—
29#16840345—21no—
30#16840323—21no—
31#16840296C2211yescharacteristic
32#16840275C2211yescharacteristic
33#16840272C2211yescharacteristic
34C22⋊Q8×D61C2211yescharacteristic
35#121×D61C2211yescharacteristic
36#16840234—21no—
37C2×C4×D244C2211yescharacteristic
38#16839835—21no—
39#16839835—21no—
40#16839832—21no—
41#16839832—21no—
42#16839819C2211yescharacteristic, complemented
43#16839724C2211yescharacteristic
44#16839724C2211yescharacteristic
45C22⋊C8×D61C2211yescharacteristic, complemented
46C22⋊C8×D61C2211yescharacteristic, complemented
47#16839664—21no—
48#16839652—21no—
49#16839652—21no—
50#16839628C2211yescharacteristic, complemented
51#16839624C2211yescharacteristic
52#16839624C2211yescharacteristic, complemented
53C4×C4⋊Dic61—21no—
54#16839609C2211yescharacteristic
55#16839609C2211yescharacteristic, complemented
56#16839500C2211yescharacteristic, complemented
57#16839500C2211yescharacteristic, complemented
58#16839499C2211yescharacteristic, complemented
59#16839499C2211yescharacteristic, complemented
60#16839498C2211yescharacteristic, complemented
61#16839498C2211yescharacteristic, complemented
62#16839497C2211yescharacteristic
63#16839497C2211yescharacteristic
64#16839496C2211yescharacteristic
65#16839496C2211yescharacteristic
66#16839495C2211yescharacteristic
67#16839495C2211yescharacteristic
68C61×#529C2211yescharacteristic
69C61×#432C2211yescharacteristic, complemented
70C4×C4⋊C4×C61C2211yescharacteristic, complemented
71C61×#328C2211yescharacteristic, complemented
72C61×#328C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758226C2×C411yescharacteristic
76C2×#11758224C2×C411yescharacteristic
77C2×Q8×D61C2×C411yescharacteristic
78C22×D244D411yescharacteristic
79C2×D4×D61—21no—
80C2×D4×D61C2×C411yescharacteristic
81C22×C4×D61C2311yescharacteristic
82C22×C4×D61C2311yescharacteristic
83C2×#11758189—21no—
84C2×#11758189—21no—
85C2×C8×D61—21no—
86C2×C8×D61—21no—
87#14519772—21no—
88#14519772—21no—
89#14519771—21no—
90#14519771—21no—
91#14519770—21no—
92#14519769C2×C411yescharacteristic
93#14519768—21no—
94#14519767—21no—
95#14519765—21no—
96#14519765C2×C411yescharacteristic
97#14519763—21no—
98#14519762—21no—
99#14519762—21no—
100#14519762—21no—
101#14519762—21no—
102#14519761—21no—
103#14519760—21no—
104#14519760—21no—
105#14519759—21no—
106#14519759—21no—
107#14519757—21no—
108#14519757C2×C411yescharacteristic
109#14519757C2×C411yescharacteristic
110#14519756C2311yescharacteristic
111#14519755—21no—
112#14519754—21no—
113#14519754—21no—
114#14519753C2×C411yescharacteristic
115#14519753C2×C411yescharacteristic
116#14519752—21no—
117#14519752—21no—
118#14519752C2×C411yescharacteristic
119#14519752C2×C411yescharacteristic
120#14519751—21no—
121#14519751C2311yescharacteristic
122#14519750—21no—
123#14519750—21no—
124#14519750—21no—
125#14519750—21no—
126#14519749—21no—
127#14519748C2×C411yescharacteristic
128#14519748C2×C411yescharacteristic
129#14519747—21no—
130#14519747—21no—
131#14519747—21no—
132#14519745—21no—
133C4×Dic122C2×C411yescharacteristic
134C4×D244—21no—
135C4×D244C2×C411yescharacteristic
136C4×D244C2×C411yescharacteristic
137C4×D244C2×C411yescharacteristic
138C4×D244C2×C411yescharacteristic
139C4×D244C2×C411yescharacteristic
140C4×D244D411yescharacteristic
141C4×D244D411yescharacteristic
142C4×D244D411yescharacteristic
143C4×D244D411yescharacteristic
144D4×Dic61—21no—
145#14519739—21no—
146#14519739—21no—
147C4×C22⋊D61—21no—
148C4×C22⋊D61—21no—
149#14519737—21no—
150#14519737—21no—
151#14519737—21no—
152#14519735—21no—
153#14519735C2×C411yescharacteristic
154#14519735C2×C411yescharacteristic
155#14519734—21no—
156#14519734—21no—
157C2×C4⋊Dic61—21no—
158C2×C4⋊Dic61D411yescharacteristic
159C4⋊C4×D61—21no—
160C4⋊C4×D61C2×C411yescharacteristic
161C4⋊C4×D61C2×C411yescharacteristic
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198D411yescharacteristic
168C2×#11758198D411yescharacteristic
169C22⋊C4×D61—21no—
170C22⋊C4×D61—21no—
171C22⋊C4×D61—21no—
172C2×C4×Dic61—21no—
173C2×C4×Dic61—21no—
174C4⋊#92418—21no—
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519689—21no—
181#14519688—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187#126×C61—21no—
188#125×C61C2×C411yescharacteristic
189#124×C61C2×C411yescharacteristic
190#123×C61—21no—
191C22⋊Q8×C61C2311yescharacteristic
192#121×C61C2311yescharacteristic
193C4×Q8×C61C2×C411yescharacteristic
194C4×D4×C61—21no—
195C4×D4×C61C2×C411yescharacteristic
196#117×C61—21no—
197C2×C4⋊C4×C61—21no—
198C2×C42×C61—21no—
199C2×C42×C61C2311yescharacteristic
200C4⋊C8×C61—21no—
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203#97×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C23×D61—21no—
207C23×D61C2×D411yescharacteristic
208C23×D61C2×D411yescharacteristic
209C2×Q8×C61C22×C411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61C22×C411yescharacteristic
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2411yescharacteristic
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228#11758226—81no—
229Q8×D61—81no—
230#11758224—81no—
231D4×D61—42no—
232D4×D61—42no—
233D4×D61—81no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—41no—
238C2×D244—41no—
239C2×D244C22⋊C411yescharacteristic
240C2×D244C22⋊C411yescharacteristic
241C2×D244C22⋊C411yescharacteristic
242C2×D244C22⋊C411yescharacteristic
243C2×D244C22×C411yescharacteristic
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—81no—
250C2×C4×D61—81no—
251C2×C4×D61C22×C411yescharacteristic
252C2×C4×D61C22×C411yescharacteristic
253C2×C4×D61C22×C411yescharacteristic
254C2×C4×D61C22×C411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×Dic122—21no—
260C2×Dic122C22×C411yescharacteristic
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—42no—
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—
276C42×C61—42no—
277C42×C61C22×C411yescharacteristic
278C42×C61C22×C411yescharacteristic
279C42×C61C2×D411yescharacteristic
280C42×C61C2×D411yescharacteristic
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—42no—
297#11758198—42no—
298#11758198—81no—
299#11758198—81no—
300#11758198C22⋊C411yescharacteristic
301#11758198C22⋊C411yescharacteristic
302#11758198C22⋊C411yescharacteristic
303#11758198C22⋊C411yescharacteristic
304#11758198C22⋊C411yescharacteristic
305#11758198C22⋊C411yescharacteristic
306#11758198C22⋊C411yescharacteristic
307#11758198C22⋊C411yescharacteristic
308C4⋊Dic61—21no—
309C4⋊Dic61—21no—
310C4⋊Dic61—42no—
311C4⋊Dic61C22⋊C411yescharacteristic
312C4⋊Dic61C22⋊C411yescharacteristic
313C4⋊Dic61C22⋊C411yescharacteristic
314C4⋊Dic61C22⋊C411yescharacteristic
315C4⋊Dic61C22×C411yescharacteristic
316C4⋊Dic61C22×C411yescharacteristic
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325C4×Dic61—21no—
326C4×Dic61—21no—
327C4×Dic61—21no—
328C4×Dic61—81no—
329C4×Dic61—81no—
330C2×#92418—21no—
331C2×#92418—21no—
332#11758189—81no—
333#11758189—81no—
334C8×D61—81no—
335C8×D61—81no—
336C23×C61—21no—
337C23×C61C22×D411yescharacteristic
338C22×D61—21no—
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—21no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—42no—
348C22×D61—81no—
349C22×D61—81no—
350C22×D61C2×C22⋊C411yescharacteristic
351C22×D61C2×C22⋊C411yescharacteristic
352C22×D61C2×C22⋊C411yescharacteristic
353C22×D61C2×C22⋊C411yescharacteristic
354Q8×C61—41no—
355D4×C61—41no—
356D4×C61—41no—
357D4×C61—41no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
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—81no—
372C2×C4×C61C2×C22⋊C411yescharacteristic
373C2×C4×C61C2×C22⋊C411yescharacteristic
374C2×C4×C61C2×C22⋊C411yescharacteristic
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C23×C411yescharacteristic
377C2×C4×C61C22×D411yescharacteristic
378C22⋊D61—42no—
379C22⋊D61—41no—
380C22⋊D61—41no—
381C22⋊D61—81no—
382C22⋊D61—81no—
383C22⋊D61—81no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—81no—
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400D244—41no—
401D244—41no—
402D244—41no—
403D244—41no—
404D244—41no—
405D244—42no—
406D244—81no—
407D244—81no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—42no—
417C4×D61—81no—
418C4×D61—81no—
419C4×D61—81no—
420C4×D61—81no—
421Dic122—41no—
422Dic122—81no—
423C8×C61—41no—
424C8×C61—41no—
425#92418—41no—
426#92418—41no—
427#17625—611nomaximal, Sylow
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61C22×C22⋊C411yescharacteristic
434C22×C61#57511yescharacteristic
435C22×C61#57511yescharacteristic
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61—81no—
455C2×D61—162no—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—21no—
460C4×C61—21no—
461C4×C61—21no—
462C4×C61—42no—
463C4×C61—41no—
464C4×C61—41no—
465C4×C61—41no—
466C4×C61—81no—
467Dic61—21no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—41no—
472Dic61—41no—
473Dic61—41no—
474Dic61—81no—
475Dic61—81no—
476#3505—611no—
477#2973—611no—
478#2357—611no—
479#1516—611no—
480#1516—611no—
481#1512—611no—
482#1512—611no—
483#1511—611no—
484#1510—611no—
485#1509—611no—
486#1509D6111yescharacteristic, complemented
487#1508—611no—
488#1507—611no—
489#1501—611no—
490#1501—611no—
491C2×C61—21no—
492C2×C61—21no—
493C2×C61—81no—
494C2×C61#288311yescharacteristic
495C2×C61#289611yescharacteristic
496C2×C61#290111yescharacteristic
497D61—41no—
498D61—41no—
499D61—41no—
500D61—41no—
501D61—81no—
502#553—611no—
503#553—611no—
504#553—1221no—
505#553—1221no—
506#552—611no—
507#552—611no—
508#551—1221no—
509#551—1221no—
510#548—611no—
511#548—611no—
512#546—611no—
513#546—611no—
514#539—1221no—
515#538—1221no—
516#534—1221no—
517#529—611no—
518#529C2×D6111yescharacteristic
519#525—611no—
520#525—611no—
521C2×C22⋊Q8—611no—
522C2×#121—611no—
523#518—1221no—
524C2×C4×D4—611no—
525#435—1221no—
526#435—1221no—
527#435—1221no—
528#435—1221no—
529#432—611no—
530#432C2×D6111yescharacteristic, complemented
531#407—611no—
532#407—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535#390—1221no—
536#388—1221no—
537#388—1221no—
538#382—611no—
539#381—611no—
540#381—611no—
541C4×C4⋊C4—1221no—
542C4×C4⋊C4C2×D6111yescharacteristic, complemented
543C4×C22⋊C4—611no—
544C4×C22⋊C4—611no—
545#328—611no—
546#328—611no—
547#328—611no—
548#328—611no—
549#328—611no—
550#328—611no—
551#328C2×D6111yescharacteristic, complemented
552#328C2×D6111yescharacteristic, complemented
553#327—611no—
554#327—611no—
555#327—611no—
556#327—611no—
557#327—611no—
558#327—611no—
559#327C2×D6111yescharacteristic
560#327C2×D6111yescharacteristic
561C61#1762511yescharacteristic, complemented, Sylow
562C2×#41—611no—
563C2×#41—611no—
564C22×Q8—611no—
565C22×D4—611no—
566C22×D4—611no—
567C22×D4—1221no—
568C23×C4—611no—
569C23×C4—611no—
570C2×M16—1221no—
571C2×M16—1221no—
572C22×C8—1221no—
573C22×C8—1221no—
574#126—21no—
575#126—1221no—
576#126—1221no—
577#126—1221no—
578#126—1221no—
579#126—1221no—
580#125—611no—
581#125—1221no—
582#125—1221no—
583#125C4×D6111yescharacteristic
584#124—611no—
585#124—1221no—
586#124—1221no—
587#124C4×D6111yescharacteristic
588#123—21no—
589#123—1221no—
590#123—1221no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
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⋊Q8C22×D6111yescharacteristic
608#121—611no—
609#121—611no—
610#121—611no—
611#121—611no—
612#121—611no—
613#121—1221no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#121C22×D6111yescharacteristic
622#120—1221no—
623#120—1221no—
624#120—1221no—
625#120—1221no—
626C4×Q8—611no—
627C4×Q8C4×D6111yescharacteristic
628C4×D4—21no—
629C4×D4—611no—
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—1221no—
639C4×D4—1221no—
640C4×D4—1221no—
641C4×D4—1221no—
642C4×D4—1221no—
643C4×D4—1221no—
644C4×D4—1221no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4C4×D6111yescharacteristic
648#117—21no—
649#117—611no—
650#117—611no—
651#117—1221no—
652#117—1221no—
653#117—1221no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—611no—
656C2×C4⋊C4—611no—
657C2×C4⋊C4—611no—
658C2×C4⋊C4—1221no—
659C2×C4⋊C4—1221no—
660C2×C22⋊C4—611no—
661C2×C22⋊C4—611no—
662C2×C22⋊C4—1221no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C22⋊C4—1221no—
670C2×C42—21no—
671C2×C42—1221no—
672C2×C42—1221no—
673C2×C42C22×D6111yescharacteristic
674C4⋊C8—21no—
675C4⋊C8—1221no—
676C22⋊C8—611no—
677C22⋊C8—611no—
678C22⋊C8—1221no—
679C22⋊C8—1221no—
680C22⋊C8—1221no—
681C22⋊C8—1221no—
682C22⋊C8C22×D6111yescharacteristic
683C22⋊C8C22×D6111yescharacteristic
684#97—21no—
685#97—1221no—
686#95—611no—
687#95—611no—
688#95—1221no—
689#95—1221no—
690#95—1221no—
691#95C22×D6111yescharacteristic
692#95C22×D6111yescharacteristic
693C24—611no—
694C24—611no—
695C24—1221no—
696#41—4881no—
697#41—4881no—
698C2×Q8—611no—
699C2×Q8—1221no—
700C2×Q8—4881no—
701C2×Q8C2×C4×D6111yescharacteristic
702C2×D4—21no—
703C2×D4—611no—
704C2×D4—611no—
705C2×D4—611no—
706C2×D4—611no—
707C2×D4—611no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—4881no—
717C2×D4—2441no—
718C2×D4—2441no—
719C2×D4—2442no—
720C2×D4—2442no—
721C2×D4C2×C4×D6111yescharacteristic
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—4881no—
744C22×C4—4881no—
745C22×C4D4×D6111yescharacteristic
746C22×C4D4×D6111yescharacteristic
747C22×C4C23×D6111yescharacteristic
748M16—4881no—
749M16—4881no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—4881no—
755C2×C8—4881no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—42no—
761C4⋊C4—611no—
762C4⋊C4—611no—
763C4⋊C4—611no—
764C4⋊C4—611no—
765C4⋊C4—611no—
766C4⋊C4—611no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—2442no—
778C4⋊C4C2×C4×D6111yescharacteristic
779C4⋊C4C2×C4×D6111yescharacteristic
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—611no—
786C22⋊C4—611no—
787C22⋊C4—611no—
788C22⋊C4—611no—
789C22⋊C4—611no—
790C22⋊C4—611no—
791C22⋊C4—611no—
792C22⋊C4—611no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1221no—
801C22⋊C4—1221no—
802C22⋊C4—1221no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—4881no—
809C22⋊C4—4881no—
810C22⋊C4—2442no—
811C22⋊C4—2442no—
812C42—21no—
813C42—42no—
814C42—1221no—
815C42—1221no—
816C42—1221no—
817C42—4881no—
818C42—4881no—
819C42C2×C4×D6111yescharacteristic
820C42C2×C4×D6111yescharacteristic
821C42D4×D6111yescharacteristic
822C42D4×D6111yescharacteristic
823C23—21no—
824C23—611no—
825C23—611no—
826C23—611no—
827C23—611no—
828C23—1221no—
829C23—1221no—
830C23—1221no—
831C23—1221no—
832C23—1221no—
833C23—4881no—
834C23—4881no—
835C23—2441no—
836C23—2441no—
837C23—2441no—
838C23—2441no—
839C23—2442no—
840C23C2×D4×D6111yescharacteristic
841Q8—41no—
842Q8—4881no—
843Q8—2441no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—4881no—
848D4—4881no—
849D4—4881no—
850D4—4881no—
851D4—4881no—
852D4—2441no—
853D4—2441no—
854D4—2441no—
855D4—2441no—
856D4—2441no—
857D4—2442no—
858D4—2442no—
859D4—2441no—
860D4—2441no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—81no—
875C2×C4—611no—
876C2×C4—611no—
877C2×C4—611no—
878C2×C4—611no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—4881no—
883C2×C4—4881no—
884C2×C4—4881no—
885C2×C4—4881no—
886C2×C4—4881no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2442no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4C22⋊C4×D6111yescharacteristic
905C2×C4C22⋊C4×D6111yescharacteristic
906C2×C4C22⋊C4×D6111yescharacteristic
907C2×C4C22⋊C4×D6111yescharacteristic
908C2×C4C22×C4×D6111yescharacteristic
909C2×C4C2×D4×D6111yescharacteristic
910C8—41no—
911C8—41no—
912C8—2441no—
913C8—2441no—
914C22—21no—
915C22—21no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—1221no—
920C22—1221no—
921C22—1221no—
922C22—1221no—
923C22—1221no—
924C22—1221no—
925C22—1221no—
926C22—1221no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—9762no—
932C22—4881no—
933C22—4881no—
934C22—4881no—
935C22—4881no—
936C22—2441no—
937C22—2441no—
938C22—2441no—
939C22C2×C22⋊C4×D6111yescharacteristic
940C22#1684055811yescharacteristic
941C22#1684056111yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—42no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—81no—
953C4—1221no—
954C4—1221no—
955C4—1221no—
956C4—1221no—
957C4—4881no—
958C4—4881no—
959C4—2441no—
960C4—2441no—
961C4—2441no—
962C2—21no—
963C2—21no—
964C2—81no—
965C2—4881no—
966C2—2441no—
967C2—2441no—
968C2—2441no—
969C2—2441no—
970C2#2145427811yescharacteristic
971C2#2145433511yescharacteristic
972C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1509C2
socleC22×C61C22×C22⋊C4
prime radical#21459654C2
cosocleC22×C4×C61C24
hypercenter#1509D61
hypocenterC61#17625
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. #21454847C2semidirect
3. #21448790C2semidirect
4. #21444374C2semidirect
5. #21444372C2semidirect
6. #21444358C2semidirect
7. #21444357C2semidirect
8. #21444350C2semidirect
9. #21444346C2semidirect
10. #21444342C2semidirect
11. #21444337C2semidirect
12. #21444333C2semidirect
13. #21444309C2semidirect
14. #21444307C2semidirect
15. C61×#1509C2semidirect
16. #16840465C4semidirect
18. #16840462C4semidirect
20. #16840453C4semidirect
21. #16840450C4semidirect
24. #16840424C4semidirect
25. #16840420C4semidirect
26. #16840407C4semidirect
27. #16840405C4semidirect
42. #16839819C22semidirect
45. C22⋊C8×D61C22semidirect
46. C22⋊C8×D61C22semidirect
50. #16839628C22semidirect
52. #16839624C22semidirect
55. #16839609C22semidirect
56. #16839500C22semidirect
57. #16839500C22semidirect
58. #16839499C22semidirect
59. #16839499C22semidirect
60. #16839498C22semidirect
61. #16839498C22semidirect
69. C61×#432C22semidirect
70. C4×C4⋊C4×C61C22semidirect
71. C61×#328C22semidirect
72. C61×#328C22semidirect
486. #1509D61semidirect
530. #432C2×D61semidirect
542. C4×C4⋊C4C2×D61semidirect
551. #328C2×D61semidirect
552. #328C2×D61semidirect
561. C61#17625semidirect

Maximal subgroups

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

subgroupindex
#214596542
#214548472
#214487902
#214443742
#214443722
#214443582
#214443572
#214443502
#214443462
#214443422
#214443372
#214443332
#214443092
#214443072
C61×#15092
#1762561