Finite Group Databasebeta

← #29647544

Subgroups — #29647544

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459839C211yesmaximal, characteristic
2#21454850C211yesmaximal, characteristic, complemented
3#21448446C211yesmaximal, characteristic, complemented
4#21444395C211yesmaximal, characteristic, complemented
5#21444385C211yesmaximal, characteristic, complemented
6#21444377C211yesmaximal, characteristic, complemented
7#21444374C211yesmaximal, characteristic, complemented
8#21444364C211yesmaximal, characteristic, complemented
9#21444361C211yesmaximal, characteristic, complemented
10#21444356C211yesmaximal, characteristic, complemented
11#21444346C211yesmaximal, characteristic, complemented
12#21444334C211yesmaximal, characteristic, complemented
13#21444323C211yesmaximal, characteristic, complemented
14C2×#16839497C211yesmaximal, characteristic, complemented
15C61×#1501C211yesmaximal, characteristic, complemented
16#16840475C411yescharacteristic, complemented
17#16840470C411yescharacteristic, complemented
18#16840464C411yescharacteristic, complemented
19#16840461—21no—
20#16840456C411yescharacteristic, complemented
21#16840431C411yescharacteristic, complemented
22#16840407—21no—
23#16840403C411yescharacteristic, complemented
24#16840400C411yescharacteristic, complemented
25#16840399—21no—
26#16840396C411yescharacteristic, complemented
27#16840394—21no—
28#16840364—21no—
29#16840348—21no—
30#16840345—21no—
31#16840307C2211yescharacteristic
32#16840298C2211yescharacteristic
33#16840275C2211yescharacteristic
34C2×#14519751C2211yescharacteristic
35#121×D61C2211yescharacteristic
36#16840234—21no—
37C2×C4×C22⋊D61C2211yescharacteristic
38#16839837—21no—
39#16839836—21no—
40#16839833—21no—
41C8×C22⋊D61—21no—
42#16839816C2211yescharacteristic, complemented
43#16839812C2211yescharacteristic, complemented
44#16839726C2211yescharacteristic, complemented
45#16839724C2211yescharacteristic, complemented
46C22⋊C8×D61C2211yescharacteristic, complemented
47#16839653—21no—
48#16839646—21no—
49#16839639—21no—
50#16839634—21no—
51#16839629C2211yescharacteristic, complemented
52#16839626C2211yescharacteristic, complemented
53#16839624C2211yescharacteristic, complemented
54#16839621C2211yescharacteristic, complemented
55C2×#14519684C2211yescharacteristic, complemented
56#16839499C2211yescharacteristic, complemented
57#16839499C2211yescharacteristic, complemented
58#16839497C2211yescharacteristic
59#16839497C2211yescharacteristic
60#16839497C2211yescharacteristic, complemented
61#16839497C2211yescharacteristic, complemented
62#16839496C2211yescharacteristic, complemented
63#16839496C2211yescharacteristic, complemented
64#16839495C2211yescharacteristic
65#16839495C2211yescharacteristic
66#16839495C2211yescharacteristic, complemented
67#16839495C2211yescharacteristic, complemented
68C61×#525C2211yescharacteristic
69C2×C22⋊C8×C61C2211yescharacteristic, complemented
70C4×C22⋊C4×C61C2211yescharacteristic, complemented
71C61×#328C2211yescharacteristic, complemented
72C61×#328C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic, complemented
74C61×#327C2211yescharacteristic, complemented
75C2×#11758226C2×C411yescharacteristic, complemented
76C2×#11758224—21no—
77C22×D244C2×C411yescharacteristic
78C22×C22⋊D61—21no—
79C22×C22⋊D61D411yescharacteristic
80C2×D4×D61—21no—
81C2×D4×D61—21no—
82C2×D4×D61C2×C411yescharacteristic, complemented
83C23×Dic61—21no—
84C22×C4×D61C2311yescharacteristic
85C2×#11758194—21no—
86C2×#11758189—21no—
87C2×C8×D61—21no—
88#14519776C2×C411yescharacteristic, complemented
89#14519773—21no—
90#14519773C2×C411yescharacteristic, complemented
91#14519772—21no—
92#14519771—21no—
93#14519770—21no—
94#14519768C2×C411yescharacteristic, complemented
95#14519767—21no—
96#14519766C2×C411yescharacteristic, complemented
97#14519765—21no—
98#14519763—21no—
99#14519763—21no—
100#14519762—21no—
101#14519762—21no—
102#14519761—21no—
103#14519761—21no—
104#14519760—21no—
105#14519759—21no—
106#14519757—21no—
107#14519754—21no—
108#14519753C2×C411yescharacteristic, complemented
109#14519752—21no—
110#14519752C2×C411yescharacteristic, complemented
111#14519752C2×C411yescharacteristic, complemented
112#14519751—21no—
113#14519751—21no—
114#14519751—21no—
115#14519751C2×C411yescharacteristic
116#14519751C2×C411yescharacteristic
117#14519751C2311yescharacteristic
118#14519751C2311yescharacteristic
119#14519750—21no—
120#14519750—21no—
121#14519750—21no—
122#14519750—21no—
123#14519749—21no—
124#14519749—21no—
125#14519749—21no—
126#14519749—21no—
127#14519748—21no—
128#14519748C2×C411yescharacteristic, complemented
129#14519747—21no—
130#14519747—21no—
131#14519747—21no—
132#14519745—21no—
133#14519745—21no—
134Q8×Dic61C2×C411yescharacteristic, complemented
135C4×D244—21no—
136D4×Dic61—21no—
137D4×Dic61C2×C411yescharacteristic, complemented
138#14519739—21no—
139#14519739C2×C411yescharacteristic, complemented
140#14519739C2×C411yescharacteristic, complemented
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#14519737—21no—
153#14519737—21no—
154#14519735—21no—
155#14519735C2×C411yescharacteristic, complemented
156#14519734—21no—
157C2×C4⋊Dic61C2×C411yescharacteristic
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196D411yescharacteristic
161C4⋊C4×D61C2×C411yescharacteristic, complemented
162C2×C22⋊Dic61D411yescharacteristic
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198D411yescharacteristic
168C22⋊C4×D61—21no—
169C22⋊C4×D61—21no—
170C2×C4×Dic61C2311yescharacteristic
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418—21no—
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176#14519689—21no—
177#14519689—21no—
178#14519687—21no—
179C8×Dic61—21no—
180#14519684—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187C2×#41×C61C2×C411yescharacteristic
188C23×C4×C61C2311yescharacteristic
189C22×C8×C61—21no—
190#123×C61—21no—
191C22⋊Q8×C61C2×C411yescharacteristic
192C22⋊Q8×C61C2311yescharacteristic
193#121×C61C2×C411yescharacteristic
194#121×C61C2311yescharacteristic
195#120×C61—21no—
196C4×D4×C61—21no—
197C4×D4×C61—21no—
198#117×C61C2×C411yescharacteristic
199C2×C22⋊C4×C61—21no—
200C2×C42×C61—21no—
201C22⋊C8×C61—21no—
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61C2×D411yescharacteristic
207C23×D61—21no—
208C23×D61—21no—
209C23×D61C2×D411yescharacteristic
210#41×C61—81no—
211C2×Q8×C61C22×C411yescharacteristic
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61C22×C411yescharacteristic
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—81no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2411yescharacteristic
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—42no—
235C2×C22⋊D61—81no—
236C2×C22⋊D61—81no—
237C2×C22⋊D61C22⋊C411yescharacteristic
238C2×C22⋊D61C22⋊C411yescharacteristic
239C2×C22⋊D61C22⋊C411yescharacteristic
240C2×C22⋊D61C22⋊C411yescharacteristic
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—42no—
246C22×Dic61—81no—
247C22×Dic61—81no—
248C22×Dic61C2×D411yescharacteristic
249C22×Dic61C2×D411yescharacteristic
250C22×Dic61C2×D411yescharacteristic
251#11758226—81no—
252#11758224—81no—
253#11758224—81no—
254D4×D61—44no—
255D4×D61—81no—
256D4×D61—81no—
257D4×D61—81no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244—21no—
261C2×D244—21no—
262C2×D244—81no—
263C2×D244C22×C411yescharacteristic
264C2×D244C22×C411yescharacteristic
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—81no—
270C2×C4×D61C22×C411yescharacteristic
271C2×C4×D61C22×C411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×Dic122—21no—
275C2×C8×C61—21no—
276C2×C8×C61—21no—
277C2×C8×C61—81no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61C22×C411yescharacteristic
281C4⋊C4×C61C22×C411yescharacteristic
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—42no—
288C42×C61—21no—
289C42×C61—81no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61C22⋊C411yescharacteristic
293C22⋊Dic61C22⋊C411yescharacteristic
294C22⋊Dic61C22⋊C411yescharacteristic
295C22⋊Dic61C22⋊C411yescharacteristic
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—81no—
309#11758198—81no—
310#11758198C22⋊C411yescharacteristic
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313#11758198C22⋊C411yescharacteristic
314C4⋊Dic61—21no—
315C4⋊Dic61—21no—
316C4⋊Dic61—21no—
317C4⋊Dic61C22×C411yescharacteristic
318C4⋊Dic61C22×C411yescharacteristic
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—81no—
324#11758196—81no—
325#11758196C22⋊C411yescharacteristic
326#11758196C22⋊C411yescharacteristic
327#11758196C22⋊C411yescharacteristic
328#11758196C22⋊C411yescharacteristic
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61C22×C411yescharacteristic
332C4×Dic61C22×C411yescharacteristic
333C4×Dic61C2×D411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335#11758194—81no—
336C2×#92418—21no—
337C2×#92418—21no—
338#11758189—81no—
339C8×D61—81no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—22no—
343C23×C61—21no—
344C23×C61—41no—
345C23×C61C2×C22⋊C411yescharacteristic
346C23×C61C2×C22⋊C411yescharacteristic
347C23×C61C22×D411yescharacteristic
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—42no—
355C22×D61—42no—
356C22×D61—81no—
357C22×D61—81no—
358C22×D61—81no—
359C22×D61—81no—
360C22×D61C2×C22⋊C411yescharacteristic
361C22×D61C2×C22⋊C411yescharacteristic
362Q8×C61—41no—
363D4×C61—41no—
364D4×C61—41no—
365D4×C61—41no—
366D4×C61—42no—
367D4×C61—81no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—81no—
384C2×C4×C61C2×C22⋊C411yescharacteristic
385C2×C4×C61C2×C22⋊C411yescharacteristic
386C2×C4×C61C23×C411yescharacteristic
387C2×C4×C61C22×D411yescharacteristic
388C22⋊D61—22no—
389C22⋊D61—22no—
390C22⋊D61—41no—
391C22⋊D61—41no—
392C22⋊D61—42no—
393C22⋊D61—41no—
394C22⋊D61—41no—
395C22⋊D61—41no—
396C22⋊D61—41no—
397C22⋊D61—81no—
398C22⋊D61—81no—
399C22⋊D61—81no—
400C22⋊D61—81no—
401C22⋊D61—81no—
402C2×Dic61—21no—
403C2×Dic61—21no—
404C2×Dic61—21no—
405C2×Dic61—21no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—81no—
415C2×Dic61—81no—
416C2×Dic61—84no—
417C2×Dic61C2×C22⋊C411yescharacteristic
418C2×Dic61C2×C22⋊C411yescharacteristic
419C2×Dic61C2×C22⋊C411yescharacteristic
420C2×Dic61C2×C22⋊C411yescharacteristic
421C2×Dic61C2×C22⋊C411yescharacteristic
422C2×Dic61C2×C22⋊C411yescharacteristic
423D244—41no—
424D244—41no—
425D244—42no—
426D244—81no—
427D244—81no—
428D244—81no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—42no—
434C4×D61—81no—
435C4×D61—81no—
436C4×D61—81no—
437Dic122—81no—
438C8×C61—41no—
439C8×C61—41no—
440#92418—41no—
441#92418—41no—
442#17597—611nomaximal, Sylow
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—42no—
451C22×C61—42no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61#42112yes—
456C22×C61C22×C22⋊C411yescharacteristic
457C22×C61#57611yescharacteristic
458C22×C61#57711yescharacteristic
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—41no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—41no—
471C2×D61—81no—
472C2×D61—81no—
473C2×D61—162no—
474C2×D61—162no—
475C4×C61—21no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—41no—
480C4×C61—41no—
481C4×C61—41no—
482C4×C61—81no—
483C4×C61—81no—
484Dic61—21no—
485Dic61—21no—
486Dic61—21no—
487Dic61—21no—
488Dic61—21no—
489Dic61—21no—
490Dic61—41no—
491Dic61—41no—
492Dic61—81no—
493Dic61—81no—
494#3519—611no—
495#2974—611no—
496#2318—611no—
497#1521—611no—
498#1519—611no—
499#1517—611no—
500#1516—611no—
501#1514—611no—
502#1513—611no—
503#1512—611no—
504#1510—611no—
505#1507—611no—
506#1504—611no—
507#1501D6111yescharacteristic, complemented
508C2×#327—611no—
509C2×C61—21no—
510C2×C61—21no—
511C2×C61—22no—
512C2×C61—41no—
513C2×C61—81no—
514C2×C61#288311yescharacteristic
515C2×C61#289711yescharacteristic
516C2×C61C2×#42111yescharacteristic
517D61—41no—
518D61—41no—
519D61—81no—
520D61—81no—
521#555—611no—
522#554—611no—
523#553—611no—
524#553—611no—
525#553—1221no—
526#550—611no—
527#546—611no—
528#546—611no—
529#546—1221no—
530#546—1221no—
531D42—611no—
532D42—1221no—
533#540—1221no—
534#538—1221no—
535#538—1221no—
536#532—611no—
537#529—611no—
538#525—611no—
539#525C2×D6111yescharacteristic
540C2×#121—611no—
541C2×#121—611no—
542#518—1221no—
543C2×C4×D4—611no—
544#436—1221no—
545#435—1221no—
546#435—1221no—
547C8×D4—1221no—
548#432—611no—
549#431—611no—
550#407—611no—
551#407—611no—
552C2×C22⋊C8—611no—
553C2×C22⋊C8C2×D6111yescharacteristic, complemented
554#388—1221no—
555#387—1221no—
556#386—1221no—
557#385—1221no—
558#383—611no—
559#382—611no—
560#381—611no—
561#380—611no—
562C4×C22⋊C4C2×D6111yescharacteristic, complemented
563C2×#95—611no—
564#328—611no—
565#328—611no—
566#328C2×D6111yescharacteristic, complemented
567#328C2×D6111yescharacteristic, complemented
568#327—611no—
569#327—611no—
570#327—611no—
571#327—611no—
572#327—611no—
573#327—611no—
574#327—611no—
575#327—611no—
576#327—611no—
577#327—611no—
578#327C2×D6111yescharacteristic, complemented
579#327C2×D6111yescharacteristic, complemented
580C61#1759711yescharacteristic, complemented, Sylow
581C2×#41—611no—
582C2×#41—1221no—
583C2×#41C4×D6111yescharacteristic
584C22×D4—611no—
585C22×D4—611no—
586C22×D4—611no—
587C22×D4—1221no—
588C22×D4—1221no—
589C22×D4—1221no—
590C23×C4—611no—
591C23×C4—1221no—
592C23×C4C22×D6111yescharacteristic
593C2×M16—1221no—
594C2×M16—1221no—
595C22×C8—21no—
596C22×C8—1221no—
597C4⋊Q8—611no—
598#127—611no—
599#127—1221no—
600#126—1221no—
601#126—1221no—
602#126—1221no—
603#125—611no—
604#125—1221no—
605#124—611no—
606#124—1221no—
607#124—1221no—
608#124—1221no—
609#123—21no—
610#123—1221no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614#123—1221no—
615#123—1221no—
616C22⋊Q8—611no—
617C22⋊Q8—1221no—
618C22⋊Q8—1221no—
619C22⋊Q8C4×D6111yescharacteristic
620C22⋊Q8C22×D6111yescharacteristic
621#121—611no—
622#121—611no—
623#121—611no—
624#121—611no—
625#121—611no—
626#121—611no—
627#121—611no—
628#121—1221no—
629#121—1221no—
630#121—1221no—
631#121—1221no—
632#121—1221no—
633#121—1221no—
634#121—1221no—
635#121—1221no—
636#121—1221no—
637#121—1221no—
638#121—1221no—
639#121—1221no—
640#121—1221no—
641#121C4×D6111yescharacteristic
642#121C22×D6111yescharacteristic
643#120—21no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649C4×Q8—611no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—611no—
653C4×D4—611no—
654C4×D4—611no—
655C4×D4—611no—
656C4×D4—611no—
657C4×D4—611no—
658C4×D4—611no—
659C4×D4—611no—
660C4×D4—611no—
661C4×D4—611no—
662C4×D4—611no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4—1221no—
670C4×D4—1221no—
671#117—611no—
672#117—1221no—
673#117—1221no—
674#117C4×D6111yescharacteristic
675C2×C4⋊C4—611no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—611no—
678C2×C4⋊C4—1221no—
679C2×C4⋊C4—1221no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—611no—
682C2×C22⋊C4—611no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4—1221no—
687C2×C22⋊C4—1221no—
688C2×C22⋊C4—1221no—
689C2×C42—21no—
690C2×C42—611no—
691C4⋊C8—1221no—
692C4⋊C8—1221no—
693C22⋊C8—21no—
694C22⋊C8—611no—
695C22⋊C8—611no—
696C22⋊C8—1221no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8C22×D6111yescharacteristic
700C22⋊C8C22×D6111yescharacteristic
701#97—1221no—
702C4×C8—1221no—
703#95—611no—
704#95—611no—
705#95—1221no—
706#95—1221no—
707#95—1221no—
708#95—1221no—
709#95—1221no—
710#95C22×D6111yescharacteristic
711#95C22×D6111yescharacteristic
712C24—611no—
713C24—1221no—
714C24—1221no—
715C24D4×D6111yescharacteristic
716#41—81no—
717#41—4881no—
718#41—4881no—
719#41—4881no—
720C2×Q8—1221no—
721C2×Q8C2×C4×D6111yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—611no—
726C2×D4—611no—
727C2×D4—611no—
728C2×D4—611no—
729C2×D4—611no—
730C2×D4—611no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—4881no—
744C2×D4—4881no—
745C2×D4—4881no—
746C2×D4—4881no—
747C2×D4—4881no—
748C2×D4—4881no—
749C2×D4—2444no—
750C2×D4—2442no—
751C2×D4C2×C4×D6111yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—81no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—4881no—
772C22×C4—4881no—
773C22×C4—4881no—
774C22×C4—2442no—
775C22×C4C2×C4×D6111yescharacteristic
776C22×C4C2×C4×D6111yescharacteristic
777C22×C4D4×D6111yescharacteristic
778C22×C4D4×D6111yescharacteristic
779C22×C4D4×D6111yescharacteristic
780C22×C4C23×D6111yescharacteristic
781M16—4881no—
782M16—4881no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—81no—
786C2×C8—1221no—
787C2×C8—1221no—
788C2×C8—4881no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—611no—
794C4⋊C4—611no—
795C4⋊C4—611no—
796C4⋊C4—611no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1221no—
804C4⋊C4—4881no—
805C4⋊C4—4881no—
806C4⋊C4C2×C4×D6111yescharacteristic
807C4⋊C4C2×C4×D6111yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—42no—
814C22⋊C4—611no—
815C22⋊C4—611no—
816C22⋊C4—611no—
817C22⋊C4—611no—
818C22⋊C4—611no—
819C22⋊C4—611no—
820C22⋊C4—611no—
821C22⋊C4—611no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—1221no—
825C22⋊C4—1221no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—1221no—
836C22⋊C4—4881no—
837C22⋊C4—4881no—
838C42—21no—
839C42—81no—
840C42—611no—
841C42—611no—
842C42—611no—
843C42—611no—
844C42—1221no—
845C42—1221no—
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—41no—
851C23—611no—
852C23—611no—
853C23—1221no—
854C23—1221no—
855C23—1221no—
856C23—1221no—
857C23—4881no—
858C23—4881no—
859C23—4881no—
860C23—4881no—
861C23—2441no—
862C23—2441no—
863C23—2442no—
864C23—2442no—
865C23C22⋊C4×D6111yescharacteristic
866C23C22⋊C4×D6111yescharacteristic
867C23C2×D4×D6111yescharacteristic
868Q8—41no—
869Q8—4881no—
870D4—41no—
871D4—42no—
872D4—41no—
873D4—41no—
874D4—81no—
875D4—1222no—
876D4—1222no—
877D4—4881no—
878D4—4881no—
879D4—4881no—
880D4—4881no—
881D4—4881no—
882D4—4881no—
883D4—4881no—
884D4—4881no—
885D4—2441no—
886D4—2441no—
887D4—2442no—
888D4—2441no—
889D4—2441no—
890D4—2442no—
891D4—2441no—
892D4—2441no—
893D4—2441no—
894D4—2441no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—81no—
911C2×C4—611no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—611no—
915C2×C4—611no—
916C2×C4—611no—
917C2×C4—1221no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—4881no—
922C2×C4—4881no—
923C2×C4—4881no—
924C2×C4—4881no—
925C2×C4—4884no—
926C2×C4—4881no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2442no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4C22⋊C4×D6111yescharacteristic
941C2×C4C22⋊C4×D6111yescharacteristic
942C2×C4C22×C4×D6111yescharacteristic
943C2×C4C2×D4×D6111yescharacteristic
944C8—41no—
945C8—41no—
946C8—2441no—
947C8—2441no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—42no—
956C22—42no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—1221no—
961C22—1221no—
962C22—1221no—
963C22—1221no—
964C22—1221no—
965C22—1221no—
966C22—9762no—
967C22—9762no—
968C22—4881no—
969C22—4881no—
970C22—2441no—
971C22—2441no—
972C22—2441no—
973C22—2441no—
974C22—2441no—
975C22—2441no—
976C22#1683977712yes—
977C22C2×C22⋊C4×D6111yescharacteristic
978C22#1684056411yescharacteristic
979C22#1684056911yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4—1221no—
990C4—1221no—
991C4—1221no—
992C4—1221no—
993C4—1221no—
994C4—1221no—
995C4—4881no—
996C4—4881no—
997C4—2441no—
998C4—2441no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—81no—
1004C2—4881no—
1005C2—4881no—
1006C2—2441no—
1007C2—2441no—
1008C2#2145427711yescharacteristic
1009C2#2145434111yescharacteristic
1010C2C2×#1683977711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1501C2
socleC22×C61C22×C22⋊C4
prime radical#21459839C2
cosocleC22×C4×C61C24
hypercenter#1501D61
hypocenterC61#17597
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
2. #21454850C2semidirect
3. #21448446C2semidirect
4. #21444395C2semidirect
5. #21444385C2semidirect
6. #21444377C2semidirect
7. #21444374C2semidirect
8. #21444364C2semidirect
9. #21444361C2semidirect
10. #21444356C2semidirect
11. #21444346C2semidirect
12. #21444334C2semidirect
13. #21444323C2semidirect
14. C2×#16839497C2semidirect
15. C61×#1501C2semidirect
16. #16840475C4semidirect
17. #16840470C4semidirect
18. #16840464C4semidirect
20. #16840456C4semidirect
21. #16840431C4semidirect
23. #16840403C4semidirect
24. #16840400C4semidirect
26. #16840396C4semidirect
42. #16839816C22semidirect
43. #16839812C22semidirect
44. #16839726C22semidirect
45. #16839724C22semidirect
46. C22⋊C8×D61C22semidirect
51. #16839629C22semidirect
52. #16839626C22semidirect
53. #16839624C22semidirect
54. #16839621C22semidirect
55. C2×#14519684C22semidirect
56. #16839499C22semidirect
57. #16839499C22semidirect
60. #16839497C22semidirect
61. #16839497C22semidirect
62. #16839496C22semidirect
63. #16839496C22semidirect
66. #16839495C22semidirect
67. #16839495C22semidirect
69. C2×C22⋊C8×C61C22semidirect
70. C4×C22⋊C4×C61C22semidirect
71. C61×#328C22semidirect
72. C61×#328C22semidirect
73. C61×#327C22semidirect
74. C61×#327C22semidirect
75. C2×#11758226C2×C4semidirect
82. C2×D4×D61C2×C4semidirect
88. #14519776C2×C4semidirect
90. #14519773C2×C4semidirect
94. #14519768C2×C4semidirect
96. #14519766C2×C4semidirect
108. #14519753C2×C4semidirect
110. #14519752C2×C4semidirect
111. #14519752C2×C4semidirect
128. #14519748C2×C4semidirect
134. Q8×Dic61C2×C4semidirect
137. D4×Dic61C2×C4semidirect
139. #14519739C2×C4semidirect
140. #14519739C2×C4semidirect
155. #14519735C2×C4semidirect
161. C4⋊C4×D61C2×C4semidirect
507. #1501D61semidirect
553. C2×C22⋊C8C2×D61semidirect
562. C4×C22⋊C4C2×D61semidirect
566. #328C2×D61semidirect
567. #328C2×D61semidirect
578. #327C2×D61semidirect
579. #327C2×D61semidirect
580. C61#17597semidirect

Maximal subgroups

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

subgroupindex
#214598392
#214548502
#214484462
#214443952
#214443852
#214443772
#214443742
#214443642
#214443612
#214443562
#214443462
#214443342
#214443232
C2×#168394972
C61×#15012
#1759761