Finite Group Databasebeta

← D61×#3237 #30552159

Subgroups — D61×#3237 #30552159

Order 15616.

1758 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic
2#533×D61C211yesmaximal, characteristic
3#21457035C211yesmaximal, characteristic, complemented
4#21457034C212yesmaximal, complemented
5#21457033C211yesmaximal, characteristic, complemented
6#21457032C212yesmaximal, complemented
7#21457031C212yesmaximal, complemented
8#21457030C214yesmaximal, complemented
9#21457029C211yesmaximal, characteristic, complemented
10#21457028C212yesmaximal, complemented
11#501×D61C212yesmaximal, complemented
12#491×D61C212yesmaximal, complemented
13#485×D61C214yesmaximal
14#477×D61C212yesmaximal, complemented
15#475×D61C212yesmaximal, complemented
16#432×D61C211yesmaximal, characteristic
17C61×#3237C211yesmaximal, characteristic, complemented
18#16840319C2211yescharacteristic
19#16840319C2211yescharacteristic
20#16840318—21no—
21#16840318C2212yes—
22#16840317C2211yescharacteristic
23#16840317C2211yescharacteristic
24#16840317C2211yescharacteristic
25#16840317C2211yescharacteristic
26#16840316—21no—
27#16840316—21no—
28#16840316—21no—
29#16840316C2212yes—
30#16840315—21no—
31#16840315C2212yes—
32#16840314—21no—
33#16840314—21no—
34#16840314—21no—
35#16840314C2212yes—
36C4⋊Q8×D61C2211yescharacteristic
37C4⋊Q8×D61C2211yescharacteristic
38C4⋊Q8×D61C2211yescharacteristic
39C4⋊Q8×D61C2211yescharacteristic
40#125×D61—21no—
41#125×D61C2212yes—
42C22⋊Q8×D61—21no—
43C22⋊Q8×D61—21no—
44C22⋊Q8×D61—21no—
45C22⋊Q8×D61C2212yes—
46C4×Q8×D61—21no—
47C4×Q8×D61—21no—
48C4×Q8×D61—21no—
49C4×Q8×D61C2212yes—
50#117×D61—21no—
51#117×D61C2212yes—
52C2×C42×D61C2211yescharacteristic
53#16840172C2212yescomplemented
54#16840171C2212yescomplemented
55#16840170C2214yescomplemented
56#16840169C2214yescomplemented
57#16840168C2212yescomplemented
58#16840132C2212yescomplemented
59#16840131C2212yescomplemented
60#16840130C2212yescomplemented
61#16840129C2214yescomplemented
62#16840129C2214yescomplemented
63#16840106C2214yes—
64#16840105C2214yes—
65#16840104C2214yes—
66#16840103C2214yes—
67#16840102C2214yes—
68#16840101C2214yes—
69#16840100C2214yes—
70#16840058C2212yescomplemented
71#16840057C2212yescomplemented
72#16840056C2214yescomplemented
73#16840055C2214yescomplemented
74#16840054C2212yescomplemented
75#16840048C2212yescomplemented
76#16840047C2212yescomplemented
77#16840046C2214yescomplemented
78#16840045C2214yescomplemented
79#16840044C2212yescomplemented
80#16839819C2211yescharacteristic
81#16839818C2212yes—
82#16839817C2212yes—
83#16839816C2212yes—
84#107×D61C2214yes—
85#106×D61C2214yes—
86C4⋊C8×D61C2212yes—
87#103×D61C2214yes—
88#103×D61C2214yes—
89C22⋊C8×D61C2212yes—
90#97×D61C2212yes—
91C61×#533C2211yescharacteristic
92C61×#533C2211yescharacteristic
93C61×#501C2212yescomplemented
94C61×#491C2212yescomplemented
95C61×#485C2214yes—
96C61×#477C2212yescomplemented
97C61×#475C2212yescomplemented
98C61×#432C2211yescharacteristic
99C2×Q8×D61—21no—
100C2×Q8×D61—21no—
101C2×Q8×D61—21no—
102C2×Q8×D61C2312yes—
103C22×C4×D61D411yescharacteristic
104C22×C4×D61D411yescharacteristic
105C22×C4×D61C2311yescharacteristic
106C2×C8×D61C2314yes—
107#14519777C2311yescharacteristic
108#14519777C2311yescharacteristic
109#14519777C2311yescharacteristic
110#14519777C2311yescharacteristic
111#14519776—21no—
112#14519776—21no—
113#14519776—21no—
114#14519776—21no—
115#14519776—21no—
116#14519776C2312yes—
117#14519776C2312yes—
118#14519776C2312yes—
119#14519775—21no—
120#14519775—21no—
121#14519775—21no—
122#14519775C2312yes—
123#14519769—21no—
124#14519769C2312yes—
125#14519768—21no—
126#14519768—21no—
127#14519768C2312yes—
128#14519768C2312yes—
129#14519767—22no—
130#14519767—22no—
131#14519767—22no—
132#14519767—22no—
133#14519757—21no—
134#14519757—21no—
135#14519757—21no—
136#14519757C2312yes—
137#14519756—21no—
138#14519756—21no—
139#14519756—21no—
140#14519756C2312yes—
141#14519755—22no—
142#14519755—22no—
143#14519755—22no—
144#14519755—22no—
145#14519754—22no—
146#14519754—22no—
147#14519754—22no—
148#14519754—22no—
149#14519753—21no—
150#14519753—21no—
151#14519753—21no—
152#14519753C2312yes—
153Q8×Dic61—21no—
154Q8×Dic61—21no—
155Q8×Dic61—21no—
156Q8×Dic61C2312yes—
157C4×Dic122—21no—
158C4×Dic122—21no—
159C4×Dic122—21no—
160C4×Dic122—22no—
161C4×Dic122—22no—
162C4×Dic122—22no—
163C4×Dic122—22no—
164C4×Dic122C2312yes—
165#14519742—21no—
166#14519742—21no—
167#14519742—21no—
168#14519742—22no—
169#14519742—22no—
170#14519742—22no—
171#14519742—22no—
172#14519742C2312yes—
173#14519736—21no—
174#14519736C2312yes—
175#14519735—21no—
176#14519735—21no—
177#14519735C2312yes—
178#14519735C2312yes—
179#14519734—22no—
180#14519734—22no—
181#14519733—22no—
182#14519733—22no—
183C4⋊C4×D61—21no—
184C4⋊C4×D61—21no—
185C4⋊C4×D61—22no—
186C4⋊C4×D61—22no—
187C4⋊C4×D61—21no—
188C4⋊C4×D61—21no—
189C4⋊C4×D61—21no—
190C4⋊C4×D61—22no—
191C4⋊C4×D61—22no—
192C4⋊C4×D61C2312yes—
193C4⋊C4×D61C2312yes—
194C4⋊C4×D61C2312yes—
195C22⋊C4×D61—22no—
196C22⋊C4×D61—22no—
197C2×C4×Dic61D411yescharacteristic
198C2×C4×Dic61D411yescharacteristic
199C2×C4×Dic61C2311yescharacteristic
200C42×D61—22no—
201C42×D61—22no—
202C42×D61D411yescharacteristic
203C42×D61D411yescharacteristic
204C42×D61D411yescharacteristic
205C42×D61D411yescharacteristic
206C42×D61C2311yescharacteristic
207C42×D61C2311yescharacteristic
208C42×D61C2311yescharacteristic
209C42×D61C2311yescharacteristic
210#14519711C2314yes—
211#14519710C2314yes—
212#14519710C2314yes—
213#14519709C2314yes—
214#14519708C2314yes—
215#14519708C2314yes—
216C4⋊#92418C2312yes—
217#14519706C2314yes—
218#14519702C2314yes—
219#14519702C2314yes—
220#14519701C2314yes—
221#14519701C2314yes—
222#14519700C2314yes—
223#14519700C2314yes—
224C22⋊#92418C2312yes—
225#14519689C2314yes—
226#14519688C2312yes—
227#14519687C2314yes—
228C4⋊Q8×C61C2311yescharacteristic
229C4⋊Q8×C61C2311yescharacteristic
230C4⋊Q8×C61C2311yescharacteristic
231C4⋊Q8×C61C2311yescharacteristic
232#125×C61—21no—
233#125×C61C2312yes—
234C22⋊Q8×C61—21no—
235C22⋊Q8×C61—21no—
236C22⋊Q8×C61—21no—
237C22⋊Q8×C61C2312yes—
238C4×Q8×C61—21no—
239C4×Q8×C61—21no—
240C4×Q8×C61—21no—
241C4×Q8×C61C2312yes—
242#117×C61—21no—
243#117×C61C2312yes—
244C2×C42×C61C2311yescharacteristic
245#107×C61C2314yes—
246#106×C61C2314yes—
247C4⋊C8×C61C2312yes—
248#103×C61C2314yes—
249#103×C61C2314yes—
250C22⋊C8×C61C2312yes—
251#97×C61C2312yes—
252C23×D61C2×D411yescharacteristic
253C2×Q8×C61—21no—
254C2×Q8×C61—21no—
255C2×Q8×C61—21no—
256C2×Q8×C61C2412yes—
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2×D411yescharacteristic
259C22×C4×C61C2411yescharacteristic
260C22×Dic61C2×D411yescharacteristic
261C22×Dic61C2×D411yescharacteristic
262C22×Dic61C2×D411yescharacteristic
263Q8×D61—28no—
264Q8×D61—44no—
265Q8×D61—44no—
266Q8×D61—44no—
267C2×C4×D61—24no—
268C2×C4×D61—24no—
269C2×C4×D61—22no—
270C2×C4×D61—22no—
271C2×C4×D61—22no—
272C2×C4×D61—22no—
273C2×C4×D61—42no—
274C2×C4×D61C2×D411yescharacteristic
275C2×C4×D61C2×D411yescharacteristic
276C2×C4×D61C2×D411yescharacteristic
277C2×C4×D61C2×D411yescharacteristic
278C2×C4×D61C2×D411yescharacteristic
279C2×C4×D61C2×D411yescharacteristic
280C2×C4×D61C2×D411yescharacteristic
281C2×C4×D61C2×D411yescharacteristic
282C2×C4×D61C2×D411yescharacteristic
283C2×C4×D61C2×D411yescharacteristic
284C2×C4×D61C2411yescharacteristic
285C2×C4×D61C2411yescharacteristic
286C2×Dic122—21no—
287C2×Dic122—21no—
288C2×Dic122—21no—
289C2×Dic122—22no—
290C2×Dic122—22no—
291C2×Dic122—22no—
292C2×Dic122—22no—
293C2×Dic122C2412yes—
294C2×C8×C61C2414yes—
295C4⋊C4×C61—21no—
296C4⋊C4×C61—21no—
297C4⋊C4×C61—22no—
298C4⋊C4×C61—22no—
299C4⋊C4×C61—21no—
300C4⋊C4×C61—21no—
301C4⋊C4×C61—21no—
302C4⋊C4×C61—22no—
303C4⋊C4×C61—22no—
304C4⋊C4×C61C2412yes—
305C4⋊C4×C61C2412yes—
306C4⋊C4×C61C2412yes—
307C22⋊C4×C61—22no—
308C22⋊C4×C61—22no—
309C42×C61—22no—
310C42×C61—22no—
311C42×C61C2×D411yescharacteristic
312C42×C61C2×D411yescharacteristic
313C42×C61C2411yescharacteristic
314C42×C61C2411yescharacteristic
315C22⋊Dic61—22no—
316C22⋊Dic61—22no—
317#11758198—22no—
318#11758198—22no—
319#11758198—22no—
320#11758198—22no—
321C4⋊Dic61—21no—
322C4⋊Dic61—21no—
323C4⋊Dic61—21no—
324C4⋊Dic61—21no—
325C4⋊Dic61—21no—
326C4⋊Dic61—22no—
327C4⋊Dic61—22no—
328C4⋊Dic61—22no—
329C4⋊Dic61—22no—
330C4⋊Dic61C2412yes—
331C4⋊Dic61C2412yes—
332C4⋊Dic61C2412yes—
333#11758196—22no—
334#11758196—22no—
335#11758196—22no—
336#11758196—22no—
337#11758196—22no—
338#11758196—22no—
339#11758196—22no—
340#11758196—22no—
341#11758196—22no—
342#11758196—22no—
343#11758196—22no—
344#11758196—22no—
345#11758196—22no—
346#11758196—22no—
347#11758196—22no—
348#11758196—22no—
349C4×Dic61—22no—
350C4×Dic61—22no—
351C4×Dic61—22no—
352C4×Dic61—22no—
353C4×Dic61—22no—
354C4×Dic61—22no—
355C4×Dic61C2×D411yescharacteristic
356C4×Dic61C2×D411yescharacteristic
357C4×Dic61C2×D411yescharacteristic
358C4×Dic61C2×D411yescharacteristic
359C4×Dic61C2×D411yescharacteristic
360C4×Dic61C2×D411yescharacteristic
361C4×Dic61C2×D411yescharacteristic
362C4×Dic61C2×D411yescharacteristic
363C4×Dic61C2×D411yescharacteristic
364C4×Dic61C2×D411yescharacteristic
365C4×Dic61C2411yescharacteristic
366C4×Dic61C2411yescharacteristic
367C2×#92418C2414yes—
368C8×D61—28no—
369C23×C61C22×D411yescharacteristic
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61C22×D411yescharacteristic
374C22×D61C22×D411yescharacteristic
375Q8×C61—24no—
376Q8×C61—42no—
377Q8×C61—42no—
378Q8×C61—42no—
379C2×C4×C61—22no—
380C2×C4×C61—22no—
381C2×C4×C61—22no—
382C2×C4×C61—22no—
383C2×C4×C61—22no—
384C2×C4×C61—22no—
385C2×C4×C61—41no—
386C2×C4×C61C22×D411yescharacteristic
387C2×C4×C61C22×D411yescharacteristic
388C2×C4×C61C22×D411yescharacteristic
389C2×C4×C61C22×D411yescharacteristic
390C2×C4×C61C22×D411yescharacteristic
391C2×C4×C61C2511yescharacteristic
392C2×Dic61—22no—
393C2×Dic61—22no—
394C2×Dic61—22no—
395C2×Dic61—22no—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—41no—
399C2×Dic61C22×D411yescharacteristic
400C2×Dic61C22×D411yescharacteristic
401C2×Dic61C22×D411yescharacteristic
402C2×Dic61C22×D411yescharacteristic
403C2×Dic61C22×D411yescharacteristic
404C2×Dic61C22×D411yescharacteristic
405C4×D61—22no—
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—44no—
416C4×D61—44no—
417C4×D61—44no—
418C4×D61—44no—
419C4×D61#13714yes—
420C4×D612−1+414yes—
421Dic122—24no—
422Dic122—44no—
423Dic122—44no—
424Dic122—42no—
425Dic122—42no—
426Dic122—42no—
427Dic122—44no—
428Dic122—44no—
429C8×C61—24no—
430#92418—24no—
431C2×#3237—611nomaximal, Sylow
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61C23×D411yescharacteristic
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—44no—
440C2×D61#53612yes—
441C2×D61C2×#13712yes—
442C2×D61#57512yes—
443C4×C61—21no—
444C4×C61—21no—
445C4×C61—21no—
446C4×C61—21no—
447C4×C61—42no—
448C4×C61—42no—
449C4×C61—42no—
450C4×C61—42no—
451C4×C61C2×#13712yes—
452C4×C61C2×2−1+412yes—
453Dic61—21no—
454Dic61—21no—
455Dic61—21no—
456Dic61—21no—
457Dic61—42no—
458Dic61—42no—
459Dic61—42no—
460Dic61—42no—
461Dic61#53612yes—
462Dic61C2×#13712yes—
463C2×#533—611no—
464C2×#533—611no—
465#3237—612no—
466#3237—612no—
467#3237—614no—
468#3237—612no—
469#3237—612no—
470#3237—611no—
471#3237—611no—
472#3237—611no—
473#3237D6111yescharacteristic, direct product factor
474C2×#501—612no—
475C2×#491—612no—
476C2×#485—614no—
477C2×#477—612no—
478C2×#475—612no—
479C2×#432—611no—
480C2×C61—41no—
481C2×C61C2×#53611yescharacteristic
482C2×C61C22×#13711yescharacteristic
483C2×C61C2×#57511yescharacteristic
484D61—41no—
485D61#323714yesdirect product factor
486#533—611no—
487#533—611no—
488#533—612no—
489#533—612no—
490#533—611no—
491#533—611no—
492#533—612no—
493#533—612no—
494#533—611no—
495#533—611no—
496#533—1221no—
497#533—1221no—
498#533—1221no—
499#533—1221no—
500#533—1221no—
501#533—1221no—
502#533—1221no—
503#533—1221no—
504#533C2×D6111yescharacteristic
505#533C2×D6111yescharacteristic
506C2×C4⋊Q8—611no—
507C2×C4⋊Q8—611no—
508C2×C4⋊Q8—611no—
509C2×C4⋊Q8—611no—
510C2×#125—612no—
511C2×#125—1221no—
512C2×C22⋊Q8—612no—
513C2×C22⋊Q8—1221no—
514C2×C22⋊Q8—1221no—
515C2×C22⋊Q8—1221no—
516C2×C4×Q8—612no—
517C2×C4×Q8—1221no—
518C2×C4×Q8—1221no—
519C2×C4×Q8—1221no—
520C2×#117—612no—
521C2×#117—1221no—
522C22×C42—611no—
523#501—612no—
524#501—612no—
525#501—614no—
526#501—614no—
527#501—612no—
528#501C2×D6112yescomplemented
529#491—612no—
530#491—612no—
531#491—614no—
532#491—614no—
533#491—612no—
534#491C2×D6112yescomplemented
535#485—614no—
536#485—614no—
537#485—614no—
538#485—614no—
539#485—614no—
540#485—614no—
541#485—614no—
542#485C2×D6114yes—
543#477—612no—
544#477—612no—
545#477—614no—
546#477—612no—
547#477—614no—
548#477C2×D6112yescomplemented
549#475—612no—
550#475—612no—
551#475—614no—
552#475—612no—
553#475—614no—
554#475C2×D6112yescomplemented
555#432—611no—
556#432—612no—
557#432—612no—
558#432—612no—
559#432C2×D6111yescharacteristic
560C2×#107—614no—
561C2×#106—614no—
562C2×C4⋊C8—612no—
563C2×#103—614no—
564C2×#103—614no—
565C2×C22⋊C8—612no—
566C2×#97—612no—
567C61C2×#323711yescharacteristic, complemented, Sylow
568C22×Q8—612no—
569C22×Q8—1221no—
570C22×Q8—1221no—
571C22×Q8—1221no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C22×C8—614no—
576C4⋊Q8—612no—
577C4⋊Q8—612no—
578C4⋊Q8—612no—
579C4⋊Q8—612no—
580C4⋊Q8—611no—
581C4⋊Q8—611no—
582C4⋊Q8—611no—
583C4⋊Q8—611no—
584C4⋊Q8—1221no—
585C4⋊Q8—1221no—
586C4⋊Q8—1221no—
587C4⋊Q8—1221no—
588C4⋊Q8—1221no—
589C4⋊Q8—1221no—
590C4⋊Q8—1221no—
591C4⋊Q8—1221no—
592C4⋊Q8C22×D6111yescharacteristic
593C4⋊Q8C22×D6111yescharacteristic
594C4⋊Q8C22×D6111yescharacteristic
595C4⋊Q8C22×D6111yescharacteristic
596#125—21no—
597#125—612no—
598#125—612no—
599#125—612no—
600#125—1222no—
601#125—1222no—
602#125—1222no—
603#125—1222no—
604#125—1221no—
605#125—1221no—
606#125—1221no—
607#125C22×D6112yes—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—612no—
612C22⋊Q8—612no—
613C22⋊Q8—612no—
614C22⋊Q8—1222no—
615C22⋊Q8—1222no—
616C22⋊Q8—1222no—
617C22⋊Q8—1222no—
618C22⋊Q8—1222no—
619C22⋊Q8—1222no—
620C22⋊Q8—1222no—
621C22⋊Q8—1222no—
622C22⋊Q8—1221no—
623C22⋊Q8—1221no—
624C22⋊Q8—1221no—
625C22⋊Q8—1221no—
626C22⋊Q8—1221no—
627C22⋊Q8—1221no—
628C22⋊Q8—1221no—
629C22⋊Q8—1221no—
630C22⋊Q8—1221no—
631C22⋊Q8C22×D6112yes—
632C4×Q8—21no—
633C4×Q8—21no—
634C4×Q8—21no—
635C4×Q8—612no—
636C4×Q8—612no—
637C4×Q8—612no—
638C4×Q8—1222no—
639C4×Q8—1222no—
640C4×Q8—1222no—
641C4×Q8—1222no—
642C4×Q8—1222no—
643C4×Q8—1222no—
644C4×Q8—1221no—
645C4×Q8—1221no—
646C4×Q8—1222no—
647C4×Q8—1222no—
648C4×Q8—1221no—
649C4×Q8—1221no—
650C4×Q8—1221no—
651C4×Q8—1221no—
652C4×Q8—1221no—
653C4×Q8—1221no—
654C4×Q8—1221no—
655C4×Q8C22×D6112yes—
656#117—21no—
657#117—612no—
658#117—612no—
659#117—612no—
660#117—1222no—
661#117—1222no—
662#117—1222no—
663#117—1222no—
664#117—1221no—
665#117—1221no—
666#117—1221no—
667#117C22×D6112yes—
668C2×C4⋊C4—612no—
669C2×C4⋊C4—612no—
670C2×C4⋊C4—612no—
671C2×C4⋊C4—1221no—
672C2×C4⋊C4—1221no—
673C2×C4⋊C4—1222no—
674C2×C4⋊C4—1222no—
675C2×C4⋊C4—1222no—
676C2×C4⋊C4—1222no—
677C2×C4⋊C4—1221no—
678C2×C4⋊C4—1221no—
679C2×C4⋊C4—1221no—
680C2×C22⋊C4—1222no—
681C2×C22⋊C4—1222no—
682C2×C42—611no—
683C2×C42—611no—
684C2×C42—611no—
685C2×C42—611no—
686C2×C42—611no—
687C2×C42—611no—
688C2×C42—611no—
689C2×C42—611no—
690C2×C42—611no—
691C2×C42—611no—
692C2×C42—611no—
693C2×C42—1222no—
694C2×C42—1222no—
695C2×C42C22×D6111yescharacteristic
696#107—614no—
697#107—614no—
698#107—614no—
699#107C22×D6114yes—
700#106—614no—
701#106—614no—
702#106—614no—
703#106C22×D6114yes—
704C4⋊C8—614no—
705C4⋊C8—612no—
706C4⋊C8C22×D6112yes—
707#103—614no—
708#103—614no—
709#103—614no—
710#103—614no—
711#103—614no—
712#103—614no—
713#103C22×D6114yes—
714#103C22×D6114yes—
715C22⋊C8—612no—
716C22⋊C8—614no—
717C22⋊C8C22×D6112yes—
718#97—614no—
719#97—612no—
720#97C22×D6112yes—
721C24—611no—
722C2×Q8—21no—
723C2×Q8—21no—
724C2×Q8—21no—
725C2×Q8—612no—
726C2×Q8—1222no—
727C2×Q8—1222no—
728C2×Q8—1222no—
729C2×Q8—1222no—
730C2×Q8—1228no—
731C2×Q8—1221no—
732C2×Q8—1221no—
733C2×Q8—1221no—
734C2×Q8—2444no—
735C2×Q8—2444no—
736C2×Q8—2444no—
737C2×Q8C23×D6112yes—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—611no—
744C22×C4—611no—
745C22×C4—611no—
746C22×C4—611no—
747C22×C4—611no—
748C22×C4—611no—
749C22×C4—611no—
750C22×C4—611no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—1224no—
754C22×C4—1224no—
755C22×C4—1222no—
756C22×C4—1222no—
757C22×C4—1222no—
758C22×C4—1222no—
759C22×C4—2442no—
760C22×C4D4×D6111yescharacteristic
761C22×C4D4×D6111yescharacteristic
762C22×C4C23×D6111yescharacteristic
763C2×C8—614no—
764C2×C8—1228no—
765C2×C8C23×D6114yes—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—22no—
774C4⋊C4—22no—
775C4⋊C4—612no—
776C4⋊C4—612no—
777C4⋊C4—612no—
778C4⋊C4—1222no—
779C4⋊C4—1222no—
780C4⋊C4—1222no—
781C4⋊C4—1222no—
782C4⋊C4—1222no—
783C4⋊C4—1222no—
784C4⋊C4—1222no—
785C4⋊C4—1222no—
786C4⋊C4—1222no—
787C4⋊C4—1222no—
788C4⋊C4—1222no—
789C4⋊C4—1222no—
790C4⋊C4—1222no—
791C4⋊C4—1222no—
792C4⋊C4—1222no—
793C4⋊C4—1222no—
794C4⋊C4—1222no—
795C4⋊C4—1222no—
796C4⋊C4—1222no—
797C4⋊C4—1222no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4C23×D6112yes—
804C4⋊C4C23×D6112yes—
805C4⋊C4C23×D6112yes—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—1222no—
809C22⋊C4—1222no—
810C22⋊C4—1222no—
811C22⋊C4—1222no—
812C22⋊C4—1222no—
813C22⋊C4—1222no—
814C42—22no—
815C42—22no—
816C42—611no—
817C42—611no—
818C42—611no—
819C42—611no—
820C42—611no—
821C42—611no—
822C42—611no—
823C42—611no—
824C42—611no—
825C42—611no—
826C42—611no—
827C42—611no—
828C42—1222no—
829C42—1222no—
830C42—1222no—
831C42—1222no—
832C42—1222no—
833C42—1222no—
834C42D4×D6111yescharacteristic
835C42D4×D6111yescharacteristic
836C42C23×D6111yescharacteristic
837C42C23×D6111yescharacteristic
838C23—611no—
839C23—611no—
840C23—1222no—
841C23—1222no—
842C23—1222no—
843C23C2×D4×D6111yescharacteristic
844Q8—24no—
845Q8—42no—
846Q8—42no—
847Q8—42no—
848Q8—1224no—
849Q8—2442no—
850Q8—2442no—
851Q8—2444no—
852Q8—2444no—
853Q8—2444no—
854Q8—2444no—
855Q8—2442no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—41no—
863C2×C4—611no—
864C2×C4—611no—
865C2×C4—614no—
866C2×C4—614no—
867C2×C4—611no—
868C2×C4—611no—
869C2×C4—611no—
870C2×C4—611no—
871C2×C4—1222no—
872C2×C4—1222no—
873C2×C4—1222no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2444no—
888C2×C4—2444no—
889C2×C4—2444no—
890C2×C4—2444no—
891C2×C4—2441no—
892C2×C4C2×D4×D6111yescharacteristic
893C2×C4C2×D4×D6111yescharacteristic
894C2×C4C2×D4×D6111yescharacteristic
895C2×C4C2×D4×D6111yescharacteristic
896C2×C4C2×D4×D6111yescharacteristic
897C2×C4C24×D6111yescharacteristic
898C8—24no—
899C8—1224no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—612no—
904C22—612no—
905C22—612no—
906C22—1221no—
907C22—1221no—
908C22—1221no—
909C22—2444no—
910C22C22×D4×D6111yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—42no—
917C4—42no—
918C4—42no—
919C4—612no—
920C4—612no—
921C4—1221no—
922C4—1221no—
923C4—1221no—
924C4—1221no—
925C4—2442no—
926C4—2442no—
927C4—2442no—
928C4—2442no—
929C4#137×D6112yes—
930C42−1+4×D6112yes—
931C2—41no—
932C2—614no—
933C2—2441no—
934C2#536×D6111yescharacteristic
935C2C2×#137×D6111yescharacteristic
936C2#575×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3237C2
socleC22×C61C23×D4
prime radicalC23×D61C2×D4
hypercenter#3237D61
hypocenterC61C2×#3237
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3237

Complements

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

NH ≅ G/Ntype
3. #21457035C2semidirect
4. #21457034C2semidirect
5. #21457033C2semidirect
6. #21457032C2semidirect
7. #21457031C2semidirect
8. #21457030C2semidirect
9. #21457029C2semidirect
10. #21457028C2semidirect
11. #501×D61C2semidirect
12. #491×D61C2semidirect
14. #477×D61C2semidirect
15. #475×D61C2semidirect
17. C61×#3237C2semidirect
53. #16840172C22semidirect
54. #16840171C22semidirect
55. #16840170C22semidirect
56. #16840169C22semidirect
57. #16840168C22semidirect
58. #16840132C22semidirect
59. #16840131C22semidirect
60. #16840130C22semidirect
61. #16840129C22semidirect
62. #16840129C22semidirect
70. #16840058C22semidirect
71. #16840057C22semidirect
72. #16840056C22semidirect
73. #16840055C22semidirect
74. #16840054C22semidirect
75. #16840048C22semidirect
76. #16840047C22semidirect
77. #16840046C22semidirect
78. #16840045C22semidirect
79. #16840044C22semidirect
93. C61×#501C22semidirect
94. C61×#491C22semidirect
96. C61×#477C22semidirect
97. C61×#475C22semidirect
473. #3237D61direct (N × H)
485. D61#3237direct (N × H)
528. #501C2×D61semidirect
534. #491C2×D61semidirect
548. #477C2×D61semidirect
554. #475C2×D61semidirect
567. C61C2×#3237semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#214570352
#214570342
#214570332
#214570322
#214570312
#214570302
#214570292
#214570282
#501×D612
#491×D612
#485×D612
#477×D612
#475×D612
#432×D612
C61×#32372
C2×#323761