Finite Group Databasebeta

← D61×#3236 #30552121

Subgroups — D61×#3236 #30552121

Order 15616.

1770 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
2C2×#125×D61C211yesmaximal, characteristic
3#21457027C211yesmaximal, characteristic, complemented
4#21457026C212yesmaximal, complemented
5#21457025C211yesmaximal, characteristic, complemented
6#21457024C212yesmaximal, complemented
7#21457023C214yesmaximal, complemented
8#21457022C212yesmaximal, complemented
9#21457021C211yesmaximal, characteristic, complemented
10#21457020C212yesmaximal, complemented
11#501×D61C212yesmaximal, complemented
12#491×D61C212yesmaximal, complemented
13#484×D61C212yesmaximal
14#483×D61C212yesmaximal
15#479×D61C214yesmaximal, complemented
16#432×D61C211yesmaximal, characteristic
17C61×#3236C211yesmaximal, characteristic, complemented
18#16840319C2211yescharacteristic
19#16840318—21no—
20#16840317C2211yescharacteristic
21#16840317C2211yescharacteristic
22#16840316—21no—
23#16840316C2212yes—
24#16840315—21no—
25#16840314—21no—
26#16840314C2212yes—
27C4⋊Q8×D61C2211yescharacteristic
28C4⋊Q8×D61C2211yescharacteristic
29C2×#14519769C2211yescharacteristic
30C2×#14519768C2211yescharacteristic
31C2×#14519768C2211yescharacteristic
32C2×#14519767—21no—
33C2×#14519767—21no—
34#125×D61—21no—
35#125×D61—21no—
36#125×D61—21no—
37#125×D61—21no—
38#125×D61—21no—
39#125×D61C2212yes—
40#125×D61C2212yes—
41#125×D61C2212yes—
42#125×D61C2212yes—
43C22⋊Q8×D61—21no—
44C22⋊Q8×D61C2212yes—
45C4×Q8×D61—21no—
46C4×Q8×D61C2212yes—
47#117×D61—21no—
48C2×C4⋊C4×D61—21no—
49C2×C4⋊C4×D61—21no—
50C2×C4⋊C4×D61C2211yescharacteristic
51C2×C4⋊C4×D61C2211yescharacteristic
52C2×C42×D61C2211yescharacteristic
53#16840172C2212yescomplemented
54#16840171C2212yescomplemented
55#16840170C2214yescomplemented
56#16840169C2214yescomplemented
57#16840168C2212yescomplemented
58#16840132C2212yescomplemented
59#16840131C2212yescomplemented
60#16840130C2212yescomplemented
61#16840129C2214yescomplemented
62#16840129C2214yescomplemented
63#16840099C2214yes—
64#16840098C2212yes—
65#16840097C2212yes—
66#16840096C2214yes—
67#16840095C2212yes—
68#16840094C2214yes—
69#16840093C2212yes—
70#16840092C2212yes—
71#16840091C2214yes—
72#16840090C2212yes—
73#16840072C2214yescomplemented
74#16840071C2214yescomplemented
75#16840070C2214yescomplemented
76#16840069C2214yescomplemented
77#16840068C2214yescomplemented
78#16840067C2214yescomplemented
79#16840066C2214yescomplemented
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
92C2×#125×C61C2211yescharacteristic
93C61×#501C2212yescomplemented
94C61×#491C2212yescomplemented
95C61×#484C2212yes—
96C61×#483C2212yes—
97C61×#479C2214yescomplemented
98C61×#432C2211yescharacteristic
99C2×Q8×D61—21no—
100C2×Q8×D61C2312yes—
101C22×C4×D61—21no—
102C22×C4×D61—21no—
103C22×C4×D61D411yescharacteristic
104C22×C4×D61D411yescharacteristic
105C22×C4×D61C2311yescharacteristic
106C2×C8×D61C2314yes—
107#14519777C2311yescharacteristic
108#14519777C2311yescharacteristic
109#14519776—21no—
110#14519776—21no—
111#14519776—21no—
112#14519776C2312yes—
113#14519775—21no—
114#14519775C2312yes—
115#14519769—21no—
116#14519769—21no—
117#14519769—21no—
118#14519769C2312yes—
119#14519769C2312yes—
120#14519768—21no—
121#14519768—21no—
122#14519768—21no—
123#14519768—21no—
124#14519768—21no—
125#14519768—21no—
126#14519768C2312yes—
127#14519768C2312yes—
128#14519768C2312yes—
129#14519768C2312yes—
130#14519767—22no—
131#14519767—22no—
132#14519767—22no—
133#14519767—22no—
134#14519767—22no—
135#14519767—22no—
136#14519767—22no—
137#14519767—22no—
138#14519767—22no—
139#14519767—22no—
140#14519757—21no—
141#14519757C2312yes—
142#14519756—21no—
143#14519756C2312yes—
144#14519755—22no—
145#14519755—22no—
146#14519754—22no—
147#14519754—22no—
148#14519753—21no—
149#14519753C2312yes—
150Q8×Dic61—21no—
151Q8×Dic61C2312yes—
152C4×Dic122—21no—
153C4×Dic122—22no—
154C4×Dic122—22no—
155C4×Dic122C2312yes—
156#14519742—21no—
157#14519742—22no—
158#14519742—22no—
159#14519742C2312yes—
160#14519736—21no—
161#14519735—21no—
162#14519735—21no—
163#14519734—22no—
164#14519733—22no—
165C2×C4⋊Dic61—21no—
166C2×C4⋊Dic61—21no—
167C2×C4⋊Dic61C2311yescharacteristic
168C2×C4⋊Dic61C2311yescharacteristic
169C2×#11758196—21no—
170C2×#11758196—21no—
171C2×#11758196—21no—
172C2×#11758196—21no—
173C2×#11758196—21no—
174C2×#11758196—21no—
175C4⋊C4×D61—22no—
176C4⋊C4×D61—22no—
177C4⋊C4×D61—22no—
178C4⋊C4×D61—22no—
179C4⋊C4×D61—22no—
180C4⋊C4×D61—22no—
181C4⋊C4×D61—22no—
182C4⋊C4×D61—22no—
183C4⋊C4×D61—21no—
184C4⋊C4×D61—21no—
185C4⋊C4×D61—21no—
186C4⋊C4×D61—21no—
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—
195C4⋊C4×D61C2312yes—
196C4⋊C4×D61C2312yes—
197C22⋊C4×D61—22no—
198C2×C4×Dic61D411yescharacteristic
199C2×C4×Dic61D411yescharacteristic
200C2×C4×Dic61C2311yescharacteristic
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
230#125×C61—21no—
231#125×C61—21no—
232#125×C61—21no—
233#125×C61C2312yes—
234#125×C61C2312yes—
235C22⋊Q8×C61—21no—
236C22⋊Q8×C61C2312yes—
237C4×Q8×C61—21no—
238C4×Q8×C61C2312yes—
239#117×C61—21no—
240C2×C4⋊C4×C61—21no—
241C2×C4⋊C4×C61—21no—
242C2×C4⋊C4×C61C2311yescharacteristic
243C2×C4⋊C4×C61C2311yescharacteristic
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×C61C2412yes—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2×D411yescharacteristic
259C22×C4×C61C2411yescharacteristic
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61C2×D411yescharacteristic
263C22×Dic61C2×D411yescharacteristic
264C22×Dic61C2×D411yescharacteristic
265Q8×D61—28no—
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—22no—
274C2×C4×D61—22no—
275C2×C4×D61—42no—
276C2×C4×D61—44no—
277C2×C4×D61—44no—
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×D61C2×D411yescharacteristic
285C2×C4×D61C2×D411yescharacteristic
286C2×C4×D61C2×D411yescharacteristic
287C2×C4×D61C2×D411yescharacteristic
288C2×C4×D61C2411yescharacteristic
289C2×C4×D61C2411yescharacteristic
290C2×Dic122—21no—
291C2×Dic122—22no—
292C2×Dic122—22no—
293C2×Dic122C2412yes—
294C2×C8×C61C2414yes—
295C4⋊C4×C61—22no—
296C4⋊C4×C61—22no—
297C4⋊C4×C61—22no—
298C4⋊C4×C61—22no—
299C4⋊C4×C61—21no—
300C4⋊C4×C61—21no—
301C4⋊C4×C61—21no—
302C4⋊C4×C61—21no—
303C4⋊C4×C61—21no—
304C4⋊C4×C61—22no—
305C4⋊C4×C61—22no—
306C4⋊C4×C61C2412yes—
307C4⋊C4×C61C2412yes—
308C4⋊C4×C61C2412yes—
309C22⋊C4×C61—22no—
310C42×C61—22no—
311C42×C61C2×D411yescharacteristic
312C42×C61C2×D411yescharacteristic
313C42×C61C2411yescharacteristic
314C42×C61C2411yescharacteristic
315C22⋊Dic61—22no—
316#11758198—22no—
317#11758198—22no—
318C4⋊Dic61—21no—
319C4⋊Dic61—21no—
320C4⋊Dic61—21no—
321C4⋊Dic61—21no—
322C4⋊Dic61—21no—
323C4⋊Dic61—22no—
324C4⋊Dic61—22no—
325C4⋊Dic61—22no—
326C4⋊Dic61—22no—
327C4⋊Dic61—22no—
328C4⋊Dic61—22no—
329C4⋊Dic61C2412yes—
330C4⋊Dic61C2412yes—
331C4⋊Dic61C2412yes—
332#11758196—22no—
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—
349#11758196—22no—
350#11758196—22no—
351#11758196—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#13714yes—
373C22×D61C22×D411yescharacteristic
374C22×D61C22×D411yescharacteristic
375Q8×C61—24no—
376Q8×C61—42no—
377C2×C4×C61—22no—
378C2×C4×C61—22no—
379C2×C4×C61—22no—
380C2×C4×C61—22no—
381C2×C4×C61—22no—
382C2×C4×C61—22no—
383C2×C4×C61—41no—
384C2×C4×C61—42no—
385C2×C4×C61—42no—
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×Dic61—42no—
400C2×Dic61—42no—
401C2×Dic61C22×D411yescharacteristic
402C2×Dic61C22×D411yescharacteristic
403C2×Dic61C22×D411yescharacteristic
404C2×Dic61C22×D411yescharacteristic
405C2×Dic61C22×D411yescharacteristic
406C2×Dic61C22×D411yescharacteristic
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—44no—
419C4×D61—44no—
420C4×D61—44no—
421C4×D61—44no—
422C4×D61—44no—
423C4×D61—44no—
424C4×D612−1+414yes—
425Dic122—24no—
426Dic122—44no—
427Dic122—42no—
428Dic122—44no—
429C8×C61—24no—
430#92418—24no—
431C2×#3236—611nomaximal, Sylow
432C22×C61—21no—
433C22×C61—21no—
434C22×C61C2×#13712yes—
435C22×C61C23×D411yescharacteristic
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—28no—
439C2×D61#53612yes—
440C2×D61C2×#13712yes—
441C2×D61C2×#13712yes—
442C2×D61#57512yes—
443C4×C61—21no—
444C4×C61—21no—
445C4×C61—21no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—42no—
449C4×C61—42no—
450C4×C61—42no—
451C4×C61—42no—
452C4×C61C2×2−1+412yes—
453Dic61—21no—
454Dic61—21no—
455Dic61—21no—
456Dic61—21no—
457Dic61—21no—
458Dic61—42no—
459Dic61—42no—
460Dic61—42no—
461Dic61—42no—
462Dic61#53612yes—
463C2×#533—611no—
464C22×#125—611no—
465#3236—612no—
466#3236—612no—
467#3236—612no—
468#3236—612no—
469#3236—614no—
470#3236—611no—
471#3236—611no—
472#3236—611no—
473#3236D6111yescharacteristic, direct product factor
474C2×#501—612no—
475C2×#491—612no—
476C2×#484—612no—
477C2×#483—612no—
478C2×#479—614no—
479C2×#432—611no—
480C2×C61—22no—
481C2×C61C2×#53611yescharacteristic
482C2×C61C22×#13711yescharacteristic
483C2×C61C2×#57511yescharacteristic
484D61—22no—
485D61#323614yesdirect product factor
486#533—611no—
487#533—611no—
488#533—612no—
489#533—612no—
490#533—611no—
491#533—1221no—
492#533—1221no—
493#533—1221no—
494#533—1221no—
495#533C2×D6111yescharacteristic
496C2×C4⋊Q8—611no—
497C2×C4⋊Q8—611no—
498C2×#125—612no—
499C2×#125—612no—
500C2×#125—612no—
501C2×#125—612no—
502C2×#125—611no—
503C2×#125—611no—
504C2×#125—611no—
505C2×#125—1221no—
506C2×#125—1221no—
507C2×#125—1221no—
508C2×#125—1221no—
509C2×#125—1221no—
510C2×#125—1221no—
511C2×#125—1221no—
512C2×#125C2×D6111yescharacteristic
513C2×C22⋊Q8—612no—
514C2×C22⋊Q8—1221no—
515C2×C4×Q8—612no—
516C2×C4×Q8—1221no—
517C2×#117—1221no—
518C22×C4⋊C4—611no—
519C22×C4⋊C4—611no—
520C22×C4⋊C4—1221no—
521C22×C4⋊C4—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#484—612no—
536#484—612no—
537#484—614no—
538#484—614no—
539#484—612no—
540#484C2×D6112yes—
541#483—612no—
542#483—612no—
543#483—614no—
544#483—614no—
545#483—612no—
546#483C2×D6112yes—
547#479—614no—
548#479—614no—
549#479—614no—
550#479—614no—
551#479—614no—
552#479—614no—
553#479—614no—
554#479C2×D6114yescomplemented
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×#323611yescharacteristic, complemented, Sylow
568C22×Q8—612no—
569C22×Q8—1221no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—1221no—
574C23×C4—1221no—
575C22×C8—614no—
576C4⋊Q8—612no—
577C4⋊Q8—612no—
578C4⋊Q8—611no—
579C4⋊Q8—611no—
580C4⋊Q8—1221no—
581C4⋊Q8—1221no—
582C4⋊Q8—1221no—
583C4⋊Q8—1221no—
584C4⋊Q8C22×D6111yescharacteristic
585C4⋊Q8C22×D6111yescharacteristic
586#125—21no—
587#125—21no—
588#125—21no—
589#125—612no—
590#125—612no—
591#125—612no—
592#125—612no—
593#125—612no—
594#125—612no—
595#125—1222no—
596#125—1222no—
597#125—1222no—
598#125—1222no—
599#125—1222no—
600#125—1222no—
601#125—1222no—
602#125—1222no—
603#125—1221no—
604#125—1221no—
605#125—1221no—
606#125—1221no—
607#125—1222no—
608#125—1222no—
609#125—1221no—
610#125—1221no—
611#125—1221no—
612#125—1221no—
613#125—1221no—
614#125C22×D6112yes—
615#125C22×D6112yes—
616C22⋊Q8—21no—
617C22⋊Q8—612no—
618C22⋊Q8—612no—
619C22⋊Q8—612no—
620C22⋊Q8—1222no—
621C22⋊Q8—1222no—
622C22⋊Q8—1222no—
623C22⋊Q8—1222no—
624C22⋊Q8—1221no—
625C22⋊Q8—1221no—
626C22⋊Q8—1221no—
627C22⋊Q8C22×D6112yes—
628C4×Q8—21no—
629C4×Q8—612no—
630C4×Q8—612no—
631C4×Q8—612no—
632C4×Q8—1222no—
633C4×Q8—1222no—
634C4×Q8—1222no—
635C4×Q8—1221no—
636C4×Q8—1222no—
637C4×Q8—1221no—
638C4×Q8—1221no—
639C4×Q8C22×D6112yes—
640#117—21no—
641#117—1222no—
642#117—1222no—
643#117—1221no—
644#117—1221no—
645#117—1221no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—611no—
649C2×C4⋊C4—611no—
650C2×C4⋊C4—612no—
651C2×C4⋊C4—612no—
652C2×C4⋊C4—612no—
653C2×C4⋊C4—612no—
654C2×C4⋊C4—612no—
655C2×C4⋊C4—1221no—
656C2×C4⋊C4—1221no—
657C2×C4⋊C4—1221no—
658C2×C4⋊C4—1221no—
659C2×C4⋊C4—1222no—
660C2×C4⋊C4—1222no—
661C2×C4⋊C4—1222no—
662C2×C4⋊C4—1222no—
663C2×C4⋊C4—1222no—
664C2×C4⋊C4—1222no—
665C2×C4⋊C4—1222no—
666C2×C4⋊C4—1222no—
667C2×C4⋊C4—1221no—
668C2×C4⋊C4—1221no—
669C2×C4⋊C4—1222no—
670C2×C4⋊C4—1222no—
671C2×C4⋊C4—1221no—
672C2×C4⋊C4—1221no—
673C2×C4⋊C4—1221no—
674C2×C4⋊C4—1221no—
675C2×C4⋊C4—1221no—
676C2×C4⋊C4—1221no—
677C2×C4⋊C4—1221no—
678C2×C4⋊C4—1221no—
679C2×C4⋊C4—1221no—
680C2×C4⋊C4C22×D6111yescharacteristic
681C2×C4⋊C4C22×D6111yescharacteristic
682C2×C22⋊C4—1222no—
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—611no—
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—612no—
724C2×Q8—1222no—
725C2×Q8—1222no—
726C2×Q8—1228no—
727C2×Q8—1221no—
728C2×Q8—2444no—
729C2×Q8C23×D6112yes—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—611no—
737C22×C4—611no—
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—1224no—
748C22×C4—1224no—
749C22×C4—1222no—
750C22×C4—1222no—
751C22×C4—1222no—
752C22×C4—1222no—
753C22×C4—1222no—
754C22×C4—1222no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—2442no—
758C22×C4—2444no—
759C22×C4—2444no—
760C22×C4D4×D6111yescharacteristic
761C22×C4D4×D6111yescharacteristic
762C22×C4C23×D6111yescharacteristic
763C2×C8—614no—
764C2×C8—1228no—
765C2×C8C23×D6114yes—
766C4⋊C4—22no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—22no—
776C4⋊C4—22no—
777C4⋊C4—612no—
778C4⋊C4—612no—
779C4⋊C4—612no—
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—1222no—
799C4⋊C4—1222no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1222no—
803C4⋊C4—1222no—
804C4⋊C4—1222no—
805C4⋊C4—1222no—
806C4⋊C4—1222no—
807C4⋊C4—1222no—
808C4⋊C4—1221no—
809C4⋊C4—1221no—
810C4⋊C4—1221no—
811C4⋊C4C23×D6112yes—
812C4⋊C4C23×D6112yes—
813C4⋊C4C23×D6112yes—
814C22⋊C4—22no—
815C22⋊C4—1222no—
816C22⋊C4—1222no—
817C22⋊C4—1222no—
818C42—22no—
819C42—611no—
820C42—611no—
821C42—611no—
822C42—611no—
823C42—611no—
824C42—611no—
825C42—611no—
826C42—611no—
827C42—611no—
828C42—611no—
829C42—611no—
830C42—611no—
831C42—1222no—
832C42—1222no—
833C42—1222no—
834C42D4×D6111yescharacteristic
835C42D4×D6111yescharacteristic
836C42C23×D6111yescharacteristic
837C42C23×D6111yescharacteristic
838C23—611no—
839C23—614no—
840C23—611no—
841C23—1222no—
842C23—1222no—
843C23C2×D4×D6111yescharacteristic
844Q8—24no—
845Q8—42no—
846Q8—1224no—
847Q8—2442no—
848Q8—2444no—
849Q8—2444no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—611no—
860C2×C4—614no—
861C2×C4—611no—
862C2×C4—611no—
863C2×C4—611no—
864C2×C4—611no—
865C2×C4—611no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
870C2×C4—1222no—
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—2441no—
882C2×C4—2441no—
883C2×C4—2444no—
884C2×C4—2444no—
885C2×C4—2444no—
886C2×C4—2444no—
887C2×C4—2444no—
888C2×C4—2444no—
889C2×C4—2441no—
890C2×C4—2442no—
891C2×C4—2442no—
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—612no—
903C22—612no—
904C22—612no—
905C22—612no—
906C22—1228no—
907C22—1221no—
908C22—1221no—
909C22#137×D6112yes—
910C22C22×D4×D6111yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—42no—
917C4—42no—
918C4—42no—
919C4—42no—
920C4—612no—
921C4—1221no—
922C4—1221no—
923C4—1221no—
924C4—1221no—
925C4—1221no—
926C4—2442no—
927C4—2442no—
928C4—2442no—
929C4—2442no—
930C42−1+4×D6112yes—
931C2—22no—
932C2—614no—
933C2—1222no—
934C2#536×D6111yescharacteristic
935C2C2×#137×D6111yescharacteristic
936C2#575×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3236C2
socleC22×C61C23×D4
prime radicalC23×D61C2×D4
hypercenter#3236D61
hypocenterC61C2×#3236
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3236

Complements

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

NH ≅ G/Ntype
3. #21457027C2semidirect
4. #21457026C2semidirect
5. #21457025C2semidirect
6. #21457024C2semidirect
7. #21457023C2semidirect
8. #21457022C2semidirect
9. #21457021C2semidirect
10. #21457020C2semidirect
11. #501×D61C2semidirect
12. #491×D61C2semidirect
15. #479×D61C2semidirect
17. C61×#3236C2semidirect
53. #16840172C22semidirect
54. #16840171C22semidirect
55. #16840170C22semidirect
56. #16840169C22semidirect
57. #16840168C22semidirect
58. #16840132C22semidirect
59. #16840131C22semidirect
60. #16840130C22semidirect
61. #16840129C22semidirect
62. #16840129C22semidirect
73. #16840072C22semidirect
74. #16840071C22semidirect
75. #16840070C22semidirect
76. #16840069C22semidirect
77. #16840068C22semidirect
78. #16840067C22semidirect
79. #16840066C22semidirect
93. C61×#501C22semidirect
94. C61×#491C22semidirect
97. C61×#479C22semidirect
473. #3236D61direct (N × H)
485. D61#3236direct (N × H)
528. #501C2×D61semidirect
534. #491C2×D61semidirect
554. #479C2×D61semidirect
567. C61C2×#3236semidirect

Maximal subgroups

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

subgroupindex
#533×D612
C2×#125×D612
#214570272
#214570262
#214570252
#214570242
#214570232
#214570222
#214570212
#214570202
#501×D612
#491×D612
#484×D612
#483×D612
#479×D612
#432×D612
C61×#32362
C2×#323661