Finite Group Databasebeta

← #30587845

Subgroups — #30587845

Order 15616.

7270 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460248C214yesmaximal, complemented
2#21460224C211yesmaximal, characteristic, complemented
3#21460219C212yesmaximal, complemented
4#21460204C214yesmaximal, complemented
5#21460194C214yesmaximal, complemented
6#21460177C214yesmaximal, complemented
7#21460164C212yesmaximal, complemented
8#21460153C212yesmaximal, complemented
9#21460131C218yesmaximal, complemented
10#21459960C214yesmaximal, complemented
11#21459446C212yesmaximal, complemented
12#21459428C212yesmaximal, complemented
13#21459380C214yesmaximal, complemented
14D4×#11758226C214yesmaximal, complemented
15#21459239C218yesmaximal, complemented
16#21459151C214yesmaximal, complemented
17#21459116C212yesmaximal, complemented
18#532×D61C211yesmaximal, characteristic, complemented
19C61×#3550C211yesmaximal, characteristic, complemented
20C22×#11758226C2214yescomplemented
21C2×#41×D61C2212yescomplemented
22#16840511C2218yescomplemented
23#16840510C2218yescomplemented
24#16840508C22116yescomplemented
25#16840504C2214yescomplemented
26#16840503C22116yescomplemented
27#16840502C2218yescomplemented
28#16840478C2212yescomplemented
29#16840478C2218yescomplemented
30#16840478C2218yescomplemented
31#16840477C2214yescomplemented
32#16840472C2214yescomplemented
33#16840472C2214yescomplemented
34#16840462C2218yescomplemented
35#16840456C2218yescomplemented
36#16840453C2218yescomplemented
37#16840446C2218yescomplemented
38#16840440C2218yescomplemented
39#16840437C22116yescomplemented
40#16840434C2214yescomplemented
41#16840434C2218yescomplemented
42#16840434C2214yescomplemented
43#16840423C2218yescomplemented
44#16840415C2218yescomplemented
45#16840415C2214yescomplemented
46#16840415C2214yescomplemented
47#16840405C2218yescomplemented
48#16840405C2218yescomplemented
49#16840403C2218yescomplemented
50#16840403C22116yescomplemented
51D4×D244C2214yescomplemented
52D4×D244C2218yescomplemented
53#16840397C2212yescomplemented
54#16840389C2218yescomplemented
55#16840384C2218yescomplemented
56#16840382C22116yescomplemented
57#16840367C2218yescomplemented
58#16840364C22116yescomplemented
59#16840363C2218yescomplemented
60#16840351C22116yescomplemented
61#16840346C22116yescomplemented
62#16840342C2218yescomplemented
63#16840342C2218yescomplemented
64#16840342C2218yescomplemented
65#16840337C2218yescomplemented
66#16840336C2214yescomplemented
67#16840331C2214yescomplemented
68#16840330C2218yescomplemented
69#16840330C2218yescomplemented
70#16840328C2218yescomplemented
71#16840326C2214yescomplemented
72#16840323C2218yescomplemented
73#16840323C2218yescomplemented
74#16840317C2212yescomplemented
75#16840317C2212yescomplemented
76#16840313C2212yes—
77#16840313C2218yescomplemented
78#16840313C2211yescharacteristic, complemented
79#16840313C2212yescomplemented
80#16840313C2218yescomplemented
81#16840312C2212yescomplemented
82#16840312C2211yescharacteristic, complemented
83#16840311C2218yescomplemented
84#16840311C2212yescomplemented
85#16840310C2211yescharacteristic
86#16840309C2214yescomplemented
87#16840308C2212yescomplemented
88#16840307C2214yescomplemented
89C4⋊Q8×D61C2211yescharacteristic, complemented
90#127×D61C2211yescharacteristic
91#16840299C2214yescomplemented
92#16840299C2214yescomplemented
93#16840298C2214yescomplemented
94#16840298C2214yescomplemented
95#16840297C2214yescomplemented
96#16840297C2214yescomplemented
97#16840295C22116yescomplemented
98#16840291C2218yescomplemented
99#124×D61C2212yescomplemented
100#16840275C22116yescomplemented
101#16840275C2218yescomplemented
102#16840275C2214yescomplemented
103#16840275C2214yescomplemented
104#16840274C2214yescomplemented
105#16840270C2218yescomplemented
106#16840270C2218yescomplemented
107#121×D61C2214yescomplemented
108C4×#11758226C2218yescomplemented
109C4×#11758226C2214yescomplemented
110C4×#11758226C2214yescomplemented
111#16840230C2214yescomplemented
112C4×D4×D61C2218yescomplemented
113C4×D4×D61C2214yescomplemented
114#117×D61C2214yescomplemented
115C2×C42×D61C2211yescharacteristic, complemented
116C61×#563C2214yescomplemented
117C61×#559C2212yescomplemented
118Q82×C61C2212yescomplemented
119C61×#556C2214yescomplemented
120D4×Q8×C61C2214yescomplemented
121C61×#542C2218yescomplemented
122C61×#536C2214yescomplemented
123C61×#533C2212yescomplemented
124C61×#532C2211yescharacteristic
125C2×#11758226—416no—
126C2×#11758226C2314yes—
127C2×#11758226C2314yes—
128C2×#11758226C2318yes—
129C2×#11758226C2318yes—
130C2×#11758226C2312yes—
131C2×#11758226C2318yes—
132C2×#11758226C2318yes—
133C2×#11758222C2314yes—
134C2×#11758222C2312yes—
135C2×#11758222C2314yes—
136C2×#11758224C2312yes—
137C2×#11758224C2314yes—
138#41×D61—48no—
139C2×Q8×D61C2312yes—
140C22×D244C2318yes—
141C22×D244C2314yes—
142C2×D4×D61C2314yes—
143C2×D4×D61C2318yes—
144C2×D4×D61C2314yes—
145C2×D4×D61C2312yes—
146C22×C4×D61C2311yescharacteristic
147C22×C4×D61C2314yes—
148C22×C4×D61C2312yes—
149C22×C4×D61C2318yes—
150#14519777C2311yescharacteristic
151#14519777C2312yes—
152#14519776C2314yes—
153#14519775C2312yes—
154#14519775C2318yes—
155#14519774C2318yes—
156#14519774C2311yescharacteristic
157#14519774C2312yes—
158#14519774C2318yes—
159#14519773C2312yes—
160#14519773C2314yes—
161#14519773C2318yes—
162#14519772C2318yes—
163#14519772C2318yes—
164#14519771C23116yes—
165#14519770C23116yes—
166#14519769C2318yes—
167#14519768C2314yes—
168#14519768C2314yes—
169#14519767C23116yes—
170#14519766C2312yes—
171#14519766C2318yes—
172#14519766C2318yes—
173#14519766C23116yes—
174#14519766C2314yes—
175#14519766C2314yes—
176#14519765C2314yes—
177#14519765C2312yes—
178#14519765C2318yes—
179#14519764C2312yes—
180#14519763C23116yes—
181#14519763C2318yes—
182#14519762C23116yes—
183#14519762C2318yes—
184#14519762C23116yes—
185#14519762C23116yes—
186#14519762C23116yes—
187#14519762C2318yes—
188#14519761C2318yes—
189#14519760C2318yes—
190#14519760C2318yes—
191#14519759C23116yes—
192#14519759C23116yes—
193#14519757C2314yes—
194#14519757C2314yes—
195#14519755C23116yes—
196#14519755C23116yes—
197#14519755C23116yes—
198#14519753C2314yes—
199#14519753C2318yes—
200#14519753C2318yes—
201#14519753C23116yes—
202#14519753C2314yes—
203#14519752C2318yes—
204#14519752C2314yes—
205#14519752C23116yes—
206#14519752C23116yes—
207#14519752C2318yes—
208#14519752C2318yes—
209#14519752C23116yes—
210#14519752C2314yes—
211#14519752C23116yes—
212#14519752C2314yes—
213#14519752C2314yes—
214#14519752C2314yes—
215#14519751C2318yes—
216#14519751C23116yes—
217#14519751C2314yes—
218#14519751C2314yes—
219#14519751C2314yes—
220#14519750C23116yes—
221#14519750C23116yes—
222#14519750C2318yes—
223#14519750C23116yes—
224#14519750C23116yes—
225#14519750C23116yes—
226#14519749C2318yes—
227#14519748C2314yes—
228#14519748C2318yes—
229#14519747C23116yes—
230#14519747C2318yes—
231#14519747C23116yes—
232#14519747C2318yes—
233#14519747C2318yes—
234#14519747C23116yes—
235#14519745C2318yes—
236#14519745C2318yes—
237Q8×Dic61C2314yes—
238Q8×Dic61C2314yes—
239#14519742C2314yes—
240#14519742C2314yes—
241C4×D244C2318yes—
242C4×D244C23116yes—
243C4×D244C2318yes—
244C4×D244C2314yes—
245C4×D244C2318yes—
246C4×D244C2314yes—
247C4×D244C2318yes—
248C4×D244C2314yes—
249D4×Dic61C2314yes—
250#14519739C2314yes—
251#14519739C2314yes—
252#14519739C2314yes—
253#14519739C2314yes—
254#14519739C2314yes—
255#14519739C2318yes—
256#14519739C23116yes—
257#14519739C2318yes—
258C4×C22⋊D61C2318yes—
259C4×C22⋊D61C23116yes—
260#14519737C23116yes—
261#14519737C2318yes—
262#14519737C2318yes—
263#14519737C2318yes—
264#14519736C2314yes—
265#14519735C2318yes—
266#14519735C2314yes—
267#14519735C2314yes—
268#14519735C2318yes—
269#14519735C23116yes—
270#14519735C2318yes—
271#14519734C2318yes—
272#14519734C2318yes—
273#14519733C2318yes—
274C4⋊C4×D61C2314yes—
275C4⋊C4×D61C2318yes—
276C4⋊C4×D61C2318yes—
277C22⋊C4×D61C2318yes—
278C22⋊C4×D61C2318yes—
279C22⋊C4×D61C23116yes—
280C2×C4×Dic61C2312yes—
281C2×C4×Dic61C2311yescharacteristic
282C42×D61C2312yes—
283C42×D61C2311yescharacteristic
284C42×D61C2311yescharacteristic
285C42×D61C2311yescharacteristic
286C42×D61C2311yescharacteristic
287C42×D61C2312yes—
288C42×D61C2318yes—
289C42×D61C2318yes—
290C2×#41×C61C2312yes—
291C22×Q8×C61C2314yes—
292C4⋊Q8×C61C2311yescharacteristic
293C4⋊Q8×C61C2312yes—
294C4⋊Q8×C61C2312yes—
295C4⋊Q8×C61C2318yes—
296C4⋊Q8×C61C2318yes—
297#127×C61C2311yescharacteristic
298#126×C61C23116yes—
299#125×C61C2314yes—
300#124×C61C2312yes—
301#124×C61C2318yes—
302#124×C61C2318yes—
303#123×C61C2318yes—
304#123×C61C2318yes—
305C22⋊Q8×C61C2314yes—
306C22⋊Q8×C61C2314yes—
307C22⋊Q8×C61C2318yes—
308C22⋊Q8×C61C23116yes—
309#121×C61C2314yes—
310C4×Q8×C61C2314yes—
311C4×Q8×C61C2314yes—
312C4×Q8×C61C2318yes—
313C4×D4×C61C2314yes—
314C4×D4×C61C2318yes—
315#117×C61C2314yes—
316#117×C61C2314yes—
317C2×C42×C61C2311yescharacteristic
318C23×D61C2411yescharacteristic
319C23×D61C2414yes—
320C23×D61C2418yes—
321#41×C61—44no—
322C2×Q8×C61—48no—
323C2×Q8×C61C2414yes—
324C2×Q8×C61C2414yes—
325C2×Q8×C61C2412yes—
326C2×Q8×C61C2418yes—
327C2×D4×C61C2414yes—
328C2×D4×C61C2414yes—
329C2×D4×C61C2412yes—
330C22×C4×C61C2414yes—
331C22×C4×C61C2412yes—
332C22×C4×C61C2411yescharacteristic
333C22×C4×C61C2418yes—
334C2×C22⋊D61C2414yes—
335C2×C22⋊D61C2414yes—
336C2×C22⋊D61C2414yes—
337C2×C22⋊D61C24116yes—
338C2×C22⋊D61C2418yes—
339C2×C22⋊D61C2418yes—
340C22×Dic61C2414yes—
341C22×Dic61C2411yescharacteristic
342C22×Dic61C2412yes—
343#11758226—216no—
344#11758226—44no—
345#11758226—416no—
346#11758226—416no—
347#11758226—416no—
348#11758226—48no—
349#11758226—416no—
350Q8×D61—44no—
351#11758224—44no—
352#11758224—48no—
353D4×D61—48no—
354D4×D61—416no—
355D4×D61—44no—
356D4×D61—48no—
357#11758222—48no—
358#11758222—44no—
359#11758222—48no—
360C2×D244—48no—
361C2×D244—416no—
362C2×D244C2414yes—
363C2×D244C2414yes—
364C2×D244C2418yes—
365C2×D244C2414yes—
366C2×D244C2414yes—
367C2×D244C2412yes—
368C2×D244C2418yes—
369C2×D244C24116yes—
370C2×D244C2414yes—
371C2×D244C2418yes—
372C2×D244C24116yes—
373C2×C4×D61—24no—
374C2×C4×D61—216no—
375C2×C4×D61—416no—
376C2×C4×D61—44no—
377C2×C4×D61C2418yes—
378C2×C4×D61C2411yescharacteristic
379C2×C4×D61C2412yes—
380C2×C4×D61C2414yes—
381C2×C4×D61C2411yescharacteristic
382C2×C4×D61C2414yes—
383C2×C4×D61C2411yescharacteristic
384C2×C4×D61C2414yes—
385C2×C4×D61C2412yes—
386C2×C4×D61C2418yes—
387C2×C4×D61C24116yes—
388C2×C4×D61C2412yes—
389C2×C4×D61C2412yes—
390C2×C4×D61C2418yes—
391C2×C4×D61C24116yes—
392C2×C4×D61C2411yescharacteristic
393C2×Dic122C2412yes—
394C2×Dic122C2414yes—
395C2×Dic122C2414yes—
396C4⋊C4×C61C2414yes—
397C4⋊C4×C61C2414yes—
398C4⋊C4×C61C2414yes—
399C4⋊C4×C61C2414yes—
400C4⋊C4×C61C2414yes—
401C4⋊C4×C61C2418yes—
402C4⋊C4×C61C24116yes—
403C4⋊C4×C61C2418yes—
404C22⋊C4×C61C2418yes—
405C22⋊C4×C61C2418yes—
406C22⋊C4×C61C2418yes—
407C22⋊C4×C61C24116yes—
408C42×C61C2412yes—
409C42×C61C2411yescharacteristic
410C42×C61C2411yescharacteristic
411C42×C61C2418yes—
412C42×C61C2418yes—
413C22⋊Dic61C2418yes—
414C22⋊Dic61C2418yes—
415#11758198C2418yes—
416#11758198C2418yes—
417#11758198C2418yes—
418#11758198C24116yes—
419#11758198C2418yes—
420#11758198C2418yes—
421#11758198C2418yes—
422#11758198C2418yes—
423#11758198C24116yes—
424#11758198C2418yes—
425#11758198C2418yes—
426#11758198C2418yes—
427#11758198C24116yes—
428C4⋊Dic61C2414yes—
429C4⋊Dic61C2414yes—
430C4⋊Dic61C2414yes—
431C4⋊Dic61C2418yes—
432C4⋊Dic61C2418yes—
433#11758196C24116yes—
434#11758196C2418yes—
435#11758196C24116yes—
436#11758196C2418yes—
437#11758196C2418yes—
438C4×Dic61C2412yes—
439C4×Dic61C2418yes—
440C4×Dic61C2412yes—
441C4×Dic61C2411yescharacteristic
442C4×Dic61C2412yes—
443C4×Dic61C2412yes—
444C4×Dic61C2412yes—
445C4×Dic61C2411yescharacteristic
446C4×Dic61C2418yes—
447C4×Dic61C2418yes—
448C23×C61C2514yes—
449C23×C61C2511yescharacteristic
450C22×D61—22no—
451C22×D61—28no—
452C22×D61—42no—
453C22×D61—48no—
454C22×D61—48no—
455C22×D61—416no—
456C22×D61C2518yes—
457C22×D61C2514yes—
458C22×D61C2511yescharacteristic
459C22×D61C2511yescharacteristic
460Q8×C61—28no—
461Q8×C61—28no—
462Q8×C61—42no—
463Q8×C61—48no—
464D4×C61—28no—
465D4×C61—42no—
466D4×C61—44no—
467C2×C4×C61—28no—
468C2×C4×C61—22no—
469C2×C4×C61—24no—
470C2×C4×C61—48no—
471C2×C4×C61C2514yes—
472C2×C4×C61C2512yes—
473C2×C4×C61C2511yescharacteristic
474C2×C4×C61C2518yes—
475C2×C4×C61C2518yes—
476C2×C4×C61C2511yescharacteristic
477C2×C4×C61C2512yes—
478C22⋊D61—44no—
479C22⋊D61—44no—
480C22⋊D61—44no—
481C22⋊D61—48no—
482C22⋊D61—416no—
483C22⋊D61—48no—
484C2×Dic61—28no—
485C2×Dic61—22no—
486C2×Dic61—42no—
487C2×Dic61C2512yes—
488C2×Dic61C2512yes—
489C2×Dic61C2511yescharacteristic
490C2×Dic61C2518yes—
491C2×Dic61C2514yes—
492C2×Dic61C2511yescharacteristic
493D244—216no—
494D244—28no—
495D244—28no—
496D244—28no—
497D244—48no—
498D244—416no—
499D244—44no—
500D244—42no—
501D244—44no—
502D244—48no—
503D244—416no—
504C4×D61—22no—
505C4×D61—28no—
506C4×D61—22no—
507C4×D61—28no—
508C4×D61—24no—
509C4×D61—24no—
510C4×D61—216no—
511C4×D61—22no—
512C4×D61—28no—
513C4×D61—216no—
514C4×D61—42no—
515C4×D61—42no—
516C4×D61—416no—
517C4×D61—416no—
518C4×D61—48no—
519C4×D61H(5,𝔽2)14yes—
520Dic122—44no—
521Dic122—44no—
522Dic122—42no—
523#62759—611nomaximal, Sylow
524C22×C61—21no—
525C22×C61—24no—
526C22×C61—22no—
527C22×C61—28no—
528C22×C61C2611yescharacteristic
529C2×D61—22no—
530C2×D61—24no—
531C2×D61—21no—
532C2×D61—28no—
533C2×D61—22no—
534C2×D61—28no—
535C2×D61—28no—
536C2×D61—28no—
537C2×D61—44no—
538C2×D61—88no—
539C2×D61—816no—
540C2×D61C2×H(5,𝔽2)12yes—
541C4×C61—21no—
542C4×C61—24no—
543C4×C61—28no—
544C4×C61—22no—
545C4×C61—28no—
546C4×C61C2×H(5,𝔽2)12yes—
547C4×C61#58514yes—
548Dic61—21no—
549Dic61—24no—
550Dic61—28no—
551Dic61—22no—
552Dic61—22no—
553Dic61C2×H(5,𝔽2)12yes—
554#3551—614no—
555#3550D6111yescharacteristic, complemented
556#3549—611no—
557#3548—612no—
558#3547—614no—
559#3546—614no—
560#3545—614no—
561#3544—612no—
562#3543—612no—
563#3542—618no—
564#3529—614no—
565#3483—612no—
566#3481—612no—
567#3475—614no—
568D4×#41—614no—
569#3460—618no—
570#3449—614no—
571#3444—612no—
572C2×#532—611no—
573C2×C61—41no—
574C2×C61—44no—
575C2×C61C22×H(5,𝔽2)11yescharacteristic
576C2×C61C2×#58512yes—
577D61—22no—
578D61—41no—
579D61—44no—
580D61—48no—
581C22×#41—612no—
582C22×#41—614no—
583#563—618no—
584#563C2×D6114yescomplemented
585#562—618no—
586#562—6116no—
587H(3,𝔽4)—614no—
588#560—6116no—
589#560—618no—
590#559C2×D6112yescomplemented
591Q82C2×D6112yescomplemented
592#556C2×D6114yescomplemented
593#555—618no—
594#555—612no—
595#555—618no—
596#555—614no—
597#554—614no—
598#554—614no—
599#553—618no—
600#553—618no—
601#552—618no—
602#552—618no—
603#551—6116no—
604#551—618no—
605#550—614no—
606#550—618no—
607#550—614no—
608D4×Q8C2×D6114yescomplemented
609#548—618no—
610#547—618no—
611#547—614no—
612#547—614no—
613#546—618no—
614#546—618no—
615#546—6116no—
616#546—618no—
617D42—612no—
618D42—618no—
619D42—614no—
620#544—618no—
621#542—6116no—
622#542—618no—
623#542C2×D6118yescomplemented
624#540—6116no—
625#540—618no—
626#540—618no—
627#538—6116no—
628#538—6116no—
629#537—618no—
630#537—618no—
631#537—618no—
632#536—614no—
633#536—618no—
634#536C2×D6114yescomplemented
635#535—614no—
636#535—618no—
637#535—618no—
638#535—618no—
639#535—614no—
640#534—618no—
641#534—618no—
642#533—612no—
643#533—612no—
644#533C2×D6112yescomplemented
645#532—612no—
646#532—611no—
647#532—612no—
648#532—612no—
649#532—618no—
650#532—618no—
651#532—611no—
652#532—612no—
653#532—618no—
654#532—614no—
655#532—614no—
656#532—611no—
657#532—612no—
658#532C2×D6111yescharacteristic
659C2×C4⋊Q8—611no—
660C2×#127—611no—
661#529—6116no—
662#529—614no—
663#529—614no—
664#529—618no—
665#529—614no—
666#529—614no—
667#529—614no—
668#529—614no—
669C2×#124—612no—
670#525—618no—
671#525—618no—
672#525—614no—
673#525—614no—
674#525—618no—
675#525—6116no—
676#525—614no—
677C2×#121—614no—
678C4×#41—614no—
679C4×#41—614no—
680C4×#41—618no—
681C4×#41—614no—
682C2×C4×D4—614no—
683C2×C4×D4—618no—
684C2×#117—614no—
685C22×C42—611no—
686C61#6275911yescharacteristic, complemented, Sylow
687C2×#41—614no—
688C2×#41—614no—
689C2×#41—618no—
690C2×#41—618no—
691C2×#41—612no—
692C2×#41—618no—
693C2×#41—618no—
694C2×#41—612no—
695C2×#41—614no—
696C2×#41—614no—
697C2×#41—614no—
698C2×#41—612no—
699C2×#41—2448no—
700C2×#41—24416no—
701C2×#41C22×D6112yes—
702C22×Q8—612no—
703C22×Q8C22×D6114yes—
704C22×D4—614no—
705C22×D4—618no—
706C22×D4—614no—
707C22×D4—612no—
708C22×D4—618no—
709C22×D4—614no—
710C23×C4—614no—
711C23×C4—611no—
712C23×C4—618no—
713C23×C4—612no—
714C4⋊Q8—612no—
715C4⋊Q8—618no—
716C4⋊Q8—614no—
717C4⋊Q8—611no—
718C4⋊Q8—612no—
719C4⋊Q8C22×D6111yescharacteristic
720C4⋊Q8C22×D6112yes—
721C4⋊Q8C22×D6112yes—
722C4⋊Q8C22×D6118yes—
723C4⋊Q8C22×D6118yes—
724#127—614no—
725#127—612no—
726#127—618no—
727#127—611no—
728#127—612no—
729#127—618no—
730#127—618no—
731#127C22×D6111yescharacteristic
732#126—618no—
733#126—618no—
734#126—6116no—
735#126—6116no—
736#126C22×D61116yes—
737#125—614no—
738#125—614no—
739#125—6116no—
740#125—618no—
741#125C22×D6114yes—
742#124—612no—
743#124—614no—
744#124—614no—
745#124—618no—
746#124—618no—
747#124—6116no—
748#124—612no—
749#124—618no—
750#124—6116no—
751#124—612no—
752#124—614no—
753#124—618no—
754#124C22×D6112yes—
755#124C22×D6118yes—
756#124C22×D6118yes—
757#123—618no—
758#123—618no—
759#123—618no—
760#123—618no—
761#123—6116no—
762#123—6116no—
763#123—6116no—
764#123—6116no—
765#123—618no—
766#123—6116no—
767#123—6116no—
768#123C22×D6118yes—
769#123C22×D6118yes—
770C22⋊Q8—614no—
771C22⋊Q8—614no—
772C22⋊Q8—618no—
773C22⋊Q8—6116no—
774C22⋊Q8—618no—
775C22⋊Q8—614no—
776C22⋊Q8—614no—
777C22⋊Q8—6116no—
778C22⋊Q8—6116no—
779C22⋊Q8—6116no—
780C22⋊Q8C22×D6114yes—
781C22⋊Q8C22×D6114yes—
782C22⋊Q8C22×D6118yes—
783C22⋊Q8C22×D61116yes—
784#121—618no—
785#121—614no—
786#121—618no—
787#121—614no—
788#121—614no—
789#121—614no—
790#121—618no—
791#121—6116no—
792#121—614no—
793#121—614no—
794#121—614no—
795#121—614no—
796#121—614no—
797#121—618no—
798#121—6116no—
799#121—6116no—
800#121—6116no—
801#121—618no—
802#121—618no—
803#121—6116no—
804#121—618no—
805#121—6116no—
806#121—6116no—
807#121—6116no—
808#121—6116no—
809#121—6116no—
810#121C22×D6114yes—
811#120—618no—
812#120—618no—
813#120—618no—
814#120—618no—
815#120—6116no—
816#120—618no—
817#120—6116no—
818#120—6116no—
819C4×Q8—614no—
820C4×Q8—614no—
821C4×Q8—614no—
822C4×Q8—614no—
823C4×Q8C22×D6114yes—
824C4×Q8C22×D6114yes—
825C4×Q8C22×D6118yes—
826C4×D4—614no—
827C4×D4—618no—
828C4×D4—6116no—
829C4×D4—614no—
830C4×D4—614no—
831C4×D4—614no—
832C4×D4—618no—
833C4×D4—6116no—
834C4×D4—618no—
835C4×D4—614no—
836C4×D4—614no—
837C4×D4—6116no—
838C4×D4—618no—
839C4×D4—618no—
840C4×D4—618no—
841C4×D4—614no—
842C4×D4—618no—
843C4×D4—618no—
844C4×D4—618no—
845C4×D4—614no—
846C4×D4—614no—
847C4×D4—6116no—
848C4×D4—618no—
849C4×D4C22×D6114yes—
850C4×D4C22×D6118yes—
851#117—614no—
852#117—614no—
853#117—618no—
854#117—614no—
855#117—618no—
856#117—618no—
857#117—6116no—
858#117—618no—
859#117—618no—
860#117—618no—
861#117C22×D6114yes—
862#117C22×D6114yes—
863C2×C4⋊C4—618no—
864C2×C4⋊C4—614no—
865C2×C4⋊C4—618no—
866C2×C22⋊C4—618no—
867C2×C22⋊C4—618no—
868C2×C22⋊C4—6116no—
869C2×C42—612no—
870C2×C42—611no—
871C2×C42—618no—
872C2×C42—612no—
873C2×C42—618no—
874C2×C42—611no—
875C2×C42—611no—
876C2×C42—611no—
877C2×C42—611no—
878C2×C42—612no—
879C2×C42C22×D6111yescharacteristic
880C24—614no—
881C24—611no—
882C24—618no—
883#41—44no—
884#41—12216no—
885#41—2448no—
886#41—2444no—
887#41—2448no—
888#41—2444no—
889#41—2448no—
890#41—2444no—
891#41—24416no—
892#41—24416no—
893#41—24416no—
894#41—2448no—
895#41—24416no—
896C2×Q8—48no—
897C2×Q8—614no—
898C2×Q8—612no—
899C2×Q8—614no—
900C2×Q8—2444no—
901C2×Q8C23×D6114yes—
902C2×Q8C23×D6114yes—
903C2×Q8C23×D6118yes—
904C2×Q8C23×D6112yes—
905C2×D4—6116no—
906C2×D4—618no—
907C2×D4—618no—
908C2×D4—614no—
909C2×D4—614no—
910C2×D4—614no—
911C2×D4—614no—
912C2×D4—614no—
913C2×D4—618no—
914C2×D4—614no—
915C2×D4—614no—
916C2×D4—618no—
917C2×D4—6116no—
918C2×D4—618no—
919C2×D4—6116no—
920C2×D4—612no—
921C2×D4—614no—
922C2×D4—2448no—
923C2×D4—24416no—
924C2×D4—2448no—
925C2×D4—24416no—
926C2×D4—2444no—
927C2×D4—2448no—
928C2×D4C23×D6114yes—
929C2×D4C23×D6112yes—
930C2×D4C23×D6114yes—
931C22×C4—611no—
932C22×C4—611no—
933C22×C4—614no—
934C22×C4—612no—
935C22×C4—612no—
936C22×C4—612no—
937C22×C4—611no—
938C22×C4—614no—
939C22×C4—611no—
940C22×C4—611no—
941C22×C4—618no—
942C22×C4—618no—
943C22×C4—614no—
944C22×C4—614no—
945C22×C4—612no—
946C22×C4—612no—
947C22×C4—618no—
948C22×C4—6116no—
949C22×C4—6116no—
950C22×C4—12216no—
951C22×C4—1224no—
952C22×C4—2444no—
953C22×C4—24416no—
954C22×C4C23×D6112yes—
955C22×C4C23×D6111yescharacteristic
956C22×C4C23×D6114yes—
957C22×C4C23×D6118yes—
958C4⋊C4—614no—
959C4⋊C4—614no—
960C4⋊C4—6116no—
961C4⋊C4—618no—
962C4⋊C4—6116no—
963C4⋊C4—618no—
964C4⋊C4—618no—
965C4⋊C4—614no—
966C4⋊C4—618no—
967C4⋊C4—618no—
968C4⋊C4C23×D6114yes—
969C4⋊C4C23×D6114yes—
970C4⋊C4C23×D6114yes—
971C4⋊C4C23×D6118yes—
972C4⋊C4C23×D6118yes—
973C4⋊C4C23×D61116yes—
974C4⋊C4C23×D6114yes—
975C4⋊C4C23×D6114yes—
976C22⋊C4—618no—
977C22⋊C4—618no—
978C22⋊C4—618no—
979C22⋊C4—618no—
980C22⋊C4—618no—
981C22⋊C4—6116no—
982C22⋊C4—618no—
983C22⋊C4—618no—
984C22⋊C4—618no—
985C22⋊C4—6116no—
986C22⋊C4—618no—
987C22⋊C4—618no—
988C22⋊C4—618no—
989C22⋊C4—618no—
990C22⋊C4—6116no—
991C22⋊C4C23×D6118yes—
992C22⋊C4C23×D61116yes—
993C22⋊C4C23×D6118yes—
994C22⋊C4C23×D6118yes—
995C42—612no—
996C42—611no—
997C42—618no—
998C42—612no—
999C42—612no—
1000C42—612no—
1001C42—612no—
1002C42—611no—
1003C42—618no—
1004C42—618no—
1005C42C23×D6112yes—
1006C42C23×D6111yescharacteristic
1007C42C23×D6111yescharacteristic
1008C42C23×D6118yes—
1009C42C23×D6118yes—
1010C23—611no—
1011C23—618no—
1012C23—611no—
1013C23—614no—
1014C23—1228no—
1015C23—1222no—
1016C23—2448no—
1017C23—2448no—
1018C23—24416no—
1019C23—2442no—
1020C23C24×D6114yes—
1021C23C24×D6111yescharacteristic
1022Q8—28no—
1023Q8—28no—
1024Q8—48no—
1025Q8—42no—
1026Q8—2442no—
1027Q8—2444no—
1028Q8—2444no—
1029D4—28no—
1030D4—42no—
1031D4—44no—
1032D4—12216no—
1033D4—1228no—
1034D4—1228no—
1035D4—1228no—
1036D4—2442no—
1037D4—2444no—
1038D4—2448no—
1039D4—24416no—
1040D4—2444no—
1041D4—2448no—
1042D4—24416no—
1043D4—2448no—
1044D4—24416no—
1045D4—2444no—
1046D4—2444no—
1047D4—2444no—
1048D4—2448no—
1049C2×C4—28no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—48no—
1053C2×C4—611no—
1054C2×C4—614no—
1055C2×C4—612no—
1056C2×C4—618no—
1057C2×C4—612no—
1058C2×C4—611no—
1059C2×C4—614no—
1060C2×C4—1222no—
1061C2×C4—1228no—
1062C2×C4—12216no—
1063C2×C4—1222no—
1064C2×C4—1228no—
1065C2×C4—1228no—
1066C2×C4—1222no—
1067C2×C4—1228no—
1068C2×C4—1222no—
1069C2×C4—1224no—
1070C2×C4—1224no—
1071C2×C4—12216no—
1072C2×C4—2442no—
1073C2×C4—2442no—
1074C2×C4—24416no—
1075C2×C4—2448no—
1076C2×C4—24416no—
1077C2×C4—2442no—
1078C2×C4C24×D6112yes—
1079C2×C4C24×D6111yescharacteristic
1080C2×C4C24×D6114yes—
1081C2×C4C24×D6118yes—
1082C2×C4C24×D6118yes—
1083C2×C4C24×D6111yescharacteristic
1084C2×C4C24×D6112yes—
1085C22—24no—
1086C22—21no—
1087C22—22no—
1088C22—28no—
1089C22—612no—
1090C22—1222no—
1091C22—1224no—
1092C22—1221no—
1093C22—1228no—
1094C22—1222no—
1095C22—1228no—
1096C22—1228no—
1097C22—1228no—
1098C22—4888no—
1099C22—48816no—
1100C22—2444no—
1101C22C25×D6111yescharacteristic
1102C4—21no—
1103C4—24no—
1104C4—28no—
1105C4—22no—
1106C4—28no—
1107C4—612no—
1108C4—1224no—
1109C4—1221no—
1110C4—1222no—
1111C4—1222no—
1112C4—1228no—
1113C4H(5,𝔽2)×D6112yes—
1114C4#1684059914yes—
1115C2—44no—
1116C2—41no—
1117C2—1222no—
1118C2—2448no—
1119C2—2444no—
1120C2—2441no—
1121C2C2×H(5,𝔽2)×D6111yescharacteristic
1122C2C2×#1684059912yes—
subgroupG/H
center, FrattiniC22C25×D61
commutator, socle, cosocleC22×C61C26
FittingC61×#3550C2
hypercenter#3550D61
hypocenterC61#62759
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #21460248C2semidirect
2. #21460224C2semidirect
3. #21460219C2semidirect
4. #21460204C2semidirect
5. #21460194C2semidirect
6. #21460177C2semidirect
7. #21460164C2semidirect
8. #21460153C2semidirect
9. #21460131C2semidirect
10. #21459960C2semidirect
11. #21459446C2semidirect
12. #21459428C2semidirect
13. #21459380C2semidirect
14. D4×#11758226C2semidirect
15. #21459239C2semidirect
16. #21459151C2semidirect
17. #21459116C2semidirect
18. #532×D61C2semidirect
19. C61×#3550C2semidirect
20. C22×#11758226C22semidirect
21. C2×#41×D61C22semidirect
22. #16840511C22semidirect
23. #16840510C22semidirect
24. #16840508C22semidirect
25. #16840504C22semidirect
26. #16840503C22semidirect
27. #16840502C22semidirect
28. #16840478C22semidirect
29. #16840478C22semidirect
30. #16840478C22semidirect
31. #16840477C22semidirect
32. #16840472C22semidirect
33. #16840472C22semidirect
34. #16840462C22semidirect
35. #16840456C22semidirect
36. #16840453C22semidirect
37. #16840446C22semidirect
38. #16840440C22semidirect
39. #16840437C22semidirect
40. #16840434C22semidirect
41. #16840434C22semidirect
42. #16840434C22semidirect
43. #16840423C22semidirect
44. #16840415C22semidirect
45. #16840415C22semidirect
46. #16840415C22semidirect
47. #16840405C22semidirect
48. #16840405C22semidirect
49. #16840403C22semidirect
50. #16840403C22semidirect
51. D4×D244C22semidirect
52. D4×D244C22semidirect
53. #16840397C22semidirect
54. #16840389C22semidirect
55. #16840384C22semidirect
56. #16840382C22semidirect
57. #16840367C22semidirect
58. #16840364C22semidirect
59. #16840363C22semidirect
60. #16840351C22semidirect
61. #16840346C22semidirect
62. #16840342C22semidirect
63. #16840342C22semidirect
64. #16840342C22semidirect
65. #16840337C22semidirect
66. #16840336C22semidirect
67. #16840331C22semidirect
68. #16840330C22semidirect
69. #16840330C22semidirect
70. #16840328C22semidirect
71. #16840326C22semidirect
72. #16840323C22semidirect
73. #16840323C22semidirect
74. #16840317C22semidirect
75. #16840317C22semidirect
77. #16840313C22semidirect
78. #16840313C22semidirect
79. #16840313C22semidirect
80. #16840313C22semidirect
81. #16840312C22semidirect
82. #16840312C22semidirect
83. #16840311C22semidirect
84. #16840311C22semidirect
86. #16840309C22semidirect
87. #16840308C22semidirect
88. #16840307C22semidirect
89. C4⋊Q8×D61C22semidirect
91. #16840299C22semidirect
92. #16840299C22semidirect
93. #16840298C22semidirect
94. #16840298C22semidirect
95. #16840297C22semidirect
96. #16840297C22semidirect
97. #16840295C22semidirect
98. #16840291C22semidirect
99. #124×D61C22semidirect
100. #16840275C22semidirect
101. #16840275C22semidirect
102. #16840275C22semidirect
103. #16840275C22semidirect
104. #16840274C22semidirect
105. #16840270C22semidirect
106. #16840270C22semidirect
107. #121×D61C22semidirect
108. C4×#11758226C22semidirect
109. C4×#11758226C22semidirect
110. C4×#11758226C22semidirect
111. #16840230C22semidirect
112. C4×D4×D61C22semidirect
113. C4×D4×D61C22semidirect
114. #117×D61C22semidirect
115. C2×C42×D61C22semidirect
116. C61×#563C22semidirect
117. C61×#559C22semidirect
118. Q82×C61C22semidirect
119. C61×#556C22semidirect
120. D4×Q8×C61C22semidirect
121. C61×#542C22semidirect
122. C61×#536C22semidirect
123. C61×#533C22semidirect
555. #3550D61semidirect
584. #563C2×D61semidirect
590. #559C2×D61semidirect
591. Q82C2×D61semidirect
592. #556C2×D61semidirect
608. D4×Q8C2×D61semidirect
623. #542C2×D61semidirect
634. #536C2×D61semidirect
644. #533C2×D61semidirect
686. C61#62759semidirect

Maximal subgroups

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

subgroupindex
#214602482
#214602242
#214602192
#214602042
#214601942
#214601772
#214601642
#214601532
#214601312
#214599602
#214594462
#214594282
#214593802
D4×#117582262
#214592392
#214591512
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