Finite Group Databasebeta

← D61×#3550 #30587817

Subgroups — D61×#3550 #30587817

Order 15616.

7074 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460233C211yesmaximal, characteristic, complemented
2#21460232C214yesmaximal, complemented
3#21460231C212yesmaximal, complemented
4#21460230C212yesmaximal, complemented
5#21460229C214yesmaximal, complemented
6#21460228C214yesmaximal, complemented
7#21460227C218yesmaximal, complemented
8#21460226C214yesmaximal, complemented
9#21460225C212yesmaximal, complemented
10#563×D61C214yesmaximal, complemented
11#559×D61C212yesmaximal, complemented
12Q82×D61C212yesmaximal, complemented
13#556×D61C214yesmaximal, complemented
14D4×Q8×D61C214yesmaximal, complemented
15#542×D61C218yesmaximal, complemented
16#536×D61C214yesmaximal, complemented
17#533×D61C212yesmaximal, complemented
18#532×D61C211yesmaximal, characteristic
19C61×#3550C211yesmaximal, characteristic, complemented
20C2×#41×D61C2212yes—
21C22×Q8×D61C2214yes—
22#16840516C2218yescomplemented
23#16840515C2218yescomplemented
24#16840514C22116yescomplemented
25#16840513C22116yescomplemented
26#16840512C2214yescomplemented
27#16840511C2218yescomplemented
28#16840498C2212yescomplemented
29#16840497C2214yescomplemented
30#16840496C2218yescomplemented
31#16840495C2218yescomplemented
32#16840494C2218yescomplemented
33Q8×Dic122C2218yescomplemented
34Q8×Dic122C2214yescomplemented
35#16840492C2212yescomplemented
36#16840492C2218yescomplemented
37#16840492C2218yescomplemented
38#16840486C2214yescomplemented
39#16840485C2214yescomplemented
40#16840484C2218yescomplemented
41#16840483C2218yescomplemented
42#16840482C2214yescomplemented
43#16840481C2218yescomplemented
44#16840480C2218yescomplemented
45#16840479C22116yescomplemented
46Q8×D244C2214yescomplemented
47D4×Dic122C2218yescomplemented
48D4×Dic122C2214yescomplemented
49#16840427C2218yescomplemented
50#16840427C2214yescomplemented
51Q8×C22⋊D61C2218yescomplemented
52#16840425C22116yescomplemented
53#16840425C2218yescomplemented
54#16840386C2218yescomplemented
55#16840385C2218yescomplemented
56#16840384C2218yescomplemented
57#16840383C2218yescomplemented
58#16840382C22116yescomplemented
59#16840381C2218yescomplemented
60#16840380C22116yescomplemented
61#16840379C2218yescomplemented
62#16840378C22116yescomplemented
63#16840377C2218yescomplemented
64#16840376C22116yescomplemented
65#16840338C2214yescomplemented
66#16840337C2218yescomplemented
67#16840336C2214yescomplemented
68#16840335C2218yescomplemented
69#16840335C2218yescomplemented
70#16840334C2218yescomplemented
71#16840334C2218yescomplemented
72#16840333C2214yescomplemented
73#16840332C2218yescomplemented
74#16840319C2212yescomplemented
75#16840318C2214yescomplemented
76#16840317C2212yescomplemented
77#16840317C2212yescomplemented
78#16840316C2214yescomplemented
79#16840316C2214yescomplemented
80#16840315C2214yescomplemented
81#16840314C2214yescomplemented
82#16840314C2214yescomplemented
83#16840313C2211yescharacteristic
84#16840312C2211yescharacteristic
85#16840311C2212yes—
86#16840310C2211yescharacteristic
87#16840309C2214yes—
88#16840308C2212yes—
89#16840307C2214yes—
90C4⋊Q8×D61C2212yes—
91C4⋊Q8×D61C2218yes—
92C4⋊Q8×D61C2211yescharacteristic
93C4⋊Q8×D61C2212yes—
94C4⋊Q8×D61C2218yes—
95#127×D61C2211yescharacteristic
96#126×D61C22116yes—
97#125×D61C2214yes—
98#124×D61C2212yes—
99#124×D61C2218yes—
100#124×D61C2218yes—
101#123×D61C2218yes—
102#123×D61C2218yes—
103C22⋊Q8×D61C2218yes—
104C22⋊Q8×D61C22116yes—
105C22⋊Q8×D61C2214yes—
106C22⋊Q8×D61C2214yes—
107#121×D61C2214yes—
108C4×Q8×D61C2214yes—
109C4×Q8×D61C2214yes—
110C4×Q8×D61C2218yes—
111C4×D4×D61C2214yes—
112C4×D4×D61C2218yes—
113#117×D61C2214yes—
114#117×D61C2214yes—
115C2×C42×D61C2211yescharacteristic
116C61×#563C2214yescomplemented
117C61×#559C2212yescomplemented
118Q82×C61C2212yescomplemented
119C61×#556C2214yescomplemented
120D4×Q8×C61C2214yescomplemented
121C61×#542C2218yescomplemented
122C61×#536C2214yescomplemented
123C61×#533C2212yescomplemented
124C61×#532C2211yescharacteristic
125C2×#11758226C2312yes—
126C2×#11758222C2312yes—
127C2×#11758222C2314yes—
128C2×#11758224C2314yes—
129C2×#11758224C2312yes—
130#41×D61—48no—
131C22×Dic122C2314yes—
132C22×Dic122C2318yes—
133C2×Q8×D61—416no—
134C2×Q8×D61C2314yes—
135C2×Q8×D61C2314yes—
136C2×Q8×D61C2318yes—
137C2×Q8×D61C2312yes—
138C2×Q8×D61C2318yes—
139C2×Q8×D61C2318yes—
140C2×D4×D61C2314yes—
141C2×D4×D61C2314yes—
142C2×D4×D61C2312yes—
143C22×C4×D61C2312yes—
144C22×C4×D61C2311yescharacteristic
145C22×C4×D61C2314yes—
146C22×C4×D61C2318yes—
147#14519777C2312yes—
148#14519777C2311yescharacteristic
149#14519777C2318yes—
150#14519777C2318yes—
151#14519777C2312yes—
152#14519776C2314yes—
153#14519776C2314yes—
154#14519776C2314yes—
155#14519776C23116yes—
156#14519776C23116yes—
157#14519776C2318yes—
158#14519776C23116yes—
159#14519776C2318yes—
160#14519776C2314yes—
161#14519776C2314yes—
162#14519775C2314yes—
163#14519775C2312yes—
164#14519775C2318yes—
165#14519775C2318yes—
166#14519775C23116yes—
167#14519775C2314yes—
168#14519774C2311yescharacteristic
169#14519773C2314yes—
170#14519773C2312yes—
171#14519772C23116yes—
172#14519772C23116yes—
173#14519772C23116yes—
174#14519771C23116yes—
175#14519770C23116yes—
176#14519770C23116yes—
177#14519770C23116yes—
178#14519769C2314yes—
179#14519768C2314yes—
180#14519768C2314yes—
181#14519767C2318yes—
182#14519767C2318yes—
183#14519766C2318yes—
184#14519766C2312yes—
185#14519766C2318yes—
186#14519765C2318yes—
187#14519765C2312yes—
188#14519765C2318yes—
189#14519764C2318yes—
190#14519764C2312yes—
191#14519764C2318yes—
192#14519763C23116yes—
193#14519763C23116yes—
194#14519763C2318yes—
195#14519763C23116yes—
196#14519763C23116yes—
197#14519762C23116yes—
198#14519762C23116yes—
199#14519761C2318yes—
200#14519761C2318yes—
201#14519760C2318yes—
202#14519760C2318yes—
203#14519759C23116yes—
204#14519759C23116yes—
205#14519758C2318yes—
206#14519758C2318yes—
207#14519757C2318yes—
208#14519757C23116yes—
209#14519757C2314yes—
210#14519757C2314yes—
211#14519756C2318yes—
212#14519756C23116yes—
213#14519756C2314yes—
214#14519756C2314yes—
215#14519755C23116yes—
216#14519755C23116yes—
217#14519755C23116yes—
218#14519755C2318yes—
219#14519755C2318yes—
220#14519754C23116yes—
221#14519754C23116yes—
222#14519754C23116yes—
223#14519754C2318yes—
224#14519754C2318yes—
225#14519753C2318yes—
226#14519753C23116yes—
227#14519753C2314yes—
228#14519753C2314yes—
229#14519752C2314yes—
230#14519751C2314yes—
231#14519750C2318yes—
232#14519749C2318yes—
233#14519748C2314yes—
234Q8×Dic61C2318yes—
235Q8×Dic61C2314yes—
236Q8×Dic61C2314yes—
237C4×Dic122C23116yes—
238C4×Dic122C2318yes—
239C4×Dic122C2318yes—
240C4×Dic122C2314yes—
241C4×Dic122C2318yes—
242C4×Dic122C2314yes—
243#14519742C2318yes—
244#14519742C23116yes—
245#14519742C2314yes—
246#14519742C2318yes—
247#14519742C2314yes—
248#14519742C2318yes—
249C4×D244C2314yes—
250C4×D244C2318yes—
251D4×Dic61C2314yes—
252D4×Dic61C2318yes—
253#14519739C2314yes—
254#14519739C2318yes—
255C4×C22⋊D61C2318yes—
256C4×C22⋊D61C23116yes—
257#14519737C2318yes—
258#14519737C23116yes—
259#14519736C2314yes—
260#14519736C2314yes—
261#14519735C2318yes—
262#14519735C2314yes—
263#14519735C2314yes—
264#14519734C2318yes—
265#14519734C2318yes—
266#14519733C2318yes—
267#14519733C2318yes—
268C4⋊C4×D61C2314yes—
269C4⋊C4×D61C2314yes—
270C4⋊C4×D61C2314yes—
271C4⋊C4×D61C2314yes—
272C4⋊C4×D61C2314yes—
273C4⋊C4×D61C2318yes—
274C4⋊C4×D61C23116yes—
275C4⋊C4×D61C2318yes—
276C22⋊C4×D61C2318yes—
277C22⋊C4×D61C2318yes—
278C22⋊C4×D61C2318yes—
279C22⋊C4×D61C23116yes—
280C2×C4×Dic61C2312yes—
281C2×C4×Dic61C2311yescharacteristic
282C42×D61C2312yes—
283C42×D61C2311yescharacteristic
284C42×D61C2311yescharacteristic
285C42×D61C2312yes—
286C42×D61C2311yescharacteristic
287C42×D61C2311yescharacteristic
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×D61C2414yes—
319C23×D61C2411yescharacteristic
320#41×C61—44no—
321C2×Q8×C61—48no—
322C2×Q8×C61C2414yes—
323C2×Q8×C61C2414yes—
324C2×Q8×C61C2418yes—
325C2×Q8×C61C2412yes—
326C2×D4×C61C2414yes—
327C2×D4×C61C2414yes—
328C2×D4×C61C2412yes—
329C22×C4×C61C2414yes—
330C22×C4×C61C2411yescharacteristic
331C22×C4×C61C2412yes—
332C22×C4×C61C2418yes—
333C2×C22⋊D61C2418yes—
334C2×C22⋊D61C2414yes—
335C2×C22⋊D61C2414yes—
336C2×C22⋊D61C2414yes—
337C22×Dic61C2414yes—
338C22×Dic61C2411yescharacteristic
339C22×Dic61C2412yes—
340C22×Dic61C2418yes—
341#11758226—44no—
342Q8×D61—216no—
343Q8×D61—216no—
344Q8×D61—416no—
345Q8×D61—416no—
346Q8×D61—416no—
347Q8×D61—44no—
348#11758224—44no—
349#11758224—48no—
350D4×D61—216no—
351D4×D61—44no—
352D4×D61—48no—
353#11758222—48no—
354#11758222—44no—
355C2×D244C2414yes—
356C2×D244C2414yes—
357C2×D244C2412yes—
358C2×C4×D61—216no—
359C2×C4×D61—24no—
360C2×C4×D61—28no—
361C2×C4×D61—416no—
362C2×C4×D61C2418yes—
363C2×C4×D61C2411yescharacteristic
364C2×C4×D61C2414yes—
365C2×C4×D61C2414yes—
366C2×C4×D61C2414yes—
367C2×C4×D61C2411yescharacteristic
368C2×C4×D61C2411yescharacteristic
369C2×C4×D61C2412yes—
370C2×C4×D61C2412yes—
371C2×C4×D61C2412yes—
372C2×C4×D61C2418yes—
373C2×C4×D61C24116yes—
374C2×C4×D61C2411yescharacteristic
375C2×C4×D61C2412yes—
376C2×Dic122—416no—
377C2×Dic122—48no—
378C2×Dic122C2418yes—
379C2×Dic122C2414yes—
380C2×Dic122C2418yes—
381C2×Dic122C2414yes—
382C2×Dic122C2418yes—
383C2×Dic122C24116yes—
384C2×Dic122C2414yes—
385C2×Dic122C2412yes—
386C4⋊C4×C61C2414yes—
387C4⋊C4×C61C2414yes—
388C4⋊C4×C61C2414yes—
389C4⋊C4×C61C2414yes—
390C4⋊C4×C61C2414yes—
391C4⋊C4×C61C2418yes—
392C4⋊C4×C61C24116yes—
393C4⋊C4×C61C2418yes—
394C22⋊C4×C61C2418yes—
395C22⋊C4×C61C2418yes—
396C22⋊C4×C61C2418yes—
397C22⋊C4×C61C24116yes—
398C42×C61C2412yes—
399C42×C61C2411yescharacteristic
400C42×C61C2411yescharacteristic
401C42×C61C2418yes—
402C42×C61C2418yes—
403C22⋊Dic61C2418yes—
404C22⋊Dic61C2418yes—
405C22⋊Dic61C2418yes—
406C22⋊Dic61C24116yes—
407#11758198C2418yes—
408#11758198C2418yes—
409#11758198C24116yes—
410#11758198C2418yes—
411#11758198C24116yes—
412#11758198C2418yes—
413#11758198C24116yes—
414C4⋊Dic61C2414yes—
415C4⋊Dic61C2414yes—
416C4⋊Dic61C2414yes—
417C4⋊Dic61C2414yes—
418C4⋊Dic61C2414yes—
419C4⋊Dic61C2418yes—
420C4⋊Dic61C24116yes—
421C4⋊Dic61C2418yes—
422#11758196C2418yes—
423#11758196C2418yes—
424#11758196C2418yes—
425#11758196C2418yes—
426#11758196C2418yes—
427#11758196C2418yes—
428#11758196C24116yes—
429#11758196C24116yes—
430#11758196C2418yes—
431#11758196C2418yes—
432#11758196C2418yes—
433C4×Dic61C2412yes—
434C4×Dic61C2412yes—
435C4×Dic61C2412yes—
436C4×Dic61C2411yescharacteristic
437C4×Dic61C2412yes—
438C4×Dic61C2412yes—
439C4×Dic61C2411yescharacteristic
440C4×Dic61C2418yes—
441C4×Dic61C2418yes—
442C4×Dic61C24116yes—
443C4×Dic61C2418yes—
444C4×Dic61C2418yes—
445C23×C61C2514yes—
446C23×C61C2511yescharacteristic
447C22×D61—28no—
448C22×D61—22no—
449C22×D61—24no—
450C22×D61—216no—
451C22×D61C2514yes—
452C22×D61C2511yescharacteristic
453C22×D61C2511yescharacteristic
454Q8×C61—28no—
455Q8×C61—28no—
456Q8×C61—48no—
457Q8×C61—42no—
458D4×C61—28no—
459D4×C61—44no—
460D4×C61—42no—
461C2×C4×C61—28no—
462C2×C4×C61—22no—
463C2×C4×C61—24no—
464C2×C4×C61—48no—
465C2×C4×C61C2518yes—
466C2×C4×C61C2511yescharacteristic
467C2×C4×C61C2514yes—
468C2×C4×C61C2512yes—
469C2×C4×C61C2518yes—
470C2×C4×C61C2511yescharacteristic
471C2×C4×C61C2512yes—
472C22⋊D61—216no—
473C22⋊D61—44no—
474C22⋊D61—44no—
475C22⋊D61—44no—
476C2×Dic61—28no—
477C2×Dic61—22no—
478C2×Dic61—24no—
479C2×Dic61—48no—
480C2×Dic61C2518yes—
481C2×Dic61C2512yes—
482C2×Dic61C2511yescharacteristic
483C2×Dic61C2514yes—
484C2×Dic61C2518yes—
485C2×Dic61C2511yescharacteristic
486C2×Dic61C2512yes—
487D244—28no—
488D244—44no—
489D244—42no—
490C4×D61—22no—
491C4×D61—28no—
492C4×D61—216no—
493C4×D61—24no—
494C4×D61—216no—
495C4×D61—22no—
496C4×D61—28no—
497C4×D61—24no—
498C4×D61—22no—
499C4×D61—28no—
500C4×D61—24no—
501C4×D61—416no—
502C4×D61H(5,𝔽2)14yes—
503C4×D612−1+418yes—
504Dic122—28no—
505Dic122—28no—
506Dic122—216no—
507Dic122—216no—
508Dic122—48no—
509Dic122—416no—
510Dic122—42no—
511Dic122—44no—
512C2×#3550—611nomaximal, Sylow
513C22×C61—24no—
514C22×C61—21no—
515C22×C61—22no—
516C22×C61—28no—
517C22×C61C2611yescharacteristic
518C2×D61—24no—
519C2×D61—21no—
520C2×D61—22no—
521C2×D61—28no—
522C2×D61—416no—
523C2×D61—44no—
524C2×D61C2×H(5,𝔽2)12yes—
525C2×D61C2×2−1+414yes—
526C4×C61—28no—
527C4×C61—24no—
528C4×C61—21no—
529C4×C61—28no—
530C4×C61—22no—
531C4×C61C2×H(5,𝔽2)12yes—
532C4×C61C2×2−1+414yes—
533Dic61—28no—
534Dic61—24no—
535Dic61—21no—
536Dic61—28no—
537Dic61—22no—
538Dic61C2×H(5,𝔽2)12yes—
539Dic61C2×2−1+414yes—
540#3550—614no—
541#3550—612no—
542#3550—612no—
543#3550—614no—
544#3550—614no—
545#3550—618no—
546#3550—614no—
547#3550—612no—
548#3550—611no—
549#3550D6111yescharacteristic, direct product factor
550C2×#563—614no—
551C2×#559—612no—
552C2×Q82—612no—
553C2×#556—614no—
554C2×D4×Q8—614no—
555C2×#542—618no—
556C2×#536—614no—
557C2×#533—612no—
558C2×#532—611no—
559C2×C61—44no—
560C2×C61—41no—
561C2×C61C22×H(5,𝔽2)11yescharacteristic
562C2×C61C22×2−1+412yes—
563D61—44no—
564D61—41no—
565D61#355014yesdirect product factor
566C22×#41—612no—
567C23×Q8—614no—
568#563—618no—
569#563—6116no—
570#563—618no—
571#563—614no—
572#563—618no—
573#563—6116no—
574#563C2×D6114yescomplemented
575#559—612no—
576#559—618no—
577#559—618no—
578#559—614no—
579#559—618no—
580#559C2×D6112yescomplemented
581Q82—618no—
582Q82—618no—
583Q82—612no—
584Q82—618no—
585Q82—614no—
586Q82C2×D6112yescomplemented
587#556—614no—
588#556—6116no—
589#556—618no—
590#556—618no—
591#556—618no—
592#556—614no—
593#556—614no—
594#556—618no—
595#556C2×D6114yescomplemented
596D4×Q8—618no—
597D4×Q8—618no—
598D4×Q8—614no—
599D4×Q8—618no—
600D4×Q8—6116no—
601D4×Q8—614no—
602D4×Q8—618no—
603D4×Q8—614no—
604D4×Q8C2×D6114yescomplemented
605#542—618no—
606#542—6116no—
607#542—6116no—
608#542—618no—
609#542—6116no—
610#542—6116no—
611#542—618no—
612#542—618no—
613#542—618no—
614#542—618no—
615#542—618no—
616#542C2×D6118yescomplemented
617#536—614no—
618#536—614no—
619#536—618no—
620#536—618no—
621#536—618no—
622#536—618no—
623#536—618no—
624#536—618no—
625#536—614no—
626#536C2×D6114yescomplemented
627#533—612no—
628#533—612no—
629#533—614no—
630#533—614no—
631#533—614no—
632#533—614no—
633#533—614no—
634#533—614no—
635#533—612no—
636#533C2×D6112yescomplemented
637#532—612no—
638#532—611no—
639#532—611no—
640#532—612no—
641#532—614no—
642#532—614no—
643#532—611no—
644#532C2×D6111yescharacteristic
645C2×C4⋊Q8—611no—
646C2×C4⋊Q8—612no—
647C2×C4⋊Q8—612no—
648C2×C4⋊Q8—618no—
649C2×C4⋊Q8—618no—
650C2×#127—611no—
651C2×#126—6116no—
652C2×#125—614no—
653C2×#124—612no—
654C2×#124—618no—
655C2×#124—618no—
656C2×#123—618no—
657C2×#123—618no—
658C2×C22⋊Q8—614no—
659C2×C22⋊Q8—614no—
660C2×C22⋊Q8—618no—
661C2×C22⋊Q8—6116no—
662C2×#121—614no—
663C2×C4×Q8—614no—
664C2×C4×Q8—614no—
665C2×C4×Q8—618no—
666C2×C4×D4—614no—
667C2×C4×D4—618no—
668C2×#117—614no—
669C2×#117—614no—
670C22×C42—611no—
671C61C2×#355011yescharacteristic, complemented, Sylow
672C2×#41—612no—
673C2×#41—614no—
674C2×#41—612no—
675C2×#41—614no—
676C2×#41—612no—
677C2×#41—2448no—
678C2×#41C22×D6112yes—
679C22×Q8—614no—
680C22×Q8—614no—
681C22×Q8—618no—
682C22×Q8—612no—
683C22×Q8—618no—
684C22×Q8—618no—
685C22×Q8—618no—
686C22×Q8—614no—
687C22×Q8—24416no—
688C22×Q8C22×D6114yes—
689C22×D4—614no—
690C22×D4—614no—
691C22×D4—612no—
692C23×C4—612no—
693C23×C4—614no—
694C23×C4—611no—
695C23×C4—618no—
696C4⋊Q8—612no—
697C4⋊Q8—614no—
698C4⋊Q8—614no—
699C4⋊Q8—618no—
700C4⋊Q8—618no—
701C4⋊Q8—6116no—
702C4⋊Q8—614no—
703C4⋊Q8—614no—
704C4⋊Q8—614no—
705C4⋊Q8—614no—
706C4⋊Q8—614no—
707C4⋊Q8—6116no—
708C4⋊Q8—6116no—
709C4⋊Q8—6116no—
710C4⋊Q8—618no—
711C4⋊Q8—618no—
712C4⋊Q8—611no—
713C4⋊Q8—612no—
714C4⋊Q8—612no—
715C4⋊Q8—618no—
716C4⋊Q8—618no—
717C4⋊Q8C22×D6111yescharacteristic
718C4⋊Q8C22×D6112yes—
719C4⋊Q8C22×D6112yes—
720C4⋊Q8C22×D6118yes—
721C4⋊Q8C22×D6118yes—
722#127—612no—
723#127—614no—
724#127—611no—
725#127C22×D6111yescharacteristic
726#126—6116no—
727#126—6116no—
728#126—6116no—
729#126—6116no—
730#126—6116no—
731#126—6116no—
732#126—6116no—
733#126C22×D61116yes—
734#125—618no—
735#125—618no—
736#125—614no—
737#125—614no—
738#125—614no—
739#125C22×D6114yes—
740#124—612no—
741#124—618no—
742#124—618no—
743#124—612no—
744#124—618no—
745#124—618no—
746#124—618no—
747#124—6116no—
748#124—6116no—
749#124—6116no—
750#124—6116no—
751#124—612no—
752#124—618no—
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—618no—
765#123—6116no—
766#123—618no—
767#123C22×D6118yes—
768#123C22×D6118yes—
769C22⋊Q8—614no—
770C22⋊Q8—614no—
771C22⋊Q8—618no—
772C22⋊Q8—6116no—
773C22⋊Q8—614no—
774C22⋊Q8—614no—
775C22⋊Q8—618no—
776C22⋊Q8—6116no—
777C22⋊Q8—618no—
778C22⋊Q8—614no—
779C22⋊Q8—618no—
780C22⋊Q8—614no—
781C22⋊Q8—6116no—
782C22⋊Q8—618no—
783C22⋊Q8—6116no—
784C22⋊Q8—6116no—
785C22⋊Q8—6116no—
786C22⋊Q8—618no—
787C22⋊Q8—618no—
788C22⋊Q8—6116no—
789C22⋊Q8—6116no—
790C22⋊Q8—6116no—
791C22⋊Q8C22×D6114yes—
792C22⋊Q8C22×D6114yes—
793C22⋊Q8C22×D6118yes—
794C22⋊Q8C22×D61116yes—
795#121—614no—
796#121—618no—
797#121—614no—
798#121—614no—
799#121—618no—
800#121C22×D6114yes—
801C4×Q8—614no—
802C4×Q8—614no—
803C4×Q8—618no—
804C4×Q8—618no—
805C4×Q8—614no—
806C4×Q8—618no—
807C4×Q8—614no—
808C4×Q8—6116no—
809C4×Q8—618no—
810C4×Q8—618no—
811C4×Q8—614no—
812C4×Q8—618no—
813C4×Q8—614no—
814C4×Q8—6116no—
815C4×Q8—618no—
816C4×Q8C22×D6114yes—
817C4×Q8C22×D6114yes—
818C4×Q8C22×D6118yes—
819C4×D4—614no—
820C4×D4—618no—
821C4×D4—618no—
822C4×D4—6116no—
823C4×D4—614no—
824C4×D4—618no—
825C4×D4—618no—
826C4×D4—6116no—
827C4×D4—614no—
828C4×D4—618no—
829C4×D4C22×D6114yes—
830C4×D4C22×D6118yes—
831#117—614no—
832#117—614no—
833#117—614no—
834#117—614no—
835#117—618no—
836#117—618no—
837#117—618no—
838#117—618no—
839#117—618no—
840#117C22×D6114yes—
841#117C22×D6114yes—
842C2×C4⋊C4—614no—
843C2×C4⋊C4—614no—
844C2×C4⋊C4—614no—
845C2×C4⋊C4—614no—
846C2×C4⋊C4—614no—
847C2×C4⋊C4—618no—
848C2×C4⋊C4—6116no—
849C2×C4⋊C4—618no—
850C2×C22⋊C4—618no—
851C2×C22⋊C4—618no—
852C2×C22⋊C4—618no—
853C2×C22⋊C4—6116no—
854C2×C42—611no—
855C2×C42—612no—
856C2×C42—618no—
857C2×C42—618no—
858C2×C42—612no—
859C2×C42—611no—
860C2×C42—611no—
861C2×C42—611no—
862C2×C42—611no—
863C2×C42—612no—
864C2×C42C22×D6111yescharacteristic
865C24—614no—
866C24—611no—
867#41—44no—
868#41—2448no—
869#41—2444no—
870#41—2448no—
871#41—2444no—
872#41—2444no—
873C2×Q8—48no—
874C2×Q8—618no—
875C2×Q8—614no—
876C2×Q8—618no—
877C2×Q8—614no—
878C2×Q8—6116no—
879C2×Q8—618no—
880C2×Q8—612no—
881C2×Q8—614no—
882C2×Q8—12216no—
883C2×Q8—12216no—
884C2×Q8—2448no—
885C2×Q8—24416no—
886C2×Q8—24416no—
887C2×Q8—2444no—
888C2×Q8—24416no—
889C2×Q8—24416no—
890C2×Q8C23×D6114yes—
891C2×Q8C23×D6114yes—
892C2×Q8C23×D6118yes—
893C2×Q8C23×D6112yes—
894C2×D4—618no—
895C2×D4—614no—
896C2×D4—614no—
897C2×D4—614no—
898C2×D4—614no—
899C2×D4—614no—
900C2×D4—612no—
901C2×D4—12216no—
902C2×D4—2444no—
903C2×D4—2448no—
904C2×D4C23×D6114yes—
905C2×D4C23×D6114yes—
906C2×D4C23×D6112yes—
907C22×C4—612no—
908C22×C4—611no—
909C22×C4—612no—
910C22×C4—611no—
911C22×C4—614no—
912C22×C4—618no—
913C22×C4—618no—
914C22×C4—612no—
915C22×C4—614no—
916C22×C4—611no—
917C22×C4—612no—
918C22×C4—612no—
919C22×C4—611no—
920C22×C4—611no—
921C22×C4—618no—
922C22×C4—614no—
923C22×C4—614no—
924C22×C4—6116no—
925C22×C4—12216no—
926C22×C4—1228no—
927C22×C4—1224no—
928C22×C4—24416no—
929C22×C4C23×D6112yes—
930C22×C4C23×D6111yescharacteristic
931C22×C4C23×D6114yes—
932C22×C4C23×D6118yes—
933C4⋊C4—618no—
934C4⋊C4—618no—
935C4⋊C4—618no—
936C4⋊C4—618no—
937C4⋊C4—618no—
938C4⋊C4—618no—
939C4⋊C4—618no—
940C4⋊C4—6116no—
941C4⋊C4—6116no—
942C4⋊C4—618no—
943C4⋊C4—618no—
944C4⋊C4—614no—
945C4⋊C4—614no—
946C4⋊C4—614no—
947C4⋊C4—614no—
948C4⋊C4—614no—
949C4⋊C4—618no—
950C4⋊C4—6116no—
951C4⋊C4—618no—
952C4⋊C4C23×D6114yes—
953C4⋊C4C23×D6114yes—
954C4⋊C4C23×D6114yes—
955C4⋊C4C23×D6114yes—
956C4⋊C4C23×D6114yes—
957C4⋊C4C23×D6118yes—
958C4⋊C4C23×D61116yes—
959C4⋊C4C23×D6118yes—
960C22⋊C4—618no—
961C22⋊C4—618no—
962C22⋊C4—618no—
963C22⋊C4—6116no—
964C22⋊C4—618no—
965C22⋊C4—618no—
966C22⋊C4—6116no—
967C22⋊C4—618no—
968C22⋊C4—618no—
969C22⋊C4—6116no—
970C22⋊C4—6116no—
971C22⋊C4C23×D6118yes—
972C22⋊C4C23×D6118yes—
973C22⋊C4C23×D6118yes—
974C22⋊C4C23×D61116yes—
975C42—612no—
976C42—612no—
977C42—612no—
978C42—611no—
979C42—612no—
980C42—611no—
981C42—612no—
982C42—618no—
983C42—618no—
984C42—618no—
985C42—618no—
986C42—6116no—
987C42C23×D6112yes—
988C42C23×D6111yescharacteristic
989C42C23×D6111yescharacteristic
990C42C23×D6118yes—
991C42C23×D6118yes—
992C23—611no—
993C23—614no—
994C23—611no—
995C23—1228no—
996C23—1222no—
997C23—1224no—
998C23—12216no—
999C23C24×D6114yes—
1000C23C24×D6111yescharacteristic
1001Q8—28no—
1002Q8—28no—
1003Q8—48no—
1004Q8—42no—
1005Q8—12216no—
1006Q8—12216no—
1007Q8—1228no—
1008Q8—1228no—
1009Q8—2448no—
1010Q8—24416no—
1011Q8—2442no—
1012Q8—2444no—
1013D4—28no—
1014D4—42no—
1015D4—44no—
1016D4—12216no—
1017D4—1228no—
1018D4—2442no—
1019D4—2444no—
1020D4—2444no—
1021D4—2444no—
1022D4—2444no—
1023C2×C4—28no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—48no—
1027C2×C4—612no—
1028C2×C4—611no—
1029C2×C4—614no—
1030C2×C4—618no—
1031C2×C4—618no—
1032C2×C4—612no—
1033C2×C4—614no—
1034C2×C4—611no—
1035C2×C4—618no—
1036C2×C4—1224no—
1037C2×C4—1228no—
1038C2×C4—1222no—
1039C2×C4—1224no—
1040C2×C4—1222no—
1041C2×C4—1228no—
1042C2×C4—12216no—
1043C2×C4—12216no—
1044C2×C4—1224no—
1045C2×C4—1228no—
1046C2×C4—1222no—
1047C2×C4—1228no—
1048C2×C4—1222no—
1049C2×C4—1224no—
1050C2×C4—24416no—
1051C2×C4—2448no—
1052C2×C4C24×D6118yes—
1053C2×C4C24×D6112yes—
1054C2×C4C24×D6114yes—
1055C2×C4C24×D6111yescharacteristic
1056C2×C4C24×D6118yes—
1057C2×C4C24×D6111yescharacteristic
1058C2×C4C24×D6112yes—
1059C22—24no—
1060C22—21no—
1061C22—22no—
1062C22—28no—
1063C22—612no—
1064C22—614no—
1065C22—1224no—
1066C22—1221no—
1067C22—1222no—
1068C22—1228no—
1069C22—24416no—
1070C22—2444no—
1071C22C25×D6111yescharacteristic
1072C4—21no—
1073C4—24no—
1074C4—28no—
1075C4—22no—
1076C4—28no—
1077C4—612no—
1078C4—614no—
1079C4—1221no—
1080C4—1224no—
1081C4—1228no—
1082C4—1222no—
1083C4—1228no—
1084C4H(5,𝔽2)×D6112yes—
1085C42−1+4×D6114yes—
1086C2—44no—
1087C2—41no—
1088C2—614no—
1089C2—2444no—
1090C2—2441no—
1091C2C2×H(5,𝔽2)×D6111yescharacteristic
1092C2C2×2−1+4×D6112yes—
subgroupG/H
center, FrattiniC22C25×D61
commutator, socle, cosocleC22×C61C26
FittingC61×#3550C2
prime radical#532×D61C2
hypercenter#3550D61
hypocenterC61C2×#3550
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #21460233C2semidirect
2. #21460232C2semidirect
3. #21460231C2semidirect
4. #21460230C2semidirect
5. #21460229C2semidirect
6. #21460228C2semidirect
7. #21460227C2semidirect
8. #21460226C2semidirect
9. #21460225C2semidirect
10. #563×D61C2semidirect
11. #559×D61C2semidirect
12. Q82×D61C2semidirect
13. #556×D61C2semidirect
14. D4×Q8×D61C2semidirect
15. #542×D61C2semidirect
16. #536×D61C2semidirect
17. #533×D61C2semidirect
19. C61×#3550C2semidirect
22. #16840516C22semidirect
23. #16840515C22semidirect
24. #16840514C22semidirect
25. #16840513C22semidirect
26. #16840512C22semidirect
27. #16840511C22semidirect
28. #16840498C22semidirect
29. #16840497C22semidirect
30. #16840496C22semidirect
31. #16840495C22semidirect
32. #16840494C22semidirect
33. Q8×Dic122C22semidirect
34. Q8×Dic122C22semidirect
35. #16840492C22semidirect
36. #16840492C22semidirect
37. #16840492C22semidirect
38. #16840486C22semidirect
39. #16840485C22semidirect
40. #16840484C22semidirect
41. #16840483C22semidirect
42. #16840482C22semidirect
43. #16840481C22semidirect
44. #16840480C22semidirect
45. #16840479C22semidirect
46. Q8×D244C22semidirect
47. D4×Dic122C22semidirect
48. D4×Dic122C22semidirect
49. #16840427C22semidirect
50. #16840427C22semidirect
51. Q8×C22⋊D61C22semidirect
52. #16840425C22semidirect
53. #16840425C22semidirect
54. #16840386C22semidirect
55. #16840385C22semidirect
56. #16840384C22semidirect
57. #16840383C22semidirect
58. #16840382C22semidirect
59. #16840381C22semidirect
60. #16840380C22semidirect
61. #16840379C22semidirect
62. #16840378C22semidirect
63. #16840377C22semidirect
64. #16840376C22semidirect
65. #16840338C22semidirect
66. #16840337C22semidirect
67. #16840336C22semidirect
68. #16840335C22semidirect
69. #16840335C22semidirect
70. #16840334C22semidirect
71. #16840334C22semidirect
72. #16840333C22semidirect
73. #16840332C22semidirect
74. #16840319C22semidirect
75. #16840318C22semidirect
76. #16840317C22semidirect
77. #16840317C22semidirect
78. #16840316C22semidirect
79. #16840316C22semidirect
80. #16840315C22semidirect
81. #16840314C22semidirect
82. #16840314C22semidirect
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
549. #3550D61direct (N × H)
565. D61#3550direct (N × H)
574. #563C2×D61semidirect
580. #559C2×D61semidirect
586. Q82C2×D61semidirect
595. #556C2×D61semidirect
604. D4×Q8C2×D61semidirect
616. #542C2×D61semidirect
626. #536C2×D61semidirect
636. #533C2×D61semidirect
671. C61C2×#3550semidirect

Maximal subgroups

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

subgroupindex
#214602332
#214602322
#214602312
#214602302
#214602292
#214602282
#214602272
#214602262
#214602252
#563×D612
#559×D612
Q82×D612
#556×D612
D4×Q8×D612
#542×D612
#536×D612
#533×D612
#532×D612
C61×#35502
C2×#355061