Finite Group Databasebeta

← D61×#3216 #30551301

Subgroups — D61×#3216 #30551301

Order 15616.

2166 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic, complemented
2#532×D61C211yesmaximal, characteristic
3#21456832C211yesmaximal, characteristic, complemented
4#21456831C212yesmaximal, complemented
5#21456830C211yesmaximal, characteristic, complemented
6#21456829C212yesmaximal, complemented
7#21456828C212yesmaximal, complemented
8#21456827C214yesmaximal, complemented
9#21456826C211yesmaximal, characteristic, complemented
10#21456825C212yesmaximal, complemented
11#497×D61C212yesmaximal, complemented
12#489×D61C212yesmaximal, complemented
13#462×D61C212yesmaximal, complemented
14#460×D61C212yesmaximal, complemented
15#452×D61C214yesmaximal, complemented
16#432×D61C211yesmaximal, characteristic, complemented
17C61×#3216C211yesmaximal, characteristic, complemented
18C2×#41×D61C2212yes—
19C2×Q16×D61C2214yes—
20C2×SD16×D61C2214yes—
21#16840319C2211yescharacteristic, complemented
22#16840318—21no—
23#16840317C2211yescharacteristic, complemented
24#16840317C2211yescharacteristic, complemented
25#16840316—21no—
26#16840316C2212yescomplemented
27#16840315—21no—
28#16840314—21no—
29#16840314C2212yescomplemented
30#16840313C2211yescharacteristic
31#16840312C2211yescharacteristic
32#16840311C2212yes—
33#16840310C2211yescharacteristic
34#16840309—21no—
35#16840309—21no—
36#16840308C2212yes—
37#16840307—21no—
38#16840307—21no—
39C4⋊Q8×D61C2211yescharacteristic
40C4⋊Q8×D61C2211yescharacteristic
41C4⋊Q8×D61C2211yescharacteristic
42#127×D61C2211yescharacteristic
43#125×D61—21no—
44#124×D61C2212yes—
45C22⋊Q8×D61—21no—
46C22⋊Q8×D61C2212yes—
47#121×D61—21no—
48#121×D61—21no—
49C4×Q8×D61—21no—
50C4×Q8×D61C2212yes—
51C4×D4×D61—21no—
52C4×D4×D61—21no—
53#117×D61—21no—
54C2×C42×D61C2211yescharacteristic
55#16840157C2212yescomplemented
56#16840156C2212yescomplemented
57#16840155C2214yescomplemented
58#16840154C2212yescomplemented
59#16840153C2214yescomplemented
60#16840124C2212yescomplemented
61#16840123C2214yescomplemented
62#16840122C2212yescomplemented
63#16840121C2212yescomplemented
64#16840120C2214yescomplemented
65#16839973C2212yescomplemented
66#16839972C2212yescomplemented
67#16839971C2214yescomplemented
68#16839970C2214yescomplemented
69#16839969C2212yescomplemented
70#16839963C2212yescomplemented
71#16839962C2212yescomplemented
72#16839961C2214yescomplemented
73#16839960C2214yescomplemented
74#16839959C2212yescomplemented
75#16839927C2214yescomplemented
76#16839926C2214yescomplemented
77#16839925C2214yescomplemented
78#16839924C2214yescomplemented
79#16839923C2214yescomplemented
80#16839922C2214yescomplemented
81#16839921C2214yescomplemented
82#16839819C2211yescharacteristic, complemented
83#16839818C2212yescomplemented
84#16839817C2212yescomplemented
85#16839816C2212yescomplemented
86C4⋊C8×D61C2212yes—
87#103×D61C2214yes—
88#102×D61C2214yes—
89C22⋊C8×D61C2212yes—
90#97×D61C2212yes—
91C61×#533C2211yescharacteristic, complemented
92C61×#532C2211yescharacteristic
93C61×#497C2212yescomplemented
94C61×#489C2212yescomplemented
95C61×#462C2212yescomplemented
96C61×#460C2212yescomplemented
97C61×#452C2214yescomplemented
98C61×#432C2211yescharacteristic, complemented
99C2×#11758226C2312yes—
100C2×#11758222—22no—
101C2×#11758222C2312yes—
102C2×#11758224—22no—
103C2×#11758224C2312yes—
104#41×D61—48no—
105C2×Q8×D61—21no—
106C2×Q8×D61C2312yes—
107C2×Q8×D61C2312yes—
108C2×D4×D61—22no—
109C2×D4×D61—21no—
110C2×D4×D61—21no—
111C2×D4×D61C2312yes—
112C22×C4×D61—22no—
113C22×C4×D61D411yescharacteristic
114C22×C4×D61D411yescharacteristic
115C22×C4×D61C2311yescharacteristic
116C2×Dic244C2314yes—
117C2×#11758202C2314yes—
118C2×#11758202C2314yes—
119Q16×D61—48no—
120C2×#11758190C2314yes—
121C2×#11758200C2314yes—
122C2×#11758201C2314yes—
123SD16×D61—48no—
124C2×C8×D61C2314yes—
125#14519777C2311yescharacteristic
126#14519777C2311yescharacteristic
127#14519777C2311yescharacteristic
128#14519776—21no—
129#14519776—21no—
130#14519776—21no—
131#14519776—21no—
132#14519776—21no—
133#14519776C2312yes—
134#14519775—21no—
135#14519775C2312yes—
136#14519775C2312yes—
137#14519774C2311yescharacteristic
138#14519773—21no—
139#14519773—21no—
140#14519773C2312yes—
141#14519769—21no—
142#14519768—21no—
143#14519768—21no—
144#14519767—22no—
145#14519767—22no—
146#14519766C2312yes—
147#14519765C2312yes—
148#14519764C2312yes—
149#14519763—22no—
150#14519763—22no—
151#14519757—21no—
152#14519757C2312yes—
153#14519756—21no—
154#14519756C2312yes—
155#14519755—22no—
156#14519755—22no—
157#14519754—22no—
158#14519754—22no—
159#14519753—21no—
160#14519753C2312yes—
161#14519752—21no—
162#14519752—21no—
163#14519751—21no—
164#14519751—21no—
165#14519750—22no—
166#14519750—22no—
167#14519749—22no—
168#14519749—22no—
169#14519748—21no—
170#14519748—21no—
171Q8×Dic61—21no—
172Q8×Dic61C2312yes—
173C4×Dic122—21no—
174C4×Dic122—22no—
175C4×Dic122—22no—
176C4×Dic122C2312yes—
177#14519742—21no—
178#14519742—22no—
179#14519742—22no—
180#14519742C2312yes—
181C4×D244—21no—
182C4×D244—21no—
183D4×Dic61—21no—
184D4×Dic61—21no—
185#14519739—21no—
186#14519739—21no—
187C4×C22⋊D61—22no—
188C4×C22⋊D61—22no—
189#14519737—22no—
190#14519737—22no—
191#14519736—21no—
192#14519735—21no—
193#14519735—21no—
194#14519734—22no—
195#14519733—22no—
196C4⋊C4×D61—21no—
197C4⋊C4×D61—21no—
198C4⋊C4×D61—21no—
199C4⋊C4×D61—21no—
200C4⋊C4×D61—21no—
201C4⋊C4×D61—22no—
202C4⋊C4×D61—22no—
203C4⋊C4×D61C2312yes—
204C22⋊C4×D61—22no—
205C22⋊C4×D61—22no—
206C22⋊C4×D61—22no—
207C2×C4×Dic61D411yescharacteristic
208C2×C4×Dic61D411yescharacteristic
209C2×C4×Dic61C2311yescharacteristic
210C42×D61—22no—
211C42×D61D411yescharacteristic
212C42×D61D411yescharacteristic
213C42×D61D411yescharacteristic
214C42×D61D411yescharacteristic
215C42×D61C2311yescharacteristic
216C42×D61C2311yescharacteristic
217C42×D61C2311yescharacteristic
218C42×D61C2311yescharacteristic
219C4⋊#92418C2312yes—
220#14519706C2314yes—
221#14519702C2314yes—
222#14519701C2314yes—
223#14519700C2314yes—
224#14519699C2314yes—
225#14519698C2314yes—
226#14519697C2314yes—
227C22⋊#92418C2312yes—
228#14519689C2314yes—
229#14519688C2312yes—
230#14519687C2314yes—
231C2×#41×C61C2312yes—
232C2×Q16×C61C2314yes—
233C2×SD16×C61C2314yes—
234C4⋊Q8×C61C2311yescharacteristic
235C4⋊Q8×C61C2311yescharacteristic
236C4⋊Q8×C61C2311yescharacteristic
237#127×C61C2311yescharacteristic
238#125×C61—21no—
239#124×C61C2312yes—
240C22⋊Q8×C61—21no—
241C22⋊Q8×C61C2312yes—
242#121×C61—21no—
243#121×C61—21no—
244C4×Q8×C61—21no—
245C4×Q8×C61C2312yes—
246C4×D4×C61—21no—
247C4×D4×C61—21no—
248#117×C61—21no—
249C2×C42×C61C2311yescharacteristic
250C4⋊C8×C61C2312yes—
251#103×C61C2314yes—
252#102×C61C2314yes—
253C22⋊C8×C61C2312yes—
254#97×C61C2312yes—
255C23×D61—22no—
256C23×D61C2×D411yescharacteristic
257#41×C61—44no—
258C2×Q8×C61—21no—
259C2×Q8×C61C2412yes—
260C2×Q8×C61C2412yes—
261C2×D4×C61—22no—
262C2×D4×C61—21no—
263C2×D4×C61—21no—
264C2×D4×C61C2412yes—
265C22×C4×C61—22no—
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61C2411yescharacteristic
269C2×C22⋊D61—22no—
270C2×C22⋊D61—22no—
271C2×C22⋊D61—22no—
272C2×C22⋊D61—22no—
273C2×C22⋊D61—22no—
274C22×Dic61—22no—
275C22×Dic61C2×D411yescharacteristic
276C22×Dic61C2×D411yescharacteristic
277C22×Dic61C2×D411yescharacteristic
278#11758226—44no—
279Q8×D61—28no—
280Q8×D61—24no—
281Q8×D61—24no—
282Q8×D61—44no—
283#11758224—44no—
284#11758224—48no—
285D4×D61—28no—
286D4×D61—44no—
287D4×D61—48no—
288D4×D61—44no—
289#11758222—44no—
290#11758222—48no—
291C2×D244—22no—
292C2×D244—21no—
293C2×D244—21no—
294C2×D244C2412yes—
295C2×C4×D61—24no—
296C2×C4×D61—24no—
297C2×C4×D61—22no—
298C2×C4×D61—22no—
299C2×C4×D61—22no—
300C2×C4×D61—22no—
301C2×C4×D61—22no—
302C2×C4×D61—42no—
303C2×C4×D61—48no—
304C2×C4×D61C2×D411yescharacteristic
305C2×C4×D61C2×D411yescharacteristic
306C2×C4×D61C2×D411yescharacteristic
307C2×C4×D61C2×D411yescharacteristic
308C2×C4×D61C2×D411yescharacteristic
309C2×C4×D61C2×D411yescharacteristic
310C2×C4×D61C2×D411yescharacteristic
311C2×C4×D61C2×D411yescharacteristic
312C2×C4×D61C2×D411yescharacteristic
313C2×C4×D61C2×D411yescharacteristic
314C2×C4×D61C2411yescharacteristic
315C2×C4×D61C2411yescharacteristic
316C2×Dic122—21no—
317C2×Dic122—22no—
318C2×Dic122—22no—
319C2×Dic122—22no—
320C2×Dic122C2412yes—
321C2×Dic122C2412yes—
322Q16×C61—44no—
323SD16×C61—44no—
324C2×C8×C61C2414yes—
325C4⋊C4×C61—21no—
326C4⋊C4×C61—21no—
327C4⋊C4×C61—21no—
328C4⋊C4×C61—21no—
329C4⋊C4×C61—21no—
330C4⋊C4×C61—22no—
331C4⋊C4×C61—22no—
332C4⋊C4×C61C2412yes—
333C22⋊C4×C61—22no—
334C22⋊C4×C61—22no—
335C22⋊C4×C61—22no—
336C42×C61—22no—
337C42×C61C2×D411yescharacteristic
338C42×C61C2×D411yescharacteristic
339C42×C61C2411yescharacteristic
340C42×C61C2411yescharacteristic
341C22⋊Dic61—22no—
342C22⋊Dic61—22no—
343C22⋊Dic61—22no—
344#11758202—44no—
345#11758202—44no—
346#11758201—44no—
347#11758200—44no—
348#11758198—22no—
349#11758198—22no—
350#11758198—22no—
351#11758198—22no—
352#11758198—22no—
353#11758198—22no—
354C4⋊Dic61—21no—
355C4⋊Dic61—21no—
356C4⋊Dic61—21no—
357C4⋊Dic61—21no—
358C4⋊Dic61—21no—
359C4⋊Dic61—22no—
360C4⋊Dic61—22no—
361C4⋊Dic61C2412yes—
362#11758196—22no—
363#11758196—22no—
364#11758196—22no—
365#11758196—22no—
366#11758196—22no—
367#11758196—22no—
368#11758196—22no—
369#11758196—22no—
370#11758196—22no—
371#11758196—22no—
372C4×Dic61—22no—
373C4×Dic61—22no—
374C4×Dic61—22no—
375C4×Dic61C2×D411yescharacteristic
376C4×Dic61C2×D411yescharacteristic
377C4×Dic61C2×D411yescharacteristic
378C4×Dic61C2×D411yescharacteristic
379C4×Dic61C2×D411yescharacteristic
380C4×Dic61C2×D411yescharacteristic
381C4×Dic61C2×D411yescharacteristic
382C4×Dic61C2×D411yescharacteristic
383C4×Dic61C2×D411yescharacteristic
384C4×Dic61C2×D411yescharacteristic
385C4×Dic61C2411yescharacteristic
386C4×Dic61C2411yescharacteristic
387C2×#92418C2414yes—
388Dic244—44no—
389#11758190—44no—
390C8×D61—28no—
391C23×C61—22no—
392C23×C61C22×D411yescharacteristic
393C22×D61—22no—
394C22×D61—22no—
395C22×D61—22no—
396C22×D61—22no—
397C22×D61—44no—
398C22×D61—44no—
399C22×D61—44no—
400C22×D61C22×D411yescharacteristic
401C22×D61C22×D411yescharacteristic
402Q8×C61—22no—
403Q8×C61—22no—
404Q8×C61—24no—
405Q8×C61—42no—
406D4×C61—24no—
407D4×C61—42no—
408D4×C61—44no—
409D4×C61—42no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—41no—
416C2×C4×C61—44no—
417C2×C4×C61C22×D411yescharacteristic
418C2×C4×C61C22×D411yescharacteristic
419C2×C4×C61C22×D411yescharacteristic
420C2×C4×C61C22×D411yescharacteristic
421C2×C4×C61C22×D411yescharacteristic
422C2×C4×C61C2511yescharacteristic
423C22⋊D61—44no—
424C22⋊D61—44no—
425C22⋊D61—44no—
426C22⋊D61—44no—
427C22⋊D61—44no—
428C2×Dic61—22no—
429C2×Dic61—22no—
430C2×Dic61—22no—
431C2×Dic61—22no—
432C2×Dic61—22no—
433C2×Dic61—41no—
434C2×Dic61—44no—
435C2×Dic61C22×D411yescharacteristic
436C2×Dic61C22×D411yescharacteristic
437C2×Dic61C22×D411yescharacteristic
438C2×Dic61C22×D411yescharacteristic
439C2×Dic61C22×D411yescharacteristic
440C2×Dic61C22×D411yescharacteristic
441D244—24no—
442D244—42no—
443D244—44no—
444D244—42no—
445C4×D61—22no—
446C4×D61—22no—
447C4×D61—22no—
448C4×D61—22no—
449C4×D61—22no—
450C4×D61—22no—
451C4×D61—22no—
452C4×D61—22no—
453C4×D61—41no—
454C4×D61—41no—
455C4×D61—44no—
456C4×D61—44no—
457C4×D61—44no—
458C4×D61—44no—
459C4×D61—44no—
460C4×D61#13714yes—
461C4×D61H(5,𝔽2)14yes—
462Dic122—22no—
463Dic122—22no—
464Dic122—24no—
465Dic122—44no—
466Dic122—42no—
467Dic122—44no—
468Dic122—44no—
469C8×C61—24no—
470#92418—24no—
471C2×#3216—611nomaximal, Sylow
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—42no—
476C22×C61—42no—
477C22×C61—42no—
478C22×C61C23×D411yescharacteristic
479C2×D61—21no—
480C2×D61—21no—
481C2×D61—21no—
482C2×D61—44no—
483C2×D61—42no—
484C2×D61—42no—
485C2×D61—42no—
486C2×D61—88no—
487C2×D61#53512yes—
488C2×D61C2×#13712yes—
489C2×D61#57512yes—
490C4×C61—21no—
491C4×C61—21no—
492C4×C61—21no—
493C4×C61—21no—
494C4×C61—42no—
495C4×C61—42no—
496C4×C61—42no—
497C4×C61C2×#13712yes—
498C4×C61C2×H(5,𝔽2)12yes—
499Dic61—21no—
500Dic61—21no—
501Dic61—21no—
502Dic61—21no—
503Dic61—42no—
504Dic61—42no—
505Dic61—42no—
506Dic61#53512yes—
507Dic61C2×#13712yes—
508C2×#533—611no—
509C2×#532—611no—
510#3216—612no—
511#3216—612no—
512#3216—612no—
513#3216—612no—
514#3216—614no—
515#3216—611no—
516#3216—611no—
517#3216—611no—
518#3216D6111yescharacteristic, direct product factor
519C2×#497—612no—
520C2×#489—612no—
521C2×#462—612no—
522C2×#460—612no—
523C2×#452—614no—
524C2×#432—611no—
525C2×C61—41no—
526C2×C61—82no—
527C2×C61C2×#53511yescharacteristic
528C2×C61C22×#13711yescharacteristic
529C2×C61C2×#57511yescharacteristic
530D61—41no—
531D61—82no—
532D61#321614yesdirect product factor
533C22×#41—612no—
534C22×Q16—614no—
535C22×SD16—614no—
536#533—611no—
537#533—611no—
538#533—612no—
539#533—612no—
540#533—611no—
541#533—1221no—
542#533—1221no—
543#533—1221no—
544#533—1221no—
545#533C2×D6111yescharacteristic, complemented
546#532—612no—
547#532—611no—
548#532—611no—
549#532—612no—
550#532—611no—
551#532—1221no—
552#532—1221no—
553#532—1221no—
554#532—1221no—
555#532C2×D6111yescharacteristic
556C2×C4⋊Q8—611no—
557C2×C4⋊Q8—611no—
558C2×C4⋊Q8—611no—
559C2×#127—611no—
560C2×#125—1221no—
561C2×#124—612no—
562C2×C22⋊Q8—612no—
563C2×C22⋊Q8—1221no—
564C2×#121—1221no—
565C2×#121—1221no—
566C2×C4×Q8—612no—
567C2×C4×Q8—1221no—
568C2×C4×D4—1221no—
569C2×C4×D4—1221no—
570C2×#117—1221no—
571C22×C42—611no—
572#497—614no—
573#497—614no—
574#497—612no—
575#497—612no—
576#497—612no—
577#497C2×D6112yescomplemented
578#489—612no—
579#489—612no—
580#489—614no—
581#489—614no—
582#489—612no—
583#489C2×D6112yescomplemented
584#462—614no—
585#462—612no—
586#462—612no—
587#462—612no—
588#462—614no—
589#462C2×D6112yescomplemented
590#460—614no—
591#460—612no—
592#460—612no—
593#460—612no—
594#460—614no—
595#460C2×D6112yescomplemented
596#452—614no—
597#452—614no—
598#452—614no—
599#452—614no—
600#452—614no—
601#452—614no—
602#452—614no—
603#452C2×D6114yescomplemented
604#432—611no—
605#432—612no—
606#432—612no—
607#432—612no—
608#432C2×D6111yescharacteristic, complemented
609C2×C4⋊C8—612no—
610C2×#103—614no—
611C2×#102—614no—
612C2×C22⋊C8—612no—
613C2×#97—612no—
614C61C2×#321611yescharacteristic, complemented, Sylow
615C2×#41—612no—
616C2×#41—612no—
617C2×#41—612no—
618C2×#41—1222no—
619C2×#41—1222no—
620C2×#41—2448no—
621C2×#41C22×D6112yes—
622C22×Q8—612no—
623C22×Q8—612no—
624C22×Q8—1221no—
625C22×D4—612no—
626C22×D4—1221no—
627C22×D4—1221no—
628C22×D4—1222no—
629C23×C4—611no—
630C23×C4—611no—
631C23×C4—611no—
632C23×C4—1222no—
633C2×Q16—614no—
634C2×Q16—614no—
635C2×Q16—614no—
636C2×Q16—2448no—
637C2×Q16C22×D6114yes—
638C2×SD16—614no—
639C2×SD16—614no—
640C2×SD16—614no—
641C2×SD16—2448no—
642C2×SD16C22×D6114yes—
643C22×C8—614no—
644C4⋊Q8—612no—
645C4⋊Q8—612no—
646C4⋊Q8—612no—
647C4⋊Q8—611no—
648C4⋊Q8—611no—
649C4⋊Q8—611no—
650C4⋊Q8—1221no—
651C4⋊Q8—1221no—
652C4⋊Q8—1221no—
653C4⋊Q8—1221no—
654C4⋊Q8—1221no—
655C4⋊Q8—1221no—
656C4⋊Q8C22×D6111yescharacteristic
657C4⋊Q8C22×D6111yescharacteristic
658C4⋊Q8C22×D6111yescharacteristic
659#127—612no—
660#127—611no—
661#127—1221no—
662#127—1221no—
663#127C22×D6111yescharacteristic
664#125—21no—
665#125—1222no—
666#125—1222no—
667#125—1221no—
668#125—1221no—
669#125—1221no—
670#124—612no—
671#124—612no—
672#124—612no—
673#124—1222no—
674#124—1222no—
675#124C22×D6112yes—
676C22⋊Q8—21no—
677C22⋊Q8—612no—
678C22⋊Q8—612no—
679C22⋊Q8—612no—
680C22⋊Q8—1222no—
681C22⋊Q8—1222no—
682C22⋊Q8—1222no—
683C22⋊Q8—1222no—
684C22⋊Q8—1221no—
685C22⋊Q8—1221no—
686C22⋊Q8—1221no—
687C22⋊Q8C22×D6112yes—
688#121—21no—
689#121—21no—
690#121—1222no—
691#121—1222no—
692#121—1221no—
693#121—1221no—
694#121—1221no—
695#121—1221no—
696#121—1222no—
697#121—1222no—
698#121—1221no—
699#121—1221no—
700C4×Q8—21no—
701C4×Q8—612no—
702C4×Q8—612no—
703C4×Q8—612no—
704C4×Q8—1222no—
705C4×Q8—1222no—
706C4×Q8—1222no—
707C4×Q8—1221no—
708C4×Q8—1222no—
709C4×Q8—1221no—
710C4×Q8—1221no—
711C4×Q8C22×D6112yes—
712C4×D4—21no—
713C4×D4—21no—
714C4×D4—1222no—
715C4×D4—1222no—
716C4×D4—1221no—
717C4×D4—1221no—
718C4×D4—1222no—
719C4×D4—1222no—
720C4×D4—1221no—
721C4×D4—1221no—
722C4×D4—1221no—
723C4×D4—1221no—
724#117—21no—
725#117—1222no—
726#117—1222no—
727#117—1221no—
728#117—1221no—
729#117—1221no—
730C2×C4⋊C4—612no—
731C2×C4⋊C4—1221no—
732C2×C4⋊C4—1221no—
733C2×C4⋊C4—1221no—
734C2×C4⋊C4—1221no—
735C2×C4⋊C4—1222no—
736C2×C4⋊C4—1222no—
737C2×C4⋊C4—1221no—
738C2×C22⋊C4—1222no—
739C2×C22⋊C4—1222no—
740C2×C22⋊C4—1222no—
741C2×C42—611no—
742C2×C42—611no—
743C2×C42—611no—
744C2×C42—611no—
745C2×C42—611no—
746C2×C42—611no—
747C2×C42—611no—
748C2×C42—611no—
749C2×C42—611no—
750C2×C42—611no—
751C2×C42—611no—
752C2×C42—1222no—
753C2×C42C22×D6111yescharacteristic
754C4⋊C8—614no—
755C4⋊C8—612no—
756C4⋊C8C22×D6112yes—
757#103—614no—
758#103—614no—
759#103—614no—
760#103C22×D6114yes—
761#102—614no—
762#102—614no—
763#102—614no—
764#102C22×D6114yes—
765C22⋊C8—612no—
766C22⋊C8—614no—
767C22⋊C8C22×D6112yes—
768#97—614no—
769#97—612no—
770#97C22×D6112yes—
771C24—611no—
772C24—1222no—
773#41—44no—
774#41—2444no—
775#41—2448no—
776#41—2444no—
777#41—2448no—
778#41—2444no—
779C2×Q8—21no—
780C2×Q8—612no—
781C2×Q8—612no—
782C2×Q8—1222no—
783C2×Q8—1222no—
784C2×Q8—1222no—
785C2×Q8—1224no—
786C2×Q8—1224no—
787C2×Q8—1228no—
788C2×Q8—1221no—
789C2×Q8—2444no—
790C2×Q8C23×D6112yes—
791C2×Q8C23×D6112yes—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—612no—
796C2×D4—1222no—
797C2×D4—1228no—
798C2×D4—1222no—
799C2×D4—1222no—
800C2×D4—1222no—
801C2×D4—1222no—
802C2×D4—1222no—
803C2×D4—1221no—
804C2×D4—1221no—
805C2×D4—2444no—
806C2×D4—2444no—
807C2×D4—2448no—
808C2×D4C23×D6112yes—
809C22×C4—22no—
810C22×C4—611no—
811C22×C4—611no—
812C22×C4—611no—
813C22×C4—611no—
814C22×C4—611no—
815C22×C4—611no—
816C22×C4—611no—
817C22×C4—611no—
818C22×C4—611no—
819C22×C4—611no—
820C22×C4—611no—
821C22×C4—611no—
822C22×C4—611no—
823C22×C4—611no—
824C22×C4—611no—
825C22×C4—1224no—
826C22×C4—1224no—
827C22×C4—1222no—
828C22×C4—1222no—
829C22×C4—1222no—
830C22×C4—1222no—
831C22×C4—1222no—
832C22×C4—1222no—
833C22×C4—2442no—
834C22×C4—2448no—
835C22×C4D4×D6111yescharacteristic
836C22×C4D4×D6111yescharacteristic
837C22×C4C23×D6111yescharacteristic
838Q16—44no—
839Q16—2444no—
840Q16—2444no—
841Q16—2444no—
842SD16—44no—
843SD16—2444no—
844SD16—2444no—
845SD16—2444no—
846C2×C8—614no—
847C2×C8—1228no—
848C2×C8C23×D6114yes—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—612no—
857C4⋊C4—1222no—
858C4⋊C4—1222no—
859C4⋊C4—1222no—
860C4⋊C4—1222no—
861C4⋊C4—1222no—
862C4⋊C4—1222no—
863C4⋊C4—1222no—
864C4⋊C4—1222no—
865C4⋊C4—1222no—
866C4⋊C4—1222no—
867C4⋊C4—1222no—
868C4⋊C4—1222no—
869C4⋊C4—1221no—
870C4⋊C4—1221no—
871C4⋊C4—1221no—
872C4⋊C4—1221no—
873C4⋊C4—1221no—
874C4⋊C4C23×D6112yes—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—1222no—
879C22⋊C4—1222no—
880C22⋊C4—1222no—
881C22⋊C4—1222no—
882C22⋊C4—1222no—
883C22⋊C4—1222no—
884C22⋊C4—1222no—
885C22⋊C4—1222no—
886C22⋊C4—1222no—
887C42—22no—
888C42—611no—
889C42—611no—
890C42—611no—
891C42—611no—
892C42—611no—
893C42—611no—
894C42—611no—
895C42—611no—
896C42—611no—
897C42—611no—
898C42—611no—
899C42—611no—
900C42—1222no—
901C42—1222no—
902C42—1222no—
903C42D4×D6111yescharacteristic
904C42D4×D6111yescharacteristic
905C42C23×D6111yescharacteristic
906C42C23×D6111yescharacteristic
907C23—22no—
908C23—611no—
909C23—611no—
910C23—1222no—
911C23—1222no—
912C23—1222no—
913C23—1222no—
914C23—2444no—
915C23—2444no—
916C23—2444no—
917C23C2×D4×D6111yescharacteristic
918Q8—22no—
919Q8—22no—
920Q8—24no—
921Q8—42no—
922Q8—1222no—
923Q8—1222no—
924Q8—1224no—
925Q8—2442no—
926Q8—2444no—
927Q8—2444no—
928Q8—2444no—
929D4—24no—
930D4—42no—
931D4—44no—
932D4—42no—
933D4—1224no—
934D4—2442no—
935D4—2444no—
936D4—2444no—
937D4—2444no—
938D4—2444no—
939D4—2444no—
940D4—2444no—
941D4—2442no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—41no—
948C2×C4—44no—
949C2×C4—611no—
950C2×C4—611no—
951C2×C4—614no—
952C2×C4—614no—
953C2×C4—611no—
954C2×C4—611no—
955C2×C4—611no—
956C2×C4—611no—
957C2×C4—1222no—
958C2×C4—1222no—
959C2×C4—1222no—
960C2×C4—1222no—
961C2×C4—1222no—
962C2×C4—1222no—
963C2×C4—1222no—
964C2×C4—1222no—
965C2×C4—1222no—
966C2×C4—1222no—
967C2×C4—1222no—
968C2×C4—1222no—
969C2×C4—1222no—
970C2×C4—2441no—
971C2×C4—2441no—
972C2×C4—2444no—
973C2×C4—2444no—
974C2×C4—2444no—
975C2×C4—2444no—
976C2×C4—2444no—
977C2×C4—2441no—
978C2×C4—2444no—
979C2×C4C2×D4×D6111yescharacteristic
980C2×C4C2×D4×D6111yescharacteristic
981C2×C4C2×D4×D6111yescharacteristic
982C2×C4C2×D4×D6111yescharacteristic
983C2×C4C2×D4×D6111yescharacteristic
984C2×C4C24×D6111yescharacteristic
985C8—24no—
986C8—1224no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—612no—
994C22—612no—
995C22—612no—
996C22—1221no—
997C22—1221no—
998C22—1221no—
999C22—4888no—
1000C22—2444no—
1001C22—2442no—
1002C22—2442no—
1003C22—2442no—
1004C22C22×D4×D6111yescharacteristic
1005C4—21no—
1006C4—21no—
1007C4—21no—
1008C4—21no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—612no—
1013C4—612no—
1014C4—1221no—
1015C4—1221no—
1016C4—1221no—
1017C4—1221no—
1018C4—2442no—
1019C4—2442no—
1020C4—2442no—
1021C4#137×D6112yes—
1022C4H(5,𝔽2)×D6112yes—
1023C2—41no—
1024C2—82no—
1025C2—614no—
1026C2—4882no—
1027C2—2441no—
1028C2#535×D6111yescharacteristic
1029C2C2×#137×D6111yescharacteristic
1030C2#575×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3216C2
socleC22×C61C23×D4
prime radical#532×D61C2
hypercenter#3216D61
hypocenterC61C2×#3216
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3216

Complements

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

NH ≅ G/Ntype
1. #533×D61C2semidirect
3. #21456832C2semidirect
4. #21456831C2semidirect
5. #21456830C2semidirect
6. #21456829C2semidirect
7. #21456828C2semidirect
8. #21456827C2semidirect
9. #21456826C2semidirect
10. #21456825C2semidirect
11. #497×D61C2semidirect
12. #489×D61C2semidirect
13. #462×D61C2semidirect
14. #460×D61C2semidirect
15. #452×D61C2semidirect
16. #432×D61C2semidirect
17. C61×#3216C2semidirect
21. #16840319C22semidirect
23. #16840317C22semidirect
24. #16840317C22semidirect
26. #16840316C22semidirect
29. #16840314C22semidirect
55. #16840157C22semidirect
56. #16840156C22semidirect
57. #16840155C22semidirect
58. #16840154C22semidirect
59. #16840153C22semidirect
60. #16840124C22semidirect
61. #16840123C22semidirect
62. #16840122C22semidirect
63. #16840121C22semidirect
64. #16840120C22semidirect
65. #16839973C22semidirect
66. #16839972C22semidirect
67. #16839971C22semidirect
68. #16839970C22semidirect
69. #16839969C22semidirect
70. #16839963C22semidirect
71. #16839962C22semidirect
72. #16839961C22semidirect
73. #16839960C22semidirect
74. #16839959C22semidirect
75. #16839927C22semidirect
76. #16839926C22semidirect
77. #16839925C22semidirect
78. #16839924C22semidirect
79. #16839923C22semidirect
80. #16839922C22semidirect
81. #16839921C22semidirect
82. #16839819C22semidirect
83. #16839818C22semidirect
84. #16839817C22semidirect
85. #16839816C22semidirect
91. C61×#533C22semidirect
93. C61×#497C22semidirect
94. C61×#489C22semidirect
95. C61×#462C22semidirect
96. C61×#460C22semidirect
97. C61×#452C22semidirect
98. C61×#432C22semidirect
518. #3216D61direct (N × H)
532. D61#3216direct (N × H)
545. #533C2×D61semidirect
577. #497C2×D61semidirect
583. #489C2×D61semidirect
589. #462C2×D61semidirect
595. #460C2×D61semidirect
603. #452C2×D61semidirect
608. #432C2×D61semidirect
614. C61C2×#3216semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#532×D612
#214568322
#214568312
#214568302
#214568292
#214568282
#214568272
#214568262
#214568252
#497×D612
#489×D612
#462×D612
#460×D612
#452×D612
#432×D612
C61×#32162
C2×#321661