Finite Group Databasebeta

← D61×#3235 #30552150

Subgroups — D61×#3235 #30552150

Order 15616.

2038 conjugacy classes of subgroups.

The subgroup lattice has 1006 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#21457019C211yesmaximal, characteristic, complemented
4#21457018C212yesmaximal, complemented
5#21457017C211yesmaximal, characteristic, complemented
6#21457016C212yesmaximal, complemented
7#21457015C212yesmaximal, complemented
8#21457014C214yesmaximal, complemented
9#21457013C211yesmaximal, characteristic, complemented
10#21457012C212yesmaximal, complemented
11#501×D61C212yesmaximal, complemented
12#490×D61C212yesmaximal, complemented
13#482×D61C214yesmaximal, complemented
14#476×D61C212yesmaximal, complemented
15#474×D61C212yesmaximal, complemented
16#432×D61C211yesmaximal, characteristic, complemented
17C61×#3235C211yesmaximal, characteristic, complemented
18C2×#41×D61—21no—
19#16840319C2211yescharacteristic, complemented
20#16840318C2212yescomplemented
21#16840317C2211yescharacteristic, complemented
22#16840317C2211yescharacteristic, complemented
23#16840316—21no—
24#16840316—21no—
25#16840315C2212yescomplemented
26#16840314—21no—
27#16840314—21no—
28#16840313C2211yescharacteristic
29#16840312C2211yescharacteristic
30#16840311—21no—
31#16840310C2211yescharacteristic
32#16840309—21no—
33#16840309C2212yes—
34#16840308—21no—
35#16840307—21no—
36#16840307C2212yes—
37C4⋊Q8×D61C2211yescharacteristic
38C4⋊Q8×D61C2211yescharacteristic
39C4⋊Q8×D61C2211yescharacteristic
40#127×D61C2211yescharacteristic
41#125×D61C2212yes—
42#124×D61—21no—
43C22⋊Q8×D61—21no—
44C22⋊Q8×D61—21no—
45#121×D61—21no—
46#121×D61C2212yes—
47C4×Q8×D61—21no—
48C4×Q8×D61—21no—
49C4×D4×D61—21no—
50C4×D4×D61C2212yes—
51#117×D61C2212yes—
52C2×C42×D61C2211yescharacteristic
53#16840172C2212yescomplemented
54#16840171C2212yescomplemented
55#16840170C2214yescomplemented
56#16840169C2214yescomplemented
57#16840168C2212yescomplemented
58#16840128C2212yescomplemented
59#16840127C2212yescomplemented
60#16840126C2212yescomplemented
61#16840125C2214yescomplemented
62#16840125C2214yescomplemented
63#16840089C2214yescomplemented
64#16840088C2214yescomplemented
65#16840087C2214yescomplemented
66#16840086C2214yescomplemented
67#16840085C2214yescomplemented
68#16840084C2214yescomplemented
69#16840083C2214yescomplemented
70#16840053C2212yescomplemented
71#16840052C2212yescomplemented
72#16840051C2214yescomplemented
73#16840050C2214yescomplemented
74#16840049C2212yescomplemented
75#16840043C2212yescomplemented
76#16840042C2212yescomplemented
77#16840041C2214yescomplemented
78#16840040C2214yescomplemented
79#16840039C2212yescomplemented
80#16839819C2211yescharacteristic, complemented
81#16839818C2212yescomplemented
82#16839817C2212yescomplemented
83#16839816C2212yescomplemented
84#107×D61C2214yes—
85#106×D61C2214yes—
86C4⋊C8×D61C2212yes—
87#102×D61C2214yes—
88#102×D61C2214yes—
89C22⋊C8×D61C2212yes—
90#97×D61C2212yes—
91C61×#533C2211yescharacteristic, complemented
92C61×#532C2211yescharacteristic
93C61×#501C2212yescomplemented
94C61×#490C2212yescomplemented
95C61×#482C2214yescomplemented
96C61×#476C2212yescomplemented
97C61×#474C2212yescomplemented
98C61×#432C2211yescharacteristic, complemented
99C2×#11758226—21no—
100C2×#11758222—21no—
101C2×#11758222—22no—
102C2×#11758224—22no—
103C2×#11758224—21no—
104#41×D61—48no—
105C2×Q8×D61—21no—
106C2×Q8×D61—21no—
107C2×Q8×D61—21no—
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×C8×D61C2314yes—
117#14519777C2311yescharacteristic
118#14519777C2311yescharacteristic
119#14519777C2311yescharacteristic
120#14519776—21no—
121#14519776—21no—
122#14519776—21no—
123#14519776C2312yes—
124#14519776C2312yes—
125#14519776C2312yes—
126#14519775—21no—
127#14519775—21no—
128#14519775—21no—
129#14519774C2311yescharacteristic
130#14519773—21no—
131#14519773—21no—
132#14519773C2312yes—
133#14519769C2312yes—
134#14519768C2312yes—
135#14519768C2312yes—
136#14519767—22no—
137#14519767—22no—
138#14519766—21no—
139#14519765—21no—
140#14519764—21no—
141#14519763—22no—
142#14519763—22no—
143#14519757—21no—
144#14519757—21no—
145#14519756—21no—
146#14519756—21no—
147#14519755—22no—
148#14519755—22no—
149#14519754—22no—
150#14519754—22no—
151#14519753—21no—
152#14519753—21no—
153#14519752—21no—
154#14519752C2312yes—
155#14519751—21no—
156#14519751C2312yes—
157#14519750—22no—
158#14519750—22no—
159#14519749—22no—
160#14519749—22no—
161#14519748—21no—
162#14519748C2312yes—
163Q8×Dic61—21no—
164Q8×Dic61—21no—
165C4×Dic122—21no—
166C4×Dic122—21no—
167C4×Dic122—22no—
168C4×Dic122—22no—
169#14519742—21no—
170#14519742—21no—
171#14519742—22no—
172#14519742—22no—
173C4×D244—21no—
174C4×D244C2312yes—
175D4×Dic61—21no—
176D4×Dic61C2312yes—
177#14519739—21no—
178#14519739C2312yes—
179C4×C22⋊D61—22no—
180C4×C22⋊D61—22no—
181#14519737—22no—
182#14519737—22no—
183#14519736C2312yes—
184#14519735C2312yes—
185#14519735C2312yes—
186#14519734—22no—
187#14519733—22no—
188C4⋊C4×D61—21no—
189C4⋊C4×D61—22no—
190C4⋊C4×D61—22no—
191C4⋊C4×D61—21no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61C2312yes—
194C4⋊C4×D61C2312yes—
195C4⋊C4×D61C2312yes—
196C22⋊C4×D61—22no—
197C22⋊C4×D61—22no—
198C22⋊C4×D61—22no—
199C2×C4×Dic61D411yescharacteristic
200C2×C4×Dic61D411yescharacteristic
201C2×C4×Dic61C2311yescharacteristic
202C42×D61—22no—
203C42×D61D411yescharacteristic
204C42×D61D411yescharacteristic
205C42×D61D411yescharacteristic
206C42×D61D411yescharacteristic
207C42×D61C2311yescharacteristic
208C42×D61C2311yescharacteristic
209C42×D61C2311yescharacteristic
210C42×D61C2311yescharacteristic
211#14519711C2314yes—
212#14519710C2314yes—
213#14519710C2314yes—
214#14519709C2314yes—
215#14519708C2314yes—
216#14519708C2314yes—
217C4⋊#92418C2312yes—
218#14519706C2314yes—
219#14519699C2314yes—
220#14519699C2314yes—
221#14519698C2314yes—
222#14519698C2314yes—
223#14519697C2314yes—
224#14519697C2314yes—
225C22⋊#92418C2312yes—
226#14519689C2314yes—
227#14519688C2312yes—
228#14519687C2314yes—
229C2×#41×C61—21no—
230C4⋊Q8×C61C2311yescharacteristic
231C4⋊Q8×C61C2311yescharacteristic
232C4⋊Q8×C61C2311yescharacteristic
233#127×C61C2311yescharacteristic
234#125×C61C2312yes—
235#124×C61—21no—
236C22⋊Q8×C61—21no—
237C22⋊Q8×C61—21no—
238#121×C61—21no—
239#121×C61C2312yes—
240C4×Q8×C61—21no—
241C4×Q8×C61—21no—
242C4×D4×C61—21no—
243C4×D4×C61C2312yes—
244#117×C61C2312yes—
245C2×C42×C61C2311yescharacteristic
246#107×C61C2314yes—
247#106×C61C2314yes—
248C4⋊C8×C61C2312yes—
249#102×C61C2314yes—
250#102×C61C2314yes—
251C22⋊C8×C61C2312yes—
252#97×C61C2312yes—
253C23×D61—22no—
254C23×D61C2×D411yescharacteristic
255#41×C61—44no—
256C2×Q8×C61—21no—
257C2×Q8×C61—21no—
258C2×Q8×C61—21no—
259C2×D4×C61—22no—
260C2×D4×C61—21no—
261C2×D4×C61—21no—
262C2×D4×C61C2412yes—
263C22×C4×C61—22no—
264C22×C4×C61C2×D411yescharacteristic
265C22×C4×C61C2×D411yescharacteristic
266C22×C4×C61C2411yescharacteristic
267C2×C22⋊D61—22no—
268C2×C22⋊D61—22no—
269C2×C22⋊D61—22no—
270C2×C22⋊D61—22no—
271C2×C22⋊D61—22no—
272C22×Dic61—22no—
273C22×Dic61C2×D411yescharacteristic
274C22×Dic61C2×D411yescharacteristic
275C22×Dic61C2×D411yescharacteristic
276#11758226—44no—
277Q8×D61—44no—
278Q8×D61—44no—
279Q8×D61—44no—
280#11758224—44no—
281#11758224—48no—
282D4×D61—28no—
283D4×D61—44no—
284D4×D61—44no—
285D4×D61—48no—
286#11758222—48no—
287#11758222—44no—
288C2×D244—22no—
289C2×D244—21no—
290C2×D244—21no—
291C2×D244C2412yes—
292C2×C4×D61—24no—
293C2×C4×D61—24no—
294C2×C4×D61—22no—
295C2×C4×D61—22no—
296C2×C4×D61—22no—
297C2×C4×D61—22no—
298C2×C4×D61—22no—
299C2×C4×D61—42no—
300C2×C4×D61—48no—
301C2×C4×D61C2×D411yescharacteristic
302C2×C4×D61C2×D411yescharacteristic
303C2×C4×D61C2×D411yescharacteristic
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×D61C2411yescharacteristic
312C2×C4×D61C2411yescharacteristic
313C2×Dic122—21no—
314C2×Dic122—21no—
315C2×Dic122—21no—
316C2×Dic122—22no—
317C2×Dic122—22no—
318C2×Dic122—22no—
319C2×C8×C61C2414yes—
320C4⋊C4×C61—21no—
321C4⋊C4×C61—22no—
322C4⋊C4×C61—22no—
323C4⋊C4×C61—21no—
324C4⋊C4×C61—21no—
325C4⋊C4×C61C2412yes—
326C4⋊C4×C61C2412yes—
327C4⋊C4×C61C2412yes—
328C22⋊C4×C61—22no—
329C22⋊C4×C61—22no—
330C22⋊C4×C61—22no—
331C42×C61—22no—
332C42×C61C2×D411yescharacteristic
333C42×C61C2×D411yescharacteristic
334C42×C61C2411yescharacteristic
335C42×C61C2411yescharacteristic
336C22⋊Dic61—22no—
337C22⋊Dic61—22no—
338C22⋊Dic61—22no—
339#11758198—22no—
340#11758198—22no—
341#11758198—22no—
342#11758198—22no—
343#11758198—22no—
344#11758198—22no—
345C4⋊Dic61—21no—
346C4⋊Dic61—21no—
347C4⋊Dic61—21no—
348C4⋊Dic61—22no—
349C4⋊Dic61—22no—
350C4⋊Dic61C2412yes—
351C4⋊Dic61C2412yes—
352C4⋊Dic61C2412yes—
353#11758196—22no—
354#11758196—22no—
355#11758196—22no—
356#11758196—22no—
357#11758196—22no—
358#11758196—22no—
359#11758196—22no—
360#11758196—22no—
361#11758196—22no—
362#11758196—22no—
363C4×Dic61—22no—
364C4×Dic61—22no—
365C4×Dic61—22no—
366C4×Dic61C2×D411yescharacteristic
367C4×Dic61C2×D411yescharacteristic
368C4×Dic61C2×D411yescharacteristic
369C4×Dic61C2×D411yescharacteristic
370C4×Dic61C2×D411yescharacteristic
371C4×Dic61C2×D411yescharacteristic
372C4×Dic61C2×D411yescharacteristic
373C4×Dic61C2×D411yescharacteristic
374C4×Dic61C2×D411yescharacteristic
375C4×Dic61C2×D411yescharacteristic
376C4×Dic61C2411yescharacteristic
377C4×Dic61C2411yescharacteristic
378C2×#92418C2414yes—
379C8×D61—28no—
380C23×C61—22no—
381C23×C61C22×D411yescharacteristic
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—44no—
387C22×D61—44no—
388C22×D61—44no—
389C22×D61C22×D411yescharacteristic
390C22×D61C22×D411yescharacteristic
391Q8×C61—42no—
392Q8×C61—42no—
393Q8×C61—42no—
394D4×C61—24no—
395D4×C61—42no—
396D4×C61—42no—
397D4×C61—44no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—41no—
404C2×C4×C61—44no—
405C2×C4×C61C22×D411yescharacteristic
406C2×C4×C61C22×D411yescharacteristic
407C2×C4×C61C22×D411yescharacteristic
408C2×C4×C61C22×D411yescharacteristic
409C2×C4×C61C22×D411yescharacteristic
410C2×C4×C61C2511yescharacteristic
411C22⋊D61—44no—
412C22⋊D61—44no—
413C22⋊D61—44no—
414C22⋊D61—44no—
415C22⋊D61—44no—
416C2×Dic61—22no—
417C2×Dic61—22no—
418C2×Dic61—22no—
419C2×Dic61—22no—
420C2×Dic61—22no—
421C2×Dic61—41no—
422C2×Dic61—44no—
423C2×Dic61C22×D411yescharacteristic
424C2×Dic61C22×D411yescharacteristic
425C2×Dic61C22×D411yescharacteristic
426C2×Dic61C22×D411yescharacteristic
427C2×Dic61C22×D411yescharacteristic
428C2×Dic61C22×D411yescharacteristic
429D244—24no—
430D244—42no—
431D244—42no—
432D244—44no—
433C4×D61—22no—
434C4×D61—22no—
435C4×D61—22no—
436C4×D61—22no—
437C4×D61—22no—
438C4×D61—22no—
439C4×D61—22no—
440C4×D61—22no—
441C4×D61—41no—
442C4×D61—41no—
443C4×D61—44no—
444C4×D61—44no—
445C4×D61—44no—
446C4×D61—44no—
447C4×D61—44no—
448C4×D61AGL(1,ℤ/8)14yes—
449C4×D612−1+414yes—
450Dic122—44no—
451Dic122—44no—
452Dic122—42no—
453Dic122—42no—
454Dic122—42no—
455Dic122—44no—
456C8×C61—24no—
457#92418—24no—
458C2×#3235—611nomaximal, Sylow
459C22×C61—21no—
460C22×C61—21no—
461C22×C61—21no—
462C22×C61—42no—
463C22×C61—42no—
464C22×C61—42no—
465C22×C61C23×D411yescharacteristic
466C2×D61—21no—
467C2×D61—21no—
468C2×D61—21no—
469C2×D61—44no—
470C2×D61—42no—
471C2×D61—42no—
472C2×D61—42no—
473C2×D61—88no—
474C2×D61#53612yes—
475C2×D61C2×AGL(1,ℤ/8)12yes—
476C2×D61#57512yes—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—42no—
482C4×C61—42no—
483C4×C61—42no—
484C4×C61C2×AGL(1,ℤ/8)12yes—
485C4×C61C2×2−1+412yes—
486Dic61—21no—
487Dic61—21no—
488Dic61—21no—
489Dic61—21no—
490Dic61—42no—
491Dic61—42no—
492Dic61—42no—
493Dic61#53612yes—
494Dic61C2×AGL(1,ℤ/8)12yes—
495C2×#533—611no—
496C2×#532—611no—
497#3235—612no—
498#3235—612no—
499#3235—614no—
500#3235—612no—
501#3235—612no—
502#3235—611no—
503#3235—611no—
504#3235—611no—
505#3235D6111yescharacteristic, direct product factor
506C2×#501—612no—
507C2×#490—612no—
508C2×#482—614no—
509C2×#476—612no—
510C2×#474—612no—
511C2×#432—611no—
512C2×C61—41no—
513C2×C61—82no—
514C2×C61C2×#53611yescharacteristic
515C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
516C2×C61C2×#57511yescharacteristic
517D61—41no—
518D61—82no—
519D61#323514yesdirect product factor
520C22×#41—1221no—
521#533—611no—
522#533—611no—
523#533—612no—
524#533—612no—
525#533—611no—
526#533—1221no—
527#533—1221no—
528#533—1221no—
529#533—1221no—
530#533C2×D6111yescharacteristic, complemented
531#532—611no—
532#532—611no—
533#532—612no—
534#532—612no—
535#532—611no—
536#532—1221no—
537#532—1221no—
538#532—1221no—
539#532—1221no—
540#532C2×D6111yescharacteristic
541C2×C4⋊Q8—611no—
542C2×C4⋊Q8—611no—
543C2×C4⋊Q8—611no—
544C2×#127—611no—
545C2×#125—612no—
546C2×#124—1221no—
547C2×C22⋊Q8—1221no—
548C2×C22⋊Q8—1221no—
549C2×#121—612no—
550C2×#121—1221no—
551C2×C4×Q8—1221no—
552C2×C4×Q8—1221no—
553C2×C4×D4—612no—
554C2×C4×D4—1221no—
555C2×#117—612no—
556C22×C42—611no—
557#501—612no—
558#501—612no—
559#501—614no—
560#501—614no—
561#501—612no—
562#501C2×D6112yescomplemented
563#490—612no—
564#490—612no—
565#490—614no—
566#490—614no—
567#490—612no—
568#490C2×D6112yescomplemented
569#482—614no—
570#482—614no—
571#482—614no—
572#482—614no—
573#482—614no—
574#482—614no—
575#482—614no—
576#482C2×D6114yescomplemented
577#476—612no—
578#476—612no—
579#476—614no—
580#476—612no—
581#476—614no—
582#476C2×D6112yescomplemented
583#474—612no—
584#474—612no—
585#474—614no—
586#474—612no—
587#474—614no—
588#474C2×D6112yescomplemented
589#432—611no—
590#432—612no—
591#432—612no—
592#432—612no—
593#432C2×D6111yescharacteristic, complemented
594C2×#107—614no—
595C2×#106—614no—
596C2×C4⋊C8—612no—
597C2×#102—614no—
598C2×#102—614no—
599C2×C22⋊C8—612no—
600C2×#97—612no—
601C61C2×#323511yescharacteristic, complemented, Sylow
602C2×#41—21no—
603C2×#41—1222no—
604C2×#41—1222no—
605C2×#41—1221no—
606C2×#41—1221no—
607C2×#41—1221no—
608C2×#41—2448no—
609C22×Q8—1221no—
610C22×Q8—1221no—
611C22×Q8—1221no—
612C22×D4—612no—
613C22×D4—1221no—
614C22×D4—1221no—
615C22×D4—1222no—
616C23×C4—611no—
617C23×C4—611no—
618C23×C4—611no—
619C23×C4—1222no—
620C22×C8—614no—
621C4⋊Q8—612no—
622C4⋊Q8—612no—
623C4⋊Q8—612no—
624C4⋊Q8—611no—
625C4⋊Q8—611no—
626C4⋊Q8—611no—
627C4⋊Q8—1221no—
628C4⋊Q8—1221no—
629C4⋊Q8—1221no—
630C4⋊Q8—1221no—
631C4⋊Q8—1221no—
632C4⋊Q8—1221no—
633C4⋊Q8C22×D6111yescharacteristic
634C4⋊Q8C22×D6111yescharacteristic
635C4⋊Q8C22×D6111yescharacteristic
636#127—612no—
637#127—611no—
638#127—1221no—
639#127—1221no—
640#127C22×D6111yescharacteristic
641#125—612no—
642#125—612no—
643#125—612no—
644#125—1222no—
645#125—1222no—
646#125C22×D6112yes—
647#124—21no—
648#124—1222no—
649#124—1222no—
650#124—1221no—
651#124—1221no—
652#124—1221no—
653C22⋊Q8—21no—
654C22⋊Q8—21no—
655C22⋊Q8—1222no—
656C22⋊Q8—1222no—
657C22⋊Q8—1222no—
658C22⋊Q8—1222no—
659C22⋊Q8—1221no—
660C22⋊Q8—1221no—
661C22⋊Q8—1221no—
662C22⋊Q8—1221no—
663C22⋊Q8—1221no—
664C22⋊Q8—1221no—
665#121—21no—
666#121—612no—
667#121—612no—
668#121—612no—
669#121—1222no—
670#121—1222no—
671#121—1221no—
672#121—1222no—
673#121—1221no—
674#121—1222no—
675#121—1221no—
676#121C22×D6112yes—
677C4×Q8—21no—
678C4×Q8—21no—
679C4×Q8—1222no—
680C4×Q8—1222no—
681C4×Q8—1222no—
682C4×Q8—1221no—
683C4×Q8—1222no—
684C4×Q8—1221no—
685C4×Q8—1221no—
686C4×Q8—1221no—
687C4×Q8—1221no—
688C4×Q8—1221no—
689C4×D4—21no—
690C4×D4—612no—
691C4×D4—612no—
692C4×D4—612no—
693C4×D4—1222no—
694C4×D4—1222no—
695C4×D4—1221no—
696C4×D4—1222no—
697C4×D4—1222no—
698C4×D4—1221no—
699C4×D4—1221no—
700C4×D4C22×D6112yes—
701#117—612no—
702#117—612no—
703#117—612no—
704#117—1222no—
705#117—1222no—
706#117C22×D6112yes—
707C2×C4⋊C4—612no—
708C2×C4⋊C4—612no—
709C2×C4⋊C4—612no—
710C2×C4⋊C4—1221no—
711C2×C4⋊C4—1222no—
712C2×C4⋊C4—1222no—
713C2×C4⋊C4—1221no—
714C2×C4⋊C4—1221no—
715C2×C22⋊C4—1222no—
716C2×C22⋊C4—1222no—
717C2×C22⋊C4—1222no—
718C2×C42—611no—
719C2×C42—611no—
720C2×C42—611no—
721C2×C42—611no—
722C2×C42—611no—
723C2×C42—611no—
724C2×C42—611no—
725C2×C42—611no—
726C2×C42—611no—
727C2×C42—611no—
728C2×C42—611no—
729C2×C42—1222no—
730C2×C42C22×D6111yescharacteristic
731#107—614no—
732#107—614no—
733#107—614no—
734#107C22×D6114yes—
735#106—614no—
736#106—614no—
737#106—614no—
738#106C22×D6114yes—
739C4⋊C8—614no—
740C4⋊C8—612no—
741C4⋊C8C22×D6112yes—
742#102—614no—
743#102—614no—
744#102—614no—
745#102—614no—
746#102—614no—
747#102—614no—
748#102C22×D6114yes—
749#102C22×D6114yes—
750C22⋊C8—612no—
751C22⋊C8—614no—
752C22⋊C8C22×D6112yes—
753#97—614no—
754#97—612no—
755#97C22×D6112yes—
756C24—611no—
757C24—1222no—
758#41—44no—
759#41—2444no—
760#41—2448no—
761#41—2444no—
762#41—2448no—
763#41—2444no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—1222no—
768C2×Q8—1222no—
769C2×Q8—1222no—
770C2×Q8—1221no—
771C2×Q8—1221no—
772C2×Q8—1221no—
773C2×Q8—2444no—
774C2×Q8—2444no—
775C2×Q8—2444no—
776C2×D4—22no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—612no—
780C2×D4—1222no—
781C2×D4—1228no—
782C2×D4—1222no—
783C2×D4—1222no—
784C2×D4—1222no—
785C2×D4—1222no—
786C2×D4—1222no—
787C2×D4—1221no—
788C2×D4—1221no—
789C2×D4—2444no—
790C2×D4—2444no—
791C2×D4—2448no—
792C2×D4C23×D6112yes—
793C22×C4—22no—
794C22×C4—611no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—611no—
798C22×C4—611no—
799C22×C4—611no—
800C22×C4—611no—
801C22×C4—611no—
802C22×C4—611no—
803C22×C4—611no—
804C22×C4—611no—
805C22×C4—611no—
806C22×C4—611no—
807C22×C4—611no—
808C22×C4—611no—
809C22×C4—1224no—
810C22×C4—1224no—
811C22×C4—1222no—
812C22×C4—1222no—
813C22×C4—1222no—
814C22×C4—1222no—
815C22×C4—1222no—
816C22×C4—1222no—
817C22×C4—2448no—
818C22×C4—2442no—
819C22×C4D4×D6111yescharacteristic
820C22×C4D4×D6111yescharacteristic
821C22×C4C23×D6111yescharacteristic
822C2×C8—614no—
823C2×C8—1228no—
824C2×C8C23×D6114yes—
825C4⋊C4—21no—
826C4⋊C4—22no—
827C4⋊C4—22no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—612no—
831C4⋊C4—612no—
832C4⋊C4—612no—
833C4⋊C4—1222no—
834C4⋊C4—1222no—
835C4⋊C4—1222no—
836C4⋊C4—1222no—
837C4⋊C4—1222no—
838C4⋊C4—1222no—
839C4⋊C4—1222no—
840C4⋊C4—1222no—
841C4⋊C4—1222no—
842C4⋊C4—1222no—
843C4⋊C4—1222no—
844C4⋊C4—1222no—
845C4⋊C4—1221no—
846C4⋊C4—1221no—
847C4⋊C4—1221no—
848C4⋊C4C23×D6112yes—
849C4⋊C4C23×D6112yes—
850C4⋊C4C23×D6112yes—
851C22⋊C4—22no—
852C22⋊C4—22no—
853C22⋊C4—22no—
854C22⋊C4—1222no—
855C22⋊C4—1222no—
856C22⋊C4—1222no—
857C22⋊C4—1222no—
858C22⋊C4—1222no—
859C22⋊C4—1222no—
860C22⋊C4—1222no—
861C22⋊C4—1222no—
862C22⋊C4—1222no—
863C42—22no—
864C42—611no—
865C42—611no—
866C42—611no—
867C42—611no—
868C42—611no—
869C42—611no—
870C42—611no—
871C42—611no—
872C42—611no—
873C42—611no—
874C42—611no—
875C42—611no—
876C42—1222no—
877C42—1222no—
878C42—1222no—
879C42D4×D6111yescharacteristic
880C42D4×D6111yescharacteristic
881C42C23×D6111yescharacteristic
882C42C23×D6111yescharacteristic
883C23—22no—
884C23—611no—
885C23—611no—
886C23—1222no—
887C23—1222no—
888C23—1222no—
889C23—1222no—
890C23—2444no—
891C23—2444no—
892C23—2444no—
893C23C2×D4×D6111yescharacteristic
894Q8—42no—
895Q8—42no—
896Q8—42no—
897Q8—2442no—
898Q8—2442no—
899Q8—2444no—
900Q8—2444no—
901Q8—2444no—
902Q8—2442no—
903D4—24no—
904D4—42no—
905D4—42no—
906D4—44no—
907D4—1224no—
908D4—2442no—
909D4—2442no—
910D4—2444no—
911D4—2444no—
912D4—2444no—
913D4—2444no—
914D4—2444no—
915D4—2444no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—41no—
922C2×C4—44no—
923C2×C4—611no—
924C2×C4—611no—
925C2×C4—614no—
926C2×C4—614no—
927C2×C4—611no—
928C2×C4—611no—
929C2×C4—611no—
930C2×C4—611no—
931C2×C4—1222no—
932C2×C4—1222no—
933C2×C4—1222no—
934C2×C4—1222no—
935C2×C4—1222no—
936C2×C4—1222no—
937C2×C4—1222no—
938C2×C4—1222no—
939C2×C4—1222no—
940C2×C4—1222no—
941C2×C4—1222no—
942C2×C4—1222no—
943C2×C4—1222no—
944C2×C4—2441no—
945C2×C4—2441no—
946C2×C4—2444no—
947C2×C4—2444no—
948C2×C4—2444no—
949C2×C4—2444no—
950C2×C4—2444no—
951C2×C4—2441no—
952C2×C4—2444no—
953C2×C4C2×D4×D6111yescharacteristic
954C2×C4C2×D4×D6111yescharacteristic
955C2×C4C2×D4×D6111yescharacteristic
956C2×C4C2×D4×D6111yescharacteristic
957C2×C4C2×D4×D6111yescharacteristic
958C2×C4C24×D6111yescharacteristic
959C8—24no—
960C8—1224no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—612no—
968C22—612no—
969C22—612no—
970C22—1221no—
971C22—1221no—
972C22—1221no—
973C22—4888no—
974C22—2444no—
975C22—2442no—
976C22—2442no—
977C22—2442no—
978C22C22×D4×D6111yescharacteristic
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—612no—
987C4—612no—
988C4—1221no—
989C4—1221no—
990C4—1221no—
991C4—1221no—
992C4—2442no—
993C4—2442no—
994C4—2442no—
995C4AGL(1,ℤ/8)×D6112yes—
996C42−1+4×D6112yes—
997C2—41no—
998C2—82no—
999C2—614no—
1000C2—4882no—
1001C2—2441no—
1002C2#536×D6111yescharacteristic
1003C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
1004C2#575×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3235C2
socleC22×C61C23×D4
prime radical#532×D61C2
hypercenter#3235D61
hypocenterC61C2×#3235
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3235

Complements

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

NH ≅ G/Ntype
1. #533×D61C2semidirect
3. #21457019C2semidirect
4. #21457018C2semidirect
5. #21457017C2semidirect
6. #21457016C2semidirect
7. #21457015C2semidirect
8. #21457014C2semidirect
9. #21457013C2semidirect
10. #21457012C2semidirect
11. #501×D61C2semidirect
12. #490×D61C2semidirect
13. #482×D61C2semidirect
14. #476×D61C2semidirect
15. #474×D61C2semidirect
16. #432×D61C2semidirect
17. C61×#3235C2semidirect
19. #16840319C22semidirect
20. #16840318C22semidirect
21. #16840317C22semidirect
22. #16840317C22semidirect
25. #16840315C22semidirect
53. #16840172C22semidirect
54. #16840171C22semidirect
55. #16840170C22semidirect
56. #16840169C22semidirect
57. #16840168C22semidirect
58. #16840128C22semidirect
59. #16840127C22semidirect
60. #16840126C22semidirect
61. #16840125C22semidirect
62. #16840125C22semidirect
63. #16840089C22semidirect
64. #16840088C22semidirect
65. #16840087C22semidirect
66. #16840086C22semidirect
67. #16840085C22semidirect
68. #16840084C22semidirect
69. #16840083C22semidirect
70. #16840053C22semidirect
71. #16840052C22semidirect
72. #16840051C22semidirect
73. #16840050C22semidirect
74. #16840049C22semidirect
75. #16840043C22semidirect
76. #16840042C22semidirect
77. #16840041C22semidirect
78. #16840040C22semidirect
79. #16840039C22semidirect
80. #16839819C22semidirect
81. #16839818C22semidirect
82. #16839817C22semidirect
83. #16839816C22semidirect
91. C61×#533C22semidirect
93. C61×#501C22semidirect
94. C61×#490C22semidirect
95. C61×#482C22semidirect
96. C61×#476C22semidirect
97. C61×#474C22semidirect
98. C61×#432C22semidirect
505. #3235D61direct (N × H)
519. D61#3235direct (N × H)
530. #533C2×D61semidirect
562. #501C2×D61semidirect
568. #490C2×D61semidirect
576. #482C2×D61semidirect
582. #476C2×D61semidirect
588. #474C2×D61semidirect
593. #432C2×D61semidirect
601. C61C2×#3235semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#532×D612
#214570192
#214570182
#214570172
#214570162
#214570152
#214570142
#214570132
#214570122
#501×D612
#490×D612
#482×D612
#476×D612
#474×D612
#432×D612
C61×#32352
C2×#323561