Finite Group Databasebeta

← D61×#3234 #30552112

Subgroups — D61×#3234 #30552112

Order 15616.

2050 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#532×D61C211yesmaximal, characteristic
2C2×#125×D61C211yesmaximal, characteristic, complemented
3#21457011C211yesmaximal, characteristic, complemented
4#21457010C212yesmaximal, complemented
5#21457009C211yesmaximal, characteristic, complemented
6#21457008C212yesmaximal, complemented
7#21457007C214yesmaximal, complemented
8#21457006C212yesmaximal, complemented
9#21457005C211yesmaximal, characteristic, complemented
10#21457004C212yesmaximal, complemented
11#501×D61C212yesmaximal, complemented
12#490×D61C212yesmaximal, complemented
13#481×D61C212yesmaximal, complemented
14#480×D61C212yesmaximal, complemented
15#478×D61C214yesmaximal, complemented
16#432×D61C211yesmaximal, characteristic, complemented
17C61×#3234C211yesmaximal, characteristic, complemented
18C2×#41×D61—21no—
19#16840313C2211yescharacteristic
20#16840312C2211yescharacteristic
21#16840311—21no—
22#16840310C2211yescharacteristic
23#16840309—21no—
24#16840309C2212yes—
25#16840308—21no—
26#16840307—21no—
27#16840307C2212yes—
28C4⋊Q8×D61C2211yescharacteristic
29#127×D61C2211yescharacteristic
30C2×#14519769C2211yescharacteristic, complemented
31C2×#14519768C2211yescharacteristic, complemented
32C2×#14519768C2211yescharacteristic, complemented
33C2×#14519767—21no—
34C2×#14519767—21no—
35#125×D61—21no—
36#125×D61—21no—
37#125×D61—21no—
38#125×D61—21no—
39#125×D61C2212yes—
40#125×D61C2212yes—
41#125×D61C2212yescomplemented
42#125×D61C2212yescomplemented
43#124×D61—21no—
44#121×D61—21no—
45#121×D61C2212yes—
46C4×D4×D61—21no—
47C4×D4×D61C2212yes—
48C2×C4⋊C4×D61—21no—
49C2×C4⋊C4×D61—21no—
50C2×C4⋊C4×D61C2211yescharacteristic
51C2×C4⋊C4×D61C2211yescharacteristic
52C2×C42×D61C2211yescharacteristic
53#16840172C2212yescomplemented
54#16840171C2212yescomplemented
55#16840170C2214yescomplemented
56#16840169C2214yescomplemented
57#16840168C2212yescomplemented
58#16840128C2212yescomplemented
59#16840127C2212yescomplemented
60#16840126C2212yescomplemented
61#16840125C2214yescomplemented
62#16840125C2214yescomplemented
63#16840082C2214yescomplemented
64#16840081C2212yescomplemented
65#16840080C2212yescomplemented
66#16840079C2214yescomplemented
67#16840078C2212yescomplemented
68#16840077C2214yescomplemented
69#16840076C2212yescomplemented
70#16840075C2212yescomplemented
71#16840074C2214yescomplemented
72#16840073C2212yescomplemented
73#16840065C2214yescomplemented
74#16840064C2214yescomplemented
75#16840063C2214yescomplemented
76#16840062C2214yescomplemented
77#16840061C2214yescomplemented
78#16840060C2214yescomplemented
79#16840059C2214yescomplemented
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×#532C2211yescharacteristic
92C2×#125×C61C2211yescharacteristic, complemented
93C61×#501C2212yescomplemented
94C61×#490C2212yescomplemented
95C61×#481C2212yescomplemented
96C61×#480C2212yescomplemented
97C61×#478C2214yescomplemented
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×D4×D61—22no—
107C2×D4×D61—21no—
108C2×D4×D61—21no—
109C2×D4×D61C2312yes—
110C22×C4×D61—21no—
111C22×C4×D61—21no—
112C22×C4×D61—22no—
113C22×C4×D61D411yescharacteristic
114C22×C4×D61D411yescharacteristic
115C22×C4×D61C2311yescharacteristic
116C2×C8×D61C2314yes—
117#14519777C2311yescharacteristic
118#14519776—21no—
119#14519776C2312yes—
120#14519775—21no—
121#14519774C2311yescharacteristic
122#14519773—21no—
123#14519773—21no—
124#14519773C2312yes—
125#14519769—21no—
126#14519769—21no—
127#14519769C2312yes—
128#14519769C2312yes—
129#14519768—21no—
130#14519768—21no—
131#14519768—21no—
132#14519768—21no—
133#14519768C2312yes—
134#14519768C2312yes—
135#14519768C2312yes—
136#14519768C2312yes—
137#14519767—22no—
138#14519767—22no—
139#14519767—22no—
140#14519767—22no—
141#14519767—22no—
142#14519767—22no—
143#14519767—22no—
144#14519767—22no—
145#14519766—21no—
146#14519765—21no—
147#14519764—21no—
148#14519763—22no—
149#14519763—22no—
150#14519752—21no—
151#14519752C2312yes—
152#14519751—21no—
153#14519751C2312yes—
154#14519750—22no—
155#14519750—22no—
156#14519749—22no—
157#14519749—22no—
158#14519748—21no—
159#14519748C2312yes—
160C4×D244—21no—
161C4×D244C2312yes—
162D4×Dic61—21no—
163D4×Dic61C2312yes—
164#14519739—21no—
165#14519739C2312yes—
166C4×C22⋊D61—22no—
167C4×C22⋊D61—22no—
168#14519737—22no—
169#14519737—22no—
170C2×C4⋊Dic61—21no—
171C2×C4⋊Dic61—21no—
172C2×C4⋊Dic61C2311yescharacteristic
173C2×C4⋊Dic61C2311yescharacteristic
174C2×#11758196—21no—
175C2×#11758196—21no—
176C2×#11758196—21no—
177C2×#11758196—21no—
178C2×#11758196—21no—
179C2×#11758196—21no—
180C4⋊C4×D61—22no—
181C4⋊C4×D61—22no—
182C4⋊C4×D61—22no—
183C4⋊C4×D61—22no—
184C4⋊C4×D61—22no—
185C4⋊C4×D61—22no—
186C4⋊C4×D61—22no—
187C4⋊C4×D61—22no—
188C4⋊C4×D61—21no—
189C4⋊C4×D61—21no—
190C4⋊C4×D61—21no—
191C4⋊C4×D61—21no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61C2312yes—
194C4⋊C4×D61C2312yes—
195C4⋊C4×D61C2312yes—
196C4⋊C4×D61C2312yes—
197C4⋊C4×D61C2312yes—
198C22⋊C4×D61—22no—
199C22⋊C4×D61—22no—
200C2×C4×Dic61D411yescharacteristic
201C2×C4×Dic61D411yescharacteristic
202C2×C4×Dic61C2311yescharacteristic
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
231#127×C61C2311yescharacteristic
232#125×C61—21no—
233#125×C61—21no—
234#125×C61C2312yes—
235#125×C61C2312yes—
236#124×C61—21no—
237#121×C61—21no—
238#121×C61C2312yes—
239C4×D4×C61—21no—
240C4×D4×C61C2312yes—
241C2×C4⋊C4×C61—21no—
242C2×C4⋊C4×C61—21no—
243C2×C4⋊C4×C61C2311yescharacteristic
244C2×C4⋊C4×C61C2311yescharacteristic
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×D4×C61—22no—
258C2×D4×C61—21no—
259C2×D4×C61—21no—
260C2×D4×C61C2412yes—
261C22×C4×C61—21no—
262C22×C4×C61—21no—
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—21no—
273C22×Dic61—21no—
274C22×Dic61—22no—
275C22×Dic61C2×D411yescharacteristic
276C22×Dic61C2×D411yescharacteristic
277C22×Dic61C2×D411yescharacteristic
278#11758226—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—22no—
300C2×C4×D61—22no—
301C2×C4×D61—42no—
302C2×C4×D61—48no—
303C2×C4×D61—44no—
304C2×C4×D61—44no—
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×D61C2×D411yescharacteristic
315C2×C4×D61C2411yescharacteristic
316C2×C4×D61C2411yescharacteristic
317C2×Dic122—21no—
318C2×Dic122—22no—
319C2×C8×C61C2414yes—
320C4⋊C4×C61—22no—
321C4⋊C4×C61—22no—
322C4⋊C4×C61—22no—
323C4⋊C4×C61—22no—
324C4⋊C4×C61—21no—
325C4⋊C4×C61—21no—
326C4⋊C4×C61—21no—
327C4⋊C4×C61C2412yes—
328C4⋊C4×C61C2412yes—
329C4⋊C4×C61C2412yes—
330C22⋊C4×C61—22no—
331C22⋊C4×C61—22no—
332C42×C61C2×D411yescharacteristic
333C42×C61C2×D411yescharacteristic
334C42×C61C2411yescharacteristic
335C42×C61C2411yescharacteristic
336C22⋊Dic61—22no—
337C22⋊Dic61—22no—
338#11758198—22no—
339#11758198—22no—
340#11758198—22no—
341#11758198—22no—
342C4⋊Dic61—21no—
343C4⋊Dic61—21no—
344C4⋊Dic61—21no—
345C4⋊Dic61—22no—
346C4⋊Dic61—22no—
347C4⋊Dic61—22no—
348C4⋊Dic61—22no—
349C4⋊Dic61C2412yes—
350C4⋊Dic61C2412yes—
351C4⋊Dic61C2412yes—
352#11758196—22no—
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—
363#11758196—22no—
364#11758196—22no—
365#11758196—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—44no—
386C22×D61—44no—
387C22×D61—44no—
388C22×D61AGL(1,ℤ/8)14yes—
389C22×D61C22×D411yescharacteristic
390C22×D61C22×D411yescharacteristic
391Q8×C61—42no—
392D4×C61—24no—
393D4×C61—42no—
394D4×C61—42no—
395D4×C61—44no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—41no—
402C2×C4×C61—44no—
403C2×C4×C61—42no—
404C2×C4×C61—42no—
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×Dic61—42no—
424C2×Dic61—42no—
425C2×Dic61C22×D411yescharacteristic
426C2×Dic61C22×D411yescharacteristic
427C2×Dic61C22×D411yescharacteristic
428C2×Dic61C22×D411yescharacteristic
429C2×Dic61C22×D411yescharacteristic
430C2×Dic61C22×D411yescharacteristic
431D244—24no—
432D244—42no—
433D244—42no—
434D244—44no—
435C4×D61—22no—
436C4×D61—22no—
437C4×D61—22no—
438C4×D61—22no—
439C4×D61—22no—
440C4×D61—22no—
441C4×D61—22no—
442C4×D61—22no—
443C4×D61—22no—
444C4×D61—41no—
445C4×D61—41no—
446C4×D61—44no—
447C4×D61—44no—
448C4×D61—44no—
449C4×D61—44no—
450C4×D61—44no—
451C4×D61—44no—
452C4×D61—44no—
453C4×D612−1+414yes—
454Dic122—44no—
455Dic122—42no—
456C8×C61—24no—
457#92418—24no—
458C2×#3234—611nomaximal, Sylow
459C22×C61—21no—
460C22×C61—21no—
461C22×C61—42no—
462C22×C61—42no—
463C22×C61—42no—
464C22×C61C2×AGL(1,ℤ/8)12yes—
465C22×C61C23×D411yescharacteristic
466C2×D61—21no—
467C2×D61—21no—
468C2×D61—28no—
469C2×D61—42no—
470C2×D61—42no—
471C2×D61—42no—
472C2×D61—88no—
473C2×D61#53612yes—
474C2×D61C2×AGL(1,ℤ/8)12yes—
475C2×D61C2×AGL(1,ℤ/8)12yes—
476C2×D61#57512yes—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—42no—
483C4×C61—42no—
484C4×C61—42no—
485C4×C61C2×2−1+412yes—
486Dic61—21no—
487Dic61—21no—
488Dic61—21no—
489Dic61—21no—
490Dic61—21no—
491Dic61—42no—
492Dic61—42no—
493Dic61—42no—
494Dic61#53612yes—
495C2×#532—611no—
496C22×#125—611no—
497#3234—612no—
498#3234—612no—
499#3234—612no—
500#3234—612no—
501#3234—614no—
502#3234—611no—
503#3234—611no—
504#3234—611no—
505#3234D6111yescharacteristic, direct product factor
506C2×#501—612no—
507C2×#490—612no—
508C2×#481—612no—
509C2×#480—612no—
510C2×#478—614no—
511C2×#432—611no—
512C2×C61—22no—
513C2×C61—82no—
514C2×C61C2×#53611yescharacteristic
515C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
516C2×C61C2×#57511yescharacteristic
517D61—22no—
518D61—82no—
519D61#323414yesdirect product factor
520C22×#41—1221no—
521#532—611no—
522#532—611no—
523#532—612no—
524#532—612no—
525#532—611no—
526#532—1221no—
527#532—1221no—
528#532—1221no—
529#532—1221no—
530#532C2×D6111yescharacteristic
531C2×C4⋊Q8—611no—
532C2×#127—611no—
533C2×#125—612no—
534C2×#125—612no—
535C2×#125—612no—
536C2×#125—612no—
537C2×#125—611no—
538C2×#125—611no—
539C2×#125—611no—
540C2×#125—1221no—
541C2×#125—1221no—
542C2×#125—1221no—
543C2×#125—1221no—
544C2×#125—1221no—
545C2×#125—1221no—
546C2×#125C2×D6111yescharacteristic, complemented
547C2×#124—1221no—
548C2×#121—612no—
549C2×#121—1221no—
550C2×C4×D4—612no—
551C2×C4×D4—1221no—
552C22×C4⋊C4—611no—
553C22×C4⋊C4—611no—
554C22×C4⋊C4—1221no—
555C22×C4⋊C4—1221no—
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#481—612no—
570#481—612no—
571#481—614no—
572#481—614no—
573#481—612no—
574#481C2×D6112yescomplemented
575#480—612no—
576#480—612no—
577#480—614no—
578#480—614no—
579#480—612no—
580#480C2×D6112yescomplemented
581#478—614no—
582#478—614no—
583#478—614no—
584#478—614no—
585#478—614no—
586#478—614no—
587#478—614no—
588#478C2×D6114yescomplemented
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×#323411yescharacteristic, 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×D4—612no—
611C22×D4—1221no—
612C22×D4—1221no—
613C22×D4—1222no—
614C23×C4—611no—
615C23×C4—611no—
616C23×C4—611no—
617C23×C4—1222no—
618C23×C4—1221no—
619C23×C4—1221no—
620C22×C8—614no—
621C4⋊Q8—612no—
622C4⋊Q8—611no—
623C4⋊Q8—1221no—
624C4⋊Q8—1221no—
625C4⋊Q8C22×D6111yescharacteristic
626#127—612no—
627#127—611no—
628#127—1221no—
629#127—1221no—
630#127C22×D6111yescharacteristic
631#125—21no—
632#125—21no—
633#125—612no—
634#125—612no—
635#125—612no—
636#125—612no—
637#125—612no—
638#125—612no—
639#125—1222no—
640#125—1222no—
641#125—1222no—
642#125—1222no—
643#125—1222no—
644#125—1222no—
645#125—1222no—
646#125—1222no—
647#125—1221no—
648#125—1221no—
649#125—1221no—
650#125—1221no—
651#125—1221no—
652#125—1221no—
653#125C22×D6112yes—
654#125C22×D6112yes—
655#124—21no—
656#124—1222no—
657#124—1222no—
658#124—1221no—
659#124—1221no—
660#124—1221no—
661#121—21no—
662#121—612no—
663#121—612no—
664#121—612no—
665#121—1222no—
666#121—1222no—
667#121—1221no—
668#121—1222no—
669#121—1221no—
670#121—1222no—
671#121—1221no—
672#121C22×D6112yes—
673C4×D4—21no—
674C4×D4—612no—
675C4×D4—612no—
676C4×D4—612no—
677C4×D4—1222no—
678C4×D4—1222no—
679C4×D4—1221no—
680C4×D4—1222no—
681C4×D4—1222no—
682C4×D4—1221no—
683C4×D4—1221no—
684C4×D4C22×D6112yes—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—611no—
688C2×C4⋊C4—611no—
689C2×C4⋊C4—612no—
690C2×C4⋊C4—612no—
691C2×C4⋊C4—612no—
692C2×C4⋊C4—612no—
693C2×C4⋊C4—612no—
694C2×C4⋊C4—1221no—
695C2×C4⋊C4—1221no—
696C2×C4⋊C4—1221no—
697C2×C4⋊C4—1221no—
698C2×C4⋊C4—1222no—
699C2×C4⋊C4—1222no—
700C2×C4⋊C4—1222no—
701C2×C4⋊C4—1222no—
702C2×C4⋊C4—1222no—
703C2×C4⋊C4—1222no—
704C2×C4⋊C4—1222no—
705C2×C4⋊C4—1222no—
706C2×C4⋊C4—1221no—
707C2×C4⋊C4—1221no—
708C2×C4⋊C4—1221no—
709C2×C4⋊C4—1221no—
710C2×C4⋊C4—1221no—
711C2×C4⋊C4—1221no—
712C2×C4⋊C4—1221no—
713C2×C4⋊C4—1221no—
714C2×C4⋊C4—1221no—
715C2×C4⋊C4C22×D6111yescharacteristic
716C2×C4⋊C4C22×D6111yescharacteristic
717C2×C22⋊C4—1222no—
718C2×C22⋊C4—1222no—
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—611no—
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—1222no—
766C2×Q8—1221no—
767C2×Q8—2444no—
768C2×D4—22no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—612no—
772C2×D4—1222no—
773C2×D4—1228no—
774C2×D4—1222no—
775C2×D4—1222no—
776C2×D4—1222no—
777C2×D4—1222no—
778C2×D4—1222no—
779C2×D4—1221no—
780C2×D4—1221no—
781C2×D4—2444no—
782C2×D4—2444no—
783C2×D4—2448no—
784C2×D4C23×D6112yes—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—611no—
789C22×C4—611no—
790C22×C4—611no—
791C22×C4—611no—
792C22×C4—611no—
793C22×C4—611no—
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—1224no—
804C22×C4—1222no—
805C22×C4—1224no—
806C22×C4—1222no—
807C22×C4—1222no—
808C22×C4—1222no—
809C22×C4—1222no—
810C22×C4—1222no—
811C22×C4—1222no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1222no—
815C22×C4—2442no—
816C22×C4—2448no—
817C22×C4—2444no—
818C22×C4—2444no—
819C22×C4D4×D6111yescharacteristic
820C22×C4D4×D6111yescharacteristic
821C22×C4C23×D6111yescharacteristic
822C2×C8—614no—
823C2×C8—1228no—
824C2×C8C23×D6114yes—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—612no—
833C4⋊C4—612no—
834C4⋊C4—612no—
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—1222no—
846C4⋊C4—1222no—
847C4⋊C4—1222no—
848C4⋊C4—1222no—
849C4⋊C4—1221no—
850C4⋊C4—1221no—
851C4⋊C4—1222no—
852C4⋊C4—1222no—
853C4⋊C4—1222no—
854C4⋊C4—1222no—
855C4⋊C4—1221no—
856C4⋊C4C23×D6112yes—
857C4⋊C4C23×D6112yes—
858C4⋊C4C23×D6112yes—
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—1222no—
862C22⋊C4—1222no—
863C22⋊C4—1222no—
864C22⋊C4—1222no—
865C22⋊C4—1222no—
866C22⋊C4—1222no—
867C42—611no—
868C42—611no—
869C42—611no—
870C42—611no—
871C42—611no—
872C42—611no—
873C42—611no—
874C42—611no—
875C42—611no—
876C42—611no—
877C42—611no—
878C42—611no—
879C42D4×D6111yescharacteristic
880C42D4×D6111yescharacteristic
881C42C23×D6111yescharacteristic
882C42C23×D6111yescharacteristic
883C23—22no—
884C23—611no—
885C23—614no—
886C23—611no—
887C23—1222no—
888C23—1222no—
889C23—1222no—
890C23—2444no—
891C23—2444no—
892C23—2444no—
893C23C2×D4×D6111yescharacteristic
894Q8—42no—
895Q8—2442no—
896Q8—2444no—
897D4—24no—
898D4—42no—
899D4—42no—
900D4—44no—
901D4—1224no—
902D4—2442no—
903D4—2442no—
904D4—2444no—
905D4—2444no—
906D4—2444no—
907D4—2444no—
908D4—2444no—
909D4—2444no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—41no—
916C2×C4—44no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—611no—
920C2×C4—614no—
921C2×C4—611no—
922C2×C4—611no—
923C2×C4—611no—
924C2×C4—611no—
925C2×C4—611no—
926C2×C4—1222no—
927C2×C4—1222no—
928C2×C4—1222no—
929C2×C4—1222no—
930C2×C4—1222no—
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—2441no—
941C2×C4—2441no—
942C2×C4—2444no—
943C2×C4—2444no—
944C2×C4—2444no—
945C2×C4—2444no—
946C2×C4—2444no—
947C2×C4—2444no—
948C2×C4—2444no—
949C2×C4—2441no—
950C2×C4—2444no—
951C2×C4—2442no—
952C2×C4—2442no—
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—42no—
964C22—42no—
965C22—42no—
966C22—612no—
967C22—612no—
968C22—612no—
969C22—612no—
970C22—1228no—
971C22—1221no—
972C22—1221no—
973C22—4888no—
974C22—2442no—
975C22—2442no—
976C22—2442no—
977C22AGL(1,ℤ/8)×D6112yes—
978C22C22×D4×D6111yescharacteristic
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—612no—
988C4—1221no—
989C4—1221no—
990C4—1221no—
991C4—1221no—
992C4—1221no—
993C4—2442no—
994C4—2442no—
995C4—2442no—
996C42−1+4×D6112yes—
997C2—22no—
998C2—82no—
999C2—614no—
1000C2—1222no—
1001C2—4882no—
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×#3234C2
socleC22×C61C23×D4
prime radical#532×D61C2
hypercenter#3234D61
hypocenterC61C2×#3234
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3234

Complements

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

NH ≅ G/Ntype
2. C2×#125×D61C2semidirect
3. #21457011C2semidirect
4. #21457010C2semidirect
5. #21457009C2semidirect
6. #21457008C2semidirect
7. #21457007C2semidirect
8. #21457006C2semidirect
9. #21457005C2semidirect
10. #21457004C2semidirect
11. #501×D61C2semidirect
12. #490×D61C2semidirect
13. #481×D61C2semidirect
14. #480×D61C2semidirect
15. #478×D61C2semidirect
16. #432×D61C2semidirect
17. C61×#3234C2semidirect
30. C2×#14519769C22semidirect
31. C2×#14519768C22semidirect
32. C2×#14519768C22semidirect
41. #125×D61C22semidirect
42. #125×D61C22semidirect
53. #16840172C22semidirect
54. #16840171C22semidirect
55. #16840170C22semidirect
56. #16840169C22semidirect
57. #16840168C22semidirect
58. #16840128C22semidirect
59. #16840127C22semidirect
60. #16840126C22semidirect
61. #16840125C22semidirect
62. #16840125C22semidirect
63. #16840082C22semidirect
64. #16840081C22semidirect
65. #16840080C22semidirect
66. #16840079C22semidirect
67. #16840078C22semidirect
68. #16840077C22semidirect
69. #16840076C22semidirect
70. #16840075C22semidirect
71. #16840074C22semidirect
72. #16840073C22semidirect
73. #16840065C22semidirect
74. #16840064C22semidirect
75. #16840063C22semidirect
76. #16840062C22semidirect
77. #16840061C22semidirect
78. #16840060C22semidirect
79. #16840059C22semidirect
80. #16839819C22semidirect
81. #16839818C22semidirect
82. #16839817C22semidirect
83. #16839816C22semidirect
92. C2×#125×C61C22semidirect
93. C61×#501C22semidirect
94. C61×#490C22semidirect
95. C61×#481C22semidirect
96. C61×#480C22semidirect
97. C61×#478C22semidirect
98. C61×#432C22semidirect
505. #3234D61direct (N × H)
519. D61#3234direct (N × H)
546. C2×#125C2×D61semidirect
562. #501C2×D61semidirect
568. #490C2×D61semidirect
574. #481C2×D61semidirect
580. #480C2×D61semidirect
588. #478C2×D61semidirect
593. #432C2×D61semidirect
601. C61C2×#3234semidirect

Maximal subgroups

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

subgroupindex
#532×D612
C2×#125×D612
#214570112
#214570102
#214570092
#214570082
#214570072
#214570062
#214570052
#214570042
#501×D612
#490×D612
#481×D612
#480×D612
#478×D612
#432×D612
C61×#32342
C2×#323461