Finite Group Databasebeta

← D61×#1905 #29681899

Subgroups — D61×#1905 #29681899

Order 15616.

1678 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#137×D61C211yesmaximal, characteristic
2#519×D61C211yesmaximal, characteristic, complemented
3#421×D61C211yesmaximal, characteristic
4#419×D61C211yesmaximal, characteristic, complemented
5#410×D61C211yesmaximal, characteristic
6#21446316C211yesmaximal, characteristic, complemented
7#21446315C211yesmaximal, characteristic, complemented
8#21446314C211yesmaximal, characteristic, complemented
9#21446313C211yesmaximal, characteristic, complemented
10#21446312C211yesmaximal, characteristic, complemented
11#21446311C211yesmaximal, characteristic, complemented
12#21446310C211yesmaximal, characteristic, complemented
13#344×D61C211yesmaximal, characteristic, complemented
14H(3,ℤ/4)×D61C211yesmaximal, characteristic, complemented
15C61×#1905C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C2×#14519810C2211yescharacteristic
19C2×#14519809C412yescomplemented
20C2×#14519808C2211yescharacteristic
21C2×#14519807C2211yescharacteristic
22C2×#14519806C412yescomplemented
23#137×D61—22no—
24#137×D61—22no—
25#137×D61—22no—
26#137×D61—22no—
27C2×Q16×D61C412yescomplemented
28C2×SD16×D61C412yescomplemented
29C2×M16×D61C2211yescharacteristic
30C2×M16×D61C2211yescharacteristic
31#16840240C2211yescharacteristic, complemented
32#16840239—22no—
33#16840239C2211yescharacteristic, complemented
34#16840239C2211yescharacteristic, complemented
35#16840238—22no—
36#16840238—22no—
37C4×Q8×D61—22no—
38C4×Q8×D61—22no—
39#117×D61—22no—
40#117×D61C2211yescharacteristic
41#117×D61C2211yescharacteristic
42#117×D61C2211yescharacteristic
43#16839780C2211yescharacteristic
44#16839779C2211yescharacteristic
45#16839778C2211yescharacteristic
46#16839777—22no—
47#104×D61—22no—
48#16839772C2211yescharacteristic, complemented
49#16839771C2211yescharacteristic, complemented
50#16839770C2211yescharacteristic, complemented
51#16839769—22no—
52#103×D61—22no—
53#16839736C2211yescharacteristic
54#16839735C2211yescharacteristic
55#16839735C2211yescharacteristic
56#16839734—22no—
57#99×D61—22no—
58#16839534C2211yescharacteristic, complemented
59#16839533C2211yescharacteristic, complemented
60#16839532C2211yescharacteristic, complemented
61#16839519C2211yescharacteristic, complemented
62#16839518C2211yescharacteristic, complemented
63#16839518C2211yescharacteristic, complemented
64C2×#137×C61C2211yescharacteristic
65C61×#519C2211yescharacteristic, complemented
66C61×#421C2211yescharacteristic
67C61×#419C2211yescharacteristic, complemented
68C61×#410C2211yescharacteristic
69C61×#344C2211yescharacteristic, complemented
70C61×H(3,ℤ/4)C2211yescharacteristic, complemented
71C2×#11758226C2×C411yescharacteristic
72C2×#11758222—21no—
73C2×#11758222C2311yescharacteristic
74C2×#11758224—21no—
75C2×#11758224C2×C411yescharacteristic
76#41×D61—21no—
77#41×D61—21no—
78#41×D61—21no—
79#41×D61—21no—
80#41×D61—21no—
81#41×D61—21no—
82#41×D61—21no—
83#41×D61—21no—
84C22×Dic122—21no—
85C22×Dic122C2311yescharacteristic
86C2×Q8×D61—21no—
87C2×Q8×D61—21no—
88C2×Q8×D61—21no—
89C2×Q8×D61—21no—
90C2×Q8×D61—21no—
91C2×Q8×D61—21no—
92C2×Q8×D61C2×C411yescharacteristic
93C2×Q8×D61C2×C412yes—
94C2×Q8×D61C2×C412yes—
95C2×Q8×D61D412yes—
96C2×Q8×D61D412yes—
97C2×Q8×D61D412yes—
98C2×Q8×D61D412yes—
99C2×D4×D61—21no—
100C2×D4×D61C2×C411yescharacteristic
101C22×C4×D61—21no—
102C22×C4×D61—21no—
103C22×C4×D61C2311yescharacteristic
104#14519810—22no—
105#14519810—22no—
106#14519809—24no—
107#14519809—24no—
108#14519808—22no—
109#14519808—22no—
110#14519807—22no—
111#14519807—22no—
112#14519806—24no—
113#14519806—24no—
114C2×Dic244C2×C412yescomplemented
115C2×#11758202C2×C412yescomplemented
116C2×#11758202C2×C412yescomplemented
117Q16×D61—24no—
118Q16×D61—24no—
119C2×#11758190C2×C412yescomplemented
120C2×#11758200C2×C412yescomplemented
121C2×#11758201C2×C412yescomplemented
122SD16×D61—24no—
123SD16×D61—24no—
124C2×#11758194C2311yescharacteristic
125C2×#11758194C2311yescharacteristic
126C2×#11758189—21no—
127C2×#11758189C2×C412yes—
128M16×D61—21no—
129M16×D61—21no—
130M16×D61—21no—
131M16×D61—21no—
132M16×D61—21no—
133M16×D61—21no—
134M16×D61—21no—
135M16×D61—21no—
136C2×C8×D61—21no—
137C2×C8×D61C2×C412yes—
138Q8×Dic61—22no—
139Q8×Dic61—22no—
140C4×Dic122—24no—
141C4×Dic122—24no—
142C4×Dic122—22no—
143C4×Dic122—22no—
144#14519742—24no—
145#14519742—24no—
146#14519742—22no—
147#14519742—22no—
148#14519736—22no—
149#14519736C2311yescharacteristic
150#14519736C2311yescharacteristic
151#14519736C2311yescharacteristic
152#14519735—24no—
153#14519735—21no—
154#14519735—21no—
155#14519735—21no—
156#14519734—24no—
157#14519734—21no—
158#14519734—21no—
159#14519734D412yes—
160#14519733—21no—
161#14519733—22no—
162#14519733—22no—
163#14519733—21no—
164#14519733D412yes—
165C4⋊C4×D61—24no—
166C4⋊C4×D61—21no—
167C4⋊C4×D61—21no—
168C4⋊C4×D61—21no—
169C22⋊C4×D61—21no—
170C22⋊C4×D61—21no—
171C22⋊C4×D61D412yes—
172C42×D61—24no—
173C42×D61—21no—
174C42×D61—21no—
175C42×D61D412yes—
176#14519705—22no—
177#14519704—22no—
178#14519703—22no—
179#14519702—22no—
180#14519701—22no—
181#14519700—22no—
182#14519692—22no—
183#14519691—22no—
184#14519691—22no—
185C2×#41×C61C2311yescharacteristic
186C22×Q8×C61C2311yescharacteristic
187#137×C61—22no—
188#137×C61—22no—
189C2×Q16×C61C2×C412yescomplemented
190C2×SD16×C61C2×C412yescomplemented
191C2×M16×C61C2311yescharacteristic
192C2×M16×C61C2311yescharacteristic
193C4×Q8×C61—22no—
194C4×Q8×C61—22no—
195#117×C61—22no—
196#117×C61C2311yescharacteristic
197#117×C61C2311yescharacteristic
198#117×C61C2311yescharacteristic
199#104×C61—22no—
200#103×C61—22no—
201#99×C61—22no—
202C23×D61—21no—
203C23×D61C2×D411yescharacteristic
204#41×C61—21no—
205#41×C61—21no—
206#41×C61—21no—
207#41×C61—21no—
208C2×Q8×C61—21no—
209C2×Q8×C61—21no—
210C2×Q8×C61—21no—
211C2×Q8×C61C22×C411yescharacteristic
212C2×Q8×C61C22×C412yes—
213C2×Q8×C61C2×D412yes—
214C2×Q8×C61C2×D412yes—
215C2×D4×C61—21no—
216C2×D4×C61C22×C411yescharacteristic
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61C2411yescharacteristic
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61C2×D411yescharacteristic
226#11758226—21no—
227#11758226—21no—
228#11758226—21no—
229#11758226—21no—
230Q8×D61—22no—
231Q8×D61—22no—
232Q8×D61—22no—
233Q8×D61—22no—
234Q8×D61—22no—
235Q8×D61—22no—
236Q8×D61—22no—
237Q8×D61—22no—
238Q8×D61—22no—
239Q8×D61—22no—
240Q8×D61—22no—
241Q8×D61—22no—
242Q8×D61—21no—
243Q8×D61—21no—
244Q8×D61—21no—
245Q8×D61—21no—
246Q8×D61C22⋊C414yes—
247Q8×D61C22⋊C414yes—
248Q8×D61C22⋊C414yes—
249Q8×D61C22⋊C414yes—
250#11758224—21no—
251#11758224—21no—
252#11758224—21no—
253#11758224—21no—
254#11758224—41no—
255#11758224—41no—
256#11758224—41no—
257#11758224—41no—
258D4×D61—21no—
259D4×D61—21no—
260D4×D61—21no—
261D4×D61—21no—
262D4×D61—41no—
263D4×D61—41no—
264D4×D61—41no—
265D4×D61—41no—
266#11758222—21no—
267#11758222—21no—
268#11758222—21no—
269#11758222—21no—
270#11758222—41no—
271#11758222—41no—
272#11758222—41no—
273#11758222—41no—
274C2×D244—21no—
275C2×D244C22×C411yescharacteristic
276C2×C4×D61—22no—
277C2×C4×D61—22no—
278C2×C4×D61—22no—
279C2×C4×D61—22no—
280C2×C4×D61—22no—
281C2×C4×D61—22no—
282C2×C4×D61—21no—
283C2×C4×D61—22no—
284C2×C4×D61—22no—
285C2×C4×D61—21no—
286C2×C4×D61—21no—
287C2×C4×D61—41no—
288C2×C4×D61—41no—
289C2×C4×D61—41no—
290C2×C4×D61—41no—
291C2×C4×D61—41no—
292C2×C4×D61C22×C411yescharacteristic
293C2×C4×D61C22×C411yescharacteristic
294C2×C4×D61C2×D411yescharacteristic
295C2×C4×D61C2×D411yescharacteristic
296C2×C4×D61C2×D411yescharacteristic
297C2×C4×D61C2×D411yescharacteristic
298C2×C4×D61C2×D411yescharacteristic
299C2×C4×D61C2×D411yescharacteristic
300C2×C4×D61#4111yescharacteristic
301C2×C4×D61#4111yescharacteristic
302C2×C4×D61#4111yescharacteristic
303C2×C4×D61#4111yescharacteristic
304C2×Dic122—21no—
305C2×Dic122—21no—
306C2×Dic122—21no—
307C2×Dic122—22no—
308C2×Dic122—22no—
309C2×Dic122—22no—
310C2×Dic122—22no—
311C2×Dic122—22no—
312C2×Dic122—22no—
313C2×Dic122—21no—
314C2×Dic122C22×C411yescharacteristic
315C2×Dic122C22×C412yes—
316C2×Dic122C2×D412yes—
317C2×Dic122C2×D412yes—
318Q16×C61—24no—
319SD16×C61—24no—
320M16×C61—21no—
321M16×C61—21no—
322M16×C61—21no—
323M16×C61—21no—
324C2×C8×C61—21no—
325C2×C8×C61C22×C412yes—
326C4⋊C4×C61—24no—
327C4⋊C4×C61—21no—
328C4⋊C4×C61—21no—
329C4⋊C4×C61—21no—
330C22⋊C4×C61—21no—
331C22⋊C4×C61—21no—
332C22⋊C4×C61C2×D412yes—
333C42×C61—24no—
334C42×C61—21no—
335C42×C61—21no—
336C42×C61C2×D412yes—
337C22⋊Dic61—21no—
338C22⋊Dic61—21no—
339C22⋊Dic61C2×D412yes—
340#11758202—24no—
341#11758202—24no—
342#11758201—24no—
343#11758200—24no—
344#11758198—22no—
345#11758198—22no—
346#11758198—41no—
347C4⋊Dic61—24no—
348C4⋊Dic61—21no—
349C4⋊Dic61—21no—
350C4⋊Dic61—21no—
351#11758196—24no—
352#11758196—24no—
353#11758196—22no—
354#11758196—22no—
355#11758196—41no—
356C4×Dic61—24no—
357C4×Dic61—24no—
358C4×Dic61—24no—
359C4×Dic61—21no—
360C4×Dic61—22no—
361C4×Dic61—22no—
362C4×Dic61—21no—
363C4×Dic61—41no—
364C4×Dic61C2×D412yes—
365#11758194—21no—
366#11758194—21no—
367#11758194—21no—
368#11758194—21no—
369C2×#92418—21no—
370C2×#92418C22×C412yes—
371Dic244—24no—
372#11758190—24no—
373#11758189—22no—
374#11758189—22no—
375#11758189—41no—
376#11758189—41no—
377C8×D61—22no—
378C8×D61—22no—
379C8×D61—41no—
380C8×D61—41no—
381C23×C61—21no—
382C23×C61C22×D411yescharacteristic
383C22×D61—21no—
384C22×D61—42no—
385C22×D61—41no—
386C22×D61—41no—
387C22×D61—82no—
388C22×D61C4×D411yescharacteristic
389C22×D61C4×D411yescharacteristic
390C22×D61#12011yescharacteristic
391C22×D61#12011yescharacteristic
392C22×D61#12111yescharacteristic
393C22×D61#12111yescharacteristic
394Q8×C61—22no—
395Q8×C61—22no—
396Q8×C61—22no—
397Q8×C61—21no—
398Q8×C61—21no—
399Q8×C61C2×C22⋊C414yes—
400D4×C61—21no—
401D4×C61—21no—
402D4×C61—41no—
403D4×C61—41no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—21no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61C23×C411yescharacteristic
414C2×C4×C61C22×D411yescharacteristic
415C2×C4×C61C22×D411yescharacteristic
416C2×C4×C61C22×D411yescharacteristic
417C2×C4×C61C2×#4111yescharacteristic
418C2×C4×C61C2×#4111yescharacteristic
419C22⋊D61—41no—
420C22⋊D61—41no—
421C22⋊D61—41no—
422C22⋊D61—41no—
423C22⋊D61—41no—
424C22⋊D61—41no—
425C2×Dic61—22no—
426C2×Dic61—22no—
427C2×Dic61—22no—
428C2×Dic61—21no—
429C2×Dic61—22no—
430C2×Dic61—22no—
431C2×Dic61—41no—
432C2×Dic61—41no—
433C2×Dic61—41no—
434C2×Dic61C4×D411yescharacteristic
435C2×Dic61C4×D411yescharacteristic
436C2×Dic61#12011yescharacteristic
437C2×Dic61#12011yescharacteristic
438C2×Dic61#12111yescharacteristic
439C2×Dic61#12111yescharacteristic
440D244—21no—
441D244—21no—
442D244—41no—
443D244—41no—
444C4×D61—24no—
445C4×D61—24no—
446C4×D61—24no—
447C4×D61—24no—
448C4×D61—44no—
449C4×D61—44no—
450C4×D61—41no—
451C4×D61—41no—
452C4×D61—41no—
453C4×D61—41no—
454C4×D61—41no—
455C4×D61—41no—
456C4×D61—82no—
457C4×D61C2×C22⋊C411yescharacteristic
458C4×D61C2×C22⋊C411yescharacteristic
459C4×D61C2×C22⋊C411yescharacteristic
460C4×D61C2×C22⋊C411yescharacteristic
461C4×D61C4×D411yescharacteristic
462C4×D61C4×D411yescharacteristic
463C4×D61C4×D411yescharacteristic
464C4×D61C4×D411yescharacteristic
465C4×D61#12111yescharacteristic
466C4×D61#12111yescharacteristic
467C4×D61#12111yescharacteristic
468C4×D61#12111yescharacteristic
469C4×D61#12311yescharacteristic
470C4×D61#12311yescharacteristic
471C4×D61#12311yescharacteristic
472C4×D61#12311yescharacteristic
473Dic122—22no—
474Dic122—22no—
475Dic122—22no—
476Dic122—24no—
477Dic122—24no—
478Dic122—24no—
479Dic122—24no—
480Dic122—21no—
481Dic122—21no—
482Dic122—41no—
483Dic122—41no—
484Dic122C2×C22⋊C414yes—
485C8×C61—22no—
486C8×C61—41no—
487#92418—22no—
488#92418—41no—
489C2×#1905—611nomaximal, Sylow
490C22×C61—41no—
491C22×C61—41no—
492C22×C61—81no—
493C22×C61C2×C4×D411yescharacteristic
494C22×C61C2×#12011yescharacteristic
495C22×C61C2×#12111yescharacteristic
496C2×D61—22no—
497C2×D61—22no—
498C2×D61—22no—
499C2×D61—41no—
500C2×D61—41no—
501C2×D61—41no—
502C2×D61—41no—
503C2×D61—82no—
504C2×D61—82no—
505C2×D61—81no—
506C2×D61#38611yescharacteristic
507C2×D61#38611yescharacteristic
508C2×D61#38611yescharacteristic
509C2×D61#38611yescharacteristic
510C4×C61—24no—
511C4×C61—42no—
512C4×C61—42no—
513C4×C61—41no—
514C4×C61—81no—
515C4×C61C22×C22⋊C411yescharacteristic
516C4×C61C2×C4×D411yescharacteristic
517C4×C61C2×#12111yescharacteristic
518C4×C61C2×#12311yescharacteristic
519Dic61—24no—
520Dic61—42no—
521Dic61—42no—
522Dic61—41no—
523Dic61—81no—
524Dic61#38611yescharacteristic
525Dic61#38611yescharacteristic
526Dic61#38611yescharacteristic
527Dic61#38611yescharacteristic
528C22×#137—611no—
529C2×#519—611no—
530C2×#421—611no—
531C2×#419—611no—
532C2×#410—611no—
533#1905—611no—
534#1905—611no—
535#1905—611no—
536#1905—611no—
537#1905—611no—
538#1905—611no—
539#1905—611no—
540#1905D6111yescharacteristic, direct product factor
541C2×#344—611no—
542C2×H(3,ℤ/4)—611no—
543C2×C61—21no—
544C2×C61—21no—
545C2×C61—21no—
546C2×C61—81no—
547C2×C61C2×#38611yescharacteristic
548D61—21no—
549D61—21no—
550D61—21no—
551D61—81no—
552D61#190512yesdirect product factor
553C22×#41—611no—
554C23×Q8—611no—
555C2×#137—611no—
556C2×#137—611no—
557C2×#137—612no—
558C2×#137—612no—
559C2×#137—611no—
560C2×#137—1222no—
561C2×#137—1222no—
562C2×#137—1222no—
563C2×#137—1222no—
564C2×#137C2×D6111yescharacteristic
565C22×Q16—612no—
566C22×SD16—612no—
567C22×M16—611no—
568C22×M16—611no—
569#519—611no—
570#519—611no—
571#519—611no—
572#519—1222no—
573#519—1222no—
574#519—1222no—
575#519C2×D6111yescharacteristic, complemented
576C2×C4×Q8—1222no—
577C2×C4×Q8—1222no—
578C2×#117—611no—
579C2×#117—611no—
580C2×#117—611no—
581C2×#117—1222no—
582#421—611no—
583#421—611no—
584#421—611no—
585#421—1222no—
586#421C2×D6111yescharacteristic
587C2×#104—1222no—
588#419—611no—
589#419—611no—
590#419—611no—
591#419—1222no—
592#419C2×D6111yescharacteristic, complemented
593C2×#103—1222no—
594#410—611no—
595#410—611no—
596#410—611no—
597#410—1222no—
598#410C2×D6111yescharacteristic
599C2×#99—1222no—
600#344—611no—
601#344—611no—
602#344—611no—
603#344C2×D6111yescharacteristic, complemented
604H(3,ℤ/4)—611no—
605H(3,ℤ/4)—611no—
606H(3,ℤ/4)—611no—
607H(3,ℤ/4)C2×D6111yescharacteristic, complemented
608C61C2×#190511yescharacteristic, complemented, Sylow
609C2×#41—611no—
610C2×#41—611no—
611C2×#41—611no—
612C2×#41—1221no—
613C2×#41—1221no—
614C2×#41—1221no—
615C2×#41—1221no—
616C2×#41—1221no—
617C2×#41—1221no—
618C2×#41—1221no—
619C2×#41—1221no—
620C2×#41—1221no—
621C2×#41—1221no—
622C2×#41C22×D6111yescharacteristic
623C22×Q8—612no—
624C22×Q8—612no—
625C22×Q8—612no—
626C22×Q8—612no—
627C22×Q8—612no—
628C22×Q8—612no—
629C22×Q8—611no—
630C22×Q8—611no—
631C22×Q8—1221no—
632C22×Q8—1221no—
633C22×Q8—1221no—
634C22×Q8—1221no—
635C22×Q8—1221no—
636C22×Q8—1221no—
637C22×Q8—1221no—
638C22×Q8C22×D6111yescharacteristic
639C22×D4—611no—
640C22×D4—1221no—
641C23×C4—611no—
642C23×C4—1221no—
643C23×C4—1221no—
644#137—22no—
645#137—22no—
646#137—1222no—
647#137—1222no—
648#137—1224no—
649#137—1224no—
650#137—1224no—
651#137—1224no—
652#137—1222no—
653#137—1222no—
654#137—1222no—
655#137—1222no—
656C2×Q16—612no—
657C2×Q16—612no—
658C2×Q16—612no—
659C2×Q16—1224no—
660C2×Q16—1224no—
661C2×Q16C4×D6112yescomplemented
662C2×SD16—612no—
663C2×SD16—612no—
664C2×SD16—612no—
665C2×SD16—1224no—
666C2×SD16—1224no—
667C2×SD16C4×D6112yescomplemented
668C2×M16—611no—
669C2×M16—612no—
670C2×M16—611no—
671C2×M16—1221no—
672C2×M16—1221no—
673C2×M16—1221no—
674C2×M16—1221no—
675C2×M16—1221no—
676C2×M16—1221no—
677C2×M16—1221no—
678C2×M16—1221no—
679C2×M16—1221no—
680C2×M16C22×D6111yescharacteristic
681C2×M16C22×D6111yescharacteristic
682C22×C8—612no—
683C22×C8—1221no—
684C4×Q8—22no—
685C4×Q8—22no—
686C4×Q8—1222no—
687C4×Q8—1224no—
688C4×Q8—1224no—
689C4×Q8—1222no—
690C4×Q8—1222no—
691C4×Q8—1222no—
692C4×Q8—1224no—
693C4×Q8—1224no—
694C4×Q8—1222no—
695C4×Q8—1222no—
696#117—22no—
697#117—611no—
698#117—612no—
699#117—611no—
700#117—612no—
701#117—611no—
702#117—1221no—
703#117—1224no—
704#117—1221no—
705#117—1222no—
706#117—1221no—
707#117—1222no—
708#117—1221no—
709#117—1221no—
710#117—1224no—
711#117—1222no—
712#117—1221no—
713#117—1221no—
714#117C22×D6111yescharacteristic
715#117C22×D6111yescharacteristic
716#117C22×D6111yescharacteristic
717C2×C4⋊C4—1221no—
718C2×C4⋊C4—1221no—
719C2×C4⋊C4—1224no—
720C2×C4⋊C4—1221no—
721C2×C22⋊C4—612no—
722C2×C22⋊C4—1221no—
723C2×C22⋊C4—1221no—
724C2×C42—612no—
725C2×C42—1221no—
726C2×C42—1224no—
727C2×C42—1221no—
728#104—22no—
729#104—1222no—
730#104—1222no—
731#104—1222no—
732#103—22no—
733#103—1222no—
734#103—1222no—
735#103—1222no—
736#99—22no—
737#99—1222no—
738#99—1222no—
739#99—1222no—
740C24—611no—
741C24—1221no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—1221no—
747#41—1221no—
748#41—1221no—
749#41—1221no—
750#41—1221no—
751#41—1221no—
752#41—1221no—
753#41—1221no—
754#41—1221no—
755#41—1221no—
756#41—1221no—
757#41—1221no—
758#41—2441no—
759#41—2441no—
760#41—2441no—
761#41—2441no—
762#41—2441no—
763#41—2441no—
764#41—2441no—
765#41—2441no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—614no—
770C2×Q8—614no—
771C2×Q8—614no—
772C2×Q8—614no—
773C2×Q8—612no—
774C2×Q8—611no—
775C2×Q8—612no—
776C2×Q8—612no—
777C2×Q8—1222no—
778C2×Q8—1222no—
779C2×Q8—1222no—
780C2×Q8—1222no—
781C2×Q8—1222no—
782C2×Q8—1222no—
783C2×Q8—1221no—
784C2×Q8—1222no—
785C2×Q8—1222no—
786C2×Q8—1222no—
787C2×Q8—1222no—
788C2×Q8—1222no—
789C2×Q8—1222no—
790C2×Q8—1222no—
791C2×Q8—1222no—
792C2×Q8—1222no—
793C2×Q8—1222no—
794C2×Q8—1222no—
795C2×Q8—1222no—
796C2×Q8—1221no—
797C2×Q8—1221no—
798C2×Q8—1221no—
799C2×Q8—1221no—
800C2×Q8—1221no—
801C2×Q8—1221no—
802C2×Q8—1221no—
803C2×Q8C2×C4×D6111yescharacteristic
804C2×Q8C2×C4×D6112yes—
805C2×Q8D4×D6112yes—
806C2×Q8D4×D6112yes—
807C2×D4—21no—
808C2×D4—611no—
809C2×D4—1221no—
810C2×D4—1221no—
811C2×D4—1221no—
812C2×D4—1221no—
813C2×D4—1221no—
814C2×D4—1221no—
815C2×D4—1221no—
816C2×D4—1221no—
817C2×D4—2441no—
818C2×D4—2441no—
819C2×D4—2441no—
820C2×D4—2441no—
821C2×D4C2×C4×D6111yescharacteristic
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—611no—
825C22×C4—611no—
826C22×C4—611no—
827C22×C4—611no—
828C22×C4—611no—
829C22×C4—611no—
830C22×C4—611no—
831C22×C4—611no—
832C22×C4—611no—
833C22×C4—611no—
834C22×C4—611no—
835C22×C4—611no—
836C22×C4—611no—
837C22×C4—1221no—
838C22×C4—1222no—
839C22×C4—1222no—
840C22×C4—1222no—
841C22×C4—1222no—
842C22×C4—1222no—
843C22×C4—1222no—
844C22×C4—1222no—
845C22×C4—1222no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—2441no—
851C22×C4—2441no—
852C22×C4—2441no—
853C22×C4—2441no—
854C22×C4—2441no—
855C22×C4C23×D6111yescharacteristic
856Q16—24no—
857Q16—1224no—
858Q16—1224no—
859Q16—1224no—
860SD16—24no—
861SD16—1224no—
862SD16—1224no—
863SD16—1224no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—1222no—
869M16—1222no—
870M16—1221no—
871M16—1221no—
872M16—1221no—
873M16—1221no—
874M16—2441no—
875M16—2441no—
876C2×C8—21no—
877C2×C8—612no—
878C2×C8—1222no—
879C2×C8—1222no—
880C2×C8—1221no—
881C2×C8—2441no—
882C2×C8—2441no—
883C2×C8C2×C4×D6112yes—
884C4⋊C4—24no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—1222no—
889C4⋊C4—1222no—
890C4⋊C4—1224no—
891C4⋊C4—1224no—
892C4⋊C4—1224no—
893C4⋊C4—1221no—
894C4⋊C4—1221no—
895C4⋊C4—1221no—
896C4⋊C4—2441no—
897C22⋊C4—21no—
898C22⋊C4—21no—
899C22⋊C4—612no—
900C22⋊C4—1222no—
901C22⋊C4—1222no—
902C22⋊C4—1221no—
903C22⋊C4—1221no—
904C22⋊C4—2441no—
905C22⋊C4D4×D6112yes—
906C42—24no—
907C42—21no—
908C42—21no—
909C42—612no—
910C42—1222no—
911C42—1222no—
912C42—1224no—
913C42—1224no—
914C42—1224no—
915C42—1221no—
916C42—1221no—
917C42—2441no—
918C42D4×D6112yes—
919C23—21no—
920C23—611no—
921C23—611no—
922C23—611no—
923C23—611no—
924C23—611no—
925C23—611no—
926C23—1221no—
927C23—4882no—
928C23—2441no—
929C23—2441no—
930C23—2442no—
931C23C2×D4×D6111yescharacteristic
932Q8—22no—
933Q8—22no—
934Q8—22no—
935Q8—21no—
936Q8—21no—
937Q8—614no—
938Q8—1224no—
939Q8—1224no—
940Q8—1224no—
941Q8—1224no—
942Q8—1222no—
943Q8—1222no—
944Q8—1222no—
945Q8—1221no—
946Q8—1221no—
947Q8—2441no—
948Q8—2441no—
949Q8C22⋊C4×D6114yes—
950D4—21no—
951D4—21no—
952D4—41no—
953D4—41no—
954D4—1221no—
955D4—1221no—
956D4—2441no—
957D4—2441no—
958D4—2441no—
959D4—2441no—
960D4—2441no—
961D4—2441no—
962D4—2441no—
963D4—2441no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—611no—
974C2×C4—611no—
975C2×C4—611no—
976C2×C4—611no—
977C2×C4—611no—
978C2×C4—611no—
979C2×C4—611no—
980C2×C4—611no—
981C2×C4—611no—
982C2×C4—611no—
983C2×C4—611no—
984C2×C4—611no—
985C2×C4—611no—
986C2×C4—611no—
987C2×C4—611no—
988C2×C4—611no—
989C2×C4—611no—
990C2×C4—611no—
991C2×C4—611no—
992C2×C4—611no—
993C2×C4—611no—
994C2×C4—611no—
995C2×C4—1224no—
996C2×C4—1224no—
997C2×C4—1224no—
998C2×C4—1224no—
999C2×C4—1222no—
1000C2×C4—1222no—
1001C2×C4—1222no—
1002C2×C4—1221no—
1003C2×C4—1222no—
1004C2×C4—1222no—
1005C2×C4—4882no—
1006C2×C4—2441no—
1007C2×C4—2441no—
1008C2×C4—2441no—
1009C2×C4—2441no—
1010C2×C4—2444no—
1011C2×C4—2444no—
1012C2×C4—2441no—
1013C2×C4—2441no—
1014C2×C4—2441no—
1015C2×C4—2441no—
1016C2×C4—2441no—
1017C2×C4C22×C4×D6111yescharacteristic
1018C2×C4C2×D4×D6111yescharacteristic
1019C2×C4C2×D4×D6111yescharacteristic
1020C2×C4C2×D4×D6111yescharacteristic
1021C2×C4#41×D6111yescharacteristic
1022C2×C4#41×D6111yescharacteristic
1023C8—22no—
1024C8—41no—
1025C8—1222no—
1026C8—2441no—
1027C22—41no—
1028C22—41no—
1029C22—81no—
1030C22—611no—
1031C22—611no—
1032C22—611no—
1033C22—611no—
1034C22—1222no—
1035C22—1222no—
1036C22—1222no—
1037C22—4881no—
1038C22—4882no—
1039C22—4882no—
1040C22—2441no—
1041C22—2441no—
1042C22—2441no—
1043C22—2441no—
1044C22C4×D4×D6111yescharacteristic
1045C22#120×D6111yescharacteristic
1046C22#121×D6111yescharacteristic
1047C4—24no—
1048C4—42no—
1049C4—42no—
1050C4—41no—
1051C4—81no—
1052C4—611no—
1053C4—611no—
1054C4—611no—
1055C4—611no—
1056C4—1224no—
1057C4—4881no—
1058C4—2442no—
1059C4—2442no—
1060C4—2441no—
1061C4C2×C22⋊C4×D6111yescharacteristic
1062C4C4×D4×D6111yescharacteristic
1063C4#121×D6111yescharacteristic
1064C4#123×D6111yescharacteristic
1065C2—21no—
1066C2—21no—
1067C2—21no—
1068C2—81no—
1069C2—612no—
1070C2—1221no—
1071C2—1221no—
1072C2—1221no—
1073C2—4881no—
1074C2#386×D6111yescharacteristic
subgroupG/H
centerC2#386×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1905C2
socleC2×C61C2×#386
prime radicalC2×#41×D61C22
cosocleC22×C4×C61C24
hypercenter#1905D61
hypocenterC61C2×#1905
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1905

Complements

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

NH ≅ G/Ntype
2. #519×D61C2semidirect
4. #419×D61C2semidirect
6. #21446316C2semidirect
7. #21446315C2semidirect
8. #21446314C2semidirect
9. #21446313C2semidirect
10. #21446312C2semidirect
11. #21446311C2semidirect
12. #21446310C2semidirect
13. #344×D61C2semidirect
14. H(3,ℤ/4)×D61C2semidirect
15. C61×#1905C2semidirect
19. C2×#14519809C4semidirect
22. C2×#14519806C4semidirect
27. C2×Q16×D61C4semidirect
28. C2×SD16×D61C4semidirect
31. #16840240C22semidirect
33. #16840239C22semidirect
34. #16840239C22semidirect
48. #16839772C22semidirect
49. #16839771C22semidirect
50. #16839770C22semidirect
58. #16839534C22semidirect
59. #16839533C22semidirect
60. #16839532C22semidirect
61. #16839519C22semidirect
62. #16839518C22semidirect
63. #16839518C22semidirect
65. C61×#519C22semidirect
67. C61×#419C22semidirect
69. C61×#344C22semidirect
70. C61×H(3,ℤ/4)C22semidirect
114. C2×Dic244C2×C4semidirect
115. C2×#11758202C2×C4semidirect
116. C2×#11758202C2×C4semidirect
119. C2×#11758190C2×C4semidirect
120. C2×#11758200C2×C4semidirect
121. C2×#11758201C2×C4semidirect
189. C2×Q16×C61C2×C4semidirect
190. C2×SD16×C61C2×C4semidirect
540. #1905D61direct (N × H)
552. D61#1905direct (N × H)
575. #519C2×D61semidirect
592. #419C2×D61semidirect
603. #344C2×D61semidirect
607. H(3,ℤ/4)C2×D61semidirect
608. C61C2×#1905semidirect
661. C2×Q16C4×D61semidirect
667. C2×SD16C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#137×D612
#519×D612
#421×D612
#419×D612
#410×D612
#214463162
#214463152
#214463142
#214463132
#214463122
#214463112
#214463102
#344×D612
H(3,ℤ/4)×D612
C61×#19052
C2×#190561