Finite Group Databasebeta

← D61×#1908 #29681940

Subgroups — D61×#1908 #29681940

Order 15616.

1698 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#137×D61C211yesmaximal, characteristic
2C2×#131×D61C211yesmaximal, characteristic
3#417×D61C211yesmaximal, characteristic
4C2×#103×D61C211yesmaximal, characteristic, complemented
5C2×#101×D61C211yesmaximal, characteristic, complemented
6#21446337C211yesmaximal, characteristic, complemented
7#21446336C211yesmaximal, characteristic, complemented
8#21446335C211yesmaximal, characteristic, complemented
9#21446334C211yesmaximal, characteristic, complemented
10#21446333C211yesmaximal, characteristic, complemented
11#21446332C211yesmaximal, characteristic, complemented
12#21446331C211yesmaximal, characteristic, complemented
13#343×D61C211yesmaximal, characteristic, complemented
14#341×D61C211yesmaximal, characteristic, complemented
15C61×#1908C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C2×#14519810C2211yescharacteristic
19C2×#14519809—21no—
20C2×#14519808C2211yescharacteristic
21C2×#14519807C2211yescharacteristic
22C2×#14519806—21no—
23#137×D61—24no—
24#137×D61C418yescomplemented
25C2×Q16×D61—21no—
26C2×SD16×D61—21no—
27C2×#14519785—21no—
28C2×#14519785C2211yescharacteristic
29C2×#14519784C2211yescharacteristic
30C2×#14519783—21no—
31C2×#14519783C2211yescharacteristic
32#131×D61—24no—
33#131×D61—24no—
34C2×M16×D61—21no—
35C2×M16×D61C2211yescharacteristic
36C2×M16×D61C2211yescharacteristic
37C2×M16×D61C2211yescharacteristic
38C22×C8×D61—21no—
39C22×C8×D61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41#16839764C2211yescharacteristic
42#16839763C2211yescharacteristic
43#16839762—21no—
44#16839761C2211yescharacteristic
45#16839760—21no—
46C2×#14519702C2211yescharacteristic, complemented
47C2×#14519701C2211yescharacteristic, complemented
48C2×#14519700C2211yescharacteristic, complemented
49#103×D61—21no—
50#103×D61—21no—
51#103×D61—21no—
52#103×D61—21no—
53#103×D61—21no—
54#102×D61—21no—
55C2×#14519696C2211yescharacteristic, complemented
56C2×#14519695C2211yescharacteristic, complemented
57C2×#14519695C2211yescharacteristic, complemented
58#101×D61—24no—
59#16839531C2211yescharacteristic, complemented
60#16839530C2211yescharacteristic, complemented
61#16839530C2211yescharacteristic, complemented
62#16839527C2211yescharacteristic, complemented
63#16839526C2211yescharacteristic, complemented
64#16839526C2211yescharacteristic, complemented
65C2×#137×C61C2211yescharacteristic
66C2×#131×C61C2211yescharacteristic
67C61×#417C2211yescharacteristic
68C2×#103×C61C2211yescharacteristic, complemented
69C2×#101×C61C2211yescharacteristic, complemented
70C61×#343C2211yescharacteristic, complemented
71C61×#341C2211yescharacteristic, complemented
72C2×#11758226D411yescharacteristic
73C2×#11758222—21no—
74C2×#11758222C2311yescharacteristic
75C2×#11758224—21no—
76C2×#11758224D411yescharacteristic
77#41×D61—22no—
78#41×D61—22no—
79#41×D61C2×C414yes—
80#41×D61D414yes—
81C22×Dic122—21no—
82C22×Dic122C2311yescharacteristic
83C2×Q8×D61—22no—
84C2×Q8×D61—21no—
85C2×Q8×D61—21no—
86C2×Q8×D61—21no—
87C2×Q8×D61—22no—
88C2×Q8×D61—21no—
89C2×Q8×D61—22no—
90C2×Q8×D61C2×C414yes—
91C2×Q8×D61D411yescharacteristic
92C2×D4×D61—21no—
93C2×D4×D61D411yescharacteristic
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61C2311yescharacteristic
98#14519810—22no—
99#14519810C2×C414yescomplemented
100#14519809—28no—
101#14519808—22no—
102#14519808C2×C414yescomplemented
103#14519807—22no—
104#14519807C2×C414yescomplemented
105#14519806—28no—
106C2×Dic244—21no—
107C2×#11758202—21no—
108C2×#11758202—21no—
109Q16×D61—28no—
110C2×#11758190—21no—
111C2×#11758200—21no—
112C2×#11758201—21no—
113SD16×D61—28no—
114#14519785—28no—
115#14519785—22no—
116#14519785—22no—
117#14519784—22no—
118#14519784—22no—
119#14519783—28no—
120#14519783—22no—
121#14519783—22no—
122C2×#11758194—21no—
123C2×#11758194C2311yescharacteristic
124C2×#11758194C2311yescharacteristic
125C2×#11758194C2311yescharacteristic
126C2×#11758189—21no—
127C2×#11758189—21no—
128C2×#11758189—21no—
129C2×#11758189—21no—
130C2×#11758189—21no—
131M16×D61—28no—
132M16×D61—22no—
133M16×D61—22no—
134M16×D61—22no—
135M16×D61—22no—
136M16×D61C2×C414yes—
137M16×D61D414yes—
138C22×#92418—21no—
139C22×#92418C2311yescharacteristic
140C2×C8×D61—28no—
141C2×C8×D61—21no—
142C2×C8×D61—22no—
143C2×C8×D61—22no—
144C2×C8×D61—21no—
145C2×C8×D61—21no—
146C2×C8×D61—21no—
147C2×C8×D61—21no—
148C2×C8×D61D411yescharacteristic
149C2×C8×D61D411yescharacteristic
150C2×C8×D61D411yescharacteristic
151C2×C8×D61D411yescharacteristic
152C2×C4⋊Dic61C2311yescharacteristic
153C2×#11758196—21no—
154C4⋊C4×D61—21no—
155C4⋊C4×D61—21no—
156C4⋊C4×D61—21no—
157C4⋊C4×D61—21no—
158#14519702—21no—
159#14519702—21no—
160#14519702—21no—
161#14519701—21no—
162#14519701—21no—
163#14519701—21no—
164#14519700—21no—
165#14519700—21no—
166#14519700—21no—
167#14519699—21no—
168#14519698—21no—
169#14519697—21no—
170#14519696—22no—
171#14519695—22no—
172#14519695—22no—
173C2×#41×C61C2311yescharacteristic
174C22×Q8×C61C2311yescharacteristic
175#137×C61—22no—
176#137×C61C2×C414yescomplemented
177C2×Q16×C61—21no—
178C2×SD16×C61—21no—
179#131×C61—22no—
180#131×C61—22no—
181C2×M16×C61—21no—
182C2×M16×C61C2311yescharacteristic
183C2×M16×C61C2311yescharacteristic
184C2×M16×C61C2311yescharacteristic
185C22×C8×C61—21no—
186C22×C8×C61C2311yescharacteristic
187C2×C4⋊C4×C61C2311yescharacteristic
188#103×C61—21no—
189#103×C61—21no—
190#103×C61—21no—
191#102×C61—21no—
192#101×C61—22no—
193C23×D61—21no—
194C23×D61#4111yescharacteristic
195#41×C61—21no—
196#41×C61—21no—
197#41×C61C22×C412yes—
198#41×C61C2×D412yes—
199C2×Q8×C61—21no—
200C2×Q8×C61—21no—
201C2×Q8×C61—21no—
202C2×Q8×C61—21no—
203C2×Q8×C61—21no—
204C2×Q8×C61C22×C412yes—
205C2×Q8×C61C2×D411yescharacteristic
206C2×D4×C61—21no—
207C2×D4×C61C2×D411yescharacteristic
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61C2411yescharacteristic
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61#4111yescharacteristic
219#11758226—22no—
220#11758226C22⋊C414yes—
221Q8×D61—22no—
222Q8×D61—24no—
223Q8×D61—24no—
224Q8×D61—24no—
225Q8×D61—24no—
226Q8×D61—42no—
227Q8×D61—42no—
228Q8×D61—42no—
229Q8×D61—42no—
230Q8×D61C22⋊C414yes—
231#11758224—24no—
232#11758224—24no—
233#11758224—22no—
234#11758224C22⋊C414yes—
235D4×D61—24no—
236D4×D61—24no—
237D4×D61—22no—
238D4×D61C22⋊C414yes—
239#11758222—21no—
240#11758222—21no—
241#11758222—24no—
242#11758222—24no—
243#11758222C22×C412yes—
244#11758222C2×D412yes—
245C2×D244—21no—
246C2×D244C2×D411yescharacteristic
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—24no—
251C2×C4×D61—24no—
252C2×C4×D61—24no—
253C2×C4×D61—41no—
254C2×C4×D61—41no—
255C2×C4×D61—42no—
256C2×C4×D61—41no—
257C2×C4×D61—41no—
258C2×C4×D61—82no—
259C2×C4×D61C22×C412yes—
260C2×C4×D61C2×D412yes—
261C2×C4×D61C2×D411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×D412yes—
266C2×C4×D61#4112yes—
267C2×Dic122—21no—
268C2×Dic122—21no—
269C2×Dic122—21no—
270C2×Dic122—21no—
271C2×Dic122—21no—
272C2×Dic122—21no—
273C2×Dic122—24no—
274C2×Dic122—41no—
275C2×Dic122—41no—
276C2×Dic122—42no—
277C2×Dic122C22×C412yes—
278C2×Dic122C2×D411yescharacteristic
279Q16×C61—24no—
280SD16×C61—24no—
281M16×C61—24no—
282M16×C61—21no—
283M16×C61—21no—
284M16×C61—21no—
285M16×C61—21no—
286M16×C61C22×C412yes—
287M16×C61C2×D412yes—
288C2×C8×C61—24no—
289C2×C8×C61—21no—
290C2×C8×C61—21no—
291C2×C8×C61—21no—
292C2×C8×C61—21no—
293C2×C8×C61—21no—
294C2×C8×C61C2×D411yescharacteristic
295C2×C8×C61C2×D411yescharacteristic
296C4⋊C4×C61—21no—
297C4⋊C4×C61—21no—
298#11758202—24no—
299#11758202—24no—
300#11758201—24no—
301#11758200—24no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304#11758196—41no—
305#11758196—41no—
306#11758194—24no—
307#11758194—21no—
308#11758194—21no—
309#11758194—21no—
310#11758194—21no—
311#11758194C22×C412yes—
312#11758194C2×D412yes—
313C2×#92418—24no—
314C2×#92418—21no—
315C2×#92418—21no—
316C2×#92418—21no—
317C2×#92418—21no—
318C2×#92418—21no—
319C2×#92418C2×D411yescharacteristic
320C2×#92418C2×D411yescharacteristic
321Dic244—24no—
322#11758190—24no—
323#11758189—24no—
324#11758189—24no—
325#11758189—24no—
326#11758189—24no—
327#11758189—42no—
328C8×D61—24no—
329C8×D61—24no—
330C8×D61—24no—
331C8×D61—22no—
332C8×D61—24no—
333C8×D61—22no—
334C8×D61—22no—
335C8×D61—22no—
336C8×D61—42no—
337C23×C61—21no—
338C23×C61C2×#4111yescharacteristic
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—21no—
342C22×D61—24no—
343C22×D61—42no—
344C22×D61—42no—
345C22×D61C4×D412yes—
346C22×D61#12111yescharacteristic
347C22×D61#12111yescharacteristic
348C22×D61#12312yes—
349Q8×C61—21no—
350Q8×C61—22no—
351Q8×C61—22no—
352Q8×C61—41no—
353Q8×C61—41no—
354Q8×C61C2×C22⋊C412yes—
355D4×C61—22no—
356D4×C61—22no—
357D4×C61—21no—
358D4×C61C2×C22⋊C412yes—
359C2×C4×C61—21no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—81no—
367C2×C4×C61C23×C411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C22×D411yescharacteristic
372C2×C4×C61C2×#4111yescharacteristic
373C22⋊D61—22no—
374C22⋊D61—22no—
375C22⋊D61—24no—
376C22⋊D61—24no—
377C2×Dic61—21no—
378C2×Dic61—24no—
379C2×Dic61—22no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—81no—
384C2×Dic61C4×D412yes—
385C2×Dic61#12111yescharacteristic
386C2×Dic61#12111yescharacteristic
387C2×Dic61#12312yes—
388D244—24no—
389D244—21no—
390D244C2×C22⋊C412yes—
391C4×D61—24no—
392C4×D61—22no—
393C4×D61—22no—
394C4×D61—24no—
395C4×D61—44no—
396C4×D61—44no—
397C4×D61—82no—
398C4×D61—82no—
399C4×D61C2×C22⋊C412yes—
400C4×D61C2×C22⋊C412yes—
401C4×D61C4×D412yes—
402C4×D61C4×D412yes—
403C4×D61#12012yes—
404C4×D61#12012yes—
405C4×D61#12112yes—
406C4×D61#12112yes—
407Dic122—21no—
408Dic122—24no—
409Dic122—22no—
410Dic122—22no—
411Dic122—41no—
412Dic122—41no—
413Dic122—44no—
414Dic122—44no—
415Dic122C2×C22⋊C412yes—
416C8×C61—22no—
417C8×C61—21no—
418C8×C61—22no—
419C8×C61—21no—
420C8×C61—41no—
421#92418—22no—
422#92418—21no—
423#92418—22no—
424#92418—21no—
425#92418—41no—
426C2×#1908—611nomaximal, Sylow
427C22×C61—21no—
428C22×C61—21no—
429C22×C61—22no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61C2×C4×D411yescharacteristic
433C22×C61C2×#12111yescharacteristic
434C22×C61C2×#12311yescharacteristic
435C2×D61—21no—
436C2×D61—21no—
437C2×D61—24no—
438C2×D61—24no—
439C2×D61—22no—
440C2×D61—41no—
441C2×D61—41no—
442C2×D61—48no—
443C2×D61#38612yes—
444C2×D61#38612yes—
445C2×D61#47112yes—
446C2×D61#47312yes—
447C4×C61—22no—
448C4×C61—42no—
449C4×C61—81no—
450C4×C61C22×C22⋊C411yescharacteristic
451C4×C61C2×C4×D411yescharacteristic
452C4×C61C2×#12011yescharacteristic
453C4×C61C2×#12111yescharacteristic
454Dic61—22no—
455Dic61—42no—
456Dic61—81no—
457Dic61#38612yes—
458Dic61#38612yes—
459C22×#137—611no—
460C22×#131—611no—
461C2×#417—611no—
462C22×#103—611no—
463C22×#101—611no—
464#1908—611no—
465#1908—611no—
466#1908—611no—
467#1908—611no—
468#1908—611no—
469#1908—611no—
470#1908—611no—
471#1908D6111yescharacteristic, direct product factor
472C2×#343—611no—
473C2×#341—611no—
474C2×C61—21no—
475C2×C61—21no—
476C2×C61—42no—
477C2×C61C2×#38611yescharacteristic
478C2×C61C2×#47111yescharacteristic
479C2×C61C2×#47311yescharacteristic
480D61—22no—
481D61—42no—
482D61#190814yesdirect product factor
483C22×#41—611no—
484C23×Q8—611no—
485C2×#137—611no—
486C2×#137—611no—
487C2×#137—618no—
488C2×#137—611no—
489C2×#137—1221no—
490C2×#137—1221no—
491C2×#137—1224no—
492C2×#137C2×D6111yescharacteristic
493C22×Q16—1221no—
494C22×SD16—1221no—
495C2×#131—611no—
496C2×#131—611no—
497C2×#131—611no—
498C2×#131—1221no—
499C2×#131—1221no—
500C2×#131—1224no—
501C2×#131—1224no—
502C2×#131C2×D6111yescharacteristic
503C22×M16—611no—
504C22×M16—611no—
505C22×M16—611no—
506C22×M16—1221no—
507C23×C8—611no—
508C23×C8—1221no—
509C22×C4⋊C4—611no—
510#417—611no—
511#417—611no—
512#417—611no—
513#417—1221no—
514#417—1221no—
515#417C2×D6111yescharacteristic
516C2×#103—611no—
517C2×#103—611no—
518C2×#103—611no—
519C2×#103—1221no—
520C2×#103—1221no—
521C2×#103—1221no—
522C2×#103—1221no—
523C2×#103—1221no—
524C2×#103C2×D6111yescharacteristic, complemented
525C2×#102—1221no—
526C2×#101—611no—
527C2×#101—611no—
528C2×#101—611no—
529C2×#101—1224no—
530C2×#101C2×D6111yescharacteristic, complemented
531#343—611no—
532#343—611no—
533#343—611no—
534#343C2×D6111yescharacteristic, complemented
535#341—611no—
536#341—611no—
537#341—611no—
538#341C2×D6111yescharacteristic, complemented
539C61C2×#190811yescharacteristic, complemented, Sylow
540C2×#41—614no—
541C2×#41—614no—
542C2×#41—611no—
543C2×#41—611no—
544C2×#41—611no—
545C2×#41—1221no—
546C2×#41—1221no—
547C2×#41—1222no—
548C2×#41—1222no—
549C2×#41C22×D6111yescharacteristic
550C22×Q8—611no—
551C22×Q8—614no—
552C22×Q8—611no—
553C22×Q8—1221no—
554C22×Q8—1222no—
555C22×Q8—1221no—
556C22×Q8—1221no—
557C22×Q8—1222no—
558C22×Q8—1222no—
559C22×Q8—1221no—
560C22×Q8—1221no—
561C22×Q8C22×D6111yescharacteristic
562C22×D4—611no—
563C22×D4—1221no—
564C23×C4—611no—
565C23×C4—1221no—
566C23×C4—1221no—
567C23×C4—1221no—
568#137—22no—
569#137—614no—
570#137—614no—
571#137—614no—
572#137—1222no—
573#137—1228no—
574#137—1228no—
575#137—1222no—
576#137—1222no—
577#137C4×D6114yescomplemented
578C2×Q16—21no—
579C2×Q16—1221no—
580C2×Q16—1228no—
581C2×Q16—1221no—
582C2×Q16—1221no—
583C2×SD16—21no—
584C2×SD16—1221no—
585C2×SD16—1228no—
586C2×SD16—1221no—
587C2×SD16—1221no—
588#131—22no—
589#131—22no—
590#131—1222no—
591#131—1222no—
592#131—1228no—
593#131—1222no—
594#131—1228no—
595#131—1222no—
596#131—1222no—
597#131—1222no—
598C2×M16—21no—
599C2×M16—611no—
600C2×M16—611no—
601C2×M16—614no—
602C2×M16—614no—
603C2×M16—611no—
604C2×M16—1221no—
605C2×M16—1221no—
606C2×M16—1221no—
607C2×M16—1221no—
608C2×M16—1221no—
609C2×M16—1222no—
610C2×M16—1222no—
611C2×M16—1228no—
612C2×M16—1221no—
613C2×M16—1222no—
614C2×M16—1222no—
615C2×M16C22×D6111yescharacteristic
616C2×M16C22×D6111yescharacteristic
617C2×M16C22×D6111yescharacteristic
618C22×C8—21no—
619C22×C8—611no—
620C22×C8—611no—
621C22×C8—611no—
622C22×C8—611no—
623C22×C8—611no—
624C22×C8—1221no—
625C22×C8—1222no—
626C22×C8—1222no—
627C22×C8—1221no—
628C22×C8—1221no—
629C22×C8—1228no—
630C22×C8—1221no—
631C22×C8—1221no—
632C22×C8—1221no—
633C22×C8C22×D6111yescharacteristic
634C2×C4⋊C4—611no—
635C2×C4⋊C4—1221no—
636C2×C4⋊C4—1221no—
637C2×C4⋊C4—1221no—
638C2×C4⋊C4—1221no—
639C2×C4⋊C4—1221no—
640C2×C4⋊C4C22×D6111yescharacteristic
641#103—21no—
642#103—21no—
643#103—21no—
644#103—1221no—
645#103—1221no—
646#103—1221no—
647#103—1221no—
648#103—1221no—
649#103—1221no—
650#103—1221no—
651#103—1221no—
652#103—1221no—
653#102—21no—
654#102—1221no—
655#102—1221no—
656#102—1221no—
657#101—22no—
658#101—1222no—
659#101—1222no—
660#101—1222no—
661C24—611no—
662C24—1221no—
663#41—21no—
664#41—21no—
665#41—614no—
666#41—614no—
667#41—612no—
668#41—612no—
669#41—1224no—
670#41—1224no—
671#41—1224no—
672#41—1224no—
673#41—1222no—
674#41—1222no—
675#41—1221no—
676#41—1221no—
677#41C2×C4×D6112yes—
678#41D4×D6112yes—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—614no—
685C2×Q8—612no—
686C2×Q8—611no—
687C2×Q8—1221no—
688C2×Q8—1224no—
689C2×Q8—1222no—
690C2×Q8—1224no—
691C2×Q8—1224no—
692C2×Q8—1224no—
693C2×Q8—1224no—
694C2×Q8—1221no—
695C2×Q8—1221no—
696C2×Q8—1221no—
697C2×Q8—1221no—
698C2×Q8—1221no—
699C2×Q8—2441no—
700C2×Q8—2441no—
701C2×Q8—2442no—
702C2×Q8—2442no—
703C2×Q8—2442no—
704C2×Q8—2442no—
705C2×Q8—2442no—
706C2×Q8C2×C4×D6112yes—
707C2×Q8D4×D6111yescharacteristic
708C2×D4—21no—
709C2×D4—614no—
710C2×D4—611no—
711C2×D4—1221no—
712C2×D4—1222no—
713C2×D4—1221no—
714C2×D4—1224no—
715C2×D4—1224no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4D4×D6111yescharacteristic
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—611no—
723C22×C4—612no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—612no—
729C22×C4—612no—
730C22×C4—612no—
731C22×C4—1224no—
732C22×C4—1221no—
733C22×C4—1224no—
734C22×C4—1221no—
735C22×C4—1224no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—4882no—
741C22×C4—2441no—
742C22×C4—2441no—
743C22×C4—2441no—
744C22×C4—2441no—
745C22×C4—2442no—
746C22×C4C23×D6111yescharacteristic
747Q16—24no—
748Q16—1224no—
749Q16—1224no—
750Q16—1224no—
751SD16—24no—
752SD16—1224no—
753SD16—1224no—
754SD16—1224no—
755M16—24no—
756M16—21no—
757M16—21no—
758M16—21no—
759M16—21no—
760M16—612no—
761M16—612no—
762M16—1224no—
763M16—1224no—
764M16—1224no—
765M16—1224no—
766M16—1224no—
767M16—1221no—
768M16—1221no—
769M16—1221no—
770M16—1221no—
771M16—2442no—
772M16C2×C4×D6112yes—
773M16D4×D6112yes—
774C2×C8—24no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—611no—
781C2×C8—611no—
782C2×C8—1222no—
783C2×C8—1222no—
784C2×C8—1222no—
785C2×C8—1222no—
786C2×C8—1224no—
787C2×C8—1224no—
788C2×C8—1224no—
789C2×C8—1224no—
790C2×C8—1224no—
791C2×C8—1221no—
792C2×C8—1221no—
793C2×C8—1221no—
794C2×C8—1221no—
795C2×C8—1221no—
796C2×C8—2442no—
797C2×C8D4×D6111yescharacteristic
798C2×C8D4×D6111yescharacteristic
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—2441no—
804C4⋊C4—2441no—
805C23—21no—
806C23—611no—
807C23—612no—
808C23—611no—
809C23—612no—
810C23—1222no—
811C23—1222no—
812C23—1224no—
813C23—1221no—
814C23—2442no—
815C23—2442no—
816C23#41×D6111yescharacteristic
817Q8—21no—
818Q8—22no—
819Q8—22no—
820Q8—41no—
821Q8—41no—
822Q8—612no—
823Q8—1224no—
824Q8—1221no—
825Q8—1222no—
826Q8—1222no—
827Q8—2444no—
828Q8—2444no—
829Q8—2441no—
830Q8—2441no—
831Q8C22⋊C4×D6112yes—
832D4—22no—
833D4—22no—
834D4—21no—
835D4—612no—
836D4—1224no—
837D4—1224no—
838D4—1224no—
839D4—1222no—
840D4—1222no—
841D4—1221no—
842D4C22⋊C4×D6112yes—
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—81no—
851C2×C4—612no—
852C2×C4—611no—
853C2×C4—611no—
854C2×C4—612no—
855C2×C4—612no—
856C2×C4—612no—
857C2×C4—612no—
858C2×C4—612no—
859C2×C4—612no—
860C2×C4—612no—
861C2×C4—612no—
862C2×C4—612no—
863C2×C4—1224no—
864C2×C4—1224no—
865C2×C4—1224no—
866C2×C4—1221no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
870C2×C4—4882no—
871C2×C4—4882no—
872C2×C4—4881no—
873C2×C4—2444no—
874C2×C4—2444no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4C22×C4×D6111yescharacteristic
879C2×C4C2×D4×D6111yescharacteristic
880C2×C4C2×D4×D6111yescharacteristic
881C2×C4C2×D4×D6111yescharacteristic
882C2×C4C2×D4×D6111yescharacteristic
883C2×C4#41×D6111yescharacteristic
884C8—22no—
885C8—21no—
886C8—22no—
887C8—21no—
888C8—41no—
889C8—1222no—
890C8—1221no—
891C8—1221no—
892C8—1222no—
893C8—2441no—
894C22—21no—
895C22—21no—
896C22—22no—
897C22—41no—
898C22—41no—
899C22—612no—
900C22—612no—
901C22—612no—
902C22—612no—
903C22—1224no—
904C22—1224no—
905C22—1221no—
906C22—1221no—
907C22—1222no—
908C22—2448no—
909C22—2441no—
910C22—2441no—
911C22C4×D4×D6111yescharacteristic
912C22#121×D6111yescharacteristic
913C22#123×D6111yescharacteristic
914C4—22no—
915C4—42no—
916C4—81no—
917C4—612no—
918C4—612no—
919C4—1222no—
920C4—4881no—
921C4—2442no—
922C4C2×C22⋊C4×D6111yescharacteristic
923C4C4×D4×D6111yescharacteristic
924C4#120×D6111yescharacteristic
925C4#121×D6111yescharacteristic
926C2—21no—
927C2—21no—
928C2—42no—
929C2—614no—
930C2—1222no—
931C2—2442no—
932C2#386×D6111yescharacteristic
933C2#471×D6111yescharacteristic
934C2#473×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1908C2
socleC22×C61C2×#121
prime radicalC2×#41×D61C22
cosocleC22×C4×C61C24
hypercenter#1908D61
hypocenterC61C2×#1908
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1908

Complements

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

NH ≅ G/Ntype
4. C2×#103×D61C2semidirect
5. C2×#101×D61C2semidirect
6. #21446337C2semidirect
7. #21446336C2semidirect
8. #21446335C2semidirect
9. #21446334C2semidirect
10. #21446333C2semidirect
11. #21446332C2semidirect
12. #21446331C2semidirect
13. #343×D61C2semidirect
14. #341×D61C2semidirect
15. C61×#1908C2semidirect
24. #137×D61C4semidirect
46. C2×#14519702C22semidirect
47. C2×#14519701C22semidirect
48. C2×#14519700C22semidirect
55. C2×#14519696C22semidirect
56. C2×#14519695C22semidirect
57. C2×#14519695C22semidirect
59. #16839531C22semidirect
60. #16839530C22semidirect
61. #16839530C22semidirect
62. #16839527C22semidirect
63. #16839526C22semidirect
64. #16839526C22semidirect
68. C2×#103×C61C22semidirect
69. C2×#101×C61C22semidirect
70. C61×#343C22semidirect
71. C61×#341C22semidirect
99. #14519810C2×C4semidirect
102. #14519808C2×C4semidirect
104. #14519807C2×C4semidirect
176. #137×C61C2×C4semidirect
471. #1908D61direct (N × H)
482. D61#1908direct (N × H)
524. C2×#103C2×D61semidirect
530. C2×#101C2×D61semidirect
534. #343C2×D61semidirect
538. #341C2×D61semidirect
539. C61C2×#1908semidirect
577. #137C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#137×D612
C2×#131×D612
#417×D612
C2×#103×D612
C2×#101×D612
#214463372
#214463362
#214463352
#214463342
#214463332
#214463322
#214463312
#343×D612
#341×D612
C61×#19082
C2×#190861