Finite Group Databasebeta

← #29707527

Subgroups — #29707527

Order 15616.

1650 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840275C211yesmaximal, characteristic
2C2×#16839803C211yesmaximal, characteristic, complemented
3C2×#16839762C211yesmaximal, characteristic, complemented
4C2×#16839762C211yesmaximal, characteristic, complemented
5C2×#16839724C211yesmaximal, characteristic, complemented
6#380×D61C211yesmaximal, characteristic, complemented
7#21447019C211yesmaximal, characteristic, complemented
8#21447014C211yesmaximal, characteristic, complemented
9#21447013C211yesmaximal, characteristic, complemented
10#21447009C211yesmaximal, characteristic, complemented
11#21447008C211yesmaximal, characteristic, complemented
12#21447004C211yesmaximal, characteristic, complemented
13#21447003C211yesmaximal, characteristic, complemented
14#21445537C211yesmaximal, characteristic, complemented
15C61×#2036C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20#16840275—24no—
21#16840275—24no—
22C2×#14519762—21no—
23C2×#14519753C2211yescharacteristic
24C2×#14519752C2211yescharacteristic
25C2×#14519751C2211yescharacteristic
26C2×#14519747—21no—
27C2×#14519739—21no—
28C2×#14519737—21no—
29C2×#14519735C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×C22⋊C4×D61—21no—
33#16839803—24no—
34C2×#14519710C2211yescharacteristic, complemented
35C2×#14519709C2211yescharacteristic, complemented
36C2×#14519708C2211yescharacteristic, complemented
37#16839762—24no—
38#16839762—24no—
39C2×#14519701C2211yescharacteristic, complemented
40C2×#14519701C2211yescharacteristic, complemented
41C2×#14519699C2211yescharacteristic, complemented
42C2×#14519699C2211yescharacteristic, complemented
43C2×#14519697C2211yescharacteristic, complemented
44C2×#14519697C2211yescharacteristic, complemented
45#16839724—24no—
46C2×C22⋊#92418C2211yescharacteristic
47C2×#14519689C2211yescharacteristic
48C2×#14519689C2211yescharacteristic
49#16839622C2211yescharacteristic
50#16839621—21no—
51#16839620—21no—
52#16839619C2211yescharacteristic
53#16839619C2211yescharacteristic
54#95×D61—21no—
55#16839525C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57#16839524C2211yescharacteristic, complemented
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#107×C61C2211yescharacteristic, complemented
60C2×#103×C61C2211yescharacteristic, complemented
61C2×#103×C61C2211yescharacteristic, complemented
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C61×#340C2211yescharacteristic, complemented
65C24×D61D411yescharacteristic
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—22no—
69C2×#11758226—22no—
70C2×#11758226—22no—
71C2×#11758226D414yes—
72C22×D244—21no—
73C22×D244—21no—
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C23×Dic61D411yescharacteristic
77C22×C4×D61—21no—
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61—22no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61D411yescharacteristic
87C22×C4×D61D411yescharacteristic
88C22×C4×D61C2311yescharacteristic
89C22×C4×D61C2311yescharacteristic
90C2×#11758189—22no—
91C2×#11758189—22no—
92C2×#11758189—22no—
93C2×#11758189—22no—
94C2×#11758189—22no—
95C2×#11758189D414yescomplemented
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98#14519762—28no—
99#14519753—22no—
100#14519753—22no—
101#14519752—22no—
102#14519752—22no—
103#14519751—22no—
104#14519751—22no—
105#14519747—28no—
106#14519739—28no—
107#14519737—28no—
108#14519735—22no—
109#14519735D414yes—
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196—21no—
114C2×#11758196—21no—
115C2×#11758196—21no—
116C4⋊C4×D61—22no—
117C4⋊C4×D61—22no—
118C4⋊C4×D61—22no—
119C4⋊C4×D61—22no—
120C2×C22⋊Dic61—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×#11758198—21no—
125C2×#11758198—21no—
126C2×#11758198—21no—
127C22⋊C4×D61—44no—
128C2×C4×Dic61—21no—
129#14519710—22no—
130#14519709—22no—
131#14519708—22no—
132#14519701—22no—
133#14519701—22no—
134#14519699—22no—
135#14519699—22no—
136#14519697—22no—
137#14519697—22no—
138C22⋊#92418—22no—
139#14519689—22no—
140#14519689—22no—
141#14519684—21no—
142#14519684—21no—
143#14519684—21no—
144C22×Q8×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C22⋊Q8×C61—22no—
149C22⋊Q8×C61—22no—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156#107×C61—22no—
157#103×C61—22no—
158#103×C61—22no—
159C22⋊C8×C61—22no—
160#95×C61—21no—
161C24×C61C2×D411yescharacteristic
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61—21no—
166C23×D61—22no—
167C23×D61—22no—
168C23×D61—41no—
169C23×D61—41no—
170C23×D61C2×D411yescharacteristic
171C23×D61C2×D411yescharacteristic
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61C2×D412yes—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—24no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—42no—
193C22×Dic61—21no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61C2×D411yescharacteristic
200C22×Dic61C2×D411yescharacteristic
201#11758226—28no—
202#11758226—28no—
203#11758226—44no—
204#11758226—44no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—24no—
210C2×D244—24no—
211C2×D244—21no—
212C2×D244—42no—
213C2×D244—42no—
214C2×D244—42no—
215C2×D244—42no—
216C2×D244C2×D412yes—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—22no—
227C2×C4×D61—24no—
228C2×C4×D61—22no—
229C2×C4×D61—22no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—44no—
233C2×C4×D61—44no—
234C2×C4×D61—44no—
235C2×C4×D61—44no—
236C2×C4×D61—42no—
237C2×C4×D61—42no—
238C2×C4×D61—42no—
239C2×C4×D61—42no—
240C2×C4×D61—42no—
241C2×C4×D61—42no—
242C2×C4×D61C2×D412yes—
243C2×C4×D61C2×D412yes—
244C2×C4×D61C2×D412yes—
245C2×C4×D61#4112yes—
246C2×C4×D61#4112yes—
247C2×C4×D61#4112yes—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61C2×D412yes—
254C4⋊C4×C61—24no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61C2×D412yes—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—42no—
263C22⋊Dic61—42no—
264#11758198—24no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198—42no—
269#11758198—42no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61C2×D412yes—
276#11758196—24no—
277#11758196—42no—
278#11758196—42no—
279C4×Dic61—24no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418C2×D412yes—
286#11758189—28no—
287#11758189—44no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61#13712yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—28no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—22no—
308C22×D61—44no—
309C22×D61—44no—
310C22×D61—44no—
311C22×D61—44no—
312C22×D61—44no—
313C22×D61—44no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61#12012yes—
321C22×D61#12112yes—
322C22×D61#12312yes—
323C22×D61AGL(1,ℤ/8)12yes—
324Q8×C61—22no—
325Q8×C61—22no—
326Q8×C61—41no—
327Q8×C61—41no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C2×#4111yescharacteristic
351C2×C4×C61C2×#4111yescharacteristic
352C2×C4×C61C2×#4111yescharacteristic
353C22⋊D61—48no—
354C2×Dic61—22no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—44no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61#12012yes—
368C2×Dic61#12112yes—
369C2×Dic61#12312yes—
370D244—22no—
371D244—22no—
372D244—48no—
373D244—48no—
374D244—41no—
375D244—41no—
376C4×D61—44no—
377C4×D61—41no—
378C4×D61—41no—
379C4×D61—41no—
380C4×D61—41no—
381C4×D61—44no—
382C4×D61—48no—
383C4×D61—84no—
384C4×D61—84no—
385C4×D61#12114yes—
386C4×D61#12114yes—
387C4×D61#12314yes—
388C4×D61#12414yes—
389C8×C61—22no—
390C8×C61—41no—
391#92418—22no—
392#92418—41no—
393#23482—611nomaximal, Sylow
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—22no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61C2×#12011yescharacteristic
402C22×C61C2×#12111yescharacteristic
403C22×C61C2×#12311yescharacteristic
404C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C61C2×#13711yescharacteristic
406C22×C61#57511yescharacteristic
407C22×C61#57511yescharacteristic
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—22no—
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—416no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—42no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—81no—
426C2×D61—81no—
427C2×D61—81no—
428C2×D61—81no—
429C2×D61#39414yes—
430C4×C61—41no—
431C4×C61—42no—
432C4×C61—42no—
433C4×C61—81no—
434C4×C61—81no—
435C4×C61C2×#12111yescharacteristic
436C4×C61C2×#12111yescharacteristic
437C4×C61C2×#12311yescharacteristic
438C4×C61C2×#12411yescharacteristic
439Dic61—41no—
440Dic61—42no—
441Dic61—81no—
442Dic61—81no—
443Dic61#39414yes—
444C2×#525—611no—
445C2×#428—611no—
446C2×#417—611no—
447C2×#417—611no—
448C2×#407—611no—
449C2×#380—611no—
450#2036—611no—
451#2036D6111yescharacteristic, complemented
452#2035—611no—
453#2035—611no—
454#2034—611no—
455#2034—611no—
456#2033—611no—
457#2033—611no—
458#1736—611no—
459C2×C61—42no—
460C2×C61C2×#39411yescharacteristic
461C2×C61#300611yescharacteristic
462C2×C61#300711yescharacteristic
463C2×C61#305511yescharacteristic
464C2×C61#305611yescharacteristic
465C2×C61#309211yescharacteristic
466C2×C61#309311yescharacteristic
467D61—24no—
468D61—42no—
469D61—82no—
470C22×#41—611no—
471C24×C4—611no—
472C22×M16—611no—
473C22×M16—611no—
474#525—1224no—
475#525—1224no—
476C2×#123—1221no—
477C2×C22⋊Q8—611no—
478C2×C22⋊Q8C2×D6111yescharacteristic
479C2×#121—611no—
480C2×#121—611no—
481C2×#120—1221no—
482C2×C4×D4—1221no—
483C2×C4×D4—1221no—
484C2×#117—611no—
485C22×C4⋊C4—611no—
486C22×C4⋊C4—611no—
487C22×C22⋊C4—1221no—
488#428—1224no—
489C2×#107—611no—
490C2×#107C2×D6111yescharacteristic, complemented
491C2×#106—611no—
492C2×#106—611no—
493#417—1224no—
494#417—1224no—
495C2×#103—611no—
496C2×#103—611no—
497C2×#103C2×D6111yescharacteristic, complemented
498C2×#103C2×D6111yescharacteristic, complemented
499C2×#102—611no—
500C2×#102—611no—
501C2×#102—611no—
502C2×#102—611no—
503#407—1224no—
504C2×C22⋊C8—611no—
505C2×C22⋊C8—611no—
506C2×C22⋊C8—611no—
507C2×C22⋊C8C2×D6111yescharacteristic
508#380—611no—
509#380—611no—
510#380—611no—
511#380—1221no—
512#380—1221no—
513#380C2×D6111yescharacteristic
514C2×#95—1221no—
515#340—611no—
516#340—611no—
517#340—611no—
518#340C2×D6111yescharacteristic, complemented
519C61#2348211yescharacteristic, complemented, Sylow
520C25—611no—
521C2×#41—614no—
522C2×#41—1222no—
523C2×#41—1222no—
524C2×#41—1222no—
525C2×#41—1222no—
526C2×#41—1222no—
527C22×Q8C22×D6111yescharacteristic
528C22×D4—611no—
529C22×D4—1221no—
530C22×D4—1221no—
531C22×D4—1221no—
532C23×C4—611no—
533C23×C4—611no—
534C23×C4—611no—
535C23×C4—611no—
536C23×C4—611no—
537C23×C4—1221no—
538C23×C4—1222no—
539C23×C4—1222no—
540C23×C4—1222no—
541C23×C4—1222no—
542C23×C4—1222no—
543C23×C4—1222no—
544C23×C4—1221no—
545C23×C4—1221no—
546C23×C4C22×D6111yescharacteristic
547C2×M16—614no—
548C2×M16—1222no—
549C2×M16—1222no—
550C2×M16—1222no—
551C2×M16—1222no—
552C2×M16—1222no—
553C22×C8—611no—
554C22×C8—611no—
555C22×C8C22×D6111yescharacteristic
556C22×C8C22×D6111yescharacteristic
557#123—1228no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—1222no—
561C22⋊Q8—1222no—
562#121—1222no—
563#121—1222no—
564#121—1222no—
565#121—1222no—
566#120—1228no—
567C4×D4—1228no—
568C4×D4—1228no—
569#117—614no—
570#117—1222no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—1222no—
576C2×C4⋊C4—1222no—
577C2×C4⋊C4—1222no—
578C2×C4⋊C4—1222no—
579C2×C4⋊C4—1221no—
580C2×C4⋊C4—1221no—
581C2×C4⋊C4—1221no—
582C2×C4⋊C4C22×D6111yescharacteristic
583C2×C4⋊C4C22×D6111yescharacteristic
584C2×C4⋊C4C22×D6111yescharacteristic
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C22⋊C4—1221no—
592C2×C22⋊C4—1221no—
593C2×C22⋊C4—1221no—
594C2×C22⋊C4—2444no—
595C2×C42—1221no—
596#107—22no—
597#107—1222no—
598#106—1222no—
599#106—1222no—
600#103—22no—
601#103—22no—
602#103—1222no—
603#103—1222no—
604#102—1222no—
605#102—1222no—
606#102—1222no—
607#102—1222no—
608C22⋊C8—22no—
609C22⋊C8—1222no—
610C22⋊C8—1222no—
611C22⋊C8—1222no—
612#95—21no—
613#95—1221no—
614#95—1221no—
615#95—1221no—
616C24—611no—
617C24—611no—
618C24—1222no—
619C24—1222no—
620C24—1222no—
621C24—1222no—
622C24—1222no—
623C24—1221no—
624C24—2441no—
625C24—2441no—
626C24D4×D6111yescharacteristic
627#41—1228no—
628#41—1228no—
629#41—2444no—
630#41—2444no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8D4×D6112yes—
637C2×D4—612no—
638C2×D4—1224no—
639C2×D4—1224no—
640C2×D4—1224no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4—2442no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—611no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—612no—
668C22×C4—612no—
669C22×C4—611no—
670C22×C4—1222no—
671C22×C4—1224no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4—1222no—
677C22×C4—1222no—
678C22×C4—1222no—
679C22×C4—1222no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—2444no—
690C22×C4—2444no—
691C22×C4—2444no—
692C22×C4—2444no—
693C22×C4—2442no—
694C22×C4—2442no—
695C22×C4—2442no—
696C22×C4—2442no—
697C22×C4—2442no—
698C22×C4—2442no—
699C22×C4—2442no—
700C22×C4—2442no—
701C22×C4D4×D6111yescharacteristic
702C22×C4C23×D6111yescharacteristic
703M16—1228no—
704M16—2444no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—612no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8D4×D6112yes—
717C4⋊C4—24no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—612no—
724C4⋊C4—1224no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—2442no—
731C4⋊C4—2442no—
732C4⋊C4D4×D6112yes—
733C22⋊C4—24no—
734C22⋊C4—42no—
735C22⋊C4—1224no—
736C22⋊C4—1224no—
737C22⋊C4—1224no—
738C22⋊C4—1224no—
739C22⋊C4—2442no—
740C22⋊C4—2442no—
741C22⋊C4—2442no—
742C42—1224no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—612no—
750C23—612no—
751C23—612no—
752C23—612no—
753C23—1228no—
754C23—1221no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23—1221no—
760C23—1221no—
761C23—1221no—
762C23—1221no—
763C23—1221no—
764C23—1222no—
765C23—2444no—
766C23—2444no—
767C23—2444no—
768C23—2444no—
769C23—2444no—
770C23—2444no—
771C23—2441no—
772C23—2441no—
773C23—2441no—
774C23—2441no—
775C23—2441no—
776C23—2441no—
777C23#1451980912yes—
778C23C2×D4×D6111yescharacteristic
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783D4—1222no—
784D4—1222no—
785D4—2448no—
786D4—2448no—
787D4—2448no—
788D4—2441no—
789D4—2441no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—612no—
810C2×C4—612no—
811C2×C4—612no—
812C2×C4—614no—
813C2×C4—614no—
814C2×C4—614no—
815C2×C4—614no—
816C2×C4—1222no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—4884no—
821C2×C4—4884no—
822C2×C4—2444no—
823C2×C4—2448no—
824C2×C4—2444no—
825C2×C4—2444no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2441no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4C2×D4×D6111yescharacteristic
839C2×C4C2×D4×D6111yescharacteristic
840C2×C4C2×D4×D6111yescharacteristic
841C2×C4#41×D6111yescharacteristic
842C2×C4#41×D6111yescharacteristic
843C2×C4#41×D6111yescharacteristic
844C8—22no—
845C8—41no—
846C8—1222no—
847C8—2441no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—614no—
856C22—1222no—
857C22—1222no—
858C22—1222no—
859C22—1222no—
860C22—1222no—
861C22—1222no—
862C22—1222no—
863C22—1222no—
864C22—1222no—
865C22—4881no—
866C22—4881no—
867C22—4881no—
868C22—4881no—
869C22—24416no—
870C22—2442no—
871C22—2442no—
872C22—2442no—
873C22—2441no—
874C22—2441no—
875C22—2441no—
876C22—2441no—
877C22#120×D6111yescharacteristic
878C22#121×D6111yescharacteristic
879C22#123×D6111yescharacteristic
880C22AGL(1,ℤ/8)×D6111yescharacteristic
881C22C2×#1451980911yescharacteristic
882C22#1684055911yescharacteristic
883C22#1684056111yescharacteristic
884C4—41no—
885C4—42no—
886C4—42no—
887C4—81no—
888C4—81no—
889C4—614no—
890C4—4881no—
891C4—4881no—
892C4—2441no—
893C4—2442no—
894C4#121×D6111yescharacteristic
895C4#121×D6111yescharacteristic
896C4#123×D6111yescharacteristic
897C4#124×D6111yescharacteristic
898C2—42no—
899C2—1224no—
900C2—4882no—
901C2—2442no—
902C2#394×D6111yescharacteristic
903C2#2145506811yescharacteristic
904C2#2145507811yescharacteristic
905C2#2145543311yescharacteristic
906C2#2145544611yescharacteristic
907C2#2145574611yescharacteristic
908C2#2145575111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2036C2
socleC23×C61C22×D4
prime radicalC2×#16840275C2
hypercenter#2036D61
hypocenterC61#23482
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
2. C2×#16839803C2semidirect
3. C2×#16839762C2semidirect
4. C2×#16839762C2semidirect
5. C2×#16839724C2semidirect
6. #380×D61C2semidirect
7. #21447019C2semidirect
8. #21447014C2semidirect
9. #21447013C2semidirect
10. #21447009C2semidirect
11. #21447008C2semidirect
12. #21447004C2semidirect
13. #21447003C2semidirect
14. #21445537C2semidirect
15. C61×#2036C2semidirect
34. C2×#14519710C22semidirect
35. C2×#14519709C22semidirect
36. C2×#14519708C22semidirect
39. C2×#14519701C22semidirect
40. C2×#14519701C22semidirect
41. C2×#14519699C22semidirect
42. C2×#14519699C22semidirect
43. C2×#14519697C22semidirect
44. C2×#14519697C22semidirect
55. #16839525C22semidirect
56. #16839524C22semidirect
57. #16839524C22semidirect
59. C2×#107×C61C22semidirect
60. C2×#103×C61C22semidirect
61. C2×#103×C61C22semidirect
64. C61×#340C22semidirect
95. C2×#11758189D4semidirect
451. #2036D61semidirect
490. C2×#107C2×D61semidirect
497. C2×#103C2×D61semidirect
498. C2×#103C2×D61semidirect
518. #340C2×D61semidirect
519. C61#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#168402752
C2×#168398032
C2×#168397622
C2×#168397242
#380×D612
#214470192
#214470142
#214470132
#214470092
#214470082
#214470042
#214470032
#214455372
C61×#20362
#2348261