Finite Group Databasebeta

← #29707518

Subgroups — #29707518

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×#16840272C211yesmaximal, characteristic
2C2×#16839803C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic, complemented
4C2×#16839760C211yesmaximal, characteristic, complemented
5C2×#16839724C211yesmaximal, characteristic, complemented
6#380×D61C211yesmaximal, characteristic, complemented
7#21447025C211yesmaximal, characteristic, complemented
8#21447024C211yesmaximal, characteristic, complemented
9#21447016C211yesmaximal, characteristic, complemented
10#21447015C211yesmaximal, characteristic, complemented
11#21447007C211yesmaximal, characteristic, complemented
12#21447006C211yesmaximal, characteristic, complemented
13#21446998C211yesmaximal, characteristic, complemented
14#21445537C211yesmaximal, characteristic, complemented
15C61×#2033C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20#16840272—24no—
21#16840272—24no—
22C2×#14519759—21no—
23C2×#14519757C2211yescharacteristic
24C2×#14519756C2211yescharacteristic
25C2×#14519748C2211yescharacteristic
26C2×#14519745—21no—
27C2×D4×Dic61—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#16839760—24no—
38#16839760—24no—
39C2×#14519702C2211yescharacteristic, complemented
40C2×#14519702C2211yescharacteristic, complemented
41C2×#14519700C2211yescharacteristic, complemented
42C2×#14519700C2211yescharacteristic, complemented
43C2×#14519698C2211yescharacteristic, complemented
44C2×#14519698C2211yescharacteristic, 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×#121×C61C2211yescharacteristic
59C2×#107×C61C2211yescharacteristic, complemented
60C2×#102×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic, complemented
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C61×#340C2211yescharacteristic, complemented
65C24×D61D411yescharacteristic
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224—22no—
70C2×#11758224—22no—
71C2×#11758224D414yes—
72C22×Dic122C2311yescharacteristic
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C23×Dic61—21no—
76C23×Dic61D411yescharacteristic
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D411yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C22×C4×D61C2311yescharacteristic
89C2×#11758189—22no—
90C2×#11758189—22no—
91C2×#11758189—22no—
92C2×#11758189—22no—
93C2×#11758189—22no—
94C2×#11758189D414yescomplemented
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97#14519759—28no—
98#14519757—22no—
99#14519757—22no—
100#14519756—22no—
101#14519756—22no—
102#14519748—22no—
103#14519748—22no—
104#14519745—28no—
105D4×Dic61—28no—
106#14519737—28no—
107#14519735—22no—
108#14519735D414yes—
109C2×C4⋊Dic61—21no—
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×C22⋊Dic61—21no—
122C2×C22⋊Dic61—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#14519702—22no—
133#14519702—22no—
134#14519700—22no—
135#14519700—22no—
136#14519698—22no—
137#14519698—22no—
138C22⋊#92418—22no—
139#14519689—22no—
140#14519689—22no—
141#14519684—21no—
142#14519684—21no—
143#14519684—21no—
144C22×D4×C61—21no—
145C22×D4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149#121×C61—22no—
150#121×C61—22no—
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#102×C61—22no—
158#102×C61—22no—
159C22⋊C8×C61—22no—
160#95×C61—21no—
161C24×C61—21no—
162C24×C61C2×D411yescharacteristic
163C23×D61—22no—
164C23×D61—22no—
165C23×D61—22no—
166C23×D61—22no—
167C23×D61—22no—
168C23×D61—41no—
169C23×D61—41no—
170C23×D61C2×D411yescharacteristic
171C23×D61C2×D411yescharacteristic
172C2×D4×C61—24no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—42no—
179C2×D4×C61—42no—
180C2×D4×C61C2×D412yes—
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×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2411yescharacteristic
192C2×C22⋊D61—24no—
193C2×C22⋊D61—24no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C2×C22⋊D61—42no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—22no—
201C22×Dic61—24no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—42no—
207C22×Dic61—42no—
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210#11758224—28no—
211#11758224—28no—
212#11758224—44no—
213#11758224—44no—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—22no—
224C2×C4×D61—22no—
225C2×C4×D61—22no—
226C2×C4×D61—44no—
227C2×C4×D61—44no—
228C2×C4×D61—44no—
229C2×C4×D61—44no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×C4×D61—42no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61C2×D412yes—
237C2×C4×D61C2×D412yes—
238C2×C4×D61C2×D412yes—
239C2×C4×D61#4112yes—
240C2×C4×D61#4112yes—
241C2×C4×D61#4112yes—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—21no—
247C2×Dic122C2×D412yes—
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—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61C2×D412yes—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—42no—
262C22⋊Dic61—24no—
263C22⋊Dic61—24no—
264C22⋊Dic61—42no—
265#11758198—24no—
266#11758198—24no—
267#11758198—42no—
268#11758198—42no—
269C4⋊Dic61—24no—
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—22no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61AGL(1,ℤ/8)12yes—
302C23×C61C22×D411yescharacteristic
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—28no—
308C22×D61—21no—
309C22×D61—21no—
310C22×D61—21no—
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—21no—
314C22×D61—44no—
315C22×D61—44no—
316C22×D61—44no—
317C22×D61—44no—
318C22×D61—44no—
319C22×D61—44no—
320C22×D61#12012yes—
321C22×D61#12112yes—
322C22×D61#12312yes—
323C22×D61#13712yes—
324D4×C61—22no—
325D4×C61—22no—
326D4×C61—48no—
327D4×C61—41no—
328D4×C61—41no—
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×C61C22×D411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C2×#4111yescharacteristic
349C2×C4×C61C2×#4111yescharacteristic
350C2×C4×C61C2×#4111yescharacteristic
351C22⋊D61—48no—
352C22⋊D61—48no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—44no—
363C2×Dic61—48no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61#12012yes—
371C2×Dic61#12112yes—
372C2×Dic61#12312yes—
373C4×D61—44no—
374C4×D61—41no—
375C4×D61—41no—
376C4×D61—41no—
377C4×D61—41no—
378C4×D61—44no—
379C4×D61—84no—
380C4×D61—84no—
381C4×D61#12114yes—
382C4×D61#12114yes—
383C4×D61#12314yes—
384C4×D61#12414yes—
385Dic122—22no—
386Dic122—22no—
387Dic122—41no—
388Dic122—41no—
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×C61—42no—
402C22×C61—42no—
403C22×C61—42no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61—81no—
407C22×C61—81no—
408C22×C61C2×#12011yescharacteristic
409C22×C61C2×#12111yescharacteristic
410C22×C61C2×#12311yescharacteristic
411C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
412C22×C61C2×#13711yescharacteristic
413C22×C61#57511yescharacteristic
414C22×C61#57511yescharacteristic
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—22no—
418C2×D61—22no—
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—22no—
422C2×D61—22no—
423C2×D61—22no—
424C2×D61—416no—
425C2×D61—41no—
426C2×D61—41no—
427C2×D61—41no—
428C2×D61—41no—
429C2×D61#39414yes—
430C4×C61—41no—
431C4×C61—42no—
432C4×C61—81no—
433C4×C61—81no—
434C4×C61C2×#12111yescharacteristic
435C4×C61C2×#12111yescharacteristic
436C4×C61C2×#12311yescharacteristic
437C4×C61C2×#12411yescharacteristic
438Dic61—42no—
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#2036—611no—
452#2035—611no—
453#2035—611no—
454#2034—611no—
455#2034—611no—
456#2033—611no—
457#2033D6111yescharacteristic, complemented
458#1736—611no—
459C2×C61—42no—
460C2×C61—82no—
461C2×C61C2×#39411yescharacteristic
462C2×C61#300611yescharacteristic
463C2×C61#300711yescharacteristic
464C2×C61#305511yescharacteristic
465C2×C61#305611yescharacteristic
466C2×C61#309211yescharacteristic
467C2×C61#309311yescharacteristic
468D61—24no—
469D61—42no—
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⋊Q8—611no—
479C2×#121—611no—
480C2×#121C2×D6111yescharacteristic
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×#103—611no—
498C2×#103—611no—
499C2×#102—611no—
500C2×#102—611no—
501C2×#102C2×D6111yescharacteristic, complemented
502C2×#102C2×D6111yescharacteristic, complemented
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×Q8—611no—
528C22×D4—21no—
529C22×D4—1221no—
530C22×D4—1221no—
531C22×D4C22×D6111yescharacteristic
532C23×C4—611no—
533C23×C4—611no—
534C23×C4—611no—
535C23×C4—611no—
536C23×C4—611no—
537C23×C4—1222no—
538C23×C4—1222no—
539C23×C4—1222no—
540C23×C4—1222no—
541C23×C4—1222no—
542C23×C4—1222no—
543C23×C4—1221no—
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—1222no—
559C22⋊Q8—1222no—
560C22⋊Q8—1222no—
561C22⋊Q8—1222no—
562#121—22no—
563#121—22no—
564#121—1222no—
565#121—1222no—
566#120—1228no—
567C4×D4—1228no—
568C4×D4—1228no—
569#117—614no—
570#117—1222no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—1222no—
575C2×C4⋊C4—1222no—
576C2×C4⋊C4—1222no—
577C2×C4⋊C4—1222no—
578C2×C4⋊C4—1221no—
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—1222no—
601#103—1222no—
602#103—1222no—
603#103—1222no—
604#102—22no—
605#102—22no—
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—21no—
617C24—611no—
618C24—611no—
619C24—1222no—
620C24—1222no—
621C24—1222no—
622C24—1222no—
623C24—1222no—
624C24—2441no—
625C24—2441no—
626C24D4×D6111yescharacteristic
627#41—1228no—
628#41—1228no—
629#41—2444no—
630#41—2444no—
631C2×Q8—612no—
632C2×Q8—1221no—
633C2×Q8—1221no—
634C2×Q8—1221no—
635C2×Q8—1221no—
636C2×Q8—1221no—
637C2×D4—24no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—1224no—
646C2×D4—1224no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4D4×D6112yes—
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—611no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—612no—
668C22×C4—611no—
669C22×C4—1222no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4—1224no—
677C22×C4—1222no—
678C22×C4—1222no—
679C22×C4—1221no—
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—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—612no—
723C4⋊C4—1224no—
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—22no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—612no—
757C23—612no—
758C23—612no—
759C23—612no—
760C23—1228no—
761C23—1221no—
762C23—1221no—
763C23—1221no—
764C23—1221no—
765C23—1221no—
766C23—1221no—
767C23—1221no—
768C23—1221no—
769C23—1221no—
770C23—1221no—
771C23—2444no—
772C23—2444no—
773C23—2444no—
774C23—2444no—
775C23—2444no—
776C23—2444no—
777C23#1451980112yes—
778C23C2×D4×D6111yescharacteristic
779Q8—1222no—
780Q8—1222no—
781Q8—2441no—
782Q8—2441no—
783D4—22no—
784D4—22no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—2448no—
789D4—2448no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—41no—
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—612no—
807C2×C4—612no—
808C2×C4—612no—
809C2×C4—614no—
810C2×C4—614no—
811C2×C4—614no—
812C2×C4—614no—
813C2×C4—1222no—
814C2×C4—1221no—
815C2×C4—1222no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—4884no—
819C2×C4—4884no—
820C2×C4—2444no—
821C2×C4—2444no—
822C2×C4—2444no—
823C2×C4—2448no—
824C2×C4—2441no—
825C2×C4—2441no—
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—42no—
856C22—42no—
857C22—42no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—614no—
863C22—1222no—
864C22—1222no—
865C22—1222no—
866C22—1222no—
867C22—1222no—
868C22—1222no—
869C22—1222no—
870C22—1222no—
871C22—1222no—
872C22—24416no—
873C22—2441no—
874C22—2441no—
875C22—2441no—
876C22—2441no—
877C22#120×D6111yescharacteristic
878C22#121×D6111yescharacteristic
879C22#123×D6111yescharacteristic
880C22C2×#1451980111yescharacteristic
881C22#137×D6111yescharacteristic
882C22#1684055811yescharacteristic
883C22#1684055911yescharacteristic
884C4—41no—
885C4—42no—
886C4—81no—
887C4—81no—
888C4—614no—
889C4—4881no—
890C4—4881no—
891C4—2441no—
892C4—2442no—
893C4—2442no—
894C4#121×D6111yescharacteristic
895C4#121×D6111yescharacteristic
896C4#123×D6111yescharacteristic
897C4#124×D6111yescharacteristic
898C2—42no—
899C2—82no—
900C2—1224no—
901C2—2442no—
902C2#394×D6111yescharacteristic
903C2#2145506611yescharacteristic
904C2#2145507611yescharacteristic
905C2#2145543511yescharacteristic
906C2#2145544411yescharacteristic
907C2#2145573811yescharacteristic
908C2#2145574711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2033C2
socleC23×C61C22×D4
prime radicalC2×#16840272C2
hypercenter#2033D61
hypocenterC61#23482
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
2. C2×#16839803C2semidirect
3. C2×#16839760C2semidirect
4. C2×#16839760C2semidirect
5. C2×#16839724C2semidirect
6. #380×D61C2semidirect
7. #21447025C2semidirect
8. #21447024C2semidirect
9. #21447016C2semidirect
10. #21447015C2semidirect
11. #21447007C2semidirect
12. #21447006C2semidirect
13. #21446998C2semidirect
14. #21445537C2semidirect
15. C61×#2033C2semidirect
34. C2×#14519710C22semidirect
35. C2×#14519709C22semidirect
36. C2×#14519708C22semidirect
39. C2×#14519702C22semidirect
40. C2×#14519702C22semidirect
41. C2×#14519700C22semidirect
42. C2×#14519700C22semidirect
43. C2×#14519698C22semidirect
44. C2×#14519698C22semidirect
55. #16839525C22semidirect
56. #16839524C22semidirect
57. #16839524C22semidirect
59. C2×#107×C61C22semidirect
60. C2×#102×C61C22semidirect
61. C2×#102×C61C22semidirect
64. C61×#340C22semidirect
94. C2×#11758189D4semidirect
457. #2033D61semidirect
490. C2×#107C2×D61semidirect
501. C2×#102C2×D61semidirect
502. C2×#102C2×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×#168402722
C2×#168398032
C2×#168397602
C2×#168397242
#380×D612
#214470252
#214470242
#214470162
#214470152
#214470072
#214470062
#214469982
#214455372
C61×#20332
#2348261