Finite Group Databasebeta

← #29646118

Subgroups — #29646118

Order 15616.

1406 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840270C211yesmaximal, characteristic
2C2×#16839724C211yesmaximal, characteristic, complemented
3#407×D61C211yesmaximal, characteristic, complemented
4#21444181C212yesmaximal, complemented
5#21444177C212yesmaximal, complemented
6#21444168C211yesmaximal, characteristic, complemented
7#21444167C211yesmaximal, characteristic, complemented
8#21444165C211yesmaximal, characteristic, complemented
9#21444156C212yesmaximal, complemented
10#21444154C212yesmaximal, complemented
11C61×#1468C211yesmaximal, characteristic, complemented
12C22×#11758224C411yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C22×#11758189—21no—
15C2×M16×D61—21no—
16#16840270—21no—
17#16840270—21no—
18#16840270—21no—
19#16840270—21no—
20#16840270—21no—
21#16840270—21no—
22#16840270—21no—
23#16840270—21no—
24C2×#14519760C2211yescharacteristic
25C2×#14519755C411yescharacteristic
26C2×#14519755C2211yescharacteristic
27C2×#14519750C411yescharacteristic
28C2×#14519750C2211yescharacteristic
29C2×#14519747C411yescharacteristic
30C2×#14519745C411yescharacteristic
31C2×#14519739C411yescharacteristic
32C2×#14519739C2211yescharacteristic
33C2×#14519737C411yescharacteristic
34C2×#14519737C2211yescharacteristic
35C2×#14519733C411yescharacteristic
36#16839726C2211yescharacteristic
37#16839725—21no—
38#16839724—21no—
39#16839724—21no—
40#16839724—21no—
41#16839724C2212yes—
42#16839724C2212yes—
43#16839724C2212yes—
44C2×C22⋊#92418C2211yescharacteristic
45C2×#14519689—21no—
46C22⋊C8×D61—21no—
47C22⋊C8×D61C2212yes—
48#16839488C2212yescomplemented
49#16839487C2212yescomplemented
50#16839487C2212yescomplemented
51#16839486C2212yescomplemented
52#16839485C2212yescomplemented
53#16839485C2212yescomplemented
54C2×#123×C61C2211yescharacteristic
55C61×#407C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#324C2212yescomplemented
58C61×#323C2212yescomplemented
59C24×D61C2×C411yescharacteristic
60C2×#11758224—21no—
61C2×#11758224—21no—
62C2×#11758224—21no—
63C2×#11758224—21no—
64C2×#11758224—44no—
65C22×Dic122C2×C411yescharacteristic
66C22×D244C2×C411yescharacteristic
67C22×D244C2×C411yescharacteristic
68C22×C22⋊D61C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic
71C22×C22⋊D61C2×C411yescharacteristic
72C23×Dic61C2×C411yescharacteristic
73C23×Dic61C2×C411yescharacteristic
74C22×C4×D61—44no—
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C411yescharacteristic
77C22×C4×D61C2×C411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61D411yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C2×#11758194—21no—
89C2×#11758189—22no—
90C2×#11758189—22no—
91C2×#11758189—22no—
92C2×#11758189—44no—
93M16×D61—44no—
94C22×#92418—21no—
95C2×C8×D61—22no—
96#14519760—21no—
97#14519760—21no—
98#14519760—21no—
99#14519760—21no—
100#14519755—21no—
101#14519755—21no—
102#14519755—21no—
103#14519755—21no—
104#14519755—21no—
105#14519755—21no—
106#14519755—21no—
107#14519755—21no—
108#14519750—21no—
109#14519750—21no—
110#14519750—21no—
111#14519750—21no—
112#14519750—21no—
113#14519750—21no—
114#14519750—21no—
115#14519750—21no—
116#14519747—21no—
117#14519747—21no—
118#14519747—21no—
119#14519747—21no—
120#14519745—21no—
121#14519745—21no—
122#14519745—21no—
123#14519745—21no—
124#14519739—21no—
125#14519739—21no—
126#14519739—21no—
127#14519739—21no—
128#14519739—21no—
129#14519739—21no—
130#14519739—21no—
131#14519739—21no—
132#14519737—21no—
133#14519737—21no—
134#14519737—21no—
135#14519737—21no—
136#14519737—21no—
137#14519737—21no—
138#14519737—21no—
139#14519737—21no—
140#14519733—21no—
141#14519733—21no—
142#14519733—21no—
143#14519733—21no—
144C2×#11758196C2×C411yescharacteristic
145C2×#11758196C2×C411yescharacteristic
146C2×#11758196C2×C411yescharacteristic
147C2×#11758196C2311yescharacteristic
148C2×C22⋊Dic61C2×C411yescharacteristic
149C2×#11758198C2×C411yescharacteristic
150C2×#11758198C2×C411yescharacteristic
151C2×#11758198C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2311yescharacteristic
155C2×C4×Dic61C2×C411yescharacteristic
156C2×C4×Dic61C2×C411yescharacteristic
157C22⋊#92418—21no—
158C22⋊#92418—21no—
159C22⋊#92418C2312yes—
160C22⋊#92418C2312yes—
161#14519689—22no—
162#14519689—22no—
163#14519689—22no—
164#14519689—22no—
165C22×D4×C61C2×C411yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C2×M16×C61—21no—
168C22×C8×C61—21no—
169#123×C61—21no—
170#123×C61—21no—
171#123×C61—21no—
172#123×C61—21no—
173C2×C4⋊C4×C61C2×C411yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61C2×C411yescharacteristic
176C2×C22⋊C4×C61C2×C411yescharacteristic
177C2×C22⋊C4×C61C2311yescharacteristic
178C22⋊C8×C61—21no—
179C22⋊C8×C61—21no—
180C22⋊C8×C61C2312yes—
181C22⋊C8×C61C2312yes—
182C24×C61C22×C411yescharacteristic
183C24×C61C22×C411yescharacteristic
184C23×D61—42no—
185C23×D61—42no—
186C23×D61—42no—
187C23×D61C22⋊C411yescharacteristic
188C23×D61C22⋊C411yescharacteristic
189C23×D61C22⋊C411yescharacteristic
190C23×D61C22⋊C411yescharacteristic
191C23×D61C22×C411yescharacteristic
192C23×D61C22×C411yescharacteristic
193C23×D61C22×C411yescharacteristic
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—42no—
197C22×C4×C61—42no—
198C22×C4×C61C22×C411yescharacteristic
199C22×C4×C61C22×C411yescharacteristic
200C22×C4×C61C22×C411yescharacteristic
201C22×C4×C61C22×C411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—21no—
208C2×C22⋊D61—21no—
209C2×C22⋊D61—21no—
210C2×C22⋊D61—21no—
211C2×C22⋊D61—21no—
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—42no—
216C2×C22⋊D61—42no—
217C2×C22⋊D61—42no—
218C2×C22⋊D61—42no—
219C22×Dic61—24no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—42no—
223C22×Dic61C22⋊C411yescharacteristic
224C22×Dic61C22⋊C411yescharacteristic
225C22×Dic61C22⋊C411yescharacteristic
226C22×Dic61C22⋊C411yescharacteristic
227C22×Dic61C22×C411yescharacteristic
228C22×Dic61C22×C411yescharacteristic
229C22×Dic61C22×C411yescharacteristic
230C22×Dic61C22×C411yescharacteristic
231C22×Dic61C22×C411yescharacteristic
232#11758224—44no—
233#11758224—44no—
234#11758224—44no—
235#11758224—44no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244—42no—
241C2×D244—42no—
242C2×C4×D61—24no—
243C2×C4×D61—24no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—42no—
247C2×C4×D61—42no—
248C2×C4×D61—42no—
249C2×C4×D61—42no—
250C2×C4×D61—42no—
251C2×C4×D61—42no—
252C2×C4×D61—42no—
253C2×C4×D61—42no—
254C2×C4×D61—42no—
255C2×C4×D61—42no—
256C2×C4×D61—42no—
257C2×C4×D61C22⋊C411yescharacteristic
258C2×C4×D61C22⋊C411yescharacteristic
259C2×C4×D61C22⋊C411yescharacteristic
260C2×C4×D61C22⋊C411yescharacteristic
261C2×C4×D61C22⋊C411yescharacteristic
262C2×C4×D61C22⋊C411yescharacteristic
263C2×C4×D61C22⋊C411yescharacteristic
264C2×C4×D61C22⋊C411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×Dic122—21no—
274C2×Dic122—21no—
275C2×Dic122—42no—
276M16×C61—42no—
277C2×C8×C61—22no—
278C2×C8×C61—22no—
279C2×C8×C61—42no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316#11758194—42no—
317C2×#92418—22no—
318C2×#92418—22no—
319C2×#92418—42no—
320#11758189—44no—
321#11758189—44no—
322#11758189—44no—
323C8×D61—44no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—21no—
327C23×C61—22no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61C2×C22⋊C411yescharacteristic
332C23×C61C2×C22⋊C411yescharacteristic
333C23×C61C23×C411yescharacteristic
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—21no—
342C22×D61—22no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—416no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61C2×C22⋊C411yescharacteristic
358C22×D61C2×C22⋊C411yescharacteristic
359C22×D61C2×C22⋊C411yescharacteristic
360C22×D61C2×C22⋊C411yescharacteristic
361D4×C61—42no—
362D4×C61—42no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—22no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C22×D411yescharacteristic
378C2×C4×C61C22×D411yescharacteristic
379C22⋊D61—42no—
380C22⋊D61—42no—
381C22⋊D61—42no—
382C22⋊D61—42no—
383C22⋊D61—42no—
384C22⋊D61—42no—
385C22⋊D61—42no—
386C22⋊D61—42no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—22no—
396C2×Dic61—42no—
397C2×Dic61—42no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61#9914yes—
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C2×C22⋊C411yescharacteristic
405D244—42no—
406D244—42no—
407D244—42no—
408D244—42no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—42no—
426C4×D61—42no—
427Dic122—42no—
428Dic122—42no—
429C8×C61—42no—
430C8×C61—42no—
431#92418—42no—
432#92418—42no—
433#17400—611nomaximal, Sylow
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—21no—
438C22×C61—21no—
439C22×C61—21no—
440C22×C61—21no—
441C22×C61—44no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—82no—
446C22×C61C2×#9912yes—
447C22×C61C22×C22⋊C411yescharacteristic
448C22×C61#56812yes—
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—21no—
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—21no—
458C2×D61—21no—
459C2×D61—21no—
460C2×D61—44no—
461C2×D61—44no—
462C2×D61—44no—
463C2×D61—44no—
464C2×D61—44no—
465C2×D61—44no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—82no—
470C2×D61#41312yes—
471C4×C61—21no—
472C4×C61—21no—
473C4×C61—21no—
474C4×C61—21no—
475C4×C61—41no—
476C4×C61—41no—
477C4×C61—41no—
478Dic61—21no—
479Dic61—21no—
480Dic61—41no—
481Dic61—41no—
482Dic61—41no—
483Dic61C2×#9912yes—
484Dic61C2×#9912yes—
485C2×#525—611no—
486C2×#407—611no—
487C2×#407—611no—
488#1472—612no—
489#1471—612no—
490#1468—611no—
491#1468—611no—
492#1468—611no—
493#1468D6111yescharacteristic, complemented
494#1465—612no—
495#1465—612no—
496C2×C61—22no—
497C2×C61—22no—
498C2×C61—41no—
499C2×C61—81no—
500C2×C61#287911yescharacteristic
501C2×C61C22×#9911yescharacteristic
502C2×C61C2×#41311yescharacteristic
503D61—22no—
504D61—41no—
505D61—41no—
506D61—41no—
507D61—81no—
508C22×#41—611no—
509C24×C4—611no—
510C22×M16—1221no—
511C22×M16—1221no—
512#525—1221no—
513#525—1221no—
514#525—1221no—
515#525—1221no—
516#525—1221no—
517#525—1221no—
518#525—1221no—
519#525—1221no—
520C2×#123—611no—
521C2×#123C2×D6111yescharacteristic
522C2×C22⋊Q8—611no—
523C2×C22⋊Q8—611no—
524C2×#121—611no—
525C2×#121—611no—
526C2×#120—611no—
527C2×#120—611no—
528C2×C4×D4—611no—
529C2×C4×D4—611no—
530C2×C4×D4—611no—
531C2×C4×D4—611no—
532C2×#117—611no—
533#407—611no—
534#407—612no—
535#407—612no—
536#407—612no—
537#407—1221no—
538#407—1221no—
539#407—1221no—
540#407—1221no—
541#407C2×D6111yescharacteristic
542C2×C22⋊C8—611no—
543C2×C22⋊C8—612no—
544C2×C22⋊C8—1221no—
545C2×C22⋊C8—1221no—
546C2×C22⋊C8C2×D6111yescharacteristic
547#324—612no—
548#324—612no—
549#324—612no—
550#324C2×D6112yescomplemented
551#323—612no—
552#323—612no—
553#323—612no—
554#323C2×D6112yescomplemented
555C61#1740011yescharacteristic, complemented, Sylow
556C25—611no—
557C2×#41—1221no—
558C2×#41—1221no—
559C2×#41—1221no—
560C2×#41—1221no—
561C2×#41—2444no—
562C22×Q8—611no—
563C22×D4—611no—
564C22×D4—611no—
565C22×D4—611no—
566C22×D4—611no—
567C22×D4—611no—
568C22×D4—611no—
569C22×D4C4×D6111yescharacteristic
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—611no—
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—611no—
585C23×C4—2444no—
586C23×C4C22×D6111yescharacteristic
587C2×M16—21no—
588C2×M16—1222no—
589C2×M16—1222no—
590C2×M16—1222no—
591C2×M16—1221no—
592C2×M16—2444no—
593C2×M16—2444no—
594C22×C8—21no—
595C22×C8—1222no—
596C22×C8—1221no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—1221no—
602#123—1221no—
603#123—1221no—
604#123—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8—1221no—
609C22⋊Q8—1221no—
610C22⋊Q8—1221no—
611C22⋊Q8—1221no—
612C22⋊Q8—1221no—
613#121—1221no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#120—1221no—
622#120—1221no—
623#120—1221no—
624#120—1221no—
625#120—1221no—
626#120—1221no—
627#120—1221no—
628#120—1221no—
629C4×D4—1221no—
630C4×D4—1221no—
631C4×D4—1221no—
632C4×D4—1221no—
633C4×D4—1221no—
634C4×D4—1221no—
635C4×D4—1221no—
636C4×D4—1221no—
637C4×D4—1221no—
638C4×D4—1221no—
639C4×D4—1221no—
640C4×D4—1221no—
641C4×D4—1221no—
642C4×D4—1221no—
643C4×D4—1221no—
644C4×D4—1221no—
645#117—1221no—
646#117—1221no—
647#117—1221no—
648#117—1221no—
649C2×C4⋊C4—611no—
650C2×C4⋊C4—611no—
651C2×C4⋊C4—611no—
652C2×C4⋊C4—611no—
653C2×C4⋊C4C4×D6111yescharacteristic
654C2×C4⋊C4C22×D6111yescharacteristic
655C2×C22⋊C4—611no—
656C2×C22⋊C4—611no—
657C2×C22⋊C4—611no—
658C2×C22⋊C4—611no—
659C2×C22⋊C4—611no—
660C2×C22⋊C4—611no—
661C2×C22⋊C4—611no—
662C2×C22⋊C4C4×D6111yescharacteristic
663C2×C22⋊C4C4×D6111yescharacteristic
664C2×C22⋊C4C22×D6111yescharacteristic
665C2×C42—611no—
666C2×C42—611no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8—612no—
670C22⋊C8—612no—
671C22⋊C8—1222no—
672C22⋊C8—1222no—
673C22⋊C8—1222no—
674C22⋊C8—1222no—
675C22⋊C8—1221no—
676C22⋊C8—1221no—
677C22⋊C8C22×D6112yes—
678C22⋊C8C22×D6112yes—
679C24—611no—
680C24—611no—
681C24—611no—
682C24—611no—
683C24—611no—
684C24—611no—
685C24—611no—
686C24—2442no—
687C24—2442no—
688C24—2442no—
689C24C2×C4×D6111yescharacteristic
690C24C2×C4×D6111yescharacteristic
691#41—2444no—
692#41—2444no—
693#41—2444no—
694#41—2444no—
695C2×Q8—1221no—
696C2×Q8—1221no—
697C2×Q8—2442no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—42no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—1221no—
706C2×D4—1221no—
707C2×D4—1221no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—2442no—
714C2×D4—2442no—
715C2×D4—2442no—
716C2×D4—2442no—
717C2×D4—2442no—
718C2×D4—2442no—
719C22×C4—42no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—611no—
744C22×C4—611no—
745C22×C4—1224no—
746C22×C4—1224no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1224no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—2442no—
753C22×C4—2442no—
754C22×C4—2442no—
755C22×C4—2442no—
756C22×C4—2442no—
757C22×C4—2442no—
758C22×C4—2442no—
759C22×C4—2442no—
760C22×C4—2442no—
761C22×C4—2442no—
762C22×C4—2442no—
763C22×C4—2442no—
764C22×C4C2×C4×D6111yescharacteristic
765C22×C4C2×C4×D6111yescharacteristic
766C22×C4C2×C4×D6111yescharacteristic
767C22×C4C2×C4×D6111yescharacteristic
768C22×C4D4×D6111yescharacteristic
769C22×C4D4×D6111yescharacteristic
770C22×C4D4×D6111yescharacteristic
771C22×C4D4×D6111yescharacteristic
772C22×C4C23×D6111yescharacteristic
773M16—42no—
774M16—2444no—
775M16—2444no—
776M16—2444no—
777M16—2442no—
778C2×C8—22no—
779C2×C8—22no—
780C2×C8—42no—
781C2×C8—1222no—
782C2×C8—1222no—
783C2×C8—2444no—
784C2×C8—2442no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—1221no—
790C4⋊C4—1221no—
791C4⋊C4—1221no—
792C4⋊C4—1221no—
793C4⋊C4—1221no—
794C4⋊C4—1221no—
795C4⋊C4—1221no—
796C4⋊C4—1221no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C22⋊C4—1221no—
815C22⋊C4—1221no—
816C22⋊C4—1221no—
817C42—1221no—
818C42—1221no—
819C42—1221no—
820C42—1221no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—22no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—611no—
829C23—611no—
830C23—611no—
831C23—611no—
832C23—1222no—
833C23—1222no—
834C23—1222no—
835C23—1222no—
836C23—1222no—
837C23—1222no—
838C23—1222no—
839C23—1222no—
840C23—1221no—
841C23—2441no—
842C23—2441no—
843C23—2441no—
844C23—2441no—
845C23—2441no—
846C23—2441no—
847C23—2441no—
848C23—2441no—
849C23—2441no—
850C23—2441no—
851C23—2441no—
852C23—2441no—
853C23—2441no—
854C23—24416no—
855C23C22⋊C4×D6111yescharacteristic
856C23C22⋊C4×D6111yescharacteristic
857C23C22×C4×D6111yescharacteristic
858Q8—2442no—
859Q8—2442no—
860D4—42no—
861D4—42no—
862D4—2442no—
863D4—2442no—
864D4—2442no—
865D4—2442no—
866D4—2442no—
867D4—2442no—
868D4—2442no—
869D4—2442no—
870D4—2442no—
871D4—2442no—
872D4—2442no—
873D4—2442no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—611no—
887C2×C4—611no—
888C2×C4—614no—
889C2×C4—611no—
890C2×C4—611no—
891C2×C4—1222no—
892C2×C4—1222no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—1222no—
897C2×C4—1222no—
898C2×C4—1222no—
899C2×C4—1222no—
900C2×C4—1222no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—1221no—
905C2×C4—1221no—
906C2×C4—1221no—
907C2×C4—1222no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2442no—
917C2×C4—2442no—
918C2×C4—2442no—
919C2×C4—2442no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4C22⋊C4×D6111yescharacteristic
923C2×C4C22⋊C4×D6111yescharacteristic
924C2×C4C2×D4×D6111yescharacteristic
925C2×C4C2×D4×D6111yescharacteristic
926C8—42no—
927C8—42no—
928C8—2442no—
929C8—2442no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—21no—
935C22—21no—
936C22—21no—
937C22—44no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—82no—
942C22—612no—
943C22—1221no—
944C22—1221no—
945C22—1221no—
946C22—1221no—
947C22—1221no—
948C22—1221no—
949C22—1221no—
950C22—1221no—
951C22—1221no—
952C22—1221no—
953C22—1221no—
954C22—4882no—
955C22—2444no—
956C22—2444no—
957C22—2444no—
958C22—2444no—
959C22—2444no—
960C22—2444no—
961C22—2441no—
962C22—2441no—
963C22—2441no—
964C22#99×D6112yes—
965C22C2×C22⋊C4×D6111yescharacteristic
966C22#1684052712yes—
967C4—21no—
968C4—21no—
969C4—21no—
970C4—21no—
971C4—41no—
972C4—41no—
973C4—41no—
974C4—612no—
975C4—612no—
976C4—1221no—
977C4—1221no—
978C4—2441no—
979C4—2441no—
980C4—2441no—
981C2—22no—
982C2—22no—
983C2—41no—
984C2—81no—
985C2—1222no—
986C2—4881no—
987C2—2441no—
988C2—2441no—
989C2—2441no—
990C2#2145426111yescharacteristic
991C2C2×#99×D6111yescharacteristic
992C2#413×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1468C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840270C2
cosocleC22×C4×C61C24
hypercenter#1468D61
hypocenterC61#17400
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1468

Complements

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

NH ≅ G/Ntype
2. C2×#16839724C2semidirect
3. #407×D61C2semidirect
4. #21444181C2semidirect
5. #21444177C2semidirect
6. #21444168C2semidirect
7. #21444167C2semidirect
8. #21444165C2semidirect
9. #21444156C2semidirect
10. #21444154C2semidirect
11. C61×#1468C2semidirect
48. #16839488C22semidirect
49. #16839487C22semidirect
50. #16839487C22semidirect
51. #16839486C22semidirect
52. #16839485C22semidirect
53. #16839485C22semidirect
57. C61×#324C22semidirect
58. C61×#323C22semidirect
493. #1468D61semidirect
550. #324C2×D61semidirect
554. #323C2×D61semidirect
555. C61#17400semidirect

Maximal subgroups

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

subgroupindex
C2×#168402702
C2×#168397242
#407×D612
#214441812
#214441772
#214441682
#214441672
#214441652
#214441562
#214441542
C61×#14682
#1740061