Finite Group Databasebeta

← #29685351

Subgroups — #29685351

Order 15616.

1678 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840268C211yesmaximal, characteristic
2#21448197C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
4#21446802C212yesmaximal, complemented
5#21446653C212yesmaximal, complemented
6#21446273C211yesmaximal, characteristic, complemented
7#21446272C211yesmaximal, characteristic, complemented
8#21446270C211yesmaximal, characteristic, complemented
9#99×Dic61C212yesmaximal, complemented
10#21445606C212yesmaximal, complemented
11C61×#1898C211yesmaximal, characteristic, complemented
12C22×#11758224C411yescharacteristic, complemented
13C24×Dic61C2211yescharacteristic
14#16840268—21no—
15#16840268—21no—
16#16840268—21no—
17#16840268—21no—
18#16840268—21no—
19#16840268—21no—
20#16840268—21no—
21#16840268—21no—
22C2×#14519761C411yescharacteristic, complemented
23C2×#14519758C411yescharacteristic, complemented
24C2×#14519754C411yescharacteristic, complemented
25C2×#14519754C2211yescharacteristic
26C2×#14519749C411yescharacteristic, complemented
27C2×#14519749C2211yescharacteristic
28C2×#14519746C2211yescharacteristic
29C2×D4×Dic61C411yescharacteristic, complemented
30C2×D4×Dic61C2211yescharacteristic
31C2×#14519737C411yescharacteristic, complemented
32C2×#14519737C2211yescharacteristic
33C2×#14519733—21no—
34C2×#14519733C411yescharacteristic, complemented
35C22×C22⋊Dic61C2211yescharacteristic
36C22×C4×Dic61—21no—
37C2×#14519692C2212yes—
38C2×#14519691C2212yes—
39C2×#14519691C2212yes—
40#16839623—21no—
41#16839620—21no—
42#16839620C2212yes—
43#16839618C2211yescharacteristic
44C22⋊C4×Dic61—21no—
45C22⋊C4×Dic61—21no—
46C22⋊C4×Dic61—21no—
47C22⋊C4×Dic61C2212yes—
48C22⋊C4×Dic61C2212yes—
49C22⋊C4×Dic61C2212yes—
50C2×#14519684—21no—
51#16839529C2212yes—
52#16839528C2212yes—
53#16839528C2212yes—
54C2×#120×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C2×#99×C61C2212yes—
57C61×#379C2211yescharacteristic
58C61×#342C2212yes—
59C2×#11758224—21no—
60C2×#11758224—21no—
61C2×#11758224—21no—
62C2×#11758224—21no—
63C2×#11758224—44no—
64C22×Dic122C2×C411yescharacteristic, complemented
65C22×C22⋊D61C2×C411yescharacteristic
66C22×C22⋊D61C2×C411yescharacteristic
67C22×C22⋊D61C2×C411yescharacteristic, complemented
68C22×C22⋊D61C2311yescharacteristic
69C23×Dic61—21no—
70C23×Dic61—44no—
71C23×Dic61C2×C411yescharacteristic
72C23×Dic61C2×C411yescharacteristic
73C23×Dic61C2×C411yescharacteristic
74C23×Dic61C2×C411yescharacteristic
75C23×Dic61C2×C411yescharacteristic, complemented
76C23×Dic61D411yescharacteristic
77C23×Dic61D411yescharacteristic
78C23×Dic61D411yescharacteristic
79C23×Dic61D411yescharacteristic
80C23×Dic61D411yescharacteristic
81C23×Dic61D411yescharacteristic
82C23×Dic61D411yescharacteristic
83C23×Dic61D411yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C22×C4×D61C2×C411yescharacteristic, complemented
87#14519761—21no—
88#14519761—21no—
89#14519761—21no—
90#14519761—21no—
91#14519758—21no—
92#14519758—21no—
93#14519758—21no—
94#14519758—21no—
95#14519754—21no—
96#14519754—21no—
97#14519754—21no—
98#14519754—21no—
99#14519754—21no—
100#14519754—21no—
101#14519754—21no—
102#14519754—21no—
103#14519749—21no—
104#14519749—21no—
105#14519749—21no—
106#14519749—21no—
107#14519749—21no—
108#14519749—21no—
109#14519749—21no—
110#14519749—21no—
111#14519746—21no—
112#14519746—21no—
113#14519746—21no—
114#14519746—21no—
115D4×Dic61—21no—
116D4×Dic61—21no—
117D4×Dic61—21no—
118D4×Dic61—21no—
119D4×Dic61—21no—
120D4×Dic61—21no—
121D4×Dic61—21no—
122D4×Dic61—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519737—21no—
127#14519737—21no—
128#14519737—21no—
129#14519737—21no—
130#14519737—21no—
131#14519733—21no—
132#14519733—21no—
133#14519733—21no—
134#14519733—21no—
135#14519733—44no—
136C2×C4⋊Dic61C2×C411yescharacteristic, complemented
137C2×C4⋊Dic61C2×C411yescharacteristic, complemented
138C2×#11758196—22no—
139C2×#11758196C2×C411yescharacteristic, complemented
140C2×#11758196C2×C411yescharacteristic, complemented
141C2×#11758196C2×C411yescharacteristic, complemented
142C2×#11758196C2×C411yescharacteristic, complemented
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—24no—
145C2×C22⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61C2×C411yescharacteristic
148C2×C22⋊Dic61C2×C411yescharacteristic
149C2×C22⋊Dic61C2×C411yescharacteristic, complemented
150C2×C22⋊Dic61C2×C411yescharacteristic, complemented
151C2×C22⋊Dic61C2312yes—
152C2×C22⋊Dic61C2311yescharacteristic
153C2×C22⋊Dic61C2312yes—
154C2×#11758198C2×C411yescharacteristic, complemented
155C2×#11758198C2×C411yescharacteristic, complemented
156C2×C4×Dic61—22no—
157C2×C4×Dic61—22no—
158C2×C4×Dic61—22no—
159C2×C4×Dic61—44no—
160C2×C4×Dic61C2×C411yescharacteristic, complemented
161C2×C4×Dic61C2×C411yescharacteristic, complemented
162#14519692—24no—
163#14519691—24no—
164#14519691—24no—
165#14519684—22no—
166#14519684—22no—
167#14519684—22no—
168#14519684—22no—
169C25×C61C2311yescharacteristic
170C22×D4×C61C2×C411yescharacteristic
171C22×D4×C61C2×C411yescharacteristic
172C22×D4×C61C2311yescharacteristic
173C23×C4×C61—21no—
174#120×C61—21no—
175#120×C61—21no—
176#120×C61—21no—
177#120×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—24no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61C2×C411yescharacteristic
183C2×C22⋊C4×C61C2×C411yescharacteristic
184C2×C22⋊C4×C61C2312yes—
185C2×C22⋊C4×C61C2311yescharacteristic
186C2×C22⋊C4×C61C2312yes—
187#99×C61—24no—
188C24×C61—22no—
189C24×C61—22no—
190C24×C61—42no—
191C24×C61—42no—
192C24×C61C22×C411yescharacteristic
193C24×C61C22×C411yescharacteristic
194C24×C61C22×C411yescharacteristic
195C24×C61C2×D411yescharacteristic
196C24×C61C2×D411yescharacteristic
197C24×C61C2×D411yescharacteristic
198C24×C61C2×D411yescharacteristic
199C24×C61C2411yescharacteristic
200C23×D61C22×C411yescharacteristic
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—22no—
208C2×D4×C61—22no—
209C2×D4×C61—42no—
210C2×D4×C61—42no—
211C22×C4×C61—24no—
212C22×C4×C61—22no—
213C22×C4×C61—22no—
214C22×C4×C61—42no—
215C22×C4×C61—42no—
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—22no—
226C2×C22⋊D61—22no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—42no—
230C2×C22⋊D61—42no—
231C2×C22⋊D61—42no—
232C22×Dic61—24no—
233C22×Dic61—24no—
234C22×Dic61—24no—
235C22×Dic61—24no—
236C22×Dic61—22no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—22no—
240C22×Dic61—42no—
241C22×Dic61—42no—
242C22×Dic61—42no—
243C22×Dic61—42no—
244C22×Dic61—42no—
245C22×Dic61—42no—
246C22×Dic61—42no—
247C22×Dic61—42no—
248C22×Dic61—42no—
249C22×Dic61—42no—
250C22×Dic61—42no—
251C22×Dic61—42no—
252C22×Dic61—42no—
253C22×Dic61—42no—
254C22×Dic61C22⋊C411yescharacteristic
255C22×Dic61C22⋊C411yescharacteristic
256C22×Dic61C22⋊C411yescharacteristic
257C22×Dic61C22⋊C411yescharacteristic
258C22×Dic61C22⋊C411yescharacteristic
259C22×Dic61C22⋊C411yescharacteristic
260C22×Dic61C22⋊C411yescharacteristic
261C22×Dic61C22⋊C411yescharacteristic
262C22×Dic61C22⋊C411yescharacteristic
263C22×Dic61C22⋊C411yescharacteristic
264C22×Dic61C22⋊C411yescharacteristic
265C22×Dic61C22⋊C411yescharacteristic
266C22×Dic61C22⋊C411yescharacteristic
267C22×Dic61C22⋊C411yescharacteristic
268C22×Dic61C22⋊C411yescharacteristic
269C22×Dic61C22⋊C411yescharacteristic
270C22×Dic61C22×C411yescharacteristic
271C22×Dic61C22×C411yescharacteristic
272C22×Dic61C22×C411yescharacteristic
273C22×Dic61C22×C411yescharacteristic
274C22×Dic61C22×C411yescharacteristic
275C22×Dic61C22×C411yescharacteristic
276C22×Dic61C22×C411yescharacteristic
277C22×Dic61C2×D411yescharacteristic
278C22×Dic61C2×D411yescharacteristic
279C22×Dic61C2×D411yescharacteristic
280C22×Dic61C2×D411yescharacteristic
281C22×Dic61C2×D411yescharacteristic
282C22×Dic61C2×D411yescharacteristic
283C22×Dic61C2×D411yescharacteristic
284C22×Dic61C2×D411yescharacteristic
285#11758224—44no—
286#11758224—44no—
287#11758224—44no—
288#11758224—44no—
289C2×C4×D61—21no—
290C2×C4×D61—21no—
291C2×C4×D61—42no—
292C2×Dic122—21no—
293C2×Dic122—21no—
294C2×Dic122—42no—
295C22⋊C4×C61—24no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C22⋊C4×C61—21no—
300C22⋊C4×C61—21no—
301C22⋊C4×C61—21no—
302C22⋊C4×C61—22no—
303C22⋊C4×C61—22no—
304C22⋊C4×C61—22no—
305C22⋊C4×C61—42no—
306C22⋊C4×C61—42no—
307C22⋊C4×C61#4114yescomplemented
308C22⋊Dic61—24no—
309C22⋊Dic61—21no—
310C22⋊Dic61—21no—
311C22⋊Dic61—21no—
312C22⋊Dic61—21no—
313C22⋊Dic61—21no—
314C22⋊Dic61—21no—
315C22⋊Dic61—22no—
316C22⋊Dic61—21no—
317C22⋊Dic61—21no—
318C22⋊Dic61—21no—
319C22⋊Dic61—21no—
320C22⋊Dic61—22no—
321C22⋊Dic61—22no—
322C22⋊Dic61—42no—
323C22⋊Dic61—42no—
324C22⋊Dic61#4114yescomplemented
325#11758198—21no—
326#11758198—21no—
327#11758198—21no—
328#11758198—21no—
329C4⋊Dic61—21no—
330C4⋊Dic61—21no—
331C4⋊Dic61—21no—
332C4⋊Dic61—21no—
333#11758196—21no—
334#11758196—21no—
335#11758196—21no—
336#11758196—21no—
337#11758196—21no—
338#11758196—21no—
339#11758196—21no—
340#11758196—21no—
341#11758196—44no—
342C4×Dic61—21no—
343C4×Dic61—21no—
344C4×Dic61—21no—
345C4×Dic61—21no—
346C4×Dic61—44no—
347C4×Dic61—44no—
348C4×Dic61—44no—
349C23×C61—21no—
350C23×C61—21no—
351C23×C61—22no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—22no—
355C23×C61—21no—
356C23×C61—21no—
357C23×C61—22no—
358C23×C61—22no—
359C23×C61—22no—
360C23×C61—22no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—21no—
364C23×C61—22no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—48no—
374C23×C61—48no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61C2×C22⋊C411yescharacteristic
378C23×C61C2×C22⋊C411yescharacteristic
379C23×C61C2×C22⋊C411yescharacteristic
380C23×C61C2×C22⋊C411yescharacteristic
381C23×C61C23×C411yescharacteristic
382C23×C61C22×D411yescharacteristic
383C23×C61C22×D411yescharacteristic
384C23×C61C2×#4112yes—
385C23×C61C2×#4112yes—
386C22×D61—21no—
387C22×D61—22no—
388C22×D61—41no—
389C22×D61—41no—
390D4×C61—42no—
391D4×C61—42no—
392D4×C61—41no—
393D4×C61—41no—
394D4×C61—42no—
395D4×C61—42no—
396D4×C61—42no—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—21no—
400C2×C4×C61—22no—
401C2×C4×C61—24no—
402C2×C4×C61—42no—
403C2×C4×C61—48no—
404C2×C4×C61—42no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—42no—
408C2×C4×C61—42no—
409C2×C4×C61—42no—
410C22⋊D61—42no—
411C22⋊D61—42no—
412C22⋊D61—42no—
413C22⋊D61—41no—
414C22⋊D61—41no—
415C22⋊D61—42no—
416C22⋊D61—42no—
417C22⋊D61—42no—
418C22⋊D61—42no—
419C2×Dic61—22no—
420C2×Dic61—22no—
421C2×Dic61—22no—
422C2×Dic61—22no—
423C2×Dic61—22no—
424C2×Dic61—22no—
425C2×Dic61—22no—
426C2×Dic61—22no—
427C2×Dic61—22no—
428C2×Dic61—22no—
429C2×Dic61—22no—
430C2×Dic61—22no—
431C2×Dic61—22no—
432C2×Dic61—22no—
433C2×Dic61—22no—
434C2×Dic61—21no—
435C2×Dic61—21no—
436C2×Dic61—21no—
437C2×Dic61—22no—
438C2×Dic61—24no—
439C2×Dic61—41no—
440C2×Dic61—41no—
441C2×Dic61—41no—
442C2×Dic61—41no—
443C2×Dic61—41no—
444C2×Dic61—41no—
445C2×Dic61—41no—
446C2×Dic61—41no—
447C2×Dic61—41no—
448C2×Dic61—41no—
449C2×Dic61—41no—
450C2×Dic61—41no—
451C2×Dic61—42no—
452C2×Dic61—42no—
453C2×Dic61—48no—
454C2×Dic61—42no—
455C2×Dic61—42no—
456C2×Dic61—41no—
457C2×Dic61—41no—
458C2×Dic61—42no—
459C2×Dic61—42no—
460C2×Dic61—42no—
461C2×Dic61#9914yescomplemented
462C2×Dic61C2×C22⋊C411yescharacteristic
463C2×Dic61C2×C22⋊C411yescharacteristic
464C2×Dic61C2×C22⋊C411yescharacteristic
465C2×Dic61C2×C22⋊C411yescharacteristic
466C2×Dic61C2×C22⋊C411yescharacteristic
467C2×Dic61C2×C22⋊C411yescharacteristic
468C2×Dic61C2×C22⋊C411yescharacteristic
469C2×Dic61C2×C22⋊C411yescharacteristic
470C4×D61—42no—
471C4×D61—42no—
472Dic122—42no—
473Dic122—42no—
474#21420—611nomaximal, Sylow
475C22×C61—24no—
476C22×C61—24no—
477C22×C61—21no—
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—21no—
481C22×C61—21no—
482C22×C61—21no—
483C22×C61—21no—
484C22×C61—21no—
485C22×C61—21no—
486C22×C61—21no—
487C22×C61—21no—
488C22×C61—21no—
489C22×C61—21no—
490C22×C61—21no—
491C22×C61—21no—
492C22×C61—21no—
493C22×C61—42no—
494C22×C61—42no—
495C22×C61—44no—
496C22×C61—44no—
497C22×C61—44no—
498C22×C61—44no—
499C22×C61—42no—
500C22×C61—42no—
501C22×C61—41no—
502C22×C61—41no—
503C22×C61—41no—
504C22×C61—82no—
505C22×C61C2×#9912yes—
506C22×C61#41012yes—
507C22×C61C22×C22⋊C411yescharacteristic
508C22×C61C4×#4112yes—
509C22×C61#52511yescharacteristic
510C22×C61#52511yescharacteristic
511C22×C61#53212yes—
512C2×D61—41no—
513C2×D61—41no—
514C2×D61—41no—
515C2×D61—82no—
516C4×C61—44no—
517C4×C61—41no—
518C4×C61—41no—
519C4×C61—41no—
520C4×C61—82no—
521Dic61—21no—
522Dic61—21no—
523Dic61—21no—
524Dic61—21no—
525Dic61—21no—
526Dic61—21no—
527Dic61—44no—
528Dic61—41no—
529Dic61—41no—
530Dic61—41no—
531Dic61—82no—
532Dic61C2×#9912yes—
533Dic61C2×#9912yes—
534C2×#525—611no—
535#2280—611no—
536C2×C4×C22⋊C4—611no—
537#1996—612no—
538#1964—612no—
539#1898—611no—
540#1898—611no—
541#1898—611no—
542#1898D6111yescharacteristic, complemented
543C4×#99—612no—
544C4×#99—612no—
545C2×C61—21no—
546C2×C61—22no—
547C2×C61—21no—
548C2×C61—22no—
549C2×C61—22no—
550C2×C61—22no—
551C2×C61—41no—
552C2×C61—41no—
553C2×C61—81no—
554C2×C61#229711yescharacteristic
555C2×C61C22×#9911yescharacteristic
556C2×C61C2×#41011yescharacteristic
557D61—81no—
558C22×#41—611no—
559C24×C4—611no—
560#525—1221no—
561#525—1221no—
562#525—1221no—
563#525—1221no—
564#525—1221no—
565#525—1221no—
566#525—1221no—
567#525—1221no—
568C2×#123—611no—
569C2×#123—611no—
570C2×C22⋊Q8—611no—
571C2×C22⋊Q8—611no—
572C2×#121—611no—
573C2×#121—611no—
574C2×#120—611no—
575C2×#120C2×D6111yescharacteristic
576C2×C4×D4—611no—
577C2×C4×D4—611no—
578C2×C4×D4—611no—
579C2×C4×D4—611no—
580C2×#117—611no—
581C2×#117—1221no—
582C22×C22⋊C4—611no—
583C22×C22⋊C4C2×D6111yescharacteristic
584C22×C42—1221no—
585C2×#99—612no—
586C2×#99—612no—
587C2×#99—612no—
588C2×#99C2×D6112yes—
589#381—1221no—
590#380—612no—
591#380—1221no—
592#379—611no—
593#379C2×D6111yescharacteristic
594C4×C22⋊C4—612no—
595C4×C22⋊C4—612no—
596C4×C22⋊C4—612no—
597C4×C22⋊C4—1221no—
598C4×C22⋊C4—1221no—
599C4×C22⋊C4—1221no—
600C2×#95—1221no—
601#342—612no—
602#342—612no—
603#342—612no—
604#342C2×D6112yes—
605C61#2142011yescharacteristic, complemented, Sylow
606C25C22×D6111yescharacteristic
607C2×#41—1221no—
608C2×#41—1221no—
609C2×#41—1221no—
610C2×#41—1221no—
611C2×#41—2444no—
612C22×Q8—611no—
613C22×D4—611no—
614C22×D4—611no—
615C22×D4—611no—
616C22×D4—611no—
617C22×D4C4×D6111yescharacteristic
618C22×D4C4×D6111yescharacteristic
619C22×D4C22×D6111yescharacteristic
620C23×C4—21no—
621C23×C4—611no—
622C23×C4—611no—
623C23×C4—611no—
624C23×C4—611no—
625C23×C4—611no—
626C23×C4—611no—
627C23×C4—611no—
628C23×C4—611no—
629C23×C4—611no—
630C23×C4—611no—
631C23×C4—611no—
632C23×C4—611no—
633C23×C4—611no—
634C23×C4—611no—
635C23×C4—611no—
636C23×C4—611no—
637C23×C4—1221no—
638C23×C4—2444no—
639#123—1221no—
640#123—1221no—
641#123—1221no—
642#123—1221no—
643#123—1221no—
644#123—1221no—
645#123—1221no—
646#123—1221no—
647C22⋊Q8—1221no—
648C22⋊Q8—1221no—
649C22⋊Q8—1221no—
650C22⋊Q8—1221no—
651C22⋊Q8—1221no—
652C22⋊Q8—1221no—
653C22⋊Q8—1221no—
654C22⋊Q8—1221no—
655#121—1221no—
656#121—1221no—
657#121—1221no—
658#121—1221no—
659#121—1221no—
660#121—1221no—
661#121—1221no—
662#121—1221no—
663#120—21no—
664#120—21no—
665#120—21no—
666#120—21no—
667#120—1221no—
668#120—1221no—
669#120—1221no—
670#120—1221no—
671C4×D4—1221no—
672C4×D4—1221no—
673C4×D4—1221no—
674C4×D4—1221no—
675C4×D4—1221no—
676C4×D4—1221no—
677C4×D4—1221no—
678C4×D4—1221no—
679C4×D4—1221no—
680C4×D4—1221no—
681C4×D4—1221no—
682C4×D4—1221no—
683C4×D4—1221no—
684C4×D4—1221no—
685C4×D4—1221no—
686C4×D4—1221no—
687#117—1221no—
688#117—1221no—
689#117—1221no—
690#117—1221no—
691#117—2444no—
692C2×C4⋊C4—611no—
693C2×C4⋊C4—611no—
694C2×C4⋊C4—611no—
695C2×C4⋊C4—611no—
696C2×C4⋊C4—611no—
697C2×C4⋊C4—611no—
698C2×C4⋊C4—1222no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—24no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—612no—
704C2×C22⋊C4—611no—
705C2×C22⋊C4—611no—
706C2×C22⋊C4—611no—
707C2×C22⋊C4—611no—
708C2×C22⋊C4—611no—
709C2×C22⋊C4—611no—
710C2×C22⋊C4—611no—
711C2×C22⋊C4—612no—
712C2×C22⋊C4—1224no—
713C2×C22⋊C4—1221no—
714C2×C22⋊C4—1221no—
715C2×C22⋊C4—1221no—
716C2×C22⋊C4C4×D6111yescharacteristic
717C2×C22⋊C4C4×D6111yescharacteristic
718C2×C22⋊C4C22×D6112yes—
719C2×C22⋊C4C22×D6111yescharacteristic
720C2×C22⋊C4C22×D6112yes—
721C2×C42—611no—
722C2×C42—611no—
723C2×C42—1222no—
724C2×C42—1222no—
725C2×C42—1222no—
726C2×C42—2444no—
727#99—24no—
728#99—1224no—
729#99—1224no—
730#99—1224no—
731#95—1222no—
732#95—1222no—
733#95—1222no—
734#95—1222no—
735C24—22no—
736C24—22no—
737C24—42no—
738C24—42no—
739C24—611no—
740C24C2×C4×D6111yescharacteristic
741C24C2×C4×D6111yescharacteristic
742C24C2×C4×D6111yescharacteristic
743C24D4×D6111yescharacteristic
744C24D4×D6111yescharacteristic
745C24D4×D6111yescharacteristic
746C24D4×D6111yescharacteristic
747C24C23×D6111yescharacteristic
748#41—2444no—
749#41—2444no—
750#41—2444no—
751#41—2444no—
752C2×Q8—1221no—
753C2×Q8—1221no—
754C2×Q8—2442no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—22no—
758C2×D4—22no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—42no—
764C2×D4—42no—
765C2×D4—1221no—
766C2×D4—1221no—
767C2×D4—1221no—
768C2×D4—1221no—
769C2×D4—1222no—
770C2×D4—1222no—
771C2×D4—1221no—
772C2×D4—1221no—
773C2×D4—1221no—
774C2×D4—1221no—
775C2×D4—2442no—
776C2×D4—2442no—
777C2×D4—2442no—
778C22×C4—24no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—611no—
784C22×C4—611no—
785C22×C4—611no—
786C22×C4—611no—
787C22×C4—611no—
788C22×C4—611no—
789C22×C4—611no—
790C22×C4—611no—
791C22×C4—611no—
792C22×C4—611no—
793C22×C4—611no—
794C22×C4—611no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—611no—
798C22×C4—611no—
799C22×C4—611no—
800C22×C4—611no—
801C22×C4—611no—
802C22×C4—611no—
803C22×C4—611no—
804C22×C4—611no—
805C22×C4—611no—
806C22×C4—611no—
807C22×C4—611no—
808C22×C4—611no—
809C22×C4—611no—
810C22×C4—611no—
811C22×C4—611no—
812C22×C4—611no—
813C22×C4—611no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1224no—
817C22×C4—1224no—
818C22×C4—1224no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1224no—
822C22×C4—1222no—
823C22×C4—1222no—
824C22×C4—2442no—
825C22×C4—2442no—
826C22×C4—2442no—
827C22×C4—2442no—
828C22×C4—2442no—
829C22×C4—2442no—
830C22×C4—2442no—
831C22×C4—2442no—
832C22×C4—2442no—
833C22×C4—2442no—
834C22×C4—2442no—
835C22×C4—2442no—
836C22×C4—2442no—
837C22×C4—2442no—
838C22×C4—2442no—
839C22×C4C2×C4×D6111yescharacteristic
840C22×C4C2×C4×D6111yescharacteristic
841C22×C4C2×C4×D6111yescharacteristic
842C4⋊C4—1221no—
843C4⋊C4—1221no—
844C4⋊C4—1221no—
845C4⋊C4—1221no—
846C4⋊C4—1221no—
847C4⋊C4—1221no—
848C4⋊C4—1221no—
849C4⋊C4—1221no—
850C4⋊C4—1221no—
851C4⋊C4—1221no—
852C4⋊C4—1221no—
853C4⋊C4—1221no—
854C4⋊C4—2444no—
855C22⋊C4—24no—
856C22⋊C4—21no—
857C22⋊C4—21no—
858C22⋊C4—22no—
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—22no—
864C22⋊C4—22no—
865C22⋊C4—42no—
866C22⋊C4—42no—
867C22⋊C4—614no—
868C22⋊C4—1221no—
869C22⋊C4—1221no—
870C22⋊C4—1221no—
871C22⋊C4—1221no—
872C22⋊C4—1221no—
873C22⋊C4—1221no—
874C22⋊C4—1221no—
875C22⋊C4—1221no—
876C22⋊C4—1224no—
877C22⋊C4—1221no—
878C22⋊C4—1221no—
879C22⋊C4—1222no—
880C22⋊C4—1221no—
881C22⋊C4—1221no—
882C22⋊C4—1221no—
883C22⋊C4—1221no—
884C22⋊C4—1222no—
885C22⋊C4—1222no—
886C22⋊C4—2442no—
887C22⋊C4—2442no—
888C22⋊C4#1175822414yescomplemented
889C42—1221no—
890C42—1221no—
891C42—1221no—
892C42—1221no—
893C42—2444no—
894C42—2444no—
895C42—2444no—
896C23—22no—
897C23—22no—
898C23—21no—
899C23—21no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—21no—
907C23—21no—
908C23—22no—
909C23—22no—
910C23—21no—
911C23—22no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—48no—
921C23—48no—
922C23—41no—
923C23—41no—
924C23—1222no—
925C23—1221no—
926C23—2441no—
927C23—2441no—
928C23C22⋊C4×D6111yescharacteristic
929C23C22⋊C4×D6111yescharacteristic
930C23C22⋊C4×D6111yescharacteristic
931C23C22⋊C4×D6111yescharacteristic
932C23C22×C4×D6111yescharacteristic
933C23C2×D4×D6111yescharacteristic
934C23C2×D4×D6111yescharacteristic
935C23#41×D6112yes—
936C23C2×#1175822412yes—
937Q8—2442no—
938Q8—2442no—
939D4—42no—
940D4—42no—
941D4—42no—
942D4—42no—
943D4—41no—
944D4—41no—
945D4—42no—
946D4—2442no—
947D4—2442no—
948D4—2442no—
949D4—2442no—
950D4—2442no—
951D4—2442no—
952D4—2441no—
953D4—2441no—
954D4—2442no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—42no—
961C2×C4—48no—
962C2×C4—42no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—611no—
969C2×C4—611no—
970C2×C4—614no—
971C2×C4—611no—
972C2×C4—611no—
973C2×C4—611no—
974C2×C4—611no—
975C2×C4—611no—
976C2×C4—611no—
977C2×C4—1222no—
978C2×C4—1222no—
979C2×C4—1222no—
980C2×C4—1222no—
981C2×C4—1222no—
982C2×C4—1222no—
983C2×C4—1222no—
984C2×C4—1222no—
985C2×C4—1222no—
986C2×C4—1222no—
987C2×C4—1222no—
988C2×C4—1222no—
989C2×C4—1222no—
990C2×C4—1222no—
991C2×C4—1222no—
992C2×C4—1221no—
993C2×C4—1221no—
994C2×C4—1221no—
995C2×C4—1222no—
996C2×C4—1224no—
997C2×C4—2442no—
998C2×C4—2442no—
999C2×C4—2442no—
1000C2×C4—2441no—
1001C2×C4—2441no—
1002C2×C4—2441no—
1003C2×C4—2441no—
1004C2×C4—2441no—
1005C2×C4—2441no—
1006C2×C4—2441no—
1007C2×C4—2441no—
1008C2×C4—2441no—
1009C2×C4—2441no—
1010C2×C4—2441no—
1011C2×C4—2441no—
1012C2×C4—2442no—
1013C2×C4—2442no—
1014C2×C4—2442no—
1015C2×C4—2442no—
1016C2×C4—2442no—
1017C2×C4—2448no—
1018C2×C4—2442no—
1019C2×C4—2441no—
1020C2×C4—2441no—
1021C22—24no—
1022C22—24no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—21no—
1038C22—21no—
1039C22—42no—
1040C22—42no—
1041C22—44no—
1042C22—44no—
1043C22—44no—
1044C22—44no—
1045C22—42no—
1046C22—42no—
1047C22—41no—
1048C22—41no—
1049C22—41no—
1050C22—82no—
1051C22—4882no—
1052C22—2441no—
1053C22—2441no—
1054C22—2441no—
1055C22#99×D6112yes—
1056C22#1683973412yes—
1057C22C2×C22⋊C4×D6111yescharacteristic
1058C22C4×#1175822412yes—
1059C22#1684026811yescharacteristic
1060C22#1684027011yescharacteristic
1061C22#1684030712yes—
1062C4—44no—
1063C4—41no—
1064C4—41no—
1065C4—41no—
1066C4—82no—
1067C4—612no—
1068C4—612no—
1069C4—1221no—
1070C4—1221no—
1071C4—1221no—
1072C4—1221no—
1073C4—1221no—
1074C4—1221no—
1075C4—4882no—
1076C4—2444no—
1077C4—2441no—
1078C4—2441no—
1079C4—2441no—
1080C2—21no—
1081C2—22no—
1082C2—21no—
1083C2—22no—
1084C2—22no—
1085C2—22no—
1086C2—41no—
1087C2—41no—
1088C2—81no—
1089C2—4881no—
1090C2#2144830411yescharacteristic
1091C2C2×#99×D6111yescharacteristic
1092C2C2×#1683973411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1898C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840268C2
cosocleC24×C61C24
hypercenter#1898D61
hypocenterC61#21420
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ #1898

Complements

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

NH ≅ G/Ntype
2. #21448197C2semidirect
3. C2×C22⋊C4×Dic61C2semidirect
4. #21446802C2semidirect
5. #21446653C2semidirect
6. #21446273C2semidirect
7. #21446272C2semidirect
8. #21446270C2semidirect
9. #99×Dic61C2semidirect
10. #21445606C2semidirect
11. C61×#1898C2semidirect
12. C22×#11758224C4semidirect
22. C2×#14519761C4semidirect
23. C2×#14519758C4semidirect
24. C2×#14519754C4semidirect
26. C2×#14519749C4semidirect
29. C2×D4×Dic61C4semidirect
31. C2×#14519737C4semidirect
34. C2×#14519733C4semidirect
64. C22×Dic122C2×C4semidirect
67. C22×C22⋊D61C2×C4semidirect
75. C23×Dic61C2×C4semidirect
86. C22×C4×D61C2×C4semidirect
136. C2×C4⋊Dic61C2×C4semidirect
137. C2×C4⋊Dic61C2×C4semidirect
139. C2×#11758196C2×C4semidirect
140. C2×#11758196C2×C4semidirect
141. C2×#11758196C2×C4semidirect
142. C2×#11758196C2×C4semidirect
149. C2×C22⋊Dic61C2×C4semidirect
150. C2×C22⋊Dic61C2×C4semidirect
154. C2×#11758198C2×C4semidirect
155. C2×#11758198C2×C4semidirect
160. C2×C4×Dic61C2×C4semidirect
161. C2×C4×Dic61C2×C4semidirect
307. C22⋊C4×C61#41semidirect
324. C22⋊Dic61#41semidirect
461. C2×Dic61#99semidirect
542. #1898D61semidirect
605. C61#21420semidirect
888. C22⋊C4#11758224semidirect

Maximal subgroups

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

subgroupindex
C2×#168402682
#214481972
C2×C22⋊C4×Dic612
#214468022
#214466532
#214462732
#214462722
#214462702
#99×Dic612
#214456062
C61×#18982
#2142061