Finite Group Databasebeta

← #30615173

Subgroups — #30615173

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462263C212yesmaximal, complemented
2#21461715C212yesmaximal, complemented
3#21461682C212yesmaximal, complemented
4#21461681C212yesmaximal, complemented
5#21461646C212yesmaximal
6C4×#14519836C212yesmaximal, complemented
7C4×#14519835C212yesmaximal, complemented
8C2×C4×D4×D61C211yesmaximal, characteristic
9C2×#14519856—22no—
10C2×#14519836C2214yes—
11C2×#14519835C2214yes—
12#16840705—22no—
13#16840704—22no—
14#16840704C2214yescomplemented
15#16840703C2214yes—
16C4×C22⋊#6923—22no—
17C4×C22⋊#6923C2214yescomplemented
18#16840640C2214yescomplemented
19#16840640C2214yescomplemented
20C22×D4×D61C2211yescharacteristic
21C23×C4×D61C411yescharacteristic, complemented
22C23×C4×D61C2211yescharacteristic
23C2×C4×D244C2211yescharacteristic
24C2×D4×Dic61C411yescharacteristic, complemented
25C2×#14519739C2211yescharacteristic
26C2×C4×C22⋊D61C411yescharacteristic, complemented
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519737C411yescharacteristic, complemented
29C2×#14519737C2211yescharacteristic
30C4×D4×D61—22no—
31C4×D4×D61—22no—
32C4×D4×D61—22no—
33C4×D4×D61—22no—
34C2×C4⋊C4×D61C411yescharacteristic, complemented
35C2×C22⋊C4×D61C411yescharacteristic, complemented
36C2×C22⋊C4×D61C2211yescharacteristic
37C2×C42×D61C411yescharacteristic, complemented
38C2×C4×D4×C61C411yescharacteristic, complemented
39#14519856—48no—
40C2×C4⋊#6923—24no—
41C2×C22⋊#6923—24no—
42C2×C22⋊#6923—24no—
43C2×C22⋊#6923C2318yes—
44C2×C4×#6923—24no—
45#14519836—28no—
46#14519835—28no—
47(C2×#6923)⋊C4—24no—
48(C2×#6923)⋊C4—24no—
49C24×D61C2×C411yescharacteristic
50C24×D61C2311yescharacteristic
51C22×D244C2311yescharacteristic
52C22×C22⋊D61C2×C411yescharacteristic
53C22×C22⋊D61C2311yescharacteristic
54C2×D4×D61—22no—
55C2×D4×D61—22no—
56C2×D4×D61—24no—
57C2×D4×D61—24no—
58C23×Dic61C2×C411yescharacteristic
59C23×Dic61C2×C411yescharacteristic
60C22×C4×D61—21no—
61C22×C4×D61—21no—
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C22×C4×D61—44no—
65C22×C4×D61—44no—
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2×C411yescharacteristic
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61C2×C411yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61D412yes—
74C22×C4×D61D412yes—
75C22×C4×D61D412yes—
76C22×C4×D61D412yes—
77C22×C4×D61C2311yescharacteristic
78C22×C4×D61C2311yescharacteristic
79C4×D244—22no—
80C4×D244—22no—
81D4×Dic61—22no—
82D4×Dic61—22no—
83#14519739—22no—
84#14519739—22no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—22no—
88C4×C22⋊D61—22no—
89#14519737—22no—
90#14519737—22no—
91#14519737—22no—
92#14519737—22no—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C4⋊C4×D61—22no—
97C4⋊C4×D61—22no—
98C2×C22⋊Dic61C2×C411yescharacteristic
99C2×C22⋊Dic61C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2311yescharacteristic
103C2×#11758198C2311yescharacteristic
104C22⋊C4×D61—22no—
105C22⋊C4×D61—22no—
106C22⋊C4×D61—22no—
107C22⋊C4×D61—22no—
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61C2×C411yescharacteristic
111C42×D61—21no—
112C42×D61—21no—
113C42×D61—21no—
114C42×D61—21no—
115C22×D4×C61C2×C411yescharacteristic
116C23×C4×C61C2×C411yescharacteristic
117C23×C4×C61C2×C411yescharacteristic
118C4×D4×C61—22no—
119C4×D4×C61—22no—
120C2×C4⋊C4×C61C2×C411yescharacteristic
121C2×C22⋊C4×C61C2×C411yescharacteristic
122C2×C22⋊C4×C61C2×C411yescharacteristic
123C2×C42×C61C2×C411yescharacteristic
124C24×C61C22×C411yescharacteristic
125C24×C61C22×C411yescharacteristic
126C23×D61—22no—
127C23×D61—21no—
128C23×D61—21no—
129C23×D61—22no—
130C23×D61—22no—
131C23×D61—22no—
132C23×D61—42no—
133C23×D61—42no—
134C23×D61—42no—
135C23×D61—42no—
136C23×D61C22×C411yescharacteristic
137C23×D61C22×C411yescharacteristic
138C23×D61C2×D412yes—
139C23×D61C2×D412yes—
140C23×D61C2411yescharacteristic
141C22×#6923—28no—
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—42no—
148C22×C4×C61—42no—
149C22×C4×C61C22⋊C412yes—
150C22×C4×C61C22⋊C412yes—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61#4114yes—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—42no—
165C22×Dic61—42no—
166C22×Dic61C22⋊C412yes—
167C22×Dic61C22⋊C412yes—
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173D4×D61—216no—
174D4×D61—216no—
175C2×D244—22no—
176C2×D244—22no—
177C2×D244#4114yes—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—24no—
183C2×C4×D61—28no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—44no—
193C2×C4×D61—42no—
194C2×C4×D61—44no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—44no—
198C2×C4×D61—44no—
199C2×C4×D61—44no—
200C2×C4×D61—44no—
201C2×C4×D61—44no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61C22⋊C411yescharacteristic
207C2×C4×D61C22⋊C411yescharacteristic
208C2×C4×D61C22⋊C411yescharacteristic
209C2×C4×D61C22⋊C412yes—
210C2×C4×D61C22⋊C412yes—
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C2×D412yes—
213C2×C4×D61C2×D412yes—
214C2×C4×D61C2×D412yes—
215C2×C4×D61C2×D412yes—
216C22⋊#6923—28no—
217C22⋊#6923—28no—
218C22⋊#6923—48no—
219C22⋊#6923—48no—
220C4⋊#6923—48no—
221C4×#6923—48no—
222C4⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—22no—
225C42×C61—21no—
226C42×C61—21no—
227C22⋊Dic61—22no—
228C22⋊Dic61—22no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232#11758198—22no—
233C4⋊Dic61—22no—
234#11758196—22no—
235#11758196—22no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61C2×C22⋊C412yes—
251C23×C61#11712yescomplemented
252C23×C61C23×C411yescharacteristic
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—24no—
258C22×D61—24no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—24no—
262C22×D61—24no—
263C22×D61—24no—
264C22×D61—24no—
265C22×D61—42no—
266C22×D61—41no—
267C22×D61—42no—
268C22×D61—41no—
269C22×D61—42no—
270C22×D61—48no—
271C22×D61—48no—
272C22×D61—48no—
273C22×D61—48no—
274C22×D61—42no—
275C22×D61—42no—
276C22×D61—42no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61C2×C22⋊C411yescharacteristic
280C22×D61C2×C22⋊C411yescharacteristic
281C22×D61#11712yescomplemented
282C22×D61C22×D412yes—
283C22×D61C2×#4112yes—
284C22×D61C2×#4112yes—
285C2×#6923—48no—
286C2×#6923—48no—
287C2×#6923—48no—
288D4×C61—28no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—22no—
292C2×C4×C61—24no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—42no—
296C2×C4×C61—41no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61C2×C22⋊C411yescharacteristic
302C2×C4×C61C2×C22⋊C412yes—
303C2×C4×C61C2×C22⋊C411yescharacteristic
304C2×C4×C61#11712yescomplemented
305C22⋊D61—28no—
306C22⋊D61—28no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—22no—
310C2×Dic61—24no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—42no—
314C2×Dic61—41no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61C2×C22⋊C411yescharacteristic
320C2×Dic61C2×C22⋊C412yes—
321C2×Dic61C2×C22⋊C411yescharacteristic
322C2×Dic61#11712yescomplemented
323D244—28no—
324C4×D61—24no—
325C4×D61—24no—
326C4×D61—22no—
327C4×D61—24no—
328C4×D61—24no—
329C4×D61—22no—
330C4×D61—24no—
331C4×D61—22no—
332C4×D61—42no—
333C4×D61—42no—
334C4×D61—42no—
335C4×D61—42no—
336C4×D61—42no—
337C4×D61—42no—
338C4×D61—42no—
339C4×D61—42no—
340C4×D61—42no—
341C4×D61—42no—
342C4×D61—42no—
343C4×D61#9914yescomplemented
344#20722—611nomaximal, Sylow
345C22×C61—21no—
346C22×C61—21no—
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61C22×C22⋊C411yescharacteristic
358C22×C61C2×#11711yescharacteristic
359C22×C61C2×#11711yescharacteristic
360C2×D61—24no—
361C2×D61—24no—
362C2×D61—21no—
363C2×D61—22no—
364C2×D61—21no—
365C2×D61—22no—
366C2×D61—21no—
367C2×D61—21no—
368C2×D61—22no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—48no—
372C2×D61—48no—
373C2×D61—48no—
374C2×D61—48no—
375C2×D61—42no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—42no—
379C2×D61C2×#9912yes—
380C2×D61#41012yes—
381C2×D61#52514yes—
382#6923—88no—
383C4×C61—21no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61—41no—
387C4×C61—41no—
388C4×C61C2×#9912yes—
389Dic61—21no—
390Dic61—22no—
391Dic61—22no—
392Dic61—41no—
393Dic61—41no—
394Dic61C2×#9912yes—
395C22×C4×D4—611no—
396#2280—612no—
397#1819—612no—
398#1799—612no—
399#1799—612no—
400#1781—612no—
401C4×#99—612no—
402C4×#99—612no—
403C2×C61—21no—
404C2×C61—21no—
405C2×C61—42no—
406C2×C61—42no—
407C2×C61#228011yescharacteristic
408C2×C61C22×#9911yescharacteristic
409C2×C61C2×#41011yescharacteristic
410D61—24no—
411D61—22no—
412D61—22no—
413D61—42no—
414C23×D4—611no—
415C24×C4—611no—
416C24×C4—611no—
417C2×C4×D4—611no—
418C2×C4×D4—611no—
419C2×C4×D4—611no—
420C2×C4×D4—611no—
421C2×C4×D4—611no—
422C2×C4×D4—611no—
423C2×C4×D4—611no—
424C2×C4×D4—1222no—
425C2×C4×D4—1222no—
426C2×C4×D4—1222no—
427C2×C4×D4—1222no—
428C2×C4×D4#692311yescharacteristic, complemented
429C2×#117—1222no—
430C22×C4⋊C4—611no—
431C22×C22⋊C4—611no—
432C22×C22⋊C4—611no—
433C22×C42—611no—
434C2×#99—614no—
435C2×#99—614no—
436#381—1222no—
437#380—614no—
438#380—1222no—
439#379—614no—
440C4×C22⋊C4—614no—
441C4×C22⋊C4—1222no—
442#342—614no—
443#342—614no—
444C61#2072211yescharacteristic, complemented, Sylow
445C25—611no—
446C25—611no—
447C22×D4—611no—
448C22×D4—611no—
449C22×D4—611no—
450C22×D4—1224no—
451C22×D4—1224no—
452C22×D4—1222no—
453C22×D4—1222no—
454C22×D4C2×#692311yescharacteristic
455C23×C4—611no—
456C23×C4—612no—
457C23×C4—611no—
458C23×C4—612no—
459C23×C4—612no—
460C23×C4—612no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4—1221no—
471C23×C4—1221no—
472C23×C4—1221no—
473C23×C4—1221no—
474C23×C4—2444no—
475C23×C4—2444no—
476C23×C4C2×#692311yescharacteristic
477C23×C4C2×#692311yescharacteristic
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—1222no—
481C4×D4—1222no—
482C4×D4—1222no—
483C4×D4—1222no—
484C4×D4—1222no—
485C4×D4—1222no—
486C4×D4—1222no—
487C4×D4—1222no—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—1222no—
491C4×D4—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494#117—2448no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—1222no—
499C2×C4⋊C4—1222no—
500C2×C4⋊C4—1224no—
501C2×C4⋊C4C2×#692311yescharacteristic
502C2×C22⋊C4—611no—
503C2×C22⋊C4—611no—
504C2×C22⋊C4—611no—
505C2×C22⋊C4—611no—
506C2×C22⋊C4—611no—
507C2×C22⋊C4—611no—
508C2×C22⋊C4—618no—
509C2×C22⋊C4—1222no—
510C2×C22⋊C4—1222no—
511C2×C22⋊C4—1222no—
512C2×C22⋊C4—1222no—
513C2×C22⋊C4—1224no—
514C2×C22⋊C4—1224no—
515C2×C22⋊C4C2×#692311yescharacteristic
516C2×C22⋊C4C2×#692311yescharacteristic
517C2×C42—611no—
518C2×C42—611no—
519C2×C42—611no—
520C2×C42—1221no—
521C2×C42—1221no—
522C2×C42—1221no—
523C2×C42—1221no—
524C2×C42—1224no—
525C2×C42C2×#692311yescharacteristic
526#99—1228no—
527#99—1228no—
528#95—1224no—
529#95—1224no—
530C24—611no—
531C24—611no—
532C24—612no—
533C24—612no—
534C24—611no—
535C24—1221no—
536C24—1221no—
537C24—1222no—
538C24—1222no—
539C24—1222no—
540C24—1222no—
541C24—2442no—
542C24—2442no—
543C24—2442no—
544C24—2442no—
545C24C22×#692311yescharacteristic
546C24C22×#692311yescharacteristic
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—614no—
551C2×D4—614no—
552C2×D4—1222no—
553C2×D4—1222no—
554C2×D4—1222no—
555C2×D4—12216no—
556C2×D4—12216no—
557C2×D4—1222no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—611no—
566C22×C4—612no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—612no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—612no—
574C22×C4—612no—
575C22×C4—612no—
576C22×C4—611no—
577C22×C4—612no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—1228no—
583C22×C4—1224no—
584C22×C4—1222no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1222no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1228no—
599C22×C4—2442no—
600C22×C4—2444no—
601C22×C4—2442no—
602C22×C4—2444no—
603C22×C4—2444no—
604C22×C4—2442no—
605C22×C4—2444no—
606C22×C4—2442no—
607C22×C4—2444no—
608C22×C4—2444no—
609C22×C4—2444no—
610C22×C4—2442no—
611C22×C4—2442no—
612C22×C4—2442no—
613C22×C4—2442no—
614C22×C4—2442no—
615C22×C4C22⋊#692312yes—
616C22×C4C22⋊#692312yes—
617C22×C4C22×#692311yescharacteristic
618C22×C4C22×#692311yescharacteristic
619C22×C4C22×#692311yescharacteristic
620C22×C4C22×#692311yescharacteristic
621C22×C4C22×#692311yescharacteristic
622C4⋊C4—22no—
623C4⋊C4—1222no—
624C4⋊C4—1222no—
625C4⋊C4—1222no—
626C4⋊C4—2448no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—1222no—
630C22⋊C4—1222no—
631C22⋊C4—1222no—
632C22⋊C4—1222no—
633C22⋊C4—1222no—
634C22⋊C4—1222no—
635C22⋊C4—1228no—
636C22⋊C4—1228no—
637C22⋊C4—2448no—
638C22⋊C4—2448no—
639C42—21no—
640C42—21no—
641C42—1221no—
642C42—1221no—
643C42—1221no—
644C42—1221no—
645C42—1221no—
646C42—1221no—
647C42—2448no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—611no—
657C23—611no—
658C23—612no—
659C23—612no—
660C23—612no—
661C23—612no—
662C23—1222no—
663C23—1222no—
664C23—1224no—
665C23—1224no—
666C23—1224no—
667C23—1224no—
668C23—1224no—
669C23—1224no—
670C23—1221no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—2441no—
675C23—2442no—
676C23—2441no—
677C23—2442no—
678C23—2441no—
679C23—2441no—
680C23—2442no—
681C23—2442no—
682C23—2442no—
683C23—2448no—
684C23—2448no—
685C23—2448no—
686C23—2448no—
687C23—2442no—
688C23C2×C22⋊#692312yes—
689C23#1451985612yescomplemented
690C23C23×#692311yescharacteristic
691D4—28no—
692D4—1228no—
693D4—1228no—
694D4—1228no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—611no—
708C2×C4—614no—
709C2×C4—611no—
710C2×C4—612no—
711C2×C4—612no—
712C2×C4—1224no—
713C2×C4—1222no—
714C2×C4—1224no—
715C2×C4—1222no—
716C2×C4—1224no—
717C2×C4—1224no—
718C2×C4—1224no—
719C2×C4—1222no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1224no—
723C2×C4—1222no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2442no—
733C2×C4—2442no—
734C2×C4—2442no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4—2441no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2448no—
741C2×C4—2448no—
742C2×C4—2448no—
743C2×C4—2442no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4C2×C22⋊#692311yescharacteristic
747C2×C4C2×C22⋊#692312yes—
748C2×C4C2×C22⋊#692311yescharacteristic
749C2×C4#1451985612yescomplemented
750C22—21no—
751C22—21no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—41no—
761C22—41no—
762C22—612no—
763C22—612no—
764C22—614no—
765C22—1224no—
766C22—1224no—
767C22—1222no—
768C22—1221no—
769C22—1222no—
770C22—1221no—
771C22—1221no—
772C22—1221no—
773C22—1222no—
774C22—2442no—
775C22—2442no—
776C22—2442no—
777C22—2442no—
778C22—2448no—
779C22—2448no—
780C22—2448no—
781C22—2448no—
782C22—2441no—
783C22—2441no—
784C22C22×C22⋊#692311yescharacteristic
785C22C2×#1451985611yescharacteristic
786C22C2×#1451985611yescharacteristic
787C4—21no—
788C4—22no—
789C4—22no—
790C4—41no—
791C4—41no—
792C4—612no—
793C4—1222no—
794C4—1221no—
795C4—1222no—
796C4—4888no—
797C4—2441no—
798C4—2441no—
799C4D61⋊#9912yes—
800C2—21no—
801C2—21no—
802C2—42no—
803C2—42no—
804C2—1224no—
805C2—1222no—
806C2—1222no—
807C2—2442no—
808C2#2146226311yescharacteristic
809C2C2×D61⋊#9911yescharacteristic
810C2D61⋊#41011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C22
cosocleC23×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61#20722
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21462263C2semidirect
2. #21461715C2semidirect
3. #21461682C2semidirect
4. #21461681C2semidirect
6. C4×#14519836C2semidirect
7. C4×#14519835C2semidirect
14. #16840704C22semidirect
17. C4×C22⋊#6923C22semidirect
18. #16840640C22semidirect
19. #16840640C22semidirect
21. C23×C4×D61C4semidirect
24. C2×D4×Dic61C4semidirect
26. C2×C4×C22⋊D61C4semidirect
28. C2×#14519737C4semidirect
34. C2×C4⋊C4×D61C4semidirect
35. C2×C22⋊C4×D61C4semidirect
37. C2×C42×D61C4semidirect
38. C2×C4×D4×C61C4semidirect
251. C23×C61#117semidirect
281. C22×D61#117semidirect
304. C2×C4×C61#117semidirect
322. C2×Dic61#117semidirect
343. C4×D61#99semidirect
428. C2×C4×D4#6923semidirect
444. C61#20722semidirect
689. C23#14519856semidirect
749. C2×C4#14519856semidirect

Maximal subgroups

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

subgroupindex
#214622632
#214617152
#214616822
#214616812
#214616462
C4×#145198362
C4×#145198352
C2×C4×D4×D612
#2072261