Finite Group Databasebeta

← #29685352

Subgroups — #29685352

Order 15616.

1678 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840271C211yesmaximal, characteristic
2#21448200C211yesmaximal, characteristic, complemented
3C4×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4#21446802C212yesmaximal, complemented
5#21446653C212yesmaximal, complemented
6#21446271C212yesmaximal, complemented
7#21446269C212yesmaximal, complemented
8C4×#14519691C211yesmaximal, characteristic, complemented
9C4×#14519691C211yesmaximal, characteristic, complemented
10C4×#14519692C211yesmaximal, characteristic, complemented
11C4×#99×C61C211yesmaximal, characteristic, complemented
12C22×#11758222C411yescharacteristic, complemented
13C23×C4×D61C2211yescharacteristic
14#16840271—21no—
15#16840271—21no—
16#16840271—21no—
17#16840271—21no—
18#16840271—21no—
19#16840271—21no—
20#16840271—21no—
21#16840271—21no—
22C2×#14519762C411yescharacteristic, complemented
23C2×#14519759C411yescharacteristic, complemented
24C2×#14519755C411yescharacteristic, complemented
25C2×#14519754C2211yescharacteristic
26C2×#14519750C411yescharacteristic, complemented
27C2×#14519749C2211yescharacteristic
28C2×#14519747C2211yescharacteristic
29C2×#14519745C2211yescharacteristic
30C2×C4×D244C411yescharacteristic, complemented
31C2×C4×C22⋊D61C411yescharacteristic, complemented
32C2×C4×C22⋊D61C2211yescharacteristic
33C2×#14519734—21no—
34C2×#14519734C411yescharacteristic, complemented
35C2×C22⋊C4×D61C2212yes—
36C2×C42×D61—21no—
37C2×#14519692C2212yes—
38C2×#14519691C2212yes—
39C2×#14519691C2212yes—
40#16839624—21no—
41#16839621—21no—
42#16839620C2212yes—
43#16839617C2212yes—
44C22⋊C4×Dic61C2212yes—
45C4×#11758198—21no—
46C4×#11758198—21no—
47C4×C22⋊Dic61C2211yescharacteristic
48C4×C22⋊Dic61C2211yescharacteristic
49#16839609—21no—
50#95×D61—21no—
51#16839529C2212yes—
52#16839528C2212yes—
53#16839528C2212yes—
54C2×C4×D4×C61C2211yescharacteristic
55C2×#99×C61C2212yes—
56C4×C22⋊C4×C61C2211yescharacteristic
57C4×C22⋊C4×C61C2211yescharacteristic
58C61×#342C2212yes—
59C24×D61C2311yescharacteristic
60C2×#11758222—21no—
61C2×#11758222—21no—
62C2×#11758222—21no—
63C2×#11758222—21no—
64C2×#11758222—44no—
65C22×Dic122C2×C411yescharacteristic, complemented
66C22×D244C2×C411yescharacteristic
67C22×D244C2×C411yescharacteristic
68C22×C22⋊D61C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic, complemented
71C22×C22⋊D61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C22×C4×D61—22no—
74C22×C4×D61—44no—
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C411yescharacteristic
77C22×C4×D61C2×C411yescharacteristic
78C22×C4×D61C2×C411yescharacteristic
79C22×C4×D61C2×C411yescharacteristic, complemented
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D411yescharacteristic
87C22×C4×D61D411yescharacteristic
88#14519762—21no—
89#14519762—21no—
90#14519762—21no—
91#14519762—21no—
92#14519759—21no—
93#14519759—21no—
94#14519759—21no—
95#14519759—21no—
96#14519755—21no—
97#14519755—21no—
98#14519755—21no—
99#14519755—21no—
100#14519754—21no—
101#14519754—21no—
102#14519754—21no—
103#14519754—21no—
104#14519750—21no—
105#14519750—21no—
106#14519750—21no—
107#14519750—21no—
108#14519749—21no—
109#14519749—21no—
110#14519749—21no—
111#14519749—21no—
112#14519747—21no—
113#14519747—21no—
114#14519747—21no—
115#14519747—21no—
116#14519745—21no—
117#14519745—21no—
118#14519745—21no—
119#14519745—21no—
120C4×D244—21no—
121C4×D244—21no—
122C4×D244—21no—
123C4×D244—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127C4×C22⋊D61—21no—
128C4×C22⋊D61—21no—
129C4×C22⋊D61—21no—
130C4×C22⋊D61—21no—
131C4×C22⋊D61—21no—
132#14519734—21no—
133#14519734—21no—
134#14519734—21no—
135#14519734—21no—
136#14519734—44no—
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⋊Dic61C2×C411yescharacteristic, complemented
144C2×C22⋊Dic61C2312yes—
145C2×C22⋊Dic61C2311yescharacteristic
146C2×C22⋊Dic61C2312yes—
147C2×#11758198—22no—
148C2×#11758198—22no—
149C2×#11758198—22no—
150C2×#11758198C2×C411yescharacteristic
151C2×#11758198C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic, complemented
155C2×#11758198C2×C411yescharacteristic, complemented
156C22⋊C4×D61—24no—
157C22⋊C4×D61—24no—
158C2×C4×Dic61—21no—
159C2×C4×Dic61—21no—
160C2×C4×Dic61—22no—
161C2×C4×Dic61C2×C411yescharacteristic, complemented
162C42×D61—44no—
163#14519692—24no—
164#14519691—24no—
165#14519691—24no—
166#14519684—21no—
167#14519684—21no—
168#14519684—22no—
169#14519684—22no—
170C22×D4×C61C2311yescharacteristic
171C23×C4×C61C2×C411yescharacteristic, complemented
172C23×C4×C61C2311yescharacteristic
173C4×D4×C61—21no—
174C4×D4×C61—21no—
175C4×D4×C61—21no—
176C4×D4×C61—21no—
177C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
178C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
179C2×C22⋊C4×C61C2312yes—
180C2×C22⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61C2312yes—
182C2×C42×C61—21no—
183C2×C42×C61—21no—
184C2×C42×C61C2×C411yescharacteristic, complemented
185#99×C61—24no—
186#95×C61—21no—
187#95×C61—21no—
188C24×C61C22×C411yescharacteristic
189C24×C61C2411yescharacteristic
190C23×D61—22no—
191C23×D61—22no—
192C23×D61—42no—
193C23×D61—42no—
194C23×D61C22×C411yescharacteristic
195C23×D61C22×C411yescharacteristic
196C23×D61C22×C411yescharacteristic
197C23×D61C2×D411yescharacteristic
198C23×D61C2×D411yescharacteristic
199C23×D61C2×D411yescharacteristic
200C23×D61C2×D411yescharacteristic
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—22no—
209C22×C4×C61—42no—
210C22×C4×C61—42no—
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C22×C411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—22no—
223C2×C22⋊D61—22no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—42no—
231C2×C22⋊D61—42no—
232C2×C22⋊D61—42no—
233C22×Dic61—22no—
234C22×Dic61—22no—
235C22×Dic61—42no—
236C22×Dic61C22×C411yescharacteristic
237C22×Dic61C22×C411yescharacteristic
238C22×Dic61C22×C411yescharacteristic
239C22×Dic61C22×C411yescharacteristic
240C22×Dic61C22×C411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244C22×Dic61C2×D411yescharacteristic
245#11758222—44no—
246#11758222—44no—
247#11758222—44no—
248#11758222—44no—
249C2×D244—21no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244—21no—
253C2×D244—42no—
254C2×D244—42no—
255C2×C4×D61—24no—
256C2×C4×D61—24no—
257C2×C4×D61—24no—
258C2×C4×D61—28no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—42no—
262C2×C4×D61—42no—
263C2×C4×D61—42no—
264C2×C4×D61—42no—
265C2×C4×D61—42no—
266C2×C4×D61—42no—
267C2×C4×D61—42no—
268C2×C4×D61—42no—
269C2×C4×D61—42no—
270C2×C4×D61—44no—
271C2×C4×D61—44no—
272C2×C4×D61—42no—
273C2×C4×D61C22⋊C411yescharacteristic
274C2×C4×D61C22⋊C411yescharacteristic
275C2×C4×D61C22⋊C411yescharacteristic
276C2×C4×D61C22⋊C411yescharacteristic
277C2×C4×D61C22⋊C411yescharacteristic
278C2×C4×D61C22⋊C411yescharacteristic
279C2×C4×D61C22⋊C411yescharacteristic
280C2×C4×D61C22⋊C411yescharacteristic
281C2×C4×D61C22⋊C411yescharacteristic
282C2×C4×D61C22⋊C411yescharacteristic
283C2×C4×D61C22⋊C411yescharacteristic
284C2×C4×D61C22⋊C411yescharacteristic
285C2×C4×D61C22⋊C411yescharacteristic
286C2×C4×D61C22⋊C411yescharacteristic
287C2×C4×D61C22⋊C411yescharacteristic
288C2×C4×D61C22⋊C411yescharacteristic
289C2×Dic122—21no—
290C2×Dic122—21no—
291C2×Dic122—42no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61—21no—
294C22⋊C4×C61—21no—
295C22⋊C4×C61—21no—
296C22⋊C4×C61—22no—
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C22⋊C4×C61—22no—
300C22⋊C4×C61—22no—
301C22⋊C4×C61#4114yescomplemented
302C42×C61—21no—
303C42×C61—21no—
304C42×C61—42no—
305C42×C61—42no—
306C22⋊Dic61—21no—
307C22⋊Dic61—21no—
308C22⋊Dic61—22no—
309C22⋊Dic61—21no—
310C22⋊Dic61—21no—
311C22⋊Dic61—22no—
312C22⋊Dic61—22no—
313C22⋊Dic61#4114yescomplemented
314#11758198—28no—
315#11758198—21no—
316#11758198—21no—
317#11758198—21no—
318#11758198—21no—
319#11758198—21no—
320#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324#11758198—21no—
325#11758198—21no—
326#11758198—21no—
327#11758198—44no—
328#11758198—44no—
329C4⋊Dic61—21no—
330C4⋊Dic61—21no—
331#11758196—21no—
332#11758196—21no—
333#11758196—21no—
334#11758196—21no—
335#11758196—21no—
336#11758196—21no—
337#11758196—21no—
338#11758196—21no—
339#11758196—44no—
340C4×Dic61—21no—
341C4×Dic61—21no—
342C4×Dic61—44no—
343C4×Dic61—42no—
344C4×Dic61—42no—
345C23×C61—21no—
346C23×C61—21no—
347C23×C61—21no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61C23×C411yescharacteristic
353C23×C61C22×D411yescharacteristic
354C23×C61C22×D411yescharacteristic
355C23×C61C2×#4112yes—
356C23×C61C2×#4112yes—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—21no—
361C22×D61—21no—
362C22×D61—21no—
363C22×D61—21no—
364C22×D61—22no—
365C22×D61—22no—
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—22no—
371C22×D61—21no—
372C22×D61—21no—
373C22×D61—21no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—48no—
381C22×D61—48no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61C2×C22⋊C411yescharacteristic
385C22×D61C2×C22⋊C411yescharacteristic
386C22×D61C2×C22⋊C411yescharacteristic
387C22×D61C2×C22⋊C411yescharacteristic
388D4×C61—42no—
389D4×C61—42no—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
392C2×C4×C61—22no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—21no—
398C2×C4×C61—24no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—42no—
403C2×C4×C61—42no—
404C2×C4×C61—42no—
405C2×C4×C61—42no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—42no—
409C2×C4×C61—42no—
410C2×C4×C61—42no—
411C2×C4×C61C2×C22⋊C411yescharacteristic
412C2×C4×C61C2×C22⋊C411yescharacteristic
413C2×C4×C61C2×C22⋊C411yescharacteristic
414C2×C4×C61C2×C22⋊C411yescharacteristic
415C22⋊D61—42no—
416C22⋊D61—42no—
417C22⋊D61—42no—
418C22⋊D61—42no—
419C22⋊D61—42no—
420C22⋊D61—42no—
421C22⋊D61—42no—
422C22⋊D61—42no—
423C2×Dic61—22no—
424C2×Dic61—22no—
425C2×Dic61—22no—
426C2×Dic61—21no—
427C2×Dic61—21no—
428C2×Dic61—21no—
429C2×Dic61—21no—
430C2×Dic61—21no—
431C2×Dic61—24no—
432C2×Dic61—41no—
433C2×Dic61—41no—
434C2×Dic61—41no—
435C2×Dic61—42no—
436C2×Dic61—42no—
437C2×Dic61—41no—
438C2×Dic61—41no—
439C2×Dic61—42no—
440C2×Dic61—42no—
441C2×Dic61—42no—
442C2×Dic61C2×C22⋊C411yescharacteristic
443C2×Dic61C2×C22⋊C411yescharacteristic
444C2×Dic61C2×C22⋊C411yescharacteristic
445C2×Dic61C2×C22⋊C411yescharacteristic
446D244—42no—
447D244—42no—
448D244—42no—
449D244—42no—
450C4×D61—22no—
451C4×D61—22no—
452C4×D61—22no—
453C4×D61—22no—
454C4×D61—22no—
455C4×D61—22no—
456C4×D61—22no—
457C4×D61—22no—
458C4×D61—22no—
459C4×D61—41no—
460C4×D61—41no—
461C4×D61—41no—
462C4×D61—41no—
463C4×D61—41no—
464C4×D61—41no—
465C4×D61—42no—
466C4×D61—416no—
467C4×D61—42no—
468C4×D61#9914yescomplemented
469Dic122—42no—
470Dic122—42no—
471#21420—611nomaximal, Sylow
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—42no—
479C22×C61—42no—
480C22×C61—41no—
481C22×C61—41no—
482C22×C61—41no—
483C22×C61—81no—
484C22×C61—81no—
485C22×C61C22×C22⋊C411yescharacteristic
486C22×C61C4×#4111yescharacteristic
487C22×C61C4×#4111yescharacteristic
488C22×C61#52512yes—
489C22×C61#53212yes—
490C2×D61—28no—
491C2×D61—21no—
492C2×D61—21no—
493C2×D61—21no—
494C2×D61—21no—
495C2×D61—21no—
496C2×D61—21no—
497C2×D61—21no—
498C2×D61—21no—
499C2×D61—21no—
500C2×D61—21no—
501C2×D61—44no—
502C2×D61—42no—
503C2×D61—42no—
504C2×D61—44no—
505C2×D61—42no—
506C2×D61—42no—
507C2×D61—44no—
508C2×D61—41no—
509C2×D61—41no—
510C2×D61—41no—
511C2×D61—81no—
512C2×D61—81no—
513C2×D61C2×#9912yes—
514C2×D61#41012yes—
515C4×C61—21no—
516C4×C61—21no—
517C4×C61—21no—
518C4×C61—44no—
519C4×C61—41no—
520C4×C61—41no—
521C4×C61—41no—
522C4×C61—82no—
523C4×C61C2×#9912yes—
524Dic61—21no—
525Dic61—21no—
526Dic61—21no—
527Dic61—44no—
528Dic61—41no—
529Dic61—41no—
530Dic61—41no—
531Dic61—82no—
532Dic61C2×#9912yes—
533C2×#525—611no—
534#2280—611no—
535C2×C4×C22⋊C4—611no—
536#1996—612no—
537#1964—612no—
538#1898—612no—
539#1898—612no—
540C4×#99—611no—
541C4×#99—611no—
542C4×#99—611no—
543C4×#99D6111yescharacteristic, complemented
544C2×C61—22no—
545C2×C61—22no—
546C2×C61—21no—
547C2×C61—21no—
548C2×C61—81no—
549C2×C61#229711yescharacteristic
550C2×C61C22×#9911yescharacteristic
551C2×C61C2×#41011yescharacteristic
552D61—22no—
553D61—22no—
554D61—41no—
555D61—41no—
556D61—81no—
557C22×#41—611no—
558C24×C4—611no—
559#525—1221no—
560#525—1221no—
561#525—1221no—
562#525—1221no—
563#525—1221no—
564#525—1221no—
565#525—1221no—
566#525—1221no—
567C2×#123—611no—
568C2×#123—611no—
569C2×C22⋊Q8—611no—
570C2×C22⋊Q8—611no—
571C2×#121—611no—
572C2×#121—611no—
573C2×#120—611no—
574C2×#120—611no—
575C2×C4×D4—611no—
576C2×C4×D4—611no—
577C2×C4×D4—611no—
578C2×C4×D4C2×D6111yescharacteristic
579C2×#117—611no—
580C2×#117—1221no—
581C22×C22⋊C4—612no—
582C22×C42—1221no—
583C2×#99—612no—
584C2×#99—612no—
585C2×#99—612no—
586C2×#99C2×D6112yes—
587#381—1221no—
588#380—612no—
589#380—1221no—
590#379—612no—
591C4×C22⋊C4—611no—
592C4×C22⋊C4—611no—
593C4×C22⋊C4—612no—
594C4×C22⋊C4—1221no—
595C4×C22⋊C4—1221no—
596C4×C22⋊C4—1221no—
597C4×C22⋊C4C2×D6111yescharacteristic
598C4×C22⋊C4C2×D6111yescharacteristic
599C2×#95—1221no—
600#342—612no—
601#342—612no—
602#342—612no—
603#342C2×D6112yes—
604C61#2142011yescharacteristic, complemented, Sylow
605C25—611no—
606C2×#41—1221no—
607C2×#41—1221no—
608C2×#41—1221no—
609C2×#41—1221no—
610C2×#41—2444no—
611C22×Q8—611no—
612C22×D4—611no—
613C22×D4—611no—
614C22×D4—611no—
615C22×D4—611no—
616C22×D4—611no—
617C22×D4—611no—
618C22×D4C22×D6111yescharacteristic
619C23×C4—611no—
620C23×C4—611no—
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—1222no—
634C23×C4—2444no—
635C23×C4C4×D6111yescharacteristic, complemented
636C23×C4C22×D6111yescharacteristic
637#123—1221no—
638#123—1221no—
639#123—1221no—
640#123—1221no—
641#123—1221no—
642#123—1221no—
643#123—1221no—
644#123—1221no—
645C22⋊Q8—1221no—
646C22⋊Q8—1221no—
647C22⋊Q8—1221no—
648C22⋊Q8—1221no—
649C22⋊Q8—1221no—
650C22⋊Q8—1221no—
651C22⋊Q8—1221no—
652C22⋊Q8—1221no—
653#121—1221no—
654#121—1221no—
655#121—1221no—
656#121—1221no—
657#121—1221no—
658#121—1221no—
659#121—1221no—
660#121—1221no—
661#120—1221no—
662#120—1221no—
663#120—1221no—
664#120—1221no—
665#120—1221no—
666#120—1221no—
667#120—1221no—
668#120—1221no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—21no—
672C4×D4—21no—
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—
685#117—1221no—
686#117—1221no—
687#117—1221no—
688#117—1221no—
689#117—2444no—
690C2×C4⋊C4—611no—
691C2×C4⋊C4—611no—
692C2×C4⋊C4—611no—
693C2×C4⋊C4—611no—
694C2×C4⋊C4—611no—
695C2×C4⋊C4—1222no—
696C2×C4⋊C4C4×D6111yescharacteristic, complemented
697C2×C22⋊C4—612no—
698C2×C22⋊C4—611no—
699C2×C22⋊C4—611no—
700C2×C22⋊C4—611no—
701C2×C22⋊C4—611no—
702C2×C22⋊C4—611no—
703C2×C22⋊C4—611no—
704C2×C22⋊C4—611no—
705C2×C22⋊C4—611no—
706C2×C22⋊C4—612no—
707C2×C22⋊C4—1224no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1224no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4C4×D6111yescharacteristic, complemented
713C2×C22⋊C4C22×D6112yes—
714C2×C22⋊C4C22×D6111yescharacteristic
715C2×C22⋊C4C22×D6112yes—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—611no—
719C2×C42—1222no—
720C2×C42—1221no—
721C2×C42—1221no—
722C2×C42—2444no—
723C2×C42C4×D6111yescharacteristic, complemented
724#99—24no—
725#99—1224no—
726#99—1224no—
727#99—1224no—
728#95—21no—
729#95—21no—
730#95—1222no—
731#95—1222no—
732#95—1221no—
733#95—1221no—
734C24—611no—
735C24—611no—
736C24—611no—
737C24—611no—
738C24—611no—
739C24—611no—
740C24—611no—
741C24—1222no—
742C24—1222no—
743C24—2442no—
744C24—2442no—
745C24C2×C4×D6111yescharacteristic
746C24C23×D6111yescharacteristic
747#41—2444no—
748#41—2444no—
749#41—2444no—
750#41—2444no—
751C2×Q8—1221no—
752C2×Q8—1221no—
753C2×Q8—2442no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—22no—
757C2×D4—22no—
758C2×D4—1221no—
759C2×D4—1221no—
760C2×D4—1221no—
761C2×D4—1221no—
762C2×D4—1221no—
763C2×D4—1221no—
764C2×D4—1221no—
765C2×D4—1221no—
766C2×D4—1221no—
767C2×D4—1221no—
768C2×D4—1221no—
769C2×D4—1221no—
770C2×D4—1222no—
771C2×D4—1222no—
772C2×D4—2442no—
773C2×D4—2442no—
774C2×D4—2442no—
775C2×D4—2442no—
776C2×D4—2442no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
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—1224no—
809C22×C4—1224no—
810C22×C4—1224no—
811C22×C4—1228no—
812C22×C4—1222no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1222no—
816C22×C4—2442no—
817C22×C4—2442no—
818C22×C4—2442no—
819C22×C4—2442no—
820C22×C4—2442no—
821C22×C4—2442no—
822C22×C4—2442no—
823C22×C4—2442no—
824C22×C4—2442no—
825C22×C4—2442no—
826C22×C4—2444no—
827C22×C4—2444no—
828C22×C4—2442no—
829C22×C4C2×C4×D6111yescharacteristic
830C22×C4C2×C4×D6111yescharacteristic
831C22×C4C2×C4×D6111yescharacteristic
832C22×C4C2×C4×D6111yescharacteristic
833C22×C4C2×C4×D6111yescharacteristic
834C22×C4D4×D6111yescharacteristic
835C22×C4D4×D6111yescharacteristic
836C22×C4D4×D6111yescharacteristic
837C22×C4D4×D6111yescharacteristic
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—1221no—
841C4⋊C4—1221no—
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—2444no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—22no—
854C22⋊C4—21no—
855C22⋊C4—21no—
856C22⋊C4—22no—
857C22⋊C4—22no—
858C22⋊C4—614no—
859C22⋊C4—1221no—
860C22⋊C4—1221no—
861C22⋊C4—1221no—
862C22⋊C4—1221no—
863C22⋊C4—1221no—
864C22⋊C4—1221no—
865C22⋊C4—1221no—
866C22⋊C4—1221no—
867C22⋊C4—1221no—
868C22⋊C4—1221no—
869C22⋊C4—1228no—
870C22⋊C4—1221no—
871C22⋊C4—1221no—
872C22⋊C4—1221no—
873C22⋊C4—1221no—
874C22⋊C4—1222no—
875C22⋊C4—1221no—
876C22⋊C4—1221no—
877C22⋊C4—1222no—
878C22⋊C4—1222no—
879C22⋊C4—2444no—
880C22⋊C4—2444no—
881C22⋊C4#1175822214yescomplemented
882C42—21no—
883C42—21no—
884C42—42no—
885C42—42no—
886C42—1221no—
887C42—1221no—
888C42—2442no—
889C42—2442no—
890C42—2444no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—611no—
899C23—611no—
900C23—611no—
901C23—611no—
902C23—1222no—
903C23—1222no—
904C23—1222no—
905C23—1222no—
906C23—1222no—
907C23—1222no—
908C23—1222no—
909C23—1221no—
910C23—1221no—
911C23—1221no—
912C23—1221no—
913C23—1222no—
914C23—1222no—
915C23—1222no—
916C23—1221no—
917C23—1221no—
918C23—1221no—
919C23—2441no—
920C23—2441no—
921C23—2441no—
922C23—2441no—
923C23—2441no—
924C23—2441no—
925C23—2441no—
926C23—2441no—
927C23—2448no—
928C23—2448no—
929C23C22×C4×D6111yescharacteristic
930C23C2×D4×D6111yescharacteristic
931C23C2×D4×D6111yescharacteristic
932C23#41×D6112yes—
933C23C2×#1175822212yes—
934Q8—2442no—
935Q8—2442no—
936D4—42no—
937D4—42no—
938D4—2442no—
939D4—2442no—
940D4—2442no—
941D4—2442no—
942D4—2442no—
943D4—2442no—
944D4—2442no—
945D4—2442no—
946D4—2442no—
947D4—2442no—
948D4—2442no—
949D4—2442no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—24no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—611no—
972C2×C4—614no—
973C2×C4—611no—
974C2×C4—611no—
975C2×C4—611no—
976C2×C4—1222no—
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—1221no—
989C2×C4—1221no—
990C2×C4—1221no—
991C2×C4—1221no—
992C2×C4—1221no—
993C2×C4—1224no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4—2441no—
997C2×C4—2441no—
998C2×C4—2441no—
999C2×C4—2441no—
1000C2×C4—2442no—
1001C2×C4—24416no—
1002C2×C4—2441no—
1003C2×C4—2441no—
1004C2×C4—2441no—
1005C2×C4—2442no—
1006C2×C4—2442no—
1007C2×C4—2442no—
1008C2×C4—2442no—
1009C2×C4—2442no—
1010C2×C4—2442no—
1011C2×C4—2441no—
1012C2×C4—2441no—
1013C2×C4C22⋊C4×D6111yescharacteristic
1014C2×C4C22⋊C4×D6111yescharacteristic
1015C2×C4C22⋊C4×D6111yescharacteristic
1016C2×C4C22⋊C4×D6111yescharacteristic
1017C22—21no—
1018C22—21no—
1019C22—21no—
1020C22—21no—
1021C22—21no—
1022C22—21no—
1023C22—42no—
1024C22—42no—
1025C22—41no—
1026C22—41no—
1027C22—41no—
1028C22—81no—
1029C22—81no—
1030C22—612no—
1031C22—612no—
1032C22—1228no—
1033C22—1221no—
1034C22—1221no—
1035C22—1221no—
1036C22—1221no—
1037C22—1221no—
1038C22—1221no—
1039C22—1221no—
1040C22—1221no—
1041C22—1221no—
1042C22—1221no—
1043C22—4881no—
1044C22—4881no—
1045C22—2444no—
1046C22—2444no—
1047C22—2442no—
1048C22—2442no—
1049C22—2442no—
1050C22—2442no—
1051C22—2444no—
1052C22—2441no—
1053C22—2441no—
1054C22—2441no—
1055C22C2×C22⋊C4×D6111yescharacteristic
1056C22#1684023011yescharacteristic
1057C22C4×#1175822211yescharacteristic
1058C22#1684027112yes—
1059C22#1684030912yes—
1060C4—21no—
1061C4—21no—
1062C4—21no—
1063C4—44no—
1064C4—41no—
1065C4—41no—
1066C4—41no—
1067C4—82no—
1068C4—612no—
1069C4—1221no—
1070C4—1221no—
1071C4—1221no—
1072C4—4882no—
1073C4—2444no—
1074C4—2441no—
1075C4—2441no—
1076C4—2441no—
1077C4#99×D6112yes—
1078C2—22no—
1079C2—22no—
1080C2—21no—
1081C2—21no—
1082C2—81no—
1083C2—1222no—
1084C2—1222no—
1085C2—4881no—
1086C2—2441no—
1087C2—2441no—
1088C2#2144830511yescharacteristic
1089C2C2×#99×D6111yescharacteristic
1090C2#410×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC4×#99×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840271C2
cosocleC24×C61C24
hypercenterC4×#99D61
hypocenterC61#21420
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #21448200C2semidirect
3. C4×C22⋊C4×D61C2semidirect
4. #21446802C2semidirect
5. #21446653C2semidirect
6. #21446271C2semidirect
7. #21446269C2semidirect
8. C4×#14519691C2semidirect
9. C4×#14519691C2semidirect
10. C4×#14519692C2semidirect
11. C4×#99×C61C2semidirect
12. C22×#11758222C4semidirect
22. C2×#14519762C4semidirect
23. C2×#14519759C4semidirect
24. C2×#14519755C4semidirect
26. C2×#14519750C4semidirect
30. C2×C4×D244C4semidirect
31. C2×C4×C22⋊D61C4semidirect
34. C2×#14519734C4semidirect
65. C22×Dic122C2×C4semidirect
70. C22×C22⋊D61C2×C4semidirect
79. C22×C4×D61C2×C4semidirect
137. C2×C4⋊Dic61C2×C4semidirect
139. C2×#11758196C2×C4semidirect
140. C2×#11758196C2×C4semidirect
141. C2×#11758196C2×C4semidirect
142. C2×#11758196C2×C4semidirect
143. C2×C22⋊Dic61C2×C4semidirect
154. C2×#11758198C2×C4semidirect
155. C2×#11758198C2×C4semidirect
161. C2×C4×Dic61C2×C4semidirect
171. C23×C4×C61C2×C4semidirect
177. C2×C4⋊C4×C61C2×C4semidirect
178. C2×C22⋊C4×C61C2×C4semidirect
184. C2×C42×C61C2×C4semidirect
301. C22⋊C4×C61#41semidirect
313. C22⋊Dic61#41semidirect
468. C4×D61#99semidirect
543. C4×#99D61semidirect
604. C61#21420semidirect
635. C23×C4C4×D61semidirect
696. C2×C4⋊C4C4×D61semidirect
712. C2×C22⋊C4C4×D61semidirect
723. C2×C42C4×D61semidirect
881. C22⋊C4#11758222semidirect

Maximal subgroups

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

subgroupindex
C2×#168402712
#214482002
C4×C22⋊C4×D612
#214468022
#214466532
#214462712
#214462692
C4×#145196912
C4×#145196922
C4×#99×C612
#2142061