Finite Group Databasebeta

← #29680135

Subgroups — #29680135

Order 15616.

1428 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#41×D61C211yesmaximal, characteristic
2#21454451C211yesmaximal, characteristic, complemented
3C4×#14519735C211yesmaximal, characteristic, complemented
4#21445917C212yesmaximal, complemented
5#21445840C211yesmaximal, characteristic, complemented
6#21445839C211yesmaximal, characteristic, complemented
7#21445836C211yesmaximal, characteristic, complemented
8#21445761C212yesmaximal
9#104×Dic61C212yesmaximal, complemented
10#21445623C212yesmaximal, complemented
11C61×#1806C211yesmaximal, characteristic, complemented
12C2×#41×D61C2211yescharacteristic
13#41×Dic61C2211yescharacteristic
14C4×#11758226C411yescharacteristic, complemented
15C4×#11758226C411yescharacteristic, complemented
16C4×#11758222—21no—
17C4×#11758222C2211yescharacteristic
18#16840230—21no—
19#16840230C2211yescharacteristic
20C4×#11758224—21no—
21C4×#11758224—21no—
22C4×#11758224C411yescharacteristic, complemented
23C4×#11758224C411yescharacteristic, complemented
24C4×Q8×D61C411yescharacteristic, complemented
25C4×Q8×D61C411yescharacteristic, complemented
26C4×D4×D61—21no—
27C4×D4×D61—21no—
28C4×D4×D61C411yescharacteristic, complemented
29C4×D4×D61C411yescharacteristic, complemented
30C2×#14519735—21no—
31#117×D61—21no—
32#117×D61C2211yescharacteristic
33C2×C42×D61—21no—
34C2×C42×D61C2211yescharacteristic
35#16839818—21no—
36#16839818—21no—
37#16839814—21no—
38#16839814—21no—
39#16839786C2211yescharacteristic, complemented
40C2×#14519705C2212yes—
41C2×#14519704C2212yes—
42C2×#14519703C2212yes—
43#16839725C2212yes—
44M16×Dic61C2212yescomplemented
45C4⋊C4×Dic61—21no—
46C4×C4⋊Dic61C2211yescharacteristic, complemented
47C4×#11758198C2212yes—
48#16839609—21no—
49#16839607—21no—
50C42×Dic61C2212yescomplemented
51#16839523C2212yescomplemented
52#16839522C2212yescomplemented
53#16839521C2212yescomplemented
54C4×#41×C61C2211yescharacteristic
55C61×#423C2211yescharacteristic, complemented
56C2×#104×C61C2212yes—
57C4×C4⋊C4×C61C2211yescharacteristic, complemented
58C61×#339C2212yescomplemented
59C2×#11758226C2×C411yescharacteristic
60C2×#11758222—21no—
61C2×#11758222C2311yescharacteristic
62C2×#11758224—21no—
63C2×#11758224C2×C411yescharacteristic
64#41×D61—22no—
65#41×D61—22no—
66#41×D61—22no—
67#41×D61—22no—
68C2×Q8×D61C2×C411yescharacteristic
69C2×D4×D61—21no—
70C2×D4×D61C2×C411yescharacteristic
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61D411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C2×#11758194C2312yes—
78Q8×Dic61C2×C411yescharacteristic
79Q8×Dic61C2×C411yescharacteristic
80C4×Dic122—21no—
81C4×Dic122—21no—
82C4×Dic122C2×C411yescharacteristic
83C4×Dic122C2×C411yescharacteristic
84#14519742—21no—
85#14519742—21no—
86#14519742C2×C411yescharacteristic
87#14519742C2×C411yescharacteristic
88C4×D244—21no—
89C4×D244—21no—
90C4×D244C2×C411yescharacteristic
91C4×D244C2×C411yescharacteristic
92D4×Dic61—21no—
93D4×Dic61—21no—
94D4×Dic61C2×C411yescharacteristic
95D4×Dic61C2×C411yescharacteristic
96#14519739—21no—
97#14519739—21no—
98#14519739C2×C411yescharacteristic
99#14519739C2×C411yescharacteristic
100C4×C22⋊D61—21no—
101C4×C22⋊D61—21no—
102C4×C22⋊D61—21no—
103C4×C22⋊D61—21no—
104C4×C22⋊D61—21no—
105C4×C22⋊D61—21no—
106#14519737—21no—
107#14519737—21no—
108#14519737—21no—
109#14519737—21no—
110#14519737—21no—
111#14519737—21no—
112#14519736—21no—
113#14519736C2311yescharacteristic
114#14519735—28no—
115#14519735—21no—
116#14519735—21no—
117#14519735C2×C411yescharacteristic
118#14519735C2×C411yescharacteristic
119#14519734—21no—
120#14519734—21no—
121#14519734—21no—
122#14519733—21no—
123#14519733—21no—
124#14519733—21no—
125C2×C4⋊Dic61—21no—
126C4⋊C4×D61—21no—
127C4⋊C4×D61—21no—
128C4⋊C4×D61C2×C411yescharacteristic
129C4⋊C4×D61C2×C411yescharacteristic
130C2×#11758198—22no—
131C22⋊C4×D61—21no—
132C22⋊C4×D61—21no—
133C22⋊C4×D61—21no—
134C2×C4×Dic61—22no—
135C2×C4×Dic61—21no—
136C2×C4×Dic61—21no—
137C2×C4×Dic61—21no—
138C2×C4×Dic61—22no—
139C2×C4×Dic61D411yescharacteristic
140C2×C4×Dic61D411yescharacteristic
141C2×C4×Dic61C2312yes—
142C2×C4×Dic61C2311yescharacteristic
143C42×D61—21no—
144C42×D61—21no—
145C42×D61—21no—
146C42×D61—21no—
147C42×D61—21no—
148C42×D61—21no—
149C42×D61—21no—
150C42×D61C2×C411yescharacteristic
151C42×D61C2×C411yescharacteristic
152C42×D61C2×C411yescharacteristic
153C42×D61C2×C411yescharacteristic
154C42×D61D411yescharacteristic
155C42×D61D411yescharacteristic
156C42×D61D411yescharacteristic
157C42×D61D411yescharacteristic
158C4⋊#92418—21no—
159C4⋊#92418—21no—
160#14519705—24no—
161#14519704—24no—
162#14519703—24no—
163#14519689—22no—
164#14519689—22no—
165#14519687—22no—
166C8×Dic61—22no—
167#14519684—21no—
168#14519684—22no—
169C2×#41×C61C2311yescharacteristic
170C2×M16×C61C2312yes—
171C4×Q8×C61C2×C411yescharacteristic
172C4×Q8×C61C2×C411yescharacteristic
173C4×D4×C61—21no—
174C4×D4×C61—21no—
175C4×D4×C61C2×C411yescharacteristic
176C4×D4×C61C2×C411yescharacteristic
177#117×C61—21no—
178#117×C61C2311yescharacteristic
179C2×C4⋊C4×C61—21no—
180C2×C42×C61—21no—
181C2×C42×C61C2312yes—
182C2×C42×C61C2311yescharacteristic
183C4⋊C8×C61—21no—
184C4⋊C8×C61—21no—
185#104×C61—24no—
186#95×C61—21no—
187C23×D61—21no—
188C23×D61C2×D411yescharacteristic
189#41×C61—21no—
190#41×C61—21no—
191#41×C61#4112yes—
192#41×C61#4112yes—
193C2×Q8×C61C22×C411yescharacteristic
194C2×D4×C61—21no—
195C2×D4×C61C22×C411yescharacteristic
196C22×C4×C61—21no—
197C22×C4×C61—22no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—21no—
204C2×C22⋊D61—21no—
205C2×C22⋊D61—21no—
206C22×Dic61—21no—
207C22×Dic61—22no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213#11758226—22no—
214#11758226—22no—
215Q8×D61—22no—
216Q8×D61—22no—
217#11758224—24no—
218#11758224—24no—
219#11758224—22no—
220#11758224—22no—
221D4×D61—24no—
222D4×D61—24no—
223D4×D61—22no—
224D4×D61—22no—
225#11758222—24no—
226#11758222—24no—
227#11758222—21no—
228#11758222—21no—
229#11758222#4112yes—
230#11758222#4112yes—
231C2×D244—21no—
232C2×D244C22×C411yescharacteristic
233C2×C4×D61—24no—
234C2×C4×D61—24no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—24no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—42no—
250C2×C4×D61—44no—
251C2×C4×D61—44no—
252C2×C4×D61C22⋊C411yescharacteristic
253C2×C4×D61C22⋊C411yescharacteristic
254C2×C4×D61C22⋊C411yescharacteristic
255C2×C4×D61C22⋊C411yescharacteristic
256C2×C4×D61C22⋊C411yescharacteristic
257C2×C4×D61C22⋊C411yescharacteristic
258C2×C4×D61C22⋊C411yescharacteristic
259C2×C4×D61C22⋊C411yescharacteristic
260C2×C4×D61C22×C411yescharacteristic
261C2×C4×D61C22×C411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×Dic122—21no—
265C2×Dic122C22×C411yescharacteristic
266M16×C61—22no—
267M16×C61—22no—
268C2×C8×C61—22no—
269C4⋊C4×C61—24no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61C22×C411yescharacteristic
273C4⋊C4×C61C22×C411yescharacteristic
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C42×C61—21no—
278C42×C61—21no—
279C42×C61—21no—
280C42×C61—22no—
281C42×C61—22no—
282C42×C61C22×C411yescharacteristic
283C42×C61C22×C411yescharacteristic
284C42×C61C2×D411yescharacteristic
285C42×C61C2×D411yescharacteristic
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289#11758198—28no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296C4⋊Dic61—24no—
297C4⋊Dic61—21no—
298C4⋊Dic61—21no—
299C4⋊Dic61C22×C411yescharacteristic
300C4⋊Dic61C22×C411yescharacteristic
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307C4×Dic61—28no—
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—22no—
318C4×Dic61—22no—
319C4×Dic61—44no—
320C4×Dic61C22⋊C411yescharacteristic
321C4×Dic61C22⋊C411yescharacteristic
322C4×Dic61C22⋊C411yescharacteristic
323C4×Dic61C22⋊C411yescharacteristic
324C4×Dic61C22⋊C411yescharacteristic
325C4×Dic61C22⋊C411yescharacteristic
326C4×Dic61C22⋊C411yescharacteristic
327C4×Dic61C22⋊C411yescharacteristic
328C4×Dic61C22×C411yescharacteristic
329C4×Dic61C22×C411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331C4×Dic61C2×D411yescharacteristic
332#11758194—22no—
333#11758194—22no—
334C2×#92418—22no—
335C23×C61—21no—
336C23×C61C22×D411yescharacteristic
337C22×D61—24no—
338C22×D61—21no—
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—22no—
342C22×D61—41no—
343C22×D61—42no—
344C22×D61—42no—
345C22×D61C2×C22⋊C411yescharacteristic
346C22×D61C2×C22⋊C411yescharacteristic
347Q8×C61—21no—
348Q8×C61#11712yescomplemented
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—21no—
352D4×C61#11712yescomplemented
353C2×C4×C61—21no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—24no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—41no—
361C2×C4×C61—42no—
362C2×C4×C61—42no—
363C2×C4×C61—42no—
364C2×C4×C61—42no—
365C2×C4×C61C2×C22⋊C411yescharacteristic
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C2×C22⋊C411yescharacteristic
368C2×C4×C61C2×C22⋊C411yescharacteristic
369C2×C4×C61C23×C411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C2×#4111yescharacteristic
372C2×C4×C61C2×#4111yescharacteristic
373C2×C4×C61C2×#4111yescharacteristic
374C2×C4×C61C2×#4111yescharacteristic
375C22⋊D61—24no—
376C22⋊D61—24no—
377C22⋊D61—22no—
378C22⋊D61—22no—
379C2×Dic61—24no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—24no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—42no—
389C2×Dic61—42no—
390C2×Dic61—42no—
391C2×Dic61—42no—
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C2×C22⋊C411yescharacteristic
394C2×Dic61C2×C22⋊C411yescharacteristic
395C2×Dic61C2×C22⋊C411yescharacteristic
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C2×C22⋊C411yescharacteristic
398D244—24no—
399D244—21no—
400D244#11712yescomplemented
401C4×D61—24no—
402C4×D61—24no—
403C4×D61—22no—
404C4×D61—21no—
405C4×D61—21no—
406C4×D61—21no—
407C4×D61—21no—
408C4×D61—21no—
409C4×D61—21no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—21no—
413C4×D61—21no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—42no—
421C4×D61—42no—
422C4×D61—42no—
423C4×D61—42no—
424C4×D61—42no—
425C4×D61—42no—
426C4×D61#10414yescomplemented
427Dic122—24no—
428Dic122—21no—
429Dic122#11712yescomplemented
430C8×C61—42no—
431#92418—42no—
432#20747—611nomaximal, Sylow
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—22no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61C22×C22⋊C411yescharacteristic
439C22×C61#52511yescharacteristic
440C22×C61#52511yescharacteristic
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—22no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—48no—
450C2×D61—41no—
451C2×D61—41no—
452C2×D61C2×#10412yes—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—21no—
456C4×C61—22no—
457C4×C61—44no—
458C4×C61—41no—
459C4×C61—41no—
460C4×C61C2×#10412yes—
461C4×C61C2×#11711yescharacteristic
462C4×C61C2×#11711yescharacteristic
463C4×C61#52511yescharacteristic
464C4×C61#52511yescharacteristic
465Dic61—21no—
466Dic61—21no—
467Dic61—21no—
468Dic61—22no—
469Dic61—21no—
470Dic61—44no—
471Dic61—41no—
472Dic61—41no—
473Dic61C2×#10412yes—
474Dic61#42112yes—
475C2×C4×#41—611no—
476#2920—611no—
477C4×#117—611no—
478#1826—612no—
479#1806—611no—
480#1806—611no—
481#1806—611no—
482#1806D6111yescharacteristic, complemented
483#1789—612no—
484C4×#104—612no—
485C4×#104—612no—
486C2×C61—21no—
487C2×C61—21no—
488C2×C61—42no—
489C2×C61#228011yescharacteristic
490C2×C61C22×#10411yescharacteristic
491C2×C61C2×#42111yescharacteristic
492D61—22no—
493D61—41no—
494D61—42no—
495C22×#41—611no—
496C4×#41—611no—
497C4×#41—611no—
498C4×#41—611no—
499C4×#41—611no—
500C4×#41—611no—
501C4×#41—611no—
502C4×#41—611no—
503C4×#41—1221no—
504C4×#41—1221no—
505C4×#41—1221no—
506C4×#41—1221no—
507C4×#41C2×D6111yescharacteristic
508C2×C4×Q8—611no—
509C2×C4×Q8—611no—
510C2×C4×D4—611no—
511C2×C4×D4—611no—
512C2×C4×D4—1221no—
513C2×C4×D4—1221no—
514C2×#117—611no—
515C2×#117—1221no—
516C2×#117—1221no—
517C22×C42—611no—
518C22×C42—1221no—
519#432—1221no—
520#432—1221no—
521#431—1221no—
522#431—1221no—
523#423—611no—
524#423C2×D6111yescharacteristic, complemented
525C2×#104—612no—
526C2×#104—612no—
527C2×#104—612no—
528C2×#104C2×D6112yes—
529#407—612no—
530C4×M16—612no—
531C4×C4⋊C4—611no—
532C4×C4⋊C4—1221no—
533C4×C4⋊C4C2×D6111yescharacteristic, complemented
534C4×C22⋊C4—612no—
535C4×C22⋊C4—1221no—
536#376—1221no—
537C43—612no—
538#339—612no—
539#339—612no—
540#339—612no—
541#339C2×D6112yescomplemented
542C61#2074711yescharacteristic, complemented, Sylow
543C2×#41—611no—
544C2×#41—611no—
545C2×#41—611no—
546C2×#41—1221no—
547C2×#41—1221no—
548C2×#41—1222no—
549C2×#41—1222no—
550C2×#41—1222no—
551C2×#41—1222no—
552C2×#41C22×D6111yescharacteristic
553C22×Q8—611no—
554C22×D4—611no—
555C22×D4—1221no—
556C23×C4—611no—
557C23×C4—611no—
558C23×C4—611no—
559C23×C4—1221no—
560C23×C4—1221no—
561C23×C4—1221no—
562C2×M16—612no—
563C2×M16C22×D6112yes—
564C4×Q8—611no—
565C4×Q8—611no—
566C4×Q8—611no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—1221no—
571C4×Q8—1221no—
572C4×Q8—1221no—
573C4×Q8—1221no—
574C4×Q8C4×D6111yescharacteristic
575C4×Q8C4×D6111yescharacteristic
576C4×D4—21no—
577C4×D4—21no—
578C4×D4—611no—
579C4×D4—611no—
580C4×D4—611no—
581C4×D4—611no—
582C4×D4—611no—
583C4×D4—611no—
584C4×D4—1221no—
585C4×D4—1221no—
586C4×D4—1221no—
587C4×D4—1221no—
588C4×D4—1221no—
589C4×D4—1221no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4—1221no—
598C4×D4—1221no—
599C4×D4—1221no—
600C4×D4—1221no—
601C4×D4—1221no—
602C4×D4C4×D6111yescharacteristic
603C4×D4C4×D6111yescharacteristic
604#117—21no—
605#117—611no—
606#117—611no—
607#117—611no—
608#117—1221no—
609#117—1221no—
610#117—1221no—
611#117—1221no—
612#117—1221no—
613#117—1221no—
614#117—1221no—
615#117—1221no—
616#117—1228no—
617#117—1221no—
618#117C22×D6111yescharacteristic
619C2×C4⋊C4—21no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—1221no—
623C2×C4⋊C4—1221no—
624C2×C4⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1222no—
629C2×C42—21no—
630C2×C42—611no—
631C2×C42—611no—
632C2×C42—611no—
633C2×C42—611no—
634C2×C42—611no—
635C2×C42—611no—
636C2×C42—611no—
637C2×C42—611no—
638C2×C42—611no—
639C2×C42—611no—
640C2×C42—611no—
641C2×C42—612no—
642C2×C42—1221no—
643C2×C42—1221no—
644C2×C42—1221no—
645C2×C42—1221no—
646C2×C42—1221no—
647C2×C42—1221no—
648C2×C42—1221no—
649C2×C42—1221no—
650C2×C42—1221no—
651C2×C42—1222no—
652C2×C42—1221no—
653C2×C42—1222no—
654C2×C42C22×D6112yes—
655C2×C42C22×D6111yescharacteristic
656C4⋊C8—21no—
657C4⋊C8—21no—
658C4⋊C8—1221no—
659C4⋊C8—1221no—
660#104—24no—
661#104—1224no—
662#104—1224no—
663#104—1224no—
664C22⋊C8—1222no—
665C22⋊C8—1222no—
666#97—1222no—
667C4×C8—1222no—
668#95—21no—
669#95—1222no—
670#95—1221no—
671C24—611no—
672C24—1221no—
673#41—21no—
674#41—21no—
675#41—612no—
676#41—612no—
677#41—1224no—
678#41—1224no—
679#41—1222no—
680#41—1224no—
681#41—1224no—
682#41—1222no—
683#41—1222no—
684#41—1222no—
685#41—1221no—
686#41—1221no—
687#41#1175822412yes—
688#41#1175822612yes—
689C2×Q8—611no—
690C2×Q8—1221no—
691C2×Q8—1222no—
692C2×Q8—1222no—
693C2×Q8C2×C4×D6111yescharacteristic
694C2×D4—21no—
695C2×D4—611no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4—1222no—
699C2×D4—1224no—
700C2×D4—1224no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1222no—
704C2×D4C2×C4×D6111yescharacteristic
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—1221no—
725C22×C4—1224no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1224no—
730C22×C4—1224no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1222no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—2444no—
745C22×C4—2442no—
746C22×C4—2444no—
747C22×C4D4×D6111yescharacteristic
748C22×C4D4×D6111yescharacteristic
749C22×C4C23×D6111yescharacteristic
750M16—22no—
751M16—22no—
752M16—1222no—
753M16—1222no—
754C2×C8—22no—
755C2×C8—1222no—
756C4⋊C4—24no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—611no—
760C4⋊C4—611no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1224no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4C2×C4×D6111yescharacteristic
771C4⋊C4C2×C4×D6111yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—1221no—
776C22⋊C4—1221no—
777C22⋊C4—1221no—
778C22⋊C4—1221no—
779C22⋊C4—1228no—
780C22⋊C4—1221no—
781C22⋊C4—1221no—
782C22⋊C4—1221no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
785C42—21no—
786C42—21no—
787C42—21no—
788C42—22no—
789C42—22no—
790C42—611no—
791C42—611no—
792C42—611no—
793C42—611no—
794C42—611no—
795C42—611no—
796C42—611no—
797C42—611no—
798C42—611no—
799C42—611no—
800C42—611no—
801C42—611no—
802C42—1221no—
803C42—1221no—
804C42—1221no—
805C42—1221no—
806C42—1221no—
807C42—1221no—
808C42—1228no—
809C42—1221no—
810C42—1221no—
811C42—1221no—
812C42—1222no—
813C42—1222no—
814C42—2444no—
815C42C2×C4×D6111yescharacteristic
816C42C2×C4×D6111yescharacteristic
817C42D4×D6111yescharacteristic
818C42D4×D6111yescharacteristic
819C23—21no—
820C23—611no—
821C23—611no—
822C23—1222no—
823C23—1224no—
824C23—1221no—
825C23—1221no—
826C23—1221no—
827C23—2441no—
828C23—2442no—
829C23—2442no—
830C23C2×D4×D6111yescharacteristic
831Q8—21no—
832Q8—612no—
833Q8—1224no—
834Q8—1221no—
835Q8#1451973512yescomplemented
836D4—22no—
837D4—22no—
838D4—21no—
839D4—612no—
840D4—1224no—
841D4—1224no—
842D4—1224no—
843D4—1222no—
844D4—1222no—
845D4—1221no—
846D4#1451973512yescomplemented
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—611no—
860C2×C4—611no—
861C2×C4—614no—
862C2×C4—611no—
863C2×C4—611no—
864C2×C4—611no—
865C2×C4—611no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
870C2×C4—1224no—
871C2×C4—1224no—
872C2×C4—1222no—
873C2×C4—1222no—
874C2×C4—1224no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1222no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1222no—
888C2×C4—1222no—
889C2×C4—1224no—
890C2×C4—1221no—
891C2×C4—1221no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2442no—
895C2×C4—2442no—
896C2×C4—2442no—
897C2×C4—2442no—
898C2×C4—2442no—
899C2×C4—2442no—
900C2×C4—2442no—
901C2×C4—2442no—
902C2×C4—2442no—
903C2×C4—2442no—
904C2×C4C22⋊C4×D6111yescharacteristic
905C2×C4C22⋊C4×D6111yescharacteristic
906C2×C4C22⋊C4×D6111yescharacteristic
907C2×C4C22⋊C4×D6111yescharacteristic
908C2×C4C22×C4×D6111yescharacteristic
909C2×C4C2×D4×D6111yescharacteristic
910C2×C4#41×D6111yescharacteristic
911C2×C4#41×D6111yescharacteristic
912C2×C4C2×#1175822411yescharacteristic
913C2×C4C2×#1175822611yescharacteristic
914C8—42no—
915C8—2442no—
916C22—21no—
917C22—21no—
918C22—22no—
919C22—41no—
920C22—41no—
921C22—612no—
922C22—1221no—
923C22—1221no—
924C22—1222no—
925C22—1221no—
926C22—1221no—
927C22—1221no—
928C22—2442no—
929C22—2442no—
930C22—2448no—
931C22—2441no—
932C22—2441no—
933C22C2×C22⋊C4×D6111yescharacteristic
934C22#1684027211yescharacteristic
935C22#1684027511yescharacteristic
936C4—22no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—44no—
941C4—41no—
942C4—41no—
943C4—612no—
944C4—612no—
945C4—1221no—
946C4—1221no—
947C4—1222no—
948C4—1221no—
949C4—1221no—
950C4—2444no—
951C4—2441no—
952C4—2441no—
953C4#104×D6112yes—
954C4#117×D6111yescharacteristic
955C4C2×#1451973511yescharacteristic
956C4#1684027211yescharacteristic
957C4#1684027511yescharacteristic
958C2—21no—
959C2—21no—
960C2—42no—
961C2—1222no—
962C2—2441no—
963C2—2442no—
964C2#2144820111yescharacteristic
965C2C2×#104×D6111yescharacteristic
966C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1806C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#41×D61C22
cosocleC22×C4×C61C24
hypercenter#1806D61
hypocenterC61#20747
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #21454451C2semidirect
3. C4×#14519735C2semidirect
4. #21445917C2semidirect
5. #21445840C2semidirect
6. #21445839C2semidirect
7. #21445836C2semidirect
9. #104×Dic61C2semidirect
10. #21445623C2semidirect
11. C61×#1806C2semidirect
14. C4×#11758226C4semidirect
15. C4×#11758226C4semidirect
22. C4×#11758224C4semidirect
23. C4×#11758224C4semidirect
24. C4×Q8×D61C4semidirect
25. C4×Q8×D61C4semidirect
28. C4×D4×D61C4semidirect
29. C4×D4×D61C4semidirect
39. #16839786C22semidirect
44. M16×Dic61C22semidirect
46. C4×C4⋊Dic61C22semidirect
50. C42×Dic61C22semidirect
51. #16839523C22semidirect
52. #16839522C22semidirect
53. #16839521C22semidirect
55. C61×#423C22semidirect
57. C4×C4⋊C4×C61C22semidirect
58. C61×#339C22semidirect
348. Q8×C61#117semidirect
352. D4×C61#117semidirect
400. D244#117semidirect
426. C4×D61#104semidirect
429. Dic122#117semidirect
482. #1806D61semidirect
524. #423C2×D61semidirect
533. C4×C4⋊C4C2×D61semidirect
541. #339C2×D61semidirect
542. C61#20747semidirect
835. Q8#14519735semidirect
846. D4#14519735semidirect

Maximal subgroups

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

subgroupindex
C4×#41×D612
#214544512
C4×#145197352
#214459172
#214458402
#214458392
#214458362
#214457612
#104×Dic612
#214456232
C61×#18062
#2074761