Finite Group Databasebeta

← #29695349

Subgroups — #29695349

Order 15616.

1668 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840407C211yesmaximal, characteristic
2C2×#16839734C211yesmaximal, characteristic, complemented
3C2×#99×D61C211yesmaximal, characteristic, complemented
4#21448671C212yesmaximal, complemented
5#21446655C212yesmaximal, complemented
6#21446276C212yesmaximal, complemented
7#21446271C212yesmaximal, complemented
8#21445807C211yesmaximal, characteristic, complemented
9#21445735C211yesmaximal, characteristic, complemented
10#21445732C211yesmaximal, characteristic, complemented
11C4×#99×C61C211yesmaximal, characteristic, complemented
12C22×#11758224C2211yescharacteristic
13C22×D4×D61C2211yescharacteristic
14#16840407—22no—
15#16840407—22no—
16#16840407—22no—
17#16840407—22no—
18C2×#14519765C411yescharacteristic, complemented
19C2×#14519761C411yescharacteristic, complemented
20C2×#14519761C2211yescharacteristic
21C2×#14519757C411yescharacteristic, complemented
22C2×#14519752C411yescharacteristic, complemented
23C2×#14519751C411yescharacteristic, complemented
24C2×#14519751C2211yescharacteristic
25C2×#14519747C411yescharacteristic, complemented
26C2×#14519747C2211yescharacteristic
27C2×C4×D244C411yescharacteristic, complemented
28C2×#14519733C2212yescomplemented
29C22×#11758198C411yescharacteristic, complemented
30C22×#11758198C2211yescharacteristic
31C2×C22⋊C4×D61C2212yes—
32#16839734—24no—
33C2×#14519692C2211yescharacteristic
34C2×#14519692C2211yescharacteristic
35C2×#14519691C2212yes—
36C2×#14519691C2212yes—
37C2×#14519691C2212yescomplemented
38C2×#14519691C2212yescomplemented
39#99×D61—24no—
40#16839654—22no—
41#16839653—22no—
42#16839636—22no—
43#16839623C2212yescomplemented
44#16839622C2212yescomplemented
45#16839617C2212yes—
46C4×#11758198—22no—
47#16839529C2212yescomplemented
48C2×C4×D4×C61C2211yescharacteristic
49C2×#99×C61C2211yescharacteristic
50C2×#99×C61C2211yescharacteristic
51C4×C22⋊C4×C61C2212yescomplemented
52C61×#342C2212yescomplemented
53C24×D61C2×C411yescharacteristic
54C24×D61C2311yescharacteristic
55C2×#11758224—22no—
56C2×#11758224—22no—
57C2×#11758224—22no—
58C2×#11758224—22no—
59C2×#11758224—42no—
60C22×Dic122C2×C411yescharacteristic, complemented
61C22×D244C2×C411yescharacteristic
62C22×D244C2×C411yescharacteristic
63C22×D244C2×C411yescharacteristic
64C22×D244C2×C411yescharacteristic, complemented
65C22×C22⋊D61C2×C411yescharacteristic
66C22×C22⋊D61C2×C411yescharacteristic, complemented
67C22×C22⋊D61C2311yescharacteristic
68C22×C22⋊D61C2311yescharacteristic
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61—22no—
72C2×D4×D61—22no—
73C2×D4×D61—42no—
74C23×Dic61C2×C411yescharacteristic, complemented
75C23×Dic61C2311yescharacteristic
76C22×C4×D61—22no—
77C22×C4×D61C2×C411yescharacteristic
78C22×C4×D61C2×C411yescharacteristic, complemented
79#14519765—22no—
80#14519765—22no—
81#14519761—22no—
82#14519761—22no—
83#14519761—22no—
84#14519761—22no—
85#14519757—22no—
86#14519757—22no—
87#14519752—22no—
88#14519752—22no—
89#14519751—22no—
90#14519751—22no—
91#14519751—22no—
92#14519751—22no—
93#14519747—22no—
94#14519747—22no—
95#14519747—22no—
96#14519747—22no—
97C4×D244—21no—
98C4×D244—21no—
99C4×D244—21no—
100C4×D244—21no—
101#14519733—24no—
102#14519733—42no—
103C2×C4⋊Dic61—22no—
104C2×C4⋊Dic61C2×C411yescharacteristic, complemented
105C2×C4⋊Dic61C2×C411yescharacteristic, complemented
106C2×C4⋊Dic61C2×C411yescharacteristic, complemented
107C2×#11758196—22no—
108C2×C22⋊Dic61C2312yes—
109C2×C22⋊Dic61C2312yes—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198C2×C411yescharacteristic
118C2×#11758198C2×C411yescharacteristic
119C2×#11758198C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×#11758198C2×C411yescharacteristic, complemented
124C2×#11758198C2×C411yescharacteristic, complemented
125C2×#11758198C2×C411yescharacteristic, complemented
126C2×#11758198C2×C411yescharacteristic, complemented
127C2×#11758198D412yes—
128C2×#11758198D412yes—
129C2×#11758198D412yes—
130C2×#11758198D412yes—
131C22⋊C4×D61—24no—
132C22⋊C4×D61—42no—
133C2×C4×Dic61—22no—
134#14519692—22no—
135#14519692—22no—
136#14519691—24no—
137#14519691—24no—
138#14519691—42no—
139#14519691—42no—
140#14519684—22no—
141#14519684—22no—
142#14519684—22no—
143C22×D4×C61C2311yescharacteristic
144C23×C4×C61C2×C411yescharacteristic, complemented
145C23×C4×C61C2311yescharacteristic
146C4×D4×C61—22no—
147C4×D4×C61—22no—
148C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
149C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
150C2×C22⋊C4×C61C2312yes—
151C2×C22⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61C2312yes—
153C2×C42×C61—22no—
154C2×C42×C61C2×C411yescharacteristic, complemented
155#99×C61—22no—
156#99×C61D414yescomplemented
157#95×C61—22no—
158C24×C61C22×C411yescharacteristic
159C24×C61C2411yescharacteristic
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—42no—
167C23×D61—41no—
168C23×D61—42no—
169C23×D61—81no—
170C23×D61—81no—
171C23×D61C22×C411yescharacteristic
172C23×D61C22×C411yescharacteristic
173C23×D61C22×C411yescharacteristic
174C23×D61C22×C411yescharacteristic
175C23×D61C2×D412yes—
176C23×D61C2×D412yes—
177C2×D4×C61—22no—
178C2×D4×C61—22no—
179C2×D4×C61C2×D412yes—
180C2×D4×C61#4112yes—
181C22×C4×C61—22no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—22no—
185C22×C4×C61—81no—
186C22×C4×C61—81no—
187C22×C4×C61C22×C411yescharacteristic
188C22×C4×C61C22×C411yescharacteristic
189C22×C4×C61C22×C411yescharacteristic
190C22×C4×C61C22×C411yescharacteristic
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2×D412yes—
194C2×C22⋊D61—22no—
195C2×C22⋊D61—22no—
196C2×C22⋊D61—21no—
197C2×C22⋊D61—22no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—22no—
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—22no—
203C2×C22⋊D61—22no—
204C2×C22⋊D61—22no—
205C2×C22⋊D61—22no—
206C2×C22⋊D61—41no—
207C2×C22⋊D61—41no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—41no—
217C22×Dic61C22×C411yescharacteristic
218C22×Dic61C22×C411yescharacteristic
219C22×Dic61C22×C411yescharacteristic
220C22×Dic61C22×C411yescharacteristic
221C22×Dic61C2×D412yes—
222C22×Dic61C2×D412yes—
223#11758224—44no—
224#11758224—44no—
225#11758224—44no—
226#11758224—44no—
227D4×D61—44no—
228D4×D61—44no—
229D4×D61—44no—
230D4×D61—44no—
231C2×D244—22no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—22no—
235C2×D244—22no—
236C2×D244—22no—
237C2×D244—41no—
238C2×D244—42no—
239C2×D244—81no—
240C2×D244—81no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—22no—
244C2×C4×D61—22no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—41no—
248C2×C4×D61—41no—
249C2×C4×D61—44no—
250C2×C4×D61—44no—
251C2×C4×D61—82no—
252C2×Dic122—22no—
253C2×Dic122—22no—
254C2×Dic122—41no—
255C4⋊C4×C61—22no—
256C22⋊C4×C61—22no—
257C22⋊C4×C61—22no—
258C22⋊C4×C61—22no—
259C22⋊C4×C61—22no—
260C22⋊C4×C61—22no—
261C22⋊C4×C61C2×D414yes—
262C42×C61—21no—
263C42×C61—21no—
264C42×C61—82no—
265C22⋊Dic61—22no—
266C22⋊Dic61—22no—
267C22⋊Dic61—22no—
268C22⋊Dic61—22no—
269#11758198—21no—
270#11758198—21no—
271#11758198—22no—
272#11758198—21no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—22no—
279#11758198—44no—
280#11758198—44no—
281#11758198—82no—
282#11758198C22⋊C411yescharacteristic
283#11758198C22⋊C411yescharacteristic
284#11758198C22⋊C411yescharacteristic
285#11758198C22⋊C411yescharacteristic
286#11758198C22⋊C412yes—
287#11758198C22⋊C412yes—
288#11758198C22⋊C412yes—
289#11758198C22⋊C412yes—
290#11758198C22⋊C412yes—
291#11758198C22⋊C412yes—
292C4⋊Dic61—22no—
293C4⋊Dic61—21no—
294C4⋊Dic61—21no—
295C4⋊Dic61—22no—
296C4⋊Dic61—82no—
297#11758196—44no—
298C4×Dic61—44no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61C4×D412yes—
306C23×C61C23×C411yescharacteristic
307C23×C61C22×D412yes—
308C23×C61C22×D411yescharacteristic
309C23×C61C2×#4111yescharacteristic
310C23×C61H(5,𝔽2)12yes—
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—24no—
320C22×D61—22no—
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—42no—
328C22×D61—41no—
329C22×D61—42no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—42no—
333C22×D61—42no—
334C22×D61—42no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—41no—
338C22×D61—41no—
339C22×D61—41no—
340C22×D61—41no—
341C22×D61—81no—
342C22×D61—81no—
343C22×D61—82no—
344C22×D61—84no—
345C22×D61—82no—
346C22×D61—84no—
347C22×D61—84no—
348C22×D61C2×C22⋊C411yescharacteristic
349C22×D61C2×C22⋊C412yes—
350C22×D61C2×C22⋊C411yescharacteristic
351D4×C61—24no—
352D4×C61—24no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—24no—
358C2×C4×C61—42no—
359C2×C4×C61—42no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—42no—
363C2×C4×C61—42no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—42no—
367C2×C4×C61—42no—
368C2×C4×C61—42no—
369C2×C4×C61—81no—
370C2×C4×C61—81no—
371C2×C4×C61C2×C22⋊C412yes—
372C2×C4×C61C2×C22⋊C411yescharacteristic
373C2×C4×C61C2×C22⋊C411yescharacteristic
374C2×C4×C61C4×D412yes—
375C22⋊D61—44no—
376C22⋊D61—44no—
377C22⋊D61—42no—
378C22⋊D61—42no—
379C22⋊D61—42no—
380C22⋊D61—42no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—42no—
396C2×Dic61—42no—
397C2×Dic61—42no—
398C2×Dic61—42no—
399C2×Dic61—42no—
400C2×Dic61—42no—
401C2×Dic61—42no—
402C2×Dic61—42no—
403C2×Dic61C2×C22⋊C412yes—
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406D244—44no—
407D244—42no—
408D244—42no—
409D244—82no—
410D244—82no—
411C4×D61—42no—
412C4×D61—42no—
413C4×D61—42no—
414C4×D61—42no—
415C4×D61—88no—
416Dic122—44no—
417#22405—611nomaximal, Sylow
418C22×C61—22no—
419C22×C61—21no—
420C22×C61—22no—
421C22×C61—21no—
422C22×C61—22no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61C22×C22⋊C411yescharacteristic
431C22×C61C2×C4×D411yescharacteristic
432C22×C61#51811yescharacteristic
433C22×C61D4212yes—
434C22×C61#54612yes—
435C2×D61—21no—
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—22no—
439C2×D61—21no—
440C2×D61—22no—
441C2×D61—22no—
442C2×D61—21no—
443C2×D61—44no—
444C2×D61—44no—
445C2×D61—42no—
446C2×D61—42no—
447C2×D61—41no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—41no—
452C2×D61—41no—
453C2×D61—84no—
454C2×D61—81no—
455C2×D61—81no—
456C2×D61—82no—
457C2×D61—82no—
458C2×D61—84no—
459C2×D61—81no—
460C2×D61—81no—
461C2×D61—81no—
462C2×D61—81no—
463C2×D61#41012yescomplemented
464C4×C61—22no—
465C4×C61—22no—
466C4×C61—21no—
467C4×C61—21no—
468C4×C61—44no—
469C4×C61—41no—
470C4×C61—41no—
471C4×C61—82no—
472Dic61—22no—
473Dic61—21no—
474Dic61—21no—
475Dic61—41no—
476Dic61—41no—
477Dic61—82no—
478Dic61—82no—
479C2×#546—611no—
480C2×#410—611no—
481C22×#99—611no—
482#2342—612no—
483#1964—612no—
484#1899—612no—
485#1898—612no—
486#1799—611no—
487#1782—611no—
488#1781—611no—
489C4×#99D6111yescharacteristic, complemented
490C2×C61—22no—
491C2×C61—22no—
492C2×C61—21no—
493C2×C61—21no—
494C2×C61—42no—
495C2×C61D4×C22⋊C411yescharacteristic
496C2×C61C2×#41011yescharacteristic
497C2×C61#288311yescharacteristic
498D61—22no—
499D61—42no—
500D61—41no—
501D61—81no—
502D61—81no—
503C22×#41—611no—
504C23×D4—611no—
505#546—1222no—
506#546—1222no—
507#546—1222no—
508#546—1222no—
509C2×#124—611no—
510C2×#123—611no—
511C2×#123—611no—
512C2×C22⋊Q8—611no—
513C2×#121—611no—
514C2×#121—611no—
515C2×#121—611no—
516C2×#120—611no—
517C2×#120—611no—
518C2×C4×D4—611no—
519C2×C4×D4C2×D6111yescharacteristic
520C2×#117—612no—
521C22×C22⋊C4—611no—
522C22×C22⋊C4—611no—
523C22×C22⋊C4—612no—
524#410—1224no—
525C2×#99—611no—
526C2×#99—611no—
527C2×#99—612no—
528C2×#99—612no—
529C2×#99—612no—
530C2×#99—612no—
531C2×#99—1224no—
532C2×#99C2×D6111yescharacteristic
533C2×#99C2×D6111yescharacteristic
534#388—1222no—
535#388—1222no—
536#385—1222no—
537#381—612no—
538#380—612no—
539#379—612no—
540C4×C22⋊C4—1222no—
541C4×C22⋊C4C2×D6112yescomplemented
542#342—612no—
543#342C2×D6112yescomplemented
544C61#2240511yescharacteristic, complemented, Sylow
545C25—611no—
546C25—611no—
547C2×#41—1222no—
548C2×#41—1222no—
549C2×#41—1222no—
550C2×#41—1222no—
551C2×#41—2442no—
552C22×Q8—611no—
553C22×D4—611no—
554C22×D4—611no—
555C22×D4—611no—
556C22×D4—611no—
557C22×D4—611no—
558C22×D4—611no—
559C22×D4—611no—
560C22×D4—611no—
561C22×D4—1222no—
562C22×D4—1222no—
563C22×D4—1222no—
564C22×D4—1222no—
565C22×D4—2442no—
566C22×D4C22×D6111yescharacteristic
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—1222no—
572C23×C4C4×D6111yescharacteristic, complemented
573C23×C4C22×D6111yescharacteristic
574#124—1222no—
575#124—1222no—
576#123—1222no—
577#123—1222no—
578#123—1222no—
579#123—1222no—
580C22⋊Q8—1222no—
581C22⋊Q8—1222no—
582#121—1222no—
583#121—1222no—
584#121—1222no—
585#121—1222no—
586#121—1222no—
587#121—1222no—
588#120—1222no—
589#120—1222no—
590#120—1222no—
591#120—1222no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4—1221no—
598#117—1224no—
599#117—2442no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—1222no—
604C2×C4⋊C4—1222no—
605C2×C4⋊C4C4×D6111yescharacteristic, complemented
606C2×C22⋊C4—611no—
607C2×C22⋊C4—611no—
608C2×C22⋊C4—611no—
609C2×C22⋊C4—611no—
610C2×C22⋊C4—612no—
611C2×C22⋊C4—612no—
612C2×C22⋊C4—612no—
613C2×C22⋊C4—612no—
614C2×C22⋊C4—611no—
615C2×C22⋊C4—611no—
616C2×C22⋊C4—611no—
617C2×C22⋊C4—611no—
618C2×C22⋊C4—611no—
619C2×C22⋊C4—611no—
620C2×C22⋊C4—612no—
621C2×C22⋊C4—612no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1224no—
627C2×C22⋊C4—1222no—
628C2×C22⋊C4—1222no—
629C2×C22⋊C4—1222no—
630C2×C22⋊C4—2442no—
631C2×C22⋊C4C4×D6111yescharacteristic, complemented
632C2×C22⋊C4C22×D6112yes—
633C2×C22⋊C4C22×D6111yescharacteristic
634C2×C22⋊C4C22×D6112yes—
635C2×C42—22no—
636C2×C42—1222no—
637C2×C42C4×D6111yescharacteristic, complemented
638#99—22no—
639#99—1222no—
640#99—1222no—
641#99—1224no—
642#99—1224no—
643#99—2442no—
644#99—2442no—
645#99D24414yescomplemented
646#95—22no—
647#95—1222no—
648#95—1222no—
649#95—1222no—
650C24—611no—
651C24—612no—
652C24—611no—
653C24—612no—
654C24—611no—
655C24—611no—
656C24—1221no—
657C24—1221no—
658C24—1221no—
659C24—1221no—
660C24—1222no—
661C24—1222no—
662C24—4881no—
663C24—4881no—
664C24—2441no—
665C24—2442no—
666C24—2442no—
667C24C2×C4×D6111yescharacteristic
668C24C23×D6111yescharacteristic
669#41—2444no—
670#41—2444no—
671#41—2444no—
672#41—2444no—
673C2×Q8—1222no—
674C2×Q8—1222no—
675C2×Q8—2441no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—1222no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1222no—
682C2×D4—1222no—
683C2×D4—1222no—
684C2×D4—1222no—
685C2×D4—1222no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4—1222no—
691C2×D4—1222no—
692C2×D4—1222no—
693C2×D4—1222no—
694C2×D4—1222no—
695C2×D4—1222no—
696C2×D4—4881no—
697C2×D4—4881no—
698C2×D4—2441no—
699C2×D4—2442no—
700C2×D4—2441no—
701C2×D4—2441no—
702C2×D4—2444no—
703C2×D4—2444no—
704C2×D4—2444no—
705C2×D4—2444no—
706C2×D4C2×D24412yes—
707C2×D4#1175822212yes—
708C22×C4—22no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—22no—
712C22×C4—81no—
713C22×C4—81no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—612no—
717C22×C4—612no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1222no—
729C22×C4—1222no—
730C22×C4—1222no—
731C22×C4—1222no—
732C22×C4—1222no—
733C22×C4—1222no—
734C22×C4—4882no—
735C22×C4—2441no—
736C22×C4—2441no—
737C22×C4—2444no—
738C22×C4—2444no—
739C22×C4—2441no—
740C22×C4C2×C4×D6111yescharacteristic
741C22×C4C2×C4×D6111yescharacteristic
742C22×C4C2×C4×D6111yescharacteristic
743C22×C4C2×C4×D6111yescharacteristic
744C22×C4C2×C4×D6111yescharacteristic
745C22×C4D4×D6112yes—
746C22×C4D4×D6112yes—
747C4⋊C4—22no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4—1222no—
751C4⋊C4—1222no—
752C4⋊C4—4882no—
753C4⋊C4—2444no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—22no—
759C22⋊C4—611no—
760C22⋊C4—611no—
761C22⋊C4—611no—
762C22⋊C4—611no—
763C22⋊C4—612no—
764C22⋊C4—612no—
765C22⋊C4—612no—
766C22⋊C4—612no—
767C22⋊C4—612no—
768C22⋊C4—612no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1222no—
772C22⋊C4—1221no—
773C22⋊C4—1221no—
774C22⋊C4—1222no—
775C22⋊C4—1221no—
776C22⋊C4—1221no—
777C22⋊C4—1221no—
778C22⋊C4—1221no—
779C22⋊C4—1222no—
780C22⋊C4—1222no—
781C22⋊C4—1222no—
782C22⋊C4—1222no—
783C22⋊C4—4882no—
784C22⋊C4—2444no—
785C22⋊C4—2444no—
786C22⋊C4C2×D24414yes—
787C42—21no—
788C42—21no—
789C42—82no—
790C42—2444no—
791C23—21no—
792C23—21no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—611no—
798C23—611no—
799C23—612no—
800C23—1224no—
801C23—1222no—
802C23—1221no—
803C23—1221no—
804C23—1222no—
805C23—1222no—
806C23—1221no—
807C23—1221no—
808C23—1222no—
809C23—1222no—
810C23—1221no—
811C23—1221no—
812C23—1221no—
813C23—1221no—
814C23—1221no—
815C23—1221no—
816C23—4881no—
817C23—4881no—
818C23—4884no—
819C23—4884no—
820C23—4882no—
821C23—4882no—
822C23—4884no—
823C23—2442no—
824C23—2441no—
825C23—2442no—
826C23—2441no—
827C23—2442no—
828C23—2441no—
829C23—2442no—
830C23—2442no—
831C23—2441no—
832C23—2441no—
833C23—2441no—
834C23—2441no—
835C23—2442no—
836C23—2442no—
837C23C4×D24412yes—
838C23C22×C4×D6111yescharacteristic
839C23C2×D4×D6112yes—
840C23C22×D24411yescharacteristic
841C23C2×#1175822211yescharacteristic
842C23#1451982312yes—
843Q8—2444no—
844D4—24no—
845D4—24no—
846D4—4882no—
847D4—4882no—
848D4—2444no—
849D4—2442no—
850D4—2442no—
851D4—2444no—
852D4—2444no—
853D4—2442no—
854D4—2442no—
855D4—2442no—
856D4—2442no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—24no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—81no—
874C2×C4—81no—
875C2×C4—611no—
876C2×C4—611no—
877C2×C4—612no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1222no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—1221no—
892C2×C4—4888no—
893C2×C4—2442no—
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×C4—2442no—
905C2×C4C22⋊C4×D6111yescharacteristic
906C2×C4C22⋊C4×D6111yescharacteristic
907C2×C4C22⋊C4×D6112yes—
908C2×C4C4×D24412yes—
909C22—22no—
910C22—21no—
911C22—22no—
912C22—21no—
913C22—22no—
914C22—41no—
915C22—41no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—41no—
920C22—41no—
921C22—612no—
922C22—1221no—
923C22—1221no—
924C22—1221no—
925C22—1222no—
926C22—1221no—
927C22—1222no—
928C22—1222no—
929C22—1221no—
930C22—4881no—
931C22—4881no—
932C22—4881no—
933C22—4881no—
934C22—4882no—
935C22—4882no—
936C22—4881no—
937C22—4881no—
938C22—4884no—
939C22—4884no—
940C22—2444no—
941C22—2442no—
942C22—2442no—
943C22—2444no—
944C22—2441no—
945C22—2441no—
946C22—2441no—
947C22—2441no—
948C22—2441no—
949C22—2441no—
950C22C2×C22⋊C4×D6111yescharacteristic
951C22C2×C4×D24411yescharacteristic
952C22#1684023611yescharacteristic
953C22D4×D24412yes—
954C22#1684040812yes—
955C4—22no—
956C4—21no—
957C4—21no—
958C4—22no—
959C4—44no—
960C4—41no—
961C4—41no—
962C4—82no—
963C4—1221no—
964C4—1221no—
965C4—1222no—
966C4—4882no—
967C4—4882no—
968C4—2441no—
969C4—2441no—
970C2—22no—
971C2—22no—
972C2—21no—
973C2—21no—
974C2—42no—
975C2—1222no—
976C2—4881no—
977C2—4881no—
978C2—2441no—
979C2—2442no—
980C2C22⋊C4×D24411yescharacteristic
981C2#410×D6111yescharacteristic
982C2#2145427711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC4×#99×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840407C2
cosocleC24×C61C24
hypercenterC4×#99D61
hypocenterC61#22405
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. C2×#16839734C2semidirect
3. C2×#99×D61C2semidirect
4. #21448671C2semidirect
5. #21446655C2semidirect
6. #21446276C2semidirect
7. #21446271C2semidirect
8. #21445807C2semidirect
9. #21445735C2semidirect
10. #21445732C2semidirect
11. C4×#99×C61C2semidirect
18. C2×#14519765C4semidirect
19. C2×#14519761C4semidirect
21. C2×#14519757C4semidirect
22. C2×#14519752C4semidirect
23. C2×#14519751C4semidirect
25. C2×#14519747C4semidirect
27. C2×C4×D244C4semidirect
28. C2×#14519733C22semidirect
29. C22×#11758198C4semidirect
37. C2×#14519691C22semidirect
38. C2×#14519691C22semidirect
43. #16839623C22semidirect
44. #16839622C22semidirect
47. #16839529C22semidirect
51. C4×C22⋊C4×C61C22semidirect
52. C61×#342C22semidirect
60. C22×Dic122C2×C4semidirect
64. C22×D244C2×C4semidirect
66. C22×C22⋊D61C2×C4semidirect
74. C23×Dic61C2×C4semidirect
78. C22×C4×D61C2×C4semidirect
104. C2×C4⋊Dic61C2×C4semidirect
105. C2×C4⋊Dic61C2×C4semidirect
106. C2×C4⋊Dic61C2×C4semidirect
123. C2×#11758198C2×C4semidirect
124. C2×#11758198C2×C4semidirect
125. C2×#11758198C2×C4semidirect
126. C2×#11758198C2×C4semidirect
144. C23×C4×C61C2×C4semidirect
148. C2×C4⋊C4×C61C2×C4semidirect
149. C2×C22⋊C4×C61C2×C4semidirect
154. C2×C42×C61C2×C4semidirect
156. #99×C61D4semidirect
463. C2×D61#410semidirect
489. C4×#99D61semidirect
541. C4×C22⋊C4C2×D61semidirect
543. #342C2×D61semidirect
544. C61#22405semidirect
572. C23×C4C4×D61semidirect
605. C2×C4⋊C4C4×D61semidirect
631. C2×C22⋊C4C4×D61semidirect
637. C2×C42C4×D61semidirect
645. #99D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168404072
C2×#168397342
C2×#99×D612
#214486712
#214466552
#214462762
#214462712
#214458072
#214457352
#214457322
C4×#99×C612
#2240561