Finite Group Databasebeta

← #30620127

Subgroups — #30620127

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×#16840741C211yesmaximal, characteristic, complemented
2C22×#14519836C211yesmaximal, characteristic, complemented
3#21462325C212yesmaximal, complemented
4#21461960C212yesmaximal, complemented
5#21461843C212yesmaximal, complemented
6#21461840C212yesmaximal, complemented
7#21461680C211yesmaximal, characteristic, complemented
8#21461648C211yesmaximal, characteristic, complemented
9#21461647C211yesmaximal, characteristic, complemented
10C4×#14519836C211yesmaximal, characteristic, complemented
11C2×#16840408C211yesmaximal, characteristic
12C2×#14519856C2212yescomplemented
13C22×C22⋊#6923C2212yes—
14#16840741—24no—
15C2×#14519836—24no—
16C2×#14519836C2211yescharacteristic
17C2×#14519836C2212yes—
18C2×#14519836C2211yescharacteristic
19C2×#14519836C2211yescharacteristic
20C2×#14519836C2212yes—
21C2×#14519836C2211yescharacteristic
22C2×#14519835C2212yescomplemented
23C2×#14519835C2212yescomplemented
24#16840712—22no—
25#16840712—22no—
26#16840709—22no—
27#16840705C2212yescomplemented
28#16840704C2212yescomplemented
29#16840703C2212yes—
30C22⋊C4×#6923—22no—
31C4×C22⋊#6923C2212yescomplemented
32#16840640C2212yescomplemented
33#16840640C2212yescomplemented
34C22×#11758222C2211yescharacteristic
35C23×D244C2211yescharacteristic
36#16840408—22no—
37#16840408—22no—
38#16840408—22no—
39#16840408—22no—
40C2×#14519765C411yescharacteristic, complemented
41C2×#14519762C411yescharacteristic, complemented
42C2×#14519762C2211yescharacteristic
43C2×#14519756C411yescharacteristic, complemented
44C2×#14519751C411yescharacteristic, complemented
45C2×#14519750C411yescharacteristic, complemented
46C2×#14519750C2211yescharacteristic
47C2×#14519745C411yescharacteristic, complemented
48C2×#14519745C2211yescharacteristic
49C2×C4×D244C2211yescharacteristic
50C2×C22⋊C4×D61C411yescharacteristic, complemented
51C2×C22⋊C4×D61C2211yescharacteristic
52C2×C4×D4×C61C411yescharacteristic, complemented
53C23×#6923—22no—
54#14519856—24no—
55#14519856—42no—
56C2×C4⋊#6923—22no—
57C2×C4⋊#6923—22no—
58C2×C22⋊#6923—24no—
59C2×C22⋊#6923—22no—
60C2×C22⋊#6923—22no—
61C2×C22⋊#6923—22no—
62C2×C22⋊#6923—42no—
63C2×C22⋊#6923C2312yes—
64C2×C22⋊#6923C2312yes—
65C2×C22⋊#6923C2312yes—
66C2×C22⋊#6923C2312yes—
67C2×C4×#6923—22no—
68C2×C4×#6923—22no—
69#14519836—22no—
70#14519836—22no—
71#14519836—22no—
72#14519836—24no—
73#14519836—42no—
74#14519836D414yescomplemented
75#14519835—24no—
76#14519835—42no—
77(C2×#6923)⋊C4—22no—
78(C2×#6923)⋊C4—22no—
79(C2×#6923)⋊C4—22no—
80(C2×#6923)⋊C4—22no—
81C24×D61C2×C411yescharacteristic
82C24×D61C2311yescharacteristic
83C2×#11758222—22no—
84C2×#11758222—22no—
85C2×#11758222—22no—
86C2×#11758222—22no—
87C2×#11758222—42no—
88C22×Dic122C2×C411yescharacteristic, complemented
89C22×D244—22no—
90C22×D244—22no—
91C22×D244—22no—
92C22×D244—22no—
93C22×D244—42no—
94C22×D244C2×C411yescharacteristic
95C22×D244C2×C411yescharacteristic
96C22×D244C2311yescharacteristic
97C22×D244C2311yescharacteristic
98C22×C22⋊D61C2×C411yescharacteristic
99C22×C22⋊D61C2×C411yescharacteristic, complemented
100C22×C22⋊D61C2×C411yescharacteristic, complemented
101C22×C22⋊D61C2311yescharacteristic
102C22×C4×D61C2×C411yescharacteristic, complemented
103C22×C4×D61C2×C411yescharacteristic, complemented
104C22×C4×D61C2311yescharacteristic
105C22×C4×D61C2311yescharacteristic
106#14519765—22no—
107#14519765—22no—
108#14519762—22no—
109#14519762—22no—
110#14519762—22no—
111#14519762—22no—
112#14519756—22no—
113#14519756—22no—
114#14519751—22no—
115#14519751—22no—
116#14519750—22no—
117#14519750—22no—
118#14519750—22no—
119#14519750—22no—
120#14519745—22no—
121#14519745—22no—
122#14519745—22no—
123#14519745—22no—
124C4×D244—22no—
125C4×D244—22no—
126C2×C4⋊Dic61C2×C411yescharacteristic, complemented
127C2×#11758196C2×C411yescharacteristic, complemented
128C2×#11758196C2×C411yescharacteristic, complemented
129C2×C22⋊Dic61C2×C411yescharacteristic
130C2×C22⋊Dic61C2×C411yescharacteristic
131C2×#11758198C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic, complemented
135C2×#11758198C2×C411yescharacteristic, complemented
136C2×#11758198C2×C411yescharacteristic, complemented
137C2×#11758198C2×C411yescharacteristic, complemented
138C2×#11758198C2311yescharacteristic
139C22⋊C4×D61—21no—
140C22⋊C4×D61—21no—
141C22⋊C4×D61—21no—
142C22⋊C4×D61—21no—
143C22⋊C4×D61D412yes—
144C22⋊C4×D61D412yes—
145C22⋊C4×D61D412yes—
146C22⋊C4×D61D412yes—
147C22×D4×C61C2×C411yescharacteristic
148C23×C4×C61C2×C411yescharacteristic
149C23×C4×C61C2×C411yescharacteristic, complemented
150C4×D4×C61—21no—
151C4×D4×C61—21no—
152C4×D4×C61—21no—
153C4×D4×C61—21no—
154C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
155C2×C22⋊C4×C61C2×C411yescharacteristic
156C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
157C2×C42×C61C2×C411yescharacteristic, complemented
158C24×C61C22×C411yescharacteristic
159C24×C61C22×C411yescharacteristic
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—22no—
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—22no—
166C23×D61—41no—
167C23×D61—42no—
168C23×D61—42no—
169C23×D61—81no—
170C23×D61—81no—
171C23×D61C22×C411yescharacteristic
172C23×D61C22×C411yescharacteristic
173C23×D61C22×C411yescharacteristic
174C23×D61C2×D412yes—
175C23×D61C2×D412yes—
176C23×D61C2411yescharacteristic
177C22×#6923—22no—
178C22×#6923—22no—
179C22×#6923—22no—
180C22×#6923—22no—
181C22×#6923—44no—
182C22×#6923—44no—
183C22×#6923—82no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—42no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—41no—
194C22×C4×C61—41no—
195C22×C4×C61C22×C411yescharacteristic
196C22×C4×C61C22×C411yescharacteristic
197C22×C4×C61C22×C411yescharacteristic
198C22×C4×C61C22×C411yescharacteristic
199C22×C4×C61C22×C411yescharacteristic
200C2×C22⋊D61—22no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—22no—
203C2×C22⋊D61—21no—
204C2×C22⋊D61—22no—
205C2×C22⋊D61—22no—
206C2×C22⋊D61—22no—
207C2×C22⋊D61—22no—
208C2×C22⋊D61—41no—
209C2×C22⋊D61—81no—
210C2×C22⋊D61—81no—
211C22×Dic61C22×C411yescharacteristic
212C22×Dic61C22×C411yescharacteristic
213C22×Dic61C22×C411yescharacteristic
214C22×Dic61C22×C411yescharacteristic
215#11758222—44no—
216#11758222—44no—
217#11758222—44no—
218#11758222—44no—
219C2×D244—22no—
220C2×D244—22no—
221C2×D244—22no—
222C2×D244—22no—
223C2×D244—22no—
224C2×D244—21no—
225C2×D244—22no—
226C2×D244—21no—
227C2×D244—22no—
228C2×D244—22no—
229C2×D244—44no—
230C2×D244—44no—
231C2×D244—44no—
232C2×D244—44no—
233C2×D244—41no—
234C2×D244—41no—
235C2×D244C2×D412yes—
236C2×D244#4112yes—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—22no—
240C2×C4×D61—22no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—41no—
246C2×C4×D61—81no—
247C2×C4×D61—81no—
248C2×C4×D61C2×D412yes—
249C2×C4×D61C2×D412yes—
250C2×C4×D61C2×D412yes—
251C2×C4×D61C2×D412yes—
252C2×Dic122—22no—
253C2×Dic122—22no—
254C2×Dic122—41no—
255C22⋊#6923—22no—
256C22⋊#6923—22no—
257C22⋊#6923—22no—
258C22⋊#6923—22no—
259C22⋊#6923—22no—
260C22⋊#6923—22no—
261C22⋊#6923—22no—
262C22⋊#6923—44no—
263C22⋊#6923—44no—
264C22⋊#6923—82no—
265C22⋊#6923C2×D414yes—
266C4⋊#6923—44no—
267C4⋊#6923—82no—
268C4×#6923—44no—
269C4×#6923—82no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61C22⋊C411yescharacteristic
275C22⋊C4×C61C22⋊C411yescharacteristic
276C22⋊C4×C61C22⋊C411yescharacteristic
277C22⋊C4×C61C22⋊C411yescharacteristic
278C42×C61—21no—
279C42×C61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61C22⋊C412yes—
283C22⋊Dic61C22⋊C412yes—
284#11758198—22no—
285#11758198—22no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—22no—
291#11758198—22no—
292#11758198C22⋊C412yes—
293#11758198C22⋊C412yes—
294#11758198C22⋊C412yes—
295#11758198C22⋊C412yes—
296C4⋊Dic61—22no—
297#11758196—22no—
298#11758196—22no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—22no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61C2×C22⋊C411yescharacteristic
309C23×C61C2×C22⋊C411yescharacteristic
310C23×C61C23×C411yescharacteristic
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—24no—
314C22×D61—21no—
315C22×D61—21no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—41no—
324C22×D61—42no—
325C22×D61—41no—
326C22×D61—42no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—42no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—42no—
335C22×D61—42no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—82no—
339C22×D61—82no—
340C22×D61—84no—
341C22×D61—81no—
342C22×D61—81no—
343C22×D61—84no—
344C22×D61—84no—
345C22×D61C2×C22⋊C412yes—
346C22×D61C4×D412yes—
347C22×D61C22×D412yes—
348C22×D61C22×D411yescharacteristic
349C22×D61C2×#4111yescharacteristic
350C22×D61H(5,𝔽2)12yes—
351C2×#6923—24no—
352C2×#6923—42no—
353C2×#6923—42no—
354C2×#6923—42no—
355C2×#6923—42no—
356C2×#6923—42no—
357C2×#6923—42no—
358C2×#6923—42no—
359C2×#6923—42no—
360C2×#6923—42no—
361C2×#6923—42no—
362C2×#6923—42no—
363C2×#6923—88no—
364D4×C61—42no—
365D4×C61—42no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—41no—
375C2×C4×C61—42no—
376C2×C4×C61—42no—
377C2×C4×C61—42no—
378C2×C4×C61—42no—
379C2×C4×C61—41no—
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C2×C22⋊C411yescharacteristic
383C2×C4×C61C2×C22⋊C411yescharacteristic
384C2×C4×C61C4×D412yes—
385C22⋊D61—44no—
386C22⋊D61—42no—
387C22⋊D61—42no—
388C22⋊D61—82no—
389C22⋊D61—82no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61C2×C22⋊C412yes—
399C2×Dic61C2×C22⋊C412yes—
400D244—24no—
401D244—24no—
402D244—44no—
403D244—44no—
404D244—42no—
405D244—42no—
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—42no—
411C4×D61—42no—
412C4×D61—42no—
413C4×D61—42no—
414C4×D61—81no—
415C4×D61—81no—
416Dic122—44no—
417#22405—611nomaximal, Sylow
418C22×C61—21no—
419C22×C61—21no—
420C22×C61—21no—
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—81no—
431C22×C61—81no—
432C22×C61#41012yescomplemented
433C22×C61C22×C22⋊C411yescharacteristic
434C22×C61C2×C4×D411yescharacteristic
435C22×C61#51811yescharacteristic
436C2×D61—22no—
437C2×D61—22no—
438C2×D61—22no—
439C2×D61—22no—
440C2×D61—22no—
441C2×D61—22no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—42no—
445C2×D61—44no—
446C2×D61—44no—
447C2×D61—42no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—42no—
451C2×D61—41no—
452C2×D61—41no—
453C2×D61—41no—
454C2×D61—82no—
455C2×D61—82no—
456C2×D61—81no—
457C2×D61—81no—
458C2×D61—84no—
459C2×D61—84no—
460C2×D61—81no—
461C2×D61—81no—
462C2×D61D4212yes—
463C2×D61#54612yes—
464#6923—44no—
465#6923—82no—
466#6923—82no—
467#6923—82no—
468C4×C61—22no—
469C4×C61—21no—
470C4×C61—21no—
471C4×C61—21no—
472C4×C61—21no—
473C4×C61—41no—
474C4×C61—41no—
475Dic61—22no—
476Dic61—22no—
477Dic61—41no—
478Dic61—41no—
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×#99—611no—
490C2×C61—21no—
491C2×C61—21no—
492C2×C61—22no—
493C2×C61—41no—
494C2×C61—81no—
495C2×C61D4×C22⋊C411yescharacteristic
496C2×C61C2×#41011yescharacteristic
497C2×C61#288311yescharacteristic
498D61—22no—
499D61—22no—
500D61—42no—
501D61—42no—
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×D4#692311yescharacteristic, complemented
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—611no—
528C2×#99—612no—
529C2×#99—612no—
530C2×#99—611no—
531C2×#99—612no—
532C2×#99—612no—
533C2×#99—1224no—
534#388—1222no—
535#388—1222no—
536#385—1222no—
537#381—612no—
538#380—612no—
539#379—612no—
540C4×C22⋊C4—612no—
541C4×C22⋊C4—1222no—
542#342—612no—
543#342—612no—
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×D4C2×#692311yescharacteristic
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—1222no—
572C23×C4C2×#692311yescharacteristic
573C23×C4C2×#692311yescharacteristic, complemented
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—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—1222no—
597C4×D4—1222no—
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⋊C4C2×#692311yescharacteristic, complemented
606C2×C22⋊C4—611no—
607C2×C22⋊C4—611no—
608C2×C22⋊C4—611no—
609C2×C22⋊C4—612no—
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—611no—
621C2×C22⋊C4—612no—
622C2×C22⋊C4—612no—
623C2×C22⋊C4—612no—
624C2×C22⋊C4—1224no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1222no—
630C2×C22⋊C4—1222no—
631C2×C22⋊C4—1222no—
632C2×C22⋊C4—2442no—
633C2×C22⋊C4C2×#692311yescharacteristic
634C2×C22⋊C4C2×#692311yescharacteristic, complemented
635C2×C42—1222no—
636C2×C42—1222no—
637C2×C42C2×#692311yescharacteristic, complemented
638#99—614no—
639#99—1224no—
640#99—1224no—
641#99—1222no—
642#99—1222no—
643#99—1222no—
644#99—2442no—
645#99—2442no—
646#95—1222no—
647#95—1222no—
648#95—1222no—
649#95—1222no—
650C24—611no—
651C24—612no—
652C24—612no—
653C24—611no—
654C24—611no—
655C24—611no—
656C24—1221no—
657C24—1222no—
658C24—1221no—
659C24—1222no—
660C24—1221no—
661C24—1221no—
662C24—4881no—
663C24—4881no—
664C24—2441no—
665C24—2442no—
666C24—2442no—
667C24C22×#692311yescharacteristic
668C24C22×#692311yescharacteristic
669#41—2444no—
670#41—2444no—
671#41—2444no—
672#41—2444no—
673C2×Q8—1222no—
674C2×Q8—1222no—
675C2×Q8—2441no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—42no—
679C2×D4—612no—
680C2×D4—612no—
681C2×D4—1222no—
682C2×D4—1222no—
683C2×D4—1221no—
684C2×D4—1222no—
685C2×D4—1222no—
686C2×D4—1222no—
687C2×D4—1222no—
688C2×D4—1221no—
689C2×D4—1222no—
690C2×D4—1222no—
691C2×D4—1222no—
692C2×D4—1222no—
693C2×D4—1221no—
694C2×D4—1222no—
695C2×D4—1222no—
696C2×D4—1222no—
697C2×D4—1221no—
698C2×D4—1222no—
699C2×D4—4881no—
700C2×D4—4881no—
701C2×D4—2441no—
702C2×D4—2441no—
703C2×D4—2444no—
704C2×D4—2444no—
705C2×D4—2444no—
706C2×D4—2444no—
707C2×D4—2441no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—41no—
715C22×C4—41no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—612no—
719C22×C4—612no—
720C22×C4—612no—
721C22×C4—612no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—1221no—
725C22×C4—1222no—
726C22×C4—1221no—
727C22×C4—1222no—
728C22×C4—1222no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1222no—
734C22×C4—1222no—
735C22×C4—1222no—
736C22×C4—4881no—
737C22×C4—4881no—
738C22×C4—4882no—
739C22×C4—2441no—
740C22×C4—2444no—
741C22×C4—2444no—
742C22×C4C22×#692311yescharacteristic
743C22×C4C22×#692311yescharacteristic
744C22×C4C22×#692311yescharacteristic
745C22×C4C22×#692311yescharacteristic
746C22×C4C22×#692311yescharacteristic
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—1222no—
750C4⋊C4—1222no—
751C4⋊C4—1222no—
752C4⋊C4—4882no—
753C4⋊C4—2444no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—612no—
757C22⋊C4—612no—
758C22⋊C4—612no—
759C22⋊C4—612no—
760C22⋊C4—612no—
761C22⋊C4—612no—
762C22⋊C4—614no—
763C22⋊C4—1222no—
764C22⋊C4—1222no—
765C22⋊C4—1222no—
766C22⋊C4—1222no—
767C22⋊C4—1222no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C22⋊C4—1221no—
773C22⋊C4—1221no—
774C22⋊C4—1222no—
775C22⋊C4—1222no—
776C22⋊C4—1222no—
777C22⋊C4—1222no—
778C22⋊C4—1222no—
779C22⋊C4—1222no—
780C22⋊C4—4882no—
781C22⋊C4—2444no—
782C22⋊C4—2444no—
783C22⋊C4C22⋊#692311yescharacteristic
784C22⋊C4C22⋊#692311yescharacteristic
785C22⋊C4C22⋊#692311yescharacteristic
786C22⋊C4C22⋊#692311yescharacteristic
787C42—21no—
788C42—21no—
789C42—4882no—
790C42—2444no—
791C23—22no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—612no—
801C23—611no—
802C23—611no—
803C23—612no—
804C23—612no—
805C23—612no—
806C23—1222no—
807C23—1222no—
808C23—1222no—
809C23—1222no—
810C23—1221no—
811C23—1221no—
812C23—1224no—
813C23—1221no—
814C23—1221no—
815C23—1221no—
816C23—1221no—
817C23—1221no—
818C23—4881no—
819C23—4881no—
820C23—4884no—
821C23—4884no—
822C23—4882no—
823C23—4884no—
824C23—4882no—
825C23—2442no—
826C23—2441no—
827C23—2441no—
828C23—2442no—
829C23—2441no—
830C23—2442no—
831C23—2441no—
832C23—2442no—
833C23—2442no—
834C23—2441no—
835C23—2441no—
836C23—2442no—
837C23—2441no—
838C23—2441no—
839C23—2442no—
840C23C2×C22⋊#692311yescharacteristic
841C23C2×C22⋊#692311yescharacteristic
842C23C23×#692311yescharacteristic
843Q8—2444no—
844D4—42no—
845D4—42no—
846D4—1224no—
847D4—1224no—
848D4—4882no—
849D4—4882no—
850D4—2444no—
851D4—2442no—
852D4—2442no—
853D4—2444no—
854D4—2444no—
855D4—2442no—
856D4—2442no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—41no—
871C2×C4—612no—
872C2×C4—612no—
873C2×C4—1222no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1224no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—4881no—
885C2×C4—4881no—
886C2×C4—4888no—
887C2×C4—2442no—
888C2×C4—2442no—
889C2×C4—2442no—
890C2×C4—2442no—
891C2×C4—2441no—
892C2×C4—2442no—
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—2441no—
904C2×C4C2×C22⋊#692311yescharacteristic
905C2×C4C2×C22⋊#692311yescharacteristic
906C2×C4C2×C22⋊#692311yescharacteristic
907C2×C4C2×C22⋊#692311yescharacteristic
908C2×C4D4×#692312yes—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—42no—
917C22—42no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—81no—
922C22—81no—
923C22—612no—
924C22—612no—
925C22—1222no—
926C22—1222no—
927C22—1222no—
928C22—1222no—
929C22—1222no—
930C22—1222no—
931C22—4881no—
932C22—4881no—
933C22—4884no—
934C22—4881no—
935C22—4881no—
936C22—4882no—
937C22—4882no—
938C22—4884no—
939C22—2441no—
940C22—2441no—
941C22—2442no—
942C22—2444no—
943C22—2444no—
944C22—2442no—
945C22—2442no—
946C22—2441no—
947C22—2441no—
948C22—2441no—
949C22—2441no—
950C22—2441no—
951C22#1684074112yescomplemented
952C22C22×C22⋊#692311yescharacteristic
953C22C2×D4×#692311yescharacteristic
954C22#1684082911yescharacteristic
955C4—22no—
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—41no—
961C4—41no—
962C4—1222no—
963C4—1222no—
964C4—4882no—
965C4—4882no—
966C4—4882no—
967C4—2444no—
968C4—2441no—
969C4—2441no—
970C2—21no—
971C2—21no—
972C2—22no—
973C2—41no—
974C2—81no—
975C2—1222no—
976C2—1222no—
977C2—4881no—
978C2—2442no—
979C2—2442no—
980C2D4×C22⋊#692311yescharacteristic
981C2C2×#1684074111yescharacteristic
982C2#2146241911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840408C2
cosocleC23×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61#22405
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16840741C2semidirect
2. C22×#14519836C2semidirect
3. #21462325C2semidirect
4. #21461960C2semidirect
5. #21461843C2semidirect
6. #21461840C2semidirect
7. #21461680C2semidirect
8. #21461648C2semidirect
9. #21461647C2semidirect
10. C4×#14519836C2semidirect
12. C2×#14519856C22semidirect
22. C2×#14519835C22semidirect
23. C2×#14519835C22semidirect
27. #16840705C22semidirect
28. #16840704C22semidirect
31. C4×C22⋊#6923C22semidirect
32. #16840640C22semidirect
33. #16840640C22semidirect
40. C2×#14519765C4semidirect
41. C2×#14519762C4semidirect
43. C2×#14519756C4semidirect
44. C2×#14519751C4semidirect
45. C2×#14519750C4semidirect
47. C2×#14519745C4semidirect
50. C2×C22⋊C4×D61C4semidirect
52. C2×C4×D4×C61C4semidirect
74. #14519836D4semidirect
88. C22×Dic122C2×C4semidirect
99. C22×C22⋊D61C2×C4semidirect
100. C22×C22⋊D61C2×C4semidirect
102. C22×C4×D61C2×C4semidirect
103. C22×C4×D61C2×C4semidirect
126. C2×C4⋊Dic61C2×C4semidirect
127. C2×#11758196C2×C4semidirect
128. C2×#11758196C2×C4semidirect
134. C2×#11758198C2×C4semidirect
135. C2×#11758198C2×C4semidirect
136. C2×#11758198C2×C4semidirect
137. C2×#11758198C2×C4semidirect
149. C23×C4×C61C2×C4semidirect
154. C2×C4⋊C4×C61C2×C4semidirect
156. C2×C22⋊C4×C61C2×C4semidirect
157. C2×C42×C61C2×C4semidirect
432. C22×C61#410semidirect
519. C2×C4×D4#6923semidirect
544. C61#22405semidirect
573. C23×C4C2×#6923semidirect
605. C2×C4⋊C4C2×#6923semidirect
634. C2×C22⋊C4C2×#6923semidirect
637. C2×C42C2×#6923semidirect
951. C22#16840741semidirect

Maximal subgroups

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

subgroupindex
C2×#168407412
C22×#145198362
#214623252
#214619602
#214618432
#214618402
#214616802
#214616482
#214616472
C4×#145198362
C2×#168404082
#2240561