Finite Group Databasebeta

← #30620131

Subgroups — #30620131

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×#16840743C211yesmaximal, characteristic, complemented
2C22×#14519836C211yesmaximal, characteristic, complemented
3#21462325C212yesmaximal, complemented
4#21461959C212yesmaximal, complemented
5#21461843C212yesmaximal, complemented
6#21461841C212yesmaximal, complemented
7#21461682C211yesmaximal, characteristic, complemented
8#21461650C211yesmaximal, characteristic, complemented
9#21461647C211yesmaximal, characteristic, complemented
10#21461564C211yesmaximal, characteristic, complemented
11C2×#16840403C211yesmaximal, characteristic
12C2×#14519856C2212yescomplemented
13C22×C22⋊#6923C2212yes—
14#16840743—24no—
15C2×#14519836—24no—
16C2×#14519836C2211yescharacteristic
17C2×#14519836C2212yes—
18C2×#14519836C2211yescharacteristic
19C2×#14519836C2211yescharacteristic
20C2×#14519836C2212yes—
21C2×#14519836C2211yescharacteristic
22C2×#14519836C2212yescomplemented
23C2×#14519836C2212yescomplemented
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×#11758226C2211yescharacteristic
35C23×D244C2211yescharacteristic
36#16840403—22no—
37#16840403—22no—
38#16840403—22no—
39#16840403—22no—
40C2×#14519766C411yescharacteristic, complemented
41C2×#14519762C411yescharacteristic, complemented
42C2×#14519762C2211yescharacteristic
43C2×#14519752C411yescharacteristic, complemented
44C2×#14519752C411yescharacteristic, complemented
45C2×#14519752C2211yescharacteristic
46C2×#14519747C411yescharacteristic, complemented
47C2×#14519747C2211yescharacteristic
48C2×#14519739C2211yescharacteristic
49C2×C4×C22⋊D61C411yescharacteristic, complemented
50C2×C22⋊C4×D61C411yescharacteristic, complemented
51C2×C22⋊C4×D61C2211yescharacteristic
52C2×C22⋊Q8×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—24no—
74#14519836—42no—
75#14519836—42no—
76#14519836D414yescomplemented
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×#11758226—22no—
84C2×#11758226—22no—
85C2×#11758226—22no—
86C2×#11758226—22no—
87C2×#11758226—42no—
88C22×D244—22no—
89C22×D244—22no—
90C22×D244—22no—
91C22×D244—22no—
92C22×D244—42no—
93C22×D244C2×C411yescharacteristic
94C22×D244C2×C411yescharacteristic
95C22×D244C2×C411yescharacteristic
96C22×D244C2×C411yescharacteristic, complemented
97C22×D244C2×C411yescharacteristic, complemented
98C22×D244C2311yescharacteristic
99C22×D244C2311yescharacteristic
100C22×D244C2311yescharacteristic
101C22×C22⋊D61C2×C411yescharacteristic
102C22×C4×D61C2×C411yescharacteristic, complemented
103C22×C4×D61C2×C411yescharacteristic, complemented
104C22×C4×D61C2×C411yescharacteristic, complemented
105C22×C4×D61C2311yescharacteristic
106C22×C4×D61C2311yescharacteristic
107#14519766—22no—
108#14519766—22no—
109#14519762—22no—
110#14519762—22no—
111#14519762—22no—
112#14519762—22no—
113#14519752—22no—
114#14519752—22no—
115#14519752—22no—
116#14519752—22no—
117#14519752—22no—
118#14519752—22no—
119#14519747—22no—
120#14519747—22no—
121#14519747—22no—
122#14519747—22no—
123#14519739—22no—
124#14519739—22no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127C4×C22⋊D61—21no—
128C4×C22⋊D61—21no—
129C2×#11758196C2×C411yescharacteristic, complemented
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×#11758198C2×C411yescharacteristic, complemented
139C2×#11758198C2311yescharacteristic
140C22⋊C4×D61—21no—
141C22⋊C4×D61—21no—
142C22⋊C4×D61—21no—
143C22⋊C4×D61—21no—
144C22⋊C4×D61D412yes—
145C22⋊C4×D61D412yes—
146C22⋊C4×D61D412yes—
147C22⋊C4×D61D412yes—
148C2×C4×Dic61C2×C411yescharacteristic, complemented
149C22×Q8×C61C2×C411yescharacteristic, complemented
150C23×C4×C61C2×C411yescharacteristic
151C22⋊Q8×C61—22no—
152C22⋊Q8×C61—22no—
153C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
154C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
155C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
156C2×C22⋊C4×C61C2×C411yescharacteristic
157C2×C22⋊C4×C61C2×C411yescharacteristic
158C24×C61C22×C411yescharacteristic
159C23×D61—21no—
160C23×D61—21no—
161C23×D61—22no—
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—22no—
165C23×D61—41no—
166C23×D61—42no—
167C23×D61—42no—
168C23×D61—81no—
169C23×D61—81no—
170C23×D61C22×C411yescharacteristic
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×Q8×C61—22no—
185C2×Q8×C61—22no—
186C2×Q8×C61—41no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—22no—
190C22×C4×C61—41no—
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C22×C411yescharacteristic
193C22×C4×C61C22×C411yescharacteristic
194C22×C4×C61C22×C411yescharacteristic
195C22×C4×C61C22×C411yescharacteristic
196C22×C4×C61C22×C411yescharacteristic
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—42no—
200C22×Dic61C22×C411yescharacteristic
201C22×Dic61C22×C411yescharacteristic
202C22×Dic61C22×C411yescharacteristic
203#11758226—44no—
204#11758226—44no—
205#11758226—44no—
206#11758226—44no—
207C2×D244—22no—
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—22no—
211C2×D244—22no—
212C2×D244—22no—
213C2×D244—21no—
214C2×D244—22no—
215C2×D244—21no—
216C2×D244—22no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—22no—
220C2×D244—22no—
221C2×D244—22no—
222C2×D244—22no—
223C2×D244—22no—
224C2×D244—22no—
225C2×D244—44no—
226C2×D244—44no—
227C2×D244—44no—
228C2×D244—44no—
229C2×D244—41no—
230C2×D244—41no—
231C2×D244—41no—
232C2×D244—81no—
233C2×D244—81no—
234C2×D244C2×D412yes—
235C2×D244#4112yes—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—22no—
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—21no—
246C2×C4×D61—21no—
247C2×C4×D61—41no—
248C2×C4×D61—41no—
249C2×C4×D61—81no—
250C2×C4×D61—81no—
251C2×C4×D61C2×D412yes—
252C2×C4×D61C2×D412yes—
253C2×C4×D61C2×D412yes—
254C2×C4×D61C2×D412yes—
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—22no—
271C4⋊C4×C61—22no—
272C4⋊C4×C61—22no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61C22⋊C412yes—
276C22⋊C4×C61C22⋊C412yes—
277C22⋊Dic61C22⋊C411yescharacteristic
278C22⋊Dic61C22⋊C411yescharacteristic
279C22⋊Dic61C22⋊C411yescharacteristic
280C22⋊Dic61C22⋊C411yescharacteristic
281#11758198—22no—
282#11758198—22no—
283#11758198—22no—
284#11758198—22no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198C22⋊C412yes—
292#11758198C22⋊C412yes—
293#11758198C22⋊C412yes—
294#11758198C22⋊C412yes—
295#11758196—21no—
296#11758196—21no—
297C4×Dic61—21no—
298C4×Dic61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—22no—
302C23×C61—41no—
303C23×C61C2×C22⋊C411yescharacteristic
304C23×C61C2×C22⋊C411yescharacteristic
305C23×C61C23×C411yescharacteristic
306C22×D61—21no—
307C22×D61—21no—
308C22×D61—24no—
309C22×D61—21no—
310C22×D61—21no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—41no—
322C22×D61—42no—
323C22×D61—41no—
324C22×D61—42no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—42no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—42no—
333C22×D61—42no—
334C22×D61—41no—
335C22×D61—41no—
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—
364Q8×C61—44no—
365C2×C4×C61—21no—
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—21no—
375C2×C4×C61—21no—
376C2×C4×C61—41no—
377C2×C4×C61—42no—
378C2×C4×C61—42no—
379C2×C4×C61—41no—
380C2×C4×C61C2×C22⋊C412yes—
381C2×C4×C61C2×C22⋊C412yes—
382C2×C4×C61C4×D412yes—
383C22⋊D61—42no—
384C22⋊D61—42no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C2×C22⋊C411yescharacteristic
394D244—24no—
395D244—24no—
396D244—44no—
397D244—44no—
398D244—44no—
399D244—42no—
400D244—42no—
401D244—42no—
402D244—42no—
403D244—82no—
404D244—82no—
405C4×D61—22no—
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—42no—
410C4×D61—42no—
411C4×D61—42no—
412C4×D61—42no—
413C4×D61—42no—
414C4×D61—42no—
415C4×D61—81no—
416C4×D61—81no—
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#41012yescomplemented
428C22×C61C22×C22⋊C411yescharacteristic
429C22×C61C2×C4×D411yescharacteristic
430C22×C61#51811yescharacteristic
431C2×D61—22no—
432C2×D61—22no—
433C2×D61—22no—
434C2×D61—22no—
435C2×D61—22no—
436C2×D61—22no—
437C2×D61—41no—
438C2×D61—41no—
439C2×D61—42no—
440C2×D61—44no—
441C2×D61—44no—
442C2×D61—42no—
443C2×D61—41no—
444C2×D61—41no—
445C2×D61—42no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—41no—
452C2×D61—82no—
453C2×D61—82no—
454C2×D61—81no—
455C2×D61—81no—
456C2×D61—84no—
457C2×D61—84no—
458C2×D61—81no—
459C2×D61—81no—
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—22no—
470C4×C61—22no—
471C4×C61—41no—
472C4×C61—41no—
473C4×C61—41no—
474Dic61—21no—
475Dic61—21no—
476Dic61—21no—
477Dic61—21no—
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×C61D4×C22⋊C411yescharacteristic
495C2×C61C2×#41011yescharacteristic
496C2×C61#288311yescharacteristic
497D61—22no—
498D61—22no—
499D61—42no—
500D61—42no—
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#692311yescharacteristic, complemented
513C2×#121—611no—
514C2×#121—611no—
515C2×#121—611no—
516C2×#120—611no—
517C2×#120—611no—
518C2×C4×D4—611no—
519C2×C4×D4—611no—
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—611no—
530C2×#99—612no—
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×Q8C2×#692311yescharacteristic, complemented
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—611no—
562C22×D4—1222no—
563C22×D4—1222no—
564C22×D4—1222no—
565C22×D4—1222no—
566C22×D4—2442no—
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—1222no—
573C23×C4C2×#692311yescharacteristic
574#124—1222no—
575#124—1222no—
576#123—1222no—
577#123—1222no—
578#123—1222no—
579#123—1222no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
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—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1222no—
597C4×D4—1222no—
598#117—1224no—
599#117—2442no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—1222no—
602C2×C4⋊C4—1222no—
603C2×C4⋊C4C2×#692311yescharacteristic, complemented
604C2×C4⋊C4C2×#692311yescharacteristic, complemented
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—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1224no—
629C2×C22⋊C4—1222no—
630C2×C22⋊C4—1222no—
631C2×C22⋊C4—1222no—
632C2×C22⋊C4—2442no—
633C2×C22⋊C4C2×#692311yescharacteristic
634C2×C22⋊C4C2×#692311yescharacteristic
635C2×C42—611no—
636C2×C42—1222no—
637C2×C42—1222no—
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—611no—
657C24—1221no—
658C24—1222no—
659C24—1221no—
660C24—1222no—
661C24—1221no—
662C24—1221no—
663C24—4881no—
664C24—4881no—
665C24—2441no—
666C24—2442no—
667C24—2442no—
668C24C22×#692311yescharacteristic
669#41—2444no—
670#41—2444no—
671#41—2444no—
672#41—2444no—
673C2×Q8—22no—
674C2×Q8—22no—
675C2×Q8—41no—
676C2×D4—612no—
677C2×D4—612no—
678C2×D4—1222no—
679C2×D4—1222no—
680C2×D4—1222no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—1222no—
684C2×D4—1222no—
685C2×D4—1222no—
686C2×D4—1222no—
687C2×D4—1222no—
688C2×D4—1222no—
689C2×D4—1221no—
690C2×D4—1222no—
691C2×D4—1222no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—1221no—
695C2×D4—1222no—
696C2×D4—1222no—
697C2×D4—1222no—
698C2×D4—4881no—
699C2×D4—4881no—
700C2×D4—2441no—
701C2×D4—2441no—
702C2×D4—2441no—
703C2×D4—2444no—
704C2×D4—2444no—
705C2×D4—2444no—
706C2×D4—2444no—
707C2×D4—2442no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—612no—
715C22×C4—612no—
716C22×C4—612no—
717C22×C4—612no—
718C22×C4—611no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1222no—
727C22×C4—1221no—
728C22×C4—1222no—
729C22×C4—1222no—
730C22×C4—1222no—
731C22×C4—1222no—
732C22×C4—1222no—
733C22×C4—1222no—
734C22×C4—4881no—
735C22×C4—4881no—
736C22×C4—4882no—
737C22×C4—2441no—
738C22×C4—2441no—
739C22×C4—2444no—
740C22×C4—2444no—
741C22×C4C22×#692311yescharacteristic
742C22×C4C22×#692311yescharacteristic
743C22×C4C22×#692311yescharacteristic
744C22×C4C22×#692311yescharacteristic
745C22×C4C22×#692311yescharacteristic
746C22×C4C22×#692311yescharacteristic
747C4⋊C4—22no—
748C4⋊C4—22no—
749C4⋊C4—22no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—4882no—
753C4⋊C4—2444no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—611no—
757C22⋊C4—611no—
758C22⋊C4—611no—
759C22⋊C4—611no—
760C22⋊C4—612no—
761C22⋊C4—612no—
762C22⋊C4—612no—
763C22⋊C4—612no—
764C22⋊C4—614no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1222no—
772C22⋊C4—1222no—
773C22⋊C4—1222no—
774C22⋊C4—1222no—
775C22⋊C4—1222no—
776C22⋊C4—1222no—
777C22⋊C4—1222no—
778C22⋊C4—1222no—
779C22⋊C4—1222no—
780C22⋊C4—1222no—
781C22⋊C4—1222no—
782C22⋊C4—4882no—
783C22⋊C4—2444no—
784C22⋊C4—2444no—
785C22⋊C4C22⋊#692312yes—
786C22⋊C4C22⋊#692312yes—
787C42—1221no—
788C42—1221no—
789C42—4882no—
790C42—2444no—
791C23—22no—
792C23—21no—
793C23—21no—
794C23—41no—
795C23—612no—
796C23—611no—
797C23—611no—
798C23—612no—
799C23—612no—
800C23—612no—
801C23—1222no—
802C23—1222no—
803C23—1222no—
804C23—1222no—
805C23—1221no—
806C23—1221no—
807C23—1224no—
808C23—1221no—
809C23—1221no—
810C23—1221no—
811C23—1221no—
812C23—1221no—
813C23—1221no—
814C23—1221no—
815C23—1221no—
816C23—4881no—
817C23—4881no—
818C23—4884no—
819C23—4884no—
820C23—4882no—
821C23—4884no—
822C23—4882no—
823C23—2442no—
824C23—2441no—
825C23—2441no—
826C23—2442no—
827C23—2441no—
828C23—2442no—
829C23—2441no—
830C23—2442no—
831C23—2442no—
832C23—2441no—
833C23—2441no—
834C23—2441no—
835C23—2441no—
836C23—2442no—
837C23—2441no—
838C23—2441no—
839C23—2442no—
840C23C2×C22⋊#692311yescharacteristic
841C23C2×C22⋊#692311yescharacteristic
842C23C23×#692311yescharacteristic
843Q8—44no—
844D4—1224no—
845D4—1224no—
846D4—4882no—
847D4—4882no—
848D4—2444no—
849D4—2444no—
850D4—2442no—
851D4—2442no—
852D4—2442no—
853D4—2442no—
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—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—611no—
873C2×C4—611no—
874C2×C4—611no—
875C2×C4—611no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1224no—
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—2442no—
892C2×C4—2442no—
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×C4—2442no—
905C2×C4—2441no—
906C2×C4C2×C22⋊#692312yes—
907C2×C4C2×C22⋊#692312yes—
908C2×C4D4×#692312yes—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—42no—
917C22—42no—
918C22—612no—
919C22—612no—
920C22—1222no—
921C22—1222no—
922C22—1222no—
923C22—1222no—
924C22—1222no—
925C22—1222no—
926C22—4881no—
927C22—4881no—
928C22—4881no—
929C22—4881no—
930C22—4884no—
931C22—4881no—
932C22—4881no—
933C22—4882no—
934C22—4882no—
935C22—4884no—
936C22—2441no—
937C22—2441no—
938C22—2442no—
939C22—2444no—
940C22—2444no—
941C22—2442no—
942C22—2442no—
943C22—2441no—
944C22—2441no—
945C22—2441no—
946C22—2441no—
947C22—2441no—
948C22—2441no—
949C22—2441no—
950C22—2441no—
951C22#1684074312yescomplemented
952C22C22×C22⋊#692311yescharacteristic
953C22C2×D4×#692311yescharacteristic
954C22#1684082911yescharacteristic
955C4—22no—
956C4—22no—
957C4—22no—
958C4—41no—
959C4—41no—
960C4—41no—
961C4—1221no—
962C4—1221no—
963C4—1221no—
964C4—1221no—
965C4—4882no—
966C4—4882no—
967C4—4882no—
968C4—2444no—
969C4—2441no—
970C2—21no—
971C2—21no—
972C2—22no—
973C2—41no—
974C2—1222no—
975C2—1222no—
976C2—4881no—
977C2—4881no—
978C2—2442no—
979C2—2442no—
980C2D4×C22⋊#692311yescharacteristic
981C2C2×#1684074311yescharacteristic
982C2#2146241911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840403C2
cosocleC23×D61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#22405
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16840743C2semidirect
2. C22×#14519836C2semidirect
3. #21462325C2semidirect
4. #21461959C2semidirect
5. #21461843C2semidirect
6. #21461841C2semidirect
7. #21461682C2semidirect
8. #21461650C2semidirect
9. #21461647C2semidirect
10. #21461564C2semidirect
12. C2×#14519856C22semidirect
22. C2×#14519836C22semidirect
23. C2×#14519836C22semidirect
27. #16840705C22semidirect
28. #16840704C22semidirect
31. C4×C22⋊#6923C22semidirect
32. #16840640C22semidirect
33. #16840640C22semidirect
40. C2×#14519766C4semidirect
41. C2×#14519762C4semidirect
43. C2×#14519752C4semidirect
44. C2×#14519752C4semidirect
46. C2×#14519747C4semidirect
49. C2×C4×C22⋊D61C4semidirect
50. C2×C22⋊C4×D61C4semidirect
52. C2×C22⋊Q8×C61C4semidirect
76. #14519836D4semidirect
96. C22×D244C2×C4semidirect
97. C22×D244C2×C4semidirect
102. C22×C4×D61C2×C4semidirect
103. C22×C4×D61C2×C4semidirect
104. C22×C4×D61C2×C4semidirect
129. C2×#11758196C2×C4semidirect
134. C2×#11758198C2×C4semidirect
135. C2×#11758198C2×C4semidirect
136. C2×#11758198C2×C4semidirect
137. C2×#11758198C2×C4semidirect
138. C2×#11758198C2×C4semidirect
148. C2×C4×Dic61C2×C4semidirect
149. C22×Q8×C61C2×C4semidirect
153. C2×C4⋊C4×C61C2×C4semidirect
154. C2×C4⋊C4×C61C2×C4semidirect
155. C2×C4⋊C4×C61C2×C4semidirect
427. C22×C61#410semidirect
512. C2×C22⋊Q8#6923semidirect
544. C61#22405semidirect
552. C22×Q8C2×#6923semidirect
603. C2×C4⋊C4C2×#6923semidirect
604. C2×C4⋊C4C2×#6923semidirect
605. C2×C4⋊C4C2×#6923semidirect
951. C22#16840743semidirect

Maximal subgroups

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

subgroupindex
C2×#168407432
C22×#145198362
#214623252
#214619592
#214618432
#214618412
#214616822
#214616502
#214616472
#214615642
C2×#168404032
#2240561