Finite Group Databasebeta

← #30620126

Subgroups — #30620126

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
2C2×D61⋊#99C211yesmaximal, characteristic, complemented
3#21462325C212yesmaximal, complemented
4#21461959C212yesmaximal, complemented
5#21461843C212yesmaximal, complemented
6#21461841C212yesmaximal, complemented
7#21461681C211yesmaximal, characteristic, complemented
8#21461648C211yesmaximal, characteristic, complemented
9#21461646C211yesmaximal, characteristic, complemented
10#21461566C211yesmaximal, characteristic, complemented
11C2×#16840404C211yesmaximal, characteristic
12C2×#14519856C2212yescomplemented
13C22×C22⋊#6923C2212yes—
14#16840741—24no—
15C2×#14519836C2212yes—
16C2×#14519836C2212yes—
17C2×#14519836C2212yescomplemented
18C2×#14519836C2212yescomplemented
19D61⋊#99—24no—
20C2×#14519835C2211yescharacteristic
21C2×#14519835C2211yescharacteristic
22C2×#14519835C2211yescharacteristic
23C2×#14519835C2211yescharacteristic
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
35C22×D4×D61C2211yescharacteristic
36#16840404—22no—
37#16840404—22no—
38#16840404—22no—
39#16840404—22no—
40C2×#14519763C411yescharacteristic, complemented
41C2×#14519762C2211yescharacteristic
42C2×#14519755C411yescharacteristic, complemented
43C2×#14519752C2211yescharacteristic
44C2×#14519750C411yescharacteristic, complemented
45C2×#14519749C411yescharacteristic, complemented
46C2×#14519747C411yescharacteristic, complemented
47C2×#14519747C2211yescharacteristic
48C2×#14519739C411yescharacteristic, complemented
49C2×#14519737C2211yescharacteristic
50C22×#11758198C411yescharacteristic, complemented
51C2×C22⋊C4×D61C2211yescharacteristic
52C2×#123×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—24no—
70#14519836—24no—
71#14519836—42no—
72#14519836—42no—
73#14519835—22no—
74#14519835—22no—
75#14519835—22no—
76#14519835D414yescomplemented
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×D244C2×C411yescharacteristic
90C22×D244C2×C411yescharacteristic, complemented
91C22×D244C2311yescharacteristic
92C22×D244C2311yescharacteristic
93C22×C22⋊D61C2×C411yescharacteristic
94C22×C22⋊D61C2×C411yescharacteristic
95C22×C22⋊D61C2×C411yescharacteristic, complemented
96C22×C22⋊D61C2311yescharacteristic
97C2×D4×D61—22no—
98C2×D4×D61—22no—
99C2×D4×D61—22no—
100C2×D4×D61—22no—
101C2×D4×D61—42no—
102C23×Dic61C2×C411yescharacteristic, complemented
103C22×C4×D61C2×C411yescharacteristic
104C22×C4×D61C2×C411yescharacteristic, complemented
105C22×C4×D61C2311yescharacteristic
106C22×C4×D61C2311yescharacteristic
107#14519763—22no—
108#14519763—22no—
109#14519762—22no—
110#14519762—22no—
111#14519755—22no—
112#14519755—22no—
113#14519752—22no—
114#14519752—22no—
115#14519750—22no—
116#14519750—22no—
117#14519749—22no—
118#14519749—22no—
119#14519747—22no—
120#14519747—22no—
121#14519747—22no—
122#14519747—22no—
123#14519739—21no—
124#14519739—21no—
125#14519739—21no—
126#14519739—21no—
127#14519737—22no—
128#14519737—22no—
129C2×#11758196C2×C411yescharacteristic, complemented
130C2×#11758196C2×C411yescharacteristic, complemented
131C2×C22⋊Dic61C2×C411yescharacteristic
132C2×#11758198—21no—
133C2×#11758198—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198C2×C411yescharacteristic
137C2×#11758198C2×C411yescharacteristic
138C2×#11758198C2×C411yescharacteristic
139C2×#11758198C2×C411yescharacteristic, complemented
140C2×#11758198C2×C411yescharacteristic, complemented
141C2×#11758198C2×C411yescharacteristic, complemented
142C2×#11758198C2×C411yescharacteristic, complemented
143C2×#11758198C2311yescharacteristic
144C22⋊C4×D61D412yes—
145C22⋊C4×D61D412yes—
146C22⋊C4×D61D412yes—
147C22⋊C4×D61D412yes—
148C2×C4×Dic61C2×C411yescharacteristic, complemented
149C22×D4×C61C2×C411yescharacteristic
150C23×C4×C61C2×C411yescharacteristic, complemented
151#123×C61—22no—
152#123×C61—22no—
153C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
154C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
155C2×C22⋊C4×C61C2×C411yescharacteristic
156C2×C22⋊C4×C61C2×C411yescharacteristic
157C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
158C24×C61C22×C411yescharacteristic
159C24×C61C22×C411yescharacteristic
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×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—22no—
185C2×D4×C61—22no—
186C2×D4×C61—41no—
187C22×C4×C61—22no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—41no—
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C22×C411yescharacteristic
193C22×C4×C61C22×C411yescharacteristic
194C22×C4×C61C22×C411yescharacteristic
195C22×C4×C61C22×C411yescharacteristic
196C2×C22⋊D61—22no—
197C2×C22⋊D61—22no—
198C2×C22⋊D61—22no—
199C2×C22⋊D61—22no—
200C2×C22⋊D61—22no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—22no—
203C2×C22⋊D61—41no—
204C2×C22⋊D61—41no—
205C2×C22⋊D61—81no—
206C2×C22⋊D61C2×D412yes—
207C2×C22⋊D61#4112yes—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—81no—
211C22×Dic61C22×C411yescharacteristic
212C22×Dic61C22×C411yescharacteristic
213C22×Dic61C22×C411yescharacteristic
214C22×Dic61C22×C411yescharacteristic
215D4×D61—44no—
216D4×D61—44no—
217D4×D61—44no—
218D4×D61—44no—
219#11758222—44no—
220#11758222—44no—
221#11758222—44no—
222#11758222—44no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—22no—
227C2×D244—21no—
228C2×D244—22no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—22no—
232C2×D244—22no—
233C2×D244—22no—
234C2×D244—42no—
235C2×D244—81no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—22no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—22no—
244C2×C4×D61—22no—
245C2×C4×D61—41no—
246C2×C4×D61—41no—
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—
272C4⋊C4×C61—22no—
273C22⋊C4×C61—22no—
274C22⋊C4×C61—22no—
275C22⋊C4×C61C22⋊C412yes—
276C22⋊C4×C61C22⋊C412yes—
277C22⋊Dic61C22⋊C412yes—
278C22⋊Dic61C22⋊C412yes—
279#11758198—21no—
280#11758198—21no—
281#11758198—22no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—22no—
289#11758198C22⋊C411yescharacteristic
290#11758198C22⋊C411yescharacteristic
291#11758198C22⋊C411yescharacteristic
292#11758198C22⋊C411yescharacteristic
293#11758198C22⋊C412yes—
294#11758198C22⋊C412yes—
295#11758196—22no—
296#11758196—22no—
297C4×Dic61—21no—
298C4×Dic61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61C2×C22⋊C412yes—
308C23×C61C4×D412yes—
309C23×C61C23×C411yescharacteristic
310C22×D61—21no—
311C22×D61—21no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—24no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—41no—
325C22×D61—42no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—42no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—81no—
339C22×D61—81no—
340C22×D61—82no—
341C22×D61—82no—
342C22×D61—84no—
343C22×D61—84no—
344C22×D61—84no—
345C22×D61C2×C22⋊C411yescharacteristic
346C22×D61C2×C22⋊C411yescharacteristic
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—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—41no—
375C2×C4×C61—42no—
376C2×C4×C61—42no—
377C2×C4×C61—41no—
378C2×C4×C61C2×C22⋊C412yes—
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C22⋊D61—24no—
382C22⋊D61—24no—
383C22⋊D61—44no—
384C22⋊D61—44no—
385C22⋊D61—82no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—81no—
394C2×Dic61—81no—
395C2×Dic61C2×C22⋊C411yescharacteristic
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C2×C22⋊C412yes—
398C2×Dic61C4×D412yes—
399D244—42no—
400D244—42no—
401D244—42no—
402D244—42no—
403D244—42no—
404D244—42no—
405D244—82no—
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—42no—
415C4×D61—42no—
416Dic122—44no—
417#22405—611nomaximal, Sylow
418C22×C61—21no—
419C22×C61—21no—
420C22×C61—22no—
421C22×C61—22no—
422C22×C61—22no—
423C22×C61—22no—
424C22×C61—42no—
425C22×C61—42no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—81no—
429C22×C61—81no—
430C22×C61C22×C22⋊C411yescharacteristic
431C22×C61C2×C4×D411yescharacteristic
432C22×C61#51811yescharacteristic
433C2×D61—21no—
434C2×D61—22no—
435C2×D61—22no—
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—41no—
441C2×D61—41no—
442C2×D61—42no—
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—82no—
454C2×D61—82no—
455C2×D61—84no—
456C2×D61—84no—
457C2×D61—81no—
458C2×D61—81no—
459C2×D61—81no—
460C2×D61—81no—
461C2×D61#41012yescomplemented
462C2×D61D4212yes—
463C2×D61#54612yes—
464#6923—44no—
465#6923—82no—
466#6923—82no—
467#6923—82no—
468C4×C61—21no—
469C4×C61—21no—
470C4×C61—22no—
471C4×C61—41no—
472C4×C61—41no—
473C4×C61—41no—
474Dic61—22no—
475Dic61—22no—
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—42no—
493C2×C61—42no—
494C2×C61D4×C22⋊C411yescharacteristic
495C2×C61C2×#41011yescharacteristic
496C2×C61#288311yescharacteristic
497D61—22no—
498D61—22no—
499D61—22no—
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#692311yescharacteristic, complemented
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—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—611no—
529C2×#99—612no—
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×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—611no—
572C23×C4—1222no—
573C23×C4C2×#692311yescharacteristic, complemented
574#124—1222no—
575#124—1222no—
576#123—22no—
577#123—22no—
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—1222no—
593C4×D4—1222no—
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—1222no—
603C2×C4⋊C4—1222no—
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—612no—
621C2×C22⋊C4—612no—
622C2×C22⋊C4—612no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1224no—
628C2×C22⋊C4—1222no—
629C2×C22⋊C4—1222no—
630C2×C22⋊C4—1222no—
631C2×C22⋊C4—2442no—
632C2×C22⋊C4C2×#692311yescharacteristic
633C2×C22⋊C4C2×#692311yescharacteristic
634C2×C22⋊C4C2×#692311yescharacteristic, complemented
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—611no—
653C24—612no—
654C24—611no—
655C24—611no—
656C24—1221no—
657C24—1222no—
658C24—1221no—
659C24—1221no—
660C24—1221no—
661C24—1222no—
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—22no—
677C2×D4—22no—
678C2×D4—41no—
679C2×D4—612no—
680C2×D4—612no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—1222no—
684C2×D4—1222no—
685C2×D4—1221no—
686C2×D4—1221no—
687C2×D4—1222no—
688C2×D4—1222no—
689C2×D4—1221no—
690C2×D4—1221no—
691C2×D4—1222no—
692C2×D4—1222no—
693C2×D4—1222no—
694C2×D4—1222no—
695C2×D4—1222no—
696C2×D4—1222no—
697C2×D4—1222no—
698C2×D4—1222no—
699C2×D4—4881no—
700C2×D4—4881no—
701C2×D4—2442no—
702C2×D4—2441no—
703C2×D4—2441no—
704C2×D4—2444no—
705C2×D4—2444no—
706C2×D4—2444no—
707C2×D4—2444no—
708C22×C4—22no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—41no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—612no—
716C22×C4—612no—
717C22×C4—612no—
718C22×C4—612no—
719C22×C4—611no—
720C22×C4—1222no—
721C22×C4—1222no—
722C22×C4—1221no—
723C22×C4—1222no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1222no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1222no—
733C22×C4—1222no—
734C22×C4—1222no—
735C22×C4—4881no—
736C22×C4—4882no—
737C22×C4—4881no—
738C22×C4—2441no—
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—22no—
750C4⋊C4—1222no—
751C4⋊C4—1222no—
752C4⋊C4—4882no—
753C4⋊C4—2444no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—612no—
757C22⋊C4—612no—
758C22⋊C4—611no—
759C22⋊C4—611no—
760C22⋊C4—611no—
761C22⋊C4—611no—
762C22⋊C4—612no—
763C22⋊C4—612no—
764C22⋊C4—614no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1222no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C22⋊C4—1222no—
773C22⋊C4—1222no—
774C22⋊C4—1221no—
775C22⋊C4—1221no—
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—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—611no—
800C23—612no—
801C23—611no—
802C23—611no—
803C23—612no—
804C23—611no—
805C23—1222no—
806C23—1222no—
807C23—1224no—
808C23—1222no—
809C23—1222no—
810C23—1222no—
811C23—1221no—
812C23—1221no—
813C23—1221no—
814C23—1221no—
815C23—1221no—
816C23—1221no—
817C23—1221no—
818C23—1221no—
819C23—4881no—
820C23—4881no—
821C23—4884no—
822C23—4884no—
823C23—4882no—
824C23—4884no—
825C23—4882no—
826C23—2442no—
827C23—2442no—
828C23—2441no—
829C23—2442no—
830C23—2441no—
831C23—2441no—
832C23—2442no—
833C23—2442no—
834C23—2441no—
835C23—2441no—
836C23—2441no—
837C23—2441no—
838C23—2442no—
839C23—2442no—
840C23C2×C22⋊#692312yes—
841C23D4×#692312yes—
842C23C23×#692311yescharacteristic
843Q8—2444no—
844D4—44no—
845D4—1224no—
846D4—1224no—
847D4—4882no—
848D4—4882no—
849D4—2442no—
850D4—2442no—
851D4—2442no—
852D4—2442no—
853D4—2442no—
854D4—2442no—
855D4—2444no—
856D4—2444no—
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—41no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—612no—
873C2×C4—612no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1221no—
879C2×C4—1221no—
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⋊#692311yescharacteristic
908C2×C4C2×C22⋊#692311yescharacteristic
909C22—21no—
910C22—21no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—41no—
919C22—81no—
920C22—81no—
921C22—612no—
922C22—612no—
923C22—612no—
924C22—1221no—
925C22—1222no—
926C22—1222no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—4881no—
932C22—4881no—
933C22—4881no—
934C22—4881no—
935C22—4884no—
936C22—4882no—
937C22—4882no—
938C22—4884no—
939C22—2441no—
940C22—2441no—
941C22—2442no—
942C22—2442no—
943C22—2442no—
944C22—2444no—
945C22—2444no—
946C22—2441no—
947C22—2441no—
948C22—2441no—
949C22—2441no—
950C22—2441no—
951C22—2441no—
952C22C22×C22⋊#692311yescharacteristic
953C22C2×D4×#692311yescharacteristic
954C22#1684082911yescharacteristic
955C4—21no—
956C4—21no—
957C4—22no—
958C4—41no—
959C4—41no—
960C4—41no—
961C4—1222no—
962C4—1222no—
963C4—1221no—
964C4—1221no—
965C4—4882no—
966C4—4882no—
967C4—4882no—
968C4—2444no—
969C4—2441no—
970C2—21no—
971C2—21no—
972C2—42no—
973C2—42no—
974C2—1222no—
975C2—1222no—
976C2—1222no—
977C2—4881no—
978C2—4881no—
979C2—2441no—
980C2D4×C22⋊#692311yescharacteristic
981C2D61⋊#41011yescharacteristic
982C2#2146241911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#123×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840404C2
cosocleC23×D61C24
hypercenterC2×#123#6923
hypocenterC61#22405
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#16840741C2semidirect
2. C2×D61⋊#99C2semidirect
3. #21462325C2semidirect
4. #21461959C2semidirect
5. #21461843C2semidirect
6. #21461841C2semidirect
7. #21461681C2semidirect
8. #21461648C2semidirect
9. #21461646C2semidirect
10. #21461566C2semidirect
12. C2×#14519856C22semidirect
17. C2×#14519836C22semidirect
18. C2×#14519836C22semidirect
27. #16840705C22semidirect
28. #16840704C22semidirect
31. C4×C22⋊#6923C22semidirect
32. #16840640C22semidirect
33. #16840640C22semidirect
40. C2×#14519763C4semidirect
42. C2×#14519755C4semidirect
44. C2×#14519750C4semidirect
45. C2×#14519749C4semidirect
46. C2×#14519747C4semidirect
48. C2×#14519739C4semidirect
50. C22×#11758198C4semidirect
52. C2×#123×C61C4semidirect
76. #14519835D4semidirect
88. C22×Dic122C2×C4semidirect
90. C22×D244C2×C4semidirect
95. C22×C22⋊D61C2×C4semidirect
102. C23×Dic61C2×C4semidirect
104. C22×C4×D61C2×C4semidirect
129. C2×#11758196C2×C4semidirect
130. C2×#11758196C2×C4semidirect
139. C2×#11758198C2×C4semidirect
140. C2×#11758198C2×C4semidirect
141. C2×#11758198C2×C4semidirect
142. C2×#11758198C2×C4semidirect
148. C2×C4×Dic61C2×C4semidirect
150. C23×C4×C61C2×C4semidirect
153. C2×C4⋊C4×C61C2×C4semidirect
154. C2×C4⋊C4×C61C2×C4semidirect
157. C2×C22⋊C4×C61C2×C4semidirect
461. C2×D61#410semidirect
511. C2×#123#6923semidirect
544. C61#22405semidirect
573. C23×C4C2×#6923semidirect
604. C2×C4⋊C4C2×#6923semidirect
605. C2×C4⋊C4C2×#6923semidirect
634. C2×C22⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407412
C2×D61⋊#992
#214623252
#214619592
#214618432
#214618412
#214616812
#214616482
#214616462
#214615662
C2×#168404042
#2240561