Finite Group Databasebeta

← #30620128

Subgroups — #30620128

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#21461958C212yesmaximal, complemented
5#21461842C212yesmaximal, complemented
6#21461840C212yesmaximal, complemented
7#21461682C211yesmaximal, characteristic, complemented
8#21461648C211yesmaximal, characteristic, complemented
9#21461646C211yesmaximal, characteristic, complemented
10#21461564C211yesmaximal, characteristic, complemented
11C2×#16840409C211yesmaximal, characteristic
12C2×#14519856C2212yescomplemented
13C22×C22⋊#6923C2212yes—
14#16840741—24no—
15C2×#14519836C2211yescharacteristic
16C2×#14519836C2211yescharacteristic
17C2×#14519836C2211yescharacteristic
18C2×#14519836C2211yescharacteristic
19D61⋊#99—24no—
20C2×#14519835C2212yes—
21C2×#14519835C2212yes—
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
35C22×D4×D61C2211yescharacteristic
36#16840409—22no—
37#16840409—22no—
38#16840409—22no—
39#16840409—22no—
40C2×#14519764C411yescharacteristic, complemented
41C2×#14519759C411yescharacteristic, complemented
42C2×#14519759C2211yescharacteristic
43C2×#14519757C411yescharacteristic, complemented
44C2×#14519748C411yescharacteristic, complemented
45C2×#14519748C2211yescharacteristic
46C2×#14519745C411yescharacteristic, complemented
47C2×#14519745C2211yescharacteristic
48C2×#14519739C2211yescharacteristic
49C2×C4×C22⋊D61C411yescharacteristic, complemented
50C2×C22⋊C4×D61C411yescharacteristic, complemented
51C2×C22⋊C4×D61C2211yescharacteristic
52C2×#121×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#14519836D414yescomplemented
73#14519835—24no—
74#14519835—24no—
75#14519835—42no—
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×D244C2311yescharacteristic
90C22×C22⋊D61C2×C411yescharacteristic
91C22×C22⋊D61C2×C411yescharacteristic
92C22×C22⋊D61C2×C411yescharacteristic, complemented
93C22×C22⋊D61C2311yescharacteristic
94C22×C22⋊D61C2311yescharacteristic
95C2×D4×D61—22no—
96C2×D4×D61—22no—
97C2×D4×D61—22no—
98C2×D4×D61—22no—
99C2×D4×D61—42no—
100C22×C4×D61C2×C411yescharacteristic
101C22×C4×D61C2×C411yescharacteristic, complemented
102C22×C4×D61C2×C411yescharacteristic, complemented
103C22×C4×D61C2311yescharacteristic
104C22×C4×D61C2311yescharacteristic
105#14519764—22no—
106#14519764—22no—
107#14519759—22no—
108#14519759—22no—
109#14519759—22no—
110#14519759—22no—
111#14519757—22no—
112#14519757—22no—
113#14519748—22no—
114#14519748—22no—
115#14519748—22no—
116#14519748—22no—
117#14519745—22no—
118#14519745—22no—
119#14519745—22no—
120#14519745—22no—
121#14519739—22no—
122#14519739—22no—
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127C2×C4⋊Dic61C2×C411yescharacteristic, complemented
128C2×C4⋊Dic61C2×C411yescharacteristic, complemented
129C2×#11758196C2×C411yescharacteristic, complemented
130C2×C22⋊Dic61C2×C411yescharacteristic
131C2×C22⋊Dic61C2×C411yescharacteristic
132C2×C22⋊Dic61C2×C411yescharacteristic, complemented
133C2×C22⋊Dic61C2×C411yescharacteristic, complemented
134C2×C22⋊Dic61C2×C411yescharacteristic, complemented
135C2×#11758198C2×C411yescharacteristic
136C2×#11758198C2×C411yescharacteristic
137C2×#11758198C2×C411yescharacteristic
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×D4×C61C2×C411yescharacteristic
150C22×D4×C61C2×C411yescharacteristic
151C22×D4×C61C2×C411yescharacteristic, complemented
152C23×C4×C61C2×C411yescharacteristic, complemented
153#121×C61—22no—
154#121×C61—22no—
155C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
156C2×C22⋊C4×C61C2×C411yescharacteristic
157C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
158C24×C61C22×C411yescharacteristic
159C24×C61C22×C411yescharacteristic
160C24×C61C22×C411yescharacteristic
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—22no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—22no—
167C23×D61—42no—
168C23×D61—41no—
169C23×D61—42no—
170C23×D61—81no—
171C23×D61—81no—
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—22no—
187C2×D4×C61—22no—
188C2×D4×C61—41no—
189C2×D4×C61—81no—
190C2×D4×C61—81no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—22no—
194C22×C4×C61—41no—
195C22×C4×C61C22×C411yescharacteristic
196C22×C4×C61C22×C411yescharacteristic
197C22×C4×C61C22×C411yescharacteristic
198C22×C4×C61C22×C411yescharacteristic
199C2×C22⋊D61—22no—
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—22no—
203C2×C22⋊D61—22no—
204C2×C22⋊D61—21no—
205C2×C22⋊D61—22no—
206C2×C22⋊D61—21no—
207C2×C22⋊D61—22no—
208C2×C22⋊D61—21no—
209C2×C22⋊D61—21no—
210C2×C22⋊D61—22no—
211C2×C22⋊D61—22no—
212C2×C22⋊D61—22no—
213C2×C22⋊D61—41no—
214C2×C22⋊D61—41no—
215C2×C22⋊D61—42no—
216C22×Dic61C22×C411yescharacteristic
217C22×Dic61C22×C411yescharacteristic
218C22×Dic61C22×C411yescharacteristic
219C22×Dic61C22×C411yescharacteristic
220C22×Dic61C22×C411yescharacteristic
221D4×D61—44no—
222D4×D61—44no—
223D4×D61—44no—
224D4×D61—44no—
225#11758222—44no—
226#11758222—44no—
227#11758222—44no—
228#11758222—44no—
229C2×D244—22no—
230C2×D244—22no—
231C2×D244C2×D412yes—
232C2×D244#4112yes—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—22no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—22no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—22no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—41no—
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—22no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61C22⋊C412yes—
274C22⋊C4×C61C22⋊C412yes—
275C22⋊Dic61—22no—
276C22⋊Dic61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—22no—
281C22⋊Dic61C22⋊C412yes—
282C22⋊Dic61C22⋊C412yes—
283#11758198—21no—
284#11758198—21no—
285#11758198—22no—
286#11758198—22no—
287#11758198C22⋊C411yescharacteristic
288#11758198C22⋊C411yescharacteristic
289#11758198C22⋊C411yescharacteristic
290#11758198C22⋊C411yescharacteristic
291#11758198C22⋊C412yes—
292#11758198C22⋊C412yes—
293C4⋊Dic61—22no—
294C4⋊Dic61—22no—
295#11758196—21no—
296#11758196—21no—
297C4×Dic61—21no—
298C4×Dic61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61C2×C22⋊C412yes—
314C23×C61C23×C411yescharacteristic
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—24no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—41no—
326C22×D61—42no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—42no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—42no—
337C22×D61—81no—
338C22×D61—81no—
339C22×D61—82no—
340C22×D61—82no—
341C22×D61—84no—
342C22×D61—84no—
343C22×D61—84no—
344C22×D61C2×C22⋊C411yescharacteristic
345C22×D61C2×C22⋊C411yescharacteristic
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—44no—
365D4×C61—82no—
366D4×C61—82no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—41no—
373C2×C4×C61—42no—
374C2×C4×C61—42no—
375C2×C4×C61—41no—
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C412yes—
379C2×C4×C61C4×D412yes—
380C22⋊D61—44no—
381C22⋊D61—44no—
382C22⋊D61—42no—
383C22⋊D61—42no—
384C22⋊D61—42no—
385C22⋊D61—42no—
386C22⋊D61—42no—
387C22⋊D61—42no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C412yes—
402D244—24no—
403D244—24no—
404C4×D61—22no—
405C4×D61—22no—
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—42no—
409C4×D61—42no—
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—22no—
421C22×C61—22no—
422C22×C61—22no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—81no—
430C22×C61—81no—
431C22×C61—81no—
432C22×C61—81no—
433C22×C61—81no—
434C22×C61—81no—
435C22×C61C22×C22⋊C411yescharacteristic
436C22×C61C2×C4×D411yescharacteristic
437C22×C61#51811yescharacteristic
438C2×D61—21no—
439C2×D61—22no—
440C2×D61—22no—
441C2×D61—21no—
442C2×D61—22no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—42no—
449C2×D61—44no—
450C2×D61—44no—
451C2×D61—42no—
452C2×D61—42no—
453C2×D61—42no—
454C2×D61—41no—
455C2×D61—41no—
456C2×D61—42no—
457C2×D61—82no—
458C2×D61—82no—
459C2×D61—84no—
460C2×D61—84no—
461C2×D61#41012yescomplemented
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—22no—
472C4×C61—41no—
473Dic61—22no—
474Dic61—21no—
475Dic61—21no—
476Dic61—41no—
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—42no—
493C2×C61—81no—
494C2×C61—81no—
495C2×C61D4×C22⋊C411yescharacteristic
496C2×C61C2×#41011yescharacteristic
497C2×C61#288311yescharacteristic
498D61—22no—
499D61—22no—
500D61—22no—
501D61—41no—
502D61—42no—
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#692311yescharacteristic, complemented
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—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—1222no—
560C22×D4—1222no—
561C22×D4—1222no—
562C22×D4—1222no—
563C22×D4—2442no—
564C22×D4C2×#692311yescharacteristic
565C22×D4C2×#692311yescharacteristic
566C22×D4C2×#692311yescharacteristic, complemented
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—1222no—
577#123—1222no—
578#123—1222no—
579#123—1222no—
580C22⋊Q8—1222no—
581C22⋊Q8—1222no—
582#121—22no—
583#121—22no—
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—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—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, 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—1221no—
656C24—1222no—
657C24—1221no—
658C24—1222no—
659C24—1221no—
660C24—1221no—
661C24—4881no—
662C24—4881no—
663C24—2441no—
664C24—2442no—
665C24—2442no—
666C24C22×#692311yescharacteristic
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—22no—
679C2×D4—22no—
680C2×D4—41no—
681C2×D4—81no—
682C2×D4—81no—
683C2×D4—612no—
684C2×D4—612no—
685C2×D4—1222no—
686C2×D4—1222no—
687C2×D4—1222no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4—1222no—
691C2×D4—1222no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—1222no—
695C2×D4—1222no—
696C2×D4—1222no—
697C2×D4—1221no—
698C2×D4—1222no—
699C2×D4—1221no—
700C2×D4—1222no—
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—611no—
720C22×C4—611no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1222no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1222no—
729C22×C4—1222no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1222no—
733C22×C4—1222no—
734C22×C4—1222no—
735C22×C4—1222no—
736C22×C4—4881no—
737C22×C4—4881no—
738C22×C4—4882no—
739C22×C4—2441no—
740C22×C4—2441no—
741C22×C4—2444no—
742C22×C4—2444no—
743C22×C4C22×#692311yescharacteristic
744C22×C4C22×#692311yescharacteristic
745C22×C4C22×#692311yescharacteristic
746C22×C4C22×#692311yescharacteristic
747C4⋊C4—22no—
748C4⋊C4—1222no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4—1222no—
752C4⋊C4—4882no—
753C4⋊C4—2444no—
754C22⋊C4—21no—
755C22⋊C4—21no—
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—1222no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
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—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—611no—
806C23—612no—
807C23—611no—
808C23—611no—
809C23—612no—
810C23—611no—
811C23—612no—
812C23—1222no—
813C23—1222no—
814C23—1224no—
815C23—1222no—
816C23—1222no—
817C23—1222no—
818C23—1221no—
819C23—1221no—
820C23—1221no—
821C23—1221no—
822C23—4881no—
823C23—4881no—
824C23—4884no—
825C23—4884no—
826C23—4882no—
827C23—4884no—
828C23—4882no—
829C23—2442no—
830C23—2442no—
831C23—2441no—
832C23—2442no—
833C23—2441no—
834C23—2441no—
835C23—2441no—
836C23—2441no—
837C23—2442no—
838C23—2442no—
839C23—2442no—
840C23—2442no—
841C23C2×C22⋊#692312yes—
842C23C23×#692311yescharacteristic
843Q8—2444no—
844D4—44no—
845D4—82no—
846D4—82no—
847D4—1224no—
848D4—1224no—
849D4—2444no—
850D4—2444no—
851D4—2442no—
852D4—2442no—
853D4—2442no—
854D4—2442no—
855D4—2442no—
856D4—2442no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—41no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—41no—
866C2×C4—611no—
867C2×C4—611no—
868C2×C4—612no—
869C2×C4—1222no—
870C2×C4—1222no—
871C2×C4—1222no—
872C2×C4—1222no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1224no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—4881no—
884C2×C4—4881no—
885C2×C4—4888no—
886C2×C4—2442no—
887C2×C4—2442no—
888C2×C4—2442no—
889C2×C4—2442no—
890C2×C4—2442no—
891C2×C4—2442no—
892C2×C4—2441no—
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—2441no—
905C2×C4C2×C22⋊#692311yescharacteristic
906C2×C4C2×C22⋊#692311yescharacteristic
907C2×C4C2×C22⋊#692312yes—
908C2×C4D4×#692312yes—
909C22—21no—
910C22—21no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—612no—
927C22—612no—
928C22—612no—
929C22—1221no—
930C22—1222no—
931C22—1222no—
932C22—1221no—
933C22—1222no—
934C22—1221no—
935C22—1221no—
936C22—1221no—
937C22—4882no—
938C22—4882no—
939C22—4884no—
940C22—4884no—
941C22—2441no—
942C22—2441no—
943C22—2442no—
944C22—2442no—
945C22—2442no—
946C22—2442no—
947C22—2442no—
948C22—2444no—
949C22—2444no—
950C22—2441no—
951C22—2441no—
952C22C22×C22⋊#692311yescharacteristic
953C22C2×D4×#692311yescharacteristic
954C22#1684082911yescharacteristic
955C4—21no—
956C4—21no—
957C4—22no—
958C4—22no—
959C4—41no—
960C4—1222no—
961C4—1221no—
962C4—1221no—
963C4—4882no—
964C4—4882no—
965C4—4882no—
966C4—2444no—
967C4—2441no—
968C4—2441no—
969C4—2441no—
970C2—21no—
971C2—21no—
972C2—42no—
973C2—81no—
974C2—81no—
975C2—1222no—
976C2—1222no—
977C2—1222no—
978C2—2441no—
979C2—2442no—
980C2D4×C22⋊#692311yescharacteristic
981C2D61⋊#41011yescharacteristic
982C2#2146241811yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#121×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840409C2
cosocleC23×D61C24
hypercenterC2×#121#6923
hypocenterC61#22405
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16840741C2semidirect
2. C2×D61⋊#99C2semidirect
3. #21462325C2semidirect
4. #21461958C2semidirect
5. #21461842C2semidirect
6. #21461840C2semidirect
7. #21461682C2semidirect
8. #21461648C2semidirect
9. #21461646C2semidirect
10. #21461564C2semidirect
12. C2×#14519856C22semidirect
22. C2×#14519835C22semidirect
23. C2×#14519835C22semidirect
27. #16840705C22semidirect
28. #16840704C22semidirect
31. C4×C22⋊#6923C22semidirect
32. #16840640C22semidirect
33. #16840640C22semidirect
40. C2×#14519764C4semidirect
41. C2×#14519759C4semidirect
43. C2×#14519757C4semidirect
44. C2×#14519748C4semidirect
46. C2×#14519745C4semidirect
49. C2×C4×C22⋊D61C4semidirect
50. C2×C22⋊C4×D61C4semidirect
52. C2×#121×C61C4semidirect
72. #14519836D4semidirect
88. C22×Dic122C2×C4semidirect
92. C22×C22⋊D61C2×C4semidirect
101. C22×C4×D61C2×C4semidirect
102. C22×C4×D61C2×C4semidirect
127. C2×C4⋊Dic61C2×C4semidirect
128. C2×C4⋊Dic61C2×C4semidirect
129. C2×#11758196C2×C4semidirect
132. C2×C22⋊Dic61C2×C4semidirect
133. C2×C22⋊Dic61C2×C4semidirect
134. C2×C22⋊Dic61C2×C4semidirect
138. C2×#11758198C2×C4semidirect
148. C2×C4×Dic61C2×C4semidirect
151. C22×D4×C61C2×C4semidirect
152. C23×C4×C61C2×C4semidirect
155. C2×C4⋊C4×C61C2×C4semidirect
157. C2×C22⋊C4×C61C2×C4semidirect
461. C2×D61#410semidirect
515. C2×#121#6923semidirect
544. C61#22405semidirect
566. C22×D4C2×#6923semidirect
573. C23×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
#214619582
#214618422
#214618402
#214616822
#214616482
#214616462
#214615642
C2×#168404092
#2240561