Finite Group Databasebeta

← #30620125

Subgroups — #30620125

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×#14519835C211yesmaximal, characteristic, complemented
3#21462325C212yesmaximal, complemented
4#21461960C212yesmaximal, complemented
5#21461842C212yesmaximal, complemented
6#21461841C212yesmaximal, complemented
7#21461679C211yesmaximal, characteristic, complemented
8#21461648C211yesmaximal, characteristic, complemented
9#21461645C211yesmaximal, characteristic, complemented
10C4×#14519835C211yesmaximal, characteristic, complemented
11C2×#16840402C211yesmaximal, characteristic
12C2×#14519856C2212yescomplemented
13C22×C22⋊#6923C2212yes—
14#16840741—24no—
15C2×#14519836C2212yescomplemented
16C2×#14519836C2212yescomplemented
17C2×#14519835—24no—
18C2×#14519835C2211yescharacteristic
19C2×#14519835C2212yes—
20C2×#14519835C2211yescharacteristic
21C2×#14519835C2211yescharacteristic
22C2×#14519835C2212yes—
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
35C23×C22⋊D61C2211yescharacteristic
36#16840402—22no—
37#16840402—22no—
38#16840402—22no—
39#16840402—22no—
40C2×#14519763C411yescharacteristic, complemented
41C2×#14519760C411yescharacteristic, complemented
42C2×#14519759C2211yescharacteristic
43C2×#14519754C411yescharacteristic, complemented
44C2×#14519751C411yescharacteristic, complemented
45C2×#14519750C411yescharacteristic, complemented
46C2×#14519750C2211yescharacteristic
47C2×#14519747C2211yescharacteristic
48C2×#14519746C411yescharacteristic, complemented
49C2×C4×C22⋊D61C2211yescharacteristic
50C2×#14519737C411yescharacteristic, complemented
51C2×C22⋊C4×D61C2211yescharacteristic
52C22×C22⋊C4×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—42no—
71#14519835—22no—
72#14519835—22no—
73#14519835—22no—
74#14519835—24no—
75#14519835—42no—
76#14519835D414yescomplemented
77(C2×#6923)⋊C4—22no—
78(C2×#6923)⋊C4—22no—
79(C2×#6923)⋊C4—22no—
80(C2×#6923)⋊C4—22no—
81C24×D61C2311yescharacteristic
82C2×#11758222—22no—
83C2×#11758222—22no—
84C2×#11758222—22no—
85C2×#11758222—22no—
86C2×#11758222—42no—
87C22×Dic122C2×C411yescharacteristic, complemented
88C22×D244C2×C411yescharacteristic
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—22no—
91C22×C22⋊D61—22no—
92C22×C22⋊D61—22no—
93C22×C22⋊D61—22no—
94C22×C22⋊D61—42no—
95C22×C22⋊D61C2×C411yescharacteristic
96C22×C22⋊D61C2×C411yescharacteristic
97C22×C22⋊D61C2×C411yescharacteristic
98C22×C22⋊D61C2×C411yescharacteristic, complemented
99C22×C22⋊D61C2×C411yescharacteristic, complemented
100C22×C22⋊D61C2311yescharacteristic
101C22×C22⋊D61C2311yescharacteristic
102C23×Dic61C2×C411yescharacteristic
103C22×C4×D61C2×C411yescharacteristic, complemented
104C22×C4×D61C2311yescharacteristic
105C22×C4×D61C2311yescharacteristic
106#14519763—22no—
107#14519763—22no—
108#14519760—22no—
109#14519760—22no—
110#14519759—22no—
111#14519759—22no—
112#14519754—22no—
113#14519754—22no—
114#14519751—22no—
115#14519751—22no—
116#14519750—22no—
117#14519750—22no—
118#14519750—22no—
119#14519750—22no—
120#14519747—22no—
121#14519747—22no—
122#14519746—22no—
123#14519746—22no—
124C4×C22⋊D61—22no—
125C4×C22⋊D61—22no—
126#14519737—21no—
127#14519737—21no—
128#14519737—21no—
129#14519737—21no—
130C2×C4⋊Dic61C2×C411yescharacteristic, complemented
131C2×#11758196C2×C411yescharacteristic, complemented
132C2×#11758196C2×C411yescharacteristic, complemented
133C2×#11758196C2×C411yescharacteristic, complemented
134C2×C22⋊Dic61C2×C411yescharacteristic
135C2×C22⋊Dic61C2×C411yescharacteristic, complemented
136C2×C22⋊Dic61C2×C411yescharacteristic, complemented
137C2×#11758198C2×C411yescharacteristic
138C2×#11758198C2×C411yescharacteristic
139C2×#11758198C2×C411yescharacteristic
140C2×#11758198C2×C411yescharacteristic, complemented
141C2×#11758198C2311yescharacteristic
142C22⋊C4×D61D412yes—
143C22⋊C4×D61D412yes—
144C22⋊C4×D61D412yes—
145C22⋊C4×D61D412yes—
146C2×C4×Dic61C2×C411yescharacteristic, complemented
147C25×C61C2×C411yescharacteristic
148C23×C4×C61C2×C411yescharacteristic, complemented
149C23×C4×C61C2×C411yescharacteristic, complemented
150C2×C22⋊C4×C61—21no—
151C2×C22⋊C4×C61—21no—
152C2×C22⋊C4×C61—21no—
153C2×C22⋊C4×C61—21no—
154C2×C22⋊C4×C61C2×C411yescharacteristic
155C2×C22⋊C4×C61C2×C411yescharacteristic
156C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
157C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—22no—
161C24×C61—41no—
162C24×C61—42no—
163C24×C61—81no—
164C24×C61C22×C411yescharacteristic
165C24×C61C22×C411yescharacteristic
166C24×C61C22×C411yescharacteristic
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—22no—
170C23×D61—42no—
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—
184C22×C4×C61—22no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—41no—
190C22×C4×C61—81no—
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C22×C411yescharacteristic
193C22×C4×C61C22×C411yescharacteristic
194C22×C4×C61C22×C411yescharacteristic
195C2×C22⋊D61—22no—
196C2×C22⋊D61—22no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—22no—
200C2×C22⋊D61—22no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—22no—
203C2×C22⋊D61—21no—
204C2×C22⋊D61—22no—
205C2×C22⋊D61—21no—
206C2×C22⋊D61—22no—
207C2×C22⋊D61—22no—
208C2×C22⋊D61—22no—
209C2×C22⋊D61—22no—
210C2×C22⋊D61—41no—
211C2×C22⋊D61—41no—
212C2×C22⋊D61—41no—
213C2×C22⋊D61—44no—
214C2×C22⋊D61—44no—
215C2×C22⋊D61—44no—
216C2×C22⋊D61—44no—
217C2×C22⋊D61—42no—
218C2×C22⋊D61—81no—
219C2×C22⋊D61C2×D412yes—
220C2×C22⋊D61#4112yes—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—22no—
224C22×Dic61—41no—
225C22×Dic61C22×C411yescharacteristic
226C22×Dic61C22×C411yescharacteristic
227C22×Dic61C22×C411yescharacteristic
228C22×Dic61C22×C411yescharacteristic
229C22×Dic61C22×C411yescharacteristic
230#11758222—44no—
231#11758222—44no—
232#11758222—44no—
233#11758222—44no—
234C2×D244—21no—
235C2×D244—22no—
236C2×D244—21no—
237C2×D244—22no—
238C2×D244—22no—
239C2×D244—81no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—22no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—22no—
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—
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊C4×C61C22⋊C411yescharacteristic
277C22⋊C4×C61C22⋊C411yescharacteristic
278C22⋊C4×C61C22⋊C411yescharacteristic
279C22⋊C4×C61C22⋊C411yescharacteristic
280C22⋊Dic61—22no—
281C22⋊Dic61—22no—
282C22⋊Dic61C22⋊C412yes—
283C22⋊Dic61C22⋊C412yes—
284#11758198—22no—
285#11758198—22no—
286#11758198—21no—
287#11758198—21no—
288#11758198C22⋊C412yes—
289#11758198C22⋊C412yes—
290#11758198C22⋊C412yes—
291#11758198C22⋊C412yes—
292C4⋊Dic61—22no—
293#11758196—21no—
294#11758196—21no—
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—22no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—41no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—42no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—42no—
316C23×C61—81no—
317C23×C61—81no—
318C23×C61—84no—
319C23×C61—84no—
320C23×C61C2×C22⋊C411yescharacteristic
321C23×C61C2×C22⋊C411yescharacteristic
322C23×C61C4×D412yes—
323C23×C61C23×C411yescharacteristic
324C22×D61—24no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—21no—
332C22×D61—21no—
333C22×D61—21no—
334C22×D61—41no—
335C22×D61—42no—
336C22×D61—41no—
337C22×D61—42no—
338C22×D61—41no—
339C22×D61—41no—
340C22×D61—42no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—82no—
344C22×D61—82no—
345C22×D61—84no—
346C22×D61C2×C22⋊C412yes—
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—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—41no—
371C2×C4×C61—42no—
372C2×C4×C61—42no—
373C2×C4×C61—41no—
374C2×C4×C61—81no—
375C2×C4×C61—81no—
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C22⋊D61—24no—
381C22⋊D61—24no—
382C22⋊D61—44no—
383C22⋊D61—44no—
384C22⋊D61—44no—
385C22⋊D61—42no—
386C22⋊D61—42no—
387C22⋊D61—42no—
388C22⋊D61—42no—
389C22⋊D61—82no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—21no—
398C2×Dic61—41no—
399C2×Dic61—42no—
400C2×Dic61—42no—
401C2×Dic61—41no—
402C2×Dic61C2×C22⋊C412yes—
403C2×Dic61C2×C22⋊C412yes—
404C2×Dic61C4×D412yes—
405D244—42no—
406D244—42no—
407D244—82no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
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—21no—
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—22no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—42no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—84no—
436C22×C61—81no—
437C22×C61—81no—
438C22×C61—84no—
439C22×C61#41012yescomplemented
440C22×C61C22×C22⋊C411yescharacteristic
441C22×C61C2×C4×D411yescharacteristic
442C22×C61#51811yescharacteristic
443C2×D61—22no—
444C2×D61—22no—
445C2×D61—22no—
446C2×D61—22no—
447C2×D61—22no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—42no—
451C2×D61—44no—
452C2×D61—44no—
453C2×D61—41no—
454C2×D61—41no—
455C2×D61—41no—
456C2×D61—82no—
457C2×D61—82no—
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—21no—
469C4×C61—21no—
470C4×C61—21no—
471C4×C61—21no—
472C4×C61—41no—
473C4×C61—41no—
474Dic61—22no—
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—22no—
491C2×C61—21no—
492C2×C61—21no—
493C2×C61—41no—
494C2×C61—42no—
495C2×C61—81no—
496C2×C61D4×C22⋊C411yescharacteristic
497C2×C61C2×#41011yescharacteristic
498C2×C61#288311yescharacteristic
499D61—22no—
500D61—22no—
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—611no—
520C2×#117—612no—
521C22×C22⋊C4—611no—
522C22×C22⋊C4—612no—
523C22×C22⋊C4#692311yescharacteristic, complemented
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—
546C25C2×#692311yescharacteristic
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—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—1222no—
572C23×C4C2×#692311yescharacteristic, complemented
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—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—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—1222no—
605C2×C4⋊C4—1222no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—611no—
611C2×C22⋊C4—611no—
612C2×C22⋊C4—611no—
613C2×C22⋊C4—612no—
614C2×C22⋊C4—612no—
615C2×C22⋊C4—612no—
616C2×C22⋊C4—612no—
617C2×C22⋊C4—612no—
618C2×C22⋊C4—611no—
619C2×C22⋊C4—611no—
620C2×C22⋊C4—611no—
621C2×C22⋊C4—611no—
622C2×C22⋊C4—611no—
623C2×C22⋊C4—612no—
624C2×C22⋊C4—612no—
625C2×C22⋊C4—612no—
626C2×C22⋊C4—1224no—
627C2×C22⋊C4—1222no—
628C2×C22⋊C4—1222no—
629C2×C22⋊C4—1222no—
630C2×C22⋊C4—2442no—
631C2×C22⋊C4C2×#692311yescharacteristic
632C2×C22⋊C4C2×#692311yescharacteristic
633C2×C22⋊C4C2×#692311yescharacteristic, complemented
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—21no—
651C24—21no—
652C24—22no—
653C24—41no—
654C24—42no—
655C24—81no—
656C24—611no—
657C24—612no—
658C24—612no—
659C24—611no—
660C24—611no—
661C24—1221no—
662C24—1222no—
663C24—1221no—
664C24—4881no—
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—612no—
677C2×D4—612no—
678C2×D4—1222no—
679C2×D4—1221no—
680C2×D4—1222no—
681C2×D4—1222no—
682C2×D4—1221no—
683C2×D4—1222no—
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—1221no—
695C2×D4—1221no—
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—22no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—41no—
714C22×C4—81no—
715C22×C4—611no—
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—1222no—
725C22×C4—1221no—
726C22×C4—1222no—
727C22×C4—1221no—
728C22×C4—1222no—
729C22×C4—1222no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1222no—
735C22×C4—1222no—
736C22×C4—1222no—
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—1222no—
748C4⋊C4—1222no—
749C4⋊C4—1222no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—4882no—
753C4⋊C4—2444no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—612no—
761C22⋊C4—612no—
762C22⋊C4—612no—
763C22⋊C4—612no—
764C22⋊C4—612no—
765C22⋊C4—612no—
766C22⋊C4—614no—
767C22⋊C4—1222no—
768C22⋊C4—1222no—
769C22⋊C4—1222no—
770C22⋊C4—1222no—
771C22⋊C4—1222no—
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—1221no—
788C42—1221no—
789C42—4882no—
790C42—2444no—
791C23—22no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—41no—
800C23—42no—
801C23—42no—
802C23—41no—
803C23—41no—
804C23—42no—
805C23—41no—
806C23—41no—
807C23—42no—
808C23—81no—
809C23—81no—
810C23—84no—
811C23—84no—
812C23—612no—
813C23—611no—
814C23—611no—
815C23—612no—
816C23—612no—
817C23—1222no—
818C23—1222no—
819C23—1222no—
820C23—1222no—
821C23—1221no—
822C23—1221no—
823C23—1224no—
824C23—1221no—
825C23—1221no—
826C23—1221no—
827C23—4882no—
828C23—4884no—
829C23—4882no—
830C23—2442no—
831C23—2441no—
832C23—2441no—
833C23—2442no—
834C23—2441no—
835C23—2442no—
836C23—2441no—
837C23—2441no—
838C23—2441no—
839C23C2×C22⋊#692311yescharacteristic
840C23C2×C22⋊#692311yescharacteristic
841C23D4×#692312yes—
842C23C23×#692311yescharacteristic
843Q8—2444no—
844D4—1224no—
845D4—1224no—
846D4—4882no—
847D4—4882no—
848D4—2442no—
849D4—2442no—
850D4—2444no—
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—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—41no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—612no—
870C2×C4—612no—
871C2×C4—612no—
872C2×C4—1222no—
873C2×C4—1222no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1224no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—4888no—
886C2×C4—2442no—
887C2×C4—2442no—
888C2×C4—2442no—
889C2×C4—2442no—
890C2×C4—2441no—
891C2×C4—2442no—
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—2442no—
904C2×C4—2441no—
905C2×C4C2×C22⋊#692311yescharacteristic
906C2×C4C2×C22⋊#692311yescharacteristic
907C2×C4C2×C22⋊#692311yescharacteristic
908C2×C4C2×C22⋊#692311yescharacteristic
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—22no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—84no—
927C22—81no—
928C22—81no—
929C22—84no—
930C22—612no—
931C22—612no—
932C22—1222no—
933C22—1222no—
934C22—1222no—
935C22—1222no—
936C22—1222no—
937C22—4881no—
938C22—4881no—
939C22—4881no—
940C22—4881no—
941C22—4882no—
942C22—4882no—
943C22—2441no—
944C22—2441no—
945C22—2442no—
946C22—2444no—
947C22—2444no—
948C22—2441no—
949C22—2441no—
950C22—2441no—
951C22#1684074112yescomplemented
952C22C22×C22⋊#692311yescharacteristic
953C22C2×D4×#692311yescharacteristic
954C22#1684082911yescharacteristic
955C4—21no—
956C4—21no—
957C4—21no—
958C4—21no—
959C4—41no—
960C4—41no—
961C4—1222no—
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—42no—
975C2—81no—
976C2—1222no—
977C2—1222no—
978C2—4881no—
979C2—2442no—
980C2D4×C22⋊#692311yescharacteristic
981C2C2×#1684074111yescharacteristic
982C2#2146241811yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840402C2
cosocleC23×D61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61#22405
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840741C2semidirect
2. C22×#14519835C2semidirect
3. #21462325C2semidirect
4. #21461960C2semidirect
5. #21461842C2semidirect
6. #21461841C2semidirect
7. #21461679C2semidirect
8. #21461648C2semidirect
9. #21461645C2semidirect
10. C4×#14519835C2semidirect
12. C2×#14519856C22semidirect
15. C2×#14519836C22semidirect
16. C2×#14519836C22semidirect
27. #16840705C22semidirect
28. #16840704C22semidirect
31. C4×C22⋊#6923C22semidirect
32. #16840640C22semidirect
33. #16840640C22semidirect
40. C2×#14519763C4semidirect
41. C2×#14519760C4semidirect
43. C2×#14519754C4semidirect
44. C2×#14519751C4semidirect
45. C2×#14519750C4semidirect
48. C2×#14519746C4semidirect
50. C2×#14519737C4semidirect
52. C22×C22⋊C4×C61C4semidirect
76. #14519835D4semidirect
87. C22×Dic122C2×C4semidirect
98. C22×C22⋊D61C2×C4semidirect
99. C22×C22⋊D61C2×C4semidirect
103. C22×C4×D61C2×C4semidirect
130. C2×C4⋊Dic61C2×C4semidirect
131. C2×#11758196C2×C4semidirect
132. C2×#11758196C2×C4semidirect
133. C2×#11758196C2×C4semidirect
135. C2×C22⋊Dic61C2×C4semidirect
136. C2×C22⋊Dic61C2×C4semidirect
140. C2×#11758198C2×C4semidirect
146. C2×C4×Dic61C2×C4semidirect
148. C23×C4×C61C2×C4semidirect
149. C23×C4×C61C2×C4semidirect
156. C2×C22⋊C4×C61C2×C4semidirect
157. C2×C22⋊C4×C61C2×C4semidirect
439. C22×C61#410semidirect
523. C22×C22⋊C4#6923semidirect
544. C61#22405semidirect
572. C23×C4C2×#6923semidirect
573. C23×C4C2×#6923semidirect
633. C2×C22⋊C4C2×#6923semidirect
634. C2×C22⋊C4C2×#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×#145198352
#214623252
#214619602
#214618422
#214618412
#214616792
#214616482
#214616452
C4×#145198352
C2×#168404022
#2240561