Finite Group Databasebeta

← #30615581

Subgroups — #30615581

Order 15616.

1854 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519864C211yesmaximal, characteristic, complemented
2C2×#16840735C211yesmaximal, characteristic, complemented
3C2×#16840735C211yesmaximal, characteristic, complemented
4C2×#16840735C211yesmaximal, characteristic, complemented
5#21461799C211yesmaximal, characteristic, complemented
6#21461798C211yesmaximal, characteristic, complemented
7#21461797C211yesmaximal, characteristic, complemented
8#21461796C211yesmaximal, characteristic, complemented
9#21461795C211yesmaximal, characteristic, complemented
10#21461794C211yesmaximal, characteristic, complemented
11#21461793C211yesmaximal, characteristic, complemented
12#21461792C211yesmaximal, characteristic, complemented
13#21461482C211yesmaximal, characteristic, complemented
14C2×#16840628C211yesmaximal, characteristic, complemented
15C2×#16840307C211yesmaximal, characteristic
16C2×#14519864—24no—
17C2×#14519864—24no—
18C2×#14519864—24no—
19C22×#11758213C2211yescharacteristic
20C22×#11758217C2211yescharacteristic
21C22×#11758217C2211yescharacteristic
22C22×#11758217C2211yescharacteristic
23C22×D61⋊C8C2211yescharacteristic
24C23×#92420C2211yescharacteristic
25C23×#92420C2211yescharacteristic
26C23×#92420C2211yescharacteristic
27#16840735—24no—
28#16840735—24no—
29#16840735—24no—
30C2×#14519834C2211yescharacteristic
31C2×#14519834C2211yescharacteristic
32C2×#14519834C2211yescharacteristic
33C2×#14519834C2211yescharacteristic
34C2×#14519834C2211yescharacteristic
35C2×#14519834C2211yescharacteristic
36C2×C22⋊#92420C2211yescharacteristic
37C2×C22⋊#92420C2211yescharacteristic
38C2×C22⋊#92420C2211yescharacteristic
39C2×C22⋊#92420C2211yescharacteristic
40C2×C22⋊#92420C2211yescharacteristic
41C2×C22⋊#92420C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840628C2211yescharacteristic
47#16840628C2211yescharacteristic
48#16840628C2211yescharacteristic
49#16840628C2211yescharacteristic
50C22×#11758224C2211yescharacteristic
51C22×#11758224C2211yescharacteristic
52#16840307—24no—
53#16840307—24no—
54C2×#14519776C411yescharacteristic
55C2×#14519773C411yescharacteristic
56C2×#14519763C411yescharacteristic
57C2×#14519763C411yescharacteristic
58C2×#14519751C411yescharacteristic
59C2×#14519749C411yescharacteristic
60C2×#14519749C411yescharacteristic
61C2×D4×Dic61C2211yescharacteristic
62C2×#14519739C2211yescharacteristic
63C2×#14519737C2211yescharacteristic
64C2×#14519737C2211yescharacteristic
65C22×C4×Dic61C2211yescharacteristic
66C2×#121×C61C411yescharacteristic
67#14519864—232no—
68C2×#11758213—22no—
69C2×#11758213—22no—
70C2×#11758213—22no—
71C2×#11758217—22no—
72C2×#11758217—22no—
73C2×#11758217—22no—
74C2×#11758217—22no—
75C2×#11758217—22no—
76C2×#11758217—22no—
77C2×#11758217—22no—
78C2×#11758217—22no—
79C2×#11758217D414yescomplemented
80C2×D61⋊C8—22no—
81C2×D61⋊C8—22no—
82C2×D61⋊C8—22no—
83C22×#92420—22no—
84C22×#92420—22no—
85C22×#92420—22no—
86C22×#92420—22no—
87C22×#92420—22no—
88C22×#92420—22no—
89C22×#92420—22no—
90C22×#92420—22no—
91C22×#92420D414yescomplemented
92C22×#92420C2311yescharacteristic
93C22×#92420C2311yescharacteristic
94C22×#92420C2311yescharacteristic
95C22×#92420C2311yescharacteristic
96C22×#92420C2311yescharacteristic
97C22×#92420C2311yescharacteristic
98C22×#92420C2311yescharacteristic
99C22×#92420C2311yescharacteristic
100#14519834—22no—
101#14519834—22no—
102#14519834—22no—
103#14519834—22no—
104#14519834—22no—
105#14519834—22no—
106C22⋊#92420—22no—
107C22⋊#92420—22no—
108C22⋊#92420—22no—
109C22⋊#92420—22no—
110C22⋊#92420—22no—
111C22⋊#92420—22no—
112C2×#11758224—22no—
113C2×#11758224—22no—
114C2×#11758224—22no—
115C2×#11758224—22no—
116C2×#11758224—22no—
117C2×#11758224—22no—
118C2×#11758224—22no—
119C2×#11758224—22no—
120C2×#11758224—22no—
121C2×#11758224—22no—
122C2×#11758224D414yes—
123C2×#11758224D414yes—
124C22×Dic122C2×C411yescharacteristic
125C22×Dic122C2×C411yescharacteristic
126C22×D244C2×C411yescharacteristic
127C22×C22⋊D61C2×C411yescharacteristic
128C22×C22⋊D61C2×C411yescharacteristic
129C22×C22⋊D61C2×C411yescharacteristic
130C22×C22⋊D61C2×C411yescharacteristic
131C22×C22⋊D61C2×C411yescharacteristic
132C22×C22⋊D61C2×C411yescharacteristic
133C23×Dic61C2×C411yescharacteristic
134C23×Dic61C2311yescharacteristic
135C23×Dic61C2311yescharacteristic
136C23×Dic61C2311yescharacteristic
137C22×C4×D61C2311yescharacteristic
138C22×C4×D61C2311yescharacteristic
139#14519776—24no—
140#14519773—24no—
141#14519763—24no—
142#14519763—24no—
143#14519751—24no—
144#14519749—24no—
145#14519749—24no—
146D4×Dic61—22no—
147D4×Dic61—22no—
148#14519739—22no—
149#14519739—22no—
150#14519737—22no—
151#14519737—22no—
152#14519737—22no—
153#14519737—22no—
154C2×C4⋊Dic61C2×C411yescharacteristic
155C2×#11758196C2×C411yescharacteristic
156C2×#11758196C2×C411yescharacteristic
157C2×C22⋊Dic61C2×C411yescharacteristic
158C2×C22⋊Dic61C2×C411yescharacteristic
159C2×#11758198C2×C411yescharacteristic
160C2×#11758198C2×C411yescharacteristic
161C2×#11758198C2×C411yescharacteristic
162C2×#11758198C2×C411yescharacteristic
163C2×C4×Dic61—22no—
164C2×C4×Dic61—22no—
165C2×C4×Dic61C2×C411yescharacteristic
166C2×C4×Dic61C2×C411yescharacteristic
167C2×C4×Dic61C2311yescharacteristic
168C2×C4×Dic61C2311yescharacteristic
169C22×D4×C61C2×C411yescharacteristic
170C22×D4×C61C2×C411yescharacteristic
171C22×D4×C61C2×C411yescharacteristic
172C23×C4×C61C2×C411yescharacteristic
173#121×C61—24no—
174C2×C4⋊C4×C61C2×C411yescharacteristic
175C2×C22⋊C4×C61C2×C411yescharacteristic
176C2×C22⋊C4×C61C2×C411yescharacteristic
177C24×C61C22×C411yescharacteristic
178C24×C61C22×C411yescharacteristic
179C24×C61C22×C411yescharacteristic
180C23×D61C22×C411yescharacteristic
181C23×D61C22×C411yescharacteristic
182C2×D4×C61—22no—
183C2×D4×C61—22no—
184C2×D4×C61—22no—
185C2×D4×C61—22no—
186C2×D4×C61—22no—
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61—41no—
190C2×D4×C61C22⋊C414yes—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—41no—
194C22×C4×C61C22×C411yescharacteristic
195C22×C4×C61C22×C411yescharacteristic
196C22×C4×C61C22×C411yescharacteristic
197C22×C4×C61C22×C411yescharacteristic
198C2×C22⋊D61—22no—
199C2×C22⋊D61—22no—
200C2×C22⋊D61—22no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—22no—
203C2×C22⋊D61—22no—
204C2×C22⋊D61—22no—
205C2×C22⋊D61—22no—
206C2×C22⋊D61—22no—
207C2×C22⋊D61—22no—
208C2×C22⋊D61—22no—
209C2×C22⋊D61—22no—
210C2×C22⋊D61—22no—
211C2×C22⋊D61—22no—
212C2×C22⋊D61—41no—
213C2×C22⋊D61—41no—
214C2×C22⋊D61C22⋊C414yes—
215C2×C22⋊D61C22⋊C414yes—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—41no—
229C22×Dic61C22×C411yescharacteristic
230C22×Dic61C22×C411yescharacteristic
231C22×Dic61C22×C411yescharacteristic
232C22×Dic61C22×C411yescharacteristic
233C22×Dic61C22×C411yescharacteristic
234C22×Dic61C2×D412yes—
235C22×Dic61C2×D412yes—
236C22×Dic61C2×D412yes—
237C22×Dic61C2×D412yes—
238C22×Dic61C2×D412yes—
239C22×Dic61C2×D412yes—
240C22×Dic61#4112yes—
241C22×Dic61#4112yes—
242C22×Dic61C2411yescharacteristic
243#11758224—28no—
244#11758224—28no—
245#11758224—28no—
246#11758224—28no—
247#11758224—44no—
248#11758224—44no—
249#11758224—44no—
250#11758224—44no—
251C2×D244—22no—
252C2×D244—22no—
253C2×D244—41no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61C2×D412yes—
265C2×C4×D61C2×D412yes—
266C2×Dic122—22no—
267C2×Dic122—22no—
268C2×Dic122—22no—
269C2×Dic122—22no—
270C2×Dic122—22no—
271C2×Dic122C22⋊C414yes—
272#11758217—28no—
273#11758217—28no—
274#11758217—44no—
275C2×#92420—28no—
276C2×#92420—28no—
277C2×#92420—21no—
278C2×#92420—21no—
279C2×#92420—21no—
280C2×#92420—21no—
281C2×#92420—21no—
282C2×#92420—21no—
283C2×#92420—21no—
284C2×#92420—21no—
285C2×#92420—21no—
286C2×#92420—21no—
287C2×#92420—21no—
288C2×#92420—21no—
289C2×#92420—21no—
290C2×#92420—21no—
291C2×#92420—21no—
292C2×#92420—21no—
293C2×#92420—21no—
294C2×#92420—21no—
295C2×#92420—21no—
296C2×#92420—21no—
297C2×#92420—44no—
298C2×#92420C2×D412yes—
299C2×#92420C2×D412yes—
300C2×#92420C2×D412yes—
301C2×#92420C2×D412yes—
302#11758213—28no—
303D61⋊C8—28no—
304C4⋊C4×C61—22no—
305C22⋊C4×C61—22no—
306C22⋊C4×C61—22no—
307C22⋊Dic61—22no—
308C22⋊Dic61—22no—
309#11758198—22no—
310#11758198—22no—
311#11758198—22no—
312#11758198—22no—
313C4⋊Dic61—22no—
314#11758196—22no—
315#11758196—22no—
316C4×Dic61—22no—
317C4×Dic61—22no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61—21no—
321C4×Dic61—21no—
322C23×C61—21no—
323C23×C61—21no—
324C23×C61—21no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61—21no—
328C23×C61—21no—
329C23×C61—21no—
330C23×C61—21no—
331C23×C61—21no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61C2×C22⋊C412yes—
340C23×C61C2×C22⋊C412yes—
341C23×C61C4×D412yes—
342C23×C61C4×D412yes—
343C23×C61C23×C411yescharacteristic
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—21no—
353C22×D61—21no—
354C22×D61—21no—
355C22×D61—21no—
356C22×D61—21no—
357C22×D61C2×C22⋊C412yes—
358D4×C61—28no—
359D4×C61—44no—
360D4×C61—44no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
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—21no—
371C2×C4×C61—44no—
372C2×C4×C61C2×C22⋊C412yes—
373C2×C4×C61#13112yescomplemented
374C22⋊D61—28no—
375C22⋊D61—28no—
376C22⋊D61—44no—
377C22⋊D61—44no—
378C22⋊D61—44no—
379C22⋊D61—44no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—44no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61C2×C22⋊C412yes—
400C2×Dic61C2×C22⋊C412yes—
401C2×Dic61C4×D412yes—
402C2×Dic61C4×D412yes—
403C2×Dic61#12014yes—
404C2×Dic61#12114yes—
405C2×Dic61#12114yes—
406C2×Dic61#12314yes—
407C2×Dic61#13112yescomplemented
408C2×Dic61C22×D411yescharacteristic
409C2×Dic61C22×D411yescharacteristic
410C2×Dic61C22×D411yescharacteristic
411C2×Dic61C22×D411yescharacteristic
412C2×Dic61C2×#4111yescharacteristic
413C2×Dic61C2×#4111yescharacteristic
414D244—44no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—22no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61—41no—
423Dic122—28no—
424Dic122—44no—
425#92420—22no—
426#92420—22no—
427#92420—22no—
428#92420—22no—
429#92420—41no—
430#92420—41no—
431#92420—41no—
432#92420—41no—
433#20900—611nomaximal, Sylow
434C22×C61—22no—
435C22×C61—22no—
436C22×C61—22no—
437C22×C61—22no—
438C22×C61—22no—
439C22×C61—22no—
440C22×C61—22no—
441C22×C61—22no—
442C22×C61—22no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—41no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61—41no—
449C22×C61—41no—
450C22×C61—41no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61#38614yes—
455C22×C61C22×C22⋊C411yescharacteristic
456C22×C61C2×C4×D411yescharacteristic
457C22×C61C2×C4×D411yescharacteristic
458C22×C61C2×#13111yescharacteristic
459C22×C61C2×#13111yescharacteristic
460C22×C61#56811yescharacteristic
461C22×C61#56811yescharacteristic
462C2×D61—22no—
463C2×D61—22no—
464C2×D61—22no—
465C2×D61—41no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—41no—
471C2×D61—41no—
472C2×D61—41no—
473C2×D61—41no—
474C2×D61—41no—
475C2×D61—41no—
476C4×C61—22no—
477C4×C61—22no—
478C4×C61—41no—
479C4×C61—41no—
480Dic61—22no—
481Dic61—22no—
482Dic61—41no—
483Dic61—41no—
484Dic61#38614yes—
485Dic61C2×#12011yescharacteristic
486Dic61C2×#12111yescharacteristic
487Dic61C2×#12111yescharacteristic
488Dic61C2×#12311yescharacteristic
489C22×#131—611no—
490C2×#532—611no—
491C2×#408—611no—
492C2×#408—611no—
493C2×#408—611no—
494#1870—611no—
495#1870—611no—
496#1870—611no—
497#1870—611no—
498#1869—611no—
499#1869—611no—
500#1869—611no—
501#1869—611no—
502#1728—611no—
503C2×#336—611no—
504C2×C61—24no—
505C2×C61—42no—
506C2×C61—81no—
507C2×C61C2×#38611yescharacteristic
508C2×C61#288011yescharacteristic
509C2×C61#288011yescharacteristic
510C2×C61#293111yescharacteristic
511C2×C61#293211yescharacteristic
512C2×C61#293511yescharacteristic
513C2×C61#293511yescharacteristic
514D61—42no—
515D61—81no—
516C22×#41—611no—
517C22×#41—611no—
518C2×#131—1224no—
519C2×#131—1224no—
520C2×#131—1224no—
521C22×M16—611no—
522C22×M16—611no—
523C22×M16—611no—
524C22×M16—611no—
525C23×C8—611no—
526C23×C8—611no—
527C23×C8—611no—
528C23×C8—611no—
529#532—1224no—
530#532—1224no—
531C2×C4⋊Q8—611no—
532C2×#127—611no—
533C2×#124—611no—
534C2×#124—611no—
535C2×#121—611no—
536C2×#121—611no—
537C2×#121—611no—
538C2×#121#692311yescharacteristic
539C2×C4×D4—611no—
540C2×C4×D4—611no—
541C2×C4×D4—611no—
542C2×C4×D4—611no—
543C22×C42—611no—
544#408—1224no—
545#408—1224no—
546#408—1224no—
547C2×C22⋊C8—611no—
548C2×C22⋊C8—611no—
549C2×C22⋊C8—611no—
550C2×C22⋊C8—611no—
551C2×C22⋊C8—611no—
552C2×C22⋊C8—611no—
553C2×C22⋊C8—611no—
554C2×C22⋊C8—611no—
555C2×C22⋊C8—611no—
556C2×C22⋊C8—611no—
557C2×C22⋊C8—611no—
558C2×C22⋊C8—611no—
559#336—611no—
560#336—611no—
561#336—611no—
562#336—611no—
563#336—611no—
564#336—611no—
565#336—611no—
566#336—611no—
567C61#2090011yescharacteristic, complemented, Sylow
568C2×#41—614no—
569C2×#41—614no—
570C2×#41—1222no—
571C2×#41—1222no—
572C2×#41—1222no—
573C2×#41—1222no—
574C2×#41—1222no—
575C2×#41—1222no—
576C2×#41—1222no—
577C2×#41—1222no—
578C2×#41—1222no—
579C2×#41—1222no—
580C22×Q8—611no—
581C22×Q8—611no—
582C22×D4—611no—
583C22×D4—611no—
584C22×D4—611no—
585C22×D4—611no—
586C22×D4—611no—
587C22×D4—611no—
588C22×D4—611no—
589C22×D4C2×#692311yescharacteristic
590C22×D4C2×#692311yescharacteristic
591C22×D4C2×#692311yescharacteristic
592C23×C4—611no—
593C23×C4—611no—
594C23×C4—611no—
595C23×C4—611no—
596C23×C4—611no—
597C23×C4—611no—
598C23×C4C2×#692311yescharacteristic
599#131—12232no—
600C2×M16—614no—
601C2×M16—1222no—
602C2×M16—1222no—
603C2×M16—1222no—
604C2×M16—1222no—
605C2×M16—1222no—
606C2×M16—1222no—
607C2×M16—1222no—
608C2×M16—1222no—
609C2×M16—1222no—
610C2×M16—1222no—
611C2×M16—1222no—
612C22×C8—614no—
613C22×C8—611no—
614C22×C8—611no—
615C22×C8—611no—
616C22×C8—611no—
617C22×C8—611no—
618C22×C8—611no—
619C22×C8—611no—
620C22×C8—611no—
621C22×C8—1222no—
622C22×C8—1222no—
623C22×C8—1222no—
624C22×C8—1222no—
625C22×C8—1222no—
626C22×C8—1222no—
627C22×C8—1222no—
628C22×C8—1222no—
629C22×C8—1222no—
630C22×C8—1222no—
631C22×C8—1222no—
632C4⋊Q8—1224no—
633#127—1224no—
634#124—1224no—
635#124—1224no—
636#121—24no—
637#121—1224no—
638#121—1224no—
639#121—1224no—
640C4×D4—1222no—
641C4×D4—1222no—
642C4×D4—1222no—
643C4×D4—1222no—
644C4×D4—1222no—
645C4×D4—1222no—
646C4×D4—1222no—
647C4×D4—1222no—
648C2×C4⋊C4—611no—
649C2×C4⋊C4—611no—
650C2×C4⋊C4—611no—
651C2×C4⋊C4C2×#692311yescharacteristic
652C2×C22⋊C4—611no—
653C2×C22⋊C4—611no—
654C2×C22⋊C4—611no—
655C2×C22⋊C4—611no—
656C2×C22⋊C4—611no—
657C2×C22⋊C4—611no—
658C2×C22⋊C4C2×#692311yescharacteristic
659C2×C22⋊C4C2×#692311yescharacteristic
660C2×C42—611no—
661C2×C42—611no—
662C2×C42—611no—
663C2×C42—611no—
664C2×C42—1222no—
665C2×C42—1222no—
666C22⋊C8—1222no—
667C22⋊C8—1222no—
668C22⋊C8—1222no—
669C22⋊C8—1222no—
670C22⋊C8—1222no—
671C22⋊C8—1222no—
672C22⋊C8—1222no—
673C22⋊C8—1222no—
674C22⋊C8—1222no—
675C22⋊C8—1222no—
676C22⋊C8—1222no—
677C22⋊C8—1222no—
678C24—611no—
679C24—611no—
680C24C22×#692311yescharacteristic
681C24C22×#692311yescharacteristic
682C24C22×#692311yescharacteristic
683#41—1228no—
684#41—1228no—
685#41—1228no—
686#41—1228no—
687#41—2444no—
688#41—2444no—
689#41—2444no—
690#41—2444no—
691C2×Q8—614no—
692C2×Q8—1222no—
693C2×Q8—1222no—
694C2×Q8—1222no—
695C2×Q8—1222no—
696C2×Q8—1222no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—22no—
700C2×D4—22no—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—41no—
705C2×D4—614no—
706C2×D4—614no—
707C2×D4—1222no—
708C2×D4—1222no—
709C2×D4—1222no—
710C2×D4—1222no—
711C2×D4—1222no—
712C2×D4—1222no—
713C2×D4—1222no—
714C2×D4—1222no—
715C2×D4—1222no—
716C2×D4—1222no—
717C2×D4—1222no—
718C2×D4—1222no—
719C2×D4—1222no—
720C2×D4—1222no—
721C2×D4—1222no—
722C2×D4—1222no—
723C2×D4—2441no—
724C2×D4—2441no—
725C2×D4—2441no—
726C2×D4C22⋊#692314yes—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—41no—
730C22×C4—612no—
731C22×C4—612no—
732C22×C4—612no—
733C22×C4—612no—
734C22×C4—612no—
735C22×C4—612no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—612no—
739C22×C4—612no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—612no—
743C22×C4—612no—
744C22×C4—611no—
745C22×C4—611no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1222no—
767C22×C4—1222no—
768C22×C4—2441no—
769C22×C4C22×#692311yescharacteristic
770C22×C4C22×#692311yescharacteristic
771C22×C4C22×#692311yescharacteristic
772C22×C4C22×#692311yescharacteristic
773M16—1228no—
774M16—1228no—
775M16—1228no—
776M16—2444no—
777C2×C8—612no—
778C2×C8—612no—
779C2×C8—612no—
780C2×C8—612no—
781C2×C8—1221no—
782C2×C8—1221no—
783C2×C8—1221no—
784C2×C8—1221no—
785C2×C8—1221no—
786C2×C8—1221no—
787C2×C8—1221no—
788C2×C8—1221no—
789C2×C8—1228no—
790C2×C8—1228no—
791C2×C8—1228no—
792C2×C8—1221no—
793C2×C8—1221no—
794C2×C8—1221no—
795C2×C8—1221no—
796C2×C8—1221no—
797C2×C8—1221no—
798C2×C8—1221no—
799C2×C8—1221no—
800C2×C8—1221no—
801C2×C8—1221no—
802C2×C8—1221no—
803C2×C8—1221no—
804C2×C8—2444no—
805C4⋊C4—22no—
806C4⋊C4—1222no—
807C4⋊C4—1222no—
808C4⋊C4—1222no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—1222no—
812C22⋊C4—1222no—
813C22⋊C4—1222no—
814C22⋊C4—1222no—
815C22⋊C4—1222no—
816C22⋊C4—1222no—
817C42—1221no—
818C42—1221no—
819C42—1221no—
820C42—1221no—
821C42—1222no—
822C42—1222no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—612no—
841C23—1221no—
842C23—1221no—
843C23—1221no—
844C23—1221no—
845C23—1221no—
846C23—1221no—
847C23—1221no—
848C23—1221no—
849C23—1221no—
850C23—1221no—
851C23—1221no—
852C23—1221no—
853C23—1221no—
854C23C2×C22⋊#692312yes—
855C23C2×C22⋊#692312yes—
856C23D4×#692312yes—
857C23D4×#692312yes—
858C23C23×#692311yescharacteristic
859Q8—1228no—
860Q8—2444no—
861D4—28no—
862D4—44no—
863D4—44no—
864D4—1228no—
865D4—1228no—
866D4—2444no—
867D4—2444no—
868D4—2444no—
869D4—2444no—
870D4—2444no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—44no—
882C2×C4—614no—
883C2×C4—614no—
884C2×C4—614no—
885C2×C4—614no—
886C2×C4—612no—
887C2×C4—611no—
888C2×C4—611no—
889C2×C4—612no—
890C2×C4—612no—
891C2×C4—611no—
892C2×C4—611no—
893C2×C4—611no—
894C2×C4—611no—
895C2×C4—612no—
896C2×C4—612no—
897C2×C4—1222no—
898C2×C4—1222no—
899C2×C4—1222no—
900C2×C4—1222no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—1222no—
905C2×C4—1221no—
906C2×C4—1221no—
907C2×C4—1221no—
908C2×C4—1221no—
909C2×C4—1221no—
910C2×C4—1221no—
911C2×C4—1221no—
912C2×C4—1221no—
913C2×C4—1221no—
914C2×C4—1221no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2444no—
924C2×C4C2×C22⋊#692312yes—
925C2×C4#1451986412yescomplemented
926C8—1222no—
927C8—1222no—
928C8—1222no—
929C8—1222no—
930C8—2441no—
931C8—2441no—
932C8—2441no—
933C8—2441no—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—22no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—1222no—
955C22—1222no—
956C22—1222no—
957C22—2441no—
958C22—2441no—
959C22—2441no—
960C22—2441no—
961C22—2441no—
962C22—2441no—
963C22—2441no—
964C22—2441no—
965C22—2441no—
966C22—2441no—
967C22—2441no—
968C22#1684071014yes—
969C22C22×C22⋊#692311yescharacteristic
970C22C2×D4×#692311yescharacteristic
971C22C2×D4×#692311yescharacteristic
972C22C2×#1451986411yescharacteristic
973C22D61⋊#13111yescharacteristic
974C22#1684084011yescharacteristic
975C22#1684084111yescharacteristic
976C4—22no—
977C4—22no—
978C4—41no—
979C4—41no—
980C4—611no—
981C4—611no—
982C4—611no—
983C4—611no—
984C4—614no—
985C4—1222no—
986C4—1222no—
987C4—2441no—
988C4—2441no—
989C2—24no—
990C2—42no—
991C2—81no—
992C2—4881no—
993C2—2442no—
994C2C2×#1684071011yescharacteristic
995C2#2146240711yescharacteristic
996C2#2146240911yescharacteristic
997C2#2146254211yescharacteristic
998C2#2146254711yescharacteristic
999C2#2146256111yescharacteristic
1000C2#2146256311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC2×#121×C61C4
prime radicalC2×#16840307C2
cosocleC22×Dic61C24
hypercenterC2×#121#6923
hypocenterC61#20900
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#14519864C2semidirect
2. C2×#16840735C2semidirect
3. C2×#16840735C2semidirect
4. C2×#16840735C2semidirect
5. #21461799C2semidirect
6. #21461798C2semidirect
7. #21461797C2semidirect
8. #21461796C2semidirect
9. #21461795C2semidirect
10. #21461794C2semidirect
11. #21461793C2semidirect
12. #21461792C2semidirect
13. #21461482C2semidirect
14. C2×#16840628C2semidirect
79. C2×#11758217D4semidirect
91. C22×#92420D4semidirect
373. C2×C4×C61#131semidirect
407. C2×Dic61#131semidirect
567. C61#20900semidirect
925. C2×C4#14519864semidirect

Maximal subgroups

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

subgroupindex
C22×#145198642
C2×#168407352
#214617992
#214617982
#214617972
#214617962
#214617952
#214617942
#214617932
#214617922
#214614822
C2×#168406282
C2×#168403072
#2090061