Finite Group Databasebeta

← #29587216

Subgroups — #29587216

Order 15616.

1154 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519691C211yesmaximal, characteristic
2C22×#14519691C211yesmaximal, characteristic
3C22×#14519691C211yesmaximal, characteristic
4#21448431C211yesmaximal, characteristic, complemented
5C2×#16839529C211yesmaximal, characteristic, complemented
6C2×#16839528C211yesmaximal, characteristic, complemented
7C2×C61×#342C211yesmaximal, characteristic, complemented
8C23×C22⋊D61C2211yescharacteristic
9C22×C22⋊Dic61C2211yescharacteristic
10C22×C22⋊Dic61C2211yescharacteristic
11C22×C22⋊Dic61C2211yescharacteristic
12C2×#14519691—22no—
13C2×#14519691—22no—
14C2×#14519691—22no—
15C2×#14519691—22no—
16C2×#14519691—22no—
17C2×#14519691—22no—
18C2×#14519691—22no—
19C2×#14519691—22no—
20C2×#14519691C414yescomplemented
21#16839635—22no—
22#16839634—22no—
23#16839620—22no—
24#16839529—22no—
25#16839528—22no—
26C22×C22⋊C4×C61C2211yescharacteristic
27C22×C22⋊C4×C61C2211yescharacteristic
28C22×C22⋊C4×C61C2211yescharacteristic
29C61×#342—22no—
30C24×D61Q811yescharacteristic
31C22×C22⋊D61—21no—
32C22×C22⋊D61—21no—
33C22×C22⋊D61—21no—
34C22×C22⋊D61—21no—
35C22×C22⋊D61—21no—
36C22×C22⋊D61—21no—
37C22×C22⋊D61—21no—
38C22×C22⋊D61—21no—
39C22×C22⋊D61—21no—
40C22×C22⋊D61—21no—
41C22×C22⋊D61—21no—
42C22×C22⋊D61—21no—
43C22×C22⋊D61C2×C412yes—
44C22×C22⋊D61D412yes—
45C23×Dic61—21no—
46C23×Dic61—21no—
47C23×Dic61—21no—
48C23×Dic61Q811yescharacteristic
49C2×#11758196—24no—
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61—21no—
52C2×C22⋊Dic61—21no—
53C2×C22⋊Dic61—21no—
54C2×C22⋊Dic61—21no—
55C2×C22⋊Dic61—21no—
56C2×C22⋊Dic61—21no—
57C2×C22⋊Dic61—21no—
58C2×C22⋊Dic61—21no—
59C2×C22⋊Dic61—21no—
60C2×C22⋊Dic61—21no—
61C2×C22⋊Dic61—21no—
62C2×C22⋊Dic61—21no—
63C2×C22⋊Dic61C2×C412yes—
64C2×C22⋊Dic61D412yes—
65C2×C22⋊Dic61D412yes—
66C2×C22⋊Dic61D412yes—
67C2×C22⋊Dic61D412yes—
68#14519691—28no—
69#14519691—28no—
70#14519691—28no—
71#14519684—24no—
72C25×C61C2311yescharacteristic
73C23×C4×C61—21no—
74C23×C4×C61—21no—
75C23×C4×C61—21no—
76C2×C22⋊C4×C61—21no—
77C2×C22⋊C4×C61—21no—
78C2×C22⋊C4×C61—21no—
79C2×C22⋊C4×C61—21no—
80C2×C22⋊C4×C61—21no—
81C2×C22⋊C4×C61—21no—
82C2×C22⋊C4×C61—21no—
83C2×C22⋊C4×C61—21no—
84C2×C22⋊C4×C61—21no—
85C2×C22⋊C4×C61—21no—
86C2×C22⋊C4×C61—21no—
87C2×C22⋊C4×C61—21no—
88C2×C22⋊C4×C61—21no—
89C2×C22⋊C4×C61—21no—
90C2×C22⋊C4×C61—21no—
91C2×C22⋊C4×C61C2×C412yes—
92C2×C22⋊C4×C61D412yes—
93C2×C22⋊C4×C61D412yes—
94C24×C61—82no—
95C24×C61C22×C411yescharacteristic
96C24×C61C2×D411yescharacteristic
97C24×C61C2×D411yescharacteristic
98C24×C61C2×D411yescharacteristic
99C24×C61C2×D411yescharacteristic
100C24×C61C2×D411yescharacteristic
101C24×C61C2×D411yescharacteristic
102C24×C61C2×D411yescharacteristic
103C24×C61C2×Q811yescharacteristic
104C24×C61#4111yescharacteristic
105C24×C61#4111yescharacteristic
106C24×C61#4111yescharacteristic
107C24×C61#4111yescharacteristic
108C24×C61#4111yescharacteristic
109C24×C61#4111yescharacteristic
110C23×D61—21no—
111C23×D61—21no—
112C23×D61—21no—
113C23×D61—21no—
114C23×D61—21no—
115C23×D61—21no—
116C23×D61—82no—
117C23×D61C4⋊C412yescomplemented
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—41no—
122C22×C4×C61—41no—
123C22×C4×C61—41no—
124C22×C4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61—41no—
127C22×C4×C61—82no—
128C22×C4×C61—82no—
129C22×C4×C61—82no—
130C2×C22⋊D61—22no—
131C2×C22⋊D61—22no—
132C2×C22⋊D61—22no—
133C2×C22⋊D61—22no—
134C2×C22⋊D61—22no—
135C2×C22⋊D61—22no—
136C2×C22⋊D61—22no—
137C2×C22⋊D61—22no—
138C2×C22⋊D61—22no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—22no—
141C2×C22⋊D61—22no—
142C2×C22⋊D61—41no—
143C2×C22⋊D61—41no—
144C2×C22⋊D61—41no—
145C2×C22⋊D61—41no—
146C2×C22⋊D61—41no—
147C2×C22⋊D61—41no—
148C2×C22⋊D61—41no—
149C2×C22⋊D61—41no—
150C2×C22⋊D61—41no—
151C2×C22⋊D61—41no—
152C2×C22⋊D61—41no—
153C2×C22⋊D61—41no—
154C2×C22⋊D61—41no—
155C2×C22⋊D61—41no—
156C2×C22⋊D61—41no—
157C2×C22⋊D61—41no—
158C22×Dic61—22no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—41no—
170C22×Dic61—41no—
171C22×Dic61—41no—
172C22×Dic61—41no—
173C22×Dic61—82no—
174C22×Dic61—82no—
175C22×Dic61—82no—
176C22×Dic61C4⋊C412yescomplemented
177C22⋊C4×C61—22no—
178C22⋊C4×C61—22no—
179C22⋊C4×C61—22no—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—22no—
183C22⋊C4×C61—41no—
184C22⋊C4×C61—41no—
185C22⋊C4×C61—41no—
186C22⋊C4×C61—41no—
187C22⋊C4×C61—41no—
188C22⋊C4×C61—41no—
189C22⋊Dic61—22no—
190C22⋊Dic61—22no—
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196C22⋊Dic61—41no—
197C22⋊Dic61—41no—
198C22⋊Dic61—41no—
199C22⋊Dic61—41no—
200C22⋊Dic61C22⋊C414yes—
201#11758196—84no—
202C23×C61—42no—
203C23×C61—42no—
204C23×C61—42no—
205C23×C61—42no—
206C23×C61—42no—
207C23×C61—42no—
208C23×C61—42no—
209C23×C61—81no—
210C23×C61—81no—
211C23×C61—81no—
212C23×C61—81no—
213C23×C61—81no—
214C23×C61—81no—
215C23×C61—81no—
216C23×C61—81no—
217C23×C61C2×C22⋊C411yescharacteristic
218C23×C61C2×C4⋊C411yescharacteristic
219C23×C61#11711yescharacteristic
220C23×C61C4×D411yescharacteristic
221C23×C61C4×D411yescharacteristic
222C23×C61C4×D411yescharacteristic
223C23×C61C4×D411yescharacteristic
224C23×C61#12011yescharacteristic
225C23×C61#12011yescharacteristic
226C23×C61#12011yescharacteristic
227C23×C61#12111yescharacteristic
228C23×C61#12111yescharacteristic
229C23×C61#12111yescharacteristic
230C23×C61#12111yescharacteristic
231C23×C61#12111yescharacteristic
232C23×C61#12111yescharacteristic
233C23×C61#12111yescharacteristic
234C23×C61#12111yescharacteristic
235C23×C61C22⋊Q811yescharacteristic
236C23×C61C22⋊Q811yescharacteristic
237C23×C61C22⋊Q811yescharacteristic
238C23×C61C22⋊Q811yescharacteristic
239C23×C61C22⋊Q811yescharacteristic
240C23×C61C22⋊Q811yescharacteristic
241C23×C61#12311yescharacteristic
242C23×C61#12311yescharacteristic
243C23×C61#12311yescharacteristic
244C23×C61#12311yescharacteristic
245C23×C61#12311yescharacteristic
246C23×C61#12411yescharacteristic
247C23×C61#12411yescharacteristic
248C23×C61#12411yescharacteristic
249C23×C61#12611yescharacteristic
250C23×C61#12611yescharacteristic
251C23×C61#12711yescharacteristic
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—82no—
260C22×D61—82no—
261C22×D61—82no—
262C22×D61—82no—
263C22×D61—82no—
264C22×D61—82no—
265C22×D61—82no—
266C2×C4×C61—44no—
267C2×C4×C61—42no—
268C2×C4×C61—42no—
269C2×C4×C61—42no—
270C2×C4×C61—82no—
271C2×C4×C61—82no—
272C2×C4×C61—82no—
273C2×C4×C61—82no—
274C2×C4×C61—82no—
275C2×C4×C61—82no—
276C2×C4×C61—82no—
277C2×C4×C61—82no—
278C22⋊D61—42no—
279C22⋊D61—42no—
280C22⋊D61—42no—
281C22⋊D61—42no—
282C22⋊D61—42no—
283C22⋊D61—42no—
284C22⋊D61—42no—
285C22⋊D61—42no—
286C2×Dic61—22no—
287C2×Dic61—22no—
288C2×Dic61—22no—
289C2×Dic61—24no—
290C2×Dic61—44no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—44no—
296C2×Dic61—42no—
297C2×Dic61—42no—
298C2×Dic61—82no—
299C2×Dic61—82no—
300C2×Dic61—82no—
301C2×Dic61—82no—
302C2×Dic61—82no—
303C2×Dic61—82no—
304C2×Dic61—82no—
305#11089—611nomaximal, Sylow
306C22×C61—22no—
307C22×C61—22no—
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61#38011yescharacteristic
342C22×C61#38511yescharacteristic
343C22×C61#38511yescharacteristic
344C22×C61#38611yescharacteristic
345C22×C61#38811yescharacteristic
346C22×C61#38811yescharacteristic
347C22×C61#39011yescharacteristic
348C22×C61#39211yescharacteristic
349C22×C61#39311yescharacteristic
350C22×C61#39411yescharacteristic
351C22×C61#39411yescharacteristic
352C22×C61#39611yescharacteristic
353C22×C61#39611yescharacteristic
354C22×C61#39711yescharacteristic
355C22×C61#39911yescharacteristic
356C2×D61—42no—
357C2×D61—82no—
358C2×D61—82no—
359C2×D61—82no—
360C2×D61—82no—
361C2×D61—82no—
362C2×D61—82no—
363C2×D61—82no—
364C4×C61—82no—
365C4×C61—82no—
366C4×C61—82no—
367Dic61—44no—
368Dic61—42no—
369Dic61—82no—
370Dic61—82no—
371C22×#99—611no—
372C22×#99—611no—
373C22×#99—611no—
374#2315—611no—
375C2×#342—611no—
376C2×#342—611no—
377C2×#342D6111yescharacteristic, complemented
378C2×C61—21no—
379C2×C61—21no—
380C2×C61—21no—
381C2×C61—21no—
382C2×C61—21no—
383C2×C61—21no—
384C2×C61—21no—
385C2×C61—21no—
386C2×C61—21no—
387C2×C61—21no—
388C2×C61—21no—
389C2×C61—21no—
390C2×C61—21no—
391C2×C61—21no—
392C2×C61#143911yescharacteristic
393C2×C61#203212yes—
394D61—82no—
395C23×D4—611no—
396C22×C22⋊C4—611no—
397C22×C22⋊C4—611no—
398C22×C22⋊C4—611no—
399C22×C22⋊C4C2×D6111yescharacteristic
400C22×C22⋊C4C2×D6111yescharacteristic
401C22×C22⋊C4C2×D6111yescharacteristic
402C2×#99—614no—
403C2×#99—1222no—
404C2×#99—1222no—
405C2×#99—1222no—
406C2×#99—1222no—
407C2×#99—1222no—
408C2×#99—1222no—
409C2×#99—1222no—
410C2×#99—1222no—
411#385—1222no—
412#385—1222no—
413#380—1222no—
414#342—22no—
415#342—1222no—
416#342—1222no—
417C61#1108911yescharacteristic, complemented, Sylow
418C25—611no—
419C25C22×D6111yescharacteristic
420C22×D4—612no—
421C22×D4—612no—
422C22×D4—1221no—
423C22×D4—1221no—
424C22×D4—1221no—
425C22×D4—1221no—
426C22×D4—1221no—
427C22×D4—1221no—
428C22×D4—1221no—
429C22×D4—1221no—
430C22×D4—1221no—
431C22×D4—1221no—
432C22×D4—1221no—
433C22×D4—1221no—
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—611no—
438C23×C4—1221no—
439C23×C4—1221no—
440C23×C4—1221no—
441C2×C4⋊C4—1224no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—612no—
458C2×C22⋊C4—612no—
459C2×C22⋊C4—612no—
460C2×C22⋊C4—612no—
461C2×C22⋊C4—612no—
462C2×C22⋊C4—1221no—
463C2×C22⋊C4—1221no—
464C2×C22⋊C4—1221no—
465C2×C22⋊C4—1221no—
466C2×C22⋊C4—1221no—
467C2×C22⋊C4—1221no—
468C2×C22⋊C4—1221no—
469C2×C22⋊C4—1221no—
470C2×C22⋊C4—1221no—
471C2×C22⋊C4—1221no—
472C2×C22⋊C4—1221no—
473C2×C22⋊C4—1221no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4C4×D6112yes—
476C2×C22⋊C4D24412yes—
477C2×C22⋊C4C22⋊D6112yes—
478#99—1228no—
479#99—1228no—
480#99—1228no—
481#95—1224no—
482C24—82no—
483C24—612no—
484C24—1221no—
485C24—1221no—
486C24—1221no—
487C24—1221no—
488C24—1221no—
489C24—1221no—
490C24—4882no—
491C24C2×C4×D6111yescharacteristic
492C24C2×D24411yescharacteristic
493C24#1175822211yescharacteristic
494C24#1175822211yescharacteristic
495C24#1175822211yescharacteristic
496C24#1175822211yescharacteristic
497C24D4×D6111yescharacteristic
498C24D4×D6111yescharacteristic
499C24D4×D6111yescharacteristic
500C24D4×D6111yescharacteristic
501C24D4×D6111yescharacteristic
502C24#1175822411yescharacteristic
503C24Q8×D6111yescharacteristic
504C24#1175822611yescharacteristic
505C24C2×C22⋊D6111yescharacteristic
506C2×D4—1222no—
507C2×D4—1222no—
508C2×D4—1222no—
509C2×D4—1222no—
510C2×D4—1222no—
511C2×D4—1222no—
512C2×D4—1222no—
513C2×D4—1222no—
514C2×D4—1222no—
515C2×D4—1222no—
516C2×D4—1222no—
517C2×D4—1222no—
518C2×D4—2441no—
519C2×D4—2441no—
520C2×D4—2441no—
521C2×D4—2441no—
522C2×D4—2441no—
523C2×D4—2441no—
524C2×D4—2441no—
525C2×D4—2441no—
526C2×D4—2441no—
527C2×D4—2441no—
528C2×D4—2441no—
529C2×D4—2441no—
530C2×D4—2441no—
531C2×D4—2441no—
532C2×D4—2441no—
533C2×D4—2441no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—82no—
544C22×C4—82no—
545C22×C4—82no—
546C22×C4—612no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1222no—
557C22×C4—1222no—
558C22×C4—4882no—
559C22×C4—4882no—
560C22×C4—4882no—
561C22×C4—2441no—
562C22×C4—2441no—
563C22×C4—2441no—
564C22×C4—2441no—
565C4⋊C4—4884no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—614no—
579C22⋊C4—1222no—
580C22⋊C4—1222no—
581C22⋊C4—1222no—
582C22⋊C4—1222no—
583C22⋊C4—1222no—
584C22⋊C4—1222no—
585C22⋊C4—1222no—
586C22⋊C4—2441no—
587C22⋊C4—2441no—
588C22⋊C4—2441no—
589C22⋊C4—2441no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—81no—
598C23—81no—
599C23—81no—
600C23—81no—
601C23—81no—
602C23—81no—
603C23—81no—
604C23—81no—
605C23—1222no—
606C23—1222no—
607C23—1222no—
608C23—4882no—
609C23—4882no—
610C23—4882no—
611C23—4882no—
612C23—4882no—
613C23—4882no—
614C23—4882no—
615C23—2441no—
616C23—2441no—
617C23—2441no—
618C23—2441no—
619C23C22⋊C4×D6111yescharacteristic
620C23C4⋊C4×D6111yescharacteristic
621C23#1451973411yescharacteristic
622C23#1451973711yescharacteristic
623C23C4×C22⋊D6111yescharacteristic
624C23#1451973911yescharacteristic
625C23C4×D24411yescharacteristic
626C23#1451974511yescharacteristic
627C23#1451974711yescharacteristic
628C23#1451974711yescharacteristic
629C23#1451974911yescharacteristic
630C23#1451975011yescharacteristic
631C23#1451975011yescharacteristic
632C23#1451975011yescharacteristic
633C23#1451975011yescharacteristic
634C23#1451975011yescharacteristic
635C23#1451975111yescharacteristic
636C23#1451975211yescharacteristic
637C23#1451975311yescharacteristic
638C23#1451975511yescharacteristic
639C23#1451975511yescharacteristic
640C23#1451975511yescharacteristic
641C23#1451975511yescharacteristic
642C23#1451975711yescharacteristic
643C23#1451975911yescharacteristic
644C23#1451976011yescharacteristic
645C23#1451976211yescharacteristic
646C23#1451976211yescharacteristic
647C23#1451976211yescharacteristic
648C23#1451976311yescharacteristic
649C23#1451976311yescharacteristic
650C23#1451976511yescharacteristic
651C23#1451977111yescharacteristic
652C23#1451977211yescharacteristic
653C23#1451977311yescharacteristic
654D4—2442no—
655D4—2442no—
656D4—2442no—
657D4—2442no—
658D4—2442no—
659D4—2442no—
660D4—2442no—
661D4—2442no—
662C2×C4—44no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—82no—
667C2×C4—82no—
668C2×C4—82no—
669C2×C4—82no—
670C2×C4—82no—
671C2×C4—82no—
672C2×C4—82no—
673C2×C4—82no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1224no—
678C2×C4—4882no—
679C2×C4—4882no—
680C2×C4—4882no—
681C2×C4—4882no—
682C2×C4—4882no—
683C2×C4—4882no—
684C2×C4—4882no—
685C2×C4—2444no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4—2444no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—4882no—
729C22—4882no—
730C22—4882no—
731C22—4882no—
732C22—4882no—
733C22—4882no—
734C22—4882no—
735C22—2442no—
736C22#1683962111yescharacteristic
737C22#1683963311yescharacteristic
738C22#1683963611yescharacteristic
739C22#1683964011yescharacteristic
740C22#1683965111yescharacteristic
741C22#1683965311yescharacteristic
742C22#1683966211yescharacteristic
743C22#1683967111yescharacteristic
744C22#1683967511yescharacteristic
745C22#1683967711yescharacteristic
746C22#1683968011yescharacteristic
747C22#1683968411yescharacteristic
748C22#1683968611yescharacteristic
749C22#1683969111yescharacteristic
750C22#1683969711yescharacteristic
751C4—82no—
752C4—82no—
753C4—82no—
754C4—4882no—
755C4—4882no—
756C4—2444no—
757C4—2442no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—4882no—
773C2#2144406311yescharacteristic
774C2#2144699712yes—
subgroupG/H
centerC22#16839675
commutatorC24×C61C22×C4
FrattiniC25C22×D61
FittingC2×C61×#342C2
socleC22×C61#393
prime radicalC23×C22⋊D61C22
cosocleC25×C61C23
hypercenterC2×#342D61
hypocenterC61#11089
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. #21448431C2semidirect
5. C2×#16839529C2semidirect
6. C2×#16839528C2semidirect
7. C2×C61×#342C2semidirect
20. C2×#14519691C4semidirect
117. C23×D61C4⋊C4semidirect
176. C22×Dic61C4⋊C4semidirect
377. C2×#342D61semidirect
417. C61#11089semidirect

Maximal subgroups

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

subgroupindex
C22×#145196912
#214484312
C2×#168395292
C2×#168395282
C2×C61×#3422
#1108961