Finite Group Databasebeta

← #29585305

Subgroups — #29585305

Order 15616.

1326 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D61C211yesmaximal, characteristic
2C2×#16839725C211yesmaximal, characteristic
3C22×#14519689C211yesmaximal, characteristic
4C2×#16839527C211yesmaximal, characteristic, complemented
5C2×#16839526C211yesmaximal, characteristic, complemented
6C2×#16839526C211yesmaximal, characteristic, complemented
7C2×C61×#341C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×#11758189—21no—
12C2×M16×D61—22no—
13C2×M16×D61—22no—
14C2×M16×D61—22no—
15C2×M16×D61—22no—
16C2×M16×D61—22no—
17C2×M16×D61C414yes—
18C23×#92418C2211yescharacteristic
19C22×C8×D61—21no—
20#16839725—22no—
21#16839725C414yes—
22C2×#14519689—22no—
23C2×#14519689—22no—
24C2×#14519689—21no—
25C2×#14519689—21no—
26C2×#14519689C412yes—
27C2×#14519689C412yes—
28#16839527—22no—
29#16839526—22no—
30#16839526—22no—
31C22×M16×C61C2211yescharacteristic
32C22×M16×C61C2211yescharacteristic
33C23×C8×C61C2211yescharacteristic
34C61×#341—22no—
35C24×D61Q811yescharacteristic
36C23×Dic61Q811yescharacteristic
37C22×C4×D61—21no—
38C22×C4×D61—21no—
39C22×C4×D61—21no—
40C22×C4×D61—21no—
41C22×C4×D61—21no—
42C22×C4×D61—21no—
43C22×C4×D61—21no—
44C22×C4×D61—21no—
45C22×C4×D61C2×C411yescharacteristic
46C22×C4×D61C2×C411yescharacteristic
47C22×C4×D61C2×C412yes—
48C22×C4×D61C2×C412yes—
49C22×C4×D61D412yes—
50C22×C4×D61D411yescharacteristic
51C22×C4×D61D412yes—
52C22×C4×D61D411yescharacteristic
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194C2×C412yes—
62C2×#11758194C2×C412yes—
63C2×#11758194D412yes—
64C2×#11758194D412yes—
65C2×#11758189—24no—
66C2×#11758189—24no—
67C2×#11758189—24no—
68M16×D61—28no—
69M16×D61—28no—
70M16×D61—28no—
71M16×D61—28no—
72C22×#92418—21no—
73C22×#92418—21no—
74C22×#92418—21no—
75C22×#92418—21no—
76C22×#92418—21no—
77C22×#92418—21no—
78C22×#92418—21no—
79C22×#92418—21no—
80C22×#92418C2×C412yes—
81C2×C8×D61—24no—
82C2×C8×D61—24no—
83C2×C8×D61—24no—
84#14519689—24no—
85#14519689—24no—
86#14519689—24no—
87#14519689—24no—
88C23×C4×C61C2311yescharacteristic
89C2×M16×C61—21no—
90C2×M16×C61—21no—
91C2×M16×C61—21no—
92C2×M16×C61—21no—
93C2×M16×C61—21no—
94C2×M16×C61—21no—
95C2×M16×C61—21no—
96C2×M16×C61—21no—
97C2×M16×C61C2×C412yes—
98C2×M16×C61C2×C412yes—
99C2×M16×C61D412yes—
100C2×M16×C61D412yes—
101C22×C8×C61—21no—
102C22×C8×C61—21no—
103C22×C8×C61—21no—
104C22×C8×C61—21no—
105C22×C8×C61—21no—
106C22×C8×C61—21no—
107C22×C8×C61—21no—
108C22×C8×C61—21no—
109C22×C8×C61C2×C412yes—
110C24×C61C2×Q811yescharacteristic
111C23×D61—21no—
112C23×D61—21no—
113C23×D61—21no—
114C23×D61—21no—
115C23×D61—24no—
116C23×D61—42no—
117C23×D61C4⋊C411yescharacteristic
118C23×D61C4⋊C412yes—
119C23×D61C4⋊C412yes—
120C23×D61C4⋊C411yescharacteristic
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61#4111yescharacteristic
132C22×C4×C61#4111yescharacteristic
133C22×C4×C61#4111yescharacteristic
134C22×C4×C61#4111yescharacteristic
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61C4⋊C412yes—
140C22×Dic61C4⋊C412yes—
141C22×Dic61C4⋊C411yescharacteristic
142C22×Dic61C4⋊C411yescharacteristic
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—22no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—22no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—22no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—22no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—22no—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—21no—
170C2×C4×D61—22no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—22no—
174C2×C4×D61—21no—
175C2×C4×D61C4212yes—
176C2×C4×D61C4212yes—
177C2×C4×D61C22⋊C412yes—
178C2×C4×D61C22⋊C412yes—
179C2×C4×D61C22⋊C412yes—
180C2×C4×D61C22⋊C412yes—
181C2×C4×D61C22⋊C412yes—
182C2×C4×D61C22⋊C412yes—
183M16×C61—22no—
184M16×C61—22no—
185M16×C61—22no—
186M16×C61—22no—
187M16×C61—22no—
188M16×C61—41no—
189M16×C61—41no—
190M16×C61C22⋊C414yes—
191C2×C8×C61—22no—
192C2×C8×C61—22no—
193C2×C8×C61—22no—
194C2×C8×C61—22no—
195C2×C8×C61—22no—
196C2×C8×C61—22no—
197C2×C8×C61—22no—
198C2×C8×C61—41no—
199C2×C8×C61—41no—
200C2×C8×C61—41no—
201C2×C8×C61—41no—
202C2×C8×C61—41no—
203C2×C8×C61—41no—
204#11758194—22no—
205#11758194—22no—
206#11758194—22no—
207#11758194—22no—
208#11758194—22no—
209#11758194—41no—
210#11758194—41no—
211#11758194C22⋊C414yes—
212C2×#92418—22no—
213C2×#92418—22no—
214C2×#92418—22no—
215C2×#92418—22no—
216C2×#92418—22no—
217C2×#92418—22no—
218C2×#92418—22no—
219C2×#92418—41no—
220C2×#92418—41no—
221C2×#92418—41no—
222C2×#92418—41no—
223C2×#92418—41no—
224C2×#92418—41no—
225#11758189—216no—
226C8×D61—216no—
227C23×C61—22no—
228C23×C61—22no—
229C23×C61C2×C4⋊C411yescharacteristic
230C23×C61C2×C4⋊C411yescharacteristic
231C23×C61C2×C4⋊C411yescharacteristic
232C23×C61C22⋊Q811yescharacteristic
233C23×C61C22⋊Q811yescharacteristic
234C23×C61C22⋊Q811yescharacteristic
235C23×C61C22⋊Q811yescharacteristic
236C22×D61—21no—
237C22×D61—21no—
238C22×D61—22no—
239C22×D61—22no—
240C22×D61—22no—
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—24no—
248C22×D61—24no—
249C22×D61—42no—
250C22×D61—42no—
251C22×D61—44no—
252C22×D61—44no—
253C22×D61—44no—
254C22×D61—44no—
255C22×D61#9512yes—
256C22×D61#9512yes—
257C22×D61#10814yes—
258C2×C4×C61C2×C4211yescharacteristic
259C2×C4×C61C2×C22⋊C411yescharacteristic
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61C2×C22⋊C411yescharacteristic
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61#11711yescharacteristic
265C2×C4×C61#11711yescharacteristic
266C2×C4×C61C4×D411yescharacteristic
267C2×C4×C61C4×D411yescharacteristic
268C2×C4×C61C4×D411yescharacteristic
269C2×C4×C61C4×D411yescharacteristic
270C2×C4×C61C4×D411yescharacteristic
271C2×C4×C61C4×D411yescharacteristic
272C2×C4×C61C4×D411yescharacteristic
273C2×C4×C61C4×D411yescharacteristic
274C2×C4×C61#12011yescharacteristic
275C2×C4×C61#12011yescharacteristic
276C2×C4×C61#12011yescharacteristic
277C2×C4×C61#12011yescharacteristic
278C2×C4×C61#12111yescharacteristic
279C2×C4×C61#12111yescharacteristic
280C2×C4×C61#12111yescharacteristic
281C2×C4×C61#12111yescharacteristic
282C2×C4×C61#12311yescharacteristic
283C2×C4×C61#12311yescharacteristic
284C2×C4×C61#12311yescharacteristic
285C2×C4×C61#12311yescharacteristic
286C2×Dic61—22no—
287C2×Dic61—22no—
288C2×Dic61—22no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—22no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61#9512yes—
295C2×Dic61#9512yes—
296C4×D61—22no—
297C4×D61—22no—
298C4×D61—22no—
299C4×D61—22no—
300C4×D61—22no—
301C4×D61—22no—
302C4×D61—22no—
303C4×D61—22no—
304C4×D61—22no—
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—22no—
308C4×D61—22no—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—22no—
312C8×C61—24no—
313C8×C61—42no—
314C8×C61—42no—
315#92418—24no—
316#92418—42no—
317#92418—42no—
318#10734—611nomaximal, Sylow
319C22×C61—22no—
320C22×C61—22no—
321C22×C61—22no—
322C22×C61—22no—
323C22×C61—21no—
324C22×C61—21no—
325C22×C61—21no—
326C22×C61—21no—
327C22×C61C2×#9511yescharacteristic
328C22×C61#38011yescharacteristic
329C22×C61#38011yescharacteristic
330C22×C61#38511yescharacteristic
331C22×C61#38511yescharacteristic
332C22×C61#38511yescharacteristic
333C22×C61#38511yescharacteristic
334C22×C61C2×#10812yes—
335C22×C61#43012yes—
336C2×D61—24no—
337C2×D61—24no—
338C2×D61—22no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—44no—
344C2×D61—44no—
345C2×D61—44no—
346C2×D61—44no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61#34114yescomplemented
350C4×C61C4×C22⋊C411yescharacteristic
351C4×C61C4×C22⋊C411yescharacteristic
352C4×C61#37911yescharacteristic
353C4×C61#38111yescharacteristic
354C4×C61#38611yescharacteristic
355C4×C61#38611yescharacteristic
356C4×C61#38611yescharacteristic
357C4×C61#38611yescharacteristic
358Dic61—22no—
359Dic61—22no—
360C23×M16—611no—
361C2×#407—611no—
362C22×C22⋊C8—611no—
363C2×#341—611no—
364C2×#341—611no—
365C2×#341—611no—
366C2×#341D6111yescharacteristic, complemented
367C2×C61—21no—
368C2×C61—21no—
369C2×C61—21no—
370C2×C61—21no—
371C2×C61C22⋊#9511yescharacteristic
372C2×C61C2×#34111yescharacteristic
373C2×C61#173811yescharacteristic
374C2×C61#185512yes—
375C2×C61#185512yes—
376D61—24no—
377D61—42no—
378C24×C4—611no—
379C22×M16—611no—
380C22×M16—611no—
381C22×M16—614no—
382C22×M16—1221no—
383C22×M16—1222no—
384C22×M16—1222no—
385C22×M16—1222no—
386C22×M16—1222no—
387C22×M16—1222no—
388C22×M16C2×D6111yescharacteristic
389C22×M16C2×D6111yescharacteristic
390C23×C8—611no—
391C23×C8—1221no—
392C23×C8C2×D6111yescharacteristic
393#407—614no—
394#407—1222no—
395C2×C22⋊C8—612no—
396C2×C22⋊C8—612no—
397C2×C22⋊C8—1222no—
398C2×C22⋊C8—1222no—
399C2×C22⋊C8—1221no—
400C2×C22⋊C8—1221no—
401#341—22no—
402#341—1222no—
403#341—1222no—
404#341—1222no—
405C61#1073411yescharacteristic, complemented, Sylow
406C25—611no—
407C23×C4—611no—
408C23×C4—612no—
409C23×C4—611no—
410C23×C4—611no—
411C23×C4—612no—
412C23×C4—612no—
413C23×C4—612no—
414C23×C4—611no—
415C23×C4—611no—
416C23×C4—1221no—
417C23×C4—1221no—
418C23×C4—1221no—
419C23×C4—1221no—
420C23×C4—1221no—
421C23×C4—1221no—
422C23×C4—1221no—
423C23×C4—1221no—
424C23×C4C22×D6111yescharacteristic
425C2×M16—21no—
426C2×M16—21no—
427C2×M16—21no—
428C2×M16—21no—
429C2×M16—21no—
430C2×M16—21no—
431C2×M16—21no—
432C2×M16—21no—
433C2×M16—612no—
434C2×M16—612no—
435C2×M16—612no—
436C2×M16—612no—
437C2×M16—1224no—
438C2×M16—1224no—
439C2×M16—1224no—
440C2×M16—1228no—
441C2×M16—1228no—
442C2×M16—1228no—
443C2×M16—1221no—
444C2×M16—1221no—
445C2×M16—1221no—
446C2×M16—1228no—
447C2×M16—1221no—
448C2×M16—1221no—
449C2×M16—1221no—
450C2×M16—1221no—
451C2×M16—1221no—
452C2×M16C4×D6112yes—
453C2×M16C4×D6112yes—
454C2×M16D24412yes—
455C2×M16C22⋊D6112yes—
456C22×C8—21no—
457C22×C8—21no—
458C22×C8—21no—
459C22×C8—21no—
460C22×C8—21no—
461C22×C8—21no—
462C22×C8—21no—
463C22×C8—21no—
464C22×C8—612no—
465C22×C8—1224no—
466C22×C8—1224no—
467C22×C8—1224no—
468C22×C8—1221no—
469C22×C8—1221no—
470C22×C8—1221no—
471C22×C8—1221no—
472C22×C8—1221no—
473C22×C8—1221no—
474C22×C8—1221no—
475C22×C8—1221no—
476C22×C8C4×D6112yes—
477C22⋊C8—1224no—
478C22⋊C8—1224no—
479C22⋊C8—1224no—
480C22⋊C8—1224no—
481C24—611no—
482C24—611no—
483C24—612no—
484C24—612no—
485C24—1224no—
486C24—1221no—
487C24—1221no—
488C24—1221no—
489C24—1221no—
490C24—2442no—
491C24Q8×D6111yescharacteristic
492C22×C4—612no—
493C22×C4—612no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—612no—
497C22×C4—612no—
498C22×C4—612no—
499C22×C4—612no—
500C22×C4—612no—
501C22×C4—612no—
502C22×C4—612no—
503C22×C4—612no—
504C22×C4—1221no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4—1222no—
511C22×C4—1222no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—1222no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1222no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4—1222no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1222no—
524C22×C4—1221no—
525C22×C4—1222no—
526C22×C4—1221no—
527C22×C4—1221no—
528C22×C4—1222no—
529C22×C4—1221no—
530C22×C4—1222no—
531C22×C4—1222no—
532C22×C4—1222no—
533C22×C4—1222no—
534C22×C4—1222no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1222no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4C2×C4×D6111yescharacteristic
541C22×C4C2×C4×D6111yescharacteristic
542C22×C4C2×C4×D6111yescharacteristic
543C22×C4C2×D24411yescharacteristic
544C22×C4#1175822211yescharacteristic
545C22×C4#1175822211yescharacteristic
546C22×C4D4×D6111yescharacteristic
547C22×C4D4×D6111yescharacteristic
548C22×C4D4×D6111yescharacteristic
549C22×C4D4×D6111yescharacteristic
550C22×C4D4×D6111yescharacteristic
551C22×C4#1175822411yescharacteristic
552C22×C4#1175822611yescharacteristic
553C22×C4C2×C22⋊D6111yescharacteristic
554M16—22no—
555M16—22no—
556M16—22no—
557M16—22no—
558M16—22no—
559M16—41no—
560M16—41no—
561M16—614no—
562M16—12216no—
563M16—1222no—
564M16—1222no—
565M16—1222no—
566M16—1222no—
567M16—1222no—
568M16—2441no—
569M16—2441no—
570M16#1175819814yes—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—12216no—
585C2×C8—1222no—
586C2×C8—1222no—
587C2×C8—1222no—
588C2×C8—1222no—
589C2×C8—1222no—
590C2×C8—1222no—
591C2×C8—1222no—
592C2×C8—2441no—
593C2×C8—2441no—
594C2×C8—2441no—
595C2×C8—2441no—
596C2×C8—2441no—
597C2×C8—2441no—
598C23—22no—
599C23—22no—
600C23—614no—
601C23—612no—
602C23—612no—
603C23—1224no—
604C23—1224no—
605C23—1222no—
606C23—1221no—
607C23—1221no—
608C23—1222no—
609C23—1222no—
610C23—1222no—
611C23—1222no—
612C23—1222no—
613C23—1221no—
614C23—1222no—
615C23—1221no—
616C23—2442no—
617C23—2442no—
618C23—2444no—
619C23—2444no—
620C23—2444no—
621C23—2444no—
622C23C4⋊C4×D6111yescharacteristic
623C23C4⋊C4×D6111yescharacteristic
624C23C4⋊C4×D6111yescharacteristic
625C23#1451975311yescharacteristic
626C23#1451975511yescharacteristic
627C23#1451975511yescharacteristic
628C23#1451975711yescharacteristic
629C2×C4—612no—
630C2×C4—612no—
631C2×C4—1222no—
632C2×C4—1222no—
633C2×C4—1222no—
634C2×C4—1221no—
635C2×C4—1221no—
636C2×C4—1222no—
637C2×C4—1221no—
638C2×C4—1221no—
639C2×C4—1222no—
640C2×C4—1222no—
641C2×C4—1222no—
642C2×C4—1222no—
643C2×C4—1222no—
644C2×C4—1222no—
645C2×C4—1222no—
646C2×C4—1222no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—1222no—
655C2×C4C42×D6111yescharacteristic
656C2×C4C22⋊C4×D6111yescharacteristic
657C2×C4C22⋊C4×D6111yescharacteristic
658C2×C4C22⋊C4×D6111yescharacteristic
659C2×C4C22⋊C4×D6111yescharacteristic
660C2×C4C2×#1175819811yescharacteristic
661C2×C4#1451973411yescharacteristic
662C2×C4#1451973511yescharacteristic
663C2×C4#1451973711yescharacteristic
664C2×C4#1451973711yescharacteristic
665C2×C4C4×C22⋊D6111yescharacteristic
666C2×C4C4×C22⋊D6111yescharacteristic
667C2×C4#1451973911yescharacteristic
668C2×C4#1451973911yescharacteristic
669C2×C4C4×D24411yescharacteristic
670C2×C4C4×D24411yescharacteristic
671C2×C4#1451974511yescharacteristic
672C2×C4#1451974511yescharacteristic
673C2×C4#1451974711yescharacteristic
674C2×C4#1451974711yescharacteristic
675C2×C4#1451974811yescharacteristic
676C2×C4#1451975011yescharacteristic
677C2×C4#1451975011yescharacteristic
678C2×C4#1451975211yescharacteristic
679C2×C4#1451975911yescharacteristic
680C2×C4#1451975911yescharacteristic
681C2×C4#1451976211yescharacteristic
682C2×C4#1451976211yescharacteristic
683C8—24no—
684C8—42no—
685C8—42no—
686C8—1224no—
687C8—2442no—
688C8—2442no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—614no—
698C22—1224no—
699C22—1224no—
700C22—1222no—
701C22—1222no—
702C22—1222no—
703C22—1222no—
704C22—1222no—
705C22—2444no—
706C22—2444no—
707C22—2444no—
708C22—2444no—
709C22—2442no—
710C22—2442no—
711C22#95×D6111yescharacteristic
712C22#1683961911yescharacteristic
713C22#1683962111yescharacteristic
714C22#1683963311yescharacteristic
715C22#1683963311yescharacteristic
716C22#1683963611yescharacteristic
717C22#1683963611yescharacteristic
718C22#108×D6112yes—
719C22#1683980912yes—
720C4—1222no—
721C4—1222no—
722C4#1683960911yescharacteristic
723C4C4×#1175819811yescharacteristic
724C4#1683961711yescharacteristic
725C4#1683962411yescharacteristic
726C4#1683963811yescharacteristic
727C4#1683963811yescharacteristic
728C4#1683964011yescharacteristic
729C4#1683964011yescharacteristic
730C2—21no—
731C2—21no—
732C2—21no—
733C2—21no—
734C2—1224no—
735C2—2442no—
736C2#2144404011yescharacteristic
737C2#341×D6111yescharacteristic
738C2#2144554411yescharacteristic
739C2#2144602212yes—
740C2#2144602512yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#341C2
socleC23×C61C2×C4⋊C4
prime radicalC24×D61Q8
cosocleC23×C4×C61C23
hypercenterC2×#341D61
hypocenterC61#10734
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
4. C2×#16839527C2semidirect
5. C2×#16839526C2semidirect
6. C2×#16839526C2semidirect
7. C2×C61×#341C2semidirect
349. C2×D61#341semidirect
366. C2×#341D61semidirect
405. C61#10734semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D612
C2×#168397252
C22×#145196892
C2×#168395272
C2×#168395262
C2×C61×#3412
#1073461