Finite Group Databasebeta

← #29695477

Subgroups — #29695477

Order 15616.

1542 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840430C211yesmaximal, characteristic
2C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#16839759C211yesmaximal, characteristic, complemented
4C2×#16839755C211yesmaximal, characteristic, complemented
5#21448763C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446623C211yesmaximal, characteristic, complemented
8#21446246C211yesmaximal, characteristic, complemented
9#21446142C211yesmaximal, characteristic, complemented
10#21446140C211yesmaximal, characteristic, complemented
11#21445823C211yesmaximal, characteristic, complemented
12#21445757C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#21445638C211yesmaximal, characteristic, complemented
15C61×#1893C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758224C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840430—24no—
20#16840430C418yescomplemented
21C2×#14519773—21no—
22C2×#14519773C2211yescharacteristic
23C2×#14519752C2211yescharacteristic
24C2×#14519750—21no—
25C2×#14519749—21no—
26C2×#14519742C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519737—21no—
29C2×#14519736C2211yescharacteristic
30C2×#14519735C2211yescharacteristic
31C8×C22⋊D61—24no—
32C2×#14519706C2211yescharacteristic
33#16839759—24no—
34#16839755—24no—
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×C22⋊#92418C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×C8×Dic61C2211yescharacteristic
48#16839662—21no—
49#16839656—21no—
50#16839651—21no—
51#16839631C2211yescharacteristic
52#16839619C2211yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic
54#16839613—21no—
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic
58C2×#121×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C2×#11758222C2×C414yes—
70C2×#11758224—22no—
71C2×#11758224—22no—
72C2×#11758224—22no—
73C2×#11758224—41no—
74C2×#11758224—41no—
75C2×#11758224C2×C414yes—
76C22×Dic122C2311yescharacteristic
77C22×D244—21no—
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C22⋊D61D411yescharacteristic
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C22×C4×D61C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C2×C8×D61—22no—
90C2×C8×D61—22no—
91C2×C8×D61—41no—
92#14519773—28no—
93#14519773—22no—
94#14519773C2×C414yes—
95#14519752—22no—
96#14519752C2×C414yes—
97#14519750—28no—
98#14519749—28no—
99#14519742—22no—
100#14519742C2×C414yes—
101C4×C22⋊D61C2×C414yes—
102C4×C22⋊D61D414yes—
103#14519737—28no—
104#14519736—22no—
105#14519736—41no—
106#14519735—22no—
107#14519735—41no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196D411yescharacteristic
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61D411yescharacteristic
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198D411yescharacteristic
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61—21no—
124C2×C4×Dic61C2311yescharacteristic
125#14519706—22no—
126#14519702—22no—
127#14519702D414yescomplemented
128#14519700—22no—
129#14519700—22no—
130#14519699—22no—
131#14519699—22no—
132#14519698—22no—
133#14519698—41no—
134#14519697—41no—
135#14519697—41no—
136C22⋊#92418—22no—
137#14519689—22no—
138C8×Dic61—22no—
139#14519684—21no—
140#14519684—21no—
141C22×D4×C61—21no—
142C22×D4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C22×C8×C61—22no—
145C22×C8×C61—22no—
146C22×C8×C61—41no—
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149#121×C61—22no—
150#121×C61C2×C414yes—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156#102×C61—22no—
157#102×C61—41no—
158#95×C61—21no—
159C24×C61—21no—
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
162C23×D61C2×D411yescharacteristic
163C2×D4×C61—24no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—81no—
170C2×D4×C61—81no—
171C2×D4×C61C22×C412yes—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61C22×C412yes—
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D412yes—
182C22×C4×C61C2411yescharacteristic
183C2×C22⋊D61—24no—
184C2×C22⋊D61—24no—
185C2×C22⋊D61—24no—
186C2×C22⋊D61—24no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—81no—
196C2×C22⋊D61—81no—
197C2×C22⋊D61C22⋊C414yes—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—24no—
201C22×Dic61—21no—
202C22×Dic61—42no—
203C22×Dic61—42no—
204C22×Dic61C2×D411yescharacteristic
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207#11758224—28no—
208#11758224—44no—
209#11758224—44no—
210#11758224—44no—
211#11758222—28no—
212#11758222—44no—
213#11758222—44no—
214#11758222—44no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—24no—
221C2×D244—81no—
222C2×D244—81no—
223C2×D244C22×C412yes—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—24no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61C22×C412yes—
232C2×C4×D61C2×D412yes—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122C22×C412yes—
237C2×Dic122C2×D412yes—
238C2×Dic122#4112yes—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—44no—
245C2×C8×C61C2×D412yes—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61C22×C412yes—
252C22⋊C4×C61—24no—
253C22⋊C4×C61—81no—
254C22⋊Dic61—42no—
255C22⋊Dic61C22⋊C414yes—
256#11758198—24no—
257#11758198—42no—
258#11758198—81no—
259#11758198C22⋊C414yes—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61C2×D412yes—
264#11758196—24no—
265#11758196—42no—
266#11758196—81no—
267#11758196C22⋊C414yes—
268C4×Dic61—24no—
269C4×Dic61—42no—
270C4×Dic61—42no—
271C4×Dic61—42no—
272C4×Dic61C22×C412yes—
273C4×Dic61C2×D412yes—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C8×D61—44no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—22no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61C2×C22⋊C412yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—22no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61C2×C22⋊C412yes—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61—41no—
313D4×C61—41no—
314D4×C61—84no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61C2×C22⋊C412yes—
331C2×C4×C61C23×C411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C2×#4111yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C2×C4×C61H(5,𝔽2)11yescharacteristic
337C22⋊D61—28no—
338C22⋊D61—48no—
339C22⋊D61—48no—
340C22⋊D61—48no—
341C22⋊D61—84no—
342C2×Dic61—22no—
343C2×Dic61—21no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—22no—
350C2×Dic61—48no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61C2×C22⋊C412yes—
357C2×Dic61C2×C22⋊C412yes—
358C2×Dic61C2×C22⋊C412yes—
359C2×Dic61#13512yes—
360C2×Dic61#13512yes—
361D244—22no—
362D244—22no—
363D244—41no—
364D244—41no—
365D244—84no—
366C4×D61—22no—
367C4×D61—22no—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—48no—
371Dic122—22no—
372Dic122—22no—
373Dic122—22no—
374Dic122C4×D414yes—
375C8×C61—22no—
376C8×C61—41no—
377#92418—41no—
378#92418—41no—
379#22418—611nomaximal, Sylow
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—81no—
391C22×C61—81no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61C22×C22⋊C411yescharacteristic
395C22×C61D4211yescharacteristic
396C22×C61#54611yescharacteristic
397C22×C61C2×#13511yescharacteristic
398C22×C61C2×#13511yescharacteristic
399C22×C61#57611yescharacteristic
400C22×C61#57711yescharacteristic
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—81no—
412C2×D61—81no—
413C2×D61—81no—
414C2×D61—81no—
415C4×C61—22no—
416C4×C61—42no—
417C4×C61—81no—
418C4×C61—81no—
419C4×C61C2×C4×D411yescharacteristic
420C4×C61#51811yescharacteristic
421C4×C61D4211yescharacteristic
422C4×C61#54611yescharacteristic
423Dic61—24no—
424Dic61—22no—
425Dic61—22no—
426Dic61—42no—
427Dic61—81no—
428Dic61#41614yescomplemented
429C2×#550—611no—
430C2×C8×D4—611no—
431C2×#416—611no—
432C2×#416—611no—
433#2354—611no—
434#1982—611no—
435#1957—611no—
436#1893—611no—
437#1893D6111yescharacteristic, complemented
438#1875—611no—
439#1875—611no—
440#1803—611no—
441#1788—611no—
442#1788—611no—
443C4×#103—611no—
444C2×C61—42no—
445C2×C61—82no—
446C2×C61D4×C22⋊C411yescharacteristic
447C2×C61C2×#41611yescharacteristic
448C2×C61#289711yescharacteristic
449C2×C61#328411yescharacteristic
450C2×C61#328711yescharacteristic
451C2×C61#330411yescharacteristic
452C2×C61#330511yescharacteristic
453D61—42no—
454D61—82no—
455C22×#41—611no—
456C22×#41—611no—
457C23×C8—611no—
458C23×C8C2×D6111yescharacteristic
459#550—618no—
460#550—1224no—
461C2×#127—611no—
462C2×#127—1221no—
463C2×#121—611no—
464C2×#121—1221no—
465C2×#121—1221no—
466C2×#121C2×D6111yescharacteristic
467C2×C4×Q8—611no—
468C2×C4×D4—611no—
469C2×C4×D4—1221no—
470C2×#117—611no—
471C2×#117—611no—
472C8×D4—1224no—
473C2×C4⋊C8—611no—
474#416—1224no—
475#416—1224no—
476C2×#103—611no—
477C2×#103—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#102—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×#102C2×D6111yescharacteristic
487C2×#102C2×D6111yescharacteristic
488C2×C22⋊C8—611no—
489C2×C22⋊C8—611no—
490C2×C4×C8—611no—
491#390—1221no—
492#388—1221no—
493#388—1221no—
494#384—611no—
495#380—611no—
496#380C2×D6111yescharacteristic
497C4×C4⋊C4—611no—
498C4×C4⋊C4—1221no—
499#340—611no—
500#340—611no—
501#340C2×D6111yescharacteristic
502#340C2×D6111yescharacteristic
503C61#2241811yescharacteristic, complemented, Sylow
504C2×#41—614no—
505C2×#41—614no—
506C2×#41—1222no—
507C2×#41—1222no—
508C2×#41—1222no—
509C2×#41—1222no—
510C2×#41—1222no—
511C2×#41—1222no—
512C2×#41—2441no—
513C2×#41—2441no—
514C2×#41—2441no—
515C2×#41—2441no—
516C22×Q8—611no—
517C22×D4—21no—
518C22×D4—611no—
519C22×D4—611no—
520C22×D4—1221no—
521C22×D4—1221no—
522C22×D4—1221no—
523C22×D4—1221no—
524C22×D4—1221no—
525C22×D4C22×D6111yescharacteristic
526C23×C4—611no—
527C23×C4—1221no—
528C23×C4—1221no—
529C23×C4C22×D6111yescharacteristic
530C22×C8—22no—
531C22×C8—22no—
532C22×C8—41no—
533C22×C8—611no—
534C22×C8—611no—
535C22×C8—1222no—
536C22×C8—1222no—
537C22×C8—2441no—
538C22×C8C22×D6111yescharacteristic
539C22×C8C22×D6111yescharacteristic
540#127—614no—
541#127—1222no—
542#127—1228no—
543#121—22no—
544#121—614no—
545#121—1228no—
546#121—1228no—
547#121—1222no—
548#121C4×D6114yes—
549C4×Q8—614no—
550C4×Q8—1222no—
551C4×D4—614no—
552C4×D4—614no—
553C4×D4—1228no—
554#117—1222no—
555#117—1222no—
556#117—2441no—
557#117—2441no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4C22×D6111yescharacteristic
565C2×C4⋊C4C22×D6111yescharacteristic
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—611no—
570C2×C22⋊C4—611no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C42—611no—
576C2×C42—1221no—
577C2×C42—1221no—
578C2×C42—1221no—
579C2×C42—1221no—
580C4⋊C8—1222no—
581#103—614no—
582#103—1222no—
583#103—1222no—
584#103—1222no—
585#102—22no—
586#102—41no—
587#102—1222no—
588#102—1222no—
589#102—1222no—
590#102—2441no—
591#102—2441no—
592#102—2441no—
593C22⋊C8—1222no—
594C22⋊C8—1222no—
595C4×C8—1222no—
596#95—21no—
597#95—1221no—
598#95—1221no—
599C24—21no—
600C24—611no—
601C24—1221no—
602C24D4×D6111yescharacteristic
603#41—1228no—
604#41—1228no—
605#41—2444no—
606#41—2444no—
607#41—2444no—
608#41—2444no—
609#41—2444no—
610#41—2444no—
611C2×Q8—612no—
612C2×Q8—612no—
613C2×Q8—612no—
614C2×Q8—1221no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—81no—
624C2×D4—81no—
625C2×D4—614no—
626C2×D4—612no—
627C2×D4—1224no—
628C2×D4—1222no—
629C2×D4—1222no—
630C2×D4—1224no—
631C2×D4—1224no—
632C2×D4—1224no—
633C2×D4—1224no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—4881no—
640C2×D4—4881no—
641C2×D4—4881no—
642C2×D4—4881no—
643C2×D4—2442no—
644C2×D4—2442no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4C2×C4×D6112yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—612no—
661C22×C4—612no—
662C22×C4—1224no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1224no—
670C22×C4—1221no—
671C22×C4—2442no—
672C22×C4—2442no—
673C22×C4—2442no—
674C22×C4—2442no—
675C22×C4C2×C4×D6112yes—
676C22×C4D4×D6112yes—
677C22×C4D4×D6111yescharacteristic
678C22×C4C23×D6111yescharacteristic
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—44no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—2444no—
692C2×C8D4×D6112yes—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—614no—
699C4⋊C4—612no—
700C4⋊C4—1224no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—4881no—
705C4⋊C4—2442no—
706C4⋊C4C2×C4×D6112yes—
707C22⋊C4—24no—
708C22⋊C4—81no—
709C22⋊C4—614no—
710C22⋊C4—614no—
711C22⋊C4—1224no—
712C22⋊C4—4881no—
713C22⋊C4—2442no—
714C22⋊C4—2442no—
715C42—612no—
716C42—612no—
717C42—1224no—
718C42—2442no—
719C42—2442no—
720C42—2442no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—612no—
735C23—1221no—
736C23—1221no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—1222no—
742C23—2441no—
743C23—2441no—
744C23—2441no—
745C23—2441no—
746C23—2441no—
747C23—2441no—
748C23C22⋊C4×D6112yes—
749C23C2×D4×D6111yescharacteristic
750Q8—614no—
751Q8—1222no—
752Q8—1222no—
753Q8—1222no—
754D4—22no—
755D4—22no—
756D4—41no—
757D4—41no—
758D4—84no—
759D4—1228no—
760D4—1222no—
761D4—1222no—
762D4—4884no—
763D4—4884no—
764D4—2448no—
765D4—2448no—
766D4—2448no—
767D4—2441no—
768D4—2441no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—612no—
785C2×C4—612no—
786C2×C4—612no—
787C2×C4—612no—
788C2×C4—612no—
789C2×C4—1222no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1222no—
794C2×C4—1221no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—2448no—
802C2×C4—2448no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4C22⋊C4×D6112yes—
809C2×C4C22×C4×D6111yescharacteristic
810C2×C4C2×D4×D6111yescharacteristic
811C2×C4C2×D4×D6111yescharacteristic
812C2×C4#41×D6111yescharacteristic
813C2×C4#1451982211yescharacteristic
814C2×C4#1451982311yescharacteristic
815C8—22no—
816C8—41no—
817C8—2441no—
818C8—2441no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—1222no—
834C22—1222no—
835C22—1222no—
836C22—4881no—
837C22—4881no—
838C22—4881no—
839C22—4881no—
840C22—2442no—
841C22—2442no—
842C22—2442no—
843C22—2441no—
844C22—2441no—
845C22—2441no—
846C22—2441no—
847C22C2×C22⋊C4×D6111yescharacteristic
848C22#1684039611yescharacteristic
849C22#1684040111yescharacteristic
850C22#135×D6111yescharacteristic
851C22#135×D6111yescharacteristic
852C22#1684056311yescharacteristic
853C22#1684056811yescharacteristic
854C4—22no—
855C4—42no—
856C4—81no—
857C4—81no—
858C4—614no—
859C4—1222no—
860C4—1222no—
861C4—1224no—
862C4—4881no—
863C4—2442no—
864C4C4×D4×D6111yescharacteristic
865C4#1684023411yescharacteristic
866C4#1684039411yescharacteristic
867C4#1684040411yescharacteristic
868C2—42no—
869C2—82no—
870C2—4882no—
871C2—2442no—
872C2#2144863711yescharacteristic
873C2#416×D6111yescharacteristic
874C2#2145434011yescharacteristic
875C2#2145754611yescharacteristic
876C2#2145757611yescharacteristic
877C2#2145775311yescharacteristic
878C2#2145776411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1893C2
socleC23×C61C22×D4
prime radicalC2×#16840430C2
cosocleC22×C4×C61C24
hypercenter#1893D61
hypocenterC61#22418
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D61C2semidirect
3. C2×#16839759C2semidirect
4. C2×#16839755C2semidirect
5. #21448763C2semidirect
6. #21446744C2semidirect
7. #21446623C2semidirect
8. #21446246C2semidirect
9. #21446142C2semidirect
10. #21446140C2semidirect
11. #21445823C2semidirect
12. #21445757C2semidirect
13. #21445756C2semidirect
14. #21445638C2semidirect
15. C61×#1893C2semidirect
20. #16840430C4semidirect
127. #14519702D4semidirect
428. Dic61#416semidirect
437. #1893D61semidirect
503. C61#22418semidirect

Maximal subgroups

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

subgroupindex
C2×#168404302
C2×C8×C22⋊D612
C2×#168397592
C2×#168397552
#214487632
#214467442
#214466232
#214462462
#214461422
#214461402
#214458232
#214457572
#214457562
#214456382
C61×#18932
#2241861