Finite Group Databasebeta

← #29684105

Subgroups — #29684105

Order 15616.

1534 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840332C211yesmaximal, characteristic
2C2×#16839787C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic
4C2×#16839769C211yesmaximal, characteristic, complemented
5C2×#16839755C211yesmaximal, characteristic
6C2×#103×D61C211yesmaximal, characteristic, complemented
7#21448173C211yesmaximal, characteristic, complemented
8#21446752C211yesmaximal, characteristic, complemented
9#21446750C211yesmaximal, characteristic, complemented
10#21446750C211yesmaximal, characteristic, complemented
11#21446742C211yesmaximal, characteristic, complemented
12#21446741C211yesmaximal, characteristic, complemented
13#21446740C211yesmaximal, characteristic, complemented
14#21446740C211yesmaximal, characteristic, complemented
15C61×#1983C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840332—24no—
21#16840332C418yescomplemented
22C2×#14519777C2211yescharacteristic
23C2×#14519775C2211yescharacteristic
24C2×#14519764C2211yescharacteristic
25C2×#14519759—21no—
26C2×#14519759—21no—
27C2×#14519754—21no—
28C2×#14519754—21no—
29C2×#14519735C2211yescharacteristic
30C2×#14519734C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839787—24no—
33C2×C4⋊#92418C2211yescharacteristic
34C2×#14519706C2211yescharacteristic
35C2×#14519706C2211yescharacteristic
36#16839769—24no—
37#16839760—24no—
38#16839755—24no—
39C2×#14519702C2211yescharacteristic
40C2×#14519702C2211yescharacteristic
41C2×#14519702C2211yescharacteristic
42C2×#14519702C2211yescharacteristic
43C2×#14519701C2211yescharacteristic
44C2×#14519701C2211yescharacteristic
45C2×#14519700C2211yescharacteristic
46C2×#14519700C2211yescharacteristic
47C2×#14519700C2211yescharacteristic
48C2×#14519700C2211yescharacteristic
49#103×D61—24no—
50C2×#14519698C2211yescharacteristic
51C2×#14519698C2211yescharacteristic
52C4⋊C4×Dic61C2211yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic
54C4×#11758196—21no—
55C4×C4⋊Dic61C2211yescharacteristic
56#16839613—21no—
57C4×#11758198—21no—
58#16839609—21no—
59C2×#124×C61C2211yescharacteristic
60C2×C4⋊C8×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C2×#102×C61C2211yescharacteristic
64C2×#102×C61C2211yescharacteristic
65C4×C4⋊C4×C61C2211yescharacteristic
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224—22no—
70C2×#11758224—22no—
71C2×#11758224C2×C414yes—
72C22×Dic122—21no—
73C22×Dic122C2311yescharacteristic
74C22×Dic122C2311yescharacteristic
75C2×Q8×D61—22no—
76C2×Q8×D61—22no—
77C2×Q8×D61—22no—
78C2×Q8×D61—22no—
79C2×Q8×D61—22no—
80C2×Q8×D61C2×C414yes—
81C22×C22⋊D61—21no—
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C2×#11758189—22no—
87C2×#11758189—22no—
88C2×#11758189—22no—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C2×C8×D61—22no—
92C2×C8×D61—22no—
93C2×C8×D61—22no—
94#14519777—22no—
95#14519777C2×C414yescomplemented
96#14519775—22no—
97#14519775C2×C414yescomplemented
98#14519764—22no—
99#14519764C2×C414yescomplemented
100#14519759—28no—
101#14519759—28no—
102#14519754—28no—
103#14519754—28no—
104#14519735—22no—
105#14519735D414yes—
106#14519734C2×C414yes—
107#14519734D414yes—
108C2×C4⋊Dic61—21no—
109C2×C4⋊Dic61—21no—
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×#11758196—21no—
113C2×#11758196—21no—
114C2×#11758196—21no—
115C2×#11758196D411yescharacteristic
116C2×#11758196D411yescharacteristic
117C4⋊C4×D61—22no—
118C4⋊C4×D61D414yes—
119C2×C22⋊Dic61—21no—
120C2×C22⋊Dic61—21no—
121C2×#11758198—21no—
122C2×#11758198D411yescharacteristic
123C2×#11758198D411yescharacteristic
124C2×C4×Dic61—21no—
125C2×C4×Dic61—21no—
126C2×C4×Dic61—21no—
127C2×C4×Dic61—21no—
128C2×C4×Dic61C2311yescharacteristic
129C4⋊#92418—22no—
130#14519706—22no—
131#14519706—22no—
132#14519702—22no—
133#14519702—22no—
134#14519702—22no—
135#14519702—22no—
136#14519701—22no—
137#14519701—22no—
138#14519700—22no—
139#14519700—22no—
140#14519700—22no—
141#14519700—22no—
142#14519698—22no—
143#14519698—22no—
144#14519684—21no—
145#14519684—21no—
146#14519684—21no—
147C22×Q8×C61C2311yescharacteristic
148C22×D4×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151#124×C61—22no—
152#124×C61C2×C414yescomplemented
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C22⋊C4×C61—21no—
156C2×C22⋊C4×C61—21no—
157C2×C42×C61—21no—
158C2×C42×C61C2311yescharacteristic
159C4⋊C8×C61—22no—
160#103×C61—22no—
161#103×C61—22no—
162#102×C61—22no—
163#102×C61—22no—
164#95×C61—21no—
165C24×C61—21no—
166C23×D61C2×D411yescharacteristic
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61C22×C412yes—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61C22×C412yes—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2411yescharacteristic
185C2×C22⋊D61—24no—
186C2×C22⋊D61—42no—
187C2×C22⋊D61—42no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—24no—
193C22×Dic61—42no—
194C22×Dic61—42no—
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198Q8×D61—28no—
199Q8×D61—28no—
200Q8×D61—44no—
201Q8×D61—44no—
202#11758224—28no—
203#11758224—28no—
204#11758224—44no—
205#11758224—44no—
206C2×C4×D61—24no—
207C2×C4×D61—24no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—81no—
211C2×C4×D61—81no—
212C2×C4×D61C22×C412yes—
213C2×C4×D61C2×D412yes—
214C2×C4×D61C2×D412yes—
215C2×C4×D61C2×D412yes—
216C2×C4×D61#4112yes—
217C2×C4×D61#4112yes—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—24no—
229C2×Dic122—42no—
230C2×Dic122—42no—
231C2×Dic122C22×C412yes—
232C2×Dic122C22×C412yes—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61C2×D412yes—
242C4⋊C4×C61C2×D412yes—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C42×C61—81no—
246C42×C61C22×C412yes—
247C42×C61C2×D412yes—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250#11758198—24no—
251#11758198C22⋊C414yes—
252#11758198C22⋊C414yes—
253C4⋊Dic61—24no—
254C4⋊Dic61—24no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61C2×D412yes—
258C4⋊Dic61C2×D412yes—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196C22⋊C414yes—
263#11758196C22⋊C414yes—
264C4×Dic61—24no—
265C4×Dic61—81no—
266C4×Dic61—81no—
267C4×Dic61—81no—
268C4×Dic61C22×C412yes—
269C4×Dic61C2×D412yes—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276#11758189—44no—
277C8×D61—44no—
278C23×C61—22no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61C22×D411yescharacteristic
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61C2×C22⋊C412yes—
291C22×D61#12112yes—
292C22×D61#12112yes—
293Q8×C61—22no—
294Q8×C61—22no—
295Q8×C61—41no—
296Q8×C61—41no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61—41no—
300D4×C61—41no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61C2×C22⋊C412yes—
315C2×C4×C61C2×C22⋊C412yes—
316C2×C4×C61C23×C411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61C2×#4111yescharacteristic
322C22⋊D61—48no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—48no—
340C2×Dic61C2×C22⋊C412yes—
341C2×Dic61C2×C22⋊C412yes—
342C2×Dic61C2×C22⋊C412yes—
343C2×Dic61#12112yes—
344C2×Dic61#12112yes—
345C4×D61—48no—
346C4×D61—84no—
347C4×D61C4×D414yes—
348C4×D61C4×D414yes—
349C4×D61#12414yes—
350C4×D61#12714yes—
351Dic122—22no—
352Dic122—22no—
353Dic122—22no—
354Dic122—22no—
355Dic122—41no—
356Dic122—41no—
357Dic122—41no—
358Dic122—41no—
359Dic122—48no—
360C8×C61—41no—
361C8×C61—41no—
362#92418—41no—
363#92418—41no—
364#21262—611nomaximal, Sylow
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61—81no—
371C22×C61—81no—
372C22×C61C22×C22⋊C411yescharacteristic
373C22×C61C2×#12111yescharacteristic
374C22×C61C2×#12111yescharacteristic
375C22×C61#57711yescharacteristic
376C22×C61#57711yescharacteristic
377C22×C61#57811yescharacteristic
378C22×C61#57811yescharacteristic
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61#39014yes—
386C4×C61—22no—
387C4×C61—22no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61C2×C4×D411yescharacteristic
392C4×C61C2×C4×D411yescharacteristic
393C4×C61C2×#12411yescharacteristic
394C4×C61C2×#12711yescharacteristic
395Dic61—22no—
396Dic61—22no—
397Dic61—42no—
398Dic61—42no—
399Dic61—42no—
400Dic61—42no—
401Dic61#39014yes—
402C2×#536—611no—
403C2×#424—611no—
404C2×#417—611no—
405C2×#419—611no—
406C2×#416—611no—
407C22×#103—611no—
408#2274—611no—
409#1983—611no—
410#1983—611no—
411#1983—611no—
412#1983D6111yescharacteristic, complemented
413#1981—611no—
414#1981—611no—
415#1981—611no—
416#1981—611no—
417C2×C61—82no—
418C2×C61C2×#39011yescharacteristic
419C2×C61#289811yescharacteristic
420C2×C61#289811yescharacteristic
421C2×C61#304211yescharacteristic
422C2×C61#304411yescharacteristic
423C2×C61#304611yescharacteristic
424C2×C61#304611yescharacteristic
425D61—24no—
426C22×#41—611no—
427C23×Q8—611no—
428C22×M16—611no—
429C23×C8—611no—
430#536—618no—
431#536—1224no—
432C2×C4⋊Q8—611no—
433C2×C4⋊Q8—611no—
434C2×#124—611no—
435C2×#124C2×D6111yescharacteristic
436C2×#123—1221no—
437C2×#123—1221no—
438C2×C22⋊Q8—1221no—
439C2×C22⋊Q8—1221no—
440C2×#117—611no—
441C2×#117—611no—
442C22×C4⋊C4—611no—
443#424—1224no—
444C2×C4⋊C8—611no—
445C2×C4⋊C8—611no—
446C2×C4⋊C8—611no—
447C2×C4⋊C8C2×D6111yescharacteristic
448#419—1224no—
449#417—1224no—
450#416—1224no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#103—611no—
455C2×#103—611no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—1224no—
462C2×#103C2×D6111yescharacteristic
463C2×#103C2×D6111yescharacteristic
464C2×#102—611no—
465C2×#102—611no—
466C2×#102C2×D6111yescharacteristic
467C2×#102C2×D6111yescharacteristic
468C4×C4⋊C4—611no—
469C4×C4⋊C4—611no—
470C4×C4⋊C4—611no—
471C4×C4⋊C4—1221no—
472C4×C4⋊C4—1221no—
473C4×C4⋊C4C2×D6111yescharacteristic
474C4×C22⋊C4—1221no—
475C4×C22⋊C4—1221no—
476C61#2126211yescharacteristic, complemented, Sylow
477C2×#41—614no—
478C2×#41—1222no—
479C2×#41—1222no—
480C2×#41—1222no—
481C2×#41—1222no—
482C2×#41—1222no—
483C22×Q8—614no—
484C22×Q8—611no—
485C22×Q8—611no—
486C22×Q8—1221no—
487C22×Q8—1222no—
488C22×Q8—1222no—
489C22×Q8—1222no—
490C22×Q8—1222no—
491C22×Q8—1222no—
492C22×Q8C22×D6111yescharacteristic
493C22×D4—1221no—
494C22×D4C22×D6111yescharacteristic
495C23×C4—611no—
496C23×C4—1221no—
497C23×C4—1221no—
498C23×C4—1221no—
499C2×M16—1222no—
500C2×M16—1222no—
501C2×M16—1222no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—1222no—
505C22×C8—1222no—
506C22×C8—1222no—
507C22×C8C22×D6111yescharacteristic
508C22×C8C22×D6111yescharacteristic
509C4⋊Q8—614no—
510C4⋊Q8—614no—
511C4⋊Q8—1222no—
512C4⋊Q8—1222no—
513#124—22no—
514#124—614no—
515#124—1222no—
516#124C4×D6114yescomplemented
517#123—1228no—
518#123—1228no—
519C22⋊Q8—1228no—
520C22⋊Q8—1228no—
521#117—614no—
522#117—614no—
523#117—614no—
524#117—1222no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—614no—
530C2×C4⋊C4—1222no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C4⋊C4C22×D6111yescharacteristic
537C2×C4⋊C4C22×D6111yescharacteristic
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—611no—
541C2×C22⋊C4—611no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C42—21no—
546C2×C42—611no—
547C2×C42—1221no—
548C2×C42—1221no—
549C2×C42—1221no—
550C2×C42—1221no—
551C2×C42C22×D6111yescharacteristic
552C4⋊C8—22no—
553C4⋊C8—1222no—
554C4⋊C8—1222no—
555C4⋊C8—1222no—
556#103—22no—
557#103—22no—
558#103—1222no—
559#103—1222no—
560#103—1222no—
561#103—1222no—
562#103—1222no—
563#103—1222no—
564#103—1222no—
565#103—1222no—
566#103—1222no—
567#103—1222no—
568#102—22no—
569#102—22no—
570#102—1222no—
571#102—1222no—
572#95—21no—
573#95—1221no—
574#95—1221no—
575#95—1221no—
576C24—21no—
577C24—611no—
578#41—1228no—
579#41—1228no—
580#41—2444no—
581#41—2444no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—612no—
588C2×Q8—612no—
589C2×Q8—1224no—
590C2×Q8—1228no—
591C2×Q8—1228no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8—1221no—
600C2×Q8—1221no—
601C2×Q8—1221no—
602C2×Q8—2442no—
603C2×Q8—2442no—
604C2×Q8—2444no—
605C2×Q8—2444no—
606C2×Q8C2×C4×D6112yes—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—1224no—
613C2×D4—2442no—
614C2×D4—2442no—
615C2×D4C2×C4×D6112yes—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—611no—
620C22×C4—612no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—612no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—1224no—
629C22×C4—1224no—
630C22×C4—1224no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—4881no—
636C22×C4—4881no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4D4×D6111yescharacteristic
642C22×C4D4×D6111yescharacteristic
643C22×C4C23×D6111yescharacteristic
644M16—2444no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—2444no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—614no—
661C4⋊C4—614no—
662C4⋊C4—612no—
663C4⋊C4—612no—
664C4⋊C4—1224no—
665C4⋊C4—1224no—
666C4⋊C4—1224no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1224no—
670C4⋊C4—1224no—
671C4⋊C4D4×D6112yes—
672C4⋊C4D4×D6112yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—614no—
676C22⋊C4—614no—
677C22⋊C4—1224no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C42—81no—
681C42—612no—
682C42—612no—
683C42—1224no—
684C42—4881no—
685C42—4881no—
686C42—4881no—
687C42C2×C4×D6112yes—
688C42D4×D6112yes—
689C23—22no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—612no—
697C23—612no—
698C23—612no—
699C23—1221no—
700C23—1221no—
701C23—1221no—
702C23—1221no—
703C23C2×D4×D6111yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—41no—
707Q8—41no—
708Q8—1222no—
709Q8—1222no—
710Q8—1222no—
711Q8—1222no—
712Q8—2448no—
713Q8—2441no—
714Q8—2441no—
715Q8—2441no—
716Q8—2441no—
717D4—22no—
718D4—22no—
719D4—41no—
720D4—41no—
721D4—2448no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—612no—
736C2×C4—612no—
737C2×C4—612no—
738C2×C4—614no—
739C2×C4—614no—
740C2×C4—614no—
741C2×C4—614no—
742C2×C4—612no—
743C2×C4—612no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—4884no—
753C2×C4—2448no—
754C2×C4—2448no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4C22⋊C4×D6112yes—
764C2×C4C22⋊C4×D6112yes—
765C2×C4C22×C4×D6111yescharacteristic
766C2×C4C2×D4×D6111yescharacteristic
767C2×C4C2×D4×D6111yescharacteristic
768C2×C4C2×D4×D6111yescharacteristic
769C2×C4#41×D6111yescharacteristic
770C2×C4#41×D6111yescharacteristic
771C8—41no—
772C8—41no—
773C8—2441no—
774C8—2441no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—614no—
783C22—1222no—
784C22—1222no—
785C22—1222no—
786C22—1222no—
787C22—1222no—
788C22—1222no—
789C22C2×C22⋊C4×D6111yescharacteristic
790C22#121×D6111yescharacteristic
791C22#121×D6111yescharacteristic
792C22#1684056911yescharacteristic
793C22#1684057211yescharacteristic
794C22#1684057611yescharacteristic
795C22#1684057811yescharacteristic
796C4—22no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—614no—
802C4—1222no—
803C4—1222no—
804C4—2442no—
805C4—2442no—
806C4—2442no—
807C4—2442no—
808C4C4×D4×D6111yescharacteristic
809C4C4×D4×D6111yescharacteristic
810C4#124×D6111yescharacteristic
811C4#127×D6111yescharacteristic
812C2—82no—
813C2—1224no—
814C2#390×D6111yescharacteristic
815C2#2145434811yescharacteristic
816C2#2145435011yescharacteristic
817C2#2145532911yescharacteristic
818C2#2145534711yescharacteristic
819C2#2145537011yescharacteristic
820C2#2145537211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1983C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
cosocleC22×C4×C61C24
hypercenter#1983D61
hypocenterC61#21262
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#16839787C2semidirect
4. C2×#16839769C2semidirect
6. C2×#103×D61C2semidirect
7. #21448173C2semidirect
8. #21446752C2semidirect
9. #21446750C2semidirect
10. #21446750C2semidirect
11. #21446742C2semidirect
12. #21446741C2semidirect
13. #21446740C2semidirect
14. #21446740C2semidirect
15. C61×#1983C2semidirect
21. #16840332C4semidirect
95. #14519777C2×C4semidirect
97. #14519775C2×C4semidirect
99. #14519764C2×C4semidirect
152. #124×C61C2×C4semidirect
412. #1983D61semidirect
476. C61#21262semidirect
516. #124C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403322
C2×#168397872
C2×#168397602
C2×#168397692
C2×#168397552
C2×#103×D612
#214481732
#214467522
#214467502
#214467422
#214467412
#214467402
C61×#19832
#2126261