Finite Group Databasebeta

← #29695879

Subgroups — #29695879

Order 15616.

1450 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519798C211yesmaximal, characteristic
2C2×C4×#11758202C211yesmaximal, characteristic, complemented
3C2×#16839854C211yesmaximal, characteristic, complemented
4#21448658C211yesmaximal, characteristic, complemented
5#21448657C211yesmaximal, characteristic, complemented
6#21446684C211yesmaximal, characteristic, complemented
7#21446682C211yesmaximal, characteristic, complemented
8#21446176C211yesmaximal, characteristic, complemented
9#21446175C211yesmaximal, characteristic, complemented
10#21446173C211yesmaximal, characteristic, complemented
11#21445847C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#21445589C211yesmaximal, characteristic, complemented
15C61×#1880C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758224C2211yescharacteristic
18C2×#14519798—24no—
19C2×#14519798—24no—
20C2×#14519798C418yescomplemented
21C22×#11758202C2211yescharacteristic
22C22×#11758190C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C22×C8×D61C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×#14519742C2211yescharacteristic
28C4×#11758202—24no—
29#16839854—24no—
30C2×#14519710C2211yescharacteristic
31C2×#14519710C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×C4×#92418C2211yescharacteristic
40C2×C8×Dic61C2211yescharacteristic
41#16839665C2211yescharacteristic
42#16839664—21no—
43#16839664C2211yescharacteristic
44#16839663—21no—
45#16839663C2211yescharacteristic
46#16839662—21no—
47#16839662—21no—
48#16839620—21no—
49#16839619—21no—
50#16839619C2211yescharacteristic
51#16839619C2211yescharacteristic
52C22⋊C4×Dic61—21no—
53C4×#11758198—21no—
54C4×#11758198C2211yescharacteristic
55#16839525C2211yescharacteristic
56#16839516C2211yescharacteristic
57C22×SD16×C61C2211yescharacteristic
58C2×C4×Q8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#390C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#336C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—41no—
68C2×#11758226—41no—
69C2×#11758226C2×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—
80C23×Dic61—21no—
81C22×C4×D61—21no—
82C22×C4×D61C2311yescharacteristic
83#14519798—232no—
84C2×#11758202C2×C414yes—
85C2×#11758202D414yes—
86C2×#11758202D414yes—
87C2×#11758190—22no—
88C2×#11758190—22no—
89C2×#11758190C2×C414yes—
90C2×#11758199—22no—
91C2×#11758199—22no—
92C2×#11758199C2×C414yes—
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95C2×C8×D61—22no—
96C2×C8×D61—22no—
97C2×C8×D61C2×C414yes—
98Q8×Dic61—22no—
99Q8×Dic61—41no—
100C4×Dic122—22no—
101C4×Dic122—41no—
102#14519742—22no—
103#14519742—41no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198D411yescharacteristic
118C2×#11758198D411yescharacteristic
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61C2311yescharacteristic
123#14519710—22no—
124#14519710—22no—
125#14519702—22no—
126#14519701—22no—
127#14519700—22no—
128#14519699—41no—
129#14519698—41no—
130#14519697—41no—
131#14519689—22no—
132C4×#92418—22no—
133C8×Dic61—22no—
134#14519684—21no—
135#14519684—21no—
136#14519684D411yescharacteristic
137#14519684D411yescharacteristic
138C22×Q8×C61C2311yescharacteristic
139C22×D4×C61C2311yescharacteristic
140C2×SD16×C61—22no—
141C2×SD16×C61—22no—
142C2×SD16×C61C2×C414yes—
143C22×C8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145C4×Q8×C61—22no—
146C4×Q8×C61—41no—
147C2×C4⋊C4×C61—21no—
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C22⋊C4×C61—21no—
151C2×C22⋊C4×C61—21no—
152C2×C42×C61—21no—
153C2×C42×C61C2311yescharacteristic
154#103×C61—22no—
155#102×C61—41no—
156C24×C61—21no—
157C23×D61—21no—
158C23×D61C2×D411yescharacteristic
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61C22×C412yes—
163C2×Q8×C61C2×D412yes—
164C2×Q8×C61C2×D412yes—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61C22×C412yes—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2411yescharacteristic
177C2×C22⋊D61—24no—
178C2×C22⋊D61—42no—
179C2×C22⋊D61—42no—
180C22×Dic61—21no—
181C22×Dic61—24no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—42no—
185C22×Dic61—42no—
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189#11758226—28no—
190#11758226—44no—
191#11758226—44no—
192#11758226—44no—
193#11758224—28no—
194#11758224—44no—
195#11758224—44no—
196#11758224—44no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—24no—
202C2×D244—21no—
203C2×D244—42no—
204C2×D244—42no—
205C2×D244C22×C412yes—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—24no—
211C2×C4×D61—42no—
212C2×C4×D61—42no—
213C2×C4×D61C22×C412yes—
214C2×C4×D61#4112yes—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122C22×C412yes—
219C2×Dic122C2×D412yes—
220C2×Dic122C2×D412yes—
221SD16×C61—28no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61C22×C412yes—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—42no—
233C22⋊C4×C61—42no—
234C22⋊C4×C61—81no—
235C42×C61—21no—
236C42×C61—21no—
237C42×C61—42no—
238C22⋊Dic61—42no—
239C22⋊Dic61—81no—
240#11758202C22⋊C4116yescomplemented
241#11758199—28no—
242#11758198—22no—
243#11758198—22no—
244#11758198—42no—
245#11758198—42no—
246#11758198—81no—
247#11758198—81no—
248#11758198—81no—
249#11758198—81no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—42no—
255#11758196—42no—
256#11758196—42no—
257C4×Dic61—21no—
258C4×Dic61—21no—
259C4×Dic61—42no—
260C4×Dic61—42no—
261C4×Dic61—42no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418C22×C412yes—
266C2×#92418C2×D412yes—
267C2×#92418C2×D412yes—
268#11758190—28no—
269C8×D61—28no—
270C23×C61—22no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61C22×D411yescharacteristic
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—22no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61C4×D412yes—
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61—22no—
295Q8×C61C2×C22⋊C414yes—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—41no—
299D4×C61—41no—
300C2×C4×C61—22no—
301C2×C4×C61—21no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
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×C61#13512yescomplemented
315C2×C4×C61C23×C411yescharacteristic
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61H(5,𝔽2)11yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C22⋊D61—48no—
322C2×Dic61—22no—
323C2×Dic61—21no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—48no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61C4×D412yes—
340C2×Dic61#13512yescomplemented
341D244—22no—
342D244—22no—
343D244—48no—
344D244—41no—
345D244—41no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—48no—
351Dic122—22no—
352Dic122—22no—
353Dic122—22no—
354Dic122C2×C22⋊C414yes—
355C8×C61—22no—
356C8×C61—41no—
357#92418—41no—
358#92418C2×C22⋊C414yes—
359#22451—611nomaximal, Sylow
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61C2×C4×D411yescharacteristic
368C22×C61D4211yescharacteristic
369C22×C61D4211yescharacteristic
370C22×C61C2×#13511yescharacteristic
371C22×C61C2×#13511yescharacteristic
372C22×C61#57611yescharacteristic
373C22×C61#57811yescharacteristic
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—81no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C4×C61—24no—
389C4×C61—22no—
390C4×C61—41no—
391C4×C61—81no—
392C4×C61—81no—
393C4×C61C22×C22⋊C411yescharacteristic
394C4×C61#51811yescharacteristic
395C4×C61#54611yescharacteristic
396C4×C61#54611yescharacteristic
397Dic61—24no—
398Dic61—22no—
399Dic61—22no—
400Dic61—41no—
401Dic61—81no—
402Dic61—81no—
403C22×#135—611no—
404C2×C4×Q16—611no—
405C2×C4×Q16—611no—
406#2341—611no—
407#2341—611no—
408#1970—611no—
409#1970—611no—
410#1880—611no—
411#1880—611no—
412#1880—611no—
413#1880D6111yescharacteristic, complemented
414#1808—611no—
415#1788—611no—
416#1788—611no—
417C8×C22⋊C4—611no—
418C2×C61—82no—
419C2×C61D4×C22⋊C411yescharacteristic
420C2×C61C4×#13511yescharacteristic
421C2×C61#295111yescharacteristic
422C2×C61#328511yescharacteristic
423C2×C61#328511yescharacteristic
424C2×C61#328711yescharacteristic
425C2×C61#328711yescharacteristic
426D61—42no—
427D61—82no—
428C22×#41—611no—
429C22×#41—611no—
430C2×#135—618no—
431C2×#135—1224no—
432C2×#135—1224no—
433C22×Q16—611no—
434C22×SD16—611no—
435C22×SD16C2×D6111yescharacteristic
436C22×D8—611no—
437C23×C8—611no—
438C2×C4×Q8—611no—
439C2×C4×Q8—611no—
440C2×C4×Q8—611no—
441C2×C4×Q8C2×D6111yescharacteristic
442C4×Q16—1224no—
443C4×Q16—1224no—
444C2×#107—611no—
445C2×#107—611no—
446C2×#103—611no—
447C2×#103—611no—
448C2×#103—611no—
449C2×#103C2×D6111yescharacteristic
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102C2×D6111yescharacteristic
454C2×C22⋊C8—611no—
455C2×C4×C8—611no—
456C2×C4×C8—611no—
457#390—611no—
458#390—611no—
459#390—611no—
460#390—1221no—
461#390—1221no—
462#390—1221no—
463#390—1221no—
464#390C2×D6111yescharacteristic
465#380—611no—
466#380—611no—
467#380—1221no—
468#380—1221no—
469C4×C22⋊C4—611no—
470C4×C22⋊C4—1221no—
471C4×C22⋊C4—1221no—
472#340—611no—
473#340C2×D6111yescharacteristic
474#336—611no—
475#336C2×D6111yescharacteristic
476C61#2245111yescharacteristic, complemented, Sylow
477C2×#41—614no—
478C2×#41—614no—
479C2×#41—1222no—
480C2×#41—1222no—
481C2×#41—1222no—
482C2×#41—1222no—
483C2×#41—1222no—
484C2×#41—1222no—
485C2×#41—2441no—
486C2×#41—2441no—
487C2×#41—2441no—
488C2×#41—2441no—
489C22×Q8—611no—
490C22×Q8C22×D6111yescharacteristic
491C22×D4—611no—
492C22×D4—1221no—
493C22×D4—1221no—
494C22×D4C22×D6111yescharacteristic
495C23×C4—611no—
496C23×C4—1221no—
497C23×C4—1221no—
498#135—12232no—
499C2×Q16—614no—
500C2×Q16—614no—
501C2×Q16—614no—
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—614no—
505C2×SD16—1222no—
506C2×SD16—1222no—
507C2×SD16C4×D6114yes—
508C2×D8—614no—
509C2×D8—1222no—
510C2×D8—1222no—
511C22×C8—611no—
512C22×C8—614no—
513C22×C8—611no—
514C22×C8—1222no—
515C22×C8—1222no—
516C22×C8C22×D6111yescharacteristic
517C22×C8C22×D6111yescharacteristic
518C4×Q8—22no—
519C4×Q8—41no—
520C4×Q8—1222no—
521C4×Q8—1222no—
522C4×Q8—1222no—
523C4×Q8—2441no—
524C4×Q8—2441no—
525C4×Q8—2441no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4C22×D6111yescharacteristic
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—611no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C42—21no—
547C2×C42—611no—
548C2×C42—1221no—
549C2×C42—1221no—
550C2×C42—1221no—
551C2×C42C22×D6111yescharacteristic
552#107—1222no—
553#107—1222no—
554#103—22no—
555#103—1222no—
556#103—1222no—
557#103—1222no—
558#102—41no—
559#102—2441no—
560#102—2441no—
561#102—2441no—
562C22⋊C8—1222no—
563C4×C8—1222no—
564C4×C8—1222no—
565#95—611no—
566#95—611no—
567#95—1221no—
568#95—1221no—
569C24—21no—
570C24—611no—
571C24—1221no—
572#41—1228no—
573#41—1228no—
574#41—2444no—
575#41—2444no—
576#41—2444no—
577#41—2444no—
578#41—2444no—
579#41—2444no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—612no—
584C2×Q8—612no—
585C2×Q8—612no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8C2×C4×D6112yes—
590C2×Q8D4×D6112yes—
591C2×Q8D4×D6112yes—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—612no—
598C2×D4—1224no—
599C2×D4—1224no—
600C2×D4—1221no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—2442no—
606C2×D4—2442no—
607C2×D4—2442no—
608C2×D4—2442no—
609C2×D4C2×C4×D6112yes—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—612no—
616C22×C4—612no—
617C22×C4—611no—
618C22×C4—1224no—
619C22×C4—1224no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4—2442no—
630C22×C4—2442no—
631C22×C4D4×D6111yescharacteristic
632C22×C4D4×D6111yescharacteristic
633C22×C4C23×D6111yescharacteristic
634Q16—6116no—
635SD16—28no—
636SD16—1228no—
637D8—1228no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—612no—
644C2×C8—612no—
645C2×C8—612no—
646C2×C8—1228no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8C2×C4×D6112yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—2442no—
661C4⋊C4—2442no—
662C4⋊C4—2442no—
663C22⋊C4—42no—
664C22⋊C4—81no—
665C22⋊C4—1222no—
666C22⋊C4—1222no—
667C22⋊C4—4881no—
668C22⋊C4—4881no—
669C22⋊C4—4881no—
670C22⋊C4—4881no—
671C22⋊C4—4881no—
672C22⋊C4—2442no—
673C22⋊C4—2442no—
674C22⋊C4—2442no—
675C42—21no—
676C42—21no—
677C42—42no—
678C42—1221no—
679C42—1221no—
680C42—2442no—
681C42—2442no—
682C42—2442no—
683C23—22no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—612no—
691C23—1221no—
692C23—1221no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23—1221no—
697C23—1222no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23—2441no—
704C23C2×D4×D6111yescharacteristic
705Q8—22no—
706Q8—22no—
707Q8—22no—
708Q8—614no—
709Q8—1222no—
710Q8—1222no—
711Q8—1222no—
712Q8C22⋊C4×D6114yes—
713D4—22no—
714D4—22no—
715D4—41no—
716D4—41no—
717D4—1222no—
718D4—1222no—
719D4—2448no—
720D4—2448no—
721D4—2441no—
722D4—2441no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—612no—
738C2×C4—612no—
739C2×C4—1222no—
740C2×C4—1221no—
741C2×C4—1222no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1222no—
745C2×C4—1221no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
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#1451979812yescomplemented
762C2×C4C22×C4×D6111yescharacteristic
763C2×C4C2×D4×D6111yescharacteristic
764C2×C4C2×D4×D6111yescharacteristic
765C2×C4#41×D6111yescharacteristic
766C2×C4#1451982211yescharacteristic
767C2×C4#1451982311yescharacteristic
768C8—22no—
769C8—41no—
770C8—614no—
771C8—2441no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—1222no—
780C22—1222no—
781C22—1222no—
782C22—4881no—
783C22—4881no—
784C22—4881no—
785C22—4881no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2441no—
790C22—2441no—
791C22—2441no—
792C22—2441no—
793C22C4×D4×D6111yescharacteristic
794C22#1684039411yescharacteristic
795C22#1684039611yescharacteristic
796C22#135×D6111yescharacteristic
797C22C2×#1451979811yescharacteristic
798C22#1684056611yescharacteristic
799C22#1684057811yescharacteristic
800C4—22no—
801C4—24no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—1222no—
806C4—1222no—
807C4—1224no—
808C4—4881no—
809C4—4881no—
810C4—2441no—
811C4C2×C22⋊C4×D6111yescharacteristic
812C4#1684023411yescharacteristic
813C4#1684040111yescharacteristic
814C4#1684040411yescharacteristic
815C2—82no—
816C2—4882no—
817C2—2442no—
818C2#2144863711yescharacteristic
819C2C4×#1451979811yescharacteristic
820C2#2145469111yescharacteristic
821C2#2145755311yescharacteristic
822C2#2145755511yescharacteristic
823C2#2145757211yescharacteristic
824C2#2145757411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1880C2
socleC23×C61C22×D4
prime radicalC22×#14519798C2
cosocleC22×C4×C61C24
hypercenter#1880D61
hypocenterC61#22451
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758202C2semidirect
3. C2×#16839854C2semidirect
4. #21448658C2semidirect
5. #21448657C2semidirect
6. #21446684C2semidirect
7. #21446682C2semidirect
8. #21446176C2semidirect
9. #21446175C2semidirect
10. #21446173C2semidirect
11. #21445847C2semidirect
12. #21445758C2semidirect
13. #21445756C2semidirect
14. #21445589C2semidirect
15. C61×#1880C2semidirect
20. C2×#14519798C4semidirect
240. #11758202C22⋊C4semidirect
314. C2×C4×C61#135semidirect
340. C2×Dic61#135semidirect
413. #1880D61semidirect
476. C61#22451semidirect
761. C2×C4#14519798semidirect

Maximal subgroups

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

subgroupindex
C22×#145197982
C2×C4×#117582022
C2×#168398542
#214486582
#214486572
#214466842
#214466822
#214461762
#214461752
#214461732
#214458472
#214457582
#214457562
#214455892
C61×#18802
#2245161