Finite Group Databasebeta

← #29713990

Subgroups — #29713990

Order 15616.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840458C211yesmaximal, characteristic, complemented
2C2×#16840062C211yesmaximal, characteristic, complemented
3C2×C4×#11758199C211yesmaximal, characteristic, complemented
4#21447008C211yesmaximal, characteristic, complemented
5#21447001C211yesmaximal, characteristic, complemented
6#21446815C211yesmaximal, characteristic, complemented
7#21446815C211yesmaximal, characteristic, complemented
8#21446783C211yesmaximal, characteristic, complemented
9#21446614C211yesmaximal, characteristic, complemented
10#21446142C211yesmaximal, characteristic, complemented
11#21446137C211yesmaximal, characteristic, complemented
12#21446016C211yesmaximal, characteristic, complemented
13#21446006C211yesmaximal, characteristic, complemented
14#21445826C211yesmaximal, characteristic, complemented
15C61×#2535C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17#16840458—24no—
18#16840458—24no—
19C2×#14519772—21no—
20C2×#14519769C2211yescharacteristic
21C2×#14519759—21no—
22C2×#14519751C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519749—21no—
25C2×C4×D244C2211yescharacteristic
26C2×#14519737—21no—
27C2×#14519736C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29#16840062—24no—
30C4×#11758199—24no—
31C2×#14519710C2211yescharacteristic
32C2×#14519710C2211yescharacteristic
33C2×#14519708C2211yescharacteristic
34C2×C4⋊#92418C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44C2×C22⋊#92418C2211yescharacteristic
45C2×C4×#92418C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×#121×C61C2211yescharacteristic
53C2×#121×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C61×#397—21no—
57C61×#392—21no—
58C61×#386—21no—
59C61×#386—21no—
60C61×#382C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#380C2211yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C23×Dic61—21no—
67C22×C4×D61—21no—
68C2×#11758199—22no—
69C2×#11758199—22no—
70C2×#11758199—22no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519772—28no—
76#14519769—22no—
77#14519769D414yescomplemented
78#14519759—28no—
79#14519751—22no—
80#14519751—22no—
81#14519751—22no—
82#14519751—22no—
83#14519749—28no—
84C4×D244—22no—
85C4×D244D414yescomplemented
86#14519737—28no—
87#14519736—22no—
88#14519736—22no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×C4×Dic61—21no—
102#14519710—22no—
103#14519710—22no—
104#14519708—22no—
105C4⋊#92418—22no—
106#14519698—22no—
107#14519698—22no—
108#14519698—22no—
109#14519697—22no—
110#14519697—41no—
111#14519697—41no—
112C22⋊#92418—22no—
113C22⋊#92418—22no—
114C22⋊#92418—41no—
115C22⋊#92418—41no—
116C4×#92418—22no—
117C22×D4×C61—21no—
118C22×D4×C61—21no—
119C22×D4×C61D411yescharacteristic
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61—21no—
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124#121×C61—22no—
125#121×C61—22no—
126#121×C61—41no—
127#121×C61—41no—
128C4×D4×C61—22no—
129C4×D4×C61—22no—
130C4×D4×C61—22no—
131C4×D4×C61—22no—
132C2×C4⋊C4×C61D411yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61D411yescharacteristic
142C2×C22⋊C4×C61D411yescharacteristic
143C2×C42×C61C2311yescharacteristic
144#95×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148C24×C61—21no—
149C24×C61C2×D411yescharacteristic
150C24×C61C2×D411yescharacteristic
151C23×D61—21no—
152C2×D4×C61—22no—
153C2×D4×C61—22no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—41no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61—42no—
164C2×D4×C61—81no—
165C2×D4×C61—81no—
166C2×D4×C61#4112yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
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×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—42no—
183C22×C4×C61—81no—
184C22×C4×C61—81no—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—24no—
191C2×C22⋊D61—24no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—81no—
195C2×C22⋊D61—81no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—24no—
200C22×Dic61—81no—
201C22×Dic61—81no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244C2×D412yes—
208C2×C4×D61—24no—
209C2×C4×D61—81no—
210C2×C4×D61—81no—
211C4⋊C4×C61—22no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—42no—
223C22⋊C4×C61—81no—
224C22⋊C4×C61—81no—
225C42×C61C2×D412yes—
226C42×C61C2×D412yes—
227C22⋊Dic61—24no—
228#11758199—28no—
229#11758198—24no—
230#11758198—24no—
231#11758198—24no—
232C4⋊Dic61—24no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61C2×D412yes—
237C4⋊Dic61C2×D412yes—
238C4⋊Dic61C2×D412yes—
239#11758196—24no—
240#11758196—24no—
241C4×Dic61—24no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418#4112yes—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—22no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61#13512yes—
275C23×C61C22×D411yescharacteristic
276C22×D61—22no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—44no—
286D4×C61—41no—
287D4×C61—41no—
288D4×C61—84no—
289D4×C61—84no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
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—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—84no—
318C2×C4×C61#12012yes—
319C2×C4×C61#12012yes—
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C2×#4111yescharacteristic
323C2×C4×C61C2×#4111yescharacteristic
324C2×C4×C61H(5,𝔽2)11yescharacteristic
325C2×C4×C612−1+411yescharacteristic
326C22⋊D61—48no—
327C22⋊D61—84no—
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—84no—
338D244—22no—
339D244—22no—
340D244—41no—
341D244—41no—
342C4×D61—84no—
343#92418—22no—
344#92418—41no—
345#92418—41no—
346#92418—41no—
347#24124—611nomaximal, Sylow
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—42no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—42no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—42no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61C2×#12011yescharacteristic
370C22×C61#54611yescharacteristic
371C22×C61#54711yescharacteristic
372C22×C61C2×#13511yescharacteristic
373C22×C61#57511yescharacteristic
374C22×C61#57611yescharacteristic
375C22×C61#57611yescharacteristic
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—81no—
380C2×D61—81no—
381C2×D61—81no—
382C2×D61—81no—
383C4×C61—22no—
384C4×C61—22no—
385C4×C61—41no—
386C4×C61—41no—
387C4×C61—81no—
388C4×C61—81no—
389C4×C61—81no—
390C4×C61#52511yescharacteristic
391C4×C61#53711yescharacteristic
392C4×C61#54811yescharacteristic
393C4×C61#55011yescharacteristic
394Dic61—42no—
395Dic61—42no—
396Dic61—42no—
397C2×#553—611no—
398C2×#478—611no—
399C2×C4×D8—611no—
400#2535D6111yescharacteristic, complemented
401#2034—611no—
402#2033—611no—
403#1999—611no—
404#1999—611no—
405#1991—611no—
406#1954—611no—
407#1875—611no—
408#1874—611no—
409#1854—611no—
410#1852—611no—
411#1804—611no—
412C2×C61—42no—
413C2×C61—81no—
414C2×C61—82no—
415C2×C61#240711yescharacteristic
416C2×C61#300211yescharacteristic
417C2×C61#300811yescharacteristic
418C2×C61#329711yescharacteristic
419C2×C61#332211yescharacteristic
420C2×C61#333911yescharacteristic
421C2×C61#335511yescharacteristic
422D61—82no—
423C22×D8—611no—
424#553—1224no—
425#553—1224no—
426C2×#126—1221no—
427C2×#125—611no—
428C2×#123—1221no—
429C2×#121—611no—
430C2×#121—611no—
431C2×#121—1221no—
432C2×#121C2×D6111yescharacteristic
433C2×#121C2×D6111yescharacteristic
434C2×C4×D4—611no—
435C2×C4×D4—1221no—
436C2×C4×D4C2×D6111yescharacteristic
437C2×C4×D4C2×D6111yescharacteristic
438C2×#117—611no—
439C22×C4⋊C4—611no—
440#478—1224no—
441C4×D8—1224no—
442C2×#107—611no—
443C2×#107—611no—
444C2×#106—611no—
445C2×C4⋊C8—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×C22⋊C8—611no—
453C2×C22⋊C8—611no—
454C2×C22⋊C8—611no—
455C2×C22⋊C8—611no—
456C2×C4×C8—611no—
457#397—21no—
458#392—21no—
459#386—21no—
460#386—21no—
461#382C2×D6111yescharacteristic
462#380C2×D6111yescharacteristic
463#380C2×D6111yescharacteristic
464#340—611no—
465#340—611no—
466#340—611no—
467#340—611no—
468#340—611no—
469#340—611no—
470C61#2412411yescharacteristic, complemented, Sylow
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—611no—
474C22×D4—1221no—
475C22×D4—1221no—
476C22×D4C22⋊D6111yescharacteristic
477C22×D4C22×D6111yescharacteristic
478C23×C4—21no—
479C23×C4—1221no—
480C23×C4—1221no—
481C23×C4C22×D6111yescharacteristic
482C23×C4C22×D6111yescharacteristic
483C2×D8—1222no—
484C2×D8—1222no—
485C2×D8—1222no—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8—611no—
489C22×C8—611no—
490#126—1228no—
491#125—614no—
492#125—1222no—
493#123—1228no—
494#121—22no—
495#121—22no—
496#121—41no—
497#121—41no—
498#121—1222no—
499#121—1222no—
500#121—1222no—
501#121—1222no—
502#121—1228no—
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—614no—
508C4×D4—1228no—
509C4×D4—1222no—
510#117—1222no—
511#117—1222no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—1222no—
516C2×C4⋊C4—1222no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4C22⋊D6111yescharacteristic
521C2×C4⋊C4C22×D6111yescharacteristic
522C2×C4⋊C4C22×D6111yescharacteristic
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4C22⋊D6111yescharacteristic
534C2×C22⋊C4C22⋊D6111yescharacteristic
535C2×C42—1221no—
536C2×C42C22×D6111yescharacteristic
537#107—1222no—
538#107—1222no—
539#106—1222no—
540C4⋊C8—1222no—
541#102—1222no—
542#102—1222no—
543#102—1222no—
544#102—1222no—
545#102—2441no—
546#102—2441no—
547C22⋊C8—1222no—
548C22⋊C8—1222no—
549C22⋊C8—2441no—
550C22⋊C8—2441no—
551C4×C8—1222no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—1221no—
558C24C2×C22⋊D6111yescharacteristic
559C24C2×C22⋊D6111yescharacteristic
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—41no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—612no—
575C2×D4—1224no—
576C2×D4—1224no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—4881no—
583C2×D4—4881no—
584C2×D4—2442no—
585C2×D4—2442no—
586C2×D4#1175822412yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—1224no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1224no—
610C22×C4—4881no—
611C22×C4—4881no—
612C22×C4—4881no—
613C22×C4—4881no—
614C22×C4C2×C22⋊D6111yescharacteristic
615C22×C4C2×C22⋊D6111yescharacteristic
616C22×C4C2×C22⋊D6111yescharacteristic
617C22×C4C2×C22⋊D6111yescharacteristic
618C22×C4C23×D6111yescharacteristic
619D8—1228no—
620C2×C8—612no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C4⋊C4—22no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—612no—
640C4⋊C4—612no—
641C4⋊C4—612no—
642C4⋊C4—1224no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1224no—
647C4⋊C4—1224no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—81no—
654C22⋊C4—81no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C22⋊C4—1224no—
658C22⋊C4—1224no—
659C42—1224no—
660C42D4×D6112yes—
661C42D4×D6112yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—1222no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23—2441no—
688C23—2441no—
689C23#1451979712yes—
690C23C22×C22⋊D6111yescharacteristic
691D4—22no—
692D4—22no—
693D4—44no—
694D4—41no—
695D4—41no—
696D4—84no—
697D4—84no—
698D4—1222no—
699D4—1222no—
700D4—4884no—
701D4—2448no—
702D4—2441no—
703D4—2441no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—84no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—4884no—
736C2×C4—4884no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4#1451974512yes—
744C2×C4#1451974512yes—
745C2×C4C2×D4×D6111yescharacteristic
746C2×C4C2×D4×D6111yescharacteristic
747C2×C4#41×D6111yescharacteristic
748C2×C4C2×#1175822411yescharacteristic
749C2×C4#1451982211yescharacteristic
750C2×C4#1451982411yescharacteristic
751C8—1222no—
752C8—2441no—
753C8—2441no—
754C8—2441no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—4881no—
777C22—4881no—
778C22—4881no—
779C22—4881no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22C2×#1451974511yescharacteristic
784C22#1684040611yescharacteristic
785C22#1684041111yescharacteristic
786C22C2×#1451979711yescharacteristic
787C22#1684056011yescharacteristic
788C22#1684056511yescharacteristic
789C22#1684056511yescharacteristic
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—81no—
795C4—81no—
796C4—81no—
797C4—2442no—
798C4—2442no—
799C4—2442no—
800C4#1684027211yescharacteristic
801C4#1684034111yescharacteristic
802C4#1684041811yescharacteristic
803C4#1684043011yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—4882no—
808C2#2144916011yescharacteristic
809C2#2145503511yescharacteristic
810C2#2145508511yescharacteristic
811C2#2145766911yescharacteristic
812C2#2145802011yescharacteristic
813C2#2145821511yescharacteristic
814C2#2145841911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2535C2
socleC23×C61C22×D4
hypercenter#2535D61
hypocenterC61#24124
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#16840458C2semidirect
2. C2×#16840062C2semidirect
3. C2×C4×#11758199C2semidirect
4. #21447008C2semidirect
5. #21447001C2semidirect
6. #21446815C2semidirect
7. #21446815C2semidirect
8. #21446783C2semidirect
9. #21446614C2semidirect
10. #21446142C2semidirect
11. #21446137C2semidirect
12. #21446016C2semidirect
13. #21446006C2semidirect
14. #21445826C2semidirect
15. C61×#2535C2semidirect
77. #14519769D4semidirect
85. C4×D244D4semidirect
400. #2535D61semidirect
470. C61#24124semidirect

Maximal subgroups

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

subgroupindex
C2×#168404582
C2×#168400622
C2×C4×#117581992
#214470082
#214470012
#214468152
#214467832
#214466142
#214461422
#214461372
#214460162
#214460062
#214458262
C61×#25352
#2412461