Finite Group Databasebeta

← #28600034

Subgroups — #28600034

Order 15104.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426791C211yesmaximal, characteristic, complemented
2#21426678C211yesmaximal, characteristic, complemented
3#21424973C211yesmaximal, characteristic, complemented
4#21424963C211yesmaximal, characteristic, complemented
5#21424795C211yesmaximal, characteristic, complemented
6#21424781C211yesmaximal, characteristic, complemented
7#21424725C211yesmaximal, characteristic, complemented
8#21424718C211yesmaximal, characteristic, complemented
9#21424446C211yesmaximal, characteristic, complemented
10#21424446C211yesmaximal, characteristic, complemented
11#21424419C211yesmaximal, characteristic, complemented
12#21424297C211yesmaximal, characteristic, complemented
13#21424027C211yesmaximal, characteristic, complemented
14#21423864C211yesmaximal, characteristic, complemented
15C2×C59×#447C211yesmaximal, characteristic
16C2×D4×Dic59C2211yescharacteristic, complemented
17C2×#14273686C2211yescharacteristic
18C2×#14273686C2211yescharacteristic
19C2×#14273661C2211yescharacteristic, complemented
20C2×#14273659C2211yescharacteristic, complemented
21C2×#14273648C2211yescharacteristic
22C2×#14273648C2211yescharacteristic
23C2×#14273648C2211yescharacteristic
24C2×#14273648C2211yescharacteristic
25C2×#14273648C2211yescharacteristic, complemented
26C2×#14273648C2211yescharacteristic, complemented
27C2×C22⋊(C59⋊C8)C2211yescharacteristic
28C2×#14273637C2211yescharacteristic, complemented
29C2×C8×Dic59C2211yescharacteristic, complemented
30#16837305—21no—
31#16837305—21no—
32#16837305—21no—
33#16837305C2211yescharacteristic
34#16837305C2211yescharacteristic
35#16837305C2211yescharacteristic
36#16837305C2211yescharacteristic
37#16837305C2211yescharacteristic, complemented
38#16837301C2211yescharacteristic, complemented
39#16837295—21no—
40#16837282—21no—
41#16837277—21no—
42#16837262C2211yescharacteristic
43#16837258—21no—
44#16837258—21no—
45C4⋊C4×Dic59C2211yescharacteristic, complemented
46#16837165C2211yescharacteristic, complemented
47#16837165C2211yescharacteristic, complemented
48#16837164C2211yescharacteristic, complemented
49#16837164C2211yescharacteristic, complemented
50#16837156C2211yescharacteristic, complemented
51#16837156C2211yescharacteristic, complemented
52C23×D4×C59C2211yescharacteristic
53C22×D8×C59C2211yescharacteristic
54C22×D8×C59C2211yescharacteristic
55C2×#121×C59C2211yescharacteristic
56C59×#447C418yescomplemented
57C2×#102×C59C2211yescharacteristic
58C2×#102×C59C2211yescharacteristic
59C2×C22⋊C8×C59C2211yescharacteristic
60C23×Dic59—21no—
61C22×C59⋊C8C2311yescharacteristic
62C22×C59⋊C8C2311yescharacteristic
63D4×Dic59—41no—
64D4×Dic59—41no—
65#14273686—41no—
66#14273686—41no—
67#14273686—41no—
68#14273686—41no—
69C2×C4⋊Dic59—21no—
70C2×C4⋊Dic59D411yescharacteristic
71C2×C4⋊Dic59D411yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×C22⋊Dic59—21no—
77C2×C22⋊Dic59—21no—
78C2×C22⋊Dic59—21no—
79C2×C22⋊Dic59—21no—
80C2×C22⋊Dic59—21no—
81C2×C22⋊Dic59—21no—
82C2×C22⋊Dic59—21no—
83C2×C22⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85C2×C22⋊Dic59—21no—
86C2×C22⋊Dic59—21no—
87C2×C22⋊Dic59—21no—
88C2×C22⋊Dic59—21no—
89C2×C22⋊Dic59D411yescharacteristic
90C2×C22⋊Dic59D411yescharacteristic
91C2×C4×Dic59—21no—
92C2×C4×Dic59—21no—
93C2×C4×Dic59C2311yescharacteristic
94C2×C4×Dic59C2311yescharacteristic
95#14273661—41no—
96#14273659—41no—
97#14273648—41no—
98#14273648—41no—
99#14273648—41no—
100#14273648—41no—
101#14273648—41no—
102#14273648—41no—
103C22⋊(C59⋊C8)—22no—
104#14273637—41no—
105C8×Dic59—41no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C25×C59—21no—
110C22×D4×C59—21no—
111C22×D4×C59—21no—
112C22×D4×C59—22no—
113C22×D4×C59—41no—
114C22×D4×C59—41no—
115C22×D4×C59—41no—
116C22×D4×C59—41no—
117C22×D4×C59C2×C414yescomplemented
118C22×D4×C59C2311yescharacteristic
119C22×D4×C59C2311yescharacteristic
120C22×D4×C59C2311yescharacteristic
121C23×C4×C59C2311yescharacteristic
122C2×D8×C59—41no—
123C2×D8×C59—41no—
124C2×D8×C59—41no—
125C2×D8×C59—41no—
126C2×D8×C59C2×C414yes—
127C2×D8×C59C2×C414yes—
128C22×C8×C59C2311yescharacteristic
129C22×C8×C59C2311yescharacteristic
130#121×C59—22no—
131#121×C59C2×C414yes—
132C2×C4⋊C4×C59C2311yescharacteristic
133C2×C22⋊C4×C59—21no—
134#102×C59C2×C414yescomplemented
135#102×C59C2×C414yescomplemented
136C22⋊C8×C59C2×C414yescomplemented
137C24×C59—21no—
138C24×C59—21no—
139C24×C59—21no—
140C24×C59—24no—
141C24×C59—42no—
142C24×C59—42no—
143C24×C59—81no—
144C24×C59—81no—
145C24×C59—81no—
146C24×C59—81no—
147C24×C59C2×D411yescharacteristic
148C2×D4×C59—24no—
149C2×D4×C59—24no—
150C2×D4×C59—21no—
151C2×D4×C59—21no—
152C2×D4×C59—21no—
153C2×D4×C59—21no—
154C2×D4×C59—21no—
155C2×D4×C59—21no—
156C2×D4×C59—21no—
157C2×D4×C59—21no—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—21no—
162C2×D4×C59—21no—
163C2×D4×C59—21no—
164C2×D4×C59—21no—
165C2×D4×C59—44no—
166C2×D4×C59—44no—
167C2×D4×C59—42no—
168C2×D4×C59—42no—
169C2×D4×C59—44no—
170C2×D4×C59—44no—
171C2×D4×C59—81no—
172C2×D4×C59—81no—
173C2×D4×C59C22×C412yes—
174C2×D4×C59C22×C412yes—
175C2×D4×C59C22×C412yes—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59C22×C412yes—
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59#4112yes—
184C22×C4×C59C2411yescharacteristic
185C22×Dic59—21no—
186C22×Dic59—21no—
187C22×Dic59—21no—
188C22×Dic59—21no—
189C22×Dic59—42no—
190C22×Dic59—81no—
191C22×Dic59—81no—
192C22×Dic59C2×D411yescharacteristic
193C22×Dic59C2×D411yescharacteristic
194C22×Dic59C2×D411yescharacteristic
195C22×Dic59C2×D411yescharacteristic
196D8×C59—44no—
197D8×C59—44no—
198C2×C8×C59—21no—
199C2×C8×C59—21no—
200C2×C8×C59—21no—
201C2×C8×C59—21no—
202C2×C8×C59C22×C412yes—
203C2×C8×C59C22×C412yes—
204C4⋊C4×C59—21no—
205C4⋊C4×C59C22×C412yes—
206C22⋊C4×C59—24no—
207C22⋊Dic59—41no—
208C22⋊Dic59—41no—
209C22⋊Dic59—42no—
210C22⋊Dic59—42no—
211C22⋊Dic59—81no—
212C22⋊Dic59—81no—
213C22⋊Dic59—81no—
214C22⋊Dic59—81no—
215C22⋊Dic59—81no—
216C22⋊Dic59—81no—
217C22⋊Dic59—81no—
218C22⋊Dic59—81no—
219C22⋊Dic59—81no—
220C22⋊Dic59—81no—
221C22⋊Dic59—81no—
222C4⋊Dic59—21no—
223C4⋊Dic59—21no—
224C4⋊Dic59—21no—
225C4⋊Dic59—21no—
226C4⋊Dic59—21no—
227C4⋊Dic59—21no—
228C4⋊Dic59—21no—
229C4⋊Dic59—21no—
230C4⋊Dic59—41no—
231C4⋊Dic59—41no—
232C4⋊Dic59—81no—
233C4×Dic59—21no—
234C4×Dic59—21no—
235C4×Dic59—21no—
236C4×Dic59—21no—
237C4×Dic59—42no—
238C4×Dic59—81no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8—21no—
243C2×C59⋊C8—21no—
244C2×C59⋊C8—21no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—22no—
252C23×C59—22no—
253C23×C59—22no—
254C23×C59—48no—
255C23×C59—41no—
256C23×C59—41no—
257C23×C59—41no—
258C23×C59—41no—
259C23×C59—41no—
260C23×C59—41no—
261C23×C59—41no—
262C23×C59—41no—
263C23×C59—41no—
264C23×C59—41no—
265C23×C59—41no—
266C23×C59—41no—
267C23×C59—41no—
268C23×C59—41no—
269C23×C59—41no—
270C23×C59—41no—
271C23×C59—41no—
272C23×C59—41no—
273C23×C59—84no—
274C23×C59—84no—
275C23×C59—84no—
276C23×C59—84no—
277C23×C59—84no—
278C23×C59—84no—
279C23×C59C4×D412yes—
280C23×C59C22×D411yescharacteristic
281D4×C59—22no—
282D4×C59—22no—
283D4×C59—22no—
284D4×C59—22no—
285D4×C59—22no—
286D4×C59—22no—
287D4×C59—48no—
288D4×C59—41no—
289D4×C59—41no—
290D4×C59—41no—
291D4×C59—41no—
292D4×C59—41no—
293D4×C59—41no—
294D4×C59—84no—
295C2×C4×C59—21no—
296C2×C4×C59—21no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—41no—
303C2×C4×C59—41no—
304C2×C4×C59C4×D412yes—
305C2×C4×C59C23×C411yescharacteristic
306C2×C4×C59C2×#4111yescharacteristic
307C2×C4×C59H(5,𝔽2)11yescharacteristic
308C2×C4×C59H(5,𝔽2)11yescharacteristic
309C2×C4×C59H(5,𝔽2)11yescharacteristic
310C2×C4×C59H(5,𝔽2)11yescharacteristic
311C2×Dic59—21no—
312C2×Dic59—21no—
313C2×Dic59—21no—
314C2×Dic59—21no—
315C2×Dic59—21no—
316C2×Dic59—21no—
317C2×Dic59—21no—
318C2×Dic59—21no—
319C2×Dic59—21no—
320C2×Dic59—21no—
321C2×Dic59—21no—
322C2×Dic59—21no—
323C2×Dic59—41no—
324C2×Dic59—41no—
325C2×Dic59—41no—
326C2×Dic59—41no—
327C2×Dic59—41no—
328C2×Dic59—41no—
329C2×Dic59—41no—
330C2×Dic59—41no—
331C2×Dic59—41no—
332C2×Dic59—41no—
333C2×Dic59—41no—
334C2×Dic59—41no—
335C2×Dic59—84no—
336C8×C59—22no—
337C8×C59—22no—
338C59⋊C8—41no—
339C59⋊C8—41no—
340#22056—591nomaximal, Sylow
341C22×C59—22no—
342C22×C59—22no—
343C22×C59—22no—
344C22×C59—41no—
345C22×C59—41no—
346C22×C59—41no—
347C22×C59—41no—
348C22×C59—42no—
349C22×C59—42no—
350C22×C59—42no—
351C22×C59—42no—
352C22×C59—42no—
353C22×C59—42no—
354C22×C59—42no—
355C22×C59—42no—
356C22×C59—42no—
357C22×C59—816no—
358C22×C59—81no—
359C22×C59—81no—
360C22×C59—81no—
361C22×C59—81no—
362C22×C59—81no—
363C22×C59—81no—
364C22×C59—81no—
365C22×C59—81no—
366C22×C59—81no—
367C22×C59—81no—
368C22×C59—81no—
369C22×C59—81no—
370C22×C59C2×C4×D411yescharacteristic
371C22×C59#53411yescharacteristic
372C22×C59#53511yescharacteristic
373C22×C59#57611yescharacteristic
374C22×C59#57611yescharacteristic
375C22×C59#57611yescharacteristic
376C22×C59#57711yescharacteristic
377C4×C59—22no—
378C4×C59—42no—
379C4×C59#51811yescharacteristic
380C4×C59#51811yescharacteristic
381C4×C59#53811yescharacteristic
382C4×C59#53811yescharacteristic
383Dic59—41no—
384Dic59—41no—
385Dic59—41no—
386Dic59—41no—
387Dic59—81no—
388Dic59—81no—
389Dic59—81no—
390Dic59—81no—
391C2×#447D5911yescharacteristic
392#2324—591no—
393#2309—591no—
394#1972—591no—
395#1970—591no—
396#1936—591no—
397#1934—591no—
398#1926—591no—
399#1925—591no—
400#1879—591no—
401#1879—591no—
402#1875—591no—
403#1854—591no—
404#1786—591no—
405#1750—591no—
406C2×C59—42no—
407C2×C59—82no—
408C2×C59—82no—
409C2×C59—82no—
410C2×C59#232111yescharacteristic
411C2×C59#294611yescharacteristic
412C2×C59#294811yescharacteristic
413C2×C59#319811yescharacteristic
414C2×C59#319911yescharacteristic
415C2×C59#322011yescharacteristic
416C2×C59#322411yescharacteristic
417C23×D4C2×D5911yescharacteristic
418C22×D8C2×D5911yescharacteristic
419C22×D8C2×D5911yescharacteristic
420C2×#121C2×D5911yescharacteristic
421C2×C4×D4—591no—
422C2×#117—591no—
423C2×#117—591no—
424#447Dic5918yescomplemented
425C2×#107—591no—
426C2×#106—591no—
427C2×#102—591no—
428C2×#102—591no—
429C2×#102—591no—
430C2×#102—591no—
431C2×#102—591no—
432C2×#102—591no—
433C2×#102C2×D5911yescharacteristic
434C2×#102C2×D5911yescharacteristic
435C2×C22⋊C8—591no—
436C2×C22⋊C8C2×D5911yescharacteristic
437C2×#97—591no—
438C2×C4×C8—591no—
439#390—591no—
440#390—591no—
441#390—591no—
442#390—591no—
443#390—591no—
444#390—1181no—
445#390—1181no—
446#390—1181no—
447#389—591no—
448#388—1181no—
449#386—1181no—
450#385—1181no—
451#380—591no—
452#379—1181no—
453#379—1181no—
454C4×C4⋊C4—591no—
455#340—591no—
456#340—591no—
457#340—591no—
458#340—591no—
459#336—591no—
460#336—591no—
461C59#2205611yescharacteristic, complemented, Sylow
462C25—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C2×Dic5914yescomplemented
471C22×D4C22×D5911yescharacteristic
472C22×D4C22×D5911yescharacteristic
473C22×D4C22×D5911yescharacteristic
474C23×C4—1181no—
475C23×C4C22×D5911yescharacteristic
476C2×D8—41no—
477C2×D8—41no—
478C2×D8—41no—
479C2×D8—41no—
480C2×D8C2×Dic5914yes—
481C2×D8C2×Dic5914yes—
482C22×C8—591no—
483C22×C8—591no—
484C22×C8C22×D5911yescharacteristic
485C22×C8C22×D5911yescharacteristic
486#121—22no—
487#121C2×Dic5914yes—
488C4×D4—2361no—
489C4×D4—2361no—
490#117—2361no—
491#117—2361no—
492#117—2361no—
493#117—2361no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—591no—
499C2×C4⋊C4—591no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4C22×D5911yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—591no—
504C2×C22⋊C4—591no—
505C2×C22⋊C4—1181no—
506C2×C22⋊C4—1181no—
507C2×C22⋊C4—1181no—
508C2×C22⋊C4—1181no—
509C2×C22⋊C4—1181no—
510C2×C22⋊C4—1181no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4—1181no—
515C2×C22⋊C4—1181no—
516C2×C22⋊C4—1181no—
517C2×C22⋊C4—1181no—
518C2×C42—591no—
519C2×C42—591no—
520C2×C42—1181no—
521C2×C42—1181no—
522#107—2361no—
523#106—2361no—
524#102—2361no—
525#102—2361no—
526#102—2361no—
527#102—2361no—
528#102—2361no—
529#102—2361no—
530#102C2×Dic5914yescomplemented
531#102C2×Dic5914yescomplemented
532C22⋊C8—1182no—
533C22⋊C8C2×Dic5914yescomplemented
534#97—2361no—
535C4×C8—2361no—
536#95—1181no—
537#95—1181no—
538#95—1181no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—24no—
543C24—42no—
544C24—42no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—81no—
549C24D4×D5911yescharacteristic
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C22×Dic5912yes—
576C2×D4C22×Dic5912yes—
577C2×D4C22×Dic5912yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—591no—
584C22×C4—591no—
585C22×C4—591no—
586C22×C4—591no—
587C22×C4—1181no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—1181no—
591C22×C4—4721no—
592C22×C4—4721no—
593C22×C4—2362no—
594C22×C4D4×D5911yescharacteristic
595C22×C4#1174568712yes—
596C22×C4C22×Dic5912yes—
597C22×C4C23×D5911yescharacteristic
598D8—44no—
599D8—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—1181no—
605C2×C8—1181no—
606C2×C8—1181no—
607C2×C8—1181no—
608C2×C8—1181no—
609C2×C8—1181no—
610C2×C8C22×Dic5912yes—
611C2×C8C22×Dic5912yes—
612C4⋊C4—21no—
613C4⋊C4—1181no—
614C4⋊C4—1181no—
615C4⋊C4—1181no—
616C4⋊C4—1181no—
617C4⋊C4—1181no—
618C4⋊C4—1181no—
619C4⋊C4—1181no—
620C4⋊C4—1181no—
621C4⋊C4—4721no—
622C4⋊C4—2361no—
623C4⋊C4—2361no—
624C4⋊C4C22×Dic5912yes—
625C22⋊C4—24no—
626C22⋊C4—4721no—
627C22⋊C4—4721no—
628C22⋊C4—4721no—
629C22⋊C4—4721no—
630C22⋊C4—4721no—
631C22⋊C4—4721no—
632C22⋊C4—4721no—
633C22⋊C4—4721no—
634C22⋊C4—4721no—
635C22⋊C4—4721no—
636C22⋊C4—4721no—
637C22⋊C4—2361no—
638C22⋊C4—2361no—
639C22⋊C4—2362no—
640C22⋊C4—2362no—
641C42—1181no—
642C42—1181no—
643C42—1181no—
644C42—1181no—
645C42—4721no—
646C42—2362no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—48no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23D4×Dic5912yes—
682C23C2×D4×D5911yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—1181no—
707C2×C4—1181no—
708C2×C4—1181no—
709C2×C4—1181no—
710C2×C4—1181no—
711C2×C4—1181no—
712C2×C4—1181no—
713C2×C4—1181no—
714C2×C4—1181no—
715C2×C4—1181no—
716C2×C4—1181no—
717C2×C4—1181no—
718C2×C4—4724no—
719C2×C4—2361no—
720C2×C4—2361no—
721C2×C4—2361no—
722C2×C4—2361no—
723C2×C4—2361no—
724C2×C4—2361no—
725C2×C4—2361no—
726C2×C4—2361no—
727C2×C4—2361no—
728C2×C4—2361no—
729C2×C4—2361no—
730C2×C4—2361no—
731C2×C4D4×Dic5912yes—
732C2×C4C23×Dic5911yescharacteristic
733C2×C4C2×#1174568711yescharacteristic
734C2×C4#1427377211yescharacteristic
735C2×C4#1427377211yescharacteristic
736C2×C4#1427377211yescharacteristic
737C2×C4#1427377211yescharacteristic
738C8—22no—
739C8—22no—
740C8—2361no—
741C8—2361no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—816no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22C2×D4×Dic5911yescharacteristic
772C22#1683796211yescharacteristic
773C22#1683796711yescharacteristic
774C22#1683820311yescharacteristic
775C22#1683820311yescharacteristic
776C22#1683820611yescharacteristic
777C22#1683821211yescharacteristic
778C4—22no—
779C4—42no—
780C4—4721no—
781C4—4721no—
782C4—4721no—
783C4—4721no—
784C4—2361no—
785C4—2361no—
786C4—2361no—
787C4—2361no—
788C4#1683787711yescharacteristic
789C4#1683787711yescharacteristic
790C4#1683798711yescharacteristic
791C4#1683798711yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—82no—
796C2#2142675711yescharacteristic
797C2#2143292911yescharacteristic
798C2#2143294811yescharacteristic
799C2#2143494411yescharacteristic
800C2#2143495911yescharacteristic
801C2#2143514211yescharacteristic
802C2#2143518611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×C59×#447C2
socleC23×C59C22×D4
cosocleC22×C4×C59C24
hypercenterC2×#447D59
hypocenterC59#22056
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. #21426791C2semidirect
2. #21426678C2semidirect
3. #21424973C2semidirect
4. #21424963C2semidirect
5. #21424795C2semidirect
6. #21424781C2semidirect
7. #21424725C2semidirect
8. #21424718C2semidirect
9. #21424446C2semidirect
10. #21424446C2semidirect
11. #21424419C2semidirect
12. #21424297C2semidirect
13. #21424027C2semidirect
14. #21423864C2semidirect
16. C2×D4×Dic59C22semidirect
19. C2×#14273661C22semidirect
20. C2×#14273659C22semidirect
25. C2×#14273648C22semidirect
26. C2×#14273648C22semidirect
28. C2×#14273637C22semidirect
29. C2×C8×Dic59C22semidirect
37. #16837305C22semidirect
38. #16837301C22semidirect
45. C4⋊C4×Dic59C22semidirect
46. #16837165C22semidirect
47. #16837165C22semidirect
48. #16837164C22semidirect
49. #16837164C22semidirect
50. #16837156C22semidirect
51. #16837156C22semidirect
56. C59×#447C4semidirect
117. C22×D4×C59C2×C4semidirect
134. #102×C59C2×C4semidirect
135. #102×C59C2×C4semidirect
136. C22⋊C8×C59C2×C4semidirect
424. #447Dic59semidirect
461. C59#22056semidirect
470. C22×D4C2×Dic59semidirect
530. #102C2×Dic59semidirect
531. #102C2×Dic59semidirect
533. C22⋊C8C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
#214267912
#214266782
#214249732
#214249632
#214247952
#214247812
#214247252
#214247182
#214244462
#214244192
#214242972
#214240272
#214238642
C2×C59×#4472
#2205659