Finite Group Databasebeta

← #29459326

Subgroups — #29459326

Order 15104.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837913C211yesmaximal, characteristic, complemented
2#21434933C214yesmaximal, complemented
3#21434926C212yesmaximal, complemented
4#21434922C212yesmaximal, complemented
5#21434917C211yesmaximal, characteristic, complemented
6#21434910C212yesmaximal, complemented
7#21434906C212yesmaximal, complemented
8#21434902C211yesmaximal, characteristic, complemented
9#21434898C211yesmaximal, characteristic, complemented
10#21434893C211yesmaximal, characteristic, complemented
11#21434009C212yesmaximal, complemented
12#21434005C212yesmaximal, complemented
13#21433702C214yesmaximal, complemented
14#21433314C212yesmaximal, complemented
15#21433312C212yesmaximal, complemented
16C2×#16837366C211yesmaximal, characteristic, complemented
17C2×C59×#525C211yesmaximal, characteristic, complemented
18C22×#11745685C2211yescharacteristic, complemented
19C2×#14273747C2214yescomplemented
20C22×#11745664C2212yescomplemented
21#16837913—21no—
22#16837913—21no—
23#16837913—21no—
24#16837913—21no—
25#16837913C2212yes—
26#16837913C2212yes—
27#16837913C2212yescomplemented
28#16837913C2212yescomplemented
29C2×#14273710—21no—
30C2×#14273706C2211yescharacteristic
31C2×#14273706C2211yescharacteristic, complemented
32C2×#14273701C2211yescharacteristic
33C2×#14273701C2211yescharacteristic, complemented
34C2×#14273696—21no—
35C2×C4×C22⋊D59—21no—
36C2×C4×C22⋊D59—21no—
37C2×#14273686C2211yescharacteristic, complemented
38#16837743C2214yescomplemented
39#16837740C2214yescomplemented
40#16837737C2212yescomplemented
41#16837735C2212yescomplemented
42#16837732C2212yescomplemented
43#16837730C2212yescomplemented
44#16837726C2214yescomplemented
45#16837723C2214yescomplemented
46#16837720C2212yescomplemented
47#16837718C2212yescomplemented
48#16837715C2212yescomplemented
49#16837713C2212yescomplemented
50#16837658C2214yescomplemented
51#16837658C2214yescomplemented
52#16837653C2214yescomplemented
53#16837653C2214yescomplemented
54#16837650C2214yescomplemented
55#16837650C2214yescomplemented
56#16837646C2214yescomplemented
57#16837646C2214yescomplemented
58#16837564C2214yescomplemented
59#16837562C2214yescomplemented
60#16837558C2212yescomplemented
61#16837557C2212yescomplemented
62#16837553C2212yescomplemented
63#16837552C2212yescomplemented
64#16837547C2214yescomplemented
65#16837545C2214yescomplemented
66#16837541C2212yescomplemented
67#16837540C2212yescomplemented
68#16837536C2212yescomplemented
69#16837535C2212yescomplemented
70#16837438C2214yescomplemented
71#16837398C2214yescomplemented
72#16837396C2214yescomplemented
73#16837366C2211yescharacteristic
74#16837366C2211yescharacteristic
75#16837366C2212yescomplemented
76#16837366C2212yescomplemented
77#16837366C2212yescomplemented
78C2×C22⋊(C59⋊C8)C2212yescomplemented
79C2×C22⋊(C59⋊C8)C2212yescomplemented
80C22×#41×C59C2211yescharacteristic, complemented
81C24×C4×C59C2211yescharacteristic
82C59×#525—21no—
83C59×#525—21no—
84C59×#525—21no—
85C59×#525—21no—
86C59×#525C2212yes—
87C59×#525C2212yes—
88C59×#525C2212yescomplemented
89C59×#525C2212yescomplemented
90C2×#123×C59—21no—
91C2×C22⋊Q8×C59C2211yescharacteristic
92C2×C22⋊Q8×C59C2211yescharacteristic, complemented
93C2×#121×C59C2211yescharacteristic
94C2×#121×C59C2211yescharacteristic, complemented
95C2×#120×C59—21no—
96C2×C4×D4×C59—21no—
97C2×C4×D4×C59—21no—
98C2×#117×C59C2211yescharacteristic, complemented
99C2×#11745685—21no—
100C2×#11745685—21no—
101C2×#11745685—44no—
102C2×#11745685C2312yes—
103C2×#11745685C2312yes—
104C22×Dic118C2311yescharacteristic
105C22×D236C2311yescharacteristic
106C22×C22⋊D59—21no—
107C22×C22⋊D59—21no—
108C22×C22⋊D59—21no—
109C22×C4×D59—21no—
110#14273747—48no—
111C2×#11745672C2314yescomplemented
112C2×#11745670C2314yescomplemented
113C2×#11745671C2314yescomplemented
114C2×#11745669C2314yescomplemented
115C2×#11745664—44no—
116C2×#11745664C2312yes—
117C2×#11745664C2314yes—
118C2×#11745664C2312yes—
119C22×C59⋊C8C2314yes—
120#14273710—22no—
121#14273710—22no—
122#14273710—22no—
123#14273710—22no—
124#14273706—21no—
125#14273706—21no—
126#14273706—21no—
127#14273706—21no—
128#14273706C2312yes—
129#14273706C2312yes—
130#14273706C2312yes—
131#14273706C2312yes—
132#14273701—21no—
133#14273701—21no—
134#14273701—21no—
135#14273701—21no—
136#14273701C2312yes—
137#14273701C2312yes—
138#14273701C2312yes—
139#14273701C2312yes—
140#14273696—22no—
141#14273696—22no—
142#14273696—22no—
143#14273696—22no—
144C4×C22⋊D59—22no—
145C4×C22⋊D59—22no—
146C4×C22⋊D59—22no—
147C4×C22⋊D59—22no—
148C4×C22⋊D59—22no—
149C4×C22⋊D59—22no—
150C4×C22⋊D59—22no—
151C4×C22⋊D59—22no—
152#14273686—21no—
153#14273686—21no—
154#14273686C2312yes—
155#14273686C2312yes—
156C2×C4⋊Dic59C2311yescharacteristic
157C2×C4⋊Dic59C2311yescharacteristic
158C2×Dic59⋊C4—21no—
159C2×Dic59⋊C4—21no—
160C2×C22⋊Dic59—21no—
161C2×C22⋊Dic59—21no—
162C2×C22⋊Dic59—21no—
163C2×(C2×D59)⋊C4—21no—
164C2×(C2×D59)⋊C4—21no—
165C2×C4×Dic59—21no—
166#14273660C2314yescomplemented
167#14273660C2314yescomplemented
168#14273658C2314yescomplemented
169#14273658C2314yescomplemented
170#14273651C2314yescomplemented
171#14273651C2314yescomplemented
172#14273650C2314yescomplemented
173#14273650C2314yescomplemented
174#14273648C2314yescomplemented
175#14273648C2314yescomplemented
176#14273647C2314yescomplemented
177#14273647C2314yescomplemented
178C22⋊(C59⋊C8)C2312yes—
179C22⋊(C59⋊C8)C2312yes—
180C22⋊(C59⋊C8)C2312yes—
181C22⋊(C59⋊C8)C2312yes—
182C22⋊(C59⋊C8)C2314yes—
183C22⋊(C59⋊C8)C2314yes—
184C25×C59D411yescharacteristic
185C2×#41×C59—21no—
186C2×#41×C59—21no—
187C2×#41×C59—44no—
188C2×#41×C59C2312yes—
189C2×#41×C59C2312yes—
190C22×Q8×C59C2311yescharacteristic
191C22×D4×C59—21no—
192C22×D4×C59—21no—
193C22×D4×C59—21no—
194C22×D4×C59C2311yescharacteristic
195C23×C4×C59—21no—
196C23×C4×C59—44no—
197C23×C4×C59D411yescharacteristic
198C23×C4×C59D411yescharacteristic
199C23×C4×C59D411yescharacteristic
200C23×C4×C59D411yescharacteristic
201C23×C4×C59D411yescharacteristic
202C23×C4×C59D411yescharacteristic
203C23×C4×C59D411yescharacteristic
204C23×C4×C59C2311yescharacteristic
205C23×C4×C59C2311yescharacteristic
206C23×C4×C59C2311yescharacteristic
207C23×C4×C59C2311yescharacteristic
208C23×C4×C59C2311yescharacteristic
209C23×C4×C59C2311yescharacteristic
210C23×C4×C59C2311yescharacteristic
211#123×C59—22no—
212#123×C59—22no—
213#123×C59—22no—
214#123×C59—22no—
215C22⋊Q8×C59—21no—
216C22⋊Q8×C59—21no—
217C22⋊Q8×C59—21no—
218C22⋊Q8×C59—21no—
219C22⋊Q8×C59C2312yes—
220C22⋊Q8×C59C2312yes—
221C22⋊Q8×C59C2312yes—
222C22⋊Q8×C59C2312yes—
223#121×C59—21no—
224#121×C59—21no—
225#121×C59—21no—
226#121×C59—21no—
227#121×C59C2312yes—
228#121×C59C2312yes—
229#121×C59C2312yes—
230#121×C59C2312yes—
231#120×C59—22no—
232#120×C59—22no—
233#120×C59—22no—
234#120×C59—22no—
235C4×D4×C59—22no—
236C4×D4×C59—22no—
237C4×D4×C59—22no—
238C4×D4×C59—22no—
239C4×D4×C59—22no—
240C4×D4×C59—22no—
241C4×D4×C59—22no—
242C4×D4×C59—22no—
243#117×C59—21no—
244#117×C59—21no—
245#117×C59C2312yes—
246#117×C59C2312yes—
247C2×C4⋊C4×C59—21no—
248C2×C4⋊C4×C59—21no—
249C2×C4⋊C4×C59C2311yescharacteristic
250C2×C4⋊C4×C59C2311yescharacteristic
251C2×C22⋊C4×C59—21no—
252C2×C22⋊C4×C59—21no—
253C2×C22⋊C4×C59—21no—
254C2×C22⋊C4×C59—21no—
255C2×C22⋊C4×C59—21no—
256C2×C42×C59—21no—
257C24×C59—21no—
258C24×C59—42no—
259C24×C59—42no—
260C24×C59—42no—
261C24×C59C2×D411yescharacteristic
262C24×C59C2×D411yescharacteristic
263C24×C59C2×D411yescharacteristic
264C24×C59C2×D411yescharacteristic
265C24×C59C2×D411yescharacteristic
266C24×C59C2×D411yescharacteristic
267C24×C59C2×D411yescharacteristic
268C23×D59—21no—
269#41×C59—28no—
270#41×C59—44no—
271#41×C59—44no—
272#41×C59—44no—
273C2×Q8×C59—21no—
274C2×Q8×C59—42no—
275C2×Q8×C59C2412yes—
276C2×D4×C59—22no—
277C2×D4×C59—22no—
278C2×D4×C59—22no—
279C2×D4×C59—22no—
280C2×D4×C59—22no—
281C2×D4×C59—22no—
282C2×D4×C59—21no—
283C2×D4×C59—42no—
284C2×D4×C59—44no—
285C2×D4×C59—44no—
286C2×D4×C59—44no—
287C2×D4×C59C2412yes—
288C22×C4×C59—24no—
289C22×C4×C59—24no—
290C22×C4×C59—24no—
291C22×C4×C59—21no—
292C22×C4×C59—21no—
293C22×C4×C59—21no—
294C22×C4×C59—22no—
295C22×C4×C59—22no—
296C22×C4×C59—42no—
297C22×C4×C59—42no—
298C22×C4×C59—42no—
299C22×C4×C59—42no—
300C22×C4×C59—42no—
301C22×C4×C59—42no—
302C22×C4×C59—42no—
303C22×C4×C59—42no—
304C22×C4×C59—42no—
305C22×C4×C59—42no—
306C22×C4×C59—42no—
307C22×C4×C59—44no—
308C22×C4×C59C2×D411yescharacteristic
309C22×C4×C59C2×D411yescharacteristic
310C22×C4×C59C2×D411yescharacteristic
311C22×C4×C59C2×D411yescharacteristic
312C22×C4×C59C2×D411yescharacteristic
313C22×C4×C59C2×D411yescharacteristic
314C22×C4×C59C2×D411yescharacteristic
315C22×C4×C59C2×D411yescharacteristic
316C22×C4×C59C2×D411yescharacteristic
317C22×C4×C59C2×D411yescharacteristic
318C22×C4×C59C2×D411yescharacteristic
319C22×C4×C59C2×D411yescharacteristic
320C22×C4×C59C2×D411yescharacteristic
321C22×C4×C59C2×D411yescharacteristic
322C22×C4×C59C2×D411yescharacteristic
323C22×C4×C59C2×D411yescharacteristic
324C22×C4×C59C2×D411yescharacteristic
325C22×C4×C59C2×D411yescharacteristic
326C22×C4×C59C2×D411yescharacteristic
327C22×C4×C59C2×D411yescharacteristic
328C22×C4×C59C2×D411yescharacteristic
329C22×C4×C59C2411yescharacteristic
330C22×C4×C59C2411yescharacteristic
331C22×C4×C59C2411yescharacteristic
332C22×C4×C59C2411yescharacteristic
333C22×C4×C59C2411yescharacteristic
334C22×C4×C59C2411yescharacteristic
335C22×C4×C59C2411yescharacteristic
336C2×C22⋊D59—22no—
337C2×C22⋊D59—22no—
338C2×C22⋊D59—22no—
339C2×C22⋊D59—22no—
340C2×C22⋊D59—22no—
341C2×C22⋊D59—22no—
342C2×C22⋊D59—44no—
343C2×C22⋊D59—44no—
344C2×C22⋊D59—44no—
345C22×Dic59—21no—
346C22×Dic59—21no—
347C22×Dic59—21no—
348#11745685—28no—
349#11745685—44no—
350#11745685—44no—
351#11745685—44no—
352C2×D236—21no—
353C2×D236—42no—
354C2×D236C2412yes—
355C2×C4×D59—22no—
356C2×C4×D59—22no—
357C2×C4×D59—44no—
358C2×Dic118—21no—
359C2×Dic118—42no—
360C2×Dic118C2412yes—
361C4⋊C4×C59—22no—
362C4⋊C4×C59—22no—
363C4⋊C4×C59—22no—
364C4⋊C4×C59—22no—
365C4⋊C4×C59—21no—
366C4⋊C4×C59—21no—
367C4⋊C4×C59C2412yes—
368C4⋊C4×C59C2412yes—
369C22⋊C4×C59—22no—
370C22⋊C4×C59—22no—
371C22⋊C4×C59—22no—
372C22⋊C4×C59—22no—
373C22⋊C4×C59—22no—
374C22⋊C4×C59—22no—
375C22⋊C4×C59—22no—
376C22⋊C4×C59—22no—
377C22⋊C4×C59—22no—
378C22⋊C4×C59—22no—
379C42×C59—22no—
380C42×C59—22no—
381C22⋊Dic59—22no—
382C22⋊Dic59—22no—
383C22⋊Dic59—22no—
384C22⋊Dic59—22no—
385C22⋊Dic59—22no—
386C22⋊Dic59—22no—
387#11745672—44no—
388#11745671—44no—
389#11745670—44no—
390#11745669—44no—
391(C2×D59)⋊C4—22no—
392(C2×D59)⋊C4—22no—
393(C2×D59)⋊C4—22no—
394(C2×D59)⋊C4—22no—
395C4⋊Dic59—21no—
396C4⋊Dic59—21no—
397C4⋊Dic59C2412yes—
398C4⋊Dic59C2412yes—
399Dic59⋊C4—22no—
400Dic59⋊C4—22no—
401Dic59⋊C4—22no—
402Dic59⋊C4—22no—
403C4×Dic59—22no—
404C4×Dic59—22no—
405#11745664—42no—
406#11745664—44no—
407#11745664—42no—
408C2×C59⋊C8—28no—
409C2×C59⋊C8C2414yes—
410C2×C59⋊C8C2414yes—
411C23×C59—22no—
412C23×C59—22no—
413C23×C59—22no—
414C23×C59—22no—
415C23×C59—22no—
416C23×C59—22no—
417C23×C59—22no—
418C23×C59—22no—
419C23×C59—22no—
420C23×C59—22no—
421C23×C59—41no—
422C23×C59—41no—
423C23×C59—41no—
424C23×C59—41no—
425C23×C59—41no—
426C23×C59—41no—
427C23×C59—41no—
428C23×C59—41no—
429C23×C59—41no—
430C23×C59—41no—
431C23×C59—41no—
432C23×C59—41no—
433C23×C59—42no—
434C23×C59—42no—
435C23×C59—416no—
436C23×C59—42no—
437C23×C59C22×D411yescharacteristic
438C23×C59C22×D411yescharacteristic
439C23×C59C22×D411yescharacteristic
440C23×C59C22×D411yescharacteristic
441C23×C59C22×D411yescharacteristic
442C23×C59C22×D411yescharacteristic
443C23×C59C22×D411yescharacteristic
444C22×D59—22no—
445C22×D59—42no—
446C22×D59—42no—
447C22×D59—42no—
448Q8×C59—24no—
449Q8×C59—42no—
450D4×C59—24no—
451D4×C59—42no—
452D4×C59—44no—
453D4×C59—44no—
454D4×C59—44no—
455D4×C59—44no—
456D4×C59—44no—
457D4×C59—44no—
458C2×C4×C59—22no—
459C2×C4×C59—22no—
460C2×C4×C59—22no—
461C2×C4×C59—22no—
462C2×C4×C59—22no—
463C2×C4×C59—22no—
464C2×C4×C59—22no—
465C2×C4×C59—22no—
466C2×C4×C59—22no—
467C2×C4×C59—22no—
468C2×C4×C59—22no—
469C2×C4×C59—22no—
470C2×C4×C59—22no—
471C2×C4×C59—22no—
472C2×C4×C59—22no—
473C2×C4×C59—22no—
474C2×C4×C59—22no—
475C2×C4×C59—22no—
476C2×C4×C59—41no—
477C2×C4×C59—41no—
478C2×C4×C59—41no—
479C2×C4×C59—41no—
480C2×C4×C59—41no—
481C2×C4×C59—41no—
482C2×C4×C59—41no—
483C2×C4×C59—41no—
484C2×C4×C59—41no—
485C2×C4×C59—41no—
486C2×C4×C59—41no—
487C2×C4×C59—41no—
488C2×C4×C59—44no—
489C2×C4×C59—42no—
490C2×C4×C59—42no—
491C2×C4×C59—42no—
492C2×C4×C59—44no—
493C2×C4×C59C22×D411yescharacteristic
494C2×C4×C59C22×D411yescharacteristic
495C2×C4×C59C22×D411yescharacteristic
496C2×C4×C59C22×D411yescharacteristic
497C2×C4×C59C22×D411yescharacteristic
498C2×C4×C59C22×D411yescharacteristic
499C2×C4×C59C22×D411yescharacteristic
500C2×C4×C59H(5,𝔽2)14yes—
501C2×C4×C59C2511yescharacteristic
502C22⋊D59—44no—
503C22⋊D59—44no—
504C22⋊D59—44no—
505C22⋊D59—44no—
506C22⋊D59—44no—
507C22⋊D59—44no—
508C2×Dic59—22no—
509C2×Dic59—22no—
510C2×Dic59—22no—
511C2×Dic59—42no—
512C2×Dic59—42no—
513C2×Dic59—42no—
514D236—24no—
515D236—42no—
516C4×D59—44no—
517C4×D59—44no—
518Dic118—24no—
519Dic118—42no—
520C59⋊C8—24no—
521C59⋊C8—24no—
522#60741—591nomaximal, Sylow
523C22×C59—21no—
524C22×C59—21no—
525C22×C59—21no—
526C22×C59—21no—
527C22×C59—21no—
528C22×C59—21no—
529C22×C59—21no—
530C22×C59—21no—
531C22×C59—21no—
532C22×C59—21no—
533C22×C59—21no—
534C22×C59—21no—
535C22×C59—21no—
536C22×C59—21no—
537C22×C59—21no—
538C22×C59—21no—
539C22×C59—21no—
540C22×C59—21no—
541C22×C59—44no—
542C22×C59—44no—
543C22×C59—44no—
544C22×C59—44no—
545C22×C59—44no—
546C22×C59—44no—
547C22×C59—44no—
548C22×C59—42no—
549C22×C59—42no—
550C22×C59—42no—
551C22×C59—84no—
552C22×C59#53412yes—
553C22×C59#57512yes—
554C22×C59#57512yes—
555C22×C59C23×D411yescharacteristic
556C2×D59—42no—
557C2×D59—42no—
558C2×D59—42no—
559C2×D59—84no—
560C4×C59—21no—
561C4×C59—21no—
562C4×C59—21no—
563C4×C59—21no—
564C4×C59—21no—
565C4×C59—21no—
566C4×C59—42no—
567C4×C59—42no—
568C4×C59—42no—
569C4×C59#53412yes—
570C4×C59C2×H(5,𝔽2)12yes—
571Dic59—42no—
572Dic59—42no—
573Dic59—42no—
574C2×#525—591no—
575C2×#525D5911yescharacteristic, complemented
576#3197—594no—
577#3196—592no—
578#3196—592no—
579#3195—591no—
580#3194—592no—
581#3194—592no—
582#3193—591no—
583#3193—591no—
584#3192—591no—
585#3091—592no—
586#3091—592no—
587#3054—594no—
588#3002—592no—
589#3002—592no—
590C2×#407—591no—
591C2×C59—22no—
592C2×C59—22no—
593C2×C59—22no—
594C2×C59—41no—
595C2×C59—41no—
596C2×C59—41no—
597C2×C59—41no—
598C2×C59—82no—
599C2×C59C2×#53411yescharacteristic
600C2×C59C2×#57511yescharacteristic
601C2×C59C2×#57511yescharacteristic
602D59—82no—
603C22×#41—591no—
604C22×#41C2×D5911yescharacteristic, complemented
605C24×C4C2×D5911yescharacteristic
606C2×#135—594no—
607C22×M16—592no—
608#525—21no—
609#525—21no—
610#525—21no—
611#525—21no—
612#525—592no—
613#525—592no—
614#525—592no—
615#525—592no—
616#525—1181no—
617#525—1181no—
618#525—1181no—
619#525—1181no—
620#525C2×D5912yes—
621#525C2×D5912yes—
622#525C2×D5912yescomplemented
623#525C2×D5912yescomplemented
624C2×#123—21no—
625C2×#123—1181no—
626C2×C22⋊Q8—591no—
627C2×C22⋊Q8—591no—
628C2×C22⋊Q8C2×D5911yescharacteristic
629C2×C22⋊Q8C2×D5911yescharacteristic, complemented
630C2×#121—591no—
631C2×#121—591no—
632C2×#121C2×D5911yescharacteristic
633C2×#121C2×D5911yescharacteristic, complemented
634C2×#120—21no—
635C2×#120—1181no—
636C2×C4×D4—21no—
637C2×C4×D4—21no—
638C2×C4×D4—1181no—
639C2×C4×D4—1181no—
640C2×#117—591no—
641C2×#117C2×D5911yescharacteristic, complemented
642#485—594no—
643#485—594no—
644#484—592no—
645#484—592no—
646#483—592no—
647#483—592no—
648#482—594no—
649#482—594no—
650#481—592no—
651#481—592no—
652#480—592no—
653#480—592no—
654#470—594no—
655#470—594no—
656#469—594no—
657#469—594no—
658#468—594no—
659#468—594no—
660#468—594no—
661#468—594no—
662#452—594no—
663#452—594no—
664#451—592no—
665#451—592no—
666#450—592no—
667#450—592no—
668#449—594no—
669#449—594no—
670#448—592no—
671#448—592no—
672#447—592no—
673#447—592no—
674#427—594no—
675#416—594no—
676#416—594no—
677#407—591no—
678#407—591no—
679#407—592no—
680#407—592no—
681#407—592no—
682C2×C22⋊C8—592no—
683C2×C22⋊C8—592no—
684C59#6074111yescharacteristic, complemented, Sylow
685C25C22⋊D5911yescharacteristic
686C2×#41—21no—
687C2×#41—21no—
688C2×#41—44no—
689C2×#41—592no—
690C2×#41—592no—
691C2×#41—1181no—
692C2×#41—1181no—
693C2×#41—2364no—
694C2×#41C22×D5912yes—
695C2×#41C22×D5912yes—
696C22×Q8—591no—
697C22×Q8C22×D5911yescharacteristic
698C22×D4—21no—
699C22×D4—21no—
700C22×D4—21no—
701C22×D4—591no—
702C22×D4—1181no—
703C22×D4—1181no—
704C22×D4—1181no—
705C22×D4C22×D5911yescharacteristic
706C23×C4—21no—
707C23×C4—44no—
708C23×C4—1181no—
709C23×C4C22⋊D5911yescharacteristic
710C23×C4C22⋊D5911yescharacteristic
711C23×C4C22⋊D5911yescharacteristic
712C23×C4C22⋊D5911yescharacteristic
713C23×C4C22⋊D5911yescharacteristic
714C23×C4C22⋊D5911yescharacteristic
715C23×C4C22⋊D5911yescharacteristic
716C23×C4C22×D5911yescharacteristic
717C23×C4C22×D5911yescharacteristic
718C23×C4C22×D5911yescharacteristic
719C23×C4C22×D5911yescharacteristic
720C23×C4C22×D5911yescharacteristic
721C23×C4C22×D5911yescharacteristic
722C23×C4C22×D5911yescharacteristic
723#135—2368no—
724C2×Q16—594no—
725C2×SD16—594no—
726C2×SD16—594no—
727C2×D8—594no—
728C2×M16—592no—
729C2×M16—594no—
730C2×M16—592no—
731C2×M16—2364no—
732C22×C8—594no—
733#123—22no—
734#123—22no—
735#123—22no—
736#123—22no—
737#123—1182no—
738#123—1182no—
739#123—1182no—
740#123—1182no—
741C22⋊Q8—21no—
742C22⋊Q8—21no—
743C22⋊Q8—21no—
744C22⋊Q8—21no—
745C22⋊Q8—592no—
746C22⋊Q8—592no—
747C22⋊Q8—592no—
748C22⋊Q8—592no—
749C22⋊Q8—1181no—
750C22⋊Q8—1181no—
751C22⋊Q8—1181no—
752C22⋊Q8—1181no—
753C22⋊Q8C22×D5912yes—
754C22⋊Q8C22×D5912yes—
755C22⋊Q8C22×D5912yes—
756C22⋊Q8C22×D5912yes—
757#121—21no—
758#121—21no—
759#121—21no—
760#121—21no—
761#121—592no—
762#121—592no—
763#121—592no—
764#121—592no—
765#121—1181no—
766#121—1181no—
767#121—1181no—
768#121—1181no—
769#121C22×D5912yes—
770#121C22×D5912yes—
771#121C22×D5912yes—
772#121C22×D5912yes—
773#120—22no—
774#120—22no—
775#120—22no—
776#120—22no—
777#120—1182no—
778#120—1182no—
779#120—1182no—
780#120—1182no—
781C4×D4—22no—
782C4×D4—22no—
783C4×D4—22no—
784C4×D4—22no—
785C4×D4—22no—
786C4×D4—22no—
787C4×D4—22no—
788C4×D4—22no—
789C4×D4—1182no—
790C4×D4—1182no—
791C4×D4—1182no—
792C4×D4—1182no—
793C4×D4—1182no—
794C4×D4—1182no—
795C4×D4—1182no—
796C4×D4—1182no—
797#117—21no—
798#117—21no—
799#117—592no—
800#117—592no—
801#117—1181no—
802#117—1181no—
803#117C22×D5912yes—
804#117C22×D5912yes—
805C2×C4⋊C4—21no—
806C2×C4⋊C4—21no—
807C2×C4⋊C4—591no—
808C2×C4⋊C4—591no—
809C2×C4⋊C4—1181no—
810C2×C4⋊C4—1181no—
811C2×C4⋊C4C22×D5911yescharacteristic
812C2×C4⋊C4C22×D5911yescharacteristic
813C2×C22⋊C4—21no—
814C2×C22⋊C4—21no—
815C2×C22⋊C4—21no—
816C2×C22⋊C4—21no—
817C2×C22⋊C4—21no—
818C2×C22⋊C4—1181no—
819C2×C22⋊C4—1181no—
820C2×C22⋊C4—1181no—
821C2×C22⋊C4—1181no—
822C2×C22⋊C4—1181no—
823C2×C42—21no—
824C2×C42—1181no—
825#107—594no—
826#107—594no—
827#106—594no—
828#106—594no—
829#103—594no—
830#103—594no—
831#103—594no—
832#103—594no—
833#102—594no—
834#102—594no—
835#102—594no—
836#102—594no—
837C22⋊C8—592no—
838C22⋊C8—592no—
839C22⋊C8—592no—
840C22⋊C8—592no—
841C22⋊C8—594no—
842C22⋊C8—594no—
843C24—21no—
844C24—42no—
845C24—42no—
846C24—42no—
847C24—1181no—
848C24C2×C22⋊D5911yescharacteristic
849C24C2×C22⋊D5911yescharacteristic
850C24C2×C22⋊D5911yescharacteristic
851C24C2×C22⋊D5911yescharacteristic
852C24C2×C22⋊D5911yescharacteristic
853C24C2×C22⋊D5911yescharacteristic
854C24C2×C22⋊D5911yescharacteristic
855#41—28no—
856#41—44no—
857#41—44no—
858#41—44no—
859#41—1188no—
860#41—2364no—
861#41—2364no—
862#41—2364no—
863C2×Q8—21no—
864C2×Q8—42no—
865C2×Q8—592no—
866C2×Q8—1181no—
867C2×Q8—2362no—
868C2×Q8C23×D5912yes—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—21no—
876C2×D4—42no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—592no—
881C2×D4—1182no—
882C2×D4—1182no—
883C2×D4—1182no—
884C2×D4—1182no—
885C2×D4—1182no—
886C2×D4—1182no—
887C2×D4—1181no—
888C2×D4—2362no—
889C2×D4—2364no—
890C2×D4—2364no—
891C2×D4—2364no—
892C2×D4C23×D5912yes—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—44no—
913C22×C4—1181no—
914C22×C4—1181no—
915C22×C4—1181no—
916C22×C4—1182no—
917C22×C4—1182no—
918C22×C4—2364no—
919C22×C4C2×C22⋊D5911yescharacteristic
920C22×C4C2×C22⋊D5911yescharacteristic
921C22×C4C2×C22⋊D5911yescharacteristic
922C22×C4C2×C22⋊D5911yescharacteristic
923C22×C4C2×C22⋊D5911yescharacteristic
924C22×C4C2×C22⋊D5911yescharacteristic
925C22×C4C2×C22⋊D5911yescharacteristic
926C22×C4C2×C22⋊D5911yescharacteristic
927C22×C4C2×C22⋊D5911yescharacteristic
928C22×C4C2×C22⋊D5911yescharacteristic
929C22×C4C2×C22⋊D5911yescharacteristic
930C22×C4C2×C22⋊D5911yescharacteristic
931C22×C4C2×C22⋊D5911yescharacteristic
932C22×C4C2×C22⋊D5911yescharacteristic
933C22×C4C2×C22⋊D5911yescharacteristic
934C22×C4C2×C22⋊D5911yescharacteristic
935C22×C4C2×C22⋊D5911yescharacteristic
936C22×C4C2×C22⋊D5911yescharacteristic
937C22×C4C2×C22⋊D5911yescharacteristic
938C22×C4C2×C22⋊D5911yescharacteristic
939C22×C4C2×C22⋊D5911yescharacteristic
940C22×C4C23×D5911yescharacteristic
941C22×C4C23×D5911yescharacteristic
942C22×C4C23×D5911yescharacteristic
943C22×C4C23×D5911yescharacteristic
944C22×C4C23×D5911yescharacteristic
945C22×C4C23×D5911yescharacteristic
946C22×C4C23×D5911yescharacteristic
947Q16—2364no—
948SD16—2364no—
949SD16—2364no—
950D8—2364no—
951M16—2362no—
952M16—2364no—
953M16—2362no—
954C2×C8—594no—
955C2×C8—594no—
956C2×C8—1188no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—592no—
964C4⋊C4—592no—
965C4⋊C4—1181no—
966C4⋊C4—1181no—
967C4⋊C4—1182no—
968C4⋊C4—1182no—
969C4⋊C4—1182no—
970C4⋊C4—1182no—
971C4⋊C4C23×D5912yes—
972C4⋊C4C23×D5912yes—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—1182no—
984C22⋊C4—1182no—
985C22⋊C4—1182no—
986C22⋊C4—1182no—
987C22⋊C4—1182no—
988C22⋊C4—1182no—
989C22⋊C4—1182no—
990C22⋊C4—1182no—
991C22⋊C4—1182no—
992C22⋊C4—1182no—
993C42—22no—
994C42—22no—
995C42—1182no—
996C42—1182no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—42no—
1020C23—42no—
1021C23—416no—
1022C23—42no—
1023C23—1182no—
1024C23—2362no—
1025C23—2362no—
1026C23—2362no—
1027C23C22×C22⋊D5911yescharacteristic
1028C23C22×C22⋊D5911yescharacteristic
1029C23C22×C22⋊D5911yescharacteristic
1030C23C22×C22⋊D5911yescharacteristic
1031C23C22×C22⋊D5911yescharacteristic
1032C23C22×C22⋊D5911yescharacteristic
1033C23C22×C22⋊D5911yescharacteristic
1034Q8—24no—
1035Q8—42no—
1036Q8—1184no—
1037Q8—2362no—
1038D4—24no—
1039D4—42no—
1040D4—44no—
1041D4—44no—
1042D4—44no—
1043D4—44no—
1044D4—44no—
1045D4—44no—
1046D4—1184no—
1047D4—2362no—
1048D4—2364no—
1049D4—2364no—
1050D4—2364no—
1051D4—2364no—
1052D4—2364no—
1053D4—2364no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—44no—
1085C2×C4—42no—
1086C2×C4—42no—
1087C2×C4—42no—
1088C2×C4—44no—
1089C2×C4—1182no—
1090C2×C4—1182no—
1091C2×C4—1182no—
1092C2×C4—2364no—
1093C2×C4—2362no—
1094C2×C4—2362no—
1095C2×C4—2362no—
1096C2×C4—2364no—
1097C2×C4C22×C22⋊D5911yescharacteristic
1098C2×C4C22×C22⋊D5911yescharacteristic
1099C2×C4C22×C22⋊D5911yescharacteristic
1100C2×C4C22×C22⋊D5911yescharacteristic
1101C2×C4C22×C22⋊D5911yescharacteristic
1102C2×C4C22×C22⋊D5911yescharacteristic
1103C2×C4C22×C22⋊D5911yescharacteristic
1104C2×C4#1427377214yes—
1105C2×C4C24×D5911yescharacteristic
1106C8—1184no—
1107C8—1184no—
1108C22—21no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—44no—
1127C22—44no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22—44no—
1132C22—44no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—84no—
1137C22—4724no—
1138C22—2362no—
1139C22—2362no—
1140C22—2362no—
1141C22#1683796112yes—
1142C22#1683820012yes—
1143C22#1683820012yes—
1144C22C23×C22⋊D5911yescharacteristic
1145C4—21no—
1146C4—21no—
1147C4—21no—
1148C4—21no—
1149C4—21no—
1150C4—21no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—2362no—
1155C4—2362no—
1156C4—2362no—
1157C4#1683796112yes—
1158C4C2×#1427377212yes—
1159C2—22no—
1160C2—22no—
1161C2—22no—
1162C2—41no—
1163C2—41no—
1164C2—41no—
1165C2—41no—
1166C2—82no—
1167C2—4722no—
1168C2C2×#1683796111yescharacteristic
1169C2C2×#1683820011yescharacteristic
1170C2C2×#1683820011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#525C2
socleC22×C59C23×D4
hypercenterC2×#525D59
hypocenterC59#60741
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#16837913C2semidirect
2. #21434933C2semidirect
3. #21434926C2semidirect
4. #21434922C2semidirect
5. #21434917C2semidirect
6. #21434910C2semidirect
7. #21434906C2semidirect
8. #21434902C2semidirect
9. #21434898C2semidirect
10. #21434893C2semidirect
11. #21434009C2semidirect
12. #21434005C2semidirect
13. #21433702C2semidirect
14. #21433314C2semidirect
15. #21433312C2semidirect
16. C2×#16837366C2semidirect
17. C2×C59×#525C2semidirect
18. C22×#11745685C22semidirect
19. C2×#14273747C22semidirect
20. C22×#11745664C22semidirect
27. #16837913C22semidirect
28. #16837913C22semidirect
31. C2×#14273706C22semidirect
33. C2×#14273701C22semidirect
37. C2×#14273686C22semidirect
38. #16837743C22semidirect
39. #16837740C22semidirect
40. #16837737C22semidirect
41. #16837735C22semidirect
42. #16837732C22semidirect
43. #16837730C22semidirect
44. #16837726C22semidirect
45. #16837723C22semidirect
46. #16837720C22semidirect
47. #16837718C22semidirect
48. #16837715C22semidirect
49. #16837713C22semidirect
50. #16837658C22semidirect
51. #16837658C22semidirect
52. #16837653C22semidirect
53. #16837653C22semidirect
54. #16837650C22semidirect
55. #16837650C22semidirect
56. #16837646C22semidirect
57. #16837646C22semidirect
58. #16837564C22semidirect
59. #16837562C22semidirect
60. #16837558C22semidirect
61. #16837557C22semidirect
62. #16837553C22semidirect
63. #16837552C22semidirect
64. #16837547C22semidirect
65. #16837545C22semidirect
66. #16837541C22semidirect
67. #16837540C22semidirect
68. #16837536C22semidirect
69. #16837535C22semidirect
70. #16837438C22semidirect
71. #16837398C22semidirect
72. #16837396C22semidirect
75. #16837366C22semidirect
76. #16837366C22semidirect
77. #16837366C22semidirect
78. C2×C22⋊(C59⋊C8)C22semidirect
79. C2×C22⋊(C59⋊C8)C22semidirect
80. C22×#41×C59C22semidirect
88. C59×#525C22semidirect
89. C59×#525C22semidirect
92. C2×C22⋊Q8×C59C22semidirect
94. C2×#121×C59C22semidirect
98. C2×#117×C59C22semidirect
111. C2×#11745672C23semidirect
112. C2×#11745670C23semidirect
113. C2×#11745671C23semidirect
114. C2×#11745669C23semidirect
166. #14273660C23semidirect
167. #14273660C23semidirect
168. #14273658C23semidirect
169. #14273658C23semidirect
170. #14273651C23semidirect
171. #14273651C23semidirect
172. #14273650C23semidirect
173. #14273650C23semidirect
174. #14273648C23semidirect
175. #14273648C23semidirect
176. #14273647C23semidirect
177. #14273647C23semidirect
575. C2×#525D59semidirect
604. C22×#41C2×D59semidirect
622. #525C2×D59semidirect
623. #525C2×D59semidirect
629. C2×C22⋊Q8C2×D59semidirect
633. C2×#121C2×D59semidirect
641. C2×#117C2×D59semidirect
684. C59#60741semidirect

Maximal subgroups

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

subgroupindex
C2×#168379132
#214349332
#214349262
#214349222
#214349172
#214349102
#214349062
#214349022
#214348982
#214348932
#214340092
#214340052
#214337022
#214333142
#214333122
C2×#168373662
C2×C59×#5252
#6074159