Finite Group Databasebeta

← C2×#21436383 #29465579

Subgroups — C2×#21436383 #29465579

Order 15104.

2146 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838116C211yesmaximal, characteristic
2C2×Q8×C22⋊D59C211yesmaximal, characteristic, complemented
3#21436383C2116yesmaximal, direct product factor
4C2×#16837751C211yesmaximal, characteristic, complemented
5C2×#16837744C211yesmaximal, characteristic, complemented
6C2×#16837741C211yesmaximal, characteristic, complemented
7C2×#16837695C211yesmaximal, characteristic, complemented
8C2×#16837646C211yesmaximal, characteristic, complemented
9C2×#16837645C211yesmaximal, characteristic, complemented
10C2×#16837605C211yesmaximal, characteristic, complemented
11C2×#16837539C211yesmaximal, characteristic, complemented
12C2×SD16×Dic59C211yesmaximal, characteristic, complemented
13C2×#16837477C211yesmaximal, characteristic, complemented
14C2×#16837411C211yesmaximal, characteristic, complemented
15C2×#16837409C211yesmaximal, characteristic, complemented
16C2×C59×#448C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×#11745670C2211yescharacteristic
19C22×#11745664C2211yescharacteristic
20C22×#11745659C2211yescharacteristic
21#16838116—24no—
22#16838116C2218yes—
23Q8×C22⋊D59—24no—
24Q8×C22⋊D59C2218yescomplemented
25C2×#14273726C2211yescharacteristic
26C2×#14273725—21no—
27C2×#14273725C2211yescharacteristic
28C2×#14273714—21no—
29C2×#14273713—21no—
30C2×#14273706—21no—
31C2×#14273706C2211yescharacteristic
32C2×#14273703—21no—
33C2×#14273703C2211yescharacteristic
34C2×#14273699—21no—
35C2×#14273698C2211yescharacteristic
36C2×Q8×Dic59C2211yescharacteristic
37C2×D4×Dic59C2211yescharacteristic
38C2×C4×C22⋊D59—21no—
39C2×C4×C22⋊D59C2211yescharacteristic
40C2×#14273686C2211yescharacteristic
41C2×#14273685C2211yescharacteristic
42C2×#14273683—21no—
43#16837751C2218yescomplemented
44#16837744C2218yescomplemented
45#16837741C2218yescomplemented
46#16837695C2218yescomplemented
47#16837646C2218yescomplemented
48#16837645C2218yescomplemented
49#16837605C2218yescomplemented
50#16837539C2218yescomplemented
51SD16×Dic59C2218yescomplemented
52#16837477C2218yescomplemented
53C2×#14273661C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273659C2211yescharacteristic
56C2×Dic59⋊C8C2211yescharacteristic
57#16837411C2218yescomplemented
58#16837409C2218yescomplemented
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273651C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66C2×#14273648C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C23×Q8×C59C2211yescharacteristic
70C22×SD16×C59C2211yescharacteristic
71C22×SD16×C59C2211yescharacteristic
72C2×#121×C59C2211yescharacteristic
73C59×#448C2218yescomplemented
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C2×Q8×D59—22no—
81C2×Q8×D59—24no—
82C2×Q8×D59—42no—
83C2×Q8×D59C2314yes—
84C22×C22⋊D59—21no—
85C22×C22⋊D59D411yescharacteristic
86C23×Dic59—21no—
87C22×C4×D59—21no—
88C22×C4×D59C2311yescharacteristic
89C2×#11745670—42no—
90C2×#11745670C2314yes—
91C2×#11745664—42no—
92C2×#11745664C2314yes—
93C2×#11745659—42no—
94C2×#11745659C2314yes—
95C22×C59⋊C8C2311yescharacteristic
96C22×C59⋊C8C2311yescharacteristic
97#14273726—22no—
98#14273726C2314yes—
99#14273725—28no—
100#14273725—22no—
101#14273725C2314yes—
102#14273714—28no—
103#14273713—28no—
104#14273706—22no—
105#14273706—28no—
106#14273706C2314yes—
107#14273703—22no—
108#14273703—28no—
109#14273703C2314yes—
110#14273699—28no—
111#14273698—22no—
112#14273698C2314yes—
113Q8×Dic59—22no—
114Q8×Dic59C2314yes—
115D4×Dic59—22no—
116D4×Dic59C2314yes—
117C4×C22⋊D59—28no—
118C4×C22⋊D59D414yes—
119C4×C22⋊D59C2314yes—
120#14273686—22no—
121#14273686C2314yes—
122#14273685—22no—
123#14273685C2314yes—
124#14273683—28no—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4D411yescharacteristic
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59D411yescharacteristic
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4D411yescharacteristic
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273661C2314yes—
148#14273660C2314yes—
149#14273659C2314yes—
150Dic59⋊C8C2314yes—
151#14273652C2314yes—
152#14273652C2314yes—
153#14273651C2314yes—
154#14273651C2314yes—
155#14273651C2314yes—
156#14273651C2314yes—
157#14273650C2314yes—
158#14273648C2314yes—
159(C2×D59)⋊C8C2314yes—
160C8×Dic59C2314yes—
161C22×Q8×C59—21no—
162C22×Q8×C59—22no—
163C22×Q8×C59—24no—
164C22×Q8×C59—42no—
165C22×Q8×C59C2311yescharacteristic
166C22×Q8×C59C2314yes—
167C22×Q8×C59C2311yescharacteristic
168C22×D4×C59—21no—
169C22×D4×C59C2311yescharacteristic
170C23×C4×C59—21no—
171C23×C4×C59C2311yescharacteristic
172C2×SD16×C59—24no—
173C2×SD16×C59—42no—
174C2×SD16×C59C2314yes—
175C2×SD16×C59C2314yes—
176C22×C8×C59C2311yescharacteristic
177C22×C8×C59C2311yescharacteristic
178#121×C59—22no—
179#121×C59C2314yes—
180C2×C4⋊C4×C59C2311yescharacteristic
181C2×C22⋊C4×C59—21no—
182#103×C59C2314yes—
183#103×C59C2314yes—
184C22⋊C8×C59C2314yes—
185C24×C59—21no—
186C24×C59C2×D411yescharacteristic
187C23×D59C2×D411yescharacteristic
188C2×Q8×C59—21no—
189C2×Q8×C59—24no—
190C2×Q8×C59—21no—
191C2×Q8×C59—22no—
192C2×Q8×C59—28no—
193C2×Q8×C59—22no—
194C2×Q8×C59—22no—
195C2×Q8×C59—44no—
196C2×Q8×C59—44no—
197C2×Q8×C59—48no—
198C2×Q8×C59#4114yes—
199C2×Q8×C59C2412yes—
200C2×Q8×C59C2412yes—
201C2×D4×C59—24no—
202C2×D4×C59—21no—
203C2×D4×C59—22no—
204C2×D4×C59—22no—
205C2×D4×C59—82no—
206C2×D4×C59C2412yes—
207C22×C4×C59—21no—
208C22×C4×C59—22no—
209C22×C4×C59—22no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—24no—
213C22×C4×C59—44no—
214C22×C4×C59C2×D411yescharacteristic
215C22×C4×C59C2×D412yes—
216C22×C4×C59C2412yes—
217C22×C4×C59C2411yescharacteristic
218C2×C22⋊D59—24no—
219C2×C22⋊D59—24no—
220C2×C22⋊D59—82no—
221C2×C22⋊D59C2×D414yes—
222C22×Dic59—21no—
223C22×Dic59—21no—
224C22×Dic59—21no—
225C22×Dic59—21no—
226C22×Dic59—24no—
227C22×Dic59—44no—
228C22×Dic59C2×D411yescharacteristic
229C22×Dic59C2×D411yescharacteristic
230C22×Dic59C2×D411yescharacteristic
231Q8×D59—28no—
232Q8×D59—44no—
233Q8×D59—48no—
234C2×C4×D59—22no—
235C2×C4×D59—22no—
236C2×C4×D59—24no—
237C2×C4×D59—44no—
238C2×C4×D59C2×D412yes—
239C2×C4×D59C2412yes—
240C2×Dic118—22no—
241C2×Dic118—22no—
242C2×Dic118—21no—
243C2×Dic118—24no—
244C2×Dic118—24no—
245C2×Dic118—44no—
246C2×Dic118—82no—
247C2×Dic118C2412yes—
248SD16×C59—28no—
249SD16×C59—44no—
250C2×C8×C59—22no—
251C2×C8×C59—22no—
252C2×C8×C59C2412yes—
253C2×C8×C59C2412yes—
254C4⋊C4×C59—21no—
255C4⋊C4×C59C2412yes—
256C22⋊C4×C59—24no—
257C22⋊Dic59—24no—
258C22⋊Dic59—24no—
259C22⋊Dic59—24no—
260C22⋊Dic59—24no—
261C22⋊Dic59C2×D414yes—
262#11745670—44no—
263(C2×D59)⋊C4—24no—
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4C2×D414yes—
266C4⋊Dic59—21no—
267C4⋊Dic59—21no—
268C4⋊Dic59—21no—
269C4⋊Dic59—24no—
270C4⋊Dic59C2412yes—
271C4⋊Dic59C2412yes—
272C4⋊Dic59C2412yes—
273Dic59⋊C4—24no—
274Dic59⋊C4—24no—
275Dic59⋊C4—24no—
276Dic59⋊C4—24no—
277Dic59⋊C4—24no—
278Dic59⋊C4C2×D414yes—
279C4×Dic59—24no—
280C4×Dic59—24no—
281C4×Dic59—24no—
282C4×Dic59C2×D412yes—
283C4×Dic59C2412yes—
284#11745664—44no—
285C2×C59⋊C8—22no—
286C2×C59⋊C8—22no—
287C2×C59⋊C8C2412yes—
288C2×C59⋊C8C2412yes—
289#11745659—44no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—42no—
295C23×C59—42no—
296C23×C59—42no—
297C23×C59C22×D412yes—
298C23×C59C22×D411yescharacteristic
299C22×D59—22no—
300C22×D59—22no—
301C22×D59—22no—
302C22×D59C22×D412yes—
303Q8×C59—24no—
304Q8×C59—22no—
305Q8×C59—22no—
306Q8×C59—22no—
307Q8×C59—48no—
308Q8×C59—42no—
309Q8×C59C2×#4114yes—
310D4×C59—22no—
311D4×C59—22no—
312D4×C59—42no—
313D4×C59—84no—
314C2×C4×C59—24no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—24no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—48no—
323C2×C4×C59—42no—
324C2×C4×C59—42no—
325C2×C4×C59C22×D412yes—
326C2×C4×C59C22×D411yescharacteristic
327C2×C4×C59C2×#4112yes—
328C2×C4×C59H(5,𝔽2)12yes—
329C2×C4×C59C2511yescharacteristic
330C22⋊D59—28no—
331C22⋊D59—84no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—42no—
339C2×Dic59—42no—
340C2×Dic59—42no—
341C2×Dic59—42no—
342C2×Dic59—48no—
343C2×Dic59#13714yes—
344C2×Dic59C22×D412yes—
345C2×Dic59C22×D412yes—
346C2×Dic59C22×D412yes—
347C4×D59—24no—
348C4×D59—22no—
349C4×D59—22no—
350C4×D59—48no—
351Dic118—22no—
352Dic118—22no—
353Dic118—48no—
354Dic118—42no—
355Dic118—84no—
356C8×C59—22no—
357C8×C59—22no—
358C59⋊C8—22no—
359C59⋊C8—22no—
360C2×#3329—591nomaximal, Sylow
361C22×C59—22no—
362C22×C59—22no—
363C22×C59—22no—
364C22×C59—44no—
365C22×C59—42no—
366C22×C59—42no—
367C22×C59—42no—
368C22×C59—84no—
369C22×C59#54612yes—
370C22×C59C2×#13712yes—
371C22×C59#57712yes—
372C22×C59C23×D411yescharacteristic
373C2×D59—22no—
374C2×D59—22no—
375C2×D59—22no—
376C2×D59—44no—
377C4×C59—24no—
378C4×C59—22no—
379C4×C59—42no—
380C4×C59—42no—
381C4×C59#54612yes—
382C4×C59C22×#4111yescharacteristic
383C4×C59C2×H(5,𝔽2)11yescharacteristic
384Dic59—22no—
385Dic59—22no—
386Dic59—42no—
387Dic59—42no—
388Dic59—42no—
389Dic59—42no—
390Dic59C2×#13714yes—
391C2×#555—591no—
392C2×D4×Q8—591no—
393#3329—5916no—
394C2×#487—591no—
395C2×#485—591no—
396C2×#485—591no—
397C2×#477—591no—
398C2×#468—591no—
399C2×#468—591no—
400C2×#461—591no—
401C2×#448—591no—
402C2×#448D5911yescharacteristic, complemented
403C2×C4×SD16—591no—
404C2×#436—591no—
405C2×#419—591no—
406C2×#419—591no—
407C2×C59—42no—
408C2×C59—82no—
409C2×C59#332914yescomplemented
410C2×C59C2×#54611yescharacteristic
411C2×C59C22×#13711yescharacteristic
412C2×C59C2×#57711yescharacteristic
413D59—42no—
414C23×Q8—591no—
415C23×Q8C2×D5911yescharacteristic
416C22×SD16—591no—
417C22×SD16C2×D5911yescharacteristic
418C22×SD16C2×D5911yescharacteristic
419C22×M16—591no—
420C22×M16—591no—
421#555—598no—
422#555—1184no—
423D4×Q8—598no—
424D4×Q8—1184no—
425C2×C4⋊Q8—591no—
426C2×C4⋊Q8—591no—
427C2×C4⋊Q8—1181no—
428C2×#124—1181no—
429C2×#124—1181no—
430C2×C22⋊Q8—591no—
431C2×C22⋊Q8—591no—
432C2×C22⋊Q8—1181no—
433C2×C22⋊Q8—1181no—
434C2×#121—591no—
435C2×#121—1181no—
436C2×#121C2×D5911yescharacteristic
437C2×C4×Q8—591no—
438C2×C4×D4—591no—
439C2×C4×D4—591no—
440C2×C4×D4—1181no—
441C2×#117—591no—
442C2×#117—591no—
443C2×#117—1181no—
444#487—598no—
445#485—598no—
446#485—598no—
447#477—598no—
448#468—598no—
449#468—598no—
450#461—598no—
451#448—598no—
452#448C2×D5918yescomplemented
453C4×SD16—598no—
454#436—598no—
455C2×#107—591no—
456C2×#107—591no—
457C2×#106—591no—
458C2×C4⋊C8—591no—
459#419—598no—
460#419—598no—
461C2×#103—591no—
462C2×#103—591no—
463C2×#103—591no—
464C2×#103—591no—
465C2×#103—591no—
466C2×#103—591no—
467C2×#103—591no—
468C2×#103C2×D5911yescharacteristic
469C2×#103C2×D5911yescharacteristic
470C2×#102—591no—
471C2×C22⋊C8—591no—
472C2×C22⋊C8C2×D5911yescharacteristic
473C2×C4×C8—591no—
474C59C2×#332911yescharacteristic, complemented, Sylow
475C22×Q8—21no—
476C22×Q8—22no—
477C22×Q8—24no—
478C22×Q8—42no—
479C22×Q8—594no—
480C22×Q8—591no—
481C22×Q8—1181no—
482C22×Q8—1181no—
483C22×Q8—1182no—
484C22×Q8—1184no—
485C22×Q8—2362no—
486C22×Q8C22×D5911yescharacteristic
487C22×Q8C22×D5914yes—
488C22×Q8C22×D5911yescharacteristic
489C22×D4—21no—
490C22×D4—591no—
491C22×D4—1181no—
492C22×D4C22×D5911yescharacteristic
493C23×C4—21no—
494C23×C4—591no—
495C23×C4—1181no—
496C23×C4—1181no—
497C23×C4C22×D5911yescharacteristic
498C2×SD16—24no—
499C2×SD16—42no—
500C2×SD16—594no—
501C2×SD16—2362no—
502C2×SD16C22×D5914yes—
503C2×SD16C22×D5914yes—
504C2×M16—594no—
505C2×M16—594no—
506C2×M16—2362no—
507C2×M16—2362no—
508C22×C8—591no—
509C22×C8—591no—
510C22×C8C22×D5911yescharacteristic
511C22×C8C22×D5911yescharacteristic
512C4⋊Q8—594no—
513C4⋊Q8—594no—
514C4⋊Q8—1182no—
515C4⋊Q8—1182no—
516C4⋊Q8—1188no—
517#124—1188no—
518#124—1188no—
519C22⋊Q8—594no—
520C22⋊Q8—594no—
521C22⋊Q8—1188no—
522C22⋊Q8—1188no—
523C22⋊Q8—1182no—
524C22⋊Q8—1182no—
525#121—22no—
526#121—594no—
527#121—1182no—
528#121—1188no—
529#121C22×D5914yes—
530C4×Q8—594no—
531C4×Q8—1182no—
532C4×D4—594no—
533C4×D4—594no—
534C4×D4—594no—
535C4×D4—1182no—
536C4×D4—1188no—
537#117—594no—
538#117—594no—
539#117—1188no—
540#117—1182no—
541#117—1182no—
542C2×C4⋊C4—591no—
543C2×C4⋊C4—591no—
544C2×C4⋊C4—591no—
545C2×C4⋊C4—591no—
546C2×C4⋊C4—1181no—
547C2×C4⋊C4—1181no—
548C2×C4⋊C4—1181no—
549C2×C4⋊C4—1181no—
550C2×C4⋊C4—1181no—
551C2×C4⋊C4—1181no—
552C2×C4⋊C4C22×D5911yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—591no—
555C2×C22⋊C4—591no—
556C2×C22⋊C4—1181no—
557C2×C22⋊C4—1181no—
558C2×C22⋊C4—1181no—
559C2×C22⋊C4—1181no—
560C2×C22⋊C4—1181no—
561C2×C22⋊C4—1181no—
562C2×C42—591no—
563C2×C42—1181no—
564C2×C42—1181no—
565C2×C42—1181no—
566#107—594no—
567#107—594no—
568#106—594no—
569C4⋊C8—594no—
570#103—594no—
571#103—594no—
572#103—594no—
573#103—594no—
574#103—594no—
575#103—594no—
576#103—594no—
577#103C22×D5914yes—
578#103C22×D5914yes—
579#102—594no—
580C22⋊C8—594no—
581C22⋊C8C22×D5914yes—
582C4×C8—594no—
583C24—21no—
584C24—591no—
585C24D4×D5911yescharacteristic
586C2×Q8—21no—
587C2×Q8—24no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—28no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—44no—
594C2×Q8—44no—
595C2×Q8—48no—
596C2×Q8—592no—
597C2×Q8—1184no—
598C2×Q8—1184no—
599C2×Q8—1181no—
600C2×Q8—1188no—
601C2×Q8—1182no—
602C2×Q8—1182no—
603C2×Q8—4722no—
604C2×Q8—2364no—
605C2×Q8—2364no—
606C2×Q8—2368no—
607C2×Q8#1174568714yes—
608C2×Q8C23×D5912yes—
609C2×Q8C23×D5912yes—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—82no—
615C2×D4—594no—
616C2×D4—1184no—
617C2×D4—1184no—
618C2×D4—4722no—
619C2×D4C23×D5912yes—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—44no—
627C22×C4—591no—
628C22×C4—591no—
629C22×C4—591no—
630C22×C4—592no—
631C22×C4—592no—
632C22×C4—1184no—
633C22×C4—1184no—
634C22×C4—1182no—
635C22×C4—1182no—
636C22×C4—1181no—
637C22×C4—1181no—
638C22×C4—1181no—
639C22×C4—1181no—
640C22×C4—2364no—
641C22×C4—2364no—
642C22×C4D4×D5912yes—
643C22×C4D4×D5911yescharacteristic
644C22×C4C23×D5912yes—
645C22×C4C23×D5911yescharacteristic
646SD16—28no—
647SD16—44no—
648SD16—2364no—
649M16—2364no—
650M16—2364no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—592no—
654C2×C8—592no—
655C2×C8—1182no—
656C2×C8—1182no—
657C2×C8C23×D5912yes—
658C2×C8C23×D5912yes—
659C4⋊C4—21no—
660C4⋊C4—594no—
661C4⋊C4—592no—
662C4⋊C4—592no—
663C4⋊C4—592no—
664C4⋊C4—1184no—
665C4⋊C4—1184no—
666C4⋊C4—1184no—
667C4⋊C4—1184no—
668C4⋊C4—1184no—
669C4⋊C4—1181no—
670C4⋊C4—1181no—
671C4⋊C4—1181no—
672C4⋊C4—1184no—
673C4⋊C4C23×D5912yes—
674C22⋊C4—24no—
675C22⋊C4—594no—
676C22⋊C4—594no—
677C22⋊C4—1184no—
678C22⋊C4—1184no—
679C22⋊C4—1184no—
680C22⋊C4—1184no—
681C22⋊C4—1184no—
682C22⋊C4—1184no—
683C42—592no—
684C42—592no—
685C42—1184no—
686C42—1184no—
687C42—1184no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—592no—
696C23—1182no—
697C23—1182no—
698C23—1182no—
699C23C2×D4×D5912yes—
700C23C2×D4×D5911yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—22no—
704Q8—22no—
705Q8—48no—
706Q8—42no—
707Q8—1182no—
708Q8—1182no—
709Q8—4724no—
710Q8—2368no—
711Q8—2362no—
712Q8C2×#1174568714yes—
713D4—22no—
714D4—22no—
715D4—42no—
716D4—84no—
717D4—1188no—
718D4—4724no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—48no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—594no—
731C2×C4—592no—
732C2×C4—592no—
733C2×C4—592no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—1182no—
737C2×C4—1182no—
738C2×C4—1184no—
739C2×C4—1182no—
740C2×C4—1182no—
741C2×C4—1182no—
742C2×C4—1182no—
743C2×C4—2368no—
744C2×C4—2368no—
745C2×C4—2362no—
746C2×C4—2362no—
747C2×C4—2362no—
748C2×C4—2362no—
749C2×C4C2×D4×D5912yes—
750C2×C4C2×D4×D5911yescharacteristic
751C2×C4C2×#1174568712yes—
752C2×C4#1427377212yes—
753C2×C4C24×D5911yescharacteristic
754C8—22no—
755C8—22no—
756C8—1182no—
757C8—1182no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—84no—
766C22—1182no—
767C22—1182no—
768C22—1182no—
769C22—2364no—
770C22#1683803912yes—
771C22#137×D5912yes—
772C22#1683820812yes—
773C22C22×D4×D5911yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—594no—
779C4—1182no—
780C4—1182no—
781C4—2362no—
782C4—2362no—
783C4—2362no—
784C4—2362no—
785C4#1683803912yes—
786C4C22×#1174568711yescharacteristic
787C4C2×#1427377211yescharacteristic
788C2—42no—
789C2—82no—
790C2—2362no—
791C2#2143638314yesdirect product factor
792C2C2×#1683803911yescharacteristic
793C2C2×#137×D5911yescharacteristic
794C2C2×#1683820811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#448C2
socleC23×C59C22×D4
prime radicalC2×#16838116C2
hypercenterC2×#448D59
hypocenterC59C2×#3329
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C22⋊D59C2semidirect
3. #21436383C2direct (N × H)
4. C2×#16837751C2semidirect
5. C2×#16837744C2semidirect
6. C2×#16837741C2semidirect
7. C2×#16837695C2semidirect
8. C2×#16837646C2semidirect
9. C2×#16837645C2semidirect
10. C2×#16837605C2semidirect
11. C2×#16837539C2semidirect
12. C2×SD16×Dic59C2semidirect
13. C2×#16837477C2semidirect
14. C2×#16837411C2semidirect
15. C2×#16837409C2semidirect
16. C2×C59×#448C2semidirect
24. Q8×C22⋊D59C22semidirect
43. #16837751C22semidirect
44. #16837744C22semidirect
45. #16837741C22semidirect
46. #16837695C22semidirect
47. #16837646C22semidirect
48. #16837645C22semidirect
49. #16837605C22semidirect
50. #16837539C22semidirect
51. SD16×Dic59C22semidirect
52. #16837477C22semidirect
57. #16837411C22semidirect
58. #16837409C22semidirect
73. C59×#448C22semidirect
402. C2×#448D59semidirect
409. C2×C59#3329semidirect
452. #448C2×D59semidirect
474. C59C2×#3329semidirect
791. C2#21436383direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381162
C2×Q8×C22⋊D592
#214363832
C2×#168377512
C2×#168377442
C2×#168377412
C2×#168376952
C2×#168376462
C2×#168376452
C2×#168376052
C2×#168375392
C2×SD16×Dic592
C2×#168374772
C2×#168374112
C2×#168374092
C2×C59×#4482
C2×#332959