Finite Group Databasebeta

← C2×#21436272 #29465316

Subgroups — C2×#21436272 #29465316

Order 15104.

2158 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×#16838102C211yesmaximal, characteristic
2C2×Q8×D236C211yesmaximal, characteristic, complemented
3#21436272C2116yesmaximal, direct product factor
4C2×#16837771C211yesmaximal, characteristic, complemented
5C2×#16837739C211yesmaximal, characteristic, complemented
6C2×#16837745C211yesmaximal, characteristic, complemented
7C2×#16837709C211yesmaximal, characteristic, complemented
8C2×#16837647C211yesmaximal, characteristic, complemented
9C2×#16837630C211yesmaximal, characteristic, complemented
10C2×#16837607C211yesmaximal, characteristic, complemented
11C2×#16837539C211yesmaximal, characteristic, complemented
12C2×#16837539C211yesmaximal, characteristic, complemented
13C2×#16837475C211yesmaximal, characteristic, complemented
14C2×#16837409C211yesmaximal, characteristic, complemented
15C2×#103×D59C211yesmaximal, characteristic, complemented
16C2×C59×#440C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×Q8×D59C2211yescharacteristic
19C22×#11745670C2211yescharacteristic
20C22×#11745670C2211yescharacteristic
21C22×#11745659C2211yescharacteristic
22C22×C8×D59C2211yescharacteristic
23#16838102—24no—
24#16838102C2218yes—
25Q8×D236—24no—
26Q8×D236C2218yescomplemented
27C2×#14273727—21no—
28C2×#14273727C2211yescharacteristic
29C2×#14273720—21no—
30C2×#14273719C2211yescharacteristic
31C2×#14273710—21no—
32C2×#14273707—21no—
33C2×#14273707—21no—
34C2×#14273707C2211yescharacteristic
35C2×#14273707C2211yescharacteristic
36C2×#14273700—21no—
37C2×#14273698C2211yescharacteristic
38C2×#14273698C2211yescharacteristic
39C2×C4×D236—21no—
40C2×C4×D236C2211yescharacteristic
41C2×C4×C22⋊D59—21no—
42C2×#14273685C2211yescharacteristic
43C2×C4⋊C4×D59C2211yescharacteristic
44#16837771C2218yescomplemented
45#16837745C2218yescomplemented
46#16837739C2218yescomplemented
47#16837709C2218yescomplemented
48#16837647C2218yescomplemented
49#16837630C2218yescomplemented
50#16837607C2218yescomplemented
51#16837539C2218yescomplemented
52#16837539C2218yescomplemented
53#16837475C2218yescomplemented
54C2×#14273660C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×C4⋊(C59⋊C8)C2211yescharacteristic
57#16837409C2218yescomplemented
58C2×#14273652C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66#103×D59C2218yescomplemented
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×(C2×D59)⋊C8C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C59×#440C2218yescomplemented
73C2×#107×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C22×Dic118C2311yescharacteristic
81C2×Q8×D59—22no—
82C2×Q8×D59—22no—
83C2×Q8×D59—24no—
84C2×Q8×D59—24no—
85C2×Q8×D59—42no—
86C2×Q8×D59—42no—
87C2×Q8×D59C2314yes—
88C2×Q8×D59C2314yes—
89C22×D236D411yescharacteristic
90C22×C22⋊D59—21no—
91C22×C22⋊D59—21no—
92C22×C4×D59—21no—
93C22×C4×D59—21no—
94C22×C4×D59—21no—
95C22×C4×D59C2311yescharacteristic
96C22×C4×D59C2311yescharacteristic
97C2×#11745670—42no—
98C2×#11745670—42no—
99C2×#11745670C2314yes—
100C2×#11745670C2314yes—
101C2×#11745659—42no—
102C2×#11745659C2314yes—
103C22×C59⋊C8C2311yescharacteristic
104C22×C59⋊C8C2311yescharacteristic
105C2×C8×D59—42no—
106C2×C8×D59C2314yes—
107#14273727—22no—
108#14273727—28no—
109#14273727C2314yes—
110#14273720—28no—
111#14273719—22no—
112#14273719C2314yes—
113#14273710—28no—
114#14273707—22no—
115#14273707—22no—
116#14273707—28no—
117#14273707—28no—
118#14273707C2314yes—
119#14273707C2314yes—
120#14273700—28no—
121#14273698—22no—
122#14273698—22no—
123#14273698C2314yes—
124#14273698C2314yes—
125C4×D236—28no—
126C4×D236D414yes—
127C4×D236C2314yes—
128C4×C22⋊D59—28no—
129#14273685—22no—
130#14273685C2314yes—
131C2×C4⋊Dic59—21no—
132C2×C4⋊Dic59—21no—
133C2×C4⋊Dic59—21no—
134C2×C4⋊Dic59—21no—
135C2×C4⋊Dic59D411yescharacteristic
136C2×C4⋊Dic59C2311yescharacteristic
137C2×C4⋊Dic59C2311yescharacteristic
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C2×Dic59⋊C4—21no—
141C4⋊C4×D59—22no—
142C4⋊C4×D59C2314yes—
143C2×C22⋊Dic59—21no—
144C2×C22⋊Dic59—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4D411yescharacteristic
149C2×(C2×D59)⋊C4D411yescharacteristic
150C2×C4×Dic59—21no—
151#14273660C2314yes—
152#14273658C2314yes—
153C4⋊(C59⋊C8)C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273652C2314yes—
157#14273652C2314yes—
158#14273651C2314yes—
159#14273651C2314yes—
160#14273650C2314yes—
161#14273650C2314yes—
162(C2×D59)⋊C8C2314yes—
163(C2×D59)⋊C8C2314yes—
164C22×Q8×C59C2311yescharacteristic
165C22×D4×C59C2311yescharacteristic
166C23×C4×C59—21no—
167C2×SD16×C59—24no—
168C2×SD16×C59C2314yes—
169C22×C8×C59C2311yescharacteristic
170C22×C8×C59C2311yescharacteristic
171C4×Q8×C59—22no—
172C4×Q8×C59C2314yes—
173C4×D4×C59—22no—
174C4×D4×C59C2314yes—
175C2×C4⋊C4×C59—21no—
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C22⋊C4×C59—21no—
179C2×C42×C59—21no—
180C2×C42×C59C2311yescharacteristic
181#107×C59C2314yes—
182#103×C59C2314yes—
183#102×C59C2314yes—
184#97×C59C2314yes—
185C24×C59—21no—
186C23×D59C2×D411yescharacteristic
187C23×D59C2×D411yescharacteristic
188C2×Q8×C59—21no—
189C2×Q8×C59—22no—
190C2×Q8×C59#4114yes—
191C2×Q8×C59C2412yes—
192C2×D4×C59—21no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59C2412yes—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—24no—
200C22×C4×C59—82no—
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2411yescharacteristic
204C2×C22⋊D59—24no—
205C2×C22⋊D59—24no—
206C2×C22⋊D59—44no—
207C2×C22⋊D59—82no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59C2×D411yescharacteristic
213C22×Dic59C2×D411yescharacteristic
214Q8×D59—28no—
215Q8×D59—28no—
216Q8×D59—44no—
217Q8×D59—44no—
218Q8×D59—48no—
219Q8×D59—48no—
220C2×D236—24no—
221C2×D236C2×D414yes—
222C2×C4×D59—22no—
223C2×C4×D59—22no—
224C2×C4×D59—22no—
225C2×C4×D59—22no—
226C2×C4×D59—24no—
227C2×C4×D59—24no—
228C2×C4×D59—24no—
229C2×C4×D59—44no—
230C2×C4×D59—44no—
231C2×C4×D59—82no—
232C2×C4×D59C2×D412yes—
233C2×C4×D59C2×D412yes—
234C2×C4×D59C2412yes—
235C2×C4×D59C2412yes—
236C2×Dic118—22no—
237C2×Dic118—22no—
238C2×Dic118—22no—
239C2×Dic118—22no—
240C2×Dic118—21no—
241C2×Dic118—21no—
242C2×Dic118—24no—
243C2×Dic118—24no—
244C2×Dic118—44no—
245C2×Dic118—44no—
246C2×Dic118C2412yes—
247C2×Dic118C2412yes—
248SD16×C59—28no—
249C2×C8×C59—22no—
250C2×C8×C59—22no—
251C2×C8×C59C2412yes—
252C2×C8×C59C2412yes—
253C4⋊C4×C59—24no—
254C4⋊C4×C59—21no—
255C4⋊C4×C59—21no—
256C4⋊C4×C59C2412yes—
257C4⋊C4×C59C2412yes—
258C22⋊C4×C59—24no—
259C42×C59—24no—
260C42×C59C2×D412yes—
261C42×C59C2412yes—
262C22⋊Dic59—24no—
263C22⋊Dic59—24no—
264#11745670—44no—
265#11745670—44no—
266(C2×D59)⋊C4—24no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4—24no—
269(C2×D59)⋊C4C2×D414yes—
270(C2×D59)⋊C4C2×D414yes—
271C4⋊Dic59—21no—
272C4⋊Dic59—24no—
273C4⋊Dic59—24no—
274C4⋊Dic59—21no—
275C4⋊Dic59—24no—
276C4⋊Dic59—24no—
277C4⋊Dic59C2×D414yes—
278C4⋊Dic59C2412yes—
279C4⋊Dic59C2412yes—
280Dic59⋊C4—24no—
281Dic59⋊C4—24no—
282Dic59⋊C4—24no—
283C4×Dic59—24no—
284C2×C59⋊C8—22no—
285C2×C59⋊C8—22no—
286C2×C59⋊C8C2412yes—
287C2×C59⋊C8C2412yes—
288#11745659—44no—
289C8×D59—44no—
290C23×C59—22no—
291C23×C59—42no—
292C23×C59—42no—
293C23×C59—42no—
294C23×C59C22×D411yescharacteristic
295C22×D59—22no—
296C22×D59—22no—
297C22×D59—22no—
298C22×D59—22no—
299C22×D59—22no—
300C22×D59#13714yes—
301C22×D59C22×D412yes—
302C22×D59C22×D412yes—
303Q8×C59—24no—
304Q8×C59—22no—
305Q8×C59C2×#4114yes—
306D4×C59—22no—
307D4×C59—22no—
308D4×C59—42no—
309C2×C4×C59—24no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—42no—
316C2×C4×C59—42no—
317C2×C4×C59—84no—
318C2×C4×C59C22×D412yes—
319C2×C4×C59C22×D412yes—
320C2×C4×C59C22×D411yescharacteristic
321C2×C4×C59C2×#4112yes—
322C2×C4×C59H(5,𝔽2)12yes—
323C2×C4×C59C2511yescharacteristic
324C22⋊D59—48no—
325C22⋊D59—84no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—42no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59—42no—
336C2×Dic59C22×D412yes—
337C2×Dic59C22×D412yes—
338D236—28no—
339C4×D59—24no—
340C4×D59—24no—
341C4×D59—22no—
342C4×D59—22no—
343C4×D59—22no—
344C4×D59—22no—
345C4×D59—48no—
346C4×D59—48no—
347C4×D59—84no—
348Dic118—22no—
349Dic118—22no—
350Dic118—22no—
351Dic118—22no—
352Dic118—48no—
353Dic118—48no—
354Dic118—42no—
355Dic118—42no—
356C8×C59—22no—
357C8×C59—22no—
358C59⋊C8—22no—
359C59⋊C8—22no—
360C2×#3320—591nomaximal, Sylow
361C22×C59—42no—
362C22×C59—42no—
363C22×C59—42no—
364C22×C59—84no—
365C22×C59#54612yes—
366C22×C59C2×#13712yes—
367C22×C59#57712yes—
368C22×C59C23×D411yescharacteristic
369C2×D59—22no—
370C2×D59—28no—
371C2×D59—22no—
372C2×D59—22no—
373C2×D59—22no—
374C2×D59—22no—
375C2×D59—44no—
376C2×D59C2×#13714yes—
377C4×C59—24no—
378C4×C59—22no—
379C4×C59—22no—
380C4×C59—42no—
381C4×C59—42no—
382C4×C59#54612yes—
383C4×C59C22×#4111yescharacteristic
384C4×C59C2×H(5,𝔽2)11yescharacteristic
385Dic59—22no—
386Dic59—22no—
387Dic59—42no—
388Dic59—42no—
389Dic59—42no—
390Dic59—42no—
391C2×#553—591no—
392C2×D4×Q8—591no—
393#3320—5916no—
394C2×#491—591no—
395C2×#484—591no—
396C2×#485—591no—
397C2×#479—591no—
398C2×#468—591no—
399C2×#465—591no—
400C2×#461—591no—
401C2×#448—591no—
402C2×#448—591no—
403C2×#440D5911yescharacteristic, complemented
404C2×#435—591no—
405C2×#419—591no—
406C22×#103—591no—
407C2×C59—82no—
408C2×C59#332014yescomplemented
409C2×C59C2×#54611yescharacteristic
410C2×C59C22×#13711yescharacteristic
411C2×C59C2×#57711yescharacteristic
412D59—24no—
413D59—42no—
414C23×Q8—591no—
415C23×Q8—591no—
416C22×SD16—591no—
417C22×SD16—591no—
418C22×SD16C2×D5911yescharacteristic
419C22×M16—591no—
420C23×C8—591no—
421#553—598no—
422#553—1184no—
423D4×Q8—598no—
424D4×Q8—1184no—
425C2×C4⋊Q8—591no—
426C2×C4⋊Q8—1181no—
427C2×#126—1181no—
428C2×#125—591no—
429C2×#123—1181no—
430C2×C22⋊Q8—591no—
431C2×C22⋊Q8—591no—
432C2×C22⋊Q8—1181no—
433C2×C22⋊Q8—1181no—
434C2×#121—591no—
435C2×#121—591no—
436C2×#121—1181no—
437C2×C4×Q8C2×D5911yescharacteristic
438C2×C4×D4—591no—
439C2×C4×D4—1181no—
440C2×C4×D4—1181no—
441C2×C4×D4C2×D5911yescharacteristic
442C2×#117—591no—
443C22×C4⋊C4—591no—
444#491—598no—
445#485—598no—
446#484—598no—
447#479—598no—
448#468—598no—
449#465—598no—
450#461—598no—
451#448—598no—
452#448—598no—
453#440C2×D5918yescomplemented
454#435—598no—
455C2×#107—591no—
456C2×#107C2×D5911yescharacteristic
457C2×#106—591no—
458C2×C4⋊C8—591no—
459#419—598no—
460C2×#103—591no—
461C2×#103—591no—
462C2×#103—591no—
463C2×#103—591no—
464C2×#103—591no—
465C2×#103—591no—
466C2×#103—591no—
467C2×#103—591no—
468C2×#103—598no—
469C2×#103C2×D5911yescharacteristic
470C2×#102C2×D5911yescharacteristic
471C2×C22⋊C8—591no—
472C2×C22⋊C8—591no—
473C2×#97C2×D5911yescharacteristic
474C59C2×#332011yescharacteristic, complemented, Sylow
475C22×Q8—594no—
476C22×Q8—594no—
477C22×Q8—591no—
478C22×Q8—591no—
479C22×Q8—1181no—
480C22×Q8—1181no—
481C22×Q8—1182no—
482C22×Q8—1182no—
483C22×Q8—1184no—
484C22×Q8—1184no—
485C22×Q8—2362no—
486C22×Q8—2362no—
487C22×Q8C22×D5911yescharacteristic
488C22×D4—591no—
489C22×D4—1181no—
490C22×D4—1181no—
491C22×D4C22×D5911yescharacteristic
492C23×C4—21no—
493C23×C4—591no—
494C23×C4—591no—
495C23×C4—1181no—
496C23×C4—1181no—
497C23×C4—1181no—
498C2×SD16—24no—
499C2×SD16—594no—
500C2×SD16—594no—
501C2×SD16—2362no—
502C2×SD16—2362no—
503C2×SD16C22×D5914yes—
504C2×M16—594no—
505C2×M16—2362no—
506C22×C8—591no—
507C22×C8—591no—
508C22×C8—594no—
509C22×C8—2362no—
510C22×C8C22×D5911yescharacteristic
511C22×C8C22×D5911yescharacteristic
512C4⋊Q8—594no—
513C4⋊Q8—1188no—
514C4⋊Q8—1182no—
515#126—1188no—
516#125—594no—
517#125—1182no—
518#123—1188no—
519C22⋊Q8—594no—
520C22⋊Q8—594no—
521C22⋊Q8—1188no—
522C22⋊Q8—1188no—
523C22⋊Q8—1182no—
524C22⋊Q8—1182no—
525#121—594no—
526#121—594no—
527#121—1188no—
528#121—1182no—
529#121—1182no—
530C4×Q8—22no—
531C4×Q8C22×D5914yes—
532C4×D4—22no—
533C4×D4—594no—
534C4×D4—594no—
535C4×D4—1188no—
536C4×D4—1188no—
537C4×D4C22×D5914yes—
538#117—594no—
539#117—1182no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—591no—
542C2×C4⋊C4—591no—
543C2×C4⋊C4—591no—
544C2×C4⋊C4—594no—
545C2×C4⋊C4—1182no—
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⋊C4—1181no—
553C2×C4⋊C4C22×D5911yescharacteristic
554C2×C4⋊C4C22×D5911yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—591no—
557C2×C22⋊C4—591no—
558C2×C22⋊C4—1181no—
559C2×C22⋊C4—1181no—
560C2×C22⋊C4—1181no—
561C2×C22⋊C4—1181no—
562C2×C22⋊C4—1181no—
563C2×C42—21no—
564C2×C42—1181no—
565C2×C42C22×D5911yescharacteristic
566#107—594no—
567#107C22×D5914yes—
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#103—594no—
578#103C22×D5914yes—
579#102C22×D5914yes—
580C22⋊C8—594no—
581C22⋊C8—594no—
582#97C22×D5914yes—
583C24—21no—
584C24—591no—
585C24—591no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—592no—
589C2×Q8—592no—
590C2×Q8—1184no—
591C2×Q8—1184no—
592C2×Q8—1181no—
593C2×Q8—1181no—
594C2×Q8—1188no—
595C2×Q8—1188no—
596C2×Q8—1182no—
597C2×Q8—1182no—
598C2×Q8—1182no—
599C2×Q8—1182no—
600C2×Q8—2364no—
601C2×Q8—2364no—
602C2×Q8—2364no—
603C2×Q8—2364no—
604C2×Q8—2368no—
605C2×Q8—2368no—
606C2×Q8#1174568514yes—
607C2×Q8C23×D5912yes—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—594no—
612C2×D4—1184no—
613C2×D4—1184no—
614C2×D4—1184no—
615C2×D4—4722no—
616C2×D4—2364no—
617C2×D4C23×D5912yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—24no—
622C22×C4—82no—
623C22×C4—591no—
624C22×C4—591no—
625C22×C4—592no—
626C22×C4—592no—
627C22×C4—592no—
628C22×C4—592no—
629C22×C4—1184no—
630C22×C4—1184no—
631C22×C4—1184no—
632C22×C4—1182no—
633C22×C4—1182no—
634C22×C4—1182no—
635C22×C4—1182no—
636C22×C4—1181no—
637C22×C4—1181no—
638C22×C4—1181no—
639C22×C4—1181no—
640C22×C4—4722no—
641C22×C4—2364no—
642C22×C4—2364no—
643C22×C4D4×D5911yescharacteristic
644C22×C4D4×D5911yescharacteristic
645C22×C4C23×D5911yescharacteristic
646SD16—28no—
647SD16—2364no—
648SD16—2364no—
649M16—2364no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—592no—
653C2×C8—592no—
654C2×C8—1182no—
655C2×C8—1182no—
656C2×C8—2364no—
657C2×C8C23×D5912yes—
658C2×C8C23×D5912yes—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—594no—
663C4⋊C4—592no—
664C4⋊C4—592no—
665C4⋊C4—1184no—
666C4⋊C4—1184no—
667C4⋊C4—1184no—
668C4⋊C4—1181no—
669C4⋊C4—1181no—
670C4⋊C4—1184no—
671C4⋊C4—1184no—
672C4⋊C4—1184no—
673C4⋊C4—1184no—
674C4⋊C4C23×D5912yes—
675C4⋊C4C23×D5912yes—
676C22⋊C4—24no—
677C22⋊C4—594no—
678C22⋊C4—594no—
679C22⋊C4—1184no—
680C22⋊C4—1184no—
681C22⋊C4—1184no—
682C22⋊C4—1184no—
683C22⋊C4—1184no—
684C42—24no—
685C42—1184no—
686C42D4×D5912yes—
687C42C23×D5912yes—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—594no—
693C23—592no—
694C23—592no—
695C23—1182no—
696C23—1182no—
697C23—1182no—
698C23—1182no—
699C23—1182no—
700C23C2×D4×D5911yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—1182no—
704Q8—1182no—
705Q8—1182no—
706Q8—1182no—
707Q8—2368no—
708Q8—2368no—
709Q8—2362no—
710Q8—2362no—
711Q8C2×#1174568514yes—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—1188no—
716D4—4724no—
717D4—2368no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—84no—
727C2×C4—592no—
728C2×C4—592no—
729C2×C4—1182no—
730C2×C4—1182no—
731C2×C4—1182no—
732C2×C4—1182no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1184no—
736C2×C4—1184no—
737C2×C4—1182no—
738C2×C4—1182no—
739C2×C4—1182no—
740C2×C4—1182no—
741C2×C4—4724no—
742C2×C4—2368no—
743C2×C4—2368no—
744C2×C4—2362no—
745C2×C4—2362no—
746C2×C4—2362no—
747C2×C4—2362no—
748C2×C4C2×D4×D5912yes—
749C2×C4C2×D4×D5912yes—
750C2×C4C2×D4×D5911yescharacteristic
751C2×C4C2×#1174568512yes—
752C2×C4#1427377312yes—
753C2×C4C24×D5911yescharacteristic
754C8—22no—
755C8—22no—
756C8—1182no—
757C8—1182no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22—594no—
763C22—1182no—
764C22—1188no—
765C22—1182no—
766C22—1182no—
767C22—1182no—
768C22—1182no—
769C22—2364no—
770C22#1683804812yes—
771C22#137×D5912yes—
772C22#1683821212yes—
773C22C22×D4×D5911yescharacteristic
774C4—24no—
775C4—22no—
776C4—22no—
777C4—42no—
778C4—42no—
779C4—1182no—
780C4—1182no—
781C4—2362no—
782C4—2362no—
783C4—2362no—
784C4—2362no—
785C4#1683804812yes—
786C4C22×#1174568511yescharacteristic
787C4C2×#1427377311yescharacteristic
788C2—82no—
789C2—1184no—
790C2—2362no—
791C2#2143627214yesdirect product factor
792C2C2×#1683804811yescharacteristic
793C2C2×#137×D5911yescharacteristic
794C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#440C2
socleC23×C59C22×D4
prime radicalC2×#16838102C2
hypercenterC2×#440D59
hypocenterC59C2×#3320
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×Q8×D236C2semidirect
3. #21436272C2direct (N × H)
4. C2×#16837771C2semidirect
5. C2×#16837739C2semidirect
6. C2×#16837745C2semidirect
7. C2×#16837709C2semidirect
8. C2×#16837647C2semidirect
9. C2×#16837630C2semidirect
10. C2×#16837607C2semidirect
11. C2×#16837539C2semidirect
12. C2×#16837539C2semidirect
13. C2×#16837475C2semidirect
14. C2×#16837409C2semidirect
15. C2×#103×D59C2semidirect
16. C2×C59×#440C2semidirect
26. Q8×D236C22semidirect
44. #16837771C22semidirect
45. #16837745C22semidirect
46. #16837739C22semidirect
47. #16837709C22semidirect
48. #16837647C22semidirect
49. #16837630C22semidirect
50. #16837607C22semidirect
51. #16837539C22semidirect
52. #16837539C22semidirect
53. #16837475C22semidirect
57. #16837409C22semidirect
66. #103×D59C22semidirect
72. C59×#440C22semidirect
403. C2×#440D59semidirect
408. C2×C59#3320semidirect
453. #440C2×D59semidirect
474. C59C2×#3320semidirect
791. C2#21436272direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381022
C2×Q8×D2362
#214362722
C2×#168377712
C2×#168377392
C2×#168377452
C2×#168377092
C2×#168376472
C2×#168376302
C2×#168376072
C2×#168375392
C2×#168374752
C2×#168374092
C2×#103×D592
C2×C59×#4402
C2×#332059