Finite Group Databasebeta

← C2×#21434811 #29458628

Subgroups — C2×#21434811 #29458628

Order 15104.

2234 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837956C211yesmaximal, characteristic, complemented
2C2×#16837949C211yesmaximal, characteristic
3#21434811C2116yesmaximal, direct product factor
4C2×#16837806C211yesmaximal, characteristic, complemented
5C2×#16837773C211yesmaximal, characteristic, complemented
6C2×#16837751C211yesmaximal, characteristic, complemented
7C2×#16837747C211yesmaximal, characteristic, complemented
8C2×#16837651C211yesmaximal, characteristic, complemented
9C2×#16837649C211yesmaximal, characteristic, complemented
10C2×#16837647C211yesmaximal, characteristic, complemented
11C2×#16837645C211yesmaximal, characteristic, complemented
12C2×#16837504C211yesmaximal, characteristic, complemented
13C2×#16837502C211yesmaximal, characteristic, complemented
14C2×#16837500C211yesmaximal, characteristic, complemented
15C2×#16837354C211yesmaximal, characteristic, complemented
16C2×C59×#440C211yesmaximal, characteristic, complemented
17C22×#11745685—21no—
18C22×#11745660C2211yescharacteristic
19C22×#11745670C2211yescharacteristic
20C22×#11745671C2211yescharacteristic
21C22×#11745659C2211yescharacteristic
22C22×#11745659C2211yescharacteristic
23#16837956—24no—
24#16837956C2218yescomplemented
25#16837949—24no—
26#16837949C2218yes—
27C2×#14273726C2211yescharacteristic
28C2×#14273726C2211yescharacteristic
29C2×#14273725C2211yescharacteristic
30C2×#14273723C2211yescharacteristic
31C2×#14273717—21no—
32C2×#14273713—21no—
33C2×#14273707C2211yescharacteristic
34C2×#14273705—21no—
35C2×#14273703C2211yescharacteristic
36C2×#14273702C2211yescharacteristic
37C2×#14273700—21no—
38C2×#14273698C2211yescharacteristic
39C2×C4×Dic118—21no—
40C2×C4×Dic118C2211yescharacteristic
41C2×C4×D236C2211yescharacteristic
42C2×C4×C22⋊D59—21no—
43C2×#14273684—21no—
44C2×C42×D59C2211yescharacteristic
45#16837806C2218yescomplemented
46#16837773C2218yescomplemented
47#16837751C2218yescomplemented
48#16837747C2218yescomplemented
49#16837651C2218yescomplemented
50#16837649C2218yescomplemented
51#16837647C2218yescomplemented
52#16837645C2218yescomplemented
53#16837504C2218yescomplemented
54#16837502C2218yescomplemented
55#16837500C2218yescomplemented
56C2×#14273661C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273660C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65#16837354C2218yescomplemented
66C2×#14273638C2211yescharacteristic
67C2×C8×Dic59C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
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
77C2×#11745685—28no—
78C2×#11745685—48no—
79C22×Dic118—21no—
80C22×Dic118—21no—
81C22×Dic118C2311yescharacteristic
82C22×D236—21no—
83C22×D236C2311yescharacteristic
84C22×C22⋊D59—21no—
85C22×C22⋊D59—21no—
86C22×C22⋊D59—21no—
87C22×C4×D59—21no—
88C22×C4×D59D411yescharacteristic
89C22×C4×D59D411yescharacteristic
90C22×C4×D59C2311yescharacteristic
91C2×#11745660—24no—
92C2×#11745660C2314yes—
93C2×#11745670—24no—
94C2×#11745670C2314yes—
95C2×#11745671—24no—
96C2×#11745671C2314yes—
97C2×#11745659—24no—
98C2×#11745659—24no—
99C2×#11745659C2314yes—
100C2×#11745659C2314yes—
101C22×C59⋊C8C2311yescharacteristic
102C22×C59⋊C8C2311yescharacteristic
103#14273726—22no—
104#14273726—22no—
105#14273726C2314yes—
106#14273726C2314yes—
107#14273725—22no—
108#14273725C2314yes—
109#14273723—22no—
110#14273723C2314yes—
111#14273717—28no—
112#14273713—28no—
113#14273707—22no—
114#14273707C2314yes—
115#14273705—28no—
116#14273703—22no—
117#14273703C2314yes—
118#14273702—22no—
119#14273702C2314yes—
120#14273700—28no—
121#14273698—22no—
122#14273698C2314yes—
123C4×Dic118—22no—
124C4×Dic118—28no—
125C4×Dic118C2314yes—
126C4×D236—22no—
127C4×D236C2314yes—
128C4×C22⋊D59—28no—
129#14273684—28no—
130C2×C4⋊Dic59—21no—
131C2×C4⋊Dic59C2311yescharacteristic
132C2×C4⋊Dic59C2311yescharacteristic
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×C22⋊Dic59—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59D411yescharacteristic
146C2×C4×Dic59D411yescharacteristic
147C2×C4×Dic59C2311yescharacteristic
148C42×D59D414yes—
149C42×D59C2314yes—
150#14273661C2314yes—
151#14273660C2314yes—
152#14273660C2314yes—
153#14273652C2314yes—
154#14273651C2314yes—
155#14273650C2314yes—
156#14273649C2314yes—
157#14273648C2314yes—
158#14273647C2314yes—
159#14273638C2314yes—
160C8×Dic59C2314yes—
161C8×Dic59C2314yes—
162C22×Q8×C59C2311yescharacteristic
163C22×D4×C59C2311yescharacteristic
164C23×C4×C59—21no—
165C2×SD16×C59—24no—
166C2×SD16×C59C2314yes—
167C22×C8×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169C4×Q8×C59—22no—
170C4×Q8×C59C2314yes—
171C4×D4×C59—22no—
172C4×D4×C59C2314yes—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C22⋊C4×C59—21no—
177C2×C42×C59—21no—
178C2×C42×C59C2311yescharacteristic
179#107×C59C2314yes—
180#103×C59C2314yes—
181#102×C59C2314yes—
182#97×C59C2314yes—
183C24×C59—21no—
184C23×D59—21no—
185C23×D59C2×D411yescharacteristic
186C2×Q8×C59—21no—
187C2×Q8×C59—22no—
188C2×Q8×C59—22no—
189C2×Q8×C59C2412yes—
190C2×D4×C59—21no—
191C2×D4×C59—22no—
192C2×D4×C59—22no—
193C2×D4×C59C2412yes—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—24no—
198C22×C4×C59—44no—
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2411yescharacteristic
202C2×C22⋊D59—24no—
203C2×C22⋊D59—24no—
204C2×C22⋊D59—24no—
205C2×C22⋊D59—44no—
206C2×C22⋊D59—44no—
207C2×C22⋊D59—44no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213C22×Dic59C2×D411yescharacteristic
214#11745685—432no—
215C2×D236—22no—
216C2×D236—22no—
217C2×D236—24no—
218C2×D236—21no—
219C2×D236—44no—
220C2×D236C2412yes—
221C2×C4×D59—22no—
222C2×C4×D59—22no—
223C2×C4×D59—24no—
224C2×C4×D59—24no—
225C2×C4×D59—24no—
226C2×C4×D59—44no—
227C2×C4×D59C2×D412yes—
228C2×C4×D59C2×D414yes—
229C2×C4×D59C2×D414yes—
230C2×C4×D59C2412yes—
231C2×Dic118—22no—
232C2×Dic118—22no—
233C2×Dic118—21no—
234C2×Dic118—24no—
235C2×Dic118—24no—
236C2×Dic118—44no—
237C2×Dic118—44no—
238C2×Dic118C2412yes—
239SD16×C59—28no—
240C2×C8×C59—22no—
241C2×C8×C59#4114yescomplemented
242C2×C8×C59C2412yes—
243C2×C8×C59C2412yes—
244C4⋊C4×C59—24no—
245C4⋊C4×C59—21no—
246C4⋊C4×C59—21no—
247C4⋊C4×C59C2412yes—
248C4⋊C4×C59C2412yes—
249C22⋊C4×C59—24no—
250C42×C59—24no—
251C42×C59C2×D412yes—
252C42×C59C2412yes—
253C22⋊Dic59—24no—
254#11745671—28no—
255#11745670—28no—
256(C2×D59)⋊C4—24no—
257(C2×D59)⋊C4—24no—
258(C2×D59)⋊C4—24no—
259(C2×D59)⋊C4—24no—
260C4⋊Dic59—21no—
261C4⋊Dic59—21no—
262C4⋊Dic59—24no—
263C4⋊Dic59C2412yes—
264C4⋊Dic59C2412yes—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267Dic59⋊C4—24no—
268Dic59⋊C4—24no—
269Dic59⋊C4—24no—
270Dic59⋊C4—24no—
271C4×Dic59—24no—
272C4×Dic59C2×D412yes—
273C4×Dic59C2×D414yes—
274C4×Dic59C2×D414yes—
275C4×Dic59C2412yes—
276C2×C59⋊C8—22no—
277C2×C59⋊C8#4114yescomplemented
278C2×C59⋊C8C2412yes—
279C2×C59⋊C8C2412yes—
280#11745660—28no—
281#11745659—28no—
282#11745659—28no—
283C23×C59—22no—
284C23×C59—42no—
285C23×C59—42no—
286C23×C59—42no—
287C23×C59C22×D411yescharacteristic
288C22×D59—22no—
289C22×D59—22no—
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—42no—
293C22×D59—42no—
294C22×D59—42no—
295C22×D59C22×D412yes—
296Q8×C59—22no—
297Q8×C59—22no—
298Q8×C59—42no—
299D4×C59—22no—
300D4×C59—22no—
301D4×C59—42no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—48no—
308C2×C4×C59—42no—
309C2×C4×C59—42no—
310C2×C4×C59—42no—
311C2×C4×C59C22×D412yes—
312C2×C4×C59C22×D412yes—
313C2×C4×C59C22×D411yescharacteristic
314C2×C4×C59C2×#4112yes—
315C2×C4×C59C2×#4112yes—
316C2×C4×C59C2511yescharacteristic
317C22⋊D59—48no—
318C22⋊D59—48no—
319C22⋊D59—48no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—42no—
325C2×Dic59—42no—
326C2×Dic59—42no—
327C2×Dic59AGL(1,ℤ/8)14yes—
328C2×Dic59#13714yes—
329C2×Dic59C22×D412yes—
330C2×Dic59C22×D412yes—
331C2×Dic59C22×D412yes—
332D236—22no—
333D236—22no—
334D236—48no—
335D236—42no—
336C4×D59—24no—
337C4×D59—22no—
338C4×D59—22no—
339C4×D59—28no—
340C4×D59—28no—
341C4×D59—48no—
342Dic118—22no—
343Dic118—22no—
344Dic118—42no—
345Dic118—48no—
346Dic118—48no—
347C8×C59—22no—
348C8×C59C2×#4114yescomplemented
349C59⋊C8—22no—
350C59⋊C8C2×#4114yescomplemented
351C2×#3182—591nomaximal, Sylow
352C22×C59—42no—
353C22×C59—42no—
354C22×C59—42no—
355C22×C59—84no—
356C22×C59#53212yes—
357C22×C59C2×AGL(1,ℤ/8)12yes—
358C22×C59C2×#13712yes—
359C22×C59C23×D411yescharacteristic
360C2×D59—22no—
361C2×D59—22no—
362C2×D59—22no—
363C2×D59—44no—
364C2×D59—42no—
365C2×D59—42no—
366C2×D59—42no—
367C2×D59—84no—
368C4×C59—22no—
369C4×C59—22no—
370C4×C59—42no—
371C4×C59—42no—
372C4×C59—42no—
373C4×C59#53212yes—
374C4×C59C22×#4111yescharacteristic
375C4×C59C22×#4111yescharacteristic
376Dic59—22no—
377Dic59—42no—
378Dic59—42no—
379Dic59—42no—
380Dic59C2×AGL(1,ℤ/8)14yes—
381Dic59C2×#13714yes—
382C2×#533—591no—
383C2×#532—591no—
384#3182—5916no—
385C2×#500—591no—
386C2×#492—591no—
387C2×#487—591no—
388C2×#486—591no—
389C2×#468—591no—
390C2×#468—591no—
391C2×#468—591no—
392C2×#468—591no—
393C2×#440—591no—
394C2×#440—591no—
395C2×#440—591no—
396C2×#440D5911yescharacteristic, complemented
397C2×C4×M16—591no—
398C2×C59—82no—
399C2×C59#318214yescomplemented
400C2×C59C2×#53211yescharacteristic
401C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
402C2×C59C22×#13711yescharacteristic
403D59—42no—
404D59—82no—
405C22×#41—1181no—
406C22×SD16—591no—
407C22×SD16—591no—
408C22×SD16—591no—
409C22×SD16C2×D5911yescharacteristic
410C22×M16—591no—
411C22×M16—591no—
412#533—598no—
413#533—1184no—
414#532—598no—
415#532—1184no—
416C2×C4⋊Q8—591no—
417C2×C4⋊Q8—591no—
418C2×C4⋊Q8—591no—
419C2×#127—591no—
420C2×#125—1181no—
421C2×#124—1181no—
422C2×C22⋊Q8—591no—
423C2×C22⋊Q8—591no—
424C2×C22⋊Q8—1181no—
425C2×#121—591no—
426C2×#121—591no—
427C2×#121—1181no—
428C2×C4×Q8—591no—
429C2×C4×Q8—1181no—
430C2×C4×Q8C2×D5911yescharacteristic
431C2×C4×D4—591no—
432C2×C4×D4—1181no—
433C2×C4×D4C2×D5911yescharacteristic
434C2×#117—1181no—
435C22×C42—591no—
436#500—598no—
437#492—598no—
438#487—598no—
439#486—598no—
440#468—598no—
441#468—598no—
442#468—598no—
443#468—598no—
444#440—598no—
445#440—598no—
446#440—598no—
447#440C2×D5918yescomplemented
448C2×#107—591no—
449C2×#107—591no—
450C2×#107—591no—
451C2×#107C2×D5911yescharacteristic
452C2×#103—591no—
453C2×#103—591no—
454C2×#103—591no—
455C2×#103C2×D5911yescharacteristic
456C2×#102—591no—
457C2×#102—591no—
458C2×#102—591no—
459C2×#102C2×D5911yescharacteristic
460C4×M16—598no—
461C2×#97—591no—
462C2×#97C2×D5911yescharacteristic
463C2×C4×C8—591no—
464C2×C4×C8—591no—
465C59C2×#318211yescharacteristic, complemented, Sylow
466C2×#41—1188no—
467C2×#41—2368no—
468C22×Q8—591no—
469C22×Q8—1181no—
470C22×Q8—1181no—
471C22×Q8C22×D5911yescharacteristic
472C22×D4—591no—
473C22×D4—1181no—
474C22×D4—1181no—
475C22×D4—1181no—
476C22×D4—1181no—
477C22×D4C22×D5911yescharacteristic
478C23×C4—21no—
479C23×C4—591no—
480C23×C4—591no—
481C23×C4—591no—
482C23×C4—1181no—
483C2×SD16—24no—
484C2×SD16—594no—
485C2×SD16—594no—
486C2×SD16—594no—
487C2×SD16—1184no—
488C2×SD16—1184no—
489C2×SD16—1184no—
490C2×SD16C22×D5914yes—
491C2×M16—594no—
492C2×M16—594no—
493C2×M16—1184no—
494C2×M16—1184no—
495C22×C8—591no—
496C22×C8—591no—
497C22×C8C22×D5911yescharacteristic
498C22×C8C22×D5911yescharacteristic
499C4⋊Q8—594no—
500C4⋊Q8—594no—
501C4⋊Q8—594no—
502C4⋊Q8—1182no—
503C4⋊Q8—1182no—
504C4⋊Q8—1182no—
505#127—594no—
506#127—1182no—
507#125—1188no—
508#124—1188no—
509C22⋊Q8—594no—
510C22⋊Q8—594no—
511C22⋊Q8—1182no—
512C22⋊Q8—1188no—
513C22⋊Q8—1182no—
514#121—594no—
515#121—594no—
516#121—1188no—
517#121—1182no—
518#121—1182no—
519C4×Q8—22no—
520C4×Q8—594no—
521C4×Q8—1188no—
522C4×Q8—1182no—
523C4×Q8C22×D5914yes—
524C4×D4—22no—
525C4×D4—594no—
526C4×D4—1188no—
527C4×D4—1182no—
528C4×D4C22×D5914yes—
529#117—1188no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—591no—
532C2×C4⋊C4—591no—
533C2×C4⋊C4—1181no—
534C2×C4⋊C4—1181no—
535C2×C4⋊C4—1181no—
536C2×C4⋊C4—1181no—
537C2×C4⋊C4—1181no—
538C2×C4⋊C4—1181no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4C22×D5911yescharacteristic
541C2×C4⋊C4C22×D5911yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—1181no—
544C2×C22⋊C4—1181no—
545C2×C22⋊C4—1181no—
546C2×C22⋊C4—1181no—
547C2×C22⋊C4—1181no—
548C2×C42—21no—
549C2×C42—591no—
550C2×C42—591no—
551C2×C42—591no—
552C2×C42—594no—
553C2×C42—594no—
554C2×C42—1181no—
555C2×C42C22×D5911yescharacteristic
556#107—594no—
557#107—594no—
558#107—594no—
559#107C22×D5914yes—
560#103—594no—
561#103—594no—
562#103—594no—
563#103C22×D5914yes—
564#102—594no—
565#102—594no—
566#102—594no—
567#102C22×D5914yes—
568#97—594no—
569#97C22×D5914yes—
570C4×C8—594no—
571C4×C8—594no—
572C24—21no—
573C24—591no—
574C24—1181no—
575#41—23632no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—592no—
580C2×Q8—1184no—
581C2×Q8—1184no—
582C2×Q8—1181no—
583C2×Q8—1182no—
584C2×Q8—1182no—
585C2×Q8—2364no—
586C2×Q8—2364no—
587C2×Q8C23×D5912yes—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—592no—
592C2×D4—1184no—
593C2×D4—1184no—
594C2×D4—1184no—
595C2×D4—1184no—
596C2×D4—1181no—
597C2×D4—1182no—
598C2×D4—1182no—
599C2×D4—2364no—
600C2×D4—2364no—
601C2×D4—2364no—
602C2×D4—2364no—
603C2×D4C23×D5912yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—44no—
609C22×C4—591no—
610C22×C4—591no—
611C22×C4—591no—
612C22×C4—594no—
613C22×C4—592no—
614C22×C4—594no—
615C22×C4—592no—
616C22×C4—1184no—
617C22×C4—1184no—
618C22×C4—1182no—
619C22×C4—1182no—
620C22×C4—1181no—
621C22×C4—1181no—
622C22×C4—1181no—
623C22×C4—1184no—
624C22×C4—2364no—
625C22×C4D4×D5911yescharacteristic
626C22×C4D4×D5911yescharacteristic
627C22×C4C23×D5911yescharacteristic
628SD16—28no—
629SD16—1188no—
630SD16—1188no—
631SD16—1188no—
632M16—1188no—
633M16—1188no—
634C2×C8—22no—
635C2×C8—594no—
636C2×C8—592no—
637C2×C8—592no—
638C2×C8—1182no—
639C2×C8#1174568514yescomplemented
640C2×C8C23×D5912yes—
641C2×C8C23×D5912yes—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—592no—
646C4⋊C4—592no—
647C4⋊C4—1184no—
648C4⋊C4—1184no—
649C4⋊C4—1184no—
650C4⋊C4—1184no—
651C4⋊C4—1184no—
652C4⋊C4—1184no—
653C4⋊C4—1181no—
654C4⋊C4—1181no—
655C4⋊C4—1184no—
656C4⋊C4C23×D5912yes—
657C4⋊C4C23×D5912yes—
658C22⋊C4—24no—
659C22⋊C4—1184no—
660C22⋊C4—1184no—
661C22⋊C4—1184no—
662C22⋊C4—1184no—
663C22⋊C4—1184no—
664C42—24no—
665C42—594no—
666C42—594no—
667C42—592no—
668C42—592no—
669C42—1184no—
670C42D4×D5912yes—
671C42C23×D5912yes—
672C23—22no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—592no—
677C23—1182no—
678C23—1182no—
679C23—1182no—
680C23—1182no—
681C23—2362no—
682C23—2362no—
683C23—2362no—
684C23C2×D4×D5911yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—42no—
688Q8—1182no—
689Q8—1182no—
690Q8—2368no—
691Q8—2368no—
692Q8—2362no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—1182no—
697D4—1182no—
698D4—2368no—
699D4—2368no—
700D4—2368no—
701D4—2368no—
702D4—2362no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—48no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—594no—
713C2×C4—594no—
714C2×C4—592no—
715C2×C4—592no—
716C2×C4—592no—
717C2×C4—1188no—
718C2×C4—1188no—
719C2×C4—1182no—
720C2×C4—1184no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—1182no—
724C2×C4—1182no—
725C2×C4—1182no—
726C2×C4—2368no—
727C2×C4—2362no—
728C2×C4—2362no—
729C2×C4—2362no—
730C2×C4C2×D4×D5912yes—
731C2×C4C2×D4×D5912yes—
732C2×C4C2×D4×D5911yescharacteristic
733C2×C4#41×D5912yes—
734C2×C4C2×#1174568512yes—
735C2×C4C24×D5911yescharacteristic
736C8—22no—
737C8—594no—
738C8—1182no—
739C8C2×#1174568514yescomplemented
740C22—42no—
741C22—42no—
742C22—42no—
743C22—84no—
744C22—1182no—
745C22—1182no—
746C22—1182no—
747C22—4724no—
748C22—2362no—
749C22—2362no—
750C22—2362no—
751C22—2364no—
752C22#1683794912yes—
753C22AGL(1,ℤ/8)×D5912yes—
754C22#137×D5912yes—
755C22C22×D4×D5911yescharacteristic
756C4—22no—
757C4—22no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—594no—
762C4—594no—
763C4—1182no—
764C4—2362no—
765C4—2362no—
766C4—2362no—
767C4#1683794912yes—
768C4C2×#41×D5911yescharacteristic
769C4C22×#1174568511yescharacteristic
770C2—82no—
771C2—4722no—
772C2—2362no—
773C2#2143481114yesdirect product factor
774C2C2×#1683794911yescharacteristic
775C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
776C2C2×#137×D5911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#440C2
socleC23×C59C22×D4
prime radicalC2×#16837949C2
hypercenterC2×#440D59
hypocenterC59C2×#3182
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
1. C2×#16837956C2semidirect
3. #21434811C2direct (N × H)
4. C2×#16837806C2semidirect
5. C2×#16837773C2semidirect
6. C2×#16837751C2semidirect
7. C2×#16837747C2semidirect
8. C2×#16837651C2semidirect
9. C2×#16837649C2semidirect
10. C2×#16837647C2semidirect
11. C2×#16837645C2semidirect
12. C2×#16837504C2semidirect
13. C2×#16837502C2semidirect
14. C2×#16837500C2semidirect
15. C2×#16837354C2semidirect
16. C2×C59×#440C2semidirect
24. #16837956C22semidirect
45. #16837806C22semidirect
46. #16837773C22semidirect
47. #16837751C22semidirect
48. #16837747C22semidirect
49. #16837651C22semidirect
50. #16837649C22semidirect
51. #16837647C22semidirect
52. #16837645C22semidirect
53. #16837504C22semidirect
54. #16837502C22semidirect
55. #16837500C22semidirect
65. #16837354C22semidirect
72. C59×#440C22semidirect
241. C2×C8×C59#41semidirect
277. C2×C59⋊C8#41semidirect
348. C8×C59C2×#41semidirect
350. C59⋊C8C2×#41semidirect
396. C2×#440D59semidirect
399. C2×C59#3182semidirect
447. #440C2×D59semidirect
465. C59C2×#3182semidirect
639. C2×C8#11745685semidirect
739. C8C2×#11745685semidirect
773. C2#21434811direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379562
C2×#168379492
#214348112
C2×#168378062
C2×#168377732
C2×#168377512
C2×#168377472
C2×#168376512
C2×#168376492
C2×#168376472
C2×#168376452
C2×#168375042
C2×#168375022
C2×#168375002
C2×#168373542
C2×C59×#4402
C2×#318259