Finite Group Databasebeta

← C2×#21436089 #29465265

Subgroups — C2×#21436089 #29465265

Order 15104.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838061C211yesmaximal, characteristic, complemented
2C2×#16838056C211yesmaximal, characteristic, complemented
3#21436089C2116yesmaximal, direct product factor
4C2×#16837762C211yesmaximal, characteristic, complemented
5C2×#16837738C211yesmaximal, characteristic, complemented
6C2×#16837716C211yesmaximal, characteristic, complemented
7C2×#16837698C211yesmaximal, characteristic, complemented
8C2×#16837648C211yesmaximal, characteristic, complemented
9C2×#16837638C211yesmaximal, characteristic, complemented
10C2×#16837618C211yesmaximal, characteristic, complemented
11C2×#16837549C211yesmaximal, characteristic, complemented
12C2×#16837543C211yesmaximal, characteristic, complemented
13C2×#16837504C211yesmaximal, characteristic, complemented
14C2×#16837404C211yesmaximal, characteristic, complemented
15C22×#14273652C211yesmaximal, characteristic, complemented
16C2×C59×#435C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×#11745687—21no—
19C23×Dic118C2211yescharacteristic
20C22×#11745660C2211yescharacteristic
21C22×#11745660C2211yescharacteristic
22C22×D472C2211yescharacteristic
23#16838061—24no—
24#16838061C2218yescomplemented
25#16838056—24no—
26#16838056C2218yescomplemented
27C2×#14273727C2211yescharacteristic
28C2×#14273715C2211yescharacteristic
29C2×#14273713—21no—
30C2×#14273711—21no—
31C2×#14273711—21no—
32C2×#14273707—21no—
33C2×#14273706C2211yescharacteristic
34C2×#14273705—21no—
35C2×#14273701C2211yescharacteristic
36C2×#14273701C2211yescharacteristic
37C2×#14273701C2211yescharacteristic
38C2×#14273699—21no—
39C2×C4×Dic118C2211yescharacteristic
40C2×C4×D236C2211yescharacteristic
41C2×(C22⋊D59)⋊C4—21no—
42C22×C4⋊Dic59C2211yescharacteristic
43C22×C4⋊Dic59C2211yescharacteristic
44#16837762C2218yescomplemented
45#16837738C2218yescomplemented
46#16837716C2218yescomplemented
47#16837698C2218yescomplemented
48#16837648C2218yescomplemented
49#16837638C2218yescomplemented
50#16837618C2218yescomplemented
51#16837549C2218yescomplemented
52#16837543C2218yescomplemented
53#16837504C2218yescomplemented
54C2×#14273661C2211yescharacteristic
55C2×#14273661C2211yescharacteristic
56C2×#14273661C2211yescharacteristic
57#16837404C2218yescomplemented
58C2×#14273652C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273652C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2218yescomplemented
65C2×#14273649C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic
68C2×#14273649C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C59×#435C2218yescomplemented
73C2×C4⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×C22⋊C8×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C2×#11745685—22no—
78C2×#11745685—24no—
79C2×#11745685—42no—
80C2×#11745685C2314yes—
81C2×#11745687—28no—
82C2×#11745687—48no—
83C22×Dic118—24no—
84C22×Dic118—21no—
85C22×Dic118—21no—
86C22×Dic118—22no—
87C22×Dic118—42no—
88C22×Dic118C2311yescharacteristic
89C22×Dic118C2314yes—
90C22×Dic118C2311yescharacteristic
91C22×D236C2311yescharacteristic
92C22×D236C2311yescharacteristic
93C22×C22⋊D59—21no—
94C22×C22⋊D59—21no—
95C22×C22⋊D59—21no—
96C22×C22⋊D59—21no—
97C23×Dic59—21no—
98C23×Dic59—21no—
99C23×Dic59—21no—
100C22×C4×D59—21no—
101C22×C4×D59—21no—
102C2×#11745660—24no—
103C2×#11745660—42no—
104C2×#11745660C2314yes—
105C2×#11745660C2314yes—
106C2×D472—42no—
107C2×D472C2314yes—
108#14273727—22no—
109#14273727C2314yes—
110#14273715—22no—
111#14273715C2314yes—
112#14273713—28no—
113#14273711—28no—
114#14273711—28no—
115#14273707—28no—
116#14273706—22no—
117#14273706C2314yes—
118#14273705—28no—
119#14273701—22no—
120#14273701—22no—
121#14273701—22no—
122#14273701C2314yes—
123#14273701C2314yes—
124#14273701C2314yes—
125#14273699—28no—
126C4×Dic118—22no—
127C4×Dic118C2314yes—
128C4×D236—22no—
129C4×D236C2314yes—
130(C22⋊D59)⋊C4—28no—
131C2×C4⋊Dic59—21no—
132C2×C4⋊Dic59—21no—
133C2×C4⋊Dic59—21no—
134C2×C4⋊Dic59—22no—
135C2×C4⋊Dic59—22no—
136C2×C4⋊Dic59C2311yescharacteristic
137C2×C4⋊Dic59C2311yescharacteristic
138C2×C4⋊Dic59C2311yescharacteristic
139C2×C4⋊Dic59C2311yescharacteristic
140C2×C4⋊Dic59C2314yes—
141C2×C4⋊Dic59C2314yes—
142C2×Dic59⋊C4—21no—
143C2×Dic59⋊C4—21no—
144C2×C22⋊Dic59—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—21no—
149C2×(C2×D59)⋊C4—21no—
150C2×(C2×D59)⋊C4—21no—
151C2×C4×Dic59—21no—
152#14273661C2314yes—
153#14273661C2314yes—
154#14273661C2314yes—
155#14273652C2314yes—
156#14273652C2314yes—
157#14273652C2314yes—
158#14273652C2314yes—
159#14273652C2314yes—
160#14273652C2314yes—
161#14273649C2314yes—
162#14273649C2314yes—
163#14273649C2314yes—
164#14273649C2314yes—
165C22×D4×C59D411yescharacteristic
166C23×C4×C59C2311yescharacteristic
167C23×C4×C59C2311yescharacteristic
168C2×M16×C59—42no—
169C2×M16×C59C2314yes—
170C22×C8×C59—42no—
171C22×C8×C59C2311yescharacteristic
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174C22×C8×C59C2311yescharacteristic
175C22×C8×C59C2314yes—
176C4×D4×C59D414yes—
177C4×D4×C59C2314yes—
178C2×C4⋊C4×C59D411yescharacteristic
179C2×C22⋊C4×C59D411yescharacteristic
180C2×C22⋊C4×C59D411yescharacteristic
181C2×C42×C59C2311yescharacteristic
182C4⋊C8×C59C2314yes—
183C22⋊C8×C59C2314yes—
184C22⋊C8×C59C2314yes—
185#97×C59C2314yes—
186C24×C59C2×D411yescharacteristic
187C24×C59C2×D411yescharacteristic
188C23×D59—21no—
189C23×D59—21no—
190C2×D4×C59—24no—
191C2×D4×C59C2×D414yes—
192C22×C4×C59—22no—
193C22×C4×C59—22no—
194C22×C4×C59—22no—
195C22×C4×C59—22no—
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D412yes—
201C22×C4×C59C2×D412yes—
202C22×C4×C59C2412yes—
203C22×C4×C59C2412yes—
204C22×C4×C59C2411yescharacteristic
205C2×C22⋊D59—24no—
206C2×C22⋊D59—24no—
207C2×C22⋊D59—24no—
208C2×C22⋊D59—24no—
209C2×C22⋊D59—44no—
210C2×C22⋊D59—44no—
211C2×C22⋊D59—44no—
212C2×C22⋊D59—44no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59—21no—
219C22×Dic59—24no—
220C22×Dic59—24no—
221C22×Dic59—24no—
222C22×Dic59—44no—
223C22×Dic59—44no—
224C22×Dic59—44no—
225#11745687—432no—
226#11745685—28no—
227#11745685—44no—
228#11745685—48no—
229C2×D236—22no—
230C2×D236—22no—
231C2×D236—22no—
232C2×D236—22no—
233C2×D236—21no—
234C2×D236—21no—
235C2×D236C2412yes—
236C2×D236C2412yes—
237C2×C4×D59—24no—
238C2×C4×D59—24no—
239C2×C4×D59—44no—
240C2×C4×D59—44no—
241C2×Dic118—21no—
242C2×Dic118—22no—
243C2×Dic118—22no—
244C2×Dic118—22no—
245C2×Dic118—28no—
246C2×Dic118—24no—
247C2×Dic118—21no—
248C2×Dic118—24no—
249C2×Dic118—44no—
250C2×Dic118—48no—
251C2×Dic118—44no—
252C2×Dic118—44no—
253C2×Dic118#4114yescomplemented
254C2×Dic118C2412yes—
255C2×Dic118C2412yes—
256M16×C59—44no—
257C2×C8×C59—22no—
258C2×C8×C59—22no—
259C2×C8×C59—22no—
260C2×C8×C59—22no—
261C2×C8×C59—44no—
262C2×C8×C59C2412yes—
263C2×C8×C59C2412yes—
264C2×C8×C59C2412yes—
265C2×C8×C59C2412yes—
266C4⋊C4×C59C2×D414yes—
267C22⋊C4×C59C2×D414yes—
268C22⋊C4×C59C2×D414yes—
269C42×C59C2×D412yes—
270C42×C59C2412yes—
271C22⋊Dic59—24no—
272(C2×D59)⋊C4—24no—
273(C2×D59)⋊C4—24no—
274(C2×D59)⋊C4—24no—
275(C2×D59)⋊C4—24no—
276(C2×D59)⋊C4—24no—
277(C2×D59)⋊C4—24no—
278C4⋊Dic59—21no—
279C4⋊Dic59—21no—
280C4⋊Dic59—21no—
281C4⋊Dic59—24no—
282C4⋊Dic59—24no—
283C4⋊Dic59—24no—
284C4⋊Dic59—21no—
285C4⋊Dic59C2412yes—
286C4⋊Dic59C2412yes—
287C4⋊Dic59C2412yes—
288C4⋊Dic59C2412yes—
289Dic59⋊C4—24no—
290Dic59⋊C4—24no—
291C4×Dic59—24no—
292D472—44no—
293#11745660—28no—
294#11745660—44no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59—22no—
300C23×C59AGL(1,ℤ/8)14yes—
301C23×C59C22×D412yes—
302C23×C59C22×D412yes—
303C23×C59C22×D411yescharacteristic
304C22×D59—22no—
305C22×D59—22no—
306C22×D59—42no—
307C22×D59—42no—
308C22×D59—42no—
309C22×D59—42no—
310C22×D59—42no—
311C22×D59—42no—
312D4×C59—28no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—24no—
318C2×C4×C59—24no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59C22×D412yes—
324C2×C4×C59C22×D412yes—
325C2×C4×C59C22×D412yes—
326C2×C4×C59C22×D412yes—
327C2×C4×C59C22×D411yescharacteristic
328C2×C4×C59C2×#4112yes—
329C2×C4×C59H(5,𝔽2)12yes—
330C2×C4×C59C2511yescharacteristic
331C22⋊D59—48no—
332C22⋊D59—48no—
333C22⋊D59—48no—
334C22⋊D59—48no—
335C2×Dic59—24no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—22no—
341C2×Dic59—22no—
342C2×Dic59—48no—
343C2×Dic59—48no—
344C2×Dic59—42no—
345C2×Dic59—42no—
346C2×Dic59—42no—
347C2×Dic59—42no—
348C2×Dic59—48no—
349C2×Dic59—42no—
350D236—22no—
351D236—22no—
352D236—22no—
353D236—22no—
354D236—42no—
355D236—42no—
356C4×D59—48no—
357C4×D59—48no—
358Dic118—24no—
359Dic118—22no—
360Dic118—22no—
361Dic118—22no—
362Dic118—48no—
363Dic118—48no—
364Dic118—42no—
365Dic118C2×#4114yescomplemented
366C8×C59—22no—
367C8×C59—22no—
368C8×C59—22no—
369C8×C59—22no—
370C2×#3308—591nomaximal, Sylow
371C22×C59—22no—
372C22×C59—28no—
373C22×C59—22no—
374C22×C59—22no—
375C22×C59—22no—
376C22×C59—22no—
377C22×C59—44no—
378C22×C59#54612yes—
379C22×C59C2×AGL(1,ℤ/8)14yes—
380C22×C59C2×AGL(1,ℤ/8)12yes—
381C22×C59#57812yes—
382C22×C59C23×D411yescharacteristic
383C2×D59—42no—
384C2×D59—42no—
385C2×D59—42no—
386C2×D59—42no—
387C2×D59—42no—
388C2×D59—42no—
389C2×D59—84no—
390C2×D59—84no—
391C4×C59—22no—
392C4×C59—22no—
393C4×C59—22no—
394C4×C59—22no—
395C4×C59#54612yes—
396C4×C59C22×#4111yescharacteristic
397C4×C59C2×H(5,𝔽2)11yescharacteristic
398Dic59—24no—
399Dic59—42no—
400Dic59—42no—
401Dic59—42no—
402Dic59—42no—
403Dic59—42no—
404C2×#548—591no—
405C2×#547—591no—
406#3308—5916no—
407C2×#489—591no—
408C2×#484—591no—
409C2×#480—591no—
410C2×#477—591no—
411C2×#468—591no—
412C2×#466—591no—
413C2×#463—591no—
414C2×#449—591no—
415C2×#448—591no—
416C2×#440—591no—
417C2×#435D5911yescharacteristic, complemented
418C2×#417—591no—
419C22×#103—591no—
420C2×C59—24no—
421C2×C59—42no—
422C2×C59#330814yescomplemented
423C2×C59C2×#54611yescharacteristic
424C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
425C2×C59C2×#57811yescharacteristic
426D59—82no—
427D59—82no—
428C22×#41—591no—
429C22×#41—1181no—
430C23×Q8—591no—
431C22×SD16—591no—
432C22×SD16—591no—
433C22×D8—591no—
434C22×M16C2×D5911yescharacteristic
435C23×C8C2×D5911yescharacteristic
436#548—598no—
437#548—1184no—
438#547—598no—
439#547—1184no—
440C2×C4⋊Q8—591no—
441C2×#124—591no—
442C2×#124—1181no—
443C2×#123—1181no—
444C2×#123—1181no—
445C2×C22⋊Q8—591no—
446C2×C22⋊Q8—1181no—
447C2×C22⋊Q8—1181no—
448C2×#121—591no—
449C2×#121—591no—
450C2×#121—591no—
451C2×#121—1181no—
452C2×C4×Q8—591no—
453C2×C4×D4—591no—
454C2×C4×D4—1181no—
455C2×C4×D4C2×D5911yescharacteristic
456C22×C4⋊C4—591no—
457C22×C4⋊C4—591no—
458#489—598no—
459#484—598no—
460#480—598no—
461#477—598no—
462#468—598no—
463#466—598no—
464#463—598no—
465#449—598no—
466#448—598no—
467#440—598no—
468#435C2×D5918yescomplemented
469C2×#107—591no—
470C2×#107—591no—
471C2×#107—591no—
472C2×C4⋊C8C2×D5911yescharacteristic
473#417—598no—
474C2×#103—591no—
475C2×#103—591no—
476C2×#103—591no—
477C2×#103—591no—
478C2×#103—591no—
479C2×#103—591no—
480C2×#103—598no—
481C2×#102—591no—
482C2×#102—591no—
483C2×#102—591no—
484C2×#102—591no—
485C2×C22⋊C8C2×D5911yescharacteristic
486C2×C22⋊C8C2×D5911yescharacteristic
487C2×#97C2×D5911yescharacteristic
488C59C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—594no—
490C2×#41—1184no—
491C2×#41—1188no—
492C2×#41—1182no—
493C2×#41—2362no—
494C2×#41—2368no—
495C22×Q8—591no—
496C22×Q8—591no—
497C22×Q8—594no—
498C22×Q8—1184no—
499C22×Q8—1181no—
500C22×Q8—1181no—
501C22×Q8—1182no—
502C22×Q8—2362no—
503C22×D4—591no—
504C22×D4—591no—
505C22×D4—1181no—
506C22×D4—1181no—
507C22×D4—1181no—
508C22×D4—1181no—
509C22×D4D23611yescharacteristic
510C23×C4—1181no—
511C23×C4—1181no—
512C23×C4—1181no—
513C23×C4—1181no—
514C23×C4—1181no—
515C23×C4C22×D5911yescharacteristic
516C23×C4C22×D5911yescharacteristic
517C2×SD16—594no—
518C2×SD16—594no—
519C2×SD16—1184no—
520C2×SD16—2362no—
521C2×D8—594no—
522C2×D8—2362no—
523C2×M16—42no—
524C2×M16C22×D5914yes—
525C22×C8—42no—
526C22×C8C22×D5911yescharacteristic
527C22×C8C22×D5911yescharacteristic
528C22×C8C22×D5911yescharacteristic
529C22×C8C22×D5911yescharacteristic
530C22×C8C22×D5914yes—
531C4⋊Q8—594no—
532C4⋊Q8—1182no—
533#124—594no—
534#124—1188no—
535#124—1182no—
536#123—1188no—
537#123—1188no—
538C22⋊Q8—594no—
539C22⋊Q8—1182no—
540C22⋊Q8—1188no—
541C22⋊Q8—1188no—
542#121—594no—
543#121—594no—
544#121—594no—
545#121—1188no—
546#121—1182no—
547#121—1182no—
548#121—1182no—
549C4×Q8—594no—
550C4×Q8—1182no—
551C4×D4—594no—
552C4×D4—1188no—
553C4×D4—1182no—
554C4×D4D23614yes—
555C4×D4C22×D5914yes—
556C2×C4⋊C4—591no—
557C2×C4⋊C4—591no—
558C2×C4⋊C4—591no—
559C2×C4⋊C4—594no—
560C2×C4⋊C4—594no—
561C2×C4⋊C4—591no—
562C2×C4⋊C4—1181no—
563C2×C4⋊C4—1181no—
564C2×C4⋊C4—1182no—
565C2×C4⋊C4—1182no—
566C2×C4⋊C4—1181no—
567C2×C4⋊C4—1181no—
568C2×C4⋊C4—1181no—
569C2×C4⋊C4D23611yescharacteristic
570C2×C22⋊C4—1181no—
571C2×C22⋊C4—1181no—
572C2×C22⋊C4—1181no—
573C2×C22⋊C4—1181no—
574C2×C22⋊C4—1181no—
575C2×C22⋊C4—1181no—
576C2×C22⋊C4—1181no—
577C2×C22⋊C4D23611yescharacteristic
578C2×C22⋊C4D23611yescharacteristic
579C2×C42—1181no—
580C2×C42C22×D5911yescharacteristic
581#107—594no—
582#107—594no—
583#107—594no—
584C4⋊C8C22×D5914yes—
585#103—594no—
586#103—594no—
587#103—594no—
588#103—594no—
589#103—594no—
590#103—594no—
591#102—594no—
592#102—594no—
593#102—594no—
594#102—594no—
595C22⋊C8C22×D5914yes—
596C22⋊C8C22×D5914yes—
597#97C22×D5914yes—
598C24—1181no—
599C24—1181no—
600C24C2×D23611yescharacteristic
601C24C2×D23611yescharacteristic
602#41—1188no—
603#41—2364no—
604#41—2368no—
605#41—23632no—
606C2×Q8—594no—
607C2×Q8—592no—
608C2×Q8—592no—
609C2×Q8—1188no—
610C2×Q8—1181no—
611C2×Q8—1184no—
612C2×Q8—1181no—
613C2×Q8—1184no—
614C2×Q8—1182no—
615C2×Q8—1182no—
616C2×Q8—1182no—
617C2×Q8—2364no—
618C2×Q8—2364no—
619C2×Q8—2368no—
620C2×Q8—2364no—
621C2×D4—24no—
622C2×D4—592no—
623C2×D4—592no—
624C2×D4—1184no—
625C2×D4—1184no—
626C2×D4—1184no—
627C2×D4—1184no—
628C2×D4—1181no—
629C2×D4—1181no—
630C2×D4—1182no—
631C2×D4—1182no—
632C2×D4—1182no—
633C2×D4—1182no—
634C2×D4—2364no—
635C2×D4—2364no—
636C2×D4—2364no—
637C2×D4—2364no—
638C2×D4C2×D23614yes—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—1181no—
644C22×C4—1184no—
645C22×C4—1184no—
646C22×C4—1184no—
647C22×C4—1181no—
648C22×C4—1181no—
649C22×C4—1181no—
650C22×C4—1181no—
651C22×C4—1181no—
652C22×C4—1184no—
653C22×C4—1184no—
654C22×C4—2364no—
655C22×C4—2364no—
656C22×C4—2364no—
657C22×C4—2364no—
658C22×C4—2364no—
659C22×C4C2×D23612yes—
660C22×C4C2×D23612yes—
661C22×C4C2×D23611yescharacteristic
662C22×C4C2×D23611yescharacteristic
663C22×C4C2×D23611yescharacteristic
664C22×C4C2×D23611yescharacteristic
665C22×C4C23×D5912yes—
666C22×C4C23×D5912yes—
667C22×C4C23×D5911yescharacteristic
668SD16—1188no—
669SD16—2364no—
670D8—2364no—
671M16—44no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8C23×D5912yes—
678C2×C8C23×D5912yes—
679C2×C8C23×D5912yes—
680C2×C8C23×D5912yes—
681C4⋊C4—592no—
682C4⋊C4—592no—
683C4⋊C4—592no—
684C4⋊C4—592no—
685C4⋊C4—1181no—
686C4⋊C4—1181no—
687C4⋊C4—1181no—
688C4⋊C4—1184no—
689C4⋊C4—1184no—
690C4⋊C4—1181no—
691C4⋊C4—1184no—
692C4⋊C4—1184no—
693C4⋊C4—1184no—
694C4⋊C4C2×D23614yes—
695C22⋊C4—1184no—
696C22⋊C4—1184no—
697C22⋊C4—1184no—
698C22⋊C4—1184no—
699C22⋊C4—1184no—
700C22⋊C4—1184no—
701C22⋊C4—1184no—
702C22⋊C4C2×D23614yes—
703C22⋊C4C2×D23614yes—
704C42—1184no—
705C42C2×D23612yes—
706C42C23×D5912yes—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—1182no—
713C23—1182no—
714C23—2362no—
715C23—2362no—
716C23—2362no—
717C23—2362no—
718C23—2362no—
719C23—2362no—
720C23#1427375514yes—
721C23C22×D23612yes—
722C23C22×D23612yes—
723C23C22×D23611yescharacteristic
724Q8—594no—
725Q8—1182no—
726Q8—1184no—
727Q8—1182no—
728Q8—1182no—
729Q8—2368no—
730Q8—2368no—
731Q8—2362no—
732D4—28no—
733D4—1182no—
734D4—1182no—
735D4—1182no—
736D4—1182no—
737D4—2368no—
738D4—2368no—
739D4—2368no—
740D4—2368no—
741D4—2362no—
742D4—2362no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—1182no—
754C2×C4—1184no—
755C2×C4—1182no—
756C2×C4—1182no—
757C2×C4—1182no—
758C2×C4—1182no—
759C2×C4—1182no—
760C2×C4—2368no—
761C2×C4—2368no—
762C2×C4—2368no—
763C2×C4—2368no—
764C2×C4—2362no—
765C2×C4—2362no—
766C2×C4—2362no—
767C2×C4—2368no—
768C2×C4—2362no—
769C2×C4—2362no—
770C2×C4C22×D23612yes—
771C2×C4C22×D23612yes—
772C2×C4C22×D23612yes—
773C2×C4C22×D23612yes—
774C2×C4C22×D23611yescharacteristic
775C2×C4#41×D5912yes—
776C2×C4#1427377212yes—
777C2×C4C24×D5911yescharacteristic
778C8—22no—
779C8—22no—
780C8—22no—
781C8—22no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—44no—
789C22—4724no—
790C22—4724no—
791C22—2362no—
792C22—2362no—
793C22—2362no—
794C22—2362no—
795C22—2362no—
796C22—2362no—
797C22#1683804712yes—
798C22C2×#1427375514yes—
799C22C2×#1427375512yes—
800C22#1683821912yes—
801C22C23×D23611yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—1184no—
807C4—2362no—
808C4—2362no—
809C4—2362no—
810C4—2362no—
811C4—2362no—
812C4#1683804712yes—
813C4C2×#41×D5911yescharacteristic
814C4C2×#1427377211yescharacteristic
815C2—24no—
816C2—42no—
817C2—4722no—
818C2—4722no—
819C2#2143608914yesdirect product factor
820C2C2×#1683804711yescharacteristic
821C2C22×#1427375511yescharacteristic
822C2C2×#1683821911yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#435C2
socleC23×C59C22×D4
hypercenterC2×#435D59
hypocenterC59C2×#3308
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16838061C2semidirect
2. C2×#16838056C2semidirect
3. #21436089C2direct (N × H)
4. C2×#16837762C2semidirect
5. C2×#16837738C2semidirect
6. C2×#16837716C2semidirect
7. C2×#16837698C2semidirect
8. C2×#16837648C2semidirect
9. C2×#16837638C2semidirect
10. C2×#16837618C2semidirect
11. C2×#16837549C2semidirect
12. C2×#16837543C2semidirect
13. C2×#16837504C2semidirect
14. C2×#16837404C2semidirect
15. C22×#14273652C2semidirect
16. C2×C59×#435C2semidirect
24. #16838061C22semidirect
26. #16838056C22semidirect
44. #16837762C22semidirect
45. #16837738C22semidirect
46. #16837716C22semidirect
47. #16837698C22semidirect
48. #16837648C22semidirect
49. #16837638C22semidirect
50. #16837618C22semidirect
51. #16837549C22semidirect
52. #16837543C22semidirect
53. #16837504C22semidirect
57. #16837404C22semidirect
64. C2×#14273652C22semidirect
72. C59×#435C22semidirect
253. C2×Dic118#41semidirect
365. Dic118C2×#41semidirect
417. C2×#435D59semidirect
422. C2×C59#3308semidirect
468. #435C2×D59semidirect
488. C59C2×#3308semidirect
819. C2#21436089direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380612
C2×#168380562
#214360892
C2×#168377622
C2×#168377382
C2×#168377162
C2×#168376982
C2×#168376482
C2×#168376382
C2×#168376182
C2×#168375492
C2×#168375432
C2×#168375042
C2×#168374042
C22×#142736522
C2×C59×#4352
C2×#330859