Finite Group Databasebeta

← C2×#21434707 #29458481

Subgroups — C2×#21434707 #29458481

Order 15104.

1970 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838023C211yesmaximal, characteristic, complemented
2#21434707C2116yesmaximal, direct product factor
3C2×#16837798C211yesmaximal, characteristic, complemented
4C2×#16837784C211yesmaximal, characteristic, complemented
5C2×#16837764C211yesmaximal, characteristic, complemented
6C2×#16837761C211yesmaximal, characteristic, complemented
7C2×#16837658C211yesmaximal, characteristic, complemented
8C2×#16837653C211yesmaximal, characteristic
9C2×#16837633C211yesmaximal, characteristic, complemented
10C2×#16837629C211yesmaximal, characteristic, complemented
11C2×#16837512C211yesmaximal, characteristic, complemented
12C2×#16837507C211yesmaximal, characteristic, complemented
13C2×C4×#11745671C211yesmaximal, characteristic, complemented
14C2×C4×#11745670C211yesmaximal, characteristic, complemented
15C2×#16837358C211yesmaximal, characteristic, complemented
16C2×C59×#542C211yesmaximal, characteristic, complemented
17C22×#11745672C2211yescharacteristic
18C22×#11745670C2211yescharacteristic
19C22×#11745671C2211yescharacteristic
20C22×#11745669C2211yescharacteristic
21C22×#11745664C2211yescharacteristic
22C23×C59⋊C8C2211yescharacteristic
23#16838023—24no—
24#16838023C2218yescomplemented
25C2×#14273727C2211yescharacteristic
26C2×#14273722—21no—
27C2×#14273715C2211yescharacteristic
28C2×#14273713—21no—
29C2×#14273709—21no—
30C2×#14273706C2211yescharacteristic
31C2×#14273705—21no—
32C2×#14273701C2211yescharacteristic
33C2×C4×Dic118C2211yescharacteristic
34C2×C4×D236C2211yescharacteristic
35#16837798C2218yescomplemented
36#16837784C2218yescomplemented
37#16837764C2218yescomplemented
38#16837761C2218yescomplemented
39#16837658C2218yescomplemented
40#16837653C2218yes—
41#16837633C2218yescomplemented
42#16837629C2218yescomplemented
43#16837512C2218yescomplemented
44#16837507C2218yescomplemented
45C4×#11745671C2218yescomplemented
46C4×#11745670C2218yescomplemented
47C2×#14273658C2211yescharacteristic
48C2×#14273658C2211yescharacteristic
49C2×#14273658C2211yescharacteristic
50C2×#14273658C2211yescharacteristic
51C2×#14273651C2211yescharacteristic
52C2×#14273651C2211yescharacteristic
53C2×#14273650C2211yescharacteristic
54C2×#14273650C2211yescharacteristic
55C2×#14273648C2211yescharacteristic
56C2×#14273648C2211yescharacteristic
57C2×#14273647C2211yescharacteristic
58C2×#14273647C2211yescharacteristic
59#16837358C2218yescomplemented
60C2×#14273638C2211yescharacteristic
61C2×#14273638C2211yescharacteristic
62C2×C4×C59⋊C8C2211yescharacteristic
63C2×C4×C59⋊C8C2211yescharacteristic
64C59×#542—24no—
65C59×#542C2218yescomplemented
66C2×C4⋊Q8×C59C2211yescharacteristic
67C2×#126×C59—21no—
68C2×#124×C59—21no—
69C2×#124×C59C2211yescharacteristic
70C2×#123×C59—21no—
71C2×C22⋊Q8×C59—21no—
72C2×C22⋊Q8×C59C2211yescharacteristic
73C2×#121×C59C2211yescharacteristic
74C2×C4×Q8×C59C2211yescharacteristic
75C2×C4×D4×C59C2211yescharacteristic
76C2×#117×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×D236C2311yescharacteristic
80C22×C22⋊D59—21no—
81C22×C4×D59—21no—
82C2×#11745672—24no—
83C2×#11745672C2314yes—
84C2×#11745670—24no—
85C2×#11745670C2314yes—
86C2×#11745671—24no—
87C2×#11745671C2314yes—
88C2×#11745669—24no—
89C2×#11745669C2314yes—
90C2×#11745664—24no—
91C2×#11745664C2314yes—
92C22×C59⋊C8—24no—
93C22×C59⋊C8C2314yes—
94C22×C59⋊C8C2311yescharacteristic
95C22×C59⋊C8C2311yescharacteristic
96C22×C59⋊C8C2311yescharacteristic
97C22×C59⋊C8C2311yescharacteristic
98#14273727—22no—
99#14273727C2314yes—
100#14273722—28no—
101#14273715—22no—
102#14273715C2314yes—
103#14273713—28no—
104#14273709—28no—
105#14273706—22no—
106#14273706C2314yes—
107#14273705—28no—
108#14273701—22no—
109#14273701C2314yes—
110C4×Dic118—22no—
111C4×Dic118C2314yes—
112C4×D236—22no—
113C4×D236C2314yes—
114C2×C4⋊Dic59—21no—
115C2×C4⋊Dic59C2311yescharacteristic
116C2×C4⋊Dic59C2311yescharacteristic
117C2×Dic59⋊C4—21no—
118C2×Dic59⋊C4—21no—
119C2×C22⋊Dic59—21no—
120C2×(C2×D59)⋊C4—21no—
121C2×(C2×D59)⋊C4—21no—
122C2×(C2×D59)⋊C4—21no—
123C2×(C2×D59)⋊C4—21no—
124C2×C4×Dic59—21no—
125#14273658C2314yes—
126#14273658C2314yes—
127#14273658C2314yes—
128#14273658C2314yes—
129#14273651C2314yes—
130#14273651C2314yes—
131#14273650C2314yes—
132#14273650C2314yes—
133#14273648C2314yes—
134#14273648C2314yes—
135#14273647C2314yes—
136#14273647C2314yes—
137#14273638C2314yes—
138#14273638C2314yes—
139C4×C59⋊C8C2314yes—
140C4×C59⋊C8C2314yes—
141C22×Q8×C59—21no—
142C22×Q8×C59C2311yescharacteristic
143C22×D4×C59—21no—
144C22×D4×C59C2311yescharacteristic
145C23×C4×C59—21no—
146C23×C4×C59C2311yescharacteristic
147C4⋊Q8×C59—22no—
148C4⋊Q8×C59C2314yes—
149#126×C59—28no—
150#124×C59—28no—
151#124×C59—22no—
152#124×C59C2314yes—
153#123×C59—28no—
154C22⋊Q8×C59—22no—
155C22⋊Q8×C59—28no—
156C22⋊Q8×C59C2314yes—
157#121×C59—22no—
158#121×C59C2314yes—
159C4×Q8×C59—22no—
160C4×Q8×C59C2314yes—
161C4×D4×C59—22no—
162C4×D4×C59C2314yes—
163#117×C59D414yes—
164#117×C59C2314yes—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59D411yescharacteristic
169C2×C4⋊C4×C59D411yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177C2×C22⋊C4×C59D411yescharacteristic
178C2×C22⋊C4×C59D411yescharacteristic
179C2×C42×C59—21no—
180C2×C42×C59C2311yescharacteristic
181C2×C42×C59C2311yescharacteristic
182C24×C59—21no—
183C24×C59C2×D411yescharacteristic
184C23×D59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—24no—
187C2×Q8×C59—22no—
188C2×Q8×C59—22no—
189C2×Q8×C59—82no—
190C2×Q8×C59C2412yes—
191C2×D4×C59—24no—
192C2×D4×C59—21no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59—82no—
196C2×D4×C59C2412yes—
197C22×C4×C59—22no—
198C22×C4×C59—22no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—24no—
203C22×C4×C59—82no—
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D412yes—
210C22×C4×C59C2412yes—
211C22×C4×C59C2411yescharacteristic
212C2×C22⋊D59—24no—
213C2×C22⋊D59—82no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C2×D236—22no—
218C2×D236—22no—
219C2×D236—21no—
220C2×D236C2412yes—
221C2×C4×D59—24no—
222C2×C4×D59—82no—
223C2×Dic118—22no—
224C2×Dic118—22no—
225C2×Dic118—21no—
226C2×Dic118—24no—
227C2×Dic118—82no—
228C2×Dic118C2412yes—
229C4⋊C4×C59—24no—
230C4⋊C4×C59—24no—
231C4⋊C4×C59—24no—
232C4⋊C4×C59—21no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59C2×D414yes—
235C4⋊C4×C59C2×D414yes—
236C4⋊C4×C59C2412yes—
237C4⋊C4×C59C2412yes—
238C22⋊C4×C59—24no—
239C22⋊C4×C59—24no—
240C22⋊C4×C59—24no—
241C22⋊C4×C59—24no—
242C22⋊C4×C59—24no—
243C22⋊C4×C59C2×D414yes—
244C22⋊C4×C59C2×D414yes—
245C42×C59—24no—
246C42×C59C2×D412yes—
247C42×C59C2×D412yes—
248C42×C59C2412yes—
249C42×C59C2412yes—
250C22⋊Dic59—24no—
251#11745672—28no—
252#11745671—28no—
253#11745670—28no—
254#11745669—28no—
255(C2×D59)⋊C4—24no—
256(C2×D59)⋊C4—24no—
257(C2×D59)⋊C4—24no—
258(C2×D59)⋊C4—24no—
259C4⋊Dic59—24no—
260C4⋊Dic59—21no—
261C4⋊Dic59—21no—
262C4⋊Dic59C2412yes—
263C4⋊Dic59C2412yes—
264Dic59⋊C4—24no—
265Dic59⋊C4—24no—
266C4×Dic59—24no—
267#11745664—28no—
268C2×C59⋊C8—22no—
269C2×C59⋊C8—22no—
270C2×C59⋊C8—28no—
271C2×C59⋊C8#4114yes—
272C2×C59⋊C8#4114yes—
273C2×C59⋊C8C2412yes—
274C2×C59⋊C8C2412yes—
275C2×C59⋊C8C2412yes—
276C2×C59⋊C8C2412yes—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59—22no—
280C23×C59—22no—
281C23×C59—42no—
282C23×C59—42no—
283C23×C59—42no—
284C23×C59C22×D412yes—
285C23×C59C22×D411yescharacteristic
286C22×D59—22no—
287C22×D59—42no—
288C22×D59—42no—
289C22×D59—42no—
290Q8×C59—22no—
291Q8×C59—22no—
292Q8×C59—42no—
293Q8×C59—84no—
294D4×C59—22no—
295D4×C59—22no—
296D4×C59—42no—
297D4×C59—84no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—24no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—42no—
310C2×C4×C59—42no—
311C2×C4×C59—42no—
312C2×C4×C59—84no—
313C2×C4×C59C22×D412yes—
314C2×C4×C59C22×D412yes—
315C2×C4×C59C22×D412yes—
316C2×C4×C59C22×D412yes—
317C2×C4×C59C22×D412yes—
318C2×C4×C59C22×D411yescharacteristic
319C2×C4×C59C2×#4112yes—
320C2×C4×C59C2×#4112yes—
321C2×C4×C59C2511yescharacteristic
322C22⋊D59—84no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—42no—
327C2×Dic59—42no—
328C2×Dic59—42no—
329D236—22no—
330D236—22no—
331D236—42no—
332C4×D59—84no—
333Dic118—22no—
334Dic118—22no—
335Dic118—42no—
336Dic118—84no—
337C59⋊C8—22no—
338C59⋊C8—22no—
339C59⋊C8C2×#4114yes—
340C59⋊C8C2×#4114yes—
341C2×#3173—591nomaximal, Sylow
342C22×C59—22no—
343C22×C59—22no—
344C22×C59—22no—
345C22×C59—44no—
346C22×C59—42no—
347C22×C59—42no—
348C22×C59—42no—
349C22×C59—84no—
350C22×C59#53212yes—
351C22×C59#57712yes—
352C22×C59#57712yes—
353C22×C59C23×D411yescharacteristic
354C2×D59—42no—
355C2×D59—42no—
356C2×D59—42no—
357C2×D59—84no—
358C4×C59—22no—
359C4×C59—22no—
360C4×C59—22no—
361C4×C59—22no—
362C4×C59—22no—
363C4×C59—42no—
364C4×C59—42no—
365C4×C59—42no—
366C4×C59#53212yes—
367C4×C59C22×#4111yescharacteristic
368C4×C59C22×#4111yescharacteristic
369Dic59—42no—
370Dic59—42no—
371Dic59—42no—
372C2×#542—591no—
373C2×#542D5911yescharacteristic, complemented
374#3173—5916no—
375C2×#498—591no—
376C2×#495—591no—
377C2×#489—591no—
378C2×#489—591no—
379C2×#470—591no—
380C2×#469—591no—
381C2×#465—591no—
382C2×#465—591no—
383C2×#442—591no—
384C2×#441—591no—
385C2×C4×SD16—591no—
386C2×C4×SD16—591no—
387C2×#405—591no—
388C2×C59—42no—
389C2×C59—82no—
390C2×C59#317314yescomplemented
391C2×C59C2×#53211yescharacteristic
392C2×C59C2×#57711yescharacteristic
393C2×C59C2×#57711yescharacteristic
394D59—82no—
395C22×Q16—591no—
396C22×SD16—591no—
397C22×SD16—591no—
398C22×D8—591no—
399C22×M16—591no—
400C23×C8—591no—
401#542—24no—
402#542—598no—
403#542—1184no—
404#542C2×D5918yescomplemented
405C2×C4⋊Q8—591no—
406C2×C4⋊Q8C2×D5911yescharacteristic
407C2×#126—21no—
408C2×#126—1181no—
409C2×#124—21no—
410C2×#124—591no—
411C2×#124—1181no—
412C2×#124C2×D5911yescharacteristic
413C2×#123—21no—
414C2×#123—1181no—
415C2×C22⋊Q8—21no—
416C2×C22⋊Q8—591no—
417C2×C22⋊Q8—1181no—
418C2×C22⋊Q8C2×D5911yescharacteristic
419C2×#121—591no—
420C2×#121C2×D5911yescharacteristic
421C2×C4×Q8—591no—
422C2×C4×Q8C2×D5911yescharacteristic
423C2×C4×D4—591no—
424C2×C4×D4C2×D5911yescharacteristic
425C2×#117C2×D5911yescharacteristic
426#498—598no—
427#495—598no—
428#489—598no—
429#489—598no—
430#470—598no—
431#469—598no—
432#465—598no—
433#465—598no—
434#442—598no—
435#441—598no—
436C4×SD16—598no—
437C4×SD16—598no—
438C2×#106—591no—
439C2×#106—591no—
440C2×#106—591no—
441C2×#106—591no—
442C2×#103—591no—
443C2×#103—591no—
444C2×#103—591no—
445C2×#103—591no—
446C2×#102—591no—
447C2×#102—591no—
448C2×#102—591no—
449C2×#102—591no—
450#405—598no—
451C2×#97—591no—
452C2×#97—591no—
453C2×C4×C8—591no—
454C2×C4×C8—591no—
455C59C2×#317311yescharacteristic, complemented, Sylow
456C22×Q8—21no—
457C22×Q8—591no—
458C22×Q8—1181no—
459C22×Q8C22×D5911yescharacteristic
460C22×D4—21no—
461C22×D4—591no—
462C22×D4—1181no—
463C22×D4C22×D5911yescharacteristic
464C23×C4—21no—
465C23×C4—1181no—
466C23×C4C22×D5911yescharacteristic
467C2×Q16—594no—
468C2×Q16—1184no—
469C2×SD16—594no—
470C2×SD16—594no—
471C2×SD16—1184no—
472C2×SD16—1184no—
473C2×D8—594no—
474C2×D8—1184no—
475C2×M16—594no—
476C2×M16—1184no—
477C22×C8—591no—
478C22×C8—591no—
479C22×C8—591no—
480C22×C8—594no—
481C22×C8—591no—
482C22×C8—1184no—
483C4⋊Q8—22no—
484C4⋊Q8—594no—
485C4⋊Q8—1182no—
486C4⋊Q8C22×D5914yes—
487#126—28no—
488#126—1188no—
489#124—28no—
490#124—22no—
491#124—594no—
492#124—1188no—
493#124—1182no—
494#124C22×D5914yes—
495#123—28no—
496#123—1188no—
497C22⋊Q8—22no—
498C22⋊Q8—28no—
499C22⋊Q8—594no—
500C22⋊Q8—1182no—
501C22⋊Q8—1188no—
502C22⋊Q8C22×D5914yes—
503#121—22no—
504#121—594no—
505#121—1182no—
506#121C22×D5914yes—
507C4×Q8—22no—
508C4×Q8—594no—
509C4×Q8—1182no—
510C4×Q8C22×D5914yes—
511C4×D4—22no—
512C4×D4—594no—
513C4×D4—1182no—
514C4×D4C22×D5914yes—
515#117C22⋊D5914yes—
516#117C22×D5914yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—591no—
522C2×C4⋊C4—1181no—
523C2×C4⋊C4—1181no—
524C2×C4⋊C4—1181no—
525C2×C4⋊C4C22⋊D5911yescharacteristic
526C2×C4⋊C4C22⋊D5911yescharacteristic
527C2×C4⋊C4C22×D5911yescharacteristic
528C2×C4⋊C4C22×D5911yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—1181no—
535C2×C22⋊C4—1181no—
536C2×C22⋊C4—1181no—
537C2×C22⋊C4—1181no—
538C2×C22⋊C4—1181no—
539C2×C22⋊C4C22⋊D5911yescharacteristic
540C2×C22⋊C4C22⋊D5911yescharacteristic
541C2×C42—21no—
542C2×C42—1181no—
543C2×C42C22×D5911yescharacteristic
544C2×C42C22×D5911yescharacteristic
545#106—594no—
546#106—594no—
547#106—594no—
548#106—594no—
549#103—594no—
550#103—594no—
551#103—594no—
552#103—594no—
553#102—594no—
554#102—594no—
555#102—594no—
556#102—594no—
557#97—594no—
558#97—594no—
559C4×C8—594no—
560C4×C8—594no—
561C24—21no—
562C24—1181no—
563C24C2×C22⋊D5911yescharacteristic
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—592no—
570C2×Q8—1184no—
571C2×Q8—1181no—
572C2×Q8—1182no—
573C2×Q8—1182no—
574C2×Q8—4722no—
575C2×Q8C23×D5912yes—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—82no—
581C2×D4—592no—
582C2×D4—1184no—
583C2×D4—1181no—
584C2×D4—1182no—
585C2×D4—1182no—
586C2×D4—4722no—
587C2×D4C23×D5912yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—82no—
595C22×C4—1181no—
596C22×C4—1181no—
597C22×C4—1181no—
598C22×C4—1184no—
599C22×C4—4722no—
600C22×C4C2×C22⋊D5912yes—
601C22×C4C2×C22⋊D5911yescharacteristic
602C22×C4C2×C22⋊D5911yescharacteristic
603C22×C4C2×C22⋊D5911yescharacteristic
604C22×C4C2×C22⋊D5911yescharacteristic
605C22×C4C2×C22⋊D5911yescharacteristic
606C22×C4C23×D5912yes—
607C22×C4C23×D5911yescharacteristic
608Q16—1188no—
609SD16—1188no—
610SD16—1188no—
611D8—1188no—
612M16—1188no—
613C2×C8—594no—
614C2×C8—594no—
615C2×C8—592no—
616C2×C8—592no—
617C2×C8—592no—
618C2×C8—592no—
619C2×C8—1188no—
620C2×C8—1182no—
621C2×C8—1182no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—592no—
628C4⋊C4—592no—
629C4⋊C4—1181no—
630C4⋊C4—1181no—
631C4⋊C4—1184no—
632C4⋊C4—1184no—
633C4⋊C4—1184no—
634C4⋊C4C2×C22⋊D5914yes—
635C4⋊C4C2×C22⋊D5914yes—
636C4⋊C4C23×D5912yes—
637C4⋊C4C23×D5912yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—1184no—
644C22⋊C4—1184no—
645C22⋊C4—1184no—
646C22⋊C4—1184no—
647C22⋊C4—1184no—
648C22⋊C4C2×C22⋊D5914yes—
649C22⋊C4C2×C22⋊D5914yes—
650C42—24no—
651C42—1184no—
652C42C2×C22⋊D5912yes—
653C42C2×C22⋊D5912yes—
654C42C23×D5912yes—
655C42C23×D5912yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—1182no—
664C23—2362no—
665C23—2362no—
666C23—2362no—
667C23C22×C22⋊D5912yes—
668C23C22×C22⋊D5911yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—84no—
673Q8—1182no—
674Q8—1182no—
675Q8—4724no—
676Q8—2362no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—1182no—
682D4—1182no—
683D4—4724no—
684D4—2362no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—84no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—4724no—
704C2×C4—2362no—
705C2×C4—2362no—
706C2×C4—2362no—
707C2×C4C22×C22⋊D5912yes—
708C2×C4C22×C22⋊D5912yes—
709C2×C4C22×C22⋊D5912yes—
710C2×C4C22×C22⋊D5912yes—
711C2×C4C22×C22⋊D5912yes—
712C2×C4C22×C22⋊D5911yescharacteristic
713C2×C4#41×D5912yes—
714C2×C4#41×D5912yes—
715C2×C4C24×D5911yescharacteristic
716C8—594no—
717C8—594no—
718C8—1182no—
719C8—1182no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—4724no—
729C22—2362no—
730C22—2362no—
731C22—2362no—
732C22#1683794812yes—
733C22#1683821012yes—
734C22#1683821312yes—
735C22C23×C22⋊D5911yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—2362no—
745C4—2362no—
746C4—2362no—
747C4#1683794812yes—
748C4C2×#41×D5911yescharacteristic
749C4C2×#41×D5911yescharacteristic
750C2—42no—
751C2—82no—
752C2—4722no—
753C2#2143470714yesdirect product factor
754C2C2×#1683794811yescharacteristic
755C2C2×#1683821011yescharacteristic
756C2C2×#1683821311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#542C2
socleC23×C59C22×D4
prime radicalC2×#16837653C2
hypercenterC2×#542D59
hypocenterC59C2×#3173
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16838023C2semidirect
2. #21434707C2direct (N × H)
3. C2×#16837798C2semidirect
4. C2×#16837784C2semidirect
5. C2×#16837764C2semidirect
6. C2×#16837761C2semidirect
7. C2×#16837658C2semidirect
9. C2×#16837633C2semidirect
10. C2×#16837629C2semidirect
11. C2×#16837512C2semidirect
12. C2×#16837507C2semidirect
13. C2×C4×#11745671C2semidirect
14. C2×C4×#11745670C2semidirect
15. C2×#16837358C2semidirect
16. C2×C59×#542C2semidirect
24. #16838023C22semidirect
35. #16837798C22semidirect
36. #16837784C22semidirect
37. #16837764C22semidirect
38. #16837761C22semidirect
39. #16837658C22semidirect
41. #16837633C22semidirect
42. #16837629C22semidirect
43. #16837512C22semidirect
44. #16837507C22semidirect
45. C4×#11745671C22semidirect
46. C4×#11745670C22semidirect
59. #16837358C22semidirect
65. C59×#542C22semidirect
373. C2×#542D59semidirect
390. C2×C59#3173semidirect
404. #542C2×D59semidirect
455. C59C2×#3173semidirect
753. C2#21434707direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380232
#214347072
C2×#168377982
C2×#168377842
C2×#168377642
C2×#168377612
C2×#168376582
C2×#168376532
C2×#168376332
C2×#168376292
C2×#168375122
C2×#168375072
C2×C4×#117456712
C2×C4×#117456702
C2×#168373582
C2×C59×#5422
C2×#317359