Finite Group Databasebeta

← C2×#21435002 #29459402

Subgroups — C2×#21435002 #29459402

Order 15104.

2250 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837980C211yesmaximal, characteristic, complemented
2#21435002C2116yesmaximal, direct product factor
3C2×#16837720C211yesmaximal, characteristic, complemented
4C2×#16837718C211yesmaximal, characteristic, complemented
5C2×#16837732C211yesmaximal, characteristic, complemented
6C2×#16837730C211yesmaximal, characteristic, complemented
7C2×#16837658C211yesmaximal, characteristic, complemented
8C2×#16837653C211yesmaximal, characteristic, complemented
9C2×#16837633C211yesmaximal, characteristic, complemented
10C2×#16837629C211yesmaximal, characteristic, complemented
11C2×#16837564C211yesmaximal, characteristic, complemented
12C2×#16837562C211yesmaximal, characteristic, complemented
13C2×#16837547C211yesmaximal, characteristic, complemented
14C2×#16837545C211yesmaximal, characteristic, complemented
15C2×#16837369C211yesmaximal, characteristic, complemented
16C2×C59×#537C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745670C2211yescharacteristic
20C22×#11745671C2211yescharacteristic
21C22×#11745669C2211yescharacteristic
22C22×#11745664C2211yescharacteristic
23C23×C59⋊C8C2211yescharacteristic
24#16837980—24no—
25#16837980C2218yescomplemented
26C2×#14273706C2211yescharacteristic
27C2×#14273706C2211yescharacteristic
28C2×#14273703—21no—
29C2×#14273701C2211yescharacteristic
30C2×#14273701C2211yescharacteristic
31C2×#14273699—21no—
32C2×#14273699—21no—
33C2×#14273698—21no—
34C22×C4⋊Dic59C2211yescharacteristic
35#16837732C2218yescomplemented
36#16837730C2218yescomplemented
37#16837720C2218yescomplemented
38#16837718C2218yescomplemented
39#16837658C2218yescomplemented
40#16837653C2218yescomplemented
41#16837633C2218yescomplemented
42#16837629C2218yescomplemented
43#16837564C2218yescomplemented
44#16837562C2218yescomplemented
45#16837547C2218yescomplemented
46#16837545C2218yescomplemented
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#16837369C2218yescomplemented
60C2×C22⋊(C59⋊C8)C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×C22⋊(C59⋊C8)C2211yescharacteristic
63C2×C22⋊(C59⋊C8)C2211yescharacteristic
64C22×#41×C59C2211yescharacteristic
65C22×#41×C59C2211yescharacteristic
66C59×#537—24no—
67C59×#537C2218yescomplemented
68C2×C22⋊Q8×C59—21no—
69C2×C22⋊Q8×C59C2211yescharacteristic
70C2×C22⋊Q8×C59C2211yescharacteristic
71C2×#121×C59—21no—
72C2×#121×C59—21no—
73C2×#121×C59—21no—
74C2×#121×C59C2211yescharacteristic
75C2×#121×C59C2211yescharacteristic
76C22×C4⋊C4×C59C2211yescharacteristic
77C2×#11745685—22no—
78C2×#11745685—42no—
79C2×#11745685—42no—
80C2×#11745685C2314yes—
81C22×Dic118C2311yescharacteristic
82C22×D236C2311yescharacteristic
83C22×C22⋊D59—21no—
84C22×C22⋊D59—21no—
85C22×C22⋊D59—21no—
86C23×Dic59—21no—
87C22×C4×D59—21no—
88C2×#11745672—42no—
89C2×#11745672C2314yes—
90C2×#11745670—42no—
91C2×#11745670C2314yes—
92C2×#11745671—42no—
93C2×#11745671C2314yes—
94C2×#11745669—42no—
95C2×#11745669C2314yes—
96C2×#11745664—42no—
97C2×#11745664C2314yes—
98C22×C59⋊C8—42no—
99C22×C59⋊C8C2311yescharacteristic
100C22×C59⋊C8C2311yescharacteristic
101C22×C59⋊C8C2311yescharacteristic
102C22×C59⋊C8C2311yescharacteristic
103C22×C59⋊C8C2314yes—
104#14273706—22no—
105#14273706—22no—
106#14273706C2314yes—
107#14273706C2314yes—
108#14273703—28no—
109#14273701—22no—
110#14273701—22no—
111#14273701C2314yes—
112#14273701C2314yes—
113#14273699—28no—
114#14273699—28no—
115#14273698—28no—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59—22no—
118C2×C4⋊Dic59C2311yescharacteristic
119C2×C4⋊Dic59C2311yescharacteristic
120C2×C4⋊Dic59C2314yes—
121C2×Dic59⋊C4—21no—
122C2×Dic59⋊C4—21no—
123C2×C22⋊Dic59—21no—
124C2×C22⋊Dic59—21no—
125C2×(C2×D59)⋊C4—21no—
126C2×(C2×D59)⋊C4—21no—
127#14273658C2314yes—
128#14273658C2314yes—
129#14273658C2314yes—
130#14273658C2314yes—
131#14273651C2314yes—
132#14273651C2314yes—
133#14273650C2314yes—
134#14273650C2314yes—
135#14273648C2314yes—
136#14273648C2314yes—
137#14273647C2314yes—
138#14273647C2314yes—
139C22⋊(C59⋊C8)C2314yes—
140C22⋊(C59⋊C8)C2314yes—
141C22⋊(C59⋊C8)C2314yes—
142C22⋊(C59⋊C8)C2314yes—
143C2×#41×C59—22no—
144C2×#41×C59—42no—
145C2×#41×C59—42no—
146C2×#41×C59—42no—
147C2×#41×C59—42no—
148C2×#41×C59D414yes—
149C2×#41×C59C2314yes—
150C2×#41×C59C2314yes—
151C22×Q8×C59D411yescharacteristic
152C22×Q8×C59C2311yescharacteristic
153C22×D4×C59—21no—
154C22×D4×C59—21no—
155C22×D4×C59—21no—
156C22×D4×C59D411yescharacteristic
157C22×D4×C59D411yescharacteristic
158C22×D4×C59D411yescharacteristic
159C22×D4×C59C2311yescharacteristic
160C23×C4×C59—21no—
161C23×C4×C59—21no—
162C23×C4×C59C2311yescharacteristic
163C23×C4×C59C2311yescharacteristic
164C23×C4×C59C2311yescharacteristic
165C22⋊Q8×C59—28no—
166C22⋊Q8×C59—22no—
167C22⋊Q8×C59—22no—
168C22⋊Q8×C59C2314yes—
169C22⋊Q8×C59C2314yes—
170#121×C59—28no—
171#121×C59—28no—
172#121×C59—28no—
173#121×C59—22no—
174#121×C59—22no—
175#121×C59C2314yes—
176#121×C59C2314yes—
177C2×C4⋊C4×C59—21no—
178C2×C4⋊C4×C59—22no—
179C2×C4⋊C4×C59—21no—
180C2×C4⋊C4×C59—21no—
181C2×C4⋊C4×C59C2311yescharacteristic
182C2×C4⋊C4×C59C2311yescharacteristic
183C2×C4⋊C4×C59C2314yes—
184C2×C22⋊C4×C59—21no—
185C2×C22⋊C4×C59—21no—
186C2×C22⋊C4×C59—21no—
187C2×C22⋊C4×C59—21no—
188C24×C59—21no—
189C24×C59C2×D411yescharacteristic
190C24×C59C2×D411yescharacteristic
191C24×C59C2×D411yescharacteristic
192C23×D59—21no—
193#41×C59—48no—
194#41×C59—44no—
195#41×C59—44no—
196#41×C59—44no—
197#41×C59—44no—
198#41×C59—48no—
199C2×Q8×C59—21no—
200C2×Q8×C59—22no—
201C2×Q8×C59—22no—
202C2×Q8×C59—42no—
203C2×Q8×C59C2×D414yes—
204C2×Q8×C59C2412yes—
205C2×D4×C59—24no—
206C2×D4×C59—24no—
207C2×D4×C59—24no—
208C2×D4×C59—21no—
209C2×D4×C59—22no—
210C2×D4×C59—22no—
211C2×D4×C59—42no—
212C2×D4×C59—42no—
213C2×D4×C59—42no—
214C2×D4×C59—44no—
215C2×D4×C59—82no—
216C2×D4×C59—82no—
217C2×D4×C59C2×D414yes—
218C2×D4×C59C2×D414yes—
219C2×D4×C59C2×D414yes—
220C2×D4×C59C2412yes—
221C22×C4×C59—22no—
222C22×C4×C59—22no—
223C22×C4×C59—22no—
224C22×C4×C59—22no—
225C22×C4×C59—22no—
226C22×C4×C59—22no—
227C22×C4×C59—21no—
228C22×C4×C59—21no—
229C22×C4×C59—21no—
230C22×C4×C59—24no—
231C22×C4×C59—24no—
232C22×C4×C59—44no—
233C22×C4×C59—82no—
234C22×C4×C59C2×D411yescharacteristic
235C22×C4×C59C2×D411yescharacteristic
236C22×C4×C59C2×D411yescharacteristic
237C22×C4×C59C2×D412yes—
238C22×C4×C59C2×D412yes—
239C22×C4×C59C2×D412yes—
240C22×C4×C59C2412yes—
241C22×C4×C59C2412yes—
242C22×C4×C59C2412yes—
243C22×C4×C59C2411yescharacteristic
244C2×C22⋊D59—24no—
245C2×C22⋊D59—24no—
246C2×C22⋊D59—24no—
247C2×C22⋊D59—44no—
248C2×C22⋊D59—82no—
249C2×C22⋊D59—82no—
250C22×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×Dic59—24no—
254C22×Dic59—82no—
255#11745685—44no—
256#11745685—44no—
257#11745685—48no—
258C2×D236—22no—
259C2×D236—22no—
260C2×D236—21no—
261C2×D236C2412yes—
262C2×C4×D59—24no—
263C2×C4×D59—44no—
264C2×Dic118—22no—
265C2×Dic118—22no—
266C2×Dic118—21no—
267C2×Dic118C2412yes—
268C4⋊C4×C59—24no—
269C4⋊C4×C59—21no—
270C4⋊C4×C59—21no—
271C4⋊C4×C59—24no—
272C4⋊C4×C59—24no—
273C4⋊C4×C59C2412yes—
274C4⋊C4×C59C2412yes—
275C22⋊C4×C59—24no—
276C22⋊C4×C59—24no—
277C22⋊C4×C59—24no—
278C22⋊C4×C59—24no—
279C22⋊Dic59—24no—
280C22⋊Dic59—24no—
281#11745672—44no—
282#11745671—44no—
283#11745670—44no—
284#11745669—44no—
285(C2×D59)⋊C4—24no—
286(C2×D59)⋊C4—24no—
287C4⋊Dic59—24no—
288C4⋊Dic59—21no—
289C4⋊Dic59—21no—
290C4⋊Dic59C2412yes—
291C4⋊Dic59C2412yes—
292Dic59⋊C4—24no—
293Dic59⋊C4—24no—
294#11745664—44no—
295C2×C59⋊C8—22no—
296C2×C59⋊C8—22no—
297C2×C59⋊C8—22no—
298C2×C59⋊C8—22no—
299C2×C59⋊C8—44no—
300C2×C59⋊C8C2412yes—
301C2×C59⋊C8C2412yes—
302C2×C59⋊C8C2412yes—
303C2×C59⋊C8C2412yes—
304C23×C59—22no—
305C23×C59—22no—
306C23×C59—22no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—22no—
311C23×C59—22no—
312C23×C59—22no—
313C23×C59—22no—
314C23×C59—42no—
315C23×C59—42no—
316C23×C59—42no—
317C23×C59C22×D412yes—
318C23×C59C22×D412yes—
319C23×C59C22×D412yes—
320C23×C59C22×D411yescharacteristic
321C22×D59—22no—
322C22×D59—42no—
323C22×D59—42no—
324C22×D59—42no—
325Q8×C59—22no—
326Q8×C59—22no—
327Q8×C59—44no—
328Q8×C59—42no—
329D4×C59—22no—
330D4×C59—22no—
331D4×C59—44no—
332D4×C59—44no—
333D4×C59—44no—
334D4×C59—48no—
335D4×C59—42no—
336D4×C59—84no—
337D4×C59—84no—
338C2×C4×C59—22no—
339C2×C4×C59—22no—
340C2×C4×C59—22no—
341C2×C4×C59—24no—
342C2×C4×C59—24no—
343C2×C4×C59—24no—
344C2×C4×C59—22no—
345C2×C4×C59—22no—
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—48no—
354C2×C4×C59—42no—
355C2×C4×C59—42no—
356C2×C4×C59—42no—
357C2×C4×C59—84no—
358C2×C4×C59C22×D412yes—
359C2×C4×C59C22×D412yes—
360C2×C4×C59C22×D412yes—
361C2×C4×C59C22×D411yescharacteristic
362C2×C4×C59H(5,𝔽2)12yes—
363C2×C4×C59H(5,𝔽2)12yes—
364C2×C4×C59C2511yescharacteristic
365C22⋊D59—48no—
366C22⋊D59—84no—
367C22⋊D59—84no—
368C2×Dic59—22no—
369C2×Dic59—22no—
370C2×Dic59—22no—
371C2×Dic59—42no—
372C2×Dic59—42no—
373C2×Dic59—42no—
374C2×Dic59—84no—
375D236—22no—
376D236—22no—
377D236—42no—
378C4×D59—48no—
379Dic118—22no—
380Dic118—22no—
381Dic118—42no—
382C59⋊C8—22no—
383C59⋊C8—22no—
384C59⋊C8—22no—
385C59⋊C8—22no—
386C2×#3204—591nomaximal, Sylow
387C22×C59—22no—
388C22×C59—22no—
389C22×C59—22no—
390C22×C59—22no—
391C22×C59—22no—
392C22×C59—22no—
393C22×C59—22no—
394C22×C59—22no—
395C22×C59—22no—
396C22×C59—44no—
397C22×C59—44no—
398C22×C59—44no—
399C22×C59—42no—
400C22×C59—42no—
401C22×C59—42no—
402C22×C59—84no—
403C22×C59#53412yes—
404C22×C59#57712yes—
405C22×C59#57712yes—
406C22×C59C23×D411yescharacteristic
407C2×D59—42no—
408C2×D59—42no—
409C2×D59—42no—
410C2×D59—84no—
411C4×C59—22no—
412C4×C59—22no—
413C4×C59—22no—
414C4×C59—42no—
415C4×C59—42no—
416C4×C59—42no—
417C4×C59#53412yes—
418C4×C59C2×H(5,𝔽2)11yescharacteristic
419C4×C59C2×H(5,𝔽2)11yescharacteristic
420Dic59—42no—
421Dic59—42no—
422Dic59—42no—
423C2×#537—591no—
424C2×#537D5911yescharacteristic, complemented
425#3204—5916no—
426C2×#481—591no—
427C2×#481—591no—
428C2×#483—591no—
429C2×#483—591no—
430C2×#470—591no—
431C2×#469—591no—
432C2×#465—591no—
433C2×#465—591no—
434C2×#452—591no—
435C2×#452—591no—
436C2×#449—591no—
437C2×#449—591no—
438C2×#408—591no—
439C2×C59—42no—
440C2×C59—42no—
441C2×C59—42no—
442C2×C59—82no—
443C2×C59#320414yescomplemented
444C2×C59C2×#53411yescharacteristic
445C2×C59C2×#57711yescharacteristic
446C2×C59C2×#57711yescharacteristic
447D59—82no—
448C22×#41—591no—
449C22×#41C2×D5911yescharacteristic
450C22×#41C2×D5911yescharacteristic
451C22×Q16—591no—
452C22×SD16—591no—
453C22×SD16—591no—
454C22×D8—591no—
455C22×M16—591no—
456C23×C8—591no—
457#537—24no—
458#537—598no—
459#537—1184no—
460#537C2×D5918yescomplemented
461C2×C22⋊Q8—21no—
462C2×C22⋊Q8—591no—
463C2×C22⋊Q8—591no—
464C2×C22⋊Q8—1181no—
465C2×C22⋊Q8C2×D5911yescharacteristic
466C2×C22⋊Q8C2×D5911yescharacteristic
467C2×#121—21no—
468C2×#121—21no—
469C2×#121—21no—
470C2×#121—591no—
471C2×#121—591no—
472C2×#121—1181no—
473C2×#121—1181no—
474C2×#121—1181no—
475C2×#121C2×D5911yescharacteristic
476C2×#121C2×D5911yescharacteristic
477C22×C4⋊C4—591no—
478C22×C4⋊C4C2×D5911yescharacteristic
479#483—598no—
480#483—598no—
481#481—598no—
482#481—598no—
483#470—598no—
484#469—598no—
485#465—598no—
486#465—598no—
487#452—598no—
488#452—598no—
489#449—598no—
490#449—598no—
491C2×#106—591no—
492C2×#106—591no—
493C2×#106—591no—
494C2×#106—591no—
495C2×#103—591no—
496C2×#103—591no—
497C2×#103—591no—
498C2×#103—591no—
499C2×#102—591no—
500C2×#102—591no—
501C2×#102—591no—
502C2×#102—591no—
503#408—598no—
504C2×C22⋊C8—591no—
505C2×C22⋊C8—591no—
506C2×C22⋊C8—591no—
507C2×C22⋊C8—591no—
508C59C2×#320411yescharacteristic, complemented, Sylow
509C2×#41—22no—
510C2×#41—42no—
511C2×#41—42no—
512C2×#41—42no—
513C2×#41—42no—
514C2×#41—594no—
515C2×#41—1182no—
516C2×#41—2362no—
517C2×#41—2362no—
518C2×#41C22⋊D5914yes—
519C2×#41C22×D5914yes—
520C2×#41C22×D5914yes—
521C22×Q8—591no—
522C22×Q8C22⋊D5911yescharacteristic
523C22×Q8C22×D5911yescharacteristic
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—591no—
528C22×D4—1181no—
529C22×D4—1181no—
530C22×D4—1181no—
531C22×D4C22⋊D5911yescharacteristic
532C22×D4C22⋊D5911yescharacteristic
533C22×D4C22⋊D5911yescharacteristic
534C22×D4C22×D5911yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—1181no—
538C23×C4—1181no—
539C23×C4C22×D5911yescharacteristic
540C23×C4C22×D5911yescharacteristic
541C23×C4C22×D5911yescharacteristic
542C2×Q16—594no—
543C2×Q16—2362no—
544C2×SD16—594no—
545C2×SD16—594no—
546C2×SD16—2362no—
547C2×SD16—2362no—
548C2×D8—594no—
549C2×D8—2362no—
550C2×M16—594no—
551C2×M16—2362no—
552C22×C8—591no—
553C22×C8—591no—
554C22×C8—591no—
555C22×C8—591no—
556C22×C8—594no—
557C22×C8—2362no—
558C22⋊Q8—28no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—594no—
562C22⋊Q8—594no—
563C22⋊Q8—1188no—
564C22⋊Q8—1182no—
565C22⋊Q8—1182no—
566C22⋊Q8C22×D5914yes—
567C22⋊Q8C22×D5914yes—
568#121—28no—
569#121—28no—
570#121—28no—
571#121—22no—
572#121—22no—
573#121—594no—
574#121—594no—
575#121—1188no—
576#121—1188no—
577#121—1188no—
578#121—1182no—
579#121—1182no—
580#121C22×D5914yes—
581#121C22×D5914yes—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—591no—
587C2×C4⋊C4—591no—
588C2×C4⋊C4—594no—
589C2×C4⋊C4—1181no—
590C2×C4⋊C4—1182no—
591C2×C4⋊C4—1181no—
592C2×C4⋊C4—1181no—
593C2×C4⋊C4C22×D5911yescharacteristic
594C2×C4⋊C4C22×D5911yescharacteristic
595C2×C4⋊C4C22×D5914yes—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—1181no—
601C2×C22⋊C4—1181no—
602C2×C22⋊C4—1181no—
603C2×C22⋊C4—1181no—
604#106—594no—
605#106—594no—
606#106—594no—
607#106—594no—
608#103—594no—
609#103—594no—
610#103—594no—
611#103—594no—
612#102—594no—
613#102—594no—
614#102—594no—
615#102—594no—
616C22⋊C8—594no—
617C22⋊C8—594no—
618C22⋊C8—594no—
619C22⋊C8—594no—
620C24—21no—
621C24—1181no—
622C24C2×C22⋊D5911yescharacteristic
623C24C2×C22⋊D5911yescharacteristic
624C24C2×C22⋊D5911yescharacteristic
625#41—48no—
626#41—44no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—48no—
631#41—2364no—
632#41—2364no—
633#41—2368no—
634C2×Q8—21no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—42no—
638C2×Q8—592no—
639C2×Q8—1181no—
640C2×Q8—1182no—
641C2×Q8—1182no—
642C2×Q8C2×C22⋊D5914yes—
643C2×Q8C23×D5912yes—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—21no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—44no—
654C2×D4—82no—
655C2×D4—82no—
656C2×D4—592no—
657C2×D4—1184no—
658C2×D4—1184no—
659C2×D4—1184no—
660C2×D4—1181no—
661C2×D4—1182no—
662C2×D4—1182no—
663C2×D4—4722no—
664C2×D4—4722no—
665C2×D4—2364no—
666C2×D4C2×C22⋊D5914yes—
667C2×D4C2×C22⋊D5914yes—
668C2×D4C2×C22⋊D5914yes—
669C2×D4C23×D5912yes—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—44no—
682C22×C4—82no—
683C22×C4—1184no—
684C22×C4—1181no—
685C22×C4—1181no—
686C22×C4—1181no—
687C22×C4—1184no—
688C22×C4—4722no—
689C22×C4—2364no—
690C22×C4C2×C22⋊D5912yes—
691C22×C4C2×C22⋊D5912yes—
692C22×C4C2×C22⋊D5912yes—
693C22×C4C2×C22⋊D5911yescharacteristic
694C22×C4C2×C22⋊D5911yescharacteristic
695C22×C4C2×C22⋊D5911yescharacteristic
696C22×C4C23×D5912yes—
697C22×C4C23×D5912yes—
698C22×C4C23×D5912yes—
699C22×C4C23×D5911yescharacteristic
700Q16—2364no—
701SD16—2364no—
702SD16—2364no—
703D8—2364no—
704M16—2364no—
705C2×C8—592no—
706C2×C8—592no—
707C2×C8—592no—
708C2×C8—592no—
709C2×C8—1182no—
710C2×C8—1182no—
711C2×C8—1182no—
712C2×C8—1182no—
713C2×C8—2364no—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—24no—
718C4⋊C4—24no—
719C4⋊C4—592no—
720C4⋊C4—592no—
721C4⋊C4—1184no—
722C4⋊C4—1181no—
723C4⋊C4—1181no—
724C4⋊C4—1184no—
725C4⋊C4—1184no—
726C4⋊C4C23×D5912yes—
727C4⋊C4C23×D5912yes—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—1184no—
733C22⋊C4—1184no—
734C22⋊C4—1184no—
735C22⋊C4—1184no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—1182no—
750C23—2362no—
751C23—2362no—
752C23—2362no—
753C23C22×C22⋊D5912yes—
754C23C22×C22⋊D5912yes—
755C23C22×C22⋊D5912yes—
756C23C22×C22⋊D5911yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—44no—
760Q8—42no—
761Q8—1182no—
762Q8—1182no—
763Q8—2362no—
764D4—22no—
765D4—22no—
766D4—44no—
767D4—44no—
768D4—44no—
769D4—48no—
770D4—42no—
771D4—84no—
772D4—84no—
773D4—1182no—
774D4—1182no—
775D4—4724no—
776D4—4724no—
777D4—2368no—
778D4—2362no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—48no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—84no—
799C2×C4—1182no—
800C2×C4—1182no—
801C2×C4—1182no—
802C2×C4—4724no—
803C2×C4—2368no—
804C2×C4—2362no—
805C2×C4—2362no—
806C2×C4—2362no—
807C2×C4C22×C22⋊D5912yes—
808C2×C4C22×C22⋊D5912yes—
809C2×C4C22×C22⋊D5912yes—
810C2×C4C22×C22⋊D5911yescharacteristic
811C2×C4#1427377212yes—
812C2×C4#1427377212yes—
813C2×C4C24×D5911yescharacteristic
814C8—1182no—
815C8—1182no—
816C8—1182no—
817C8—1182no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—84no—
834C22—4724no—
835C22—2362no—
836C22—2362no—
837C22—2362no—
838C22#1683796112yes—
839C22#1683821012yes—
840C22#1683821312yes—
841C22C23×C22⋊D5911yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—2362no—
849C4—2362no—
850C4—2362no—
851C4#1683796112yes—
852C4C2×#1427377211yescharacteristic
853C4C2×#1427377211yescharacteristic
854C2—42no—
855C2—42no—
856C2—42no—
857C2—82no—
858C2—4722no—
859C2#2143500214yesdirect product factor
860C2C2×#1683796111yescharacteristic
861C2C2×#1683821011yescharacteristic
862C2C2×#1683821311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#537C2
socleC23×C59C22×D4
hypercenterC2×#537D59
hypocenterC59C2×#3204
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#16837980C2semidirect
2. #21435002C2direct (N × H)
3. C2×#16837720C2semidirect
4. C2×#16837718C2semidirect
5. C2×#16837732C2semidirect
6. C2×#16837730C2semidirect
7. C2×#16837658C2semidirect
8. C2×#16837653C2semidirect
9. C2×#16837633C2semidirect
10. C2×#16837629C2semidirect
11. C2×#16837564C2semidirect
12. C2×#16837562C2semidirect
13. C2×#16837547C2semidirect
14. C2×#16837545C2semidirect
15. C2×#16837369C2semidirect
16. C2×C59×#537C2semidirect
25. #16837980C22semidirect
35. #16837732C22semidirect
36. #16837730C22semidirect
37. #16837720C22semidirect
38. #16837718C22semidirect
39. #16837658C22semidirect
40. #16837653C22semidirect
41. #16837633C22semidirect
42. #16837629C22semidirect
43. #16837564C22semidirect
44. #16837562C22semidirect
45. #16837547C22semidirect
46. #16837545C22semidirect
59. #16837369C22semidirect
67. C59×#537C22semidirect
424. C2×#537D59semidirect
443. C2×C59#3204semidirect
460. #537C2×D59semidirect
508. C59C2×#3204semidirect
859. C2#21435002direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379802
#214350022
C2×#168377202
C2×#168377182
C2×#168377322
C2×#168377302
C2×#168376582
C2×#168376532
C2×#168376332
C2×#168376292
C2×#168375642
C2×#168375622
C2×#168375472
C2×#168375452
C2×#168373692
C2×C59×#5372
C2×#320459