Finite Group Databasebeta

← C2×#21436635 #29467326

Subgroups — C2×#21436635 #29467326

Order 15104.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838122C211yesmaximal, characteristic, complemented
2#21436635C2116yesmaximal, direct product factor
3C2×#16837812C211yesmaximal, characteristic, complemented
4C2×#16837743C211yesmaximal, characteristic, complemented
5C2×#16837723C211yesmaximal, characteristic, complemented
6C2×#16837723C211yesmaximal, characteristic, complemented
7C2×#16837732C211yesmaximal, characteristic, complemented
8C2×#16837706C211yesmaximal, characteristic, complemented
9C2×#16837692C211yesmaximal, characteristic, complemented
10C2×#16837646C211yesmaximal, characteristic, complemented
11C2×#16837629C211yesmaximal, characteristic, complemented
12C2×#16837502C211yesmaximal, characteristic, complemented
13C2×#16837474C211yesmaximal, characteristic, complemented
14C2×#16837442C211yesmaximal, characteristic, complemented
15C2×#16837438C211yesmaximal, characteristic, complemented
16C2×C59×#553C211yesmaximal, characteristic
17C22×#11745670C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20#16838122—24no—
21#16838122C2218yescomplemented
22C2×#14273727C2211yescharacteristic
23C2×#14273720—21no—
24C2×#14273720—21no—
25C2×#14273714—21no—
26C2×#14273706C2211yescharacteristic
27C2×#14273706C2211yescharacteristic
28C2×C4×Dic118C2211yescharacteristic
29C2×#14273692—21no—
30C2×#14273686C2211yescharacteristic
31C2×#14273686C2211yescharacteristic
32#16837812C2218yescomplemented
33#16837743C2218yescomplemented
34#16837732C2218yescomplemented
35#16837723C2218yescomplemented
36#16837723C2218yescomplemented
37#16837706C2218yescomplemented
38#16837692C2218yescomplemented
39#16837646C2218yescomplemented
40#16837629C2218yescomplemented
41#16837502C2218yescomplemented
42#16837474C2218yescomplemented
43#16837442C2218yescomplemented
44#16837438C2218yescomplemented
45C2×#14273660C2211yescharacteristic
46C2×#14273660C2211yescharacteristic
47C2×#14273660C2211yescharacteristic
48C2×#14273660C2211yescharacteristic
49C2×#14273658C2211yescharacteristic
50C2×#14273658C2211yescharacteristic
51C2×#14273658C2211yescharacteristic
52C2×#14273658C2211yescharacteristic
53C2×#14273658C2211yescharacteristic
54C2×C4⋊(C59⋊C8)C2211yescharacteristic
55C2×#14273650C2211yescharacteristic
56C2×#14273650C2211yescharacteristic
57C2×#14273650C2211yescharacteristic
58C2×#14273648C2211yescharacteristic
59C2×#14273648C2211yescharacteristic
60C2×#14273648C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×C22⋊(C59⋊C8)C2211yescharacteristic
63C2×#14273638C2211yescharacteristic
64C59×#553—24no—
65C59×#553C2218yes—
66C2×#126×C59—21no—
67C2×#125×C59C2211yescharacteristic
68C2×#123×C59—21no—
69C2×#121×C59—21no—
70C2×#121×C59C2211yescharacteristic
71C2×#121×C59C2211yescharacteristic
72C2×C4×D4×C59—21no—
73C2×C4×D4×C59C2211yescharacteristic
74C2×C4×D4×C59C2211yescharacteristic
75C2×#117×C59C2211yescharacteristic
76C22×C4⋊C4×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C2×#11745670—24no—
80C2×#11745670C2314yes—
81C2×#11745664—24no—
82C2×#11745664C2314yes—
83C22×C59⋊C8—24no—
84C22×C59⋊C8C2311yescharacteristic
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87C22×C59⋊C8C2314yes—
88C22×C59⋊C8C2311yescharacteristic
89#14273727—22no—
90#14273727C2314yes—
91#14273720—28no—
92#14273720—28no—
93#14273714—28no—
94#14273706—22no—
95#14273706—22no—
96#14273706C2314yes—
97#14273706C2314yes—
98C4×Dic118—22no—
99C4×Dic118C2314yes—
100#14273692—28no—
101#14273686—22no—
102#14273686—22no—
103#14273686C2314yes—
104#14273686C2314yes—
105C2×C4⋊Dic59—21no—
106C2×C4⋊Dic59C2311yescharacteristic
107C2×C4⋊Dic59C2311yescharacteristic
108C2×C4⋊Dic59C2311yescharacteristic
109C2×Dic59⋊C4—21no—
110C2×Dic59⋊C4—21no—
111C2×Dic59⋊C4—21no—
112C2×C22⋊Dic59—21no—
113C2×C22⋊Dic59—21no—
114C2×C22⋊Dic59—21no—
115C2×C22⋊Dic59—21no—
116C2×C4×Dic59—21no—
117C2×C4×Dic59—21no—
118C2×C4×Dic59—21no—
119#14273660C2314yes—
120#14273660C2314yes—
121#14273660C2314yes—
122#14273660C2314yes—
123#14273658C2314yes—
124#14273658C2314yes—
125#14273658C2314yes—
126#14273658C2314yes—
127#14273658C2314yes—
128C4⋊(C59⋊C8)C2314yes—
129#14273650C2314yes—
130#14273650C2314yes—
131#14273650C2314yes—
132#14273648C2314yes—
133#14273648C2314yes—
134#14273648C2314yes—
135C22⋊(C59⋊C8)C2314yes—
136C22⋊(C59⋊C8)C2314yes—
137#14273638C2314yes—
138C22×D4×C59—21no—
139C22×D4×C59—21no—
140C22×D4×C59D411yescharacteristic
141C22×D4×C59C2311yescharacteristic
142C23×C4×C59—21no—
143C23×C4×C59—21no—
144C23×C4×C59C2311yescharacteristic
145C23×C4×C59C2311yescharacteristic
146#126×C59—28no—
147#125×C59—22no—
148#125×C59C2314yes—
149#123×C59—28no—
150#121×C59—28no—
151#121×C59—22no—
152#121×C59—22no—
153#121×C59C2314yes—
154#121×C59C2314yes—
155C4×D4×C59—28no—
156C4×D4×C59—22no—
157C4×D4×C59D414yes—
158C4×D4×C59C2314yes—
159C4×D4×C59C2314yes—
160#117×C59—22no—
161#117×C59C2314yes—
162C2×C4⋊C4×C59—21no—
163C2×C4⋊C4×C59—22no—
164C2×C4⋊C4×C59—21no—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59D411yescharacteristic
167C2×C4⋊C4×C59C2311yescharacteristic
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2314yes—
171C2×C22⋊C4×C59—21no—
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59D411yescharacteristic
176C2×C22⋊C4×C59D411yescharacteristic
177C2×C42×C59—21no—
178C2×C42×C59C2311yescharacteristic
179C24×C59—21no—
180C24×C59C2×D411yescharacteristic
181C24×C59C2×D411yescharacteristic
182C2×D4×C59—24no—
183C2×D4×C59—24no—
184C2×D4×C59—21no—
185C2×D4×C59—22no—
186C2×D4×C59—22no—
187C2×D4×C59—42no—
188C2×D4×C59—44no—
189C2×D4×C59—82no—
190C2×D4×C59C2×D414yes—
191C2×D4×C59C2412yes—
192C22×C4×C59—22no—
193C22×C4×C59—22no—
194C22×C4×C59—22no—
195C22×C4×C59—22no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—24no—
200C22×C4×C59—24no—
201C22×C4×C59—82no—
202C22×C4×C59—82no—
203C22×C4×C59C2×D411yescharacteristic
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D412yes—
208C22×C4×C59C2×D412yes—
209C22×C4×C59C2412yes—
210C22×C4×C59C2412yes—
211C22×C4×C59C2411yescharacteristic
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C2×Dic118—22no—
217C2×Dic118—22no—
218C2×Dic118—24no—
219C2×Dic118—21no—
220C2×Dic118—44no—
221C2×Dic118C2412yes—
222C4⋊C4×C59—21no—
223C4⋊C4×C59—21no—
224C4⋊C4×C59—24no—
225C4⋊C4×C59—24no—
226C4⋊C4×C59—24no—
227C4⋊C4×C59—21no—
228C4⋊C4×C59C2×D414yes—
229C4⋊C4×C59C2412yes—
230C4⋊C4×C59C2412yes—
231C4⋊C4×C59C2412yes—
232C22⋊C4×C59—24no—
233C22⋊C4×C59—24no—
234C22⋊C4×C59—24no—
235C22⋊C4×C59—24no—
236C22⋊C4×C59C2×D414yes—
237C22⋊C4×C59C2×D414yes—
238C42×C59—24no—
239C42×C59C2×D412yes—
240C42×C59C2412yes—
241C22⋊Dic59—24no—
242C22⋊Dic59—24no—
243C22⋊Dic59—24no—
244C22⋊Dic59—24no—
245#11745670—28no—
246C4⋊Dic59—24no—
247C4⋊Dic59—21no—
248C4⋊Dic59—21no—
249C4⋊Dic59—21no—
250C4⋊Dic59C2412yes—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256C4×Dic59—24no—
257C4×Dic59—24no—
258C4×Dic59—24no—
259#11745664—28no—
260C2×C59⋊C8—22no—
261C2×C59⋊C8—22no—
262C2×C59⋊C8—22no—
263C2×C59⋊C8—28no—
264C2×C59⋊C8#4114yes—
265C2×C59⋊C8C2412yes—
266C2×C59⋊C8C2412yes—
267C2×C59⋊C8C2412yes—
268C2×C59⋊C8C2412yes—
269C23×C59—22no—
270C23×C59—22no—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59—42no—
277C23×C59—42no—
278C23×C59—42no—
279C23×C59C22×D412yes—
280C23×C59C22×D412yes—
281C23×C59C22×D411yescharacteristic
282D4×C59—22no—
283D4×C59—22no—
284D4×C59—44no—
285D4×C59—48no—
286D4×C59—42no—
287D4×C59—84no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—24no—
293C2×C4×C59—24no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—42no—
302C2×C4×C59—42no—
303C2×C4×C59—42no—
304C2×C4×C59—84no—
305C2×C4×C59—84no—
306C2×C4×C59C22×D412yes—
307C2×C4×C59C22×D412yes—
308C2×C4×C59C22×D412yes—
309C2×C4×C59C22×D412yes—
310C2×C4×C59C22×D411yescharacteristic
311C2×C4×C59C2×#4112yes—
312C2×C4×C592−1+412yes—
313C2×C4×C59C2511yescharacteristic
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—42no—
319C2×Dic59—42no—
320C2×Dic59—42no—
321C2×Dic59—42no—
322Dic118—22no—
323Dic118—22no—
324Dic118—48no—
325Dic118—42no—
326C59⋊C8—22no—
327C59⋊C8—22no—
328C59⋊C8—22no—
329C59⋊C8C2×#4114yes—
330C2×#3350—591nomaximal, Sylow
331C22×C59—22no—
332C22×C59—22no—
333C22×C59—22no—
334C22×C59—22no—
335C22×C59—22no—
336C22×C59—22no—
337C22×C59—44no—
338C22×C59—44no—
339C22×C59—42no—
340C22×C59—42no—
341C22×C59—42no—
342C22×C59—84no—
343C22×C59#54712yes—
344C22×C59#57512yes—
345C22×C59#57712yes—
346C22×C59C23×D411yescharacteristic
347C4×C59—22no—
348C4×C59—22no—
349C4×C59—22no—
350C4×C59—22no—
351C4×C59—42no—
352C4×C59—42no—
353C4×C59—42no—
354C4×C59#54712yes—
355C4×C59C22×#4111yescharacteristic
356C4×C59C2×2−1+411yescharacteristic
357Dic59—42no—
358Dic59—42no—
359Dic59—42no—
360Dic59—42no—
361C2×#556—591no—
362C2×#553D5911yescharacteristic
363#3350—5916no—
364C2×#501—591no—
365C2×#485—591no—
366C2×#482—591no—
367C2×#482—591no—
368C2×#483—591no—
369C2×#479—591no—
370C2×#476—591no—
371C2×#468—591no—
372C2×#465—591no—
373C2×#440—591no—
374C2×#435—591no—
375C2×#428—591no—
376C2×#427—591no—
377C2×C59—42no—
378C2×C59—42no—
379C2×C59—82no—
380C2×C59#335014yescomplemented
381C2×C59C2×#54711yescharacteristic
382C2×C59C2×#57511yescharacteristic
383C2×C59C2×#57711yescharacteristic
384C22×SD16—591no—
385C22×M16—591no—
386C23×C8—591no—
387#556—598no—
388#556—1184no—
389#553—24no—
390#553C2×D5918yes—
391C2×C4⋊Q8—591no—
392C2×#126—21no—
393C2×#126—1181no—
394C2×#126—1181no—
395C2×#125C2×D5911yescharacteristic
396C2×#124—1181no—
397C2×#123—21no—
398C2×C22⋊Q8—591no—
399C2×C22⋊Q8—591no—
400C2×#121—21no—
401C2×#121C2×D5911yescharacteristic
402C2×#121C2×D5911yescharacteristic
403C2×C4×Q8—591no—
404C2×C4×Q8—1181no—
405C2×C4×D4—21no—
406C2×C4×D4C2×D5911yescharacteristic
407C2×C4×D4C2×D5911yescharacteristic
408C2×#117—591no—
409C2×#117—591no—
410C2×#117C2×D5911yescharacteristic
411C22×C4⋊C4C2×D5911yescharacteristic
412#501—598no—
413#485—598no—
414#483—598no—
415#482—598no—
416#482—598no—
417#479—598no—
418#476—598no—
419#468—598no—
420#465—598no—
421#440—598no—
422#435—598no—
423#428—598no—
424#427—598no—
425C2×#107—591no—
426C2×#107—591no—
427C2×#107—591no—
428C2×#107—591no—
429C2×#106—591no—
430C2×#106—591no—
431C2×#106—591no—
432C2×#106—591no—
433C2×#106—591no—
434C2×C4⋊C8—591no—
435C2×#103—591no—
436C2×#103—591no—
437C2×#103—591no—
438C2×#102—591no—
439C2×#102—591no—
440C2×#102—591no—
441C2×C22⋊C8—591no—
442C2×C22⋊C8—591no—
443C2×#97—591no—
444C59C2×#335011yescharacteristic, complemented, Sylow
445C22×Q8—591no—
446C22×Q8—1181no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4C22⋊D5911yescharacteristic
450C22×D4C22×D5911yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4C22×D5911yescharacteristic
454C23×C4C22×D5911yescharacteristic
455C2×SD16—594no—
456C2×SD16—1184no—
457C2×M16—594no—
458C2×M16—1184no—
459C22×C8—591no—
460C22×C8—591no—
461C22×C8—594no—
462C22×C8—591no—
463C22×C8—591no—
464C22×C8—1184no—
465C4⋊Q8—594no—
466C4⋊Q8—1182no—
467#126—28no—
468#126—1188no—
469#126—1188no—
470#125—22no—
471#125C22×D5914yes—
472#124—1188no—
473#123—28no—
474C22⋊Q8—594no—
475C22⋊Q8—594no—
476C22⋊Q8—1182no—
477C22⋊Q8—1182no—
478#121—28no—
479#121—22no—
480#121—22no—
481#121C22×D5914yes—
482#121C22×D5914yes—
483C4×Q8—594no—
484C4×Q8—1188no—
485C4×Q8—1182no—
486C4×D4—28no—
487C4×D4—22no—
488C4×D4C22⋊D5914yes—
489C4×D4C22×D5914yes—
490C4×D4C22×D5914yes—
491#117—22no—
492#117—594no—
493#117—594no—
494#117—1182no—
495#117—1182no—
496#117C22×D5914yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—591no—
502C2×C4⋊C4—591no—
503C2×C4⋊C4—591no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4—1181no—
507C2×C4⋊C4—1181no—
508C2×C4⋊C4C22⋊D5911yescharacteristic
509C2×C4⋊C4C22×D5911yescharacteristic
510C2×C4⋊C4C22×D5911yescharacteristic
511C2×C4⋊C4C22×D5914yes—
512C2×C4⋊C4C22×D5911yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—1181no—
518C2×C22⋊C4—1181no—
519C2×C22⋊C4—1181no—
520C2×C22⋊C4—1181no—
521C2×C22⋊C4C22⋊D5911yescharacteristic
522C2×C22⋊C4C22⋊D5911yescharacteristic
523C2×C42—21no—
524C2×C42—1181no—
525C2×C42—1181no—
526C2×C42—1181no—
527C2×C42C22×D5911yescharacteristic
528#107—594no—
529#107—594no—
530#107—594no—
531#107—594no—
532#106—594no—
533#106—594no—
534#106—594no—
535#106—594no—
536#106—594no—
537C4⋊C8—594no—
538#103—594no—
539#103—594no—
540#103—594no—
541#102—594no—
542#102—594no—
543#102—594no—
544C22⋊C8—594no—
545C22⋊C8—594no—
546#97—594no—
547C24—21no—
548C24C2×C22⋊D5911yescharacteristic
549C24C2×C22⋊D5911yescharacteristic
550C2×Q8—592no—
551C2×Q8—1181no—
552C2×Q8—1184no—
553C2×Q8—1182no—
554C2×Q8—1182no—
555C2×Q8—2364no—
556C2×D4—24no—
557C2×D4—24no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—42no—
562C2×D4—44no—
563C2×D4—82no—
564C2×D4C2×C22⋊D5914yes—
565C2×D4C23×D5912yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—82no—
576C22×C4—82no—
577C22×C4—1181no—
578C22×C4—1181no—
579C22×C4—1181no—
580C22×C4—1181no—
581C22×C4C2×C22⋊D5912yes—
582C22×C4C2×C22⋊D5912yes—
583C22×C4C2×C22⋊D5911yescharacteristic
584C22×C4C2×C22⋊D5911yescharacteristic
585C22×C4C2×C22⋊D5911yescharacteristic
586C22×C4C2×C22⋊D5911yescharacteristic
587C22×C4C23×D5912yes—
588C22×C4C23×D5912yes—
589C22×C4C23×D5911yescharacteristic
590SD16—1188no—
591M16—1188no—
592C2×C8—594no—
593C2×C8—592no—
594C2×C8—592no—
595C2×C8—592no—
596C2×C8—592no—
597C2×C8—1188no—
598C2×C8—1182no—
599C2×C8—1182no—
600C2×C8—1182no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—592no—
608C4⋊C4—592no—
609C4⋊C4—592no—
610C4⋊C4—1181no—
611C4⋊C4—1181no—
612C4⋊C4—1181no—
613C4⋊C4—1184no—
614C4⋊C4—1184no—
615C4⋊C4—1184no—
616C4⋊C4—1184no—
617C4⋊C4C2×C22⋊D5914yes—
618C4⋊C4C23×D5912yes—
619C4⋊C4C23×D5912yes—
620C4⋊C4C23×D5912yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—1184no—
626C22⋊C4—1184no—
627C22⋊C4—1184no—
628C22⋊C4—1184no—
629C22⋊C4C2×C22⋊D5914yes—
630C22⋊C4C2×C22⋊D5914yes—
631C42—24no—
632C42—1184no—
633C42—1184no—
634C42—1184no—
635C42C2×C22⋊D5912yes—
636C42C23×D5912yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23C22×C22⋊D5912yes—
648C23C22×C22⋊D5912yes—
649C23C22×C22⋊D5911yescharacteristic
650Q8—1182no—
651Q8—1182no—
652Q8—2368no—
653Q8—2362no—
654D4—22no—
655D4—22no—
656D4—44no—
657D4—48no—
658D4—42no—
659D4—84no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—84no—
677C2×C4—84no—
678C2×C4—1182no—
679C2×C4—1182no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—2362no—
683C2×C4—2362no—
684C2×C4—2362no—
685C2×C4—2362no—
686C2×C4C22×C22⋊D5912yes—
687C2×C4C22×C22⋊D5912yes—
688C2×C4C22×C22⋊D5912yes—
689C2×C4C22×C22⋊D5912yes—
690C2×C4C22×C22⋊D5911yescharacteristic
691C2×C4#41×D5912yes—
692C2×C4#1427377412yes—
693C2×C4C24×D5911yescharacteristic
694C8—594no—
695C8—1182no—
696C8—1182no—
697C8—1182no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22#1683805112yes—
711C22#1683820012yes—
712C22#1683821312yes—
713C22C23×C22⋊D5911yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—2362no—
722C4—2362no—
723C4—2362no—
724C4—2362no—
725C4#1683805112yes—
726C4C2×#41×D5911yescharacteristic
727C4C2×#1427377411yescharacteristic
728C2—42no—
729C2—42no—
730C2—82no—
731C2#2143663514yesdirect product factor
732C2C2×#1683805111yescharacteristic
733C2C2×#1683820011yescharacteristic
734C2C2×#1683821311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
Fitting, prime radicalC2×C59×#553C2
socleC23×C59C22×D4
hypercenterC2×#553D59
hypocenterC59C2×#3350
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#16838122C2semidirect
2. #21436635C2direct (N × H)
3. C2×#16837812C2semidirect
4. C2×#16837743C2semidirect
5. C2×#16837723C2semidirect
6. C2×#16837723C2semidirect
7. C2×#16837732C2semidirect
8. C2×#16837706C2semidirect
9. C2×#16837692C2semidirect
10. C2×#16837646C2semidirect
11. C2×#16837629C2semidirect
12. C2×#16837502C2semidirect
13. C2×#16837474C2semidirect
14. C2×#16837442C2semidirect
15. C2×#16837438C2semidirect
21. #16838122C22semidirect
32. #16837812C22semidirect
33. #16837743C22semidirect
34. #16837732C22semidirect
35. #16837723C22semidirect
36. #16837723C22semidirect
37. #16837706C22semidirect
38. #16837692C22semidirect
39. #16837646C22semidirect
40. #16837629C22semidirect
41. #16837502C22semidirect
42. #16837474C22semidirect
43. #16837442C22semidirect
44. #16837438C22semidirect
380. C2×C59#3350semidirect
444. C59C2×#3350semidirect
731. C2#21436635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381222
#214366352
C2×#168378122
C2×#168377432
C2×#168377232
C2×#168377322
C2×#168377062
C2×#168376922
C2×#168376462
C2×#168376292
C2×#168375022
C2×#168374742
C2×#168374422
C2×#168374382
C2×C59×#5532
C2×#335059