Finite Group Databasebeta

← C2×#21437887 #29497157

Subgroups — C2×#21437887 #29497157

Order 15104.

11534 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273775C211yesmaximal, characteristic, complemented
2C22×#14273773C211yesmaximal, characteristic, complemented
3#21437887C2132yesmaximal, direct product factor
4C2×#16838064C211yesmaximal, characteristic, complemented
5C2×#16838063C211yesmaximal, characteristic, complemented
6C2×#16838059C211yesmaximal, characteristic, complemented
7C2×#16838049C213yesmaximal, complemented
8C2×#16838048C213yesmaximal, complemented
9C2×#16838045C213yesmaximal, complemented
10C2×#16838043C213yesmaximal, complemented
11C2×#16837975C213yesmaximal, complemented
12C2×#16837968C213yesmaximal, complemented
13C2×#16837949C213yesmaximal, complemented
14C2×#124×D59C213yesmaximal, complemented
15C2×C4×#11745689C211yesmaximal, characteristic, complemented
16C2×C59×#548C211yesmaximal, characteristic, complemented
17C2×#14273775—216no—
18C2×#14273775C22116yescomplemented
19C2×#14273773—216no—
20C2×#14273773C22116yescomplemented
21C22×#11745689C2211yescharacteristic
22C22×#11745689C2211yescharacteristic
23C22×#11745689C2213yescomplemented
24C22×#11745685C2213yes—
25C22×#11745685C2213yescomplemented
26C22×#11745685C2213yescomplemented
27C22×Q8×D59C2211yescharacteristic, complemented
28C22×Q8×D59C2213yescomplemented
29C23×D236C2213yes—
30C22×D4×D59C2213yes—
31C22×D4×D59C2213yes—
32#16838064C22116yescomplemented
33#16838063C22116yescomplemented
34#16838059C22116yescomplemented
35#16838049C22148yescomplemented
36#16838048C22148yescomplemented
37#16838045C22148yescomplemented
38#16838043C22148yescomplemented
39#16837975C22148yescomplemented
40#16837968C22148yescomplemented
41#16837949C22148yescomplemented
42C2×#14273726C2213yescomplemented
43C2×#14273723C2213yescomplemented
44C2×#14273716C2213yescomplemented
45C2×#14273715C2213yescomplemented
46C2×#14273714C2213yescomplemented
47C2×#14273713C2213yescomplemented
48C2×#14273713C2216yescomplemented
49C2×#14273713C2211yescharacteristic, complemented
50#124×D59C22148yescomplemented
51C2×#14273712C2216yescomplemented
52C2×#14273709C2216yescomplemented
53C2×#14273707C2213yescomplemented
54C2×#14273706C2213yescomplemented
55C2×#14273703C2213yescomplemented
56C2×#14273702C2213yescomplemented
57C2×#14273702C2213yescomplemented
58C2×#14273701C2213yescomplemented
59C2×#14273700C2213yescomplemented
60C2×#14273700C2213yescomplemented
61C2×#14273698C2213yescomplemented
62C2×#14273698C2213yescomplemented
63C2×#14273697C2216yescomplemented
64C2×#14273695C2216yescomplemented
65C4×#11745689C22116yescomplemented
66C2×Q8×Dic59C2211yescharacteristic, complemented
67C2×C4×D236C2213yescomplemented
68C2×C4×D236C2213yescomplemented
69C2×#14273689C2213yescomplemented
70C2×C4×C22⋊D59C2213yescomplemented
71C2×C4×C22⋊D59C2213yescomplemented
72C2×#14273685C2213yescomplemented
73C2×C22⋊C4×D59C2216yescomplemented
74C2×C22⋊C4×D59C2216yescomplemented
75C2×C42×D59C2213yescomplemented
76C22×#41×C59C2211yescharacteristic
77C23×Q8×C59C2211yescharacteristic, complemented
78C59×#548C22116yescomplemented
79C2×#124×C59C2213yescomplemented
80C2×C22⋊Q8×C59C2213yescomplemented
81C2×#121×C59C2213yescomplemented
82C2×C4×Q8×C59C2211yescharacteristic, complemented
83C2×C4×D4×C59C2213yescomplemented
84C24×D59C2316yes—
85#14273775—2128no—
86#14273773—2128no—
87C2×#11745689—28no—
88C2×#11745689—224no—
89C2×#11745689D4116yescomplemented
90C2×#11745689C2318yes—
91C2×#11745689C2318yes—
92C2×#11745689C23124yescomplemented
93C2×#11745685—224no—
94C2×#11745685—224no—
95C2×#11745685—224no—
96C2×#11745685C23124yes—
97C2×#11745685C23124yescomplemented
98C2×#11745685C23124yescomplemented
99C22×Dic118C2313yes—
100C22×Dic118C2313yes—
101C22×Dic118C2311yescharacteristic
102C2×Q8×D59—28no—
103C2×Q8×D59—224no—
104C2×Q8×D59C23124yescomplemented
105C2×Q8×D59C2318yescomplemented
106C22×D236—224no—
107C22×D236C2313yes—
108C22×D236C2313yes—
109C22×D236C2313yes—
110C22×D236C23124yes—
111C22×D236C2313yes—
112C22×D236C2313yes—
113C22×C22⋊D59C2313yes—
114C22×C22⋊D59C2313yes—
115C22×C22⋊D59C2313yes—
116C22×C22⋊D59C2311yescharacteristic
117C22×C22⋊D59C2313yes—
118C22×C22⋊D59C2313yes—
119C2×D4×D59—224no—
120C2×D4×D59—224no—
121C2×D4×D59C23124yes—
122C2×D4×D59C23124yes—
123C22×C4×D59C2313yes—
124C22×C4×D59C2313yes—
125C22×C4×D59C2316yes—
126C22×C4×D59C2313yes—
127C22×C4×D59C2313yes—
128C22×C4×D59C2313yes—
129#14273726C23124yescomplemented
130#14273723C23124yescomplemented
131#14273716C23124yescomplemented
132#14273715C23124yescomplemented
133#14273714C23124yescomplemented
134#14273713C23124yescomplemented
135#14273713C23148yescomplemented
136#14273713C2318yescomplemented
137#14273712C23148yescomplemented
138#14273709C23148yescomplemented
139#14273707C23124yescomplemented
140#14273706C23124yescomplemented
141#14273703C23124yescomplemented
142#14273702C23124yescomplemented
143#14273702C23124yescomplemented
144#14273701C23124yescomplemented
145#14273700C23124yescomplemented
146#14273700C23124yescomplemented
147#14273698C23124yescomplemented
148#14273698C23124yescomplemented
149#14273697C23148yescomplemented
150#14273695C23148yescomplemented
151Q8×Dic59C2318yescomplemented
152C4×D236C23124yescomplemented
153C4×D236C23124yescomplemented
154#14273689C23124yescomplemented
155C4×C22⋊D59C23124yescomplemented
156C4×C22⋊D59C23124yescomplemented
157#14273685C23124yescomplemented
158C2×C4⋊Dic59C2313yes—
159C2×C4⋊Dic59C2313yes—
160C2×Dic59⋊C4C2313yes—
161C2×Dic59⋊C4C2313yes—
162C2×C22⋊Dic59C2311yescharacteristic
163C2×C22⋊Dic59C2316yes—
164C2×C22⋊Dic59C2313yes—
165C2×(C2×D59)⋊C4C2316yes—
166C2×(C2×D59)⋊C4C2316yes—
167C2×(C2×D59)⋊C4C2311yescharacteristic
168C2×(C2×D59)⋊C4C2313yes—
169C2×(C2×D59)⋊C4C2311yescharacteristic
170C2×(C2×D59)⋊C4C2316yes—
171C2×(C2×D59)⋊C4C2313yes—
172C22⋊C4×D59C23148yescomplemented
173C22⋊C4×D59C23148yescomplemented
174C2×C4×Dic59C2311yescharacteristic
175C2×C4×Dic59C2313yes—
176C2×C4×Dic59C2313yes—
177C42×D59C23124yescomplemented
178C2×#41×C59—28no—
179C2×#41×C59C2318yes—
180C22×Q8×C59—28no—
181C22×Q8×C59C2313yes—
182C22×Q8×C59C2311yescharacteristic
183C22×Q8×C59C2318yescomplemented
184C22×D4×C59C2313yes—
185C22×D4×C59C2313yes—
186C23×C4×C59C2313yes—
187C23×C4×C59C2313yes—
188#124×C59C23124yescomplemented
189C22⋊Q8×C59C23124yescomplemented
190#121×C59C23124yescomplemented
191C4×Q8×C59C2318yescomplemented
192C4×D4×C59C23124yescomplemented
193C2×C4⋊C4×C59C2313yes—
194C2×C4⋊C4×C59C2313yes—
195C2×C22⋊C4×C59C2316yes—
196C2×C22⋊C4×C59C2311yescharacteristic
197C2×C22⋊C4×C59C2313yes—
198C2×C42×C59C2313yes—
199C24×C59C2413yes—
200C24×C59C2411yescharacteristic
201C23×D59—224no—
202C23×D59—412no—
203C23×D59—412no—
204C23×D59C2413yes—
205C23×D59C2411yescharacteristic
206C23×D59C2413yes—
207C23×D59C24124yes—
208#41×C59—232no—
209C2×Q8×C59—232no—
210C2×Q8×C59—212no—
211C2×Q8×C59C2×D418yes—
212C2×Q8×C59C24112yes—
213C2×Q8×C59C2414yes—
214C2×D4×C59—212no—
215C2×D4×C59—46no—
216C2×D4×C59C24112yes—
217C2×D4×C59C24112yes—
218C22×C4×C59—212no—
219C22×C4×C59—212no—
220C22×C4×C59C2411yescharacteristic
221C22×C4×C59C2413yes—
222C22×C4×C59C2413yes—
223C22×C4×C59C2411yescharacteristic
224C22×C4×C59C24112yes—
225C22×C4×C59C24112yes—
226C22×C4×C59C2413yes—
227C2×C22⋊D59—212no—
228C2×C22⋊D59—212no—
229C2×C22⋊D59—212no—
230C2×C22⋊D59—24no—
231C2×C22⋊D59—46no—
232C2×C22⋊D59—46no—
233C2×C22⋊D59C24112yes—
234C2×C22⋊D59C24112yes—
235C2×C22⋊D59C24112yes—
236C2×C22⋊D59C2414yes—
237C2×C22⋊D59C24112yes—
238C2×C22⋊D59C24112yes—
239C22×Dic59C2411yescharacteristic
240C22×Dic59C2413yes—
241C22×Dic59C2413yes—
242C22×Dic59C2411yescharacteristic
243C22×Dic59C2411yescharacteristic
244#11745689—232no—
245#11745689—296no—
246#11745689C2×D4164yescomplemented
247Q8×D59—232no—
248Q8×D59—296no—
249D4×D59—296no—
250D4×D59—296no—
251#11745685—296no—
252#11745685—296no—
253#11745685—296no—
254C2×D236—212no—
255C2×D236—212no—
256C2×D236—212no—
257C2×D236—296no—
258C2×D236—46no—
259C2×D236C2×D4124yes—
260C2×D236C24112yes—
261C2×D236C24112yes—
262C2×D236C24112yes—
263C2×D236C24112yes—
264C2×D236C24112yes—
265C2×C4×D59—224no—
266C2×C4×D59—212no—
267C2×C4×D59—212no—
268C2×C4×D59—46no—
269C2×C4×D59—46no—
270C2×C4×D59C2×D4124yes—
271C2×C4×D59C24124yes—
272C2×C4×D59C24112yes—
273C2×C4×D59C24112yes—
274C2×C4×D59C24112yes—
275C2×C4×D59C24112yes—
276C2×C4×D59C24112yes—
277C2×Dic118—212no—
278C2×Dic118—212no—
279C2×Dic118—24no—
280C2×Dic118C24112yes—
281C2×Dic118C24112yes—
282C2×Dic118C2414yes—
283C4⋊C4×C59C24112yes—
284C4⋊C4×C59C24112yes—
285C22⋊C4×C59C2414yes—
286C22⋊C4×C59C24112yes—
287C22⋊C4×C59C24124yes—
288C42×C59C24112yes—
289C22⋊Dic59C24112yes—
290C22⋊Dic59C24124yes—
291C22⋊Dic59C2414yes—
292(C2×D59)⋊C4C24112yes—
293(C2×D59)⋊C4C24112yes—
294(C2×D59)⋊C4C24124yes—
295(C2×D59)⋊C4C24124yes—
296(C2×D59)⋊C4C24124yes—
297(C2×D59)⋊C4C2414yes—
298(C2×D59)⋊C4C2414yes—
299C4⋊Dic59C24112yes—
300C4⋊Dic59C24112yes—
301Dic59⋊C4C24112yes—
302Dic59⋊C4C24112yes—
303C4×Dic59C2414yes—
304C4×Dic59C24112yes—
305C4×Dic59C24112yes—
306C23×C59—22no—
307C23×C59—26no—
308C23×C59—22no—
309C23×C59—26no—
310C23×C59—22no—
311C23×C59—26no—
312C23×C59C2516yes—
313C23×C59C2512yes—
314C23×C59C2511yescharacteristic
315C22×D59—26no—
316C22×D59—26no—
317C22×D59—22no—
318C22×D59—26no—
319C22×D59—22no—
320C22×D59—26no—
321C22×D59—22no—
322C22×D59—26no—
323C22×D59—248no—
324C22×D59—424no—
325C22×D59—424no—
326C22×D59—848no—
327C22×D59C22×D4112yes—
328C22×D59C2516yes—
329C22×D59C2512yes—
330C22×D59C2516yes—
331Q8×C59—224no—
332Q8×C59C22×D4116yes—
333D4×C59—224no—
334D4×C59—412no—
335C2×C4×C59—26no—
336C2×C4×C59—22no—
337C2×C4×C59—22no—
338C2×C4×C59—26no—
339C2×C4×C59—224no—
340C2×C4×C59—224no—
341C2×C4×C59C22×D4112yes—
342C2×C4×C59C2516yes—
343C2×C4×C59C2512yes—
344C2×C4×C59C2512yes—
345C2×C4×C59C2516yes—
346C2×C4×C59C2516yes—
347C22⋊D59—224no—
348C22⋊D59—224no—
349C22⋊D59—28no—
350C22⋊D59—224no—
351C22⋊D59—412no—
352C22⋊D59—412no—
353C2×Dic59—26no—
354C2×Dic59—22no—
355C2×Dic59—22no—
356C2×Dic59—26no—
357C2×Dic59C22×D414yes—
358C2×Dic59C2512yes—
359C2×Dic59C2516yes—
360C2×Dic59C2512yes—
361C2×Dic59C2516yes—
362C2×Dic59C2512yes—
363D236—224no—
364D236—224no—
365D236—224no—
366D236—412no—
367D236C22×D4148yes—
368C4×D59—248no—
369C4×D59—224no—
370C4×D59—224no—
371C4×D59—412no—
372C4×D59—412no—
373C4×D59C22×D4148yes—
374Dic118—224no—
375Dic118—28no—
376Dic118—224no—
377C2×#3500—591nomaximal, Sylow
378C22×C59—22no—
379C22×C59—26no—
380C22×C59—22no—
381C22×C59—26no—
382C22×C59—22no—
383C22×C59—26no—
384C22×C59—412no—
385C22×C59—44no—
386C22×C59C23×D412yes—
387C22×C59#58512yes—
388C22×C59#58512yes—
389C22×C59C2611yescharacteristic
390C2×D59—26no—
391C2×D59—26no—
392C2×D59—224no—
393C2×D59—22no—
394C2×D59—26no—
395C2×D59—22no—
396C2×D59—26no—
397C2×D59—22no—
398C2×D59—26no—
399C2×D59—44no—
400C2×D59—412no—
401C2×D59—848no—
402C2×D59C23×D4112yes—
403C4×C59—26no—
404C4×C59—22no—
405C4×C59—22no—
406C4×C59—26no—
407C4×C59C23×D4112yes—
408Dic59—26no—
409Dic59—22no—
410Dic59—22no—
411Dic59—26no—
412Dic59C23×D414yes—
413C22×2−1+4—591no—
414C22×H(5,𝔽2)—591no—
415#3500—5932no—
416C2×#548—591no—
417C2×#548—591no—
418C2×#548—591no—
419C2×#548D5911yescharacteristic, complemented
420C2×#546—593no—
421C2×#546—593no—
422C2×#546—593no—
423C2×#546—593no—
424C2×#536—593no—
425C2×#535—593no—
426C2×#532—593no—
427C22×#124—593no—
428C2×C4×#41—591no—
429C2×C59—46no—
430C2×C59—42no—
431C2×C59#350014yescomplemented
432C2×C59C24×D411yescharacteristic
433C2×C59C2×#58511yescharacteristic
434C2×C59C2×#58511yescharacteristic
435D59—212no—
436D59—42no—
437D59—46no—
438C2×2−1+4—5916no—
439C2×2−1+4—11816no—
440C2×H(5,𝔽2)—5916no—
441C2×H(5,𝔽2)—11816no—
442C22×#41—591no—
443C22×#41—591no—
444C22×#41—593no—
445C22×#41—593no—
446C22×#41—593no—
447C22×#41—593no—
448C22×#41C2×D5911yescharacteristic
449C23×Q8—593no—
450C23×Q8—591no—
451C23×Q8C2×D5911yescharacteristic, complemented
452C23×D4—593no—
453C23×D4—593no—
454C23×D4—593no—
455#548—5916no—
456#548—5916no—
457#548—5916no—
458#548C2×D59116yescomplemented
459#546—5948no—
460#546—5948no—
461#546—5948no—
462#546—5948no—
463#536—5948no—
464#535—5948no—
465#532—5948no—
466C2×C4⋊Q8—593no—
467C2×#127—593no—
468C2×#124—593no—
469C2×#124—593no—
470C2×#124—5948no—
471C2×#124—593no—
472C2×#124—596no—
473C2×#124—591no—
474C2×#124—593no—
475C2×#124C2×D5913yescomplemented
476C2×#123—596no—
477C2×#123—596no—
478C2×C22⋊Q8—593no—
479C2×C22⋊Q8—593no—
480C2×C22⋊Q8—593no—
481C2×C22⋊Q8C2×D5913yescomplemented
482C2×#121—593no—
483C2×#121—593no—
484C2×#121—593no—
485C2×#121—593no—
486C2×#121—593no—
487C2×#121—593no—
488C2×#121—593no—
489C2×#121C2×D5913yescomplemented
490C2×#120—596no—
491C2×#120—596no—
492C4×#41—5916no—
493C2×C4×Q8—591no—
494C2×C4×Q8C2×D5911yescharacteristic, complemented
495C2×C4×D4—593no—
496C2×C4×D4—593no—
497C2×C4×D4—593no—
498C2×C4×D4—593no—
499C2×C4×D4—593no—
500C2×C4×D4C2×D5913yescomplemented
501C2×#117—593no—
502C22×C22⋊C4—596no—
503C22×C22⋊C4—596no—
504C22×C42—593no—
505C59C2×#350011yescharacteristic, complemented, Sylow
506C25—596no—
5072−1+4—118128no—
508H(5,𝔽2)—118128no—
509C2×#41—28no—
510C2×#41—5916no—
511C2×#41—598no—
512C2×#41—5924no—
513C2×#41—598no—
514C2×#41—5924no—
515C2×#41—5924no—
516C2×#41—5924no—
517C2×#41—11824no—
518C2×#41—11824no—
519C2×#41—11824no—
520C2×#41—11824no—
521C2×#41—1188no—
522C2×#41C22×D5918yes—
523C22×Q8—28no—
524C22×Q8—5924no—
525C22×Q8—598no—
526C22×Q8—593no—
527C22×Q8—593no—
528C22×Q8—591no—
529C22×Q8—11824no—
530C22×Q8—1188no—
531C22×Q8C22×D5913yes—
532C22×Q8C22×D5911yescharacteristic
533C22×Q8C22×D5918yescomplemented
534C22×D4—593no—
535C22×D4—593no—
536C22×D4—593no—
537C22×D4—591no—
538C22×D4—593no—
539C22×D4—593no—
540C22×D4—5924no—
541C22×D4—5924no—
542C22×D4—593no—
543C22×D4—593no—
544C22×D4—593no—
545C22×D4—593no—
546C22×D4—5924no—
547C22×D4—593no—
548C22×D4—11824no—
549C22×D4—11824no—
550C22×D4—11824no—
551C22×D4C22×D5913yes—
552C22×D4C22×D5913yes—
553C23×C4—593no—
554C23×C4—596no—
555C23×C4—593no—
556C23×C4—593no—
557C23×C4—593no—
558C23×C4—593no—
559C23×C4C22×D5913yes—
560C23×C4C22×D5913yes—
561C4⋊Q8—5924no—
562#127—5924no—
563#124—5924no—
564#124—5924no—
565#124—5924no—
566#124—5948no—
567#124—598no—
568#124—5924no—
569#124C22×D59124yescomplemented
570#123—5948no—
571#123—5948no—
572C22⋊Q8—5924no—
573C22⋊Q8—5924no—
574C22⋊Q8—5924no—
575C22⋊Q8C22×D59124yescomplemented
576#121—5924no—
577#121—5924no—
578#121—5924no—
579#121—5924no—
580#121—5924no—
581#121—5924no—
582#121—5924no—
583#121C22×D59124yescomplemented
584#120—5948no—
585#120—5948no—
586C4×Q8—598no—
587C4×Q8C22×D5918yescomplemented
588C4×D4—5924no—
589C4×D4—5924no—
590C4×D4—5924no—
591C4×D4—5924no—
592C4×D4—5924no—
593C4×D4C22×D59124yescomplemented
594#117—5924no—
595C2×C4⋊C4—593no—
596C2×C4⋊C4—593no—
597C2×C4⋊C4—593no—
598C2×C4⋊C4—593no—
599C2×C4⋊C4C22×D5913yes—
600C2×C4⋊C4C22×D5913yes—
601C2×C22⋊C4—593no—
602C2×C22⋊C4—596no—
603C2×C22⋊C4—591no—
604C2×C22⋊C4—593no—
605C2×C22⋊C4—593no—
606C2×C22⋊C4—596no—
607C2×C22⋊C4—596no—
608C2×C22⋊C4—596no—
609C2×C22⋊C4—591no—
610C2×C22⋊C4—591no—
611C2×C22⋊C4—5948no—
612C2×C22⋊C4—5948no—
613C2×C22⋊C4C22×D5913yes—
614C2×C22⋊C4C22×D5916yes—
615C2×C22⋊C4C22×D5911yescharacteristic
616C2×C42—593no—
617C2×C42—593no—
618C2×C42—591no—
619C2×C42—5924no—
620C2×C42C22×D5913yes—
621C24—593no—
622C24—593no—
623C24—591no—
624C24—5924no—
625C24—11824no—
626C24—23612no—
627C24—23612no—
628C24C23×D5913yes—
629C24C23×D5911yescharacteristic
630#41—232no—
631#41—5964no—
632#41—11896no—
633#41—11896no—
634#41—11896no—
635#41—11896no—
636#41—11832no—
637C2×Q8—232no—
638C2×Q8—212no—
639C2×Q8—5912no—
640C2×Q8—5912no—
641C2×Q8—594no—
642C2×Q8—11812no—
643C2×Q8—1184no—
644C2×Q8—11896no—
645C2×Q8—11832no—
646C2×Q8—11812no—
647C2×Q8D4×D5918yes—
648C2×Q8C23×D59112yes—
649C2×Q8C23×D5914yes—
650C2×D4—212no—
651C2×D4—46no—
652C2×D4—5912no—
653C2×D4—5912no—
654C2×D4—5912no—
655C2×D4—594no—
656C2×D4—5912no—
657C2×D4—5912no—
658C2×D4—5924no—
659C2×D4—5912no—
660C2×D4—5912no—
661C2×D4—5912no—
662C2×D4—5912no—
663C2×D4—5912no—
664C2×D4—11896no—
665C2×D4—11812no—
666C2×D4—11812no—
667C2×D4—11896no—
668C2×D4—11812no—
669C2×D4—1184no—
670C2×D4—11896no—
671C2×D4—11812no—
672C2×D4—11812no—
673C2×D4—11812no—
674C2×D4—2366no—
675C2×D4—2366no—
676C2×D4—2366no—
677C2×D4C23×D59112yes—
678C2×D4C23×D59112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—591no—
682C22×C4—5924no—
683C22×C4—5912no—
684C22×C4—591no—
685C22×C4—593no—
686C22×C4—593no—
687C22×C4—591no—
688C22×C4—5924no—
689C22×C4—5912no—
690C22×C4—5912no—
691C22×C4—5912no—
692C22×C4—5912no—
693C22×C4—11824no—
694C22×C4—11812no—
695C22×C4—11812no—
696C22×C4—2366no—
697C22×C4—2366no—
698C22×C4C23×D59112yes—
699C22×C4C23×D59112yes—
700C22×C4C23×D5911yescharacteristic
701C22×C4C23×D5913yes—
702C22×C4C23×D5913yes—
703C22×C4C23×D5911yescharacteristic
704C22×C4C23×D5913yes—
705C4⋊C4—5912no—
706C4⋊C4—5912no—
707C4⋊C4—5912no—
708C4⋊C4—5912no—
709C4⋊C4C23×D59112yes—
710C4⋊C4C23×D59112yes—
711C22⋊C4—5912no—
712C22⋊C4—5924no—
713C22⋊C4—594no—
714C22⋊C4—5912no—
715C22⋊C4—5912no—
716C22⋊C4—5924no—
717C22⋊C4—5924no—
718C22⋊C4—5924no—
719C22⋊C4—594no—
720C22⋊C4—594no—
721C22⋊C4C23×D59112yes—
722C22⋊C4C23×D59124yes—
723C22⋊C4C23×D5914yes—
724C42—594no—
725C42—5912no—
726C42—5912no—
727C42C23×D59112yes—
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—5912no—
735C23—596no—
736C23—596no—
737C23—592no—
738C23—11848no—
739C23—1186no—
740C23—1186no—
741C23—1182no—
742C23—1186no—
743C23—1182no—
744C23—1186no—
745C23—1182no—
746C23—1186no—
747C23—47248no—
748C23—23624no—
749C23—23624no—
750C23C24×D5916yes—
751C23C24×D5912yes—
752C23C24×D5911yescharacteristic
753Q8—224no—
754Q8—11824no—
755Q8—1188no—
756Q8—11824no—
757Q8C2×D4×D59116yes—
758D4—224no—
759D4—412no—
760D4—5948no—
761D4—11824no—
762D4—11824no—
763D4—11824no—
764D4—1188no—
765D4—11824no—
766D4—11824no—
767D4—11824no—
768D4—23612no—
769D4—23612no—
770D4—23612no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—22no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—594no—
778C2×C4—592no—
779C2×C4—5948no—
780C2×C4—592no—
781C2×C4—596no—
782C2×C4—596no—
783C2×C4—592no—
784C2×C4—11848no—
785C2×C4—1182no—
786C2×C4—1186no—
787C2×C4—1182no—
788C2×C4—1186no—
789C2×C4—11824no—
790C2×C4—11824no—
791C2×C4—23612no—
792C2×C4—23612no—
793C2×C4C2×D4×D59112yes—
794C2×C4C24×D5912yes—
795C2×C4C24×D5916yes—
796C2×C4C24×D5916yes—
797C2×C4C24×D5912yes—
798C2×C4C24×D5916yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—412no—
806C22—44no—
807C22—5912no—
808C22—1186no—
809C22—1186no—
810C22—11824no—
811C22—1182no—
812C22—1186no—
813C22—1182no—
814C22—1186no—
815C22—1182no—
816C22—1186no—
817C22—47248no—
818C22—23612no—
819C22—2364no—
820C22C22×D4×D5912yes—
821C22#1683823812yes—
822C22#1683823912yes—
823C22C25×D5911yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—594no—
829C4—1182no—
830C4—1186no—
831C4—1182no—
832C4—1186no—
833C4C22×D4×D59112yes—
834C2—46no—
835C2—42no—
836C2—11812no—
837C2—2366no—
838C2—2362no—
839C2#2143788714yesdirect product factor
840C2C23×D4×D5911yescharacteristic
841C2C2×#1683823811yescharacteristic
842C2C2×#1683823911yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#548C2
socleC23×C59C25
hypercenterC2×#548D59
hypocenterC59C2×#3500
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14273775C2semidirect
2. C22×#14273773C2semidirect
3. #21437887C2direct (N × H)
4. C2×#16838064C2semidirect
5. C2×#16838063C2semidirect
6. C2×#16838059C2semidirect
7. C2×#16838049C2semidirect
8. C2×#16838048C2semidirect
9. C2×#16838045C2semidirect
10. C2×#16838043C2semidirect
11. C2×#16837975C2semidirect
12. C2×#16837968C2semidirect
13. C2×#16837949C2semidirect
14. C2×#124×D59C2semidirect
15. C2×C4×#11745689C2semidirect
16. C2×C59×#548C2semidirect
18. C2×#14273775C22semidirect
20. C2×#14273773C22semidirect
23. C22×#11745689C22semidirect
25. C22×#11745685C22semidirect
26. C22×#11745685C22semidirect
27. C22×Q8×D59C22semidirect
28. C22×Q8×D59C22semidirect
32. #16838064C22semidirect
33. #16838063C22semidirect
34. #16838059C22semidirect
35. #16838049C22semidirect
36. #16838048C22semidirect
37. #16838045C22semidirect
38. #16838043C22semidirect
39. #16837975C22semidirect
40. #16837968C22semidirect
41. #16837949C22semidirect
42. C2×#14273726C22semidirect
43. C2×#14273723C22semidirect
44. C2×#14273716C22semidirect
45. C2×#14273715C22semidirect
46. C2×#14273714C22semidirect
47. C2×#14273713C22semidirect
48. C2×#14273713C22semidirect
49. C2×#14273713C22semidirect
50. #124×D59C22semidirect
51. C2×#14273712C22semidirect
52. C2×#14273709C22semidirect
53. C2×#14273707C22semidirect
54. C2×#14273706C22semidirect
55. C2×#14273703C22semidirect
56. C2×#14273702C22semidirect
57. C2×#14273702C22semidirect
58. C2×#14273701C22semidirect
59. C2×#14273700C22semidirect
60. C2×#14273700C22semidirect
61. C2×#14273698C22semidirect
62. C2×#14273698C22semidirect
63. C2×#14273697C22semidirect
64. C2×#14273695C22semidirect
65. C4×#11745689C22semidirect
66. C2×Q8×Dic59C22semidirect
67. C2×C4×D236C22semidirect
68. C2×C4×D236C22semidirect
69. C2×#14273689C22semidirect
70. C2×C4×C22⋊D59C22semidirect
71. C2×C4×C22⋊D59C22semidirect
72. C2×#14273685C22semidirect
73. C2×C22⋊C4×D59C22semidirect
74. C2×C22⋊C4×D59C22semidirect
75. C2×C42×D59C22semidirect
77. C23×Q8×C59C22semidirect
78. C59×#548C22semidirect
79. C2×#124×C59C22semidirect
80. C2×C22⋊Q8×C59C22semidirect
81. C2×#121×C59C22semidirect
82. C2×C4×Q8×C59C22semidirect
83. C2×C4×D4×C59C22semidirect
89. C2×#11745689D4semidirect
92. C2×#11745689C23semidirect
97. C2×#11745685C23semidirect
98. C2×#11745685C23semidirect
104. C2×Q8×D59C23semidirect
105. C2×Q8×D59C23semidirect
129. #14273726C23semidirect
130. #14273723C23semidirect
131. #14273716C23semidirect
132. #14273715C23semidirect
133. #14273714C23semidirect
134. #14273713C23semidirect
135. #14273713C23semidirect
136. #14273713C23semidirect
137. #14273712C23semidirect
138. #14273709C23semidirect
139. #14273707C23semidirect
140. #14273706C23semidirect
141. #14273703C23semidirect
142. #14273702C23semidirect
143. #14273702C23semidirect
144. #14273701C23semidirect
145. #14273700C23semidirect
146. #14273700C23semidirect
147. #14273698C23semidirect
148. #14273698C23semidirect
149. #14273697C23semidirect
150. #14273695C23semidirect
151. Q8×Dic59C23semidirect
152. C4×D236C23semidirect
153. C4×D236C23semidirect
154. #14273689C23semidirect
155. C4×C22⋊D59C23semidirect
156. C4×C22⋊D59C23semidirect
157. #14273685C23semidirect
172. C22⋊C4×D59C23semidirect
173. C22⋊C4×D59C23semidirect
177. C42×D59C23semidirect
183. C22×Q8×C59C23semidirect
188. #124×C59C23semidirect
189. C22⋊Q8×C59C23semidirect
190. #121×C59C23semidirect
191. C4×Q8×C59C23semidirect
192. C4×D4×C59C23semidirect
246. #11745689C2×D4semidirect
419. C2×#548D59semidirect
431. C2×C59#3500semidirect
451. C23×Q8C2×D59semidirect
458. #548C2×D59semidirect
475. C2×#124C2×D59semidirect
481. C2×C22⋊Q8C2×D59semidirect
489. C2×#121C2×D59semidirect
494. C2×C4×Q8C2×D59semidirect
500. C2×C4×D4C2×D59semidirect
505. C59C2×#3500semidirect
533. C22×Q8C22×D59semidirect
569. #124C22×D59semidirect
575. C22⋊Q8C22×D59semidirect
583. #121C22×D59semidirect
587. C4×Q8C22×D59semidirect
593. C4×D4C22×D59semidirect
839. C2#21437887direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737752
C22×#142737732
#214378872
C2×#168380642
C2×#168380632
C2×#168380592
C2×#168380492
C2×#168380482
C2×#168380452
C2×#168380432
C2×#168379752
C2×#168379682
C2×#168379492
C2×#124×D592
C2×C4×#117456892
C2×C59×#5482
C2×#350059