Finite Group Databasebeta

← C2×#21437742 #29496851

Subgroups — C2×#21437742 #29496851

Order 15104.

11254 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273774C211yesmaximal, characteristic, complemented
2C23×Q8×D59C211yesmaximal, characteristic, complemented
3#21437742C2132yesmaximal, direct product factor
4C2×Q8×D236C211yesmaximal, characteristic, complemented
5C2×D4×Dic118C213yesmaximal, complemented
6C2×Q8×C22⋊D59C211yesmaximal, characteristic, complemented
7C2×#16838065C213yesmaximal, complemented
8C2×#16838060C213yesmaximal, complemented
9C2×#16838059C211yesmaximal, characteristic, complemented
10C2×#16838058C213yesmaximal, complemented
11C2×#16837975C213yesmaximal, complemented
12C2×#16837972C213yesmaximal, complemented
13C2×#16837912C213yesmaximal, complemented
14C2×#16837911C213yesmaximal, complemented
15C2×#16837878C211yesmaximal, characteristic, complemented
16C2×C59×#548C211yesmaximal, characteristic, complemented
17C2×#14273774—216no—
18C2×#14273774C22116yescomplemented
19C22×#11745685C2213yes—
20C22×#11745687C2213yes—
21C22×#11745687C2213yescomplemented
22C23×Dic118C2213yes—
23C23×Dic118C2213yescomplemented
24C22×Q8×D59—216no—
25C22×Q8×D59C2211yescharacteristic
26C22×Q8×D59C2213yes—
27C22×Q8×D59C2213yes—
28C22×Q8×D59C2211yescharacteristic
29C22×Q8×D59C22116yescomplemented
30C22×Q8×D59C2211yescharacteristic, complemented
31C23×C4×D59C2213yes—
32Q8×D236C22116yescomplemented
33D4×Dic118C22148yescomplemented
34Q8×C22⋊D59C22116yescomplemented
35#16838065C22148yescomplemented
36#16838060C22148yescomplemented
37#16838059C22116yescomplemented
38#16838058C22148yescomplemented
39#16837975C22148yescomplemented
40#16837972C22148yescomplemented
41C2×#14273727C2213yescomplemented
42C2×#14273726C2216yescomplemented
43C2×#14273725C2213yescomplemented
44C2×#14273714C2213yescomplemented
45C2×#14273713C2216yescomplemented
46#16837912C22148yescomplemented
47#16837911C22148yescomplemented
48C2×#14273712C2213yes—
49C2×#14273709C2213yes—
50C2×#14273709C2216yes—
51C2×#14273707C2213yes—
52C2×#14273707C2213yescomplemented
53C2×#14273706C2213yes—
54C2×#14273706C2213yescomplemented
55C2×#14273705C2213yes—
56C2×#14273704C2213yes—
57C2×#14273704C2216yescomplemented
58C2×#14273704C2216yescomplemented
59C2×#14273703C2213yescomplemented
60C2×#14273700C2213yes—
61C2×#14273699C2213yes—
62C2×#14273698C2213yes—
63C2×#14273697C2211yescharacteristic
64C2×#14273695C2213yes—
65#16837878C22116yescomplemented
66C2×Q8×Dic59C2211yescharacteristic, complemented
67C2×C4×Dic118C2213yescomplemented
68C2×#14273692C2213yescomplemented
69C2×C4×D236C2213yes—
70C2×D4×Dic59C2216yes—
71C2×C4×C22⋊D59C2213yes—
72C2×C4×C22⋊D59C2213yes—
73C2×(C22⋊D59)⋊C4C2216yes—
74C2×#14273685C2213yes—
75C2×#14273684C2213yes—
76C22×#41×C59C2211yescharacteristic, complemented
77C23×Q8×C59C2211yescharacteristic
78C59×#548C22116yescomplemented
79C2×#124×C59C2213yescomplemented
80C2×C22⋊Q8×C59C2213yescomplemented
81C2×#121×C59C2213yes—
82C2×C4×Q8×C59C2211yescharacteristic, complemented
83C2×C4×D4×C59C2213yes—
84C24×D59C2311yescharacteristic
85#14273774—2128no—
86C2×#11745685—224no—
87C2×#11745685C23124yes—
88C2×#11745687—224no—
89C2×#11745687—224no—
90C2×#11745687C23124yes—
91C2×#11745687C23124yescomplemented
92C22×Dic118—224no—
93C22×Dic118—224no—
94C22×Dic118C2313yes—
95C22×Dic118C2316yes—
96C22×Dic118C2313yes—
97C22×Dic118C2313yes—
98C22×Dic118C23124yes—
99C22×Dic118C2313yes—
100C22×Dic118C23124yescomplemented
101C2×Q8×D59—28no—
102C2×Q8×D59—28no—
103C2×Q8×D59—2128no—
104C2×Q8×D59—224no—
105C2×Q8×D59—224no—
106C2×Q8×D59D4116yescomplemented
107C2×Q8×D59C23124yes—
108C2×Q8×D59C2318yes—
109C2×Q8×D59C23124yes—
110C2×Q8×D59C2318yes—
111C2×Q8×D59C2318yescomplemented
112C22×D236C2311yescharacteristic
113C22×D236C2311yescharacteristic
114C22×C22⋊D59C2311yescharacteristic
115C22×C22⋊D59C2313yes—
116C22×C22⋊D59C2313yes—
117C22×C22⋊D59C2313yes—
118C23×Dic59C2313yes—
119C23×Dic59C2316yes—
120C22×C4×D59—224no—
121C22×C4×D59C2313yes—
122C22×C4×D59C2313yes—
123C22×C4×D59C2313yes—
124C22×C4×D59C2313yes—
125C22×C4×D59C23124yes—
126C22×C4×D59C2313yes—
127#14273727C23124yescomplemented
128#14273726C23148yescomplemented
129#14273725C23124yescomplemented
130#14273714C23124yescomplemented
131#14273713C23148yescomplemented
132#14273712C23124yes—
133#14273709C23124yes—
134#14273709C23148yes—
135#14273707C23124yes—
136#14273707C23124yescomplemented
137#14273706C23124yes—
138#14273706C23124yescomplemented
139#14273705C23124yes—
140#14273704C23124yes—
141#14273704C23148yescomplemented
142#14273704C23148yescomplemented
143#14273703C23124yescomplemented
144#14273700C23124yes—
145#14273699C23124yes—
146#14273698C23124yes—
147#14273697C2318yes—
148#14273695C23124yes—
149Q8×Dic59C2318yescomplemented
150C4×Dic118C23124yescomplemented
151#14273692C23124yescomplemented
152C4×D236C23124yes—
153D4×Dic59C23148yes—
154C4×C22⋊D59C23124yes—
155C4×C22⋊D59C23124yes—
156(C22⋊D59)⋊C4C23148yes—
157#14273685C23124yes—
158#14273684C23124yes—
159C2×C4⋊Dic59C2313yes—
160C2×C4⋊Dic59C2313yes—
161C2×C4⋊Dic59C2316yes—
162C2×Dic59⋊C4C2313yes—
163C2×Dic59⋊C4C2313yes—
164C2×Dic59⋊C4C2316yes—
165C2×Dic59⋊C4C2313yes—
166C2×Dic59⋊C4C2313yes—
167C2×C22⋊Dic59C2316yes—
168C2×C22⋊Dic59C2313yes—
169C2×C22⋊Dic59C2313yes—
170C2×(C2×D59)⋊C4C2311yescharacteristic
171C2×(C2×D59)⋊C4C2311yescharacteristic
172C2×(C2×D59)⋊C4C2313yes—
173C2×(C2×D59)⋊C4C2313yes—
174C2×(C2×D59)⋊C4C2313yes—
175C2×(C2×D59)⋊C4C2313yes—
176C2×C4×Dic59C2316yes—
177C2×C4×Dic59C2313yes—
178C2×#41×C59—28no—
179C2×#41×C59C2318yescomplemented
180C22×Q8×C59—28no—
181C22×Q8×C59C2313yes—
182C22×Q8×C59C2318yes—
183C22×Q8×C59C2311yescharacteristic
184C22×D4×C59C2313yes—
185C22×D4×C59C2313yes—
186C23×C4×C59C2313yes—
187C23×C4×C59C2313yes—
188#124×C59C23124yescomplemented
189C22⋊Q8×C59C23124yescomplemented
190#121×C59C23124yes—
191C4×Q8×C59C2318yescomplemented
192C4×D4×C59C23124yes—
193C2×C4⋊C4×C59C2313yes—
194C2×C4⋊C4×C59C2313yes—
195C2×C22⋊C4×C59C2311yescharacteristic
196C2×C22⋊C4×C59C2313yes—
197C2×C22⋊C4×C59C2316yes—
198C2×C42×C59C2313yes—
199C24×C59C2413yes—
200C24×C59C2411yescharacteristic
201C23×D59—24no—
202C23×D59—24no—
203C23×D59—24no—
204C23×D59C2411yescharacteristic
205C23×D59C2414yes—
206C23×D59C2411yescharacteristic
207C23×D59C2411yescharacteristic
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—212no—
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—24no—
228C2×C22⋊D59—212no—
229C2×C22⋊D59—212no—
230C2×C22⋊D59—212no—
231C2×C22⋊D59C24112yes—
232C2×C22⋊D59C2414yes—
233C2×C22⋊D59C24112yes—
234C2×C22⋊D59C24112yes—
235C22×Dic59—212no—
236C22×Dic59—224no—
237C22×Dic59C2411yescharacteristic
238C22×Dic59C2413yes—
239C22×Dic59C2413yes—
240C22×Dic59C2413yes—
241C22×Dic59C24124yes—
242C22×Dic59C24112yes—
243C22×Dic59C2413yes—
244Q8×D59—232no—
245Q8×D59—232no—
246Q8×D59—296no—
247Q8×D59—296no—
248Q8×D59C2×D4164yescomplemented
249#11745687—296no—
250#11745687—296no—
251#11745685—296no—
252C2×D236—24no—
253C2×D236—24no—
254C2×D236C2414yes—
255C2×D236C2414yes—
256C2×C4×D59—212no—
257C2×C4×D59—212no—
258C2×C4×D59—212no—
259C2×C4×D59—212no—
260C2×C4×D59—296no—
261C2×C4×D59C2×D4124yes—
262C2×C4×D59C24112yes—
263C2×C4×D59C24112yes—
264C2×C4×D59C24112yes—
265C2×C4×D59C24112yes—
266C2×C4×D59C24112yes—
267C2×Dic118—212no—
268C2×Dic118—212no—
269C2×Dic118—224no—
270C2×Dic118—212no—
271C2×Dic118—296no—
272C2×Dic118—296no—
273C2×Dic118C2×D4124yes—
274C2×Dic118C24112yes—
275C2×Dic118C24124yes—
276C2×Dic118C24112yes—
277C2×Dic118C24112yes—
278C2×Dic118C24112yes—
279C4⋊C4×C59C24112yes—
280C4⋊C4×C59C24112yes—
281C22⋊C4×C59C2414yes—
282C22⋊C4×C59C24112yes—
283C22⋊C4×C59C24124yes—
284C42×C59C24112yes—
285C22⋊Dic59C24112yes—
286C22⋊Dic59C24112yes—
287C22⋊Dic59C24124yes—
288(C2×D59)⋊C4C2414yes—
289(C2×D59)⋊C4C24112yes—
290(C2×D59)⋊C4C24112yes—
291(C2×D59)⋊C4C2414yes—
292(C2×D59)⋊C4C24112yes—
293(C2×D59)⋊C4C24112yes—
294C4⋊Dic59C24112yes—
295C4⋊Dic59C24124yes—
296C4⋊Dic59C24112yes—
297Dic59⋊C4C24112yes—
298Dic59⋊C4C24112yes—
299Dic59⋊C4C24124yes—
300Dic59⋊C4C24112yes—
301Dic59⋊C4C24112yes—
302C4×Dic59C24112yes—
303C4×Dic59C24124yes—
304C23×C59—22no—
305C23×C59—22no—
306C23×C59—26no—
307C23×C59—26no—
308C23×C59—26no—
309C23×C592−1+414yescomplemented
310C23×C59C2516yes—
311C23×C59C2512yes—
312C23×C59C2511yescharacteristic
313C22×D59—232no—
314C22×D59—22no—
315C22×D59—22no—
316C22×D59—22no—
317C22×D59—22no—
318C22×D59—28no—
319C22×D59—28no—
320C22×D59—28no—
321C22×D59—22no—
322C22×D59—22no—
323C22×D59—22no—
324C22×D59C22×D414yes—
325C22×D592−1+414yescomplemented
326C22×D59C2512yes—
327C22×D59C2512yes—
328C22×D59C2512yes—
329Q8×C59—224no—
330Q8×C59C22×D4116yes—
331D4×C59—224no—
332D4×C59—224no—
333C2×C4×C59—22no—
334C2×C4×C59—26no—
335C2×C4×C59—22no—
336C2×C4×C59—26no—
337C2×C4×C59—224no—
338C2×C4×C59—224no—
339C2×C4×C59C22×D4112yes—
340C2×C4×C59C2516yes—
341C2×C4×C59C2512yes—
342C2×C4×C59C2516yes—
343C2×C4×C59C2512yes—
344C2×C4×C59C2516yes—
345C22⋊D59—28no—
346C22⋊D59—224no—
347C22⋊D59—224no—
348C22⋊D59—224no—
349C2×Dic59—26no—
350C2×Dic59—26no—
351C2×Dic59—26no—
352C2×Dic59—22no—
353C2×Dic59—224no—
354C2×Dic59—248no—
355C2×Dic59C22×D4112yes—
356C2×Dic59C2512yes—
357C2×Dic59C2516yes—
358C2×Dic59C2516yes—
359C2×Dic59C2516yes—
360C2×Dic59C2516yes—
361D236—28no—
362D236—28no—
363C4×D59—224no—
364C4×D59—224no—
365C4×D59—224no—
366C4×D59—224no—
367C4×D59C22×D4148yes—
368Dic118—224no—
369Dic118—224no—
370Dic118—224no—
371Dic118—248no—
372Dic118C22×D4148yes—
373C2×#3486—591nomaximal, Sylow
374C22×C59—22no—
375C22×C59—22no—
376C22×C59—28no—
377C22×C59—26no—
378C22×C59—26no—
379C22×C59—26no—
380C22×C59—412no—
381C22×C59C23×D412yes—
382C22×C59C2×2−1+412yes—
383C22×C59C2×2−1+412yes—
384C22×C59C2×2−1+414yescomplemented
385C22×C59C2611yescharacteristic
386C2×D59—232no—
387C2×D59—22no—
388C2×D59—22no—
389C2×D59—22no—
390C2×D59—22no—
391C2×D59—28no—
392C2×D59—28no—
393C2×D59—22no—
394C2×D59—22no—
395C2×D59—22no—
396C2×D59—44no—
397C2×D59C23×D414yes—
398C2×D59C2×2−1+414yescomplemented
399C4×C59—22no—
400C4×C59—26no—
401C4×C59—22no—
402C4×C59—26no—
403C4×C59C23×D4112yes—
404Dic59—26no—
405Dic59—26no—
406Dic59—26no—
407Dic59—22no—
408Dic59C23×D4112yes—
409C22×2−1+4—591no—
410C24×Q8—591no—
411#3486—5932no—
412C2×D4×Q8—591no—
413C2×D4×Q8—593no—
414C2×D4×Q8—591no—
415C2×D4×Q8—593no—
416C2×#548—591no—
417C2×#548—593no—
418C2×#548—593no—
419C2×#548D5911yescharacteristic, complemented
420C2×#536—593no—
421C2×#536—593no—
422C2×#525—593no—
423C2×#525—593no—
424C2×#519—591no—
425C2×C59—24no—
426C2×C59—46no—
427C2×C59#348614yescomplemented
428C2×C59C24×D411yescharacteristic
429C2×C59C22×2−1+411yescharacteristic
430C2×C59C22×2−1+411yescharacteristic
431D59—24no—
432D59—24no—
433D59—42no—
434C2×2−1+4—5916no—
435C2×2−1+4—11816no—
436C22×#41—593no—
437C22×#41—593no—
438C22×#41—593no—
439C22×#41C2×D5911yescharacteristic, complemented
440C23×Q8—591no—
441C23×Q8—593no—
442C23×Q8—593no—
443C23×Q8—591no—
444C23×Q8—5916no—
445C23×Q8—591no—
446C23×Q8—593no—
447C23×Q8—593no—
448C23×Q8—11816no—
449C23×Q8C2×D5911yescharacteristic
450C24×C4—593no—
451D4×Q8—5916no—
452D4×Q8—5948no—
453D4×Q8—5916no—
454D4×Q8—5948no—
455#548—5916no—
456#548—5948no—
457#548—5948no—
458#548C2×D59116yescomplemented
459#536—5948no—
460#536—5948no—
461C2×C4⋊Q8—593no—
462C2×C4⋊Q8—596no—
463C2×C4⋊Q8—593no—
464C2×#124—593no—
465C2×#124—596no—
466C2×#124C2×D5913yescomplemented
467#525—5948no—
468#525—5948no—
469C2×#123—593no—
470C2×#123—596no—
471C2×#123—593no—
472C2×C22⋊Q8—593no—
473C2×C22⋊Q8—593no—
474C2×C22⋊Q8—593no—
475C2×C22⋊Q8—593no—
476C2×C22⋊Q8—593no—
477C2×C22⋊Q8—593no—
478C2×C22⋊Q8—593no—
479C2×C22⋊Q8—596no—
480C2×C22⋊Q8—596no—
481C2×C22⋊Q8C2×D5913yescomplemented
482C2×#121—593no—
483C2×#121—593no—
484C2×#121—593no—
485C2×#121C2×D5913yes—
486C2×#120—593no—
487C2×#120—591no—
488#519—5916no—
489C2×C4×Q8—591no—
490C2×C4×Q8—593no—
491C2×C4×Q8—593no—
492C2×C4×Q8C2×D5911yescharacteristic, complemented
493C2×C4×D4—596no—
494C2×C4×D4—593no—
495C2×C4×D4—593no—
496C2×C4×D4—596no—
497C2×C4×D4—593no—
498C2×C4×D4C2×D5913yes—
499C2×#117—593no—
500C2×#117—593no—
501C59C2×#348611yescharacteristic, complemented, Sylow
502C25—591no—
5032−1+4—118128no—
504C2×#41—28no—
505C2×#41—5924no—
506C2×#41—5924no—
507C2×#41—5924no—
508C2×#41—11824no—
509C2×#41—11824no—
510C2×#41—11824no—
511C2×#41C22×D5918yescomplemented
512C22×Q8—28no—
513C22×Q8—5916no—
514C22×Q8—598no—
515C22×Q8—5924no—
516C22×Q8—5924no—
517C22×Q8—598no—
518C22×Q8—598no—
519C22×Q8—593no—
520C22×Q8—596no—
521C22×Q8—593no—
522C22×Q8—593no—
523C22×Q8—593no—
524C22×Q8—5924no—
525C22×Q8—5924no—
526C22×Q8—11824no—
527C22×Q8—11824no—
528C22×Q8—11824no—
529C22×Q8—118128no—
530C22×Q8—11824no—
531C22×Q8—1188no—
532C22×Q8—1188no—
533C22×Q8C22×D5913yes—
534C22×Q8C22×D5918yes—
535C22×Q8C22×D5911yescharacteristic
536C22×D4—593no—
537C22×D4—591no—
538C22×D4—593no—
539C22×D4—593no—
540C22×D4—591no—
541C22×D4—591no—
542C22×D4C22×D5913yes—
543C22×D4C22×D5913yes—
544C23×C4—593no—
545C23×C4—593no—
546C23×C4—596no—
547C23×C4—593no—
548C23×C4—593no—
549C23×C4—593no—
550C23×C4—593no—
551C23×C4—5924no—
552C23×C4—11824no—
553C23×C4C22×D5913yes—
554C23×C4C22×D5913yes—
555C4⋊Q8—5924no—
556C4⋊Q8—5948no—
557C4⋊Q8—5924no—
558#124—5924no—
559#124—5948no—
560#124C22×D59124yescomplemented
561#123—5924no—
562#123—5948no—
563#123—5924no—
564C22⋊Q8—5924no—
565C22⋊Q8—5924no—
566C22⋊Q8—5924no—
567C22⋊Q8—5924no—
568C22⋊Q8—5924no—
569C22⋊Q8—5924no—
570C22⋊Q8—5924no—
571C22⋊Q8—5948no—
572C22⋊Q8—5948no—
573C22⋊Q8C22×D59124yescomplemented
574#121—5924no—
575#121—5924no—
576#121—5924no—
577#121C22×D59124yes—
578#120—5924no—
579#120—598no—
580C4×Q8—598no—
581C4×Q8—5924no—
582C4×Q8—5924no—
583C4×Q8C22×D5918yescomplemented
584C4×D4—5948no—
585C4×D4—5924no—
586C4×D4—5924no—
587C4×D4—5948no—
588C4×D4—5924no—
589C4×D4C22×D59124yes—
590#117—5924no—
591#117—5924no—
592C2×C4⋊C4—593no—
593C2×C4⋊C4—593no—
594C2×C4⋊C4—593no—
595C2×C4⋊C4—593no—
596C2×C4⋊C4—593no—
597C2×C4⋊C4—596no—
598C2×C4⋊C4—596no—
599C2×C4⋊C4—593no—
600C2×C4⋊C4C22×D5913yes—
601C2×C4⋊C4C22×D5913yes—
602C2×C22⋊C4—593no—
603C2×C22⋊C4—596no—
604C2×C22⋊C4—593no—
605C2×C22⋊C4—593no—
606C2×C22⋊C4—591no—
607C2×C22⋊C4—591no—
608C2×C22⋊C4—593no—
609C2×C22⋊C4—593no—
610C2×C22⋊C4—593no—
611C2×C22⋊C4C22×D5916yes—
612C2×C22⋊C4C22×D5911yescharacteristic
613C2×C22⋊C4C22×D5913yes—
614C2×C42—596no—
615C2×C42—593no—
616C2×C42C22×D5913yes—
617C24—591no—
618C24—591no—
619C24—594no—
620C24—591no—
621C24—1184no—
622C24—1184no—
623C24—1184no—
624C24C23×D5913yes—
625C24C23×D5911yescharacteristic
626#41—232no—
627#41—11896no—
628#41—11896no—
629#41—11896no—
630C2×Q8—232no—
631C2×Q8—212no—
632C2×Q8—5964no—
633C2×Q8—5924no—
634C2×Q8—5912no—
635C2×Q8—5924no—
636C2×Q8—5912no—
637C2×Q8—5912no—
638C2×Q8—5912no—
639C2×Q8—11824no—
640C2×Q8—11812no—
641C2×Q8—11896no—
642C2×Q8—11896no—
643C2×Q8—11896no—
644C2×Q8—11896no—
645C2×Q8—11832no—
646C2×Q8—11832no—
647C2×Q8—11812no—
648C2×Q8—11812no—
649C2×Q8D4×D5918yes—
650C2×Q8C23×D59112yes—
651C2×Q8C23×D5914yes—
652C2×D4—212no—
653C2×D4—212no—
654C2×D4—5912no—
655C2×D4—594no—
656C2×D4—5912no—
657C2×D4—5912no—
658C2×D4—594no—
659C2×D4—594no—
660C2×D4—1184no—
661C2×D4—1184no—
662C2×D4—11812no—
663C2×D4—11812no—
664C2×D4—11812no—
665C2×D4—1184no—
666C2×D4C23×D59112yes—
667C2×D4C23×D59112yes—
668C22×C4—212no—
669C22×C4—212no—
670C22×C4—593no—
671C22×C4—5924no—
672C22×C4—5912no—
673C22×C4—5912no—
674C22×C4—5924no—
675C22×C4—593no—
676C22×C4—591no—
677C22×C4—593no—
678C22×C4—593no—
679C22×C4—5912no—
680C22×C4—5912no—
681C22×C4—5912no—
682C22×C4—5912no—
683C22×C4—11812no—
684C22×C4—11896no—
685C22×C4—11812no—
686C22×C4—11812no—
687C22×C4—11824no—
688C22×C4—11812no—
689C22×C4—11812no—
690C22×C4C23×D59112yes—
691C22×C4C23×D59112yes—
692C22×C4C23×D5913yes—
693C22×C4C23×D5911yescharacteristic
694C22×C4C23×D5913yes—
695C22×C4C23×D5911yescharacteristic
696C22×C4C23×D5913yes—
697C4⋊C4—5912no—
698C4⋊C4—5912no—
699C4⋊C4—5912no—
700C4⋊C4—5912no—
701C4⋊C4—5912no—
702C4⋊C4—5924no—
703C4⋊C4—5924no—
704C4⋊C4—5912no—
705C4⋊C4C23×D59112yes—
706C4⋊C4C23×D59112yes—
707C22⋊C4—5912no—
708C22⋊C4—5924no—
709C22⋊C4—5912no—
710C22⋊C4—5912no—
711C22⋊C4—594no—
712C22⋊C4—594no—
713C22⋊C4—5912no—
714C22⋊C4—5912no—
715C22⋊C4—5912no—
716C22⋊C4C23×D59124yes—
717C22⋊C4C23×D5914yes—
718C22⋊C4C23×D59112yes—
719C42—5924no—
720C42—5912no—
721C42C23×D59112yes—
722C23—22no—
723C23—22no—
724C23—26no—
725C23—26no—
726C23—26no—
727C23—594no—
728C23—594no—
729C23—592no—
730C23—592no—
731C23—592no—
732C23—1188no—
733C23—1188no—
734C23—11832no—
735C23—1182no—
736C23—1182no—
737C23—1182no—
738C23—1182no—
739C23—1188no—
740C23—1182no—
741C23—1182no—
742C23—1182no—
743C23#1427377414yescomplemented
744C23C24×D5916yes—
745C23C24×D5912yes—
746C23C24×D5911yescharacteristic
747Q8—224no—
748Q8—5948no—
749Q8—11848no—
750Q8—11824no—
751Q8—11824no—
752Q8—11824no—
753Q8C2×D4×D59116yes—
754D4—224no—
755D4—224no—
756D4—1188no—
757D4—1188no—
758D4—11824no—
759D4—11824no—
760D4—11824no—
761D4—1188no—
762C2×C4—22no—
763C2×C4—26no—
764C2×C4—22no—
765C2×C4—26no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—5912no—
769C2×C4—596no—
770C2×C4—5948no—
771C2×C4—596no—
772C2×C4—592no—
773C2×C4—596no—
774C2×C4—596no—
775C2×C4—11824no—
776C2×C4—11824no—
777C2×C4—11824no—
778C2×C4—11848no—
779C2×C4—1186no—
780C2×C4—1186no—
781C2×C4—1186no—
782C2×C4—1182no—
783C2×C4—11824no—
784C2×C4—11824no—
785C2×C4C2×D4×D59112yes—
786C2×C4C24×D5916yes—
787C2×C4C24×D5912yes—
788C2×C4C24×D5916yes—
789C2×C4C24×D5912yes—
790C2×C4C24×D5916yes—
791C22—28no—
792C22—22no—
793C22—22no—
794C22—26no—
795C22—26no—
796C22—26no—
797C22—412no—
798C22—594no—
799C22—594no—
800C22—11832no—
801C22—1188no—
802C22—1188no—
803C22—1182no—
804C22—1182no—
805C22—1182no—
806C22—1182no—
807C22—1182no—
808C22—1182no—
809C22—1182no—
810C22—2364no—
811C22C22×D4×D5912yes—
812C222−1+4×D5912yes—
813C22C2×#1427377412yes—
814C22C2×#1427377414yescomplemented
815C22C25×D5911yescharacteristic
816C4—22no—
817C4—26no—
818C4—22no—
819C4—26no—
820C4—5912no—
821C4—1186no—
822C4—1186no—
823C4—1186no—
824C4—1182no—
825C4C22×D4×D59112yes—
826C2—24no—
827C2—46no—
828C2—1184no—
829C2—1184no—
830C2—2362no—
831C2#2143774214yesdirect product factor
832C2C23×D4×D5911yescharacteristic
833C2C2×2−1+4×D5911yescharacteristic
834C2C22×#1427377411yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#548C2
socleC23×C59C25
hypercenterC2×#548D59
hypocenterC59C2×#3486
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14273774C2semidirect
2. C23×Q8×D59C2semidirect
3. #21437742C2direct (N × H)
4. C2×Q8×D236C2semidirect
5. C2×D4×Dic118C2semidirect
6. C2×Q8×C22⋊D59C2semidirect
7. C2×#16838065C2semidirect
8. C2×#16838060C2semidirect
9. C2×#16838059C2semidirect
10. C2×#16838058C2semidirect
11. C2×#16837975C2semidirect
12. C2×#16837972C2semidirect
13. C2×#16837912C2semidirect
14. C2×#16837911C2semidirect
15. C2×#16837878C2semidirect
16. C2×C59×#548C2semidirect
18. C2×#14273774C22semidirect
21. C22×#11745687C22semidirect
23. C23×Dic118C22semidirect
29. C22×Q8×D59C22semidirect
30. C22×Q8×D59C22semidirect
32. Q8×D236C22semidirect
33. D4×Dic118C22semidirect
34. Q8×C22⋊D59C22semidirect
35. #16838065C22semidirect
36. #16838060C22semidirect
37. #16838059C22semidirect
38. #16838058C22semidirect
39. #16837975C22semidirect
40. #16837972C22semidirect
41. C2×#14273727C22semidirect
42. C2×#14273726C22semidirect
43. C2×#14273725C22semidirect
44. C2×#14273714C22semidirect
45. C2×#14273713C22semidirect
46. #16837912C22semidirect
47. #16837911C22semidirect
52. C2×#14273707C22semidirect
54. C2×#14273706C22semidirect
57. C2×#14273704C22semidirect
58. C2×#14273704C22semidirect
59. C2×#14273703C22semidirect
65. #16837878C22semidirect
66. C2×Q8×Dic59C22semidirect
67. C2×C4×Dic118C22semidirect
68. C2×#14273692C22semidirect
76. C22×#41×C59C22semidirect
78. C59×#548C22semidirect
79. C2×#124×C59C22semidirect
80. C2×C22⋊Q8×C59C22semidirect
82. C2×C4×Q8×C59C22semidirect
91. C2×#11745687C23semidirect
100. C22×Dic118C23semidirect
106. C2×Q8×D59D4semidirect
111. C2×Q8×D59C23semidirect
127. #14273727C23semidirect
128. #14273726C23semidirect
129. #14273725C23semidirect
130. #14273714C23semidirect
131. #14273713C23semidirect
136. #14273707C23semidirect
138. #14273706C23semidirect
141. #14273704C23semidirect
142. #14273704C23semidirect
143. #14273703C23semidirect
149. Q8×Dic59C23semidirect
150. C4×Dic118C23semidirect
151. #14273692C23semidirect
179. C2×#41×C59C23semidirect
188. #124×C59C23semidirect
189. C22⋊Q8×C59C23semidirect
191. C4×Q8×C59C23semidirect
248. Q8×D59C2×D4semidirect
309. C23×C592−1+4semidirect
325. C22×D592−1+4semidirect
384. C22×C59C2×2−1+4semidirect
398. C2×D59C2×2−1+4semidirect
419. C2×#548D59semidirect
427. C2×C59#3486semidirect
439. C22×#41C2×D59semidirect
458. #548C2×D59semidirect
466. C2×#124C2×D59semidirect
481. C2×C22⋊Q8C2×D59semidirect
492. C2×C4×Q8C2×D59semidirect
501. C59C2×#3486semidirect
511. C2×#41C22×D59semidirect
560. #124C22×D59semidirect
573. C22⋊Q8C22×D59semidirect
583. C4×Q8C22×D59semidirect
743. C23#14273774semidirect
814. C22C2×#14273774semidirect
831. C2#21437742direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737742
C23×Q8×D592
#214377422
C2×Q8×D2362
C2×D4×Dic1182
C2×Q8×C22⋊D592
C2×#168380652
C2×#168380602
C2×#168380592
C2×#168380582
C2×#168379752
C2×#168379722
C2×#168379122
C2×#168379112
C2×#168378782
C2×C59×#5482
C2×#348659