Finite Group Databasebeta

← C2×#21437746 #29496853

Subgroups — C2×#21437746 #29496853

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×#14273775C211yesmaximal, characteristic, complemented
2C23×Q8×D59C211yesmaximal, characteristic, complemented
3#21437746C2132yesmaximal, direct product factor
4C2×#16838067C213yesmaximal, complemented
5C2×Q8×C22⋊D59C211yesmaximal, characteristic, complemented
6C2×#16838065C213yesmaximal, complemented
7C2×#16838064C211yesmaximal, characteristic, complemented
8C2×#16838063C211yesmaximal, characteristic, complemented
9C2×#16838062C213yesmaximal, complemented
10C2×#16838061C213yesmaximal, complemented
11C2×#16837977C213yesmaximal, complemented
12C2×#16837975C213yesmaximal, complemented
13C2×#16837915C213yesmaximal, complemented
14C2×#16837911C213yesmaximal, complemented
15C2×#16837878C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C59C211yesmaximal, characteristic, complemented
17C2×#14273775—216no—
18C2×#14273775C22116yescomplemented
19C22×#11745689C2213yes—
20C22×#11745689C2211yescharacteristic, complemented
21C22×#11745685C2213yes—
22C22×#11745685C2213yescomplemented
23C23×Dic118C2213yes—
24C22×Q8×D59—216no—
25C22×Q8×D59C2213yes—
26C22×Q8×D59C2211yescharacteristic
27C22×Q8×D59C2213yes—
28C22×Q8×D59C2211yescharacteristic
29C22×Q8×D59C22116yescomplemented
30C22×Q8×D59C2213yescomplemented
31C23×C4×D59C2213yes—
32#16838067C22148yescomplemented
33Q8×C22⋊D59C22116yescomplemented
34#16838065C22148yescomplemented
35#16838064C22116yescomplemented
36#16838063C22116yescomplemented
37#16838062C22148yescomplemented
38#16838061C22148yescomplemented
39#16837977C22148yescomplemented
40#16837975C22148yescomplemented
41C2×#14273726C2216yescomplemented
42C2×#14273725C2213yescomplemented
43C2×#14273716C2213yescomplemented
44C2×#14273715C2213yescomplemented
45C2×#14273713C2216yescomplemented
46#16837915C22148yescomplemented
47#16837911C22148yescomplemented
48C2×#14273712C2213yes—
49C2×#14273712C2216yes—
50C2×#14273709C2213yes—
51C2×#14273707C2213yescomplemented
52C2×#14273706C2213yescomplemented
53C2×#14273705C2213yes—
54C2×#14273705C2216yescomplemented
55C2×#14273705C2216yescomplemented
56C2×#14273704C2213yes—
57C2×#14273703C2213yes—
58C2×#14273703C2213yescomplemented
59C2×#14273702C2213yes—
60C2×#14273701C2213yes—
61C2×#14273700C2213yes—
62C2×#14273699C2213yes—
63C2×#14273697C2213yes—
64C2×#14273695C2211yescharacteristic
65#16837878C22116yescomplemented
66C2×Q8×Dic59C2211yescharacteristic, complemented
67C2×C4×Dic118C2213yescomplemented
68C2×#14273692C2213yescomplemented
69C2×C4×D236C2213yes—
70C2×#14273689C2216yes—
71C2×C4×C22⋊D59C2213yes—
72C2×C4×C22⋊D59C2213yes—
73C2×(C22⋊D59)⋊C4C2216yes—
74C2×#14273685C2213yes—
75C2×#14273684C2213yes—
76C23×Q8×C59C2211yescharacteristic
77C23×Q8×C59C2211yescharacteristic, complemented
78D4×Q8×C59C22116yescomplemented
79C2×C4⋊Q8×C59C2213yescomplemented
80C2×C22⋊Q8×C59C2213yes—
81C2×C22⋊Q8×C59C2213yescomplemented
82C2×C4×Q8×C59C2211yescharacteristic, complemented
83C2×C4×D4×C59C2213yes—
84C24×D59C2311yescharacteristic
85#14273775—2128no—
86C2×#11745689—28no—
87C2×#11745689—224no—
88C2×#11745689C23124yes—
89C2×#11745689C2318yescomplemented
90C2×#11745685—224no—
91C2×#11745685—224no—
92C2×#11745685C23124yes—
93C2×#11745685C23124yescomplemented
94C22×Dic118—224no—
95C22×Dic118C2313yes—
96C22×Dic118C2316yes—
97C22×Dic118C2313yes—
98C22×Dic118C23124yes—
99C22×Dic118C2313yes—
100C2×Q8×D59—28no—
101C2×Q8×D59—2128no—
102C2×Q8×D59—224no—
103C2×Q8×D59—224no—
104C2×Q8×D59—224no—
105C2×Q8×D59D4116yescomplemented
106C2×Q8×D59C23124yes—
107C2×Q8×D59C23124yes—
108C2×Q8×D59C2318yes—
109C2×Q8×D59C2318yes—
110C2×Q8×D59C23124yescomplemented
111C22×D236C2313yes—
112C22×D236C2313yes—
113C22×D236C2313yes—
114C22×C22⋊D59C2313yes—
115C22×C22⋊D59C2313yes—
116C22×C22⋊D59C2311yescharacteristic
117C22×C22⋊D59C2311yescharacteristic
118C23×Dic59C2313yes—
119C22×C4×D59—224no—
120C22×C4×D59C2313yes—
121C22×C4×D59C2313yes—
122C22×C4×D59C2313yes—
123C22×C4×D59C2316yes—
124C22×C4×D59C2313yes—
125C22×C4×D59C23124yes—
126C22×C4×D59C2313yes—
127#14273726C23148yescomplemented
128#14273725C23124yescomplemented
129#14273716C23124yescomplemented
130#14273715C23124yescomplemented
131#14273713C23148yescomplemented
132#14273712C23124yes—
133#14273712C23148yes—
134#14273709C23124yes—
135#14273707C23124yescomplemented
136#14273706C23124yescomplemented
137#14273705C23124yes—
138#14273705C23148yescomplemented
139#14273705C23148yescomplemented
140#14273704C23124yes—
141#14273703C23124yes—
142#14273703C23124yescomplemented
143#14273702C23124yes—
144#14273701C23124yes—
145#14273700C23124yes—
146#14273699C23124yes—
147#14273697C23124yes—
148#14273695C2318yes—
149Q8×Dic59C2318yescomplemented
150C4×Dic118C23124yescomplemented
151#14273692C23124yescomplemented
152C4×D236C23124yes—
153#14273689C23148yes—
154C4×C22⋊D59C23124yes—
155C4×C22⋊D59C23124yes—
156(C22⋊D59)⋊C4C23148yes—
157#14273685C23124yes—
158#14273684C23124yes—
159C2×C4⋊Dic59C2313yes—
160C2×C4⋊Dic59C2313yes—
161C2×Dic59⋊C4C2313yes—
162C2×Dic59⋊C4C2313yes—
163C2×Dic59⋊C4C2316yes—
164C2×Dic59⋊C4C2313yes—
165C2×Dic59⋊C4C2313yes—
166C2×C22⋊Dic59C2313yes—
167C2×C22⋊Dic59C2311yescharacteristic
168C2×(C2×D59)⋊C4C2313yes—
169C2×(C2×D59)⋊C4C2313yes—
170C2×(C2×D59)⋊C4C2313yes—
171C2×(C2×D59)⋊C4C2313yes—
172C2×(C2×D59)⋊C4C2316yes—
173C2×(C2×D59)⋊C4C2316yes—
174C2×(C2×D59)⋊C4C2311yescharacteristic
175C2×(C2×D59)⋊C4C2311yescharacteristic
176C2×C4×Dic59C2316yes—
177C2×C4×Dic59C2313yes—
178C22×Q8×C59—28no—
179C22×Q8×C59—28no—
180C22×Q8×C59C2313yes—
181C22×Q8×C59C2313yes—
182C22×Q8×C59C2318yes—
183C22×Q8×C59C2311yescharacteristic
184C22×Q8×C59C2318yescomplemented
185C22×D4×C59C2311yescharacteristic
186C23×C4×C59C2313yes—
187C23×C4×C59C2313yes—
188C4⋊Q8×C59C23124yescomplemented
189C22⋊Q8×C59C23124yes—
190C22⋊Q8×C59C23124yescomplemented
191C4×Q8×C59C2318yescomplemented
192C4×D4×C59C23124yes—
193C2×C4⋊C4×C59C2313yes—
194C2×C4⋊C4×C59C2313yes—
195C2×C4⋊C4×C59C2316yes—
196C2×C22⋊C4×C59C2313yes—
197C2×C22⋊C4×C59C2313yes—
198C2×C42×C59C2313yes—
199C24×C59C2411yescharacteristic
200C24×C59C2411yescharacteristic
201C23×D59—24no—
202C23×D59—24no—
203C23×D59—24no—
204C23×D59C2413yes—
205C23×D59C2414yes—
206C23×D59C2411yescharacteristic
207C23×D59C2411yescharacteristic
208C2×Q8×C59—232no—
209C2×Q8×C59—232no—
210C2×Q8×C59—212no—
211C2×Q8×C59—212no—
212C2×Q8×C59C2×D418yes—
213C2×Q8×C59C24112yes—
214C2×Q8×C59C24112yes—
215C2×Q8×C59C2414yes—
216C2×D4×C59—24no—
217C2×D4×C59C2414yes—
218C22×C4×C59—212no—
219C22×C4×C59—212no—
220C22×C4×C59C2411yescharacteristic
221C22×C4×C59C2413yes—
222C22×C4×C59C2413yes—
223C22×C4×C59C2413yes—
224C22×C4×C59C24112yes—
225C22×C4×C59C24112yes—
226C22×C4×C59C2413yes—
227C2×C22⋊D59—212no—
228C2×C22⋊D59—24no—
229C2×C22⋊D59—24no—
230C2×C22⋊D59—212no—
231C2×C22⋊D59C24112yes—
232C2×C22⋊D59C2414yes—
233C2×C22⋊D59C2414yes—
234C2×C22⋊D59C24112yes—
235C22×Dic59—212no—
236C22×Dic59C2411yescharacteristic
237C22×Dic59C2413yes—
238C22×Dic59C2413yes—
239C22×Dic59C2411yescharacteristic
240C22×Dic59C24112yes—
241C22×Dic59C2413yes—
242#11745689—232no—
243#11745689—296no—
244Q8×D59—232no—
245Q8×D59—296no—
246Q8×D59—296no—
247Q8×D59—296no—
248Q8×D59C2×D4164yescomplemented
249#11745685—296no—
250#11745685—296no—
251C2×D236—212no—
252C2×D236—212no—
253C2×D236—212no—
254C2×D236C24112yes—
255C2×D236C24112yes—
256C2×D236C24112yes—
257C2×C4×D59—212no—
258C2×C4×D59—212no—
259C2×C4×D59—212no—
260C2×C4×D59—212no—
261C2×C4×D59—224no—
262C2×C4×D59—296no—
263C2×C4×D59C2×D4124yes—
264C2×C4×D59C24124yes—
265C2×C4×D59C24112yes—
266C2×C4×D59C24112yes—
267C2×C4×D59C24112yes—
268C2×C4×D59C24112yes—
269C2×C4×D59C24112yes—
270C2×Dic118—212no—
271C2×Dic118—224no—
272C2×Dic118—212no—
273C2×Dic118—296no—
274C2×Dic118C2×D4124yes—
275C2×Dic118C24112yes—
276C2×Dic118C24124yes—
277C2×Dic118C24112yes—
278C2×Dic118C24112yes—
279C4⋊C4×C59C24112yes—
280C4⋊C4×C59C24112yes—
281C4⋊C4×C59C24124yes—
282C22⋊C4×C59C24112yes—
283C22⋊C4×C59C24112yes—
284C42×C59C24112yes—
285C22⋊Dic59C2414yes—
286C22⋊Dic59C24112yes—
287(C2×D59)⋊C4C2414yes—
288(C2×D59)⋊C4C24112yes—
289(C2×D59)⋊C4C24124yes—
290(C2×D59)⋊C4C24112yes—
291(C2×D59)⋊C4C24112yes—
292(C2×D59)⋊C4C24124yes—
293(C2×D59)⋊C4C2414yes—
294(C2×D59)⋊C4C24112yes—
295C4⋊Dic59C24112yes—
296C4⋊Dic59C24112yes—
297Dic59⋊C4C24112yes—
298Dic59⋊C4C24112yes—
299Dic59⋊C4C24124yes—
300Dic59⋊C4C24112yes—
301Dic59⋊C4C24112yes—
302C4×Dic59C24112yes—
303C4×Dic59C24124yes—
304C23×C59—22no—
305C23×C59—22no—
306C23×C59—22no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C592−1+414yescomplemented
310C23×C59C2512yes—
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—26no—
322C22×D59—26no—
323C22×D59—26no—
324C22×D59C22×D414yes—
325C22×D592−1+414yescomplemented
326C22×D59C2516yes—
327C22×D59C2512yes—
328C22×D59C2512yes—
329Q8×C59—224no—
330Q8×C59—224no—
331Q8×C59C22×D4116yes—
332D4×C59—28no—
333C2×C4×C59—26no—
334C2×C4×C59—26no—
335C2×C4×C59—26no—
336C2×C4×C59—22no—
337C2×C4×C59—224no—
338C2×C4×C59—224no—
339C2×C4×C59C22×D4112yes—
340C2×C4×C59C2516yes—
341C2×C4×C59C2512yes—
342C2×C4×C59C2516yes—
343C2×C4×C59C2516yes—
344C2×C4×C59C2516yes—
345C22⋊D59—224no—
346C22⋊D59—28no—
347C22⋊D59—28no—
348C22⋊D59—224no—
349C2×Dic59—26no—
350C2×Dic59—22no—
351C2×Dic59—22no—
352C2×Dic59—26no—
353C2×Dic59—224no—
354C2×Dic59C22×D4112yes—
355C2×Dic59C2512yes—
356C2×Dic59C2516yes—
357C2×Dic59C2512yes—
358C2×Dic59C2516yes—
359C2×Dic59C2516yes—
360D236—224no—
361D236—224no—
362D236—224no—
363C4×D59—224no—
364C4×D59—224no—
365C4×D59—224no—
366C4×D59—224no—
367C4×D59—248no—
368C4×D59C22×D4148yes—
369Dic118—224no—
370Dic118—248no—
371Dic118—224no—
372Dic118C22×D4148yes—
373C2×#3486—591nomaximal, Sylow
374C22×C59—22no—
375C22×C59—22no—
376C22×C59—28no—
377C22×C59—22no—
378C22×C59—22no—
379C22×C59—22no—
380C22×C59—44no—
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—26no—
394C2×D59—26no—
395C2×D59—26no—
396C2×D59—412no—
397C2×D59C23×D414yes—
398C2×D59C2×2−1+414yescomplemented
399C4×C59—26no—
400C4×C59—26no—
401C4×C59—26no—
402C4×C59—22no—
403C4×C59C23×D4112yes—
404Dic59—26no—
405Dic59—22no—
406Dic59—22no—
407Dic59—26no—
408Dic59C23×D4112yes—
409C22×2−1+4—591no—
410C24×Q8—591no—
411#3486—5932no—
412C2×D4×Q8—591no—
413C2×D4×Q8—593no—
414C2×D4×Q8—593no—
415C2×D4×Q8D5911yescharacteristic, complemented
416C2×#548—591no—
417C2×#548—593no—
418C2×#548—591no—
419C2×#548—593no—
420C2×#536—593no—
421C2×#536—593no—
422C2×#525—593no—
423C2×#525—593no—
424C2×#519—591no—
425C2×C59—24no—
426C2×C59—42no—
427C2×C59#348614yescomplemented
428C2×C59C24×D411yescharacteristic
429C2×C59C22×2−1+411yescharacteristic
430C2×C59C22×2−1+411yescharacteristic
431D59—24no—
432D59—24no—
433D59—46no—
434C2×2−1+4—5916no—
435C2×2−1+4—11816no—
436C22×#41—593no—
437C22×#41—591no—
438C22×#41—593no—
439C22×#41—593no—
440C23×Q8—591no—
441C23×Q8—593no—
442C23×Q8—593no—
443C23×Q8—591no—
444C23×Q8—5916no—
445C23×Q8—593no—
446C23×Q8—593no—
447C23×Q8—11816no—
448C23×Q8C2×D5911yescharacteristic
449C23×Q8C2×D5911yescharacteristic, complemented
450C24×C4—593no—
451D4×Q8—5916no—
452D4×Q8—5948no—
453D4×Q8—5948no—
454D4×Q8C2×D59116yescomplemented
455#548—5916no—
456#548—5948no—
457#548—5916no—
458#548—5948no—
459#536—5948no—
460#536—5948no—
461C2×C4⋊Q8—593no—
462C2×C4⋊Q8—596no—
463C2×C4⋊Q8C2×D5913yescomplemented
464C2×#124—593no—
465C2×#124—596no—
466C2×#124—593no—
467#525—5948no—
468#525—5948no—
469C2×#123—596no—
470C2×#123—593no—
471C2×#123—593no—
472C2×C22⋊Q8—593no—
473C2×C22⋊Q8—593no—
474C2×C22⋊Q8—593no—
475C2×C22⋊Q8—593no—
476C2×C22⋊Q8—596no—
477C2×C22⋊Q8—596no—
478C2×C22⋊Q8—593no—
479C2×C22⋊Q8—593no—
480C2×C22⋊Q8C2×D5913yes—
481C2×C22⋊Q8C2×D5913yescomplemented
482C2×#121—593no—
483C2×#121—593no—
484C2×#121—593no—
485C2×#121—593no—
486C2×#120—591no—
487C2×#120—593no—
488#519—5916no—
489C2×C4×Q8—591no—
490C2×C4×Q8—593no—
491C2×C4×Q8—593no—
492C2×C4×Q8C2×D5911yescharacteristic, complemented
493C2×C4×D4—593no—
494C2×C4×D4—593no—
495C2×C4×D4—596no—
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—5924no—
505C2×#41—598no—
506C2×#41—5924no—
507C2×#41—5924no—
508C2×#41—11824no—
509C2×#41—11824no—
510C2×#41—11824no—
511C2×#41—1188no—
512C22×Q8—28no—
513C22×Q8—28no—
514C22×Q8—5916no—
515C22×Q8—598no—
516C22×Q8—5924no—
517C22×Q8—5924no—
518C22×Q8—598no—
519C22×Q8—5924no—
520C22×Q8—593no—
521C22×Q8—596no—
522C22×Q8—593no—
523C22×Q8—593no—
524C22×Q8—5924no—
525C22×Q8—11824no—
526C22×Q8—11824no—
527C22×Q8—118128no—
528C22×Q8—11824no—
529C22×Q8—11824no—
530C22×Q8—1188no—
531C22×Q8C22×D5913yes—
532C22×Q8C22×D5913yes—
533C22×Q8C22×D5918yes—
534C22×Q8C22×D5911yescharacteristic
535C22×Q8C22×D5918yescomplemented
536C22×D4—591no—
537C22×D4—593no—
538C22×D4—591no—
539C22×D4—593no—
540C22×D4—593no—
541C22×D4—593no—
542C22×D4—593no—
543C22×D4C22×D5911yescharacteristic
544C23×C4—593no—
545C23×C4—593no—
546C23×C4—593no—
547C23×C4—593no—
548C23×C4—596no—
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⋊Q8C22×D59124yescomplemented
558#124—5924no—
559#124—5948no—
560#124—5924no—
561#123—5948no—
562#123—5924no—
563#123—5924no—
564C22⋊Q8—5924no—
565C22⋊Q8—5924no—
566C22⋊Q8—5924no—
567C22⋊Q8—5924no—
568C22⋊Q8—5948no—
569C22⋊Q8—5948no—
570C22⋊Q8—5924no—
571C22⋊Q8—5924no—
572C22⋊Q8C22×D59124yes—
573C22⋊Q8C22×D59124yescomplemented
574#121—5924no—
575#121—5924no—
576#121—5924no—
577#121—5924no—
578#120—598no—
579#120—5924no—
580C4×Q8—598no—
581C4×Q8—5924no—
582C4×Q8—5924no—
583C4×Q8C22×D5918yescomplemented
584C4×D4—5924no—
585C4×D4—5924no—
586C4×D4—5948no—
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—596no—
597C2×C4⋊C4—593no—
598C2×C4⋊C4—593no—
599C2×C4⋊C4C22×D5913yes—
600C2×C4⋊C4C22×D5916yes—
601C2×C4⋊C4C22×D5913yes—
602C2×C22⋊C4—591no—
603C2×C22⋊C4—593no—
604C2×C22⋊C4—593no—
605C2×C22⋊C4—591no—
606C2×C22⋊C4—593no—
607C2×C22⋊C4—591no—
608C2×C22⋊C4—593no—
609C2×C22⋊C4—596no—
610C2×C22⋊C4—596no—
611C2×C22⋊C4—593no—
612C2×C22⋊C4C22×D5913yes—
613C2×C22⋊C4C22×D5913yes—
614C2×C42—596no—
615C2×C42—593no—
616C2×C42C22×D5913yes—
617C24—591no—
618C24—591no—
619C24—594no—
620C24—593no—
621C24—1184no—
622C24—1184no—
623C24—1184no—
624C24C23×D5911yescharacteristic
625C24C23×D5911yescharacteristic
626#41—11896no—
627#41—11896no—
628#41—11896no—
629#41—11832no—
630C2×Q8—232no—
631C2×Q8—232no—
632C2×Q8—212no—
633C2×Q8—212no—
634C2×Q8—5964no—
635C2×Q8—5924no—
636C2×Q8—5912no—
637C2×Q8—5924no—
638C2×Q8—5912no—
639C2×Q8—5912no—
640C2×Q8—11824no—
641C2×Q8—11812no—
642C2×Q8—11896no—
643C2×Q8—11896no—
644C2×Q8—11896no—
645C2×Q8—11896no—
646C2×Q8—11832no—
647C2×Q8—11812no—
648C2×Q8D4×D5918yes—
649C2×Q8C23×D59112yes—
650C2×Q8C23×D59112yes—
651C2×Q8C23×D5914yes—
652C2×D4—24no—
653C2×D4—594no—
654C2×D4—5912no—
655C2×D4—594no—
656C2×D4—5912no—
657C2×D4—5912no—
658C2×D4—5912no—
659C2×D4—5912no—
660C2×D4—11812no—
661C2×D4—11812no—
662C2×D4—11812no—
663C2×D4—1184no—
664C2×D4—1184no—
665C2×D4—11812no—
666C2×D4—11812no—
667C2×D4C23×D5914yes—
668C22×C4—212no—
669C22×C4—212no—
670C22×C4—593no—
671C22×C4—5924no—
672C22×C4—5912no—
673C22×C4—5912no—
674C22×C4—591no—
675C22×C4—593no—
676C22×C4—593no—
677C22×C4—591no—
678C22×C4—5912no—
679C22×C4—5912no—
680C22×C4—5924no—
681C22×C4—5912no—
682C22×C4—5912no—
683C22×C4—11812no—
684C22×C4—11896no—
685C22×C4—11824no—
686C22×C4—11812no—
687C22×C4—11812no—
688C22×C4—11812no—
689C22×C4—11812no—
690C22×C4C23×D59112yes—
691C22×C4C23×D59112yes—
692C22×C4C23×D5913yes—
693C22×C4C23×D5911yescharacteristic
694C22×C4C23×D5913yes—
695C22×C4C23×D5913yes—
696C22×C4C23×D5913yes—
697C4⋊C4—5912no—
698C4⋊C4—5912no—
699C4⋊C4—5912no—
700C4⋊C4—5912no—
701C4⋊C4—5924no—
702C4⋊C4—5912no—
703C4⋊C4—5912no—
704C4⋊C4C23×D59112yes—
705C4⋊C4C23×D59124yes—
706C4⋊C4C23×D59112yes—
707C22⋊C4—594no—
708C22⋊C4—5912no—
709C22⋊C4—5912no—
710C22⋊C4—594no—
711C22⋊C4—5912no—
712C22⋊C4—594no—
713C22⋊C4—5912no—
714C22⋊C4—5924no—
715C22⋊C4—5924no—
716C22⋊C4—5912no—
717C22⋊C4C23×D59112yes—
718C22⋊C4C23×D59112yes—
719C42—5924no—
720C42—5912no—
721C42C23×D59112yes—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—594no—
728C23—594no—
729C23—592no—
730C23—592no—
731C23—596no—
732C23—1188no—
733C23—1188no—
734C23—11832no—
735C23—1182no—
736C23—1182no—
737C23—1182no—
738C23—1182no—
739C23—1188no—
740C23—1186no—
741C23—1186no—
742C23—1186no—
743C23#1427377514yescomplemented
744C23C24×D5912yes—
745C23C24×D5912yes—
746C23C24×D5911yescharacteristic
747Q8—224no—
748Q8—224no—
749Q8—5948no—
750Q8—11848no—
751Q8—11824no—
752Q8—11824no—
753Q8C2×D4×D59116yes—
754D4—28no—
755D4—11824no—
756D4—11824no—
757D4—11824no—
758D4—1188no—
759D4—1188no—
760D4—11824no—
761D4—11824no—
762C2×C4—26no—
763C2×C4—26no—
764C2×C4—26no—
765C2×C4—22no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—5912no—
769C2×C4—596no—
770C2×C4—5948no—
771C2×C4—592no—
772C2×C4—596no—
773C2×C4—596no—
774C2×C4—592no—
775C2×C4—11824no—
776C2×C4—11848no—
777C2×C4—11824no—
778C2×C4—11824no—
779C2×C4—1182no—
780C2×C4—1186no—
781C2×C4—1182no—
782C2×C4—1186no—
783C2×C4—11824no—
784C2×C4—11824no—
785C2×C4C2×D4×D59112yes—
786C2×C4C24×D5916yes—
787C2×C4C24×D5912yes—
788C2×C4C24×D5916yes—
789C2×C4C24×D5916yes—
790C2×C4C24×D5916yes—
791C22—28no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—594no—
799C22—594no—
800C22—11832no—
801C22—1188no—
802C22—1188no—
803C22—1182no—
804C22—1182no—
805C22—1182no—
806C22—1182no—
807C22—1186no—
808C22—1186no—
809C22—1186no—
810C22—23612no—
811C22C22×D4×D5912yes—
812C222−1+4×D5912yes—
813C22C2×#1427377512yes—
814C22C2×#1427377514yescomplemented
815C22C25×D5911yescharacteristic
816C4—26no—
817C4—26no—
818C4—26no—
819C4—22no—
820C4—5912no—
821C4—1182no—
822C4—1186no—
823C4—1182no—
824C4—1186no—
825C4C22×D4×D59112yes—
826C2—24no—
827C2—42no—
828C2—1184no—
829C2—1184no—
830C2—2366no—
831C2#2143774614yesdirect product factor
832C2C23×D4×D5911yescharacteristic
833C2C2×2−1+4×D5911yescharacteristic
834C2C22×#1427377511yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×D4×Q8×C59C2
socleC23×C59C25
hypercenterC2×D4×Q8D59
hypocenterC59C2×#3486
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14273775C2semidirect
2. C23×Q8×D59C2semidirect
3. #21437746C2direct (N × H)
4. C2×#16838067C2semidirect
5. C2×Q8×C22⋊D59C2semidirect
6. C2×#16838065C2semidirect
7. C2×#16838064C2semidirect
8. C2×#16838063C2semidirect
9. C2×#16838062C2semidirect
10. C2×#16838061C2semidirect
11. C2×#16837977C2semidirect
12. C2×#16837975C2semidirect
13. C2×#16837915C2semidirect
14. C2×#16837911C2semidirect
15. C2×#16837878C2semidirect
16. C2×D4×Q8×C59C2semidirect
18. C2×#14273775C22semidirect
20. C22×#11745689C22semidirect
22. C22×#11745685C22semidirect
29. C22×Q8×D59C22semidirect
30. C22×Q8×D59C22semidirect
32. #16838067C22semidirect
33. Q8×C22⋊D59C22semidirect
34. #16838065C22semidirect
35. #16838064C22semidirect
36. #16838063C22semidirect
37. #16838062C22semidirect
38. #16838061C22semidirect
39. #16837977C22semidirect
40. #16837975C22semidirect
41. C2×#14273726C22semidirect
42. C2×#14273725C22semidirect
43. C2×#14273716C22semidirect
44. C2×#14273715C22semidirect
45. C2×#14273713C22semidirect
46. #16837915C22semidirect
47. #16837911C22semidirect
51. C2×#14273707C22semidirect
52. C2×#14273706C22semidirect
54. C2×#14273705C22semidirect
55. C2×#14273705C22semidirect
58. C2×#14273703C22semidirect
65. #16837878C22semidirect
66. C2×Q8×Dic59C22semidirect
67. C2×C4×Dic118C22semidirect
68. C2×#14273692C22semidirect
77. C23×Q8×C59C22semidirect
78. D4×Q8×C59C22semidirect
79. C2×C4⋊Q8×C59C22semidirect
81. C2×C22⋊Q8×C59C22semidirect
82. C2×C4×Q8×C59C22semidirect
89. C2×#11745689C23semidirect
93. C2×#11745685C23semidirect
105. C2×Q8×D59D4semidirect
110. C2×Q8×D59C23semidirect
127. #14273726C23semidirect
128. #14273725C23semidirect
129. #14273716C23semidirect
130. #14273715C23semidirect
131. #14273713C23semidirect
135. #14273707C23semidirect
136. #14273706C23semidirect
138. #14273705C23semidirect
139. #14273705C23semidirect
142. #14273703C23semidirect
149. Q8×Dic59C23semidirect
150. C4×Dic118C23semidirect
151. #14273692C23semidirect
184. C22×Q8×C59C23semidirect
188. C4⋊Q8×C59C23semidirect
190. 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
415. C2×D4×Q8D59semidirect
427. C2×C59#3486semidirect
449. C23×Q8C2×D59semidirect
454. D4×Q8C2×D59semidirect
463. C2×C4⋊Q8C2×D59semidirect
481. C2×C22⋊Q8C2×D59semidirect
492. C2×C4×Q8C2×D59semidirect
501. C59C2×#3486semidirect
535. C22×Q8C22×D59semidirect
557. C4⋊Q8C22×D59semidirect
573. C22⋊Q8C22×D59semidirect
583. C4×Q8C22×D59semidirect
743. C23#14273775semidirect
814. C22C2×#14273775semidirect
831. C2#21437746direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737752
C23×Q8×D592
#214377462
C2×#168380672
C2×Q8×C22⋊D592
C2×#168380652
C2×#168380642
C2×#168380632
C2×#168380622
C2×#168380612
C2×#168379772
C2×#168379752
C2×#168379152
C2×#168379112
C2×#168378782
C2×D4×Q8×C592
C2×#348659