Finite Group Databasebeta

← C4×Q8×C22⋊D59 #28748551

Subgroups — C4×Q8×C22⋊D59 #28748551

Order 15104.

3148 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D59C211yesmaximal, characteristic
2C2×C4×Q8×D59C211yesmaximal, characteristic, complemented
3#21427150C213yesmaximal, complemented
4#21427101C213yesmaximal, complemented
5#21427097C213yesmaximal, complemented
6Q8×Dic59⋊C4C211yesmaximal, characteristic, complemented
7C4⋊C4×C22⋊D59C213yesmaximal
8Q8×C22⋊Dic59C211yesmaximal, characteristic, complemented
9Q8×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
10C4×#14273725C213yesmaximal, complemented
11C4×#14273706C213yesmaximal, complemented
12C4×#14273703C213yesmaximal, complemented
13C4×Q8×Dic59C211yesmaximal, characteristic, complemented
14C42×C22⋊D59C213yesmaximal
15C22×C4×Q8×C59C211yesmaximal, characteristic, complemented
16C22×Q8×D59C2211yescharacteristic
17Q8×C22⋊D59C4116yesdirect product factor
18C2×#14273725C2213yes—
19C2×#14273706C2213yes—
20C2×#14273703C2213yes—
21C2×Q8×Dic59C2211yescharacteristic
22C2×Q8×Dic59C2211yescharacteristic
23C2×Q8×Dic59C2211yescharacteristic
24C2×C4×Dic118C2213yes—
25C2×#14273692C2213yes—
26C4×Q8×D59—28no—
27C2×C4×C22⋊D59C2213yes—
28C2×C4×C22⋊D59C2213yes—
29C2×C4×C22⋊D59C2211yescharacteristic
30C2×C4⋊C4×D59C2213yes—
31C2×C42×D59C2213yes—
32#16837309C2213yes—
33#16837309C2213yes—
34#16837308C2213yes—
35#16837307C2213yes—
36#16837300C2213yes—
37#16837298C2213yes—
38#16837297C2216yes—
39#16837297C2216yes—
40#16837286C2216yes—
41#16837283C2216yes—
42#16837275C2216yes—
43#16837273C2216yes—
44#16837271C2213yes—
45#16837262C2213yes—
46#16837259C2213yes—
47C4⋊C4×Dic59C2213yes—
48C4⋊C4×Dic59C2213yes—
49C4×Dic59⋊C4C2213yes—
50C4×Dic59⋊C4C2213yes—
51C4×Dic59⋊C4C2213yes—
52C4×Dic59⋊C4C2216yes—
53C4×C4⋊Dic59C2213yes—
54C4×(C2×D59)⋊C4C2213yes—
55C4×(C2×D59)⋊C4C2213yes—
56C4×(C2×D59)⋊C4C2213yes—
57C4×C22⋊Dic59C2213yes—
58C4×C22⋊Dic59C2213yes—
59C4×C22⋊Dic59C2213yes—
60C42×Dic59C2213yes—
61C23×Q8×C59C2211yescharacteristic
62C2×C4×Q8×C59—28no—
63C2×C4×Q8×C59C2211yescharacteristic
64C2×C4×Q8×C59C2213yes—
65C2×C4×Q8×C59C2213yes—
66C2×C4×Q8×C59C2211yescharacteristic
67C22×C4⋊C4×C59C2213yes—
68C22×C42×C59C2213yes—
69C22×Dic118C2313yes—
70C2×Q8×D59—24no—
71C2×Q8×D59—24no—
72C2×Q8×D59C2×C418yescomplemented
73C22×C22⋊D59C2311yescharacteristic
74C22×C4×D59C2313yes—
75C22×C4×D59C2313yes—
76C22×C4×D59C2311yescharacteristic
77#14273725C2×C4124yescomplemented
78#14273706C2×C4124yescomplemented
79#14273703C2×C4124yescomplemented
80Q8×Dic59—24no—
81Q8×Dic59—24no—
82Q8×Dic59C2×C418yescomplemented
83C4×Dic118—212no—
84#14273692—212no—
85C4×C22⋊D59—212no—
86C4×C22⋊D59C2×C4124yes—
87C4×C22⋊D59Q818yesdirect product factor
88C2×C4⋊Dic59C2313yes—
89C2×C4⋊Dic59C2313yes—
90C2×C4⋊Dic59C2313yes—
91C2×Dic59⋊C4C2313yes—
92C2×Dic59⋊C4C2316yes—
93C2×Dic59⋊C4C2316yes—
94C2×Dic59⋊C4C2316yes—
95C2×Dic59⋊C4C2313yes—
96C2×Dic59⋊C4C2311yescharacteristic
97C4⋊C4×D59—212no—
98C2×C22⋊Dic59C2313yes—
99C2×C22⋊Dic59C2313yes—
100C2×C22⋊Dic59C2311yescharacteristic
101C2×(C2×D59)⋊C4C2313yes—
102C2×(C2×D59)⋊C4C2313yes—
103C2×(C2×D59)⋊C4C2311yescharacteristic
104C2×C4×Dic59C2313yes—
105C2×C4×Dic59C2313yes—
106C2×C4×Dic59C2313yes—
107C2×C4×Dic59C2313yes—
108C2×C4×Dic59C2313yes—
109C2×C4×Dic59C2313yes—
110C2×C4×Dic59C2313yes—
111C2×C4×Dic59C2313yes—
112C2×C4×Dic59C2311yescharacteristic
113C42×D59—212no—
114C59⋊#95C2313yes—
115C59⋊#95C2313yes—
116C59⋊#95C2313yes—
117C59⋊#95C2313yes—
118C59⋊#95C2313yes—
119C59⋊#95C2313yes—
120C59⋊#95C2316yes—
121C59⋊#95C2316yes—
122C59⋊#95C2316yes—
123C22×Q8×C59—24no—
124C22×Q8×C59—24no—
125C22×Q8×C59C2×C418yescomplemented
126C22×Q8×C59C2313yes—
127C22×Q8×C59C2311yescharacteristic
128C23×C4×C59C2313yes—
129C23×C4×C59C2313yes—
130C23×C4×C59C2311yescharacteristic
131C4×Q8×C59—24no—
132C4×Q8×C59—212no—
133C4×Q8×C59—212no—
134C4×Q8×C59D418yescomplemented
135C2×C4⋊C4×C59—212no—
136C2×C4⋊C4×C59C2313yes—
137C2×C4⋊C4×C59C2316yes—
138C2×C4⋊C4×C59C2313yes—
139C2×C42×C59—212no—
140C2×C42×C59C2313yes—
141C2×C42×C59C2313yes—
142C2×C42×C59C2313yes—
143C2×C42×C59C2313yes—
144C24×C59C2411yescharacteristic
145C23×D59C2411yescharacteristic
146C2×Q8×C59—232no—
147C2×Q8×C59—26no—
148C2×Q8×C59—26no—
149C2×Q8×C59C22×C4112yes—
150C2×Q8×C59C22×C414yes—
151C2×Q8×C59C2×D414yes—
152C2×Q8×C59#4114yes—
153C22×C4×C59—22no—
154C22×C4×C59—26no—
155C22×C4×C59—26no—
156C22×C4×C59—22no—
157C22×C4×C59—26no—
158C22×C4×C59—26no—
159C22×C4×C59—43no—
160C22×C4×C59C22×C4112yes—
161C22×C4×C59C2×Q814yescomplemented
162C22×C4×C59C2413yes—
163C22×C4×C59C2413yes—
164C22×C4×C59C2413yes—
165C22×C4×C59C2411yescharacteristic
166C22×C4×C59C2413yes—
167C22×C4×C59C2411yescharacteristic
168C2×C22⋊D59C22×C414yes—
169C2×C22⋊D59C2×Q814yes—
170C2×C22⋊D59#4114yes—
171C22×Dic59C2413yes—
172C22×Dic59C2413yes—
173C22×Dic59C2413yes—
174C22×Dic59C2413yes—
175C22×Dic59C2411yescharacteristic
176C22×Dic59C2411yescharacteristic
177C22×Dic59C2411yescharacteristic
178Q8×D59—232no—
179C2×C4×D59—22no—
180C2×C4×D59—26no—
181C2×C4×D59—26no—
182C2×C4×D59—22no—
183C2×C4×D59—26no—
184C2×C4×D59—26no—
185C2×C4×D59—43no—
186C2×C4×D59C22×C4112yes—
187C2×C4×D59C2×Q814yescomplemented
188C2×Dic118—26no—
189C2×Dic118—26no—
190C2×Dic118C22×C4112yes—
191C4⋊C4×C59—212no—
192C4⋊C4×C59—26no—
193C4⋊C4×C59C2×D4112yes—
194C42×C59—26no—
195C42×C59—26no—
196C42×C59—26no—
197C42×C59C2×D4112yes—
198C22⋊Dic59—26no—
199C22⋊Dic59C22×C4112yes—
200C22⋊Dic59C2×Q814yescomplemented
201(C2×D59)⋊C4—26no—
202(C2×D59)⋊C4C22×C4112yes—
203(C2×D59)⋊C4C2×Q814yescomplemented
204C4⋊Dic59—26no—
205C4⋊Dic59—26no—
206C4⋊Dic59C22×C4112yes—
207Dic59⋊C4—212no—
208Dic59⋊C4—26no—
209Dic59⋊C4—46no—
210Dic59⋊C4C22×C4112yes—
211Dic59⋊C4C22×C4124yes—
212Dic59⋊C4C2×Q814yescomplemented
213C4×Dic59—26no—
214C4×Dic59—26no—
215C4×Dic59—26no—
216C4×Dic59—26no—
217C4×Dic59—26no—
218C4×Dic59—26no—
219C4×Dic59—43no—
220C4×Dic59C22×C4112yes—
221C4×Dic59C2×Q814yescomplemented
222C23×C59—21no—
223C23×C59—21no—
224C23×C59—21no—
225C23×C59—21no—
226C23×C59C23×C412yes—
227C23×C59C22×Q812yes—
228C23×C59C2×#4112yes—
229C23×C59C2511yescharacteristic
230C22×D59—21no—
231C22×D59—21no—
232C22×D59—21no—
233C22×D59—21no—
234C22×D59C23×C412yes—
235C22×D59C22×Q812yes—
236C22×D59C2×#4112yes—
237Q8×C59—224no—
238Q8×C59C4×D4116yescomplemented
239C2×C4×C59—21no—
240C2×C4×C59—23no—
241C2×C4×C59—23no—
242C2×C4×C59—23no—
243C2×C4×C59—21no—
244C2×C4×C59—23no—
245C2×C4×C59—224no—
246C2×C4×C59—28no—
247C2×C4×C59—23no—
248C2×C4×C59—23no—
249C2×C4×C59—23no—
250C2×C4×C59—412no—
251C2×C4×C59C23×C416yes—
252C2×C4×C59C23×C416yes—
253C2×C4×C59C22×D416yes—
254C2×C4×C59C22×D416yes—
255C2×C4×C59C22×D412yes—
256C2×C4×C59C22×Q812yes—
257C2×C4×C59C22×Q812yes—
258C2×C4×C59C2×#4116yes—
259C2×C4×C592−1+412yes—
260C22⋊D59C4×Q8116yesdirect product factor
261C2×Dic59—21no—
262C2×Dic59—23no—
263C2×Dic59—21no—
264C2×Dic59—23no—
265C2×Dic59—23no—
266C2×Dic59—21no—
267C2×Dic59—21no—
268C2×Dic59—23no—
269C2×Dic59—23no—
270C2×Dic59—23no—
271C2×Dic59—23no—
272C2×Dic59—23no—
273C2×Dic59—23no—
274C2×Dic59—23no—
275C2×Dic59C23×C416yes—
276C2×Dic59C23×C416yes—
277C2×Dic59C23×C412yes—
278C2×Dic59C22×Q812yes—
279C2×Dic59C22×Q812yes—
280C2×Dic59C22×Q812yes—
281C2×Dic59C2×#4112yes—
282C4×D59—224no—
283C4×D59—28no—
284C4×D59—412no—
285Dic118—224no—
286C4×D4×Q8—591nomaximal, Sylow
287C22×C59—22no—
288C22×C59—22no—
289C22×C59—22no—
290C22×C59—22no—
291C22×C59—22no—
292C22×C59—22no—
293C22×C59C2×C4×Q814yescomplemented
294C22×C59C24×C411yescharacteristic
295C22×C59C23×D411yescharacteristic
296C22×C59C23×Q811yescharacteristic
297C22×C59C22×#4111yescharacteristic
298C22×C59C22×#4111yescharacteristic
299C22×C59C2×2−1+411yescharacteristic
300C22×C59#58511yescharacteristic
301C2×D59—22no—
302C2×D59—22no—
303C2×D59—22no—
304C2×D59—22no—
305C2×D59—22no—
306C2×D59—22no—
307C2×D59C2×C4×Q814yescomplemented
308C4×C59—26no—
309C4×C59—22no—
310C4×C59—26no—
311C4×C59—43no—
312C4×C59C2×C4×D4112yes—
313C4×C59D4×Q814yescomplemented
314Dic59—26no—
315Dic59—26no—
316Dic59—22no—
317Dic59—22no—
318Dic59—43no—
319Dic59—43no—
320Dic59C2×C4×Q814yescomplemented
321C2×D4×Q8—591no—
322C22×C4×Q8—591no—
323C22×C4×Q8D5911yescharacteristic, complemented
324#2365—593no—
325#2360—593no—
326#2360—593no—
327Q8×C4⋊C4—591no—
328D4×C4⋊C4—593no—
329Q8×C22⋊C4—591no—
330Q8×C22⋊C4—591no—
331C4×C4⋊Q8—593no—
332C4×C22⋊Q8—593no—
333C4×C22⋊Q8—593no—
334C42×Q8—591no—
335C42×D4—593no—
336C2×C59—24no—
337C2×C59C22×C4×D411yescharacteristic
338C2×C59C22×C4×Q811yescharacteristic
339C2×C59C4×2−1+411yescharacteristic
340C2×C59C2×D4×Q811yescharacteristic
341C2×C59D4×#4111yescharacteristic
342C2×C59Q8×#4111yescharacteristic
343C2×C59#348211yescharacteristic
344D59—24no—
345C23×Q8—591no—
346C23×Q8C2×D5911yescharacteristic
347D4×Q8—5916no—
348C2×C4⋊Q8—593no—
349C2×C22⋊Q8—593no—
350C2×C22⋊Q8—593no—
351C2×C4×Q8—28no—
352C2×C4×Q8—591no—
353C2×C4×Q8—591no—
354C2×C4×Q8—591no—
355C2×C4×Q8—593no—
356C2×C4×Q8—593no—
357C2×C4×Q8—1188no—
358C2×C4×Q8C2×D5913yes—
359C2×C4×Q8C2×D5911yescharacteristic
360C2×C4×Q8C2×D5913yes—
361C2×C4×Q8C2×D5911yescharacteristic
362C2×C4×D4—593no—
363C2×C4×D4—591no—
364C2×C4×D4—593no—
365C22×C4⋊C4—593no—
366C22×C4⋊C4C2×D5913yes—
367C22×C42—593no—
368C22×C42C2×D5913yes—
369#391—593no—
370#391—593no—
371#391—593no—
372#391—593no—
373#389—596no—
374#389—596no—
375#389—593no—
376#389—593no—
377#387—596no—
378#387—596no—
379#385—596no—
380#385—596no—
381#384—593no—
382#380—593no—
383#380—593no—
384C4×C4⋊C4—593no—
385C4×C4⋊C4—593no—
386C4×C4⋊C4—593no—
387C4×C4⋊C4—596no—
388C4×C4⋊C4—593no—
389C4×C4⋊C4—593no—
390C4×C4⋊C4—593no—
391C4×C22⋊C4—593no—
392C4×C22⋊C4—593no—
393C4×C22⋊C4—593no—
394C4×C22⋊C4—593no—
395C4×C22⋊C4—593no—
396C4×C22⋊C4—593no—
397C43—593no—
398C59C4×D4×Q811yescharacteristic, complemented, Sylow
399C22×Q8—24no—
400C22×Q8—24no—
401C22×Q8—598no—
402C22×Q8—593no—
403C22×Q8—1184no—
404C22×Q8—1184no—
405C22×Q8C4×D5918yescomplemented
406C22×Q8C22×D5913yes—
407C22×Q8C22×D5911yescharacteristic
408C22×D4—591no—
409C23×C4—593no—
410C23×C4—591no—
411C23×C4—593no—
412C23×C4C22×D5913yes—
413C23×C4C22×D5913yes—
414C23×C4C22×D5911yescharacteristic
415C4⋊Q8—5924no—
416C22⋊Q8—5924no—
417C22⋊Q8—5924no—
418C4×Q8—24no—
419C4×Q8—212no—
420C4×Q8—212no—
421C4×Q8—598no—
422C4×Q8—1184no—
423C4×Q8—1184no—
424C4×Q8—11812no—
425C4×Q8—11812no—
426C4×Q8C22⋊D5918yesdirect product factor
427C4×D4—5924no—
428C4×D4—598no—
429C4×D4—11812no—
430C2×C4⋊C4—212no—
431C2×C4⋊C4—593no—
432C2×C4⋊C4—591no—
433C2×C4⋊C4—593no—
434C2×C4⋊C4—596no—
435C2×C4⋊C4—593no—
436C2×C4⋊C4—596no—
437C2×C4⋊C4—593no—
438C2×C4⋊C4—593no—
439C2×C4⋊C4—596no—
440C2×C4⋊C4—11812no—
441C2×C4⋊C4C22×D5913yes—
442C2×C4⋊C4C22×D5916yes—
443C2×C4⋊C4C22×D5913yes—
444C2×C22⋊C4—593no—
445C2×C22⋊C4—591no—
446C2×C22⋊C4—593no—
447C2×C22⋊C4—591no—
448C2×C22⋊C4—593no—
449C2×C22⋊C4—593no—
450C2×C42—212no—
451C2×C42—593no—
452C2×C42—591no—
453C2×C42—593no—
454C2×C42—593no—
455C2×C42—593no—
456C2×C42—593no—
457C2×C42—593no—
458C2×C42—593no—
459C2×C42—593no—
460C2×C42—11812no—
461C2×C42C22×D5913yes—
462C2×C42C22×D5913yes—
463C2×C42C22×D5913yes—
464C2×C42C22×D5913yes—
465#95—593no—
466#95—593no—
467#95—593no—
468#95—593no—
469#95—593no—
470#95—593no—
471#95—596no—
472#95—596no—
473#95—596no—
474C24—591no—
475C24C23×D5911yescharacteristic
476C2×Q8—232no—
477C2×Q8—26no—
478C2×Q8—26no—
479C2×Q8—5912no—
480C2×Q8—11832no—
481C2×Q8—1186no—
482C2×Q8—1186no—
483C2×Q8C2×C4×D59112yes—
484C2×Q8C2×C4×D5914yes—
485C2×Q8#1174568514yes—
486C2×Q8C2×C22⋊D5914yes—
487C2×D4—594no—
488C2×D4—594no—
489C2×D4—594no—
490C22×C4—22no—
491C22×C4—26no—
492C22×C4—26no—
493C22×C4—22no—
494C22×C4—26no—
495C22×C4—26no—
496C22×C4—43no—
497C22×C4—591no—
498C22×C4—591no—
499C22×C4—591no—
500C22×C4—593no—
501C22×C4—593no—
502C22×C4—5912no—
503C22×C4—594no—
504C22×C4—593no—
505C22×C4—593no—
506C22×C4—1186no—
507C22×C4—1182no—
508C22×C4—1186no—
509C22×C4—1186no—
510C22×C4—1182no—
511C22×C4—1186no—
512C22×C4—2363no—
513C22×C4C2×C4×D59112yes—
514C22×C4Q8×D5914yescomplemented
515C22×C4C23×D5913yes—
516C22×C4C23×D5913yes—
517C22×C4C23×D5913yes—
518C22×C4C23×D5911yescharacteristic
519C22×C4C23×D5913yes—
520C22×C4C23×D5911yescharacteristic
521C4⋊C4—212no—
522C4⋊C4—26no—
523C4⋊C4—5912no—
524C4⋊C4—5912no—
525C4⋊C4—5924no—
526C4⋊C4—594no—
527C4⋊C4—1186no—
528C4⋊C4—11812no—
529C4⋊C4—1186no—
530C4⋊C4—1186no—
531C4⋊C4—2366no—
532C4⋊C4C2×C22⋊D59112yes—
533C22⋊C4—5912no—
534C22⋊C4—594no—
535C22⋊C4—5912no—
536C22⋊C4—594no—
537C22⋊C4—1186no—
538C22⋊C4—1186no—
539C42—26no—
540C42—26no—
541C42—26no—
542C42—5912no—
543C42—594no—
544C42—1186no—
545C42—1186no—
546C42—1186no—
547C42—1186no—
548C42—1186no—
549C42—1186no—
550C42—2363no—
551C42C2×C22⋊D59112yes—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—592no—
557C23—592no—
558C23—592no—
559C23—1181no—
560C23—1181no—
561C23—1181no—
562C23—1181no—
563C23C22×C4×D5912yes—
564C23C2×Q8×D5912yes—
565C23#41×D5912yes—
566C23C24×D5911yescharacteristic
567Q8—224no—
568Q8—11824no—
569Q8C4×C22⋊D59116yesdirect product factor
570D4—5916no—
571C2×C4—21no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—23no—
575C2×C4—21no—
576C2×C4—23no—
577C2×C4—28no—
578C2×C4—224no—
579C2×C4—23no—
580C2×C4—23no—
581C2×C4—23no—
582C2×C4—412no—
583C2×C4—592no—
584C2×C4—592no—
585C2×C4—592no—
586C2×C4—596no—
587C2×C4—596no—
588C2×C4—592no—
589C2×C4—592no—
590C2×C4—1181no—
591C2×C4—1183no—
592C2×C4—1181no—
593C2×C4—1183no—
594C2×C4—1183no—
595C2×C4—1181no—
596C2×C4—1181no—
597C2×C4—1183no—
598C2×C4—1188no—
599C2×C4—11824no—
600C2×C4—1183no—
601C2×C4—1183no—
602C2×C4—1183no—
603C2×C4—1183no—
604C2×C4—1183no—
605C2×C4—1183no—
606C2×C4—23612no—
607C2×C4C22×C4×D5916yes—
608C2×C4C22×C4×D5916yes—
609C2×C4C22×C22⋊D5916yes—
610C2×C4C22×C22⋊D5912yes—
611C2×C4C22×C22⋊D5916yes—
612C2×C4C2×Q8×D5912yes—
613C2×C4C2×Q8×D5912yes—
614C2×C4C2×#1174568516yes—
615C2×C4#1427377512yes—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—594no—
623C22—1182no—
624C22—1182no—
625C22—1182no—
626C22—1182no—
627C22—1182no—
628C22—1182no—
629C22C4×Q8×D5914yescomplemented
630C22C23×C4×D5911yescharacteristic
631C22C23×C22⋊D5911yescharacteristic
632C22C22×Q8×D5911yescharacteristic
633C22C2×#41×D5911yescharacteristic
634C22C22×#1174568511yescharacteristic
635C22C2×#1427377511yescharacteristic
636C22#1683823811yescharacteristic
637C4—26no—
638C4—22no—
639C4—26no—
640C4—43no—
641C4—594no—
642C4—1186no—
643C4—1186no—
644C4—1182no—
645C4—1182no—
646C4—2363no—
647C4—2363no—
648C4C2×C4×C22⋊D59112yes—
649C4Q8×C22⋊D5914yesdirect product factor
650C2—24no—
651C2—1184no—
652C2C22×C4×C22⋊D5911yescharacteristic
653C2C2×C4×Q8×D5911yescharacteristic
654C2C4×#1427377511yescharacteristic
655C2C2×Q8×C22⋊D5911yescharacteristic
656C2#41×C22⋊D5911yescharacteristic
657C2Q8×#1174568511yescharacteristic
658C2#2143771311yescharacteristic
subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC22×C4×Q8×C59C2
socle, cosocleC23×C59C25
prime radicalC22×C22⋊D59C23
hypercenterC22×C4×Q8D59
hypocenterC59C4×D4×Q8
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D59C2semidirect
3. #21427150C2semidirect
4. #21427101C2semidirect
5. #21427097C2semidirect
6. Q8×Dic59⋊C4C2semidirect
8. Q8×C22⋊Dic59C2semidirect
9. Q8×(C2×D59)⋊C4C2semidirect
10. C4×#14273725C2semidirect
11. C4×#14273706C2semidirect
12. C4×#14273703C2semidirect
13. C4×Q8×Dic59C2semidirect
15. C22×C4×Q8×C59C2semidirect
17. Q8×C22⋊D59C4direct (N × H)
72. C2×Q8×D59C2×C4semidirect
77. #14273725C2×C4semidirect
78. #14273706C2×C4semidirect
79. #14273703C2×C4semidirect
82. Q8×Dic59C2×C4semidirect
87. C4×C22⋊D59Q8direct (N × H)
125. C22×Q8×C59C2×C4semidirect
134. C4×Q8×C59D4semidirect
161. C22×C4×C59C2×Q8semidirect
187. C2×C4×D59C2×Q8semidirect
200. C22⋊Dic59C2×Q8semidirect
203. (C2×D59)⋊C4C2×Q8semidirect
212. Dic59⋊C4C2×Q8semidirect
221. C4×Dic59C2×Q8semidirect
238. Q8×C59C4×D4semidirect
260. C22⋊D59C4×Q8direct (N × H)
293. C22×C59C2×C4×Q8semidirect
307. C2×D59C2×C4×Q8semidirect
313. C4×C59D4×Q8semidirect
320. Dic59C2×C4×Q8semidirect
323. C22×C4×Q8D59semidirect
398. C59C4×D4×Q8semidirect
405. C22×Q8C4×D59semidirect
426. C4×Q8C22⋊D59direct (N × H)
514. C22×C4Q8×D59semidirect
569. Q8C4×C22⋊D59direct (N × H)
629. C22C4×Q8×D59semidirect
649. C4Q8×C22⋊D59direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D592
C2×C4×Q8×D592
#214271502
#214271012
#214270972
Q8×Dic59⋊C42
C4⋊C4×C22⋊D592
Q8×C22⋊Dic592
Q8×(C2×D59)⋊C42
C4×#142737252
C4×#142737062
C4×#142737032
C4×Q8×Dic592
C42×C22⋊D592
C22×C4×Q8×C592
C4×D4×Q859