Finite Group Databasebeta

← #548×#595 #17979025

Subgroups — #548×#595 #17979025

Order 4352.

3232 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×#595C211yesmaximal, characteristic, complemented
2C22×Q8×#595C211yesmaximal, characteristic, complemented
3#14545315C213yesmaximal, complemented
4#14545310C213yesmaximal, complemented
5#14545309C213yesmaximal, complemented
6#14545300C213yesmaximal, complemented
7#14545299C211yesmaximal, characteristic, complemented
8#14545289C211yesmaximal, characteristic, complemented
9Q8×C22⋊#595C211yesmaximal, characteristic, complemented
10#124×#595C213yesmaximal, complemented
11C22⋊Q8×#595C213yesmaximal, complemented
12#121×#595C213yesmaximal, complemented
13C4×Q8×#595C211yesmaximal, characteristic, complemented
14C4×D4×#595C213yesmaximal, complemented
15D17×#548C211yesmaximal, characteristic
16#41×#595—28no—
17C2×Q8×#595—28no—
18C2×Q8×#595C2211yescharacteristic
19C2×Q8×#595C2213yes—
20C2×Q8×#595C2211yescharacteristic
21C2×Q8×#595C2213yes—
22C2×Q8×#595C2211yescharacteristic
23C2×Q8×#595C2211yescharacteristic
24C2×D4×#595C2213yes—
25C2×D4×#595C2213yes—
26C2×D4×#595C2213yes—
27C2×D4×#595C2213yes—
28C2×#10587677C2213yes—
29C22×C4⋊#595C2213yes—
30C22×C4×#595C2213yes—
31C22×C4×#595C2213yes—
32(C2×#595)⋊Q8C2213yes—
33(C2×#595)⋊Q8C2213yes—
34#11763761C2213yes—
35#11763761C2213yes—
36#11763760C2213yes—
37#11763760C2213yes—
38#11763759C2216yes—
39#11763759C2216yes—
40#11763759C2216yes—
41#11763758C2216yes—
42#11763757C2216yes—
43#11763756C2216yes—
44#11763753C2213yes—
45#11763751C2213yes—
46#11763751C2213yes—
47C4⋊C4×#595C2213yes—
48C4⋊C4×#595C2213yes—
49C4⋊C4×#595C2213yes—
50C4⋊C4×#595C2213yes—
51C4×C4⋊#595C2213yes—
52C4×C4⋊#595C2213yes—
53C22⋊C4×#595C2211yescharacteristic
54C22⋊C4×#595C2213yes—
55C22⋊C4×#595C2213yes—
56C22⋊C4×#595C2213yes—
57C22⋊C4×#595C2216yes—
58C4×C22⋊#595C2213yes—
59C4×C22⋊#595C2213yes—
60C42×#595C2213yes—
61C2×#41×D17C2211yescharacteristic
62C22×Q8×D17C2211yescharacteristic
63#11763471C411yescharacteristic, complemented
64#11763470C411yescharacteristic, complemented
65#11763469C413yescomplemented
66#11763468C413yescomplemented
67#11763467C413yescomplemented
68#11763466C411yescharacteristic, complemented
69#11763465C413yescomplemented
70#124×D17C2213yes—
71C22⋊Q8×D17C2213yes—
72#121×D17C2213yes—
73C4×Q8×D17C2211yescharacteristic
74C4×D4×D17C2213yes—
75C17×#548C411yescharacteristic, complemented
76C23×#595C2313yes—
77C23×#595C2313yes—
78C23×#595C2313yes—
79C23×#595C2311yescharacteristic
80C2×#41×C17C2×C411yescharacteristic, complemented
81C22×Q8×C17C2×C411yescharacteristic, complemented
82#41×D17—24no—
83#41×D17—24no—
84C2×#63256C2×C411yescharacteristic, complemented
85C2×Q8×D17—24no—
86C2×Q8×D17—24no—
87C2×Q8×D17C2×C411yescharacteristic, complemented
88C2×Q8×D17C2×C413yescomplemented
89C2×Q8×D17C2313yes—
90C2×Q8×D17C2311yescharacteristic
91C2×#63254C2×C413yescomplemented
92C2×D4×D17C2313yes—
93C2×D4×D17C2313yes—
94C2×#63252C2×C413yescomplemented
95C22×C4×D17C2313yes—
96C22×C4×D17C2313yes—
97C22×Dic34C2×C413yescomplemented
98C2×C22⋊#595C2313yes—
99C2×C22⋊#595C2313yes—
100C2×C22⋊#595C2313yes—
101C2×C22⋊#595C2316yes—
102C2×C22⋊#595C2316yes—
103C2×C22⋊#595C2311yescharacteristic
104Q8×#595—24no—
105Q8×#595—24no—
106Q8×#595—24no—
107Q8×#595—212no—
108Q8×#595—212no—
109Q8×#595D418yescomplemented
110D4×#595—212no—
111D4×#595—212no—
112D4×#595—212no—
113D4×#595—212no—
114#10587677—212no—
115C2×C4⋊#595—212no—
116C2×C4⋊#595C2313yes—
117C2×C4⋊#595C2313yes—
118C2×C4⋊#595C2313yes—
119C2×C4⋊#595C2313yes—
120C2×C4⋊#595C2313yes—
121C2×C4⋊#595C2316yes—
122C2×C4⋊#595C2313yes—
123C2×C4×#595—212no—
124C2×C4×#595—212no—
125C2×C4×#595C2311yescharacteristic
126C2×C4×#595C2313yes—
127C2×C4×#595C2313yes—
128C2×C4×#595C2313yes—
129C2×C4×#595C2313yes—
130C2×C4×#595C2313yes—
131C2×C4×#595C2313yes—
132C2×C4×#595C2311yescharacteristic
133C2×C4×#595C2313yes—
134C2×C4×#595C2313yes—
135C2×C4×#595C2313yes—
136C2×C4×#595C2313yes—
137C17×#124C2×C413yescomplemented
138C17×C22⋊Q8C2×C413yescomplemented
139C17×#121C2×C413yescomplemented
140C4×Q8×C17C2×C411yescharacteristic, complemented
141C4×D4×C17C2×C413yescomplemented
142#10587633C2×C413yescomplemented
143#10587632C2×C413yescomplemented
144Q8×Dic17C2×C411yescharacteristic, complemented
145#10587625C2×C416yescomplemented
146#10587624C2×C413yescomplemented
147#10587622C2×C413yescomplemented
148D4×Dic17C2×C413yescomplemented
149#10587616C2×C413yescomplemented
150C4×C22⋊D17C2×C413yescomplemented
151C4×C22⋊D17C2×C413yescomplemented
152#10587610C2×C413yescomplemented
153#10587583C2×C413yescomplemented
154#10587582C2×C416yescomplemented
155#10587581C2×C413yescomplemented
156#10587579C2×C413yescomplemented
157C4⋊C4×D17C2313yes—
158C4⋊C4×D17C2313yes—
159#10587573C2×C413yescomplemented
160#10587571C2×C416yescomplemented
161#10587571C2×C416yescomplemented
162#10587570C2×C416yescomplemented
163#10587567C2×C413yescomplemented
164#10587567C2×C413yescomplemented
165C22⋊C4×D17C2311yescharacteristic
166C22⋊C4×D17C2313yes—
167C22⋊C4×D17C2316yes—
168#10587564C2×C416yescomplemented
169#10587561C2×C413yescomplemented
170C4×D68C2×C413yescomplemented
171C42×D17C2313yes—
172C4×Dic34C2×C413yescomplemented
173(C2×#595)⋊C4C2311yescharacteristic
174(C2×#595)⋊C4C2313yes—
175(C2×#595)⋊C4C2313yes—
176(C2×#595)⋊C4C2313yes—
177(C2×#595)⋊C4C2311yescharacteristic
178(C2×#595)⋊C4C2313yes—
179(C2×#595)⋊C4C2316yes—
180(C2×#595)⋊C4C2316yes—
181(C2×#595)⋊C4C2316yes—
182C23×D17C2413yes—
183C23×D17C2411yescharacteristic
184C22×#595—22no—
185C22×#595—22no—
186C22×#595—26no—
187C22×#595—26no—
188C22×#595—26no—
189C22×#595—26no—
190C22×#595—26no—
191C22×#595—26no—
192C22×#595—26no—
193C22×#595—43no—
194C22×#595—43no—
195C22×#595#4114yescomplemented
196C22×#595C2413yes—
197C22×#595C2413yes—
198C22×#595C2413yes—
199C22×#595C2413yes—
200C22×#595C2411yescharacteristic
201C22×#595C2411yescharacteristic
202C22×#595C2411yescharacteristic
203C22×#595C2411yescharacteristic
204#41×C17—24no—
205C2×Q8×C17—24no—
206C2×Q8×C17C22×C413yes—
207C2×Q8×C17C22×C411yescharacteristic
208C2×D4×C17C22×C413yes—
209C2×D4×C17C22×C413yes—
210C22×C4×C17C22×C413yes—
211C22×C4×C17C22×C413yes—
212C2×C22⋊D17C22×C416yes—
213C2×C22⋊D17C22×C413yes—
214C2×C22⋊D17C22×C413yes—
215C22×Dic17C22×C413yes—
216C22×Dic17C22×C413yes—
217#63256—24no—
218Q8×D17—24no—
219Q8×D17—26no—
220Q8×D17—26no—
221Q8×D17—212no—
222Q8×D17C2×D414yes—
223Q8×D17#4114yes—
224#63254—212no—
225D4×D17—26no—
226D4×D17—26no—
227D4×D17—26no—
228D4×D17—26no—
229#63252—212no—
230C2×D68C22×C413yes—
231C2×D68C22×C413yes—
232C2×C4×D17—26no—
233C2×C4×D17—26no—
234C2×C4×D17—26no—
235C2×C4×D17—26no—
236C2×C4×D17C22×C413yes—
237C2×C4×D17C22×C413yes—
238C2×C4×D17C22×C413yes—
239C2×C4×D17C22×C413yes—
240C2×C4×D17C2411yescharacteristic
241C2×C4×D17C2411yescharacteristic
242C2×C4×D17C2413yes—
243C2×C4×D17C2413yes—
244C2×C4×D17C2413yes—
245C2×Dic34—212no—
246C2×Dic34C22×C413yes—
247C2×Dic34C22×C416yes—
248C2×Dic34C22×C413yes—
249C22⋊#595—26no—
250C22⋊#595—212no—
251C22⋊#595—26no—
252C22⋊#595—26no—
253C22⋊#595—46no—
254C22⋊#595#4114yescomplemented
255C4⋊#595—212no—
256C4⋊#595—26no—
257C4⋊#595—26no—
258C4⋊#595—26no—
259C4⋊#595—26no—
260C4⋊#595—26no—
261C4⋊#595C2×D4112yes—
262C4×#595—22no—
263C4×#595—26no—
264C4×#595—26no—
265C4×#595—26no—
266C4×#595—26no—
267C4×#595—26no—
268C4×#595—22no—
269C4×#595—26no—
270C4×#595—26no—
271C4×#595—26no—
272C4×#595—43no—
273C4×#595C2×D4112yes—
274C4⋊C4×C17C22×C413yes—
275C4⋊C4×C17C22×C413yes—
276C22⋊C4×C17C22×C416yes—
277C22⋊C4×C17C22×C413yes—
278C22⋊C4×C17C22×C411yescharacteristic
279C42×C17C22×C413yes—
280C22⋊Dic17C22×C416yes—
281C22⋊Dic17C22×C413yes—
282C22⋊Dic17C22×C411yescharacteristic
283#63227C22×C411yescharacteristic
284#63227C22×C413yes—
285#63227C22×C416yes—
286#63227C22×C416yes—
287#63227C22×C413yes—
288#63227C22×C411yescharacteristic
289C4⋊Dic17C22×C413yes—
290C4⋊Dic17C22×C413yes—
291#63225C22×C416yes—
292#63225C22×C413yes—
293#63225C22×C413yes—
294C4×Dic17C22×C413yes—
295C4×Dic17C22×C413yes—
296C4×Dic17C22×C413yes—
297C4×#548—171nomaximal, Sylow
298C23×C17C23×C413yes—
299C23×C17C23×C411yescharacteristic
300C22×D17—21no—
301C22×D17—21no—
302C22×D17—21no—
303C22×D17—21no—
304C22×D17—23no—
305C22×D17—23no—
306C22×D17—23no—
307C22×D17—23no—
308C22×D17—23no—
309C22×D17—23no—
310C22×D17C23×C413yes—
311C22×D17C23×C411yescharacteristic
312C22×D17C2×#4112yes—
313C22×D17C2×#4112yes—
314C22×D17C2511yescharacteristic
315C2×#595—21no—
316C2×#595—21no—
317C2×#595—21no—
318C2×#595—23no—
319C2×#595—21no—
320C2×#595—21no—
321C2×#595—23no—
322C2×#595—21no—
323C2×#595—28no—
324C2×#595—23no—
325C2×#595—23no—
326C2×#595—23no—
327C2×#595—23no—
328C2×#595—23no—
329C2×#595—23no—
330C2×#595—23no—
331C2×#595—23no—
332C2×#595—23no—
333C2×#595—412no—
334C2×#595—412no—
335C2×#595—412no—
336C2×#595C22×D416yes—
337C2×#595C22×D412yes—
338C2×#595C2×#4112yes—
339C2×#595C2×#4112yes—
340C2×#595C2×#4112yes—
341C2×#595C2×#4112yes—
342C2×#5952−1+412yes—
343Q8×C17—26no—
344Q8×C17C4×D414yescomplemented
345D4×C17—26no—
346D4×C17—26no—
347C2×C4×C17—26no—
348C2×C4×C17—26no—
349C2×C4×C17C23×C411yescharacteristic
350C2×C4×C17C23×C413yes—
351C2×C4×C17C23×C413yes—
352C2×C4×C17C23×C411yescharacteristic
353C2×C4×C17C23×C413yes—
354C22⋊D17—26no—
355C22⋊D17—26no—
356C22⋊D17—212no—
357C2×Dic17—26no—
358C2×Dic17—26no—
359C2×Dic17C23×C411yescharacteristic
360C2×Dic17C23×C413yes—
361C2×Dic17C23×C413yes—
362C2×Dic17C23×C411yescharacteristic
363C2×Dic17C23×C413yes—
364D68—26no—
365D68—26no—
366C4×D17—21no—
367C4×D17—23no—
368C4×D17—23no—
369C4×D17—23no—
370C4×D17—21no—
371C4×D17—23no—
372C4×D17—21no—
373C4×D17—21no—
374C4×D17—26no—
375C4×D17—26no—
376C4×D17—26no—
377C4×D17—26no—
378C4×D17C22×D416yes—
379C4×D17C2×#4116yes—
380Dic34—26no—
381Dic34—212no—
382Dic34C4×D4112yescomplemented
383C2×#548—171no—
384C2×C4×#41—171no—
385C22×C4×Q8—171no—
386#2367—173no—
387#2362—173no—
388#2361—173no—
389#2352—173no—
390#2351—171no—
391#2341—171no—
392Q8×C22⋊C4—171no—
393C4×#124—173no—
394C4×C22⋊Q8—173no—
395C4×#121—173no—
396C42×Q8—171no—
397C42×D4—173no—
398C22×C17—21no—
399C22×C17—21no—
400C22×C17—23no—
401C22×C17—23no—
402C22×C17—23no—
403C22×C17C4×#4112yescomplemented
404C22×C17C24×C411yescharacteristic
405C2×D17—21no—
406C2×D17—21no—
407C2×D17—22no—
408C2×D17—22no—
409C2×D17—22no—
410C2×D17—22no—
411C2×D17—23no—
412C2×D17—23no—
413C2×D17—23no—
414C2×D17—43no—
415C2×D17—43no—
416C2×D17—43no—
417C2×D17—43no—
418C2×D17C4×#4112yescomplemented
419C2×D17C23×D411yescharacteristic
420C2×D17C22×#4111yescharacteristic
421C2×D17C22×#4111yescharacteristic
422C2×D17C22×#4111yescharacteristic
423C2×D17C2×2−1+411yescharacteristic
424C2×D17#58511yescharacteristic
425#595—22no—
426#595—22no—
427#595—26no—
428#595—22no—
429#595—43no—
430#595—43no—
431#595—43no—
432#595#54814yesdirect product factor
433C4×C17—23no—
434C4×C17—21no—
435C4×C17—23no—
436C4×C17—21no—
437C4×C17C2×C4×D416yes—
438Dic17—23no—
439Dic17—21no—
440Dic17—23no—
441Dic17—21no—
442Dic17C2×C4×D416yes—
443C22×#41—171no—
444C23×Q8—171no—
445#548—171no—
446#548—171no—
447#548—173no—
448#548—173no—
449#548—173no—
450#548—171no—
451#548—173no—
452#548#59511yescharacteristic, direct product factor
453C2×#124—173no—
454C2×C22⋊Q8—173no—
455C2×#121—173no—
456C4×#41—348no—
457C2×C4×Q8—171no—
458C2×C4×Q8—171no—
459C2×C4×Q8—171no—
460C2×C4×Q8—171no—
461C2×C4×Q8—171no—
462C2×C4×Q8—173no—
463C2×C4×Q8—173no—
464C2×C4×Q8—348no—
465C2×C4×D4—173no—
466C2×C4×D4—173no—
467C2×C4×D4—173no—
468C2×C4×D4—173no—
469C2×C4×D4—173no—
470C2×#117—173no—
471C22×C4⋊C4—173no—
472C22×C42—173no—
473C22×C42—173no—
474#391—173no—
475#391—173no—
476#390—173no—
477#390—173no—
478#389—173no—
479#389—173no—
480#388—176no—
481#388—176no—
482#388—176no—
483#387—176no—
484#386—176no—
485#385—176no—
486#382—173no—
487#380—173no—
488#380—173no—
489C4×C4⋊C4—173no—
490C4×C4⋊C4—173no—
491C4×C4⋊C4—173no—
492C4×C4⋊C4—173no—
493C4×C4⋊C4—173no—
494C4×C4⋊C4—173no—
495C4×C22⋊C4—173no—
496C4×C22⋊C4—173no—
497C4×C22⋊C4—173no—
498C4×C22⋊C4—173no—
499C4×C22⋊C4—171no—
500C4×C22⋊C4—173no—
501C4×C22⋊C4—176no—
502C43—173no—
503C2×C17—22no—
504C2×C17—43no—
505C2×C17C22×C4×D411yescharacteristic
506C2×C17C2×C4×#4111yescharacteristic
507C2×C17C4×2−1+411yescharacteristic
508D17—22no—
509D17—43no—
510D17C2×#54811yescharacteristic
511D17D4×#4111yescharacteristic
512D17#348011yescharacteristic
513D17#348211yescharacteristic
514C2×#41—171no—
515C2×#41—173no—
516C2×#41—173no—
517C2×#41—344no—
518C2×#41—344no—
519C2×#41C2×#59511yescharacteristic, complemented
520C22×Q8—171no—
521C22×Q8—173no—
522C22×Q8—173no—
523C22×Q8—171no—
524C22×Q8—173no—
525C22×Q8—344no—
526C22×Q8—344no—
527C22×Q8C2×#59511yescharacteristic, complemented
528C22×D4—173no—
529C22×D4—173no—
530C23×C4—171no—
531C23×C4—173no—
532C23×C4—173no—
533C23×C4—173no—
534C23×C4—173no—
535C23×C4—173no—
536#124—173no—
537#124—173no—
538#124—176no—
539#124—176no—
540#124—173no—
541#124C2×#59513yescomplemented
542C22⋊Q8—173no—
543C22⋊Q8—173no—
544C22⋊Q8—176no—
545C22⋊Q8—173no—
546C22⋊Q8—176no—
547C22⋊Q8C2×#59513yescomplemented
548#121—173no—
549#121—176no—
550#121—173no—
551#121—173no—
552#121—176no—
553#121C2×#59513yescomplemented
554C4×Q8—178no—
555C4×Q8—171no—
556C4×Q8—173no—
557C4×Q8—173no—
558C4×Q8—3412no—
559C4×Q8—3412no—
560C4×Q8—344no—
561C4×Q8—344no—
562C4×Q8—344no—
563C4×Q8C2×#59511yescharacteristic, complemented
564C4×D4—173no—
565C4×D4—173no—
566C4×D4—173no—
567C4×D4—173no—
568C4×D4—173no—
569C4×D4—173no—
570C4×D4—173no—
571C4×D4—3412no—
572C4×D4—3412no—
573C4×D4—3412no—
574C4×D4—3412no—
575C4×D4C2×#59513yescomplemented
576#117—3412no—
577C2×C4⋊C4—173no—
578C2×C4⋊C4—173no—
579C2×C4⋊C4—173no—
580C2×C4⋊C4—173no—
581C2×C4⋊C4—176no—
582C2×C4⋊C4—173no—
583C2×C4⋊C4—173no—
584C2×C4⋊C4—173no—
585C2×C4⋊C4—173no—
586C2×C4⋊C4—3412no—
587C2×C22⋊C4—171no—
588C2×C22⋊C4—171no—
589C2×C22⋊C4—173no—
590C2×C22⋊C4—176no—
591C2×C22⋊C4—176no—
592C2×C22⋊C4—173no—
593C2×C22⋊C4—173no—
594C2×C22⋊C4—173no—
595C2×C22⋊C4—176no—
596C2×C42—173no—
597C2×C42—173no—
598C2×C42—173no—
599C2×C42—173no—
600C2×C42—173no—
601C2×C42—173no—
602C2×C42—173no—
603C2×C42—173no—
604C2×C42—173no—
605C2×C42—173no—
606C2×C42—171no—
607C2×C42—171no—
608C2×C42—173no—
609C2×C42—3412no—
610C2×C42—3412no—
611#95—171no—
612#95—171no—
613#95—173no—
614#95—173no—
615#95—173no—
616#95—173no—
617#95—176no—
618#95—176no—
619#95—176no—
620C17C4×#54811yescharacteristic, complemented, Sylow
621C24—171no—
622C24—173no—
623#41—24no—
624#41—3412no—
625#41—3412no—
626#41—344no—
627C2×Q8—24no—
628C2×Q8—174no—
629C2×Q8—174no—
630C2×Q8—173no—
631C2×Q8—176no—
632C2×Q8—173no—
633C2×Q8—3412no—
634C2×Q8—346no—
635C2×Q8—346no—
636C2×Q8—3412no—
637C2×Q8—344no—
638C2×Q8C22×#59513yes—
639C2×Q8C22×#59511yescharacteristic
640C2×D4—173no—
641C2×D4—173no—
642C2×D4—176no—
643C2×D4—173no—
644C2×D4—173no—
645C2×D4—346no—
646C2×D4—346no—
647C2×D4—346no—
648C2×D4—346no—
649C2×D4C22×#59513yes—
650C2×D4C22×#59513yes—
651C22×C4—171no—
652C22×C4—173no—
653C22×C4—174no—
654C22×C4—171no—
655C22×C4—171no—
656C22×C4—171no—
657C22×C4—173no—
658C22×C4—173no—
659C22×C4—173no—
660C22×C4—173no—
661C22×C4—173no—
662C22×C4—173no—
663C22×C4—173no—
664C22×C4—171no—
665C22×C4—171no—
666C22×C4—173no—
667C22×C4—173no—
668C22×C4—173no—
669C22×C4—173no—
670C22×C4—173no—
671C22×C4—346no—
672C22×C4—346no—
673C22×C4—346no—
674C22×C4—346no—
675C22×C4—342no—
676C22×C4—342no—
677C22×C4—346no—
678C22×C4—346no—
679C22×C4—346no—
680C22×C4—346no—
681C22×C4—346no—
682C22×C4—346no—
683C22×C4—346no—
684C22×C4—683no—
685C22×C4—683no—
686C22×C4C22×#59513yes—
687C22×C4C22×#59513yes—
688C4⋊C4—1712no—
689C4⋊C4—173no—
690C4⋊C4—173no—
691C4⋊C4—173no—
692C4⋊C4—176no—
693C4⋊C4—173no—
694C4⋊C4—346no—
695C4⋊C4—3412no—
696C4⋊C4—346no—
697C4⋊C4—346no—
698C4⋊C4—346no—
699C4⋊C4—346no—
700C4⋊C4C22×#59513yes—
701C4⋊C4C22×#59513yes—
702C22⋊C4—174no—
703C22⋊C4—171no—
704C22⋊C4—173no—
705C22⋊C4—176no—
706C22⋊C4—171no—
707C22⋊C4—171no—
708C22⋊C4—173no—
709C22⋊C4—173no—
710C22⋊C4—176no—
711C22⋊C4—176no—
712C22⋊C4—3412no—
713C22⋊C4—346no—
714C22⋊C4—346no—
715C22⋊C4—346no—
716C22⋊C4—686no—
717C22⋊C4C22×#59511yescharacteristic
718C22⋊C4C22×#59513yes—
719C22⋊C4C22×#59516yes—
720C42—1712no—
721C42—173no—
722C42—173no—
723C42—173no—
724C42—342no—
725C42—342no—
726C42—346no—
727C42—346no—
728C42—346no—
729C42—346no—
730C42—346no—
731C42—346no—
732C42—346no—
733C42—346no—
734C42—683no—
735C42C22×#59513yes—
736C23—171no—
737C23—172no—
738C23—172no—
739C23—171no—
740C23—173no—
741C23—341no—
742C23—341no—
743C23—341no—
744C23—341no—
745C23—343no—
746C23—343no—
747C23—343no—
748C23—343no—
749C23—343no—
750C23—343no—
751C23C23×#59513yes—
752C23C23×#59511yescharacteristic
753Q8—26no—
754Q8—1712no—
755Q8—3412no—
756Q8—346no—
757Q8D4×#59514yescomplemented
758D4—26no—
759D4—26no—
760D4—346no—
761D4—3412no—
762D4—346no—
763D4—346no—
764D4—346no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—172no—
768C2×C4—172no—
769C2×C4—172no—
770C2×C4—173no—
771C2×C4—176no—
772C2×C4—176no—
773C2×C4—176no—
774C2×C4—172no—
775C2×C4—172no—
776C2×C4—172no—
777C2×C4—171no—
778C2×C4—173no—
779C2×C4—173no—
780C2×C4—171no—
781C2×C4—346no—
782C2×C4—346no—
783C2×C4—341no—
784C2×C4—343no—
785C2×C4—343no—
786C2×C4—343no—
787C2×C4—341no—
788C2×C4—341no—
789C2×C4—341no—
790C2×C4—343no—
791C2×C4—346no—
792C2×C4—346no—
793C2×C4—348no—
794C2×C4—341no—
795C2×C4—341no—
796C2×C4—341no—
797C2×C4—343no—
798C2×C4—341no—
799C2×C4—343no—
800C2×C4—341no—
801C2×C4—341no—
802C2×C4—346no—
803C2×C4—346no—
804C2×C4—343no—
805C2×C4—343no—
806C2×C4—343no—
807C2×C4—343no—
808C2×C4—343no—
809C2×C4—343no—
810C2×C4—343no—
811C2×C4—343no—
812C2×C4—343no—
813C2×C4—6812no—
814C2×C4—6812no—
815C2×C4—6812no—
816C2×C4C23×#59511yescharacteristic
817C2×C4C23×#59513yes—
818C2×C4C23×#59513yes—
819C2×C4C23×#59511yescharacteristic
820C2×C4C23×#59513yes—
821C22—21no—
822C22—21no—
823C22—23no—
824C22—23no—
825C22—23no—
826C22—171no—
827C22—171no—
828C22—171no—
829C22—171no—
830C22—171no—
831C22—171no—
832C22—172no—
833C22—342no—
834C22—342no—
835C22—342no—
836C22—342no—
837C22—341no—
838C22—341no—
839C22—343no—
840C22—343no—
841C22—343no—
842C22—683no—
843C22—683no—
844C22—683no—
845C22—683no—
846C22#41×#59512yescomplemented
847C22C24×#59511yescharacteristic
848C4—21no—
849C4—23no—
850C4—23no—
851C4—21no—
852C4—174no—
853C4—176no—
854C4—342no—
855C4—342no—
856C4—346no—
857C4—342no—
858C4—341no—
859C4—343no—
860C4—343no—
861C4—341no—
862C4—683no—
863C4—683no—
864C4—683no—
865C4C2×D4×#59516yes—
866C2—22no—
867C2—43no—
868C2—171no—
869C2—171no—
870C2—171no—
871C2—171no—
872C2—342no—
873C2—683no—
874C2C22×D4×#59511yescharacteristic
875C2C2×#41×#59511yescharacteristic
876C22−1+4×#59511yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#548C4
prime radicalD17×#548C2
cosocleC22×D17C25
hypercenter#548#595
hypocenterC17C4×#548
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×#595C2semidirect
2. C22×Q8×#595C2semidirect
3. #14545315C2semidirect
4. #14545310C2semidirect
5. #14545309C2semidirect
6. #14545300C2semidirect
7. #14545299C2semidirect
8. #14545289C2semidirect
9. Q8×C22⋊#595C2semidirect
10. #124×#595C2semidirect
11. C22⋊Q8×#595C2semidirect
12. #121×#595C2semidirect
13. C4×Q8×#595C2semidirect
14. C4×D4×#595C2semidirect
63. #11763471C4semidirect
64. #11763470C4semidirect
65. #11763469C4semidirect
66. #11763468C4semidirect
67. #11763467C4semidirect
68. #11763466C4semidirect
69. #11763465C4semidirect
75. C17×#548C4semidirect
80. C2×#41×C17C2×C4semidirect
81. C22×Q8×C17C2×C4semidirect
84. C2×#63256C2×C4semidirect
87. C2×Q8×D17C2×C4semidirect
88. C2×Q8×D17C2×C4semidirect
91. C2×#63254C2×C4semidirect
94. C2×#63252C2×C4semidirect
97. C22×Dic34C2×C4semidirect
109. Q8×#595D4semidirect
137. C17×#124C2×C4semidirect
138. C17×C22⋊Q8C2×C4semidirect
139. C17×#121C2×C4semidirect
140. C4×Q8×C17C2×C4semidirect
141. C4×D4×C17C2×C4semidirect
142. #10587633C2×C4semidirect
143. #10587632C2×C4semidirect
144. Q8×Dic17C2×C4semidirect
145. #10587625C2×C4semidirect
146. #10587624C2×C4semidirect
147. #10587622C2×C4semidirect
148. D4×Dic17C2×C4semidirect
149. #10587616C2×C4semidirect
150. C4×C22⋊D17C2×C4semidirect
151. C4×C22⋊D17C2×C4semidirect
152. #10587610C2×C4semidirect
153. #10587583C2×C4semidirect
154. #10587582C2×C4semidirect
155. #10587581C2×C4semidirect
156. #10587579C2×C4semidirect
159. #10587573C2×C4semidirect
160. #10587571C2×C4semidirect
161. #10587571C2×C4semidirect
162. #10587570C2×C4semidirect
163. #10587567C2×C4semidirect
164. #10587567C2×C4semidirect
168. #10587564C2×C4semidirect
169. #10587561C2×C4semidirect
170. C4×D68C2×C4semidirect
172. C4×Dic34C2×C4semidirect
195. C22×#595#41semidirect
254. C22⋊#595#41semidirect
344. Q8×C17C4×D4semidirect
382. Dic34C4×D4semidirect
403. C22×C17C4×#41semidirect
418. C2×D17C4×#41semidirect
432. #595#548direct (N × H)
452. #548#595direct (N × H)
519. C2×#41C2×#595semidirect
527. C22×Q8C2×#595semidirect
541. #124C2×#595semidirect
547. C22⋊Q8C2×#595semidirect
553. #121C2×#595semidirect
563. C4×Q8C2×#595semidirect
575. C4×D4C2×#595semidirect
620. C17C4×#548semidirect
757. Q8D4×#595semidirect
846. C22#41×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#41×#5952
C22×Q8×#5952
#145453152
#145453102
#145453092
#145453002
#145452992
#145452892
Q8×C22⋊#5952
#124×#5952
C22⋊Q8×#5952
#121×#5952
C4×Q8×#5952
C4×D4×#5952
D17×#5482
C4×#54817