Finite Group Databasebeta

← #17979161

Subgroups — #17979161

Order 4352.

3112 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763878C211yesmaximal, characteristic, complemented
2C22×Q8×#595C211yesmaximal, characteristic, complemented
3#14545315C213yesmaximal, complemented
4#14545309C213yesmaximal, complemented
5#14545308C213yesmaximal, complemented
6Q8×C4⋊#595C211yesmaximal, characteristic, complemented
7D4×C4⋊#595C213yesmaximal, complemented
8#14545289C211yesmaximal, characteristic, complemented
9Q8×C22⋊#595C211yesmaximal, characteristic, complemented
10#14545274C213yesmaximal, complemented
11#14545271C213yesmaximal, complemented
12#121×#595C213yesmaximal, complemented
13#14545238C213yesmaximal, complemented
14#14545224C211yesmaximal, characteristic, complemented
15D17×#548C211yesmaximal, characteristic
16#11763878—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×#595C2216yes—
27C2×#10587677C2213yes—
28C22×C4⋊#595C2213yes—
29C22×C4⋊#595C2213yes—
30C22×C4×#595C2213yes—
31(C2×#595)⋊Q8C2213yes—
32(C2×#595)⋊Q8C2213yes—
33#11763761C2213yes—
34#11763761C2213yes—
35#11763760C2213yes—
36#11763760C2216yes—
37#11763760C2213yes—
38#11763759C2213yes—
39#11763759C2213yes—
40#11763759C2216yes—
41#11763759C2216yes—
42#11763758C2213yes—
43#11763758C2213yes—
44#11763757C2213yes—
45#11763757C2213yes—
46#11763756C2211yescharacteristic
47#11763756C2213yes—
48#11763756C2216yes—
49#11763756C2216yes—
50#11763755C2213yes—
51#11763751C2213yes—
52#11763751C2213yes—
53C4⋊C4×#595C2213yes—
54C4⋊C4×#595C2213yes—
55C4×C4⋊#595C2213yes—
56C4×C4⋊#595C2213yes—
57C22⋊C4×#595C2216yes—
58C4×C22⋊#595C2213yes—
59C4×C22⋊#595C2213yes—
60#11763745C2213yes—
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×#595C2311yescharacteristic
77C23×#595C2313yes—
78C23×#595C2316yes—
79C2×#41×C17C2×C411yescharacteristic, complemented
80C22×Q8×C17C2×C411yescharacteristic, complemented
81#41×D17—24no—
82#41×D17—24no—
83C2×#63256C2×C411yescharacteristic, complemented
84C2×Q8×D17—24no—
85C2×Q8×D17—24no—
86C2×Q8×D17C2×C411yescharacteristic, complemented
87C2×Q8×D17C2×C413yescomplemented
88C2×Q8×D17C2313yes—
89C2×Q8×D17C2311yescharacteristic
90C2×#63254C2×C413yescomplemented
91C2×D4×D17C2313yes—
92C2×D4×D17C2313yes—
93C2×#63252C2×C413yescomplemented
94C22×C4×D17C2313yes—
95C22×C4×D17C2313yes—
96C22×Dic34C2×C413yescomplemented
97C2×C22⋊#595C2311yescharacteristic
98C2×C22⋊#595C2313yes—
99C2×C22⋊#595C2313yes—
100C2×C22⋊#595C2313yes—
101C2×C22⋊#595C2313yes—
102C2×C22⋊#595C2313yes—
103C2×C22⋊#595C2316yes—
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—412no—
113#10587677—212no—
114C2×C4⋊#595—212no—
115C2×C4⋊#595—212no—
116C2×C4⋊#595C2311yescharacteristic
117C2×C4⋊#595C2313yes—
118C2×C4⋊#595C2313yes—
119C2×C4⋊#595C2313yes—
120C2×C4⋊#595C2316yes—
121C2×C4⋊#595C2311yescharacteristic
122C2×C4⋊#595C2313yes—
123C2×C4⋊#595C2313yes—
124C2×C4⋊#595C2316yes—
125C2×C4⋊#595C2313yes—
126C2×C4×#595—212no—
127C2×C4×#595C2313yes—
128C2×C4×#595C2313yes—
129C2×C4×#595C2313yes—
130C2×C4×#595C2313yes—
131C2×C4×#595C2313yes—
132C2×C4×#595C2316yes—
133C2×C4×#595C2313yes—
134C17×#124C2×C413yescomplemented
135C17×C22⋊Q8C2×C413yescomplemented
136C17×#121C2×C413yescomplemented
137C4×Q8×C17C2×C411yescharacteristic, complemented
138C4×D4×C17C2×C413yescomplemented
139#10587633C2×C413yescomplemented
140#10587632C2×C413yescomplemented
141Q8×Dic17C2×C411yescharacteristic, complemented
142#10587625C2×C416yescomplemented
143#10587624C2×C413yescomplemented
144#10587622C2×C413yescomplemented
145D4×Dic17C2×C413yescomplemented
146#10587616C2×C413yescomplemented
147C4×C22⋊D17C2×C413yescomplemented
148C4×C22⋊D17C2×C413yescomplemented
149#10587610C2×C413yescomplemented
150#10587583C2×C413yescomplemented
151#10587582C2×C416yescomplemented
152#10587581C2×C413yescomplemented
153#10587579C2×C413yescomplemented
154C4⋊C4×D17C2313yes—
155C4⋊C4×D17C2313yes—
156#10587573C2×C413yescomplemented
157#10587571C2×C416yescomplemented
158#10587571C2×C416yescomplemented
159#10587570C2×C416yescomplemented
160#10587567C2×C413yescomplemented
161#10587567C2×C413yescomplemented
162C22⋊C4×D17C2316yes—
163C22⋊C4×D17C2311yescharacteristic
164C22⋊C4×D17C2313yes—
165#10587564C2×C416yescomplemented
166#10587561C2×C413yescomplemented
167C4×D68C2×C413yescomplemented
168C42×D17C2313yes—
169C4×Dic34C2×C413yescomplemented
170(C2×#595)⋊C4C2311yescharacteristic
171(C2×#595)⋊C4C2313yes—
172(C2×#595)⋊C4C2313yes—
173(C2×#595)⋊C4C2313yes—
174(C2×#595)⋊C4C2311yescharacteristic
175(C2×#595)⋊C4C2313yes—
176(C2×#595)⋊C4C2313yes—
177(C2×#595)⋊C4C2313yes—
178(C2×#595)⋊C4C2313yes—
179(C2×#595)⋊C4C2316yes—
180(C2×#595)⋊C4C2313yes—
181C23×D17C2413yes—
182C23×D17C2411yescharacteristic
183C22×#595—22no—
184C22×#595—22no—
185C22×#595—22no—
186C22×#595—26no—
187C22×#595—26no—
188C22×#595—212no—
189C22×#595—43no—
190C22×#595—46no—
191C22×#595—46no—
192C22×#595C2411yescharacteristic
193C22×#595C2413yes—
194C22×#595C2411yescharacteristic
195C22×#595C2413yes—
196C22×#595C2413yes—
197C22×#595C2411yescharacteristic
198C22×#595C2413yes—
199C22×#595C2411yescharacteristic
200#41×C17—24no—
201C2×Q8×C17—24no—
202C2×Q8×C17C22×C413yes—
203C2×Q8×C17C22×C411yescharacteristic
204C2×D4×C17C22×C413yes—
205C2×D4×C17C22×C413yes—
206C22×C4×C17C22×C413yes—
207C22×C4×C17C22×C413yes—
208C2×C22⋊D17C22×C416yes—
209C2×C22⋊D17C22×C413yes—
210C2×C22⋊D17C22×C413yes—
211C22×Dic17C22×C413yes—
212C22×Dic17C22×C413yes—
213#63256—24no—
214Q8×D17—24no—
215Q8×D17—26no—
216Q8×D17—26no—
217Q8×D17—212no—
218Q8×D17C2×D414yes—
219Q8×D17#4114yes—
220#63254—212no—
221D4×D17—26no—
222D4×D17—26no—
223D4×D17—26no—
224D4×D17—26no—
225#63252—212no—
226C2×D68C22×C413yes—
227C2×D68C22×C413yes—
228C2×C4×D17—26no—
229C2×C4×D17—26no—
230C2×C4×D17—26no—
231C2×C4×D17—26no—
232C2×C4×D17C22×C413yes—
233C2×C4×D17C22×C413yes—
234C2×C4×D17C22×C413yes—
235C2×C4×D17C22×C413yes—
236C2×C4×D17C2413yes—
237C2×C4×D17C2413yes—
238C2×C4×D17C2411yescharacteristic
239C2×C4×D17C2411yescharacteristic
240C2×C4×D17C2413yes—
241C2×Dic34—212no—
242C2×Dic34C22×C413yes—
243C2×Dic34C22×C416yes—
244C2×Dic34C22×C413yes—
245C22⋊#595—26no—
246C22⋊#595—22no—
247C22⋊#595—26no—
248C22⋊#595—26no—
249C22⋊#595—26no—
250C22⋊#595—46no—
251C22⋊#595—43no—
252C4⋊#595—26no—
253C4⋊#595—212no—
254C4⋊#595—22no—
255C4⋊#595—22no—
256C4⋊#595—26no—
257C4⋊#595—26no—
258C4⋊#595—26no—
259C4⋊#595—43no—
260C4⋊#595—46no—
261C4⋊#595C2×D4112yes—
262C4×#595—26no—
263C4×#595—26no—
264C4×#595—26no—
265C4×#595—26no—
266C4×#595—26no—
267C4×#595—46no—
268C4×#595C2×D4112yes—
269C4⋊C4×C17C22×C413yes—
270C4⋊C4×C17C22×C413yes—
271C22⋊C4×C17C22×C416yes—
272C22⋊C4×C17C22×C413yes—
273C22⋊C4×C17C22×C411yescharacteristic
274C42×C17C22×C413yes—
275C22⋊Dic17C22×C416yes—
276C22⋊Dic17C22×C413yes—
277C22⋊Dic17C22×C411yescharacteristic
278#63227C22×C411yescharacteristic
279#63227C22×C413yes—
280#63227C22×C416yes—
281#63227C22×C416yes—
282#63227C22×C413yes—
283#63227C22×C411yescharacteristic
284C4⋊Dic17C22×C413yes—
285C4⋊Dic17C22×C413yes—
286#63225C22×C416yes—
287#63225C22×C413yes—
288#63225C22×C413yes—
289C4×Dic17C22×C413yes—
290C4×Dic17C22×C413yes—
291C4×Dic17C22×C413yes—
292#34294—171nomaximal, Sylow
293C23×C17C23×C413yes—
294C23×C17C23×C411yescharacteristic
295C22×D17—21no—
296C22×D17—21no—
297C22×D17—21no—
298C22×D17—21no—
299C22×D17—23no—
300C22×D17—23no—
301C22×D17—23no—
302C22×D17—23no—
303C22×D17—23no—
304C22×D17—23no—
305C22×D17C23×C413yes—
306C22×D17C23×C411yescharacteristic
307C22×D17H(5,𝔽2)12yes—
308C22×D172−1+412yes—
309C22×D17C2511yescharacteristic
310C2×#595—28no—
311C2×#595—21no—
312C2×#595—23no—
313C2×#595—21no—
314C2×#595—21no—
315C2×#595—21no—
316C2×#595—23no—
317C2×#595—21no—
318C2×#595—23no—
319C2×#595—23no—
320C2×#595—21no—
321C2×#595—23no—
322C2×#595—23no—
323C2×#595—23no—
324C2×#595—23no—
325C2×#595—21no—
326C2×#595—21no—
327C2×#595—21no—
328C2×#595—23no—
329C2×#595—23no—
330C2×#595—23no—
331C2×#595—21no—
332C2×#595—412no—
333C2×#595—812no—
334C2×#595C22×D412yes—
335C2×#595C22×D416yes—
336C2×#5952−1+412yes—
337Q8×C17—26no—
338Q8×C17C4×D414yescomplemented
339D4×C17—26no—
340D4×C17—26no—
341C2×C4×C17—26no—
342C2×C4×C17—26no—
343C2×C4×C17C23×C411yescharacteristic
344C2×C4×C17C23×C413yes—
345C2×C4×C17C23×C413yes—
346C2×C4×C17C23×C411yescharacteristic
347C2×C4×C17C23×C413yes—
348C22⋊D17—26no—
349C22⋊D17—26no—
350C22⋊D17—212no—
351C2×Dic17—26no—
352C2×Dic17—26no—
353C2×Dic17C23×C411yescharacteristic
354C2×Dic17C23×C413yes—
355C2×Dic17C23×C413yes—
356C2×Dic17C23×C411yescharacteristic
357C2×Dic17C23×C413yes—
358D68—26no—
359D68—26no—
360C4×D17—23no—
361C4×D17—21no—
362C4×D17—21no—
363C4×D17—23no—
364C4×D17—23no—
365C4×D17—21no—
366C4×D17—23no—
367C4×D17—21no—
368C4×D17—26no—
369C4×D17—26no—
370C4×D17—26no—
371C4×D17—26no—
372C4×D17C22×D416yes—
373C4×D17C2×#4116yes—
374Dic34—26no—
375Dic34—212no—
376Dic34C4×D4112yescomplemented
377C2×#548—171no—
378C2×#520—171no—
379C22×C4×Q8—171no—
380#2367—173no—
381#2361—173no—
382#2360—173no—
383Q8×C4⋊C4—171no—
384D4×C4⋊C4—173no—
385#2341—171no—
386Q8×C22⋊C4—171no—
387#2326—173no—
388#2323—173no—
389C4×#121—173no—
390#2290—173no—
391#2276—171no—
392C22×C17—21no—
393C22×C17—21no—
394C22×C17—23no—
395C22×C17—23no—
396C22×C17—23no—
397C22×C17#52012yescomplemented
398C22×C17C24×C411yescharacteristic
399C2×D17—21no—
400C2×D17—21no—
401C2×D17—22no—
402C2×D17—22no—
403C2×D17—22no—
404C2×D17—22no—
405C2×D17—23no—
406C2×D17—23no—
407C2×D17—23no—
408C2×D17—43no—
409C2×D17—43no—
410C2×D17—43no—
411C2×D17—43no—
412C2×D17#52012yescomplemented
413C2×D17C23×D411yescharacteristic
414C2×D17C22×#4111yescharacteristic
415C2×D17C2×H(5,𝔽2)11yescharacteristic
416C2×D17C2×2−1+411yescharacteristic
417C2×D17C2×2−1+411yescharacteristic
418C2×D17#58511yescharacteristic
419#595—22no—
420#595—22no—
421#595—26no—
422#595—41no—
423#595—43no—
424#595—43no—
425#595—41no—
426#595—43no—
427C4×C17—23no—
428C4×C17—21no—
429C4×C17—23no—
430C4×C17—21no—
431C4×C17C2×C4×D416yes—
432Dic17—23no—
433Dic17—21no—
434Dic17—23no—
435Dic17—21no—
436Dic17C2×C4×D416yes—
437C22×#41—171no—
438C23×Q8—171no—
439#548—171no—
440#548—171no—
441#548—173no—
442#548—173no—
443#548—173no—
444#548—171no—
445#548—173no—
446#548#59511yescharacteristic, complemented
447C2×#124—173no—
448C2×C22⋊Q8—173no—
449C2×#121—173no—
450#520—348no—
451C2×C4×Q8—171no—
452C2×C4×Q8—171no—
453C2×C4×Q8—173no—
454C2×C4×Q8—171no—
455C2×C4×Q8—171no—
456C2×C4×Q8—171no—
457C2×C4×Q8—173no—
458C2×C4×Q8—348no—
459C2×C4×D4—173no—
460C2×C4×D4—173no—
461C2×C4×D4—173no—
462C2×C4×D4—176no—
463C2×#117—173no—
464C22×C4⋊C4—173no—
465C22×C4⋊C4—173no—
466C22×C42—173no—
467#391—173no—
468#391—173no—
469#390—173no—
470#390—173no—
471#389—176no—
472#389—173no—
473#389—173no—
474#388—176no—
475#388—176no—
476#388—173no—
477#388—173no—
478#387—173no—
479#387—173no—
480#386—173no—
481#386—173no—
482#385—176no—
483#385—176no—
484#385—173no—
485#385—171no—
486#384—173no—
487#380—173no—
488#380—173no—
489C4×C4⋊C4—173no—
490C4×C4⋊C4—173no—
491C4×C4⋊C4—173no—
492C4×C4⋊C4—173no—
493C4×C22⋊C4—173no—
494C4×C22⋊C4—173no—
495C4×C22⋊C4—176no—
496#376—173no—
497C2×C17—22no—
498C2×C17—43no—
499C2×C17C22×C4×D411yescharacteristic
500C2×C17C2×#52011yescharacteristic
501C2×C17C4×2−1+411yescharacteristic
502D17—22no—
503D17—43no—
504D17#348611yescharacteristic
505D17#348811yescharacteristic
506D17#351611yescharacteristic
507D17#352211yescharacteristic
508C2×#41—171no—
509C2×#41—173no—
510C2×#41—173no—
511C2×#41—344no—
512C2×#41—344no—
513C2×#41C2×#59511yescharacteristic, complemented
514C22×Q8—171no—
515C22×Q8—173no—
516C22×Q8—173no—
517C22×Q8—171no—
518C22×Q8—173no—
519C22×Q8—344no—
520C22×Q8—344no—
521C22×Q8C2×#59511yescharacteristic, complemented
522C22×D4—173no—
523C22×D4—173no—
524C23×C4—173no—
525C23×C4—173no—
526C23×C4—171no—
527C23×C4—173no—
528C23×C4—176no—
529#124—173no—
530#124—173no—
531#124—176no—
532#124—176no—
533#124—173no—
534#124C2×#59513yescomplemented
535C22⋊Q8—173no—
536C22⋊Q8—173no—
537C22⋊Q8—176no—
538C22⋊Q8—173no—
539C22⋊Q8—176no—
540C22⋊Q8C2×#59513yescomplemented
541#121—173no—
542#121—176no—
543#121—173no—
544#121—173no—
545#121—176no—
546#121C2×#59513yescomplemented
547C4×Q8—178no—
548C4×Q8—171no—
549C4×Q8—173no—
550C4×Q8—173no—
551C4×Q8—3412no—
552C4×Q8—3412no—
553C4×Q8—344no—
554C4×Q8—344no—
555C4×Q8—344no—
556C4×Q8C2×#59511yescharacteristic, complemented
557C4×D4—173no—
558C4×D4—173no—
559C4×D4—173no—
560C4×D4—173no—
561C4×D4—173no—
562C4×D4—173no—
563C4×D4—173no—
564C4×D4—3412no—
565C4×D4—3412no—
566C4×D4—6812no—
567C4×D4C2×#59513yescomplemented
568#117—3412no—
569C2×C4⋊C4—173no—
570C2×C4⋊C4—173no—
571C2×C4⋊C4—173no—
572C2×C4⋊C4—173no—
573C2×C4⋊C4—173no—
574C2×C4⋊C4—173no—
575C2×C4⋊C4—176no—
576C2×C4⋊C4—171no—
577C2×C4⋊C4—173no—
578C2×C4⋊C4—171no—
579C2×C4⋊C4—176no—
580C2×C4⋊C4—173no—
581C2×C4⋊C4—3412no—
582C2×C4⋊C4—3412no—
583C2×C22⋊C4—171no—
584C2×C22⋊C4—173no—
585C2×C22⋊C4—176no—
586C2×C22⋊C4—173no—
587C2×C22⋊C4—173no—
588C2×C22⋊C4—173no—
589C2×C22⋊C4—171no—
590C2×C22⋊C4—173no—
591C2×C22⋊C4—176no—
592C2×C22⋊C4—173no—
593C2×C42—173no—
594C2×C42—173no—
595C2×C42—173no—
596C2×C42—173no—
597C2×C42—173no—
598C2×C42—173no—
599C2×C42—173no—
600C2×C42—176no—
601C2×C42—3412no—
602#95—171no—
603#95—173no—
604#95—173no—
605#95—173no—
606#95—171no—
607#95—173no—
608#95—173no—
609#95—176no—
610#95—173no—
611#95—173no—
612#95—173no—
613C17#3429411yescharacteristic, complemented, Sylow
614C24—171no—
615C24—173no—
616#41—24no—
617#41—3412no—
618#41—3412no—
619#41—344no—
620C2×Q8—24no—
621C2×Q8—174no—
622C2×Q8—174no—
623C2×Q8—173no—
624C2×Q8—176no—
625C2×Q8—173no—
626C2×Q8—3412no—
627C2×Q8—346no—
628C2×Q8—346no—
629C2×Q8—3412no—
630C2×Q8—344no—
631C2×Q8C22×#59513yes—
632C2×Q8C22×#59511yescharacteristic
633C2×D4—173no—
634C2×D4—173no—
635C2×D4—176no—
636C2×D4—173no—
637C2×D4—173no—
638C2×D4—346no—
639C2×D4—346no—
640C2×D4—346no—
641C2×D4—346no—
642C2×D4C22×#59513yes—
643C2×D4C22×#59513yes—
644C22×C4—173no—
645C22×C4—171no—
646C22×C4—171no—
647C22×C4—173no—
648C22×C4—173no—
649C22×C4—173no—
650C22×C4—173no—
651C22×C4—173no—
652C22×C4—173no—
653C22×C4—173no—
654C22×C4—171no—
655C22×C4—173no—
656C22×C4—173no—
657C22×C4—171no—
658C22×C4—171no—
659C22×C4—171no—
660C22×C4—173no—
661C22×C4—173no—
662C22×C4—173no—
663C22×C4—346no—
664C22×C4—346no—
665C22×C4—346no—
666C22×C4—346no—
667C22×C4—342no—
668C22×C4—342no—
669C22×C4—346no—
670C22×C4—3412no—
671C22×C4—342no—
672C22×C4—346no—
673C22×C4—683no—
674C22×C4—686no—
675C22×C4—686no—
676C22×C4C22×#59513yes—
677C22×C4C22×#59513yes—
678C4⋊C4—1712no—
679C4⋊C4—173no—
680C4⋊C4—173no—
681C4⋊C4—173no—
682C4⋊C4—176no—
683C4⋊C4—173no—
684C4⋊C4—342no—
685C4⋊C4—346no—
686C4⋊C4—346no—
687C4⋊C4—346no—
688C4⋊C4—3412no—
689C4⋊C4—342no—
690C4⋊C4—346no—
691C4⋊C4—683no—
692C4⋊C4—686no—
693C4⋊C4C22×#59513yes—
694C4⋊C4C22×#59513yes—
695C22⋊C4—171no—
696C22⋊C4—173no—
697C22⋊C4—176no—
698C22⋊C4—171no—
699C22⋊C4—171no—
700C22⋊C4—173no—
701C22⋊C4—173no—
702C22⋊C4—176no—
703C22⋊C4—176no—
704C22⋊C4—346no—
705C22⋊C4—346no—
706C22⋊C4—346no—
707C22⋊C4—342no—
708C22⋊C4—346no—
709C22⋊C4—683no—
710C22⋊C4—686no—
711C22⋊C4C22×#59511yescharacteristic
712C22⋊C4C22×#59513yes—
713C22⋊C4C22×#59516yes—
714C42—1712no—
715C42—173no—
716C42—173no—
717C42—173no—
718C42—346no—
719C42—346no—
720C42—346no—
721C42—346no—
722C42—346no—
723C42—686no—
724C42C22×#59513yes—
725C23—171no—
726C23—172no—
727C23—172no—
728C23—171no—
729C23—173no—
730C23—341no—
731C23—341no—
732C23—341no—
733C23—341no—
734C23—343no—
735C23—343no—
736C23—343no—
737C23—343no—
738C23—343no—
739C23—343no—
740C23C23×#59513yes—
741C23C23×#59511yescharacteristic
742Q8—26no—
743Q8—1712no—
744Q8—3412no—
745Q8—346no—
746Q8D4×#59514yescomplemented
747D4—26no—
748D4—26no—
749D4—346no—
750D4—3412no—
751D4—346no—
752D4—346no—
753D4—346no—
754C2×C4—26no—
755C2×C4—26no—
756C2×C4—173no—
757C2×C4—176no—
758C2×C4—176no—
759C2×C4—172no—
760C2×C4—176no—
761C2×C4—172no—
762C2×C4—171no—
763C2×C4—173no—
764C2×C4—173no—
765C2×C4—171no—
766C2×C4—346no—
767C2×C4—346no—
768C2×C4—343no—
769C2×C4—343no—
770C2×C4—341no—
771C2×C4—341no—
772C2×C4—341no—
773C2×C4—341no—
774C2×C4—343no—
775C2×C4—343no—
776C2×C4—346no—
777C2×C4—346no—
778C2×C4—341no—
779C2×C4—343no—
780C2×C4—341no—
781C2×C4—341no—
782C2×C4—341no—
783C2×C4—343no—
784C2×C4—348no—
785C2×C4—346no—
786C2×C4—346no—
787C2×C4—341no—
788C2×C4—341no—
789C2×C4—343no—
790C2×C4—343no—
791C2×C4—343no—
792C2×C4—343no—
793C2×C4—343no—
794C2×C4—341no—
795C2×C4—341no—
796C2×C4—343no—
797C2×C4—341no—
798C2×C4—343no—
799C2×C4—343no—
800C2×C4—341no—
801C2×C4—343no—
802C2×C4—6812no—
803C2×C4—13612no—
804C2×C4C23×#59511yescharacteristic
805C2×C4C23×#59513yes—
806C2×C4C23×#59513yes—
807C2×C4C23×#59511yescharacteristic
808C2×C4C23×#59513yes—
809C22—21no—
810C22—21no—
811C22—23no—
812C22—23no—
813C22—23no—
814C22—171no—
815C22—171no—
816C22—171no—
817C22—171no—
818C22—171no—
819C22—171no—
820C22—172no—
821C22—342no—
822C22—342no—
823C22—342no—
824C22—342no—
825C22—341no—
826C22—341no—
827C22—343no—
828C22—343no—
829C22—343no—
830C22—683no—
831C22—683no—
832C22—683no—
833C22—683no—
834C22#1176387812yescomplemented
835C22C24×#59511yescharacteristic
836C4—21no—
837C4—23no—
838C4—23no—
839C4—21no—
840C4—176no—
841C4—342no—
842C4—342no—
843C4—346no—
844C4—341no—
845C4—343no—
846C4—343no—
847C4—341no—
848C4—683no—
849C4—683no—
850C4—681no—
851C4—683no—
852C4—681no—
853C4C2×D4×#59516yes—
854C2—22no—
855C2—43no—
856C2—171no—
857C2—171no—
858C2—171no—
859C2—171no—
860C2—342no—
861C2—683no—
862C2C22×D4×#59511yescharacteristic
863C2C2×#1176387811yescharacteristic
864C22−1+4×#59511yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#548C4
prime radicalD17×#548C2
cosocleC22×D17C25
hypercenter#548#595
hypocenterC17#34294
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#11763878C2semidirect
2. C22×Q8×#595C2semidirect
3. #14545315C2semidirect
4. #14545309C2semidirect
5. #14545308C2semidirect
6. Q8×C4⋊#595C2semidirect
7. D4×C4⋊#595C2semidirect
8. #14545289C2semidirect
9. Q8×C22⋊#595C2semidirect
10. #14545274C2semidirect
11. #14545271C2semidirect
12. #121×#595C2semidirect
13. #14545238C2semidirect
14. #14545224C2semidirect
63. #11763471C4semidirect
64. #11763470C4semidirect
65. #11763469C4semidirect
66. #11763468C4semidirect
67. #11763467C4semidirect
68. #11763466C4semidirect
69. #11763465C4semidirect
75. C17×#548C4semidirect
79. C2×#41×C17C2×C4semidirect
80. C22×Q8×C17C2×C4semidirect
83. C2×#63256C2×C4semidirect
86. C2×Q8×D17C2×C4semidirect
87. C2×Q8×D17C2×C4semidirect
90. C2×#63254C2×C4semidirect
93. C2×#63252C2×C4semidirect
96. C22×Dic34C2×C4semidirect
109. Q8×#595D4semidirect
134. C17×#124C2×C4semidirect
135. C17×C22⋊Q8C2×C4semidirect
136. C17×#121C2×C4semidirect
137. C4×Q8×C17C2×C4semidirect
138. C4×D4×C17C2×C4semidirect
139. #10587633C2×C4semidirect
140. #10587632C2×C4semidirect
141. Q8×Dic17C2×C4semidirect
142. #10587625C2×C4semidirect
143. #10587624C2×C4semidirect
144. #10587622C2×C4semidirect
145. D4×Dic17C2×C4semidirect
146. #10587616C2×C4semidirect
147. C4×C22⋊D17C2×C4semidirect
148. C4×C22⋊D17C2×C4semidirect
149. #10587610C2×C4semidirect
150. #10587583C2×C4semidirect
151. #10587582C2×C4semidirect
152. #10587581C2×C4semidirect
153. #10587579C2×C4semidirect
156. #10587573C2×C4semidirect
157. #10587571C2×C4semidirect
158. #10587571C2×C4semidirect
159. #10587570C2×C4semidirect
160. #10587567C2×C4semidirect
161. #10587567C2×C4semidirect
165. #10587564C2×C4semidirect
166. #10587561C2×C4semidirect
167. C4×D68C2×C4semidirect
169. C4×Dic34C2×C4semidirect
338. Q8×C17C4×D4semidirect
376. Dic34C4×D4semidirect
397. C22×C17#520semidirect
412. C2×D17#520semidirect
446. #548#595semidirect
513. C2×#41C2×#595semidirect
521. C22×Q8C2×#595semidirect
534. #124C2×#595semidirect
540. C22⋊Q8C2×#595semidirect
546. #121C2×#595semidirect
556. C4×Q8C2×#595semidirect
567. C4×D4C2×#595semidirect
613. C17#34294semidirect
746. Q8D4×#595semidirect
834. C22#11763878semidirect

Maximal subgroups

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

subgroupindex
C2×#117638782
C22×Q8×#5952
#145453152
#145453092
#145453082
Q8×C4⋊#5952
D4×C4⋊#5952
#145452892
Q8×C22⋊#5952
#145452742
#145452712
#121×#5952
#145452382
#145452242
D17×#5482
#3429417