Finite Group Databasebeta

← #17979158

Subgroups — #17979158

Order 4352.

2912 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763877C211yesmaximal, characteristic, complemented
2C22×Q8×#595C211yesmaximal, characteristic, complemented
3#14545313C213yesmaximal, complemented
4#14545310C213yesmaximal, complemented
5#14545308C213yesmaximal, complemented
6#14545300C213yesmaximal
7#14545299C211yesmaximal, characteristic, complemented
8Q8×C22⋊#595C211yesmaximal, characteristic, complemented
9Q8×C22⋊#595C211yesmaximal, characteristic, complemented
10#14545275C213yesmaximal, complemented
11#14545271C213yesmaximal, complemented
12C22⋊Q8×#595C213yesmaximal, complemented
13#14545238C213yesmaximal
14#14545224C211yesmaximal, characteristic, complemented
15D4×Q8×D17C211yesmaximal, characteristic
16#11763877—28no—
17C2×Q8×#595—28no—
18C2×Q8×#595C2211yescharacteristic
19C2×Q8×#595C2213yes—
20C2×Q8×#595C2211yescharacteristic
21C2×Q8×#595C2213yes—
22C2×Q8×#595C2213yes—
23C2×Q8×#595C2211yescharacteristic
24C2×Q8×#595C2213yes—
25C2×Q8×#595C2211yescharacteristic
26C2×#10587677C2213yes—
27C2×#10587677C2213yes—
28C22×C4⋊#595C2213yes—
29C22×C4×#595C2213yes—
30(C2×#595)⋊Q8C2213yes—
31(C2×#595)⋊Q8C2213yes—
32(C2×#595)⋊Q8C2213yes—
33(C2×#595)⋊Q8C2213yes—
34#11763760C2213yes—
35#11763760C2213yes—
36#11763760C2216yes—
37#11763759C2213yes—
38#11763759C2213yes—
39#11763759C2216yes—
40#11763758C2213yes—
41#11763758C2213yes—
42#11763758C2216yes—
43#11763758C2216yes—
44#11763758C2216yes—
45#11763757C2211yescharacteristic
46#11763757C2213yes—
47#11763756C2213yes—
48#11763756C2213yes—
49#11763753C2213yes—
50#11763751C2213yes—
51#11763751C2213yes—
52C4⋊C4×#595C2213yes—
53C4⋊C4×#595C2213yes—
54C4⋊C4×#595C2216yes—
55C4×C4⋊#595C2213yes—
56C4×C4⋊#595C2213yes—
57C22⋊C4×#595C2216yes—
58C4×C22⋊#595C2213yes—
59C4×C22⋊#595C2213yes—
60#11763745C2213yes—
61C22×Q8×D17C2211yescharacteristic
62C22×Q8×D17C2211yescharacteristic
63Q8×D68C411yescharacteristic, complemented
64D4×Dic34C413yescomplemented
65#11763474C413yescomplemented
66Q8×C22⋊D17C411yescharacteristic, complemented
67Q8×C22⋊D17C411yescharacteristic, complemented
68#11763472C413yescomplemented
69#11763472C413yescomplemented
70C4⋊Q8×D17C2213yes—
71C22⋊Q8×D17C2213yes—
72C22⋊Q8×D17C2213yes—
73C4×Q8×D17C2211yescharacteristic
74C4×D4×D17C2213yes—
75D4×Q8×C17C411yescharacteristic, complemented
76C23×#595C2311yescharacteristic
77C23×#595C2313yes—
78C22×Q8×C17C2×C411yescharacteristic
79C22×Q8×C17C2×C411yescharacteristic, complemented
80C2×Q8×D17—24no—
81C2×Q8×D17—24no—
82C2×Q8×D17—24no—
83C2×Q8×D17—24no—
84C2×Q8×D17C2×C413yes—
85C2×Q8×D17C2×C411yescharacteristic
86C2×Q8×D17C2×C413yescomplemented
87C2×Q8×D17C2×C411yescharacteristic, complemented
88C2×Q8×D17C2313yes—
89C2×Q8×D17C2313yes—
90C2×Q8×D17C2311yescharacteristic
91C2×D4×D17C2311yescharacteristic
92C22×C4×D17C2313yes—
93C22×C4×D17C2313yes—
94C22×Dic34C2×C413yes—
95C22×Dic34C2×C413yescomplemented
96C2×C22⋊#595C2311yescharacteristic
97C2×C22⋊#595C2311yescharacteristic
98C2×C22⋊#595C2313yes—
99C2×C22⋊#595C2311yescharacteristic
100C2×C22⋊#595C2313yes—
101C2×C22⋊#595C2313yes—
102Q8×#595—24no—
103Q8×#595—24no—
104Q8×#595—24no—
105Q8×#595—212no—
106Q8×#595—212no—
107Q8×#595—212no—
108Q8×#595—212no—
109Q8×#595D418yescomplemented
110#10587677—212no—
111#10587677—212no—
112C2×C4⋊#595—212no—
113C2×C4⋊#595C2313yes—
114C2×C4⋊#595C2313yes—
115C2×C4⋊#595C2313yes—
116C2×C4⋊#595C2313yes—
117C2×C4⋊#595C2313yes—
118C2×C4⋊#595C2313yes—
119C2×C4⋊#595C2316yes—
120C2×C4⋊#595C2313yes—
121C2×C4⋊#595C2313yes—
122C2×C4×#595—212no—
123C2×C4×#595C2313yes—
124C2×C4×#595C2313yes—
125C2×C4×#595C2313yes—
126C2×C4×#595C2316yes—
127C2×C4×#595C2313yes—
128C2×C4×#595C2313yes—
129C2×C4×#595C2316yes—
130C2×C4×#595C2313yes—
131C17×C4⋊Q8C2×C413yescomplemented
132C17×C22⋊Q8C2×C413yes—
133C17×C22⋊Q8C2×C413yescomplemented
134C4×Q8×C17C2×C411yescharacteristic, complemented
135C4×D4×C17C2×C413yes—
136#10587632C2×C413yes—
137#10587632C2×C413yescomplemented
138Q8×Dic17C2×C411yescharacteristic, complemented
139#10587630C2×C413yescomplemented
140#10587630C2×C413yescomplemented
141D4×Dic17C2×C413yes—
142C4×C22⋊D17C2×C413yes—
143C4×C22⋊D17C2×C413yes—
144#10587610C2×C413yes—
145#10587610C2×C413yescomplemented
146#10587583C2×C413yes—
147#10587583C2×C413yescomplemented
148#10587582C2×C416yes—
149#10587582C2×C416yescomplemented
150#10587579C2×C413yes—
151C4⋊C4×D17C2313yes—
152C4⋊C4×D17C2316yes—
153C4⋊C4×D17C2313yes—
154#10587574C2×C416yescomplemented
155#10587574C2×C416yescomplemented
156#10587573C2×C413yescomplemented
157#10587567C2×C413yes—
158#10587567C2×C413yes—
159C22⋊C4×D17C2313yes—
160C22⋊C4×D17C2313yes—
161#10587564C2×C416yes—
162#10587564C2×C416yescomplemented
163C4×D68C2×C413yes—
164C42×D17C2313yes—
165#10587555C2×C413yescomplemented
166C4×Dic34C2×C413yescomplemented
167(C2×#595)⋊C4C2311yescharacteristic
168(C2×#595)⋊C4C2313yes—
169(C2×#595)⋊C4C2313yes—
170(C2×#595)⋊C4C2313yes—
171(C2×#595)⋊C4C2313yes—
172(C2×#595)⋊C4C2313yes—
173(C2×#595)⋊C4C2313yes—
174(C2×#595)⋊C4C2313yes—
175(C2×#595)⋊C4C2316yes—
176(C2×#595)⋊C4C2316yes—
177(C2×#595)⋊C4C2311yescharacteristic
178(C2×#595)⋊C4C2313yes—
179(C2×#595)⋊C4C2316yes—
180C23×D17C2411yescharacteristic
181C23×D17C2411yescharacteristic
182C22×#595—22no—
183C22×#595—22no—
184C22×#595—22no—
185C22×#595—26no—
186C22×#595—26no—
187C22×#595—43no—
188C22×#595C2411yescharacteristic
189C22×#595C2413yes—
190C22×#595C2413yes—
191C22×#595C2411yescharacteristic
192C22×#595C2413yes—
193C22×#595C2413yes—
194C22×#595C2411yescharacteristic
195C22×#595C2411yescharacteristic
196C2×Q8×C17—24no—
197C2×Q8×C17—24no—
198C2×Q8×C17C22×C413yes—
199C2×Q8×C17C22×C413yes—
200C2×Q8×C17C22×C411yescharacteristic
201C2×D4×C17C22×C411yescharacteristic
202C22×C4×C17C22×C413yes—
203C22×C4×C17C22×C413yes—
204C2×C22⋊D17C22×C411yescharacteristic
205C2×C22⋊D17C22×C411yescharacteristic
206C22×Dic17C22×C413yes—
207C22×Dic17C22×C413yes—
208Q8×D17—24no—
209Q8×D17—24no—
210Q8×D17—26no—
211Q8×D17—26no—
212Q8×D17—26no—
213Q8×D17—26no—
214Q8×D17—212no—
215Q8×D17—212no—
216Q8×D17C2×D414yes—
217Q8×D17#4114yes—
218D4×D17—22no—
219D4×D17—22no—
220C2×D68C22×C411yescharacteristic
221C2×C4×D17—26no—
222C2×C4×D17—26no—
223C2×C4×D17—26no—
224C2×C4×D17—26no—
225C2×C4×D17C22×C413yes—
226C2×C4×D17C22×C413yes—
227C2×C4×D17C22×C413yes—
228C2×C4×D17C22×C413yes—
229C2×C4×D17C2413yes—
230C2×C4×D17C2413yes—
231C2×C4×D17C2413yes—
232C2×C4×D17C2411yescharacteristic
233C2×C4×D17C2413yes—
234C2×Dic34—212no—
235C2×Dic34—212no—
236C2×Dic34C22×C413yes—
237C2×Dic34C22×C416yes—
238C2×Dic34C22×C413yes—
239C2×Dic34C22×C416yes—
240C2×Dic34C22×C413yes—
241C22⋊#595—26no—
242C22⋊#595—22no—
243C22⋊#595—22no—
244C22⋊#595—26no—
245C22⋊#595—22no—
246C22⋊#595—43no—
247C4⋊#595—212no—
248C4⋊#595—26no—
249C4⋊#595—26no—
250C4⋊#595—26no—
251C4⋊#595—26no—
252C4⋊#595—26no—
253C4⋊#595—26no—
254C4⋊#595—43no—
255C4⋊#595C2×D4112yes—
256C4×#595—26no—
257C4×#595—26no—
258C4×#595—212no—
259C4×#595—26no—
260C4×#595—26no—
261C4×#595—26no—
262C4×#595—46no—
263C4×#595C2×D4112yes—
264C4⋊C4×C17C22×C416yes—
265C4⋊C4×C17C22×C413yes—
266C4⋊C4×C17C22×C413yes—
267C22⋊C4×C17C22×C413yes—
268C22⋊C4×C17C22×C413yes—
269C42×C17C22×C413yes—
270C22⋊Dic17C22×C413yes—
271C22⋊Dic17C22×C413yes—
272#63227C22×C413yes—
273#63227C22×C413yes—
274#63227C22×C413yes—
275#63227C22×C413yes—
276C4⋊Dic17C22×C413yes—
277C4⋊Dic17C22×C413yes—
278C4⋊Dic17C22×C416yes—
279#63225C22×C416yes—
280#63225C22×C416yes—
281#63225C22×C416yes—
282#63225C22×C413yes—
283#63225C22×C413yes—
284C4×Dic17C22×C413yes—
285C4×Dic17C22×C413yes—
286C4×Dic17C22×C413yes—
287#34291—171nomaximal, Sylow
288C23×C17C23×C411yescharacteristic
289C23×C17C23×C411yescharacteristic
290C22×D17—21no—
291C22×D17—21no—
292C22×D17—21no—
293C22×D17—21no—
294C22×D17—21no—
295C22×D17—21no—
296C22×D17—21no—
297C22×D17—21no—
298C22×D17—21no—
299C22×D17—21no—
300C22×D17C23×C411yescharacteristic
301C22×D17C23×C411yescharacteristic
302C22×D172−1+412yes—
303C22×D172−1+412yes—
304C22×D17C2511yescharacteristic
305C2×#595—28no—
306C2×#595—21no—
307C2×#595—21no—
308C2×#595—21no—
309C2×#595—21no—
310C2×#595—23no—
311C2×#595—23no—
312C2×#595—23no—
313C2×#595—21no—
314C2×#595—23no—
315C2×#595—21no—
316C2×#595—23no—
317C2×#595—23no—
318C2×#595—23no—
319C2×#595—21no—
320C2×#595—23no—
321C2×#595—21no—
322C2×#595—21no—
323C2×#595—23no—
324C2×#595—23no—
325C2×#595—21no—
326C2×#595—23no—
327C2×#595—412no—
328C2×#595C22×D412yes—
329C2×#595C22×D416yes—
330C2×#5952−1+412yes—
331Q8×C17—26no—
332Q8×C17—26no—
333Q8×C17C4×D414yes—
334D4×C17—22no—
335C2×C4×C17—26no—
336C2×C4×C17—26no—
337C2×C4×C17C23×C411yescharacteristic
338C2×C4×C17C23×C413yes—
339C2×C4×C17C23×C413yes—
340C2×C4×C17C23×C413yes—
341C2×C4×C17C23×C413yes—
342C22⋊D17—22no—
343C22⋊D17—22no—
344C2×Dic17—26no—
345C2×Dic17—26no—
346C2×Dic17C23×C413yes—
347C2×Dic17C23×C413yes—
348C2×Dic17C23×C413yes—
349C2×Dic17C23×C411yescharacteristic
350C2×Dic17C23×C413yes—
351D68—22no—
352C4×D17—23no—
353C4×D17—23no—
354C4×D17—23no—
355C4×D17—23no—
356C4×D17—23no—
357C4×D17—21no—
358C4×D17—21no—
359C4×D17—23no—
360C4×D17—26no—
361C4×D17—26no—
362C4×D17—26no—
363C4×D17—26no—
364C4×D17C22×D416yes—
365C4×D17C2×#4116yes—
366Dic34—26no—
367Dic34—26no—
368Dic34—212no—
369Dic34—212no—
370Dic34C4×D4112yes—
371C2×D4×Q8—171no—
372C2×#519—171no—
373C22×C4×Q8—171no—
374#2365—173no—
375#2362—173no—
376#2360—173no—
377#2352—173no—
378#2351—171no—
379Q8×C22⋊C4—171no—
380Q8×C22⋊C4—171no—
381#2327—173no—
382#2323—173no—
383C4×C22⋊Q8—173no—
384#2290—173no—
385#2276—171no—
386C22×C17—21no—
387C22×C17—21no—
388C22×C17—21no—
389C22×C17—21no—
390C22×C17—21no—
391C22×C17#51912yescomplemented
392C22×C17C24×C411yescharacteristic
393C2×D17—21no—
394C2×D17—21no—
395C2×D17—22no—
396C2×D17—22no—
397C2×D17—22no—
398C2×D17—22no—
399C2×D17—21no—
400C2×D17—21no—
401C2×D17—21no—
402C2×D17—41no—
403C2×D17—41no—
404C2×D17—41no—
405C2×D17—41no—
406C2×D17#51912yescomplemented
407C2×D17C23×D411yescharacteristic
408C2×D17C22×#4111yescharacteristic
409C2×D17C2×2−1+411yescharacteristic
410C2×D17C2×2−1+411yescharacteristic
411C2×D17C2×2−1+411yescharacteristic
412C2×D17#58511yescharacteristic
413#595—22no—
414#595—22no—
415#595—26no—
416#595—43no—
417#595—41no—
418#595—43no—
419#595—43no—
420#595—41no—
421C4×C17—23no—
422C4×C17—23no—
423C4×C17—21no—
424C4×C17—23no—
425C4×C17C2×C4×D416yes—
426Dic17—23no—
427Dic17—23no—
428Dic17—21no—
429Dic17—23no—
430Dic17C2×C4×D416yes—
431C23×Q8—171no—
432C23×Q8—171no—
433D4×Q8—171no—
434D4×Q8—171no—
435D4×Q8—173no—
436D4×Q8—173no—
437D4×Q8—173no—
438D4×Q8—171no—
439D4×Q8—173no—
440D4×Q8#59511yescharacteristic, complemented
441C2×C4⋊Q8—173no—
442C2×C22⋊Q8—173no—
443C2×C22⋊Q8—173no—
444#519—348no—
445C2×C4×Q8—171no—
446C2×C4×Q8—171no—
447C2×C4×Q8—173no—
448C2×C4×Q8—173no—
449C2×C4×Q8—171no—
450C2×C4×Q8—171no—
451C2×C4×Q8—171no—
452C2×C4×Q8—173no—
453C2×C4×Q8—173no—
454C2×C4×Q8—348no—
455C2×C4×D4—173no—
456C2×#117—173no—
457C2×#117—173no—
458C22×C4⋊C4—173no—
459C22×C42—173no—
460#391—173no—
461#391—173no—
462#391—173no—
463#391—173no—
464#389—173no—
465#389—176no—
466#389—173no—
467#388—173no—
468#388—176no—
469#388—173no—
470#387—176no—
471#387—173no—
472#387—176no—
473#387—176no—
474#387—173no—
475#386—173no—
476#386—171no—
477#385—173no—
478#385—173no—
479#382—173no—
480#380—173no—
481#380—173no—
482C4×C4⋊C4—173no—
483C4×C4⋊C4—173no—
484C4×C4⋊C4—173no—
485C4×C4⋊C4—173no—
486C4×C4⋊C4—176no—
487C4×C22⋊C4—173no—
488C4×C22⋊C4—173no—
489C4×C22⋊C4—176no—
490#376—173no—
491C2×C17—22no—
492C2×C17—41no—
493C2×C17C22×C4×D411yescharacteristic
494C2×C17C2×#51911yescharacteristic
495C2×C17C4×2−1+411yescharacteristic
496D17—22no—
497D17—41no—
498D17#348611yescharacteristic
499D17#348911yescharacteristic
500D17#351611yescharacteristic
501D17#352311yescharacteristic
502C22×Q8—171no—
503C22×Q8—173no—
504C22×Q8—173no—
505C22×Q8—173no—
506C22×Q8—171no—
507C22×Q8—173no—
508C22×Q8—171no—
509C22×Q8—173no—
510C22×Q8—173no—
511C22×Q8—344no—
512C22×Q8—344no—
513C22×Q8—344no—
514C22×Q8—344no—
515C22×Q8C2×#59511yescharacteristic
516C22×Q8C2×#59511yescharacteristic, complemented
517C22×D4—171no—
518C23×C4—173no—
519C23×C4—173no—
520C23×C4—171no—
521C23×C4—173no—
522C4⋊Q8—173no—
523C4⋊Q8—173no—
524C4⋊Q8—176no—
525C4⋊Q8—176no—
526C4⋊Q8—173no—
527C4⋊Q8C2×#59513yescomplemented
528C22⋊Q8—173no—
529C22⋊Q8—173no—
530C22⋊Q8—173no—
531C22⋊Q8—173no—
532C22⋊Q8—176no—
533C22⋊Q8—176no—
534C22⋊Q8—173no—
535C22⋊Q8—173no—
536C22⋊Q8—176no—
537C22⋊Q8—176no—
538C22⋊Q8C2×#59513yes—
539C22⋊Q8C2×#59513yescomplemented
540C4×Q8—178no—
541C4×Q8—171no—
542C4×Q8—173no—
543C4×Q8—173no—
544C4×Q8—3412no—
545C4×Q8—3412no—
546C4×Q8—3412no—
547C4×Q8—3412no—
548C4×Q8—344no—
549C4×Q8—344no—
550C4×Q8—344no—
551C4×Q8C2×#59511yescharacteristic, complemented
552C4×D4—173no—
553C4×D4—173no—
554C4×D4—173no—
555C4×D4—173no—
556C4×D4—173no—
557C4×D4—173no—
558C4×D4—173no—
559C4×D4C2×#59513yes—
560#117—3412no—
561#117—3412no—
562C2×C4⋊C4—173no—
563C2×C4⋊C4—173no—
564C2×C4⋊C4—173no—
565C2×C4⋊C4—176no—
566C2×C4⋊C4—173no—
567C2×C4⋊C4—176no—
568C2×C4⋊C4—173no—
569C2×C4⋊C4—173no—
570C2×C4⋊C4—173no—
571C2×C4⋊C4—173no—
572C2×C4⋊C4—173no—
573C2×C4⋊C4—173no—
574C2×C4⋊C4—3412no—
575C2×C22⋊C4—173no—
576C2×C22⋊C4—173no—
577C2×C22⋊C4—171no—
578C2×C22⋊C4—173no—
579C2×C22⋊C4—173no—
580C2×C22⋊C4—171no—
581C2×C22⋊C4—171no—
582C2×C22⋊C4—173no—
583C2×C42—173no—
584C2×C42—173no—
585C2×C42—176no—
586C2×C42—173no—
587C2×C42—173no—
588C2×C42—173no—
589C2×C42—173no—
590C2×C42—173no—
591C2×C42—176no—
592C2×C42—3412no—
593#95—171no—
594#95—173no—
595#95—173no—
596#95—173no—
597#95—173no—
598#95—176no—
599#95—176no—
600#95—173no—
601#95—173no—
602#95—173no—
603#95—171no—
604#95—176no—
605#95—173no—
606C17#3429111yescharacteristic, complemented, Sylow
607C24—171no—
608C24—171no—
609C2×Q8—24no—
610C2×Q8—24no—
611C2×Q8—174no—
612C2×Q8—174no—
613C2×Q8—173no—
614C2×Q8—176no—
615C2×Q8—176no—
616C2×Q8—173no—
617C2×Q8—173no—
618C2×Q8—3412no—
619C2×Q8—3412no—
620C2×Q8—346no—
621C2×Q8—346no—
622C2×Q8—346no—
623C2×Q8—346no—
624C2×Q8—3412no—
625C2×Q8—3412no—
626C2×Q8—344no—
627C2×Q8—344no—
628C2×Q8C22×#59513yes—
629C2×Q8C22×#59513yes—
630C2×Q8C22×#59511yescharacteristic
631C2×D4—171no—
632C2×D4—171no—
633C2×D4—171no—
634C2×D4—342no—
635C2×D4—342no—
636C2×D4C22×#59511yescharacteristic
637C22×C4—173no—
638C22×C4—171no—
639C22×C4—171no—
640C22×C4—173no—
641C22×C4—173no—
642C22×C4—173no—
643C22×C4—173no—
644C22×C4—173no—
645C22×C4—173no—
646C22×C4—173no—
647C22×C4—171no—
648C22×C4—173no—
649C22×C4—173no—
650C22×C4—173no—
651C22×C4—171no—
652C22×C4—173no—
653C22×C4—173no—
654C22×C4—173no—
655C22×C4—171no—
656C22×C4—346no—
657C22×C4—346no—
658C22×C4—346no—
659C22×C4—346no—
660C22×C4—342no—
661C22×C4—342no—
662C22×C4—346no—
663C22×C4—342no—
664C22×C4—346no—
665C22×C4—683no—
666C22×C4C22×#59513yes—
667C22×C4C22×#59513yes—
668C4⋊C4—1712no—
669C4⋊C4—173no—
670C4⋊C4—173no—
671C4⋊C4—173no—
672C4⋊C4—176no—
673C4⋊C4—173no—
674C4⋊C4—176no—
675C4⋊C4—176no—
676C4⋊C4—176no—
677C4⋊C4—346no—
678C4⋊C4—346no—
679C4⋊C4—3412no—
680C4⋊C4—346no—
681C4⋊C4—346no—
682C4⋊C4—346no—
683C4⋊C4—346no—
684C4⋊C4—683no—
685C4⋊C4C22×#59513yes—
686C4⋊C4C22×#59513yes—
687C4⋊C4C22×#59516yes—
688C22⋊C4—173no—
689C22⋊C4—173no—
690C22⋊C4—173no—
691C22⋊C4—173no—
692C22⋊C4—173no—
693C22⋊C4—173no—
694C22⋊C4—342no—
695C22⋊C4—342no—
696C22⋊C4—346no—
697C22⋊C4—346no—
698C22⋊C4—342no—
699C22⋊C4—683no—
700C22⋊C4C22×#59513yes—
701C22⋊C4C22×#59513yes—
702C42—1712no—
703C42—173no—
704C42—173no—
705C42—173no—
706C42—346no—
707C42—346no—
708C42—346no—
709C42—346no—
710C42—3412no—
711C42—346no—
712C42—686no—
713C42C22×#59513yes—
714C23—171no—
715C23—172no—
716C23—172no—
717C23—171no—
718C23—171no—
719C23—341no—
720C23—341no—
721C23—341no—
722C23—341no—
723C23—341no—
724C23—341no—
725C23—341no—
726C23—341no—
727C23—341no—
728C23—341no—
729C23C23×#59511yescharacteristic
730C23C23×#59511yescharacteristic
731Q8—26no—
732Q8—26no—
733Q8—1712no—
734Q8—3412no—
735Q8—3412no—
736Q8—346no—
737Q8—346no—
738Q8D4×#59514yes—
739D4—22no—
740D4—342no—
741D4—342no—
742D4—342no—
743C2×C4—26no—
744C2×C4—26no—
745C2×C4—173no—
746C2×C4—176no—
747C2×C4—176no—
748C2×C4—172no—
749C2×C4—176no—
750C2×C4—172no—
751C2×C4—171no—
752C2×C4—173no—
753C2×C4—173no—
754C2×C4—173no—
755C2×C4—346no—
756C2×C4—346no—
757C2×C4—343no—
758C2×C4—343no—
759C2×C4—343no—
760C2×C4—343no—
761C2×C4—343no—
762C2×C4—343no—
763C2×C4—341no—
764C2×C4—341no—
765C2×C4—346no—
766C2×C4—346no—
767C2×C4—341no—
768C2×C4—343no—
769C2×C4—341no—
770C2×C4—341no—
771C2×C4—341no—
772C2×C4—343no—
773C2×C4—348no—
774C2×C4—346no—
775C2×C4—346no—
776C2×C4—343no—
777C2×C4—341no—
778C2×C4—341no—
779C2×C4—343no—
780C2×C4—343no—
781C2×C4—343no—
782C2×C4—341no—
783C2×C4—343no—
784C2×C4—343no—
785C2×C4—341no—
786C2×C4—341no—
787C2×C4—343no—
788C2×C4—343no—
789C2×C4—341no—
790C2×C4—343no—
791C2×C4—6812no—
792C2×C4C23×#59511yescharacteristic
793C2×C4C23×#59513yes—
794C2×C4C23×#59513yes—
795C2×C4C23×#59513yes—
796C2×C4C23×#59513yes—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—171no—
803C22—171no—
804C22—171no—
805C22—171no—
806C22—171no—
807C22—171no—
808C22—172no—
809C22—342no—
810C22—342no—
811C22—342no—
812C22—342no—
813C22—341no—
814C22—341no—
815C22—341no—
816C22—341no—
817C22—341no—
818C22—681no—
819C22—681no—
820C22—681no—
821C22—681no—
822C22#1176387712yescomplemented
823C22C24×#59511yescharacteristic
824C4—23no—
825C4—23no—
826C4—21no—
827C4—23no—
828C4—176no—
829C4—342no—
830C4—342no—
831C4—346no—
832C4—343no—
833C4—343no—
834C4—341no—
835C4—343no—
836C4—683no—
837C4—681no—
838C4—683no—
839C4—683no—
840C4—681no—
841C4C2×D4×#59516yes—
842C2—22no—
843C2—41no—
844C2—171no—
845C2—171no—
846C2—171no—
847C2—171no—
848C2—342no—
849C2—681no—
850C2C22×D4×#59511yescharacteristic
851C2C2×#1176387711yescharacteristic
852C22−1+4×#59511yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingD4×Q8×C17C4
prime radicalC2×D4×D17C23
cosocleC22×D17C25
hypercenterD4×Q8#595
hypocenterC17#34291
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11763877C2semidirect
2. C22×Q8×#595C2semidirect
3. #14545313C2semidirect
4. #14545310C2semidirect
5. #14545308C2semidirect
7. #14545299C2semidirect
8. Q8×C22⋊#595C2semidirect
9. Q8×C22⋊#595C2semidirect
10. #14545275C2semidirect
11. #14545271C2semidirect
12. C22⋊Q8×#595C2semidirect
14. #14545224C2semidirect
63. Q8×D68C4semidirect
64. D4×Dic34C4semidirect
65. #11763474C4semidirect
66. Q8×C22⋊D17C4semidirect
67. Q8×C22⋊D17C4semidirect
68. #11763472C4semidirect
69. #11763472C4semidirect
75. D4×Q8×C17C4semidirect
79. C22×Q8×C17C2×C4semidirect
86. C2×Q8×D17C2×C4semidirect
87. C2×Q8×D17C2×C4semidirect
95. C22×Dic34C2×C4semidirect
109. Q8×#595D4semidirect
131. C17×C4⋊Q8C2×C4semidirect
133. C17×C22⋊Q8C2×C4semidirect
134. C4×Q8×C17C2×C4semidirect
137. #10587632C2×C4semidirect
138. Q8×Dic17C2×C4semidirect
139. #10587630C2×C4semidirect
140. #10587630C2×C4semidirect
145. #10587610C2×C4semidirect
147. #10587583C2×C4semidirect
149. #10587582C2×C4semidirect
154. #10587574C2×C4semidirect
155. #10587574C2×C4semidirect
156. #10587573C2×C4semidirect
162. #10587564C2×C4semidirect
165. #10587555C2×C4semidirect
166. C4×Dic34C2×C4semidirect
391. C22×C17#519semidirect
406. C2×D17#519semidirect
440. D4×Q8#595semidirect
516. C22×Q8C2×#595semidirect
527. C4⋊Q8C2×#595semidirect
539. C22⋊Q8C2×#595semidirect
551. C4×Q8C2×#595semidirect
606. C17#34291semidirect
822. C22#11763877semidirect

Maximal subgroups

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

subgroupindex
C2×#117638772
C22×Q8×#5952
#145453132
#145453102
#145453082
#145453002
#145452992
Q8×C22⋊#5952
#145452752
#145452712
C22⋊Q8×#5952
#145452382
#145452242
D4×Q8×D172
#3429117