Finite Group Databasebeta

← #17979162

Subgroups — #17979162

Order 4352.

3200 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×#11763878C211yesmaximal, characteristic, complemented
2C2×#41×#595C211yesmaximal, characteristic, complemented
3#14545314C213yesmaximal, complemented
4#14545311C213yesmaximal, complemented
5#14545309C213yesmaximal, complemented
6#14545300C213yesmaximal, complemented
7#14545299C211yesmaximal, characteristic, complemented
8#14545289C211yesmaximal, characteristic, complemented
9#14545289C211yesmaximal, characteristic, complemented
10#14545276C213yesmaximal, complemented
11#14545272C213yesmaximal, complemented
12#121×#595C213yesmaximal, complemented
13#14545238C213yesmaximal, complemented
14#14545224C211yesmaximal, characteristic, complemented
15D17×#550C211yesmaximal, characteristic
16#11763878—28no—
17#41×#595—28no—
18C2×Q8×#595C2211yescharacteristic
19C2×Q8×#595C2211yescharacteristic
20C2×Q8×#595C2211yescharacteristic
21C2×Q8×#595C2211yescharacteristic
22C2×D4×#595C2213yes—
23C2×D4×#595C2213yes—
24C2×D4×#595C2213yes—
25C2×D4×#595C2213yes—
26C2×D4×#595C2216yes—
27C2×#10587677C2213yes—
28C2×#10587677C2213yes—
29C22×C4⋊#595C2213yes—
30C22×C4×#595C2213yes—
31#11763761C2213yes—
32#11763761C2213yes—
33#11763761C2216yes—
34#11763761C2213yes—
35#11763761C2213yes—
36#11763760C2213yes—
37#11763760C2213yes—
38#11763759C2213yes—
39#11763759C2213yes—
40#11763759C2216yes—
41#11763758C2211yescharacteristic
42#11763758C2213yes—
43#11763757C2213yes—
44#11763757C2213yes—
45#11763757C2216yes—
46#11763757C2216yes—
47#11763757C2216yes—
48#11763756C2213yes—
49#11763756C2213yes—
50#11763753C2213yes—
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
62C2×#41×D17C2211yescharacteristic
63#11763481C411yescharacteristic, complemented
64#11763480C413yescomplemented
65#11763479C413yescomplemented
66#11763478C411yescharacteristic, complemented
67#11763478C411yescharacteristic, complemented
68#11763477C413yescomplemented
69#11763477C413yescomplemented
70#127×D17C2213yes—
71#121×D17C2213yes—
72#121×D17C2213yes—
73C4×Q8×D17C2211yescharacteristic
74C4×D4×D17C2213yes—
75C17×#550C411yescharacteristic, complemented
76C23×#595C2313yes—
77C23×#595C2316yes—
78C23×#595C2313yes—
79C2×#41×C17C2×C411yescharacteristic, complemented
80C2×#41×C17C2×C411yescharacteristic, complemented
81#41×D17—24no—
82#41×D17—24no—
83#41×D17—24no—
84#41×D17—24no—
85C2×#63256C2×C411yescharacteristic, complemented
86C2×#63256C2×C411yescharacteristic, complemented
87C2×Q8×D17C2311yescharacteristic
88C2×#63254C2×C413yescomplemented
89C2×#63254C2×C413yescomplemented
90C2×D4×D17C2313yes—
91C2×D4×D17C2313yes—
92C2×D4×D17C2313yes—
93C2×D4×D17C2316yes—
94C2×#63252C2×C413yescomplemented
95C2×#63252C2×C413yescomplemented
96C22×C4×D17C2313yes—
97C22×C4×D17C2313yes—
98C2×C22⋊#595C2313yes—
99C2×C22⋊#595C2313yes—
100C2×C22⋊#595C2316yes—
101C2×C22⋊#595C2313yes—
102C2×C22⋊#595C2313yes—
103C2×C22⋊#595C2313yes—
104C2×C22⋊#595C2313yes—
105C2×C22⋊#595C2316yes—
106C2×C22⋊#595C2316yes—
107Q8×#595—24no—
108Q8×#595—24no—
109Q8×#595—24no—
110Q8×#595D418yescomplemented
111D4×#595—212no—
112D4×#595—212no—
113D4×#595—212no—
114D4×#595—212no—
115D4×#595—412no—
116#10587677—212no—
117#10587677—212no—
118C2×C4⋊#595—212no—
119C2×C4⋊#595C2313yes—
120C2×C4⋊#595C2313yes—
121C2×C4⋊#595C2313yes—
122C2×C4⋊#595C2313yes—
123C2×C4⋊#595C2311yescharacteristic
124C2×C4⋊#595C2313yes—
125C2×C4⋊#595C2313yes—
126C2×C4⋊#595C2313yes—
127C2×C4×#595—212no—
128C2×C4×#595C2313yes—
129C2×C4×#595C2313yes—
130C2×C4×#595C2313yes—
131C2×C4×#595C2313yes—
132C2×C4×#595C2311yescharacteristic
133C2×C4×#595C2316yes—
134C2×C4×#595C2313yes—
135C17×#127C2×C413yescomplemented
136C17×#121C2×C413yescomplemented
137C17×#121C2×C413yescomplemented
138C4×Q8×C17C2×C411yescharacteristic, complemented
139C4×D4×C17C2×C413yescomplemented
140Q8×Dic17C2×C411yescharacteristic, complemented
141#10587626C2×C416yescomplemented
142#10587626C2×C413yescomplemented
143#10587626C2×C413yescomplemented
144#10587626C2×C416yescomplemented
145#10587625C2×C416yescomplemented
146#10587625C2×C416yescomplemented
147#10587624C2×C413yescomplemented
148#10587624C2×C413yescomplemented
149D4×Dic17C2×C413yescomplemented
150#10587616C2×C413yescomplemented
151#10587616C2×C413yescomplemented
152C4×C22⋊D17C2×C413yescomplemented
153C4×C22⋊D17C2×C413yescomplemented
154#10587581C2×C413yescomplemented
155#10587581C2×C413yescomplemented
156#10587579C2×C413yescomplemented
157C4⋊C4×D17C2313yes—
158C4⋊C4×D17C2311yescharacteristic
159#10587573C2×C413yescomplemented
160#10587570C2×C416yescomplemented
161#10587570C2×C416yescomplemented
162#10587567C2×C413yescomplemented
163#10587567C2×C413yescomplemented
164C22⋊C4×D17C2313yes—
165C22⋊C4×D17C2313yes—
166#10587560C2×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)⋊C4C2311yescharacteristic
176(C2×#595)⋊C4C2313yes—
177(C2×#595)⋊C4C2313yes—
178(C2×#595)⋊C4C2316yes—
179(C2×#595)⋊C4C2311yescharacteristic
180(C2×#595)⋊C4C2313yes—
181C23×D17C2413yes—
182C23×D17C2413yes—
183C22×#595—26no—
184C22×#595—26no—
185C22×#595—26no—
186C22×#595—212no—
187C22×#595—43no—
188C22×#595—43no—
189C22×#595—43no—
190C22×#595—46no—
191C22×#595—46no—
192C22×#595C2411yescharacteristic
193C22×#595C2413yes—
194C22×#595C2411yescharacteristic
195C22×#595C2413yes—
196C22×#595C2413yes—
197C22×#595C2413yes—
198C22×#595C2411yescharacteristic
199C22×#595C2411yescharacteristic
200#41×C17—24no—
201#41×C17—24no—
202C2×Q8×C17C22×C411yescharacteristic
203C2×D4×C17C22×C413yes—
204C2×D4×C17C22×C413yes—
205C2×D4×C17C22×C413yes—
206C2×D4×C17C22×C416yes—
207C22×C4×C17C22×C413yes—
208C22×C4×C17C22×C413yes—
209C2×C22⋊D17C22×C416yes—
210C2×C22⋊D17C22×C416yes—
211C2×C22⋊D17C22×C413yes—
212C2×C22⋊D17C22×C413yes—
213C2×C22⋊D17C22×C416yes—
214C2×C22⋊D17C22×C416yes—
215C22×Dic17C22×C413yes—
216C22×Dic17C22×C413yes—
217#63256—24no—
218#63256—24no—
219Q8×D17C2×D414yes—
220Q8×D17#4114yes—
221#63254—212no—
222#63254—212no—
223D4×D17—26no—
224D4×D17—26no—
225D4×D17—26no—
226D4×D17—26no—
227D4×D17—46no—
228D4×D17—46no—
229D4×D17—43no—
230D4×D17—43no—
231#63252—212no—
232#63252—212no—
233C2×D68C22×C413yes—
234C2×D68C22×C413yes—
235C2×D68C22×C413yes—
236C2×D68C22×C416yes—
237C2×C4×D17—26no—
238C2×C4×D17—26no—
239C2×C4×D17—26no—
240C2×C4×D17—26no—
241C2×C4×D17C22×C413yes—
242C2×C4×D17C22×C413yes—
243C2×C4×D17C22×C413yes—
244C2×C4×D17C22×C413yes—
245C2×C4×D17C2411yescharacteristic
246C2×C4×D17C2413yes—
247C2×C4×D17C2411yescharacteristic
248C2×C4×D17C2411yescharacteristic
249C2×C4×D17C2413yes—
250C2×Dic34C22×C413yes—
251C22⋊#595—26no—
252C22⋊#595—212no—
253C22⋊#595—26no—
254C22⋊#595—26no—
255C22⋊#595—46no—
256C22⋊#595—43no—
257C22⋊#595—43no—
258C22⋊#595—46no—
259C22⋊#595—43no—
260C4⋊#595—26no—
261C4⋊#595—22no—
262C4⋊#595—26no—
263C4⋊#595—26no—
264C4⋊#595—26no—
265C4⋊#595—26no—
266C4⋊#595—43no—
267C4⋊#595C2×D4112yes—
268C4×#595—22no—
269C4×#595—26no—
270C4×#595—26no—
271C4×#595—26no—
272C4×#595—26no—
273C4×#595—46no—
274C4×#595C2×D4112yes—
275C4⋊C4×C17C22×C413yes—
276C4⋊C4×C17C22×C411yescharacteristic
277C22⋊C4×C17C22×C413yes—
278C22⋊C4×C17C22×C413yes—
279C42×C17C22×C413yes—
280C22⋊Dic17C22×C413yes—
281C22⋊Dic17C22×C413yes—
282#63227C22×C413yes—
283#63227C22×C413yes—
284#63227C22×C413yes—
285#63227C22×C413yes—
286C4⋊Dic17C22×C413yes—
287C4⋊Dic17C22×C411yescharacteristic
288#63225C22×C416yes—
289#63225C22×C411yescharacteristic
290#63225C22×C411yescharacteristic
291C4×Dic17C22×C413yes—
292C4×Dic17C22×C413yes—
293C4×Dic17C22×C413yes—
294#34295—171nomaximal, Sylow
295C23×C17C23×C413yes—
296C23×C17C23×C413yes—
297C22×D17—23no—
298C22×D17—23no—
299C22×D17—23no—
300C22×D17—23no—
301C22×D17—23no—
302C22×D17—23no—
303C22×D17—23no—
304C22×D17—23no—
305C22×D17—23no—
306C22×D17—23no—
307C22×D17—23no—
308C22×D17—23no—
309C22×D17C23×C413yes—
310C22×D17C23×C413yes—
311C22×D17C2511yescharacteristic
312C2×#595—21no—
313C2×#595—23no—
314C2×#595—21no—
315C2×#595—21no—
316C2×#595—21no—
317C2×#595—23no—
318C2×#595—21no—
319C2×#595—23no—
320C2×#595—23no—
321C2×#595—21no—
322C2×#595—23no—
323C2×#595—23no—
324C2×#595—23no—
325C2×#595—21no—
326C2×#595—23no—
327C2×#595—21no—
328C2×#595—23no—
329C2×#595—21no—
330C2×#595—21no—
331C2×#595—23no—
332C2×#595—23no—
333C2×#595—412no—
334C2×#595—412no—
335C2×#595—812no—
336C2×#595C22×D412yes—
337C2×#595C22×D416yes—
338C2×#595H(5,𝔽2)12yes—
339Q8×C17C4×D414yescomplemented
340D4×C17—26no—
341D4×C17—26no—
342D4×C17—43no—
343D4×C17—46no—
344C2×C4×C17—26no—
345C2×C4×C17—26no—
346C2×C4×C17C23×C411yescharacteristic
347C2×C4×C17C23×C413yes—
348C2×C4×C17C23×C411yescharacteristic
349C2×C4×C17C23×C411yescharacteristic
350C2×C4×C17C23×C413yes—
351C22⋊D17—212no—
352C22⋊D17—212no—
353C22⋊D17—43no—
354C22⋊D17—43no—
355C22⋊D17—46no—
356C22⋊D17—46no—
357C2×Dic17—26no—
358C2×Dic17—26no—
359C2×Dic17C23×C411yescharacteristic
360C2×Dic17C23×C411yescharacteristic
361C2×Dic17C23×C413yes—
362C2×Dic17C23×C411yescharacteristic
363C2×Dic17C23×C413yes—
364D68—26no—
365D68—26no—
366D68—43no—
367D68—46no—
368C4×D17—21no—
369C4×D17—21no—
370C4×D17—21no—
371C4×D17—21no—
372C4×D17—23no—
373C4×D17—23no—
374C4×D17—21no—
375C4×D17—21no—
376C4×D17—26no—
377C4×D17—26no—
378C4×D17—26no—
379C4×D17—26no—
380C4×D17C22×D416yes—
381C4×D17C2×#4116yes—
382Dic34C4×D4112yescomplemented
383C2×#550—171no—
384C2×#520—171no—
385C2×C4×#41—171no—
386#2366—173no—
387#2363—173no—
388#2361—173no—
389#2352—173no—
390#2351—171no—
391#2341—171no—
392#2341—171no—
393#2328—173no—
394#2324—173no—
395C4×#121—173no—
396#2290—173no—
397#2276—171no—
398C22×C17—23no—
399C22×C17—23no—
400C22×C17—23no—
401C22×C17—23no—
402C22×C17—23no—
403C22×C17—23no—
404C22×C17C24×C411yescharacteristic
405C2×D17—23no—
406C2×D17—23no—
407C2×D17—23no—
408C2×D17—23no—
409C2×D17—23no—
410C2×D17—23no—
411C2×D17—43no—
412C2×D17—43no—
413C2×D17—43no—
414C2×D17—43no—
415C2×D17—43no—
416C2×D17—43no—
417C2×D17—43no—
418C2×D17—43no—
419C2×D17C23×D411yescharacteristic
420C2×D17C22×#4111yescharacteristic
421C2×D17C2×H(5,𝔽2)11yescharacteristic
422C2×D17#58511yescharacteristic
423C2×D17#58511yescharacteristic
424C2×D17#58511yescharacteristic
425#595—22no—
426#595—22no—
427#595—26no—
428#595—41no—
429#595—43no—
430#595—43no—
431#595—43no—
432#595—41no—
433C4×C17—21no—
434C4×C17—21no—
435C4×C17—21no—
436C4×C17—23no—
437C4×C17C2×C4×D416yes—
438Dic17—21no—
439Dic17—21no—
440Dic17—21no—
441Dic17—23no—
442Dic17C2×C4×D416yes—
443C22×#41—171no—
444C22×#41—171no—
445#550—171no—
446#550—171no—
447#550—173no—
448#550—173no—
449#550—173no—
450#550—171no—
451#550—173no—
452#550#59511yescharacteristic, complemented
453C2×#127—173no—
454C2×#121—173no—
455C2×#121—173no—
456#520—348no—
457C4×#41—348no—
458C2×C4×Q8—171no—
459C2×C4×Q8—171no—
460C2×C4×Q8—171no—
461C2×C4×Q8—171no—
462C2×C4×Q8—171no—
463C2×C4×D4—173no—
464C2×C4×D4—173no—
465C2×C4×D4—173no—
466C2×C4×D4—173no—
467C2×C4×D4—173no—
468C2×C4×D4—176no—
469C2×#117—173no—
470C2×#117—173no—
471C22×C4⋊C4—173no—
472C22×C42—173no—
473#390—173no—
474#390—176no—
475#390—173no—
476#390—173no—
477#390—173no—
478#389—173no—
479#389—173no—
480#388—176no—
481#388—173no—
482#388—173no—
483#387—173no—
484#387—171no—
485#386—176no—
486#386—173no—
487#386—176no—
488#386—176no—
489#386—173no—
490#385—173no—
491#385—173no—
492#382—173no—
493#380—173no—
494#380—173no—
495C4×C4⋊C4—173no—
496C4×C4⋊C4—173no—
497C4×C4⋊C4—173no—
498C4×C4⋊C4—173no—
499C4×C22⋊C4—173no—
500C4×C22⋊C4—173no—
501C4×C22⋊C4—176no—
502#376—173no—
503C2×C17—43no—
504C2×C17—43no—
505C2×C17C22×C4×D411yescharacteristic
506C2×C17#342811yescharacteristic
507C2×C17C4×H(5,𝔽2)11yescharacteristic
508D17—43no—
509D17—43no—
510D17#348711yescharacteristic
511D17#348811yescharacteristic
512D17#351711yescharacteristic
513D17#352411yescharacteristic
514C2×#41—171no—
515C2×#41—171no—
516C2×#41—173no—
517C2×#41—173no—
518C2×#41—173no—
519C2×#41—173no—
520C2×#41—344no—
521C2×#41—344no—
522C2×#41—344no—
523C2×#41—344no—
524C2×#41C2×#59511yescharacteristic, complemented
525C2×#41C2×#59511yescharacteristic, complemented
526C22×Q8—171no—
527C22×D4—173no—
528C22×D4—173no—
529C22×D4—176no—
530C22×D4—173no—
531C23×C4—173no—
532C23×C4—173no—
533C23×C4—173no—
534C23×C4—176no—
535C23×C4—173no—
536#127—176no—
537#127—176no—
538#127—173no—
539#127—173no—
540#127—173no—
541#127C2×#59513yescomplemented
542#121—173no—
543#121—173no—
544#121—176no—
545#121—176no—
546#121—173no—
547#121—173no—
548#121—173no—
549#121—173no—
550#121—176no—
551#121—176no—
552#121C2×#59513yescomplemented
553#121C2×#59513yescomplemented
554C4×Q8—178no—
555C4×Q8—171no—
556C4×Q8—173no—
557C4×Q8—173no—
558C4×Q8—344no—
559C4×Q8—344no—
560C4×Q8—344no—
561C4×Q8C2×#59511yescharacteristic, complemented
562C4×D4—173no—
563C4×D4—173no—
564C4×D4—173no—
565C4×D4—173no—
566C4×D4—173no—
567C4×D4—173no—
568C4×D4—173no—
569C4×D4—3412no—
570C4×D4—3412no—
571C4×D4—3412no—
572C4×D4—3412no—
573C4×D4—6812no—
574C4×D4C2×#59513yescomplemented
575#117—3412no—
576#117—3412no—
577C2×C4⋊C4—173no—
578C2×C4⋊C4—171no—
579C2×C4⋊C4—173no—
580C2×C4⋊C4—173no—
581C2×C4⋊C4—173no—
582C2×C4⋊C4—171no—
583C2×C4⋊C4—173no—
584C2×C4⋊C4—173no—
585C2×C4⋊C4—173no—
586C2×C4⋊C4—173no—
587C2×C4⋊C4—3412no—
588C2×C22⋊C4—173no—
589C2×C22⋊C4—173no—
590C2×C22⋊C4—173no—
591C2×C22⋊C4—176no—
592C2×C22⋊C4—173no—
593C2×C22⋊C4—173no—
594C2×C22⋊C4—176no—
595C2×C22⋊C4—176no—
596C2×C22⋊C4—173no—
597C2×C22⋊C4—173no—
598C2×C22⋊C4—173no—
599C2×C42—173no—
600C2×C42—173no—
601C2×C42—173no—
602C2×C42—173no—
603C2×C42—173no—
604C2×C42—173no—
605C2×C42—171no—
606C2×C42—176no—
607C2×C42—3412no—
608#95—171no—
609#95—173no—
610#95—173no—
611#95—173no—
612#95—173no—
613#95—171no—
614#95—171no—
615#95—173no—
616#95—176no—
617#95—171no—
618#95—173no—
619C17#3429511yescharacteristic, complemented, Sylow
620C24—173no—
621C24—173no—
622#41—24no—
623#41—24no—
624#41—3412no—
625#41—3412no—
626#41—3412no—
627#41—3412no—
628#41—344no—
629#41—344no—
630C2×Q8—174no—
631C2×Q8—174no—
632C2×Q8—173no—
633C2×Q8C22×#59511yescharacteristic
634C2×D4—176no—
635C2×D4—176no—
636C2×D4—173no—
637C2×D4—173no—
638C2×D4—176no—
639C2×D4—176no—
640C2×D4—173no—
641C2×D4—173no—
642C2×D4—173no—
643C2×D4—176no—
644C2×D4—346no—
645C2×D4—346no—
646C2×D4—346no—
647C2×D4—346no—
648C2×D4—686no—
649C2×D4—686no—
650C2×D4—683no—
651C2×D4—683no—
652C2×D4C22×#59513yes—
653C2×D4C22×#59513yes—
654C2×D4C22×#59513yes—
655C2×D4C22×#59516yes—
656C22×C4—173no—
657C22×C4—171no—
658C22×C4—173no—
659C22×C4—171no—
660C22×C4—173no—
661C22×C4—173no—
662C22×C4—173no—
663C22×C4—173no—
664C22×C4—173no—
665C22×C4—173no—
666C22×C4—171no—
667C22×C4—171no—
668C22×C4—173no—
669C22×C4—171no—
670C22×C4—171no—
671C22×C4—173no—
672C22×C4—173no—
673C22×C4—173no—
674C22×C4—171no—
675C22×C4—346no—
676C22×C4—346no—
677C22×C4—346no—
678C22×C4—346no—
679C22×C4—346no—
680C22×C4—346no—
681C22×C4—346no—
682C22×C4—3412no—
683C22×C4—683no—
684C22×C4—683no—
685C22×C4—683no—
686C22×C4—686no—
687C22×C4—686no—
688C22×C4C22×#59513yes—
689C22×C4C22×#59513yes—
690C4⋊C4—1712no—
691C4⋊C4—171no—
692C4⋊C4—171no—
693C4⋊C4—171no—
694C4⋊C4—176no—
695C4⋊C4—173no—
696C4⋊C4—346no—
697C4⋊C4—346no—
698C4⋊C4—342no—
699C4⋊C4—346no—
700C4⋊C4—346no—
701C4⋊C4—346no—
702C4⋊C4—683no—
703C4⋊C4C22×#59511yescharacteristic
704C4⋊C4C22×#59513yes—
705C22⋊C4—173no—
706C22⋊C4—173no—
707C22⋊C4—173no—
708C22⋊C4—173no—
709C22⋊C4—173no—
710C22⋊C4—173no—
711C22⋊C4—346no—
712C22⋊C4—346no—
713C22⋊C4—3412no—
714C22⋊C4—346no—
715C22⋊C4—683no—
716C22⋊C4—686no—
717C22⋊C4—683no—
718C22⋊C4—683no—
719C22⋊C4—686no—
720C22⋊C4C22×#59513yes—
721C22⋊C4C22×#59513yes—
722C42—1712no—
723C42—173no—
724C42—173no—
725C42—173no—
726C42—342no—
727C42—346no—
728C42—346no—
729C42—346no—
730C42—346no—
731C42—686no—
732C42C22×#59513yes—
733C23—171no—
734C23—173no—
735C23—173no—
736C23—343no—
737C23—343no—
738C23—343no—
739C23—343no—
740C23—343no—
741C23—343no—
742C23—343no—
743C23—343no—
744C23—343no—
745C23—343no—
746C23—343no—
747C23—343no—
748C23C23×#59513yes—
749C23C23×#59513yes—
750Q8—1712no—
751Q8D4×#59514yescomplemented
752D4—26no—
753D4—26no—
754D4—43no—
755D4—46no—
756D4—3412no—
757D4—3412no—
758D4—346no—
759D4—346no—
760D4—683no—
761D4—686no—
762D4—683no—
763D4—683no—
764D4—686no—
765D4—686no—
766C2×C4—26no—
767C2×C4—26no—
768C2×C4—173no—
769C2×C4—176no—
770C2×C4—176no—
771C2×C4—172no—
772C2×C4—176no—
773C2×C4—172no—
774C2×C4—171no—
775C2×C4—173no—
776C2×C4—171no—
777C2×C4—171no—
778C2×C4—346no—
779C2×C4—346no—
780C2×C4—341no—
781C2×C4—343no—
782C2×C4—341no—
783C2×C4—343no—
784C2×C4—341no—
785C2×C4—341no—
786C2×C4—341no—
787C2×C4—341no—
788C2×C4—346no—
789C2×C4—346no—
790C2×C4—341no—
791C2×C4—343no—
792C2×C4—341no—
793C2×C4—341no—
794C2×C4—341no—
795C2×C4—343no—
796C2×C4—346no—
797C2×C4—346no—
798C2×C4—341no—
799C2×C4—341no—
800C2×C4—343no—
801C2×C4—343no—
802C2×C4—343no—
803C2×C4—343no—
804C2×C4—341no—
805C2×C4—343no—
806C2×C4—341no—
807C2×C4—341no—
808C2×C4—343no—
809C2×C4—343no—
810C2×C4—343no—
811C2×C4—343no—
812C2×C4—341no—
813C2×C4—6812no—
814C2×C4—6812no—
815C2×C4—13612no—
816C2×C4C23×#59511yescharacteristic
817C2×C4C23×#59513yes—
818C2×C4C23×#59511yescharacteristic
819C2×C4C23×#59511yescharacteristic
820C2×C4C23×#59513yes—
821C22—23no—
822C22—23no—
823C22—23no—
824C22—23no—
825C22—23no—
826C22—23no—
827C22—171no—
828C22—171no—
829C22—171no—
830C22—171no—
831C22—171no—
832C22—171no—
833C22—343no—
834C22—343no—
835C22—343no—
836C22—343no—
837C22—343no—
838C22—343no—
839C22—683no—
840C22—683no—
841C22—683no—
842C22—683no—
843C22—683no—
844C22—683no—
845C22—683no—
846C22—683no—
847C22C24×#59511yescharacteristic
848C4—21no—
849C4—21no—
850C4—21no—
851C4—23no—
852C4—176no—
853C4—342no—
854C4—342no—
855C4—346no—
856C4—341no—
857C4—341no—
858C4—341no—
859C4—343no—
860C4—683no—
861C4—683no—
862C4—681no—
863C4—683no—
864C4—681no—
865C4C2×D4×#59516yes—
866C2—43no—
867C2—43no—
868C2—171no—
869C2—171no—
870C2—171no—
871C2—171no—
872C2—683no—
873C2—683no—
874C2C22×D4×#59511yescharacteristic
875C2#1454576411yescharacteristic
876C2H(5,𝔽2)×#59511yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#550C4
prime radicalD17×#550C2
cosocleC22×D17C25
hypercenter#550#595
hypocenterC17#34295
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#11763878C2semidirect
2. C2×#41×#595C2semidirect
3. #14545314C2semidirect
4. #14545311C2semidirect
5. #14545309C2semidirect
6. #14545300C2semidirect
7. #14545299C2semidirect
8. #14545289C2semidirect
9. #14545289C2semidirect
10. #14545276C2semidirect
11. #14545272C2semidirect
12. #121×#595C2semidirect
13. #14545238C2semidirect
14. #14545224C2semidirect
63. #11763481C4semidirect
64. #11763480C4semidirect
65. #11763479C4semidirect
66. #11763478C4semidirect
67. #11763478C4semidirect
68. #11763477C4semidirect
69. #11763477C4semidirect
75. C17×#550C4semidirect
79. C2×#41×C17C2×C4semidirect
80. C2×#41×C17C2×C4semidirect
85. C2×#63256C2×C4semidirect
86. C2×#63256C2×C4semidirect
88. C2×#63254C2×C4semidirect
89. C2×#63254C2×C4semidirect
94. C2×#63252C2×C4semidirect
95. C2×#63252C2×C4semidirect
110. Q8×#595D4semidirect
135. C17×#127C2×C4semidirect
136. C17×#121C2×C4semidirect
137. C17×#121C2×C4semidirect
138. C4×Q8×C17C2×C4semidirect
139. C4×D4×C17C2×C4semidirect
140. Q8×Dic17C2×C4semidirect
141. #10587626C2×C4semidirect
142. #10587626C2×C4semidirect
143. #10587626C2×C4semidirect
144. #10587626C2×C4semidirect
145. #10587625C2×C4semidirect
146. #10587625C2×C4semidirect
147. #10587624C2×C4semidirect
148. #10587624C2×C4semidirect
149. D4×Dic17C2×C4semidirect
150. #10587616C2×C4semidirect
151. #10587616C2×C4semidirect
152. C4×C22⋊D17C2×C4semidirect
153. C4×C22⋊D17C2×C4semidirect
154. #10587581C2×C4semidirect
155. #10587581C2×C4semidirect
156. #10587579C2×C4semidirect
159. #10587573C2×C4semidirect
160. #10587570C2×C4semidirect
161. #10587570C2×C4semidirect
162. #10587567C2×C4semidirect
163. #10587567C2×C4semidirect
166. #10587560C2×C4semidirect
167. C4×D68C2×C4semidirect
169. C4×Dic34C2×C4semidirect
339. Q8×C17C4×D4semidirect
382. Dic34C4×D4semidirect
452. #550#595semidirect
524. C2×#41C2×#595semidirect
525. C2×#41C2×#595semidirect
541. #127C2×#595semidirect
552. #121C2×#595semidirect
553. #121C2×#595semidirect
561. C4×Q8C2×#595semidirect
574. C4×D4C2×#595semidirect
619. C17#34295semidirect
751. Q8D4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117638782
C2×#41×#5952
#145453142
#145453112
#145453092
#145453002
#145452992
#145452892
#145452762
#145452722
#121×#5952
#145452382
#145452242
D17×#5502
#3429517