Finite Group Databasebeta

← #17979160

Subgroups — #17979160

Order 4352.

2984 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763877C211yesmaximal, characteristic, complemented
2C2×#41×#595C211yesmaximal, characteristic, complemented
3#14545315C213yesmaximal, complemented
4#14545311C213yesmaximal, complemented
5#14545310C213yesmaximal, complemented
6#14545302C213yesmaximal, complemented
7Q8×C4⋊#595C211yesmaximal, characteristic, complemented
8#14545289C211yesmaximal, characteristic, complemented
9Q8×C22⋊#595C211yesmaximal, characteristic, complemented
10#14545274C213yesmaximal, complemented
11#14545272C213yesmaximal, complemented
12C22⋊Q8×#595C213yesmaximal, complemented
13#14545238C213yesmaximal, complemented
14#14545224C211yesmaximal, characteristic, complemented
15D17×#548C211yesmaximal, characteristic
16#11763877—28no—
17#41×#595—28no—
18C2×Q8×#595C2211yescharacteristic
19C2×Q8×#595C2211yescharacteristic
20C2×Q8×#595C2213yes—
21C2×Q8×#595C2211yescharacteristic
22C2×Q8×#595C2213yes—
23C2×Q8×#595C2211yescharacteristic
24C2×D4×#595C2213yes—
25C2×D4×#595C2213yes—
26C2×#10587677C2213yes—
27C2×#10587677C2213yes—
28C2×#10587677C2213yes—
29C22×C4×#595C2213yes—
30(C2×#595)⋊Q8C2213yes—
31(C2×#595)⋊Q8C2213yes—
32#11763761C2213yes—
33#11763761C2216yes—
34#11763761C2213yes—
35#11763760C2213yes—
36#11763760C2213yes—
37#11763759C2211yescharacteristic
38#11763759C2213yes—
39#11763759C2216yes—
40#11763759C2216yes—
41#11763759C2216yes—
42#11763758C2213yes—
43#11763758C2213yes—
44#11763757C2213yes—
45#11763757C2213yes—
46#11763756C2213yes—
47#11763756C2213yes—
48#11763756C2216yes—
49#11763755C2213yes—
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—
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—
78C2×#41×C17C2×C411yescharacteristic
79C22×Q8×C17C2×C411yescharacteristic, complemented
80#41×D17—24no—
81#41×D17—24no—
82C2×#63256C2×C411yescharacteristic
83C2×Q8×D17—24no—
84C2×Q8×D17—24no—
85C2×Q8×D17C2×C411yescharacteristic, complemented
86C2×Q8×D17C2×C413yescomplemented
87C2×Q8×D17C2313yes—
88C2×Q8×D17C2311yescharacteristic
89C2×#63254C2×C413yes—
90C2×D4×D17C2313yes—
91C2×D4×D17C2313yes—
92C2×#63252C2×C413yes—
93C22×C4×D17C2313yes—
94C22×C4×D17C2313yes—
95C22×Dic34C2×C413yescomplemented
96C2×C22⋊#595C2311yescharacteristic
97C2×C22⋊#595C2311yescharacteristic
98C2×C22⋊#595C2313yes—
99C2×C22⋊#595C2316yes—
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—
112#10587677—212no—
113#10587677—212no—
114#10587677—212no—
115C2×C4⋊#595C2311yescharacteristic
116C2×C4⋊#595C2313yes—
117C2×C4⋊#595C2313yes—
118C2×C4⋊#595C2313yes—
119C2×C4⋊#595C2313yes—
120C2×C4⋊#595C2313yes—
121C2×C4⋊#595C2313yes—
122C2×C4⋊#595C2316yes—
123C2×C4⋊#595C2313yes—
124C2×C4×#595—212no—
125C2×C4×#595C2313yes—
126C2×C4×#595C2313yes—
127C2×C4×#595C2313yes—
128C2×C4×#595C2316yes—
129C2×C4×#595C2313yes—
130C2×C4×#595C2311yescharacteristic
131C2×C4×#595C2316yes—
132C2×C4×#595C2313yes—
133C17×#124C2×C413yescomplemented
134C17×C22⋊Q8C2×C413yescomplemented
135C17×#121C2×C413yescomplemented
136C4×Q8×C17C2×C411yescharacteristic, complemented
137C4×D4×C17C2×C413yescomplemented
138#10587633C2×C413yescomplemented
139#10587632C2×C413yescomplemented
140Q8×Dic17C2×C411yescharacteristic, complemented
141#10587625C2×C416yescomplemented
142#10587624C2×C413yescomplemented
143#10587622C2×C413yescomplemented
144D4×Dic17C2×C413yescomplemented
145#10587616C2×C413yescomplemented
146C4×C22⋊D17C2×C413yescomplemented
147C4×C22⋊D17C2×C413yescomplemented
148#10587610C2×C413yescomplemented
149#10587583C2×C413yescomplemented
150#10587582C2×C416yescomplemented
151#10587581C2×C413yescomplemented
152#10587579C2×C413yescomplemented
153C4⋊C4×D17C2313yes—
154C4⋊C4×D17C2313yes—
155#10587573C2×C413yescomplemented
156#10587571C2×C416yescomplemented
157#10587571C2×C416yescomplemented
158#10587570C2×C416yescomplemented
159#10587567C2×C413yescomplemented
160#10587567C2×C413yescomplemented
161C22⋊C4×D17C2316yes—
162C22⋊C4×D17C2313yes—
163C22⋊C4×D17C2311yescharacteristic
164#10587564C2×C416yescomplemented
165#10587561C2×C413yescomplemented
166C4×D68C2×C413yescomplemented
167C42×D17C2313yes—
168C4×Dic34C2×C413yescomplemented
169(C2×#595)⋊C4C2311yescharacteristic
170(C2×#595)⋊C4C2313yes—
171(C2×#595)⋊C4C2313yes—
172(C2×#595)⋊C4C2313yes—
173(C2×#595)⋊C4C2311yescharacteristic
174(C2×#595)⋊C4C2313yes—
175(C2×#595)⋊C4C2313yes—
176(C2×#595)⋊C4C2313yes—
177(C2×#595)⋊C4C2313yes—
178(C2×#595)⋊C4C2313yes—
179(C2×#595)⋊C4C2316yes—
180C23×D17C2411yescharacteristic
181C23×D17C2413yes—
182C22×#595—26no—
183C22×#595—26no—
184C22×#595—26no—
185C22×#595—43no—
186C22×#595—43no—
187C22×#595—43no—
188C22×#595C2413yes—
189C22×#595C2411yescharacteristic
190C22×#595C2413yes—
191C22×#595C2411yescharacteristic
192C22×#595C2413yes—
193C22×#595C2413yes—
194C22×#595C2411yescharacteristic
195C22×#595C2411yescharacteristic
196#41×C17—24no—
197C2×Q8×C17—24no—
198C2×Q8×C17C22×C413yes—
199C2×Q8×C17C22×C411yescharacteristic
200C2×D4×C17C22×C413yes—
201C2×D4×C17C22×C413yes—
202C22×C4×C17C22×C413yes—
203C22×C4×C17C22×C413yes—
204C2×C22⋊D17C22×C416yes—
205C2×C22⋊D17C22×C413yes—
206C2×C22⋊D17C22×C413yes—
207C22×Dic17C22×C413yes—
208C22×Dic17C22×C413yes—
209#63256—24no—
210Q8×D17—24no—
211Q8×D17—26no—
212Q8×D17—26no—
213Q8×D17—212no—
214Q8×D17C2×D414yes—
215Q8×D17#4114yes—
216#63254—212no—
217D4×D17—26no—
218D4×D17—26no—
219D4×D17—43no—
220D4×D17—43no—
221#63252—212no—
222C2×D68C22×C413yes—
223C2×D68C22×C413yes—
224C2×C4×D17—26no—
225C2×C4×D17—26no—
226C2×C4×D17—26no—
227C2×C4×D17—26no—
228C2×C4×D17C22×C413yes—
229C2×C4×D17C22×C413yes—
230C2×C4×D17C22×C413yes—
231C2×C4×D17C22×C413yes—
232C2×C4×D17C2411yescharacteristic
233C2×C4×D17C2413yes—
234C2×C4×D17C2413yes—
235C2×C4×D17C2411yescharacteristic
236C2×C4×D17C2413yes—
237C2×Dic34—212no—
238C2×Dic34C22×C413yes—
239C2×Dic34C22×C416yes—
240C2×Dic34C22×C413yes—
241C22⋊#595—26no—
242C22⋊#595—22no—
243C22⋊#595—212no—
244C22⋊#595—22no—
245C22⋊#595—43no—
246C22⋊#595—43no—
247C22⋊#595—46no—
248C22⋊#595—43no—
249C4⋊#595—26no—
250C4⋊#595—26no—
251C4⋊#595—22no—
252C4⋊#595—26no—
253C4⋊#595—26no—
254C4⋊#595—26no—
255C4⋊#595—43no—
256C4⋊#595—46no—
257C4⋊#595C2×D4112yes—
258C4×#595—22no—
259C4×#595—26no—
260C4×#595—212no—
261C4×#595—26no—
262C4×#595—26no—
263C4×#595—26no—
264C4×#595—46no—
265C4×#595C2×D4112yes—
266C4⋊C4×C17C22×C413yes—
267C4⋊C4×C17C22×C413yes—
268C22⋊C4×C17C22×C416yes—
269C22⋊C4×C17C22×C413yes—
270C22⋊C4×C17C22×C411yescharacteristic
271C42×C17C22×C413yes—
272C22⋊Dic17C22×C416yes—
273C22⋊Dic17C22×C413yes—
274C22⋊Dic17C22×C411yescharacteristic
275#63227C22×C411yescharacteristic
276#63227C22×C413yes—
277#63227C22×C416yes—
278#63227C22×C416yes—
279#63227C22×C413yes—
280#63227C22×C411yescharacteristic
281C4⋊Dic17C22×C413yes—
282C4⋊Dic17C22×C413yes—
283#63225C22×C416yes—
284#63225C22×C413yes—
285#63225C22×C413yes—
286C4×Dic17C22×C413yes—
287C4×Dic17C22×C413yes—
288C4×Dic17C22×C413yes—
289#34293—171nomaximal, Sylow
290C23×C17C23×C413yes—
291C23×C17C23×C411yescharacteristic
292C22×D17—21no—
293C22×D17—23no—
294C22×D17—21no—
295C22×D17—23no—
296C22×D17—21no—
297C22×D17—23no—
298C22×D17—21no—
299C22×D17—23no—
300C22×D17—23no—
301C22×D17—23no—
302C22×D17—21no—
303C22×D17—21no—
304C22×D17C23×C411yescharacteristic
305C22×D17C23×C413yes—
306C22×D17C2511yescharacteristic
307C2×#595—21no—
308C2×#595—23no—
309C2×#595—23no—
310C2×#595—21no—
311C2×#595—21no—
312C2×#595—21no—
313C2×#595—23no—
314C2×#595—21no—
315C2×#595—23no—
316C2×#595—21no—
317C2×#595—23no—
318C2×#595—21no—
319C2×#595—21no—
320C2×#595—23no—
321C2×#595—23no—
322C2×#595—23no—
323C2×#595—23no—
324C2×#595—23no—
325C2×#595—21no—
326C2×#595—21no—
327C2×#595—23no—
328C2×#595—412no—
329C2×#595—412no—
330C2×#595C22×D416yes—
331C2×#595C22×D412yes—
332C2×#5952−1+412yes—
333Q8×C17—26no—
334Q8×C17C4×D414yes—
335D4×C17—26no—
336D4×C17—43no—
337C2×C4×C17—26no—
338C2×C4×C17—26no—
339C2×C4×C17C23×C411yescharacteristic
340C2×C4×C17C23×C413yes—
341C2×C4×C17C23×C413yes—
342C2×C4×C17C23×C411yescharacteristic
343C2×C4×C17C23×C413yes—
344C22⋊D17—212no—
345C22⋊D17—43no—
346C22⋊D17—43no—
347C2×Dic17—26no—
348C2×Dic17—26no—
349C2×Dic17C23×C411yescharacteristic
350C2×Dic17C23×C413yes—
351C2×Dic17C23×C413yes—
352C2×Dic17C23×C411yescharacteristic
353C2×Dic17C23×C413yes—
354D68—26no—
355D68—43no—
356C4×D17—21no—
357C4×D17—23no—
358C4×D17—21no—
359C4×D17—23no—
360C4×D17—21no—
361C4×D17—23no—
362C4×D17—21no—
363C4×D17—23no—
364C4×D17—26no—
365C4×D17—26no—
366C4×D17—26no—
367C4×D17—26no—
368C4×D17C22×D416yes—
369C4×D17C2×#4116yes—
370Dic34—26no—
371Dic34—212no—
372Dic34C4×D4112yes—
373C2×#548—171no—
374C2×#519—171no—
375C2×C4×#41—171no—
376#2367—173no—
377#2363—173no—
378#2362—173no—
379#2354—173no—
380Q8×C4⋊C4—171no—
381#2341—171no—
382Q8×C22⋊C4—171no—
383#2326—173no—
384#2324—173no—
385C4×C22⋊Q8—173no—
386#2290—173no—
387#2276—171no—
388C22×C17—21no—
389C22×C17—23no—
390C22×C17—21no—
391C22×C17—23no—
392C22×C17—21no—
393C22×C17—23no—
394C22×C17C24×C411yescharacteristic
395C2×D17—21no—
396C2×D17—23no—
397C2×D17—21no—
398C2×D17—23no—
399C2×D17—21no—
400C2×D17—23no—
401C2×D17—43no—
402C2×D17—41no—
403C2×D17—43no—
404C2×D17—41no—
405C2×D17—41no—
406C2×D17—43no—
407C2×D17—41no—
408C2×D17—43no—
409C2×D17C23×D411yescharacteristic
410C2×D17C22×#4111yescharacteristic
411C2×D17C2×2−1+411yescharacteristic
412C2×D17#58511yescharacteristic
413C2×D17#58511yescharacteristic
414C2×D17#58511yescharacteristic
415#595—22no—
416#595—22no—
417#595—26no—
418#595—43no—
419#595—43no—
420#595—41no—
421#595—41no—
422#595—43no—
423C4×C17—23no—
424C4×C17—21no—
425C4×C17—23no—
426C4×C17—21no—
427C4×C17C2×C4×D416yes—
428Dic17—23no—
429Dic17—21no—
430Dic17—23no—
431Dic17—21no—
432Dic17C2×C4×D416yes—
433C22×#41—171no—
434C23×Q8—171no—
435#548—171no—
436#548—171no—
437#548—173no—
438#548—173no—
439#548—173no—
440#548—171no—
441#548—173no—
442#548#59511yescharacteristic, complemented
443C2×#124—173no—
444C2×C22⋊Q8—173no—
445C2×#121—173no—
446#519—348no—
447C4×#41—348no—
448C2×C4×Q8—171no—
449C2×C4×Q8—171no—
450C2×C4×Q8—173no—
451C2×C4×Q8—171no—
452C2×C4×Q8—171no—
453C2×C4×Q8—171no—
454C2×C4×Q8—173no—
455C2×C4×D4—173no—
456C2×C4×D4—173no—
457C2×C4×D4—173no—
458C2×#117—173no—
459C2×#117—173no—
460C2×#117—173no—
461C22×C42—173no—
462#391—173no—
463#391—173no—
464#390—173no—
465#390—176no—
466#390—173no—
467#389—173no—
468#389—173no—
469#388—176no—
470#388—176no—
471#388—176no—
472#388—173no—
473#388—171no—
474#387—173no—
475#387—173no—
476#386—173no—
477#386—173no—
478#385—176no—
479#385—173no—
480#385—173no—
481#384—173no—
482#380—173no—
483#380—173no—
484C4×C4⋊C4—173no—
485C4×C4⋊C4—173no—
486C4×C4⋊C4—173no—
487C4×C4⋊C4—176no—
488C4×C4⋊C4—173no—
489C4×C22⋊C4—173no—
490C4×C22⋊C4—173no—
491C4×C22⋊C4—176no—
492#376—173no—
493C2×C17—43no—
494C2×C17—41no—
495C2×C17C22×C4×D411yescharacteristic
496C2×C17#342811yescharacteristic
497C2×C17C4×2−1+411yescharacteristic
498D17—41no—
499D17—43no—
500D17#348711yescharacteristic
501D17#348911yescharacteristic
502D17#351811yescharacteristic
503D17#352411yescharacteristic
504C2×#41—171no—
505C2×#41—173no—
506C2×#41—173no—
507C2×#41—344no—
508C2×#41—344no—
509C2×#41C2×#59511yescharacteristic
510C22×Q8—171no—
511C22×Q8—173no—
512C22×Q8—173no—
513C22×Q8—171no—
514C22×Q8—173no—
515C22×Q8—344no—
516C22×Q8—344no—
517C22×Q8C2×#59511yescharacteristic, complemented
518C22×D4—173no—
519C22×D4—173no—
520C23×C4—173no—
521C23×C4—173no—
522C23×C4—173no—
523C23×C4—173no—
524#124—173no—
525#124—173no—
526#124—176no—
527#124—176no—
528#124—173no—
529#124C2×#59513yescomplemented
530C22⋊Q8—173no—
531C22⋊Q8—173no—
532C22⋊Q8—176no—
533C22⋊Q8—173no—
534C22⋊Q8—176no—
535C22⋊Q8C2×#59513yescomplemented
536#121—173no—
537#121—176no—
538#121—173no—
539#121—173no—
540#121—176no—
541#121C2×#59513yescomplemented
542C4×Q8—178no—
543C4×Q8—171no—
544C4×Q8—173no—
545C4×Q8—173no—
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×D4—3412no—
560C4×D4—3412no—
561C4×D4C2×#59513yescomplemented
562#117—3412no—
563#117—3412no—
564#117—3412no—
565C2×C4⋊C4—173no—
566C2×C4⋊C4—173no—
567C2×C4⋊C4—173no—
568C2×C4⋊C4—173no—
569C2×C4⋊C4—173no—
570C2×C4⋊C4—173no—
571C2×C4⋊C4—173no—
572C2×C4⋊C4—173no—
573C2×C4⋊C4—171no—
574C2×C4⋊C4—173no—
575C2×C4⋊C4—176no—
576C2×C22⋊C4—171no—
577C2×C22⋊C4—173no—
578C2×C22⋊C4—176no—
579C2×C22⋊C4—171no—
580C2×C22⋊C4—173no—
581C2×C22⋊C4—176no—
582C2×C22⋊C4—171no—
583C2×C22⋊C4—173no—
584C2×C22⋊C4—176no—
585C2×C22⋊C4—173no—
586C2×C22⋊C4—173no—
587C2×C42—173no—
588C2×C42—173no—
589C2×C42—173no—
590C2×C42—176no—
591C2×C42—173no—
592C2×C42—173no—
593C2×C42—173no—
594C2×C42—171no—
595C2×C42—176no—
596C2×C42—3412no—
597#95—171no—
598#95—173no—
599#95—173no—
600#95—173no—
601#95—173no—
602#95—171no—
603#95—173no—
604#95—173no—
605#95—173no—
606#95—176no—
607#95—173no—
608C17#3429311yescharacteristic, complemented, Sylow
609C24—173no—
610C24—171no—
611#41—24no—
612#41—3412no—
613#41—3412no—
614#41—344no—
615C2×Q8—24no—
616C2×Q8—174no—
617C2×Q8—174no—
618C2×Q8—173no—
619C2×Q8—176no—
620C2×Q8—173no—
621C2×Q8—3412no—
622C2×Q8—346no—
623C2×Q8—346no—
624C2×Q8—3412no—
625C2×Q8—344no—
626C2×Q8C22×#59513yes—
627C2×Q8C22×#59511yescharacteristic
628C2×D4—176no—
629C2×D4—173no—
630C2×D4—173no—
631C2×D4—173no—
632C2×D4—173no—
633C2×D4—346no—
634C2×D4—346no—
635C2×D4—683no—
636C2×D4—683no—
637C2×D4C22×#59513yes—
638C2×D4C22×#59513yes—
639C22×C4—173no—
640C22×C4—171no—
641C22×C4—171no—
642C22×C4—173no—
643C22×C4—173no—
644C22×C4—173no—
645C22×C4—173no—
646C22×C4—173no—
647C22×C4—173no—
648C22×C4—173no—
649C22×C4—171no—
650C22×C4—171no—
651C22×C4—173no—
652C22×C4—173no—
653C22×C4—171no—
654C22×C4—173no—
655C22×C4—171no—
656C22×C4—173no—
657C22×C4—173no—
658C22×C4—346no—
659C22×C4—346no—
660C22×C4—346no—
661C22×C4—346no—
662C22×C4—346no—
663C22×C4—346no—
664C22×C4—346no—
665C22×C4—683no—
666C22×C4—683no—
667C22×C4—683no—
668C22×C4C22×#59513yes—
669C22×C4C22×#59513yes—
670C4⋊C4—1712no—
671C4⋊C4—173no—
672C4⋊C4—173no—
673C4⋊C4—173no—
674C4⋊C4—176no—
675C4⋊C4—173no—
676C4⋊C4—342no—
677C4⋊C4—346no—
678C4⋊C4—346no—
679C4⋊C4—346no—
680C4⋊C4—346no—
681C4⋊C4—346no—
682C4⋊C4—683no—
683C4⋊C4—686no—
684C4⋊C4C22×#59513yes—
685C4⋊C4C22×#59513yes—
686C22⋊C4—171no—
687C22⋊C4—173no—
688C22⋊C4—176no—
689C22⋊C4—171no—
690C22⋊C4—171no—
691C22⋊C4—173no—
692C22⋊C4—173no—
693C22⋊C4—176no—
694C22⋊C4—176no—
695C22⋊C4—342no—
696C22⋊C4—342no—
697C22⋊C4—346no—
698C22⋊C4—3412no—
699C22⋊C4—683no—
700C22⋊C4—686no—
701C22⋊C4—683no—
702C22⋊C4—683no—
703C22⋊C4C22×#59511yescharacteristic
704C22⋊C4C22×#59513yes—
705C22⋊C4C22×#59516yes—
706C42—1712no—
707C42—173no—
708C42—173no—
709C42—173no—
710C42—342no—
711C42—346no—
712C42—346no—
713C42—346no—
714C42—3412no—
715C42—346no—
716C42—686no—
717C42C22×#59513yes—
718C23—171no—
719C23—173no—
720C23—171no—
721C23—341no—
722C23—343no—
723C23—341no—
724C23—341no—
725C23—343no—
726C23—343no—
727C23—343no—
728C23—341no—
729C23—343no—
730C23—343no—
731C23—341no—
732C23—341no—
733C23C23×#59513yes—
734C23C23×#59511yescharacteristic
735Q8—26no—
736Q8—1712no—
737Q8—3412no—
738Q8—346no—
739Q8D4×#59514yes—
740D4—26no—
741D4—43no—
742D4—3412no—
743D4—346no—
744D4—683no—
745D4—683no—
746D4—683no—
747C2×C4—26no—
748C2×C4—26no—
749C2×C4—173no—
750C2×C4—176no—
751C2×C4—176no—
752C2×C4—172no—
753C2×C4—176no—
754C2×C4—172no—
755C2×C4—171no—
756C2×C4—173no—
757C2×C4—173no—
758C2×C4—171no—
759C2×C4—346no—
760C2×C4—346no—
761C2×C4—341no—
762C2×C4—343no—
763C2×C4—343no—
764C2×C4—341no—
765C2×C4—341no—
766C2×C4—343no—
767C2×C4—341no—
768C2×C4—343no—
769C2×C4—346no—
770C2×C4—346no—
771C2×C4—341no—
772C2×C4—343no—
773C2×C4—343no—
774C2×C4—341no—
775C2×C4—341no—
776C2×C4—341no—
777C2×C4—346no—
778C2×C4—346no—
779C2×C4—341no—
780C2×C4—343no—
781C2×C4—341no—
782C2×C4—343no—
783C2×C4—343no—
784C2×C4—343no—
785C2×C4—341no—
786C2×C4—341no—
787C2×C4—341no—
788C2×C4—343no—
789C2×C4—343no—
790C2×C4—343no—
791C2×C4—343no—
792C2×C4—341no—
793C2×C4—343no—
794C2×C4—6812no—
795C2×C4—6812no—
796C2×C4C23×#59511yescharacteristic
797C2×C4C23×#59513yes—
798C2×C4C23×#59513yes—
799C2×C4C23×#59511yescharacteristic
800C2×C4C23×#59513yes—
801C22—21no—
802C22—23no—
803C22—21no—
804C22—23no—
805C22—21no—
806C22—23no—
807C22—171no—
808C22—171no—
809C22—171no—
810C22—171no—
811C22—171no—
812C22—171no—
813C22—341no—
814C22—343no—
815C22—341no—
816C22—343no—
817C22—343no—
818C22—341no—
819C22—683no—
820C22—683no—
821C22—681no—
822C22—681no—
823C22—681no—
824C22—683no—
825C22—681no—
826C22—683no—
827C22C24×#59511yescharacteristic
828C4—21no—
829C4—23no—
830C4—23no—
831C4—21no—
832C4—176no—
833C4—342no—
834C4—342no—
835C4—346no—
836C4—341no—
837C4—343no—
838C4—343no—
839C4—341no—
840C4—683no—
841C4—681no—
842C4—683no—
843C4—683no—
844C4—681no—
845C4C2×D4×#59516yes—
846C2—41no—
847C2—43no—
848C2—171no—
849C2—171no—
850C2—171no—
851C2—171no—
852C2—681no—
853C2—683no—
854C2C22×D4×#59511yescharacteristic
855C2#1454576411yescharacteristic
856C22−1+4×#59511yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#548C4
prime radicalD17×#548C2
cosocleC22×D17C25
hypercenter#548#595
hypocenterC17#34293
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#11763877C2semidirect
2. C2×#41×#595C2semidirect
3. #14545315C2semidirect
4. #14545311C2semidirect
5. #14545310C2semidirect
6. #14545302C2semidirect
7. Q8×C4⋊#595C2semidirect
8. #14545289C2semidirect
9. Q8×C22⋊#595C2semidirect
10. #14545274C2semidirect
11. #14545272C2semidirect
12. C22⋊Q8×#595C2semidirect
13. #14545238C2semidirect
14. #14545224C2semidirect
63. #11763471C4semidirect
64. #11763470C4semidirect
65. #11763469C4semidirect
66. #11763468C4semidirect
67. #11763467C4semidirect
68. #11763466C4semidirect
69. #11763465C4semidirect
75. C17×#548C4semidirect
79. C22×Q8×C17C2×C4semidirect
85. C2×Q8×D17C2×C4semidirect
86. C2×Q8×D17C2×C4semidirect
95. C22×Dic34C2×C4semidirect
109. Q8×#595D4semidirect
133. C17×#124C2×C4semidirect
134. C17×C22⋊Q8C2×C4semidirect
135. C17×#121C2×C4semidirect
136. C4×Q8×C17C2×C4semidirect
137. C4×D4×C17C2×C4semidirect
138. #10587633C2×C4semidirect
139. #10587632C2×C4semidirect
140. Q8×Dic17C2×C4semidirect
141. #10587625C2×C4semidirect
142. #10587624C2×C4semidirect
143. #10587622C2×C4semidirect
144. D4×Dic17C2×C4semidirect
145. #10587616C2×C4semidirect
146. C4×C22⋊D17C2×C4semidirect
147. C4×C22⋊D17C2×C4semidirect
148. #10587610C2×C4semidirect
149. #10587583C2×C4semidirect
150. #10587582C2×C4semidirect
151. #10587581C2×C4semidirect
152. #10587579C2×C4semidirect
155. #10587573C2×C4semidirect
156. #10587571C2×C4semidirect
157. #10587571C2×C4semidirect
158. #10587570C2×C4semidirect
159. #10587567C2×C4semidirect
160. #10587567C2×C4semidirect
164. #10587564C2×C4semidirect
165. #10587561C2×C4semidirect
166. C4×D68C2×C4semidirect
168. C4×Dic34C2×C4semidirect
442. #548#595semidirect
517. C22×Q8C2×#595semidirect
529. #124C2×#595semidirect
535. C22⋊Q8C2×#595semidirect
541. #121C2×#595semidirect
551. C4×Q8C2×#595semidirect
561. C4×D4C2×#595semidirect
608. C17#34293semidirect

Maximal subgroups

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

subgroupindex
C2×#117638772
C2×#41×#5952
#145453152
#145453112
#145453102
#145453022
Q8×C4⋊#5952
#145452892
Q8×C22⋊#5952
#145452742
#145452722
C22⋊Q8×#5952
#145452382
#145452242
D17×#5482
#3429317