Finite Group Databasebeta

← #17197660

Subgroups — #17197660

Order 4352.

1990 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763340C211yesmaximal, characteristic
2#14531967C212yesmaximal, complemented
3#14531954C212yesmaximal, complemented
4#14531905C212yesmaximal, complemented
5#14531901C212yesmaximal, complemented
6#14531746C212yesmaximal, complemented
7#14531722C212yesmaximal, complemented
8#14531674C212yesmaximal, complemented
9#14531638C212yesmaximal, complemented
10#14531575C212yesmaximal, complemented
11#14531571C212yesmaximal, complemented
12#14531551C211yesmaximal, characteristic
13#14531540C211yesmaximal, characteristic, complemented
14#14531537C211yesmaximal, characteristic, complemented
15#14531421C212yesmaximal, complemented
16#14531410C212yesmaximal, complemented
17#14531178C211yesmaximal, characteristic, complemented
18#14531175C211yesmaximal, characteristic, complemented
19C17×#2333C211yesmaximal, characteristic
20#11763340C4116yescomplemented
21C2×#10587565C2212yes—
22C2×#10587576C2211yescharacteristic
23C2×#10587622C2211yescharacteristic
24C2×#10587621C2212yes—
25C2×#10587610C2211yescharacteristic
26C2×#10587573C2211yescharacteristic
27C2×D4×Dic17C2211yescharacteristic
28C2×D4×Dic17C2212yes—
29C2×#10587563C2212yes—
30C22×C4×Dic17C2211yescharacteristic
31#11762713C2212yes—
32#11762713C2212yes—
33#11762712C2212yes—
34#11762707C2212yes—
35#11762706C2212yes—
36#11762705C2212yes—
37#11762704C2212yes—
38#11762703C2212yes—
39#11762703C2212yes—
40#11762703C2212yes—
41#11762703C2212yes—
42#11762703C2212yes—
43#11762702C2212yes—
44#11762697C2212yes—
45#11762697C2212yes—
46#11762697C2212yes—
47#11762697C2212yes—
48#11762697C2212yes—
49#11762696C2212yes—
50#11762695C2212yes—
51#11762694C2212yes—
52#11762694C2212yes—
53#11762693C2212yes—
54#11762693C2212yes—
55#11762692C2212yes—
56#11762692C2212yes—
57#11762691C2212yes—
58#11762691C2212yes—
59#11762690C2212yes—
60#11762689C2212yes—
61#11762689C2212yes—
62#11762682C2212yes—
63#11762682C2212yes—
64#11762681C2212yes—
65#11762681C2212yes—
66#11762676C2212yes—
67#11762676C2212yes—
68#11762676C2212yes—
69#11762673C2212yes—
70#11762673C2212yes—
71#11762673C2212yes—
72#11762672C2211yescharacteristic
73#11762670C2212yes—
74#11762670C2212yes—
75#11762667C2211yescharacteristic
76#11762667C2212yes—
77#11762667C2211yescharacteristic
78#11762667C2212yes—
79C4⋊C4×Dic17C2212yes—
80C4×#63225C2211yescharacteristic
81C4×#63225C2212yes—
82C4×#63225C2212yes—
83C4×#63225C2211yescharacteristic
84#11762660C2212yes—
85#11762660C2212yes—
86#11762660C2212yes—
87C22⋊C4×Dic17C2212yes—
88C22⋊C4×Dic17C2212yes—
89C22⋊C4×Dic17C2212yes—
90C22⋊C4×Dic17C2211yescharacteristic
91C22⋊C4×Dic17C2211yescharacteristic
92C4×C22⋊Dic17C2212yes—
93C4×C22⋊Dic17C2211yescharacteristic
94#11762655C2212yes—
95#11762655C2211yescharacteristic
96#11762655C2211yescharacteristic
97#11762654C2212yes—
98C2×#10587502C2212yes—
99C2×C17×#121C2211yescharacteristic
100C17×#390C2212yes—
101C17×#388C2212yes—
102C17×#387C2212yes—
103C17×#386C2212yes—
104C17×#386C2212yes—
105C17×#381C2211yescharacteristic
106C4×C22⋊C4×C17C2212yes—
107C4×C22⋊C4×C17C2211yescharacteristic
108C22×D4×C17C2311yescharacteristic
109C22×D4×C17C2312yes—
110C23×C4×C17C2312yes—
111C23×C4×C17C2311yescharacteristic
112C23×Dic17C2312yes—
113C23×Dic17C2311yescharacteristic
114C23×Dic17C2311yescharacteristic
115C23×Dic17C2312yes—
116C22×Dic34C2311yescharacteristic
117C17×#121C2×C418yes—
118C2×C4⋊C4×C17C2312yes—
119C2×C4⋊C4×C17C2311yescharacteristic
120C2×C22⋊C4×C17C2311yescharacteristic
121C2×C22⋊C4×C17C2312yes—
122C2×C22⋊C4×C17C2312yes—
123C2×C22⋊C4×C17C2312yes—
124C2×C22⋊C4×C17C2312yes—
125C2×C22⋊C4×C17C2311yescharacteristic
126C2×C22⋊C4×C17C2312yes—
127C2×C42×C17C2311yescharacteristic
128C2×C42×C17C2312yes—
129C2×C42×C17C2311yescharacteristic
130C2×C22⋊Dic17C2311yescharacteristic
131C2×C22⋊Dic17C2312yes—
132C2×C22⋊Dic17C2312yes—
133C2×C22⋊Dic17C2312yes—
134C2×C22⋊Dic17C2312yes—
135C2×C22⋊Dic17C2311yescharacteristic
136C2×C22⋊Dic17C2312yes—
137C2×C22⋊Dic17C2312yes—
138C2×C22⋊Dic17C2312yes—
139C2×C22⋊Dic17C2312yes—
140#10587622C2×C418yes—
141#10587621C2×C4116yescomplemented
142D4×Dic17C2×C418yes—
143D4×Dic17C2×C4116yescomplemented
144C2×C4⋊Dic17C2312yes—
145C2×C4⋊Dic17C2311yescharacteristic
146C2×C4⋊Dic17C2312yes—
147#10587610C2×C418yescomplemented
148C2×#63225C2312yes—
149C2×#63225C2312yes—
150C2×#63225C2312yes—
151C2×#63225C2312yes—
152C2×#63225C2312yes—
153C2×#63225C2312yes—
154C2×#63225C2312yes—
155C2×#63225C2312yes—
156C2×#63225C2312yes—
157C2×#63225C2312yes—
158C2×#63225C2312yes—
159C2×C4×Dic17C2×C418yescomplemented
160C2×C4×Dic17C2312yes—
161C2×C4×Dic17C2311yescharacteristic
162C2×C4×Dic17C2312yes—
163C2×C4×Dic17C2312yes—
164C2×C4×Dic17C2312yes—
165C2×C4×Dic17C2312yes—
166C2×C4×Dic17C2312yes—
167C2×C4×Dic17C2312yes—
168C2×C4×Dic17C2311yescharacteristic
169C2×C4×Dic17C2311yescharacteristic
170C2×C4×Dic17C2311yescharacteristic
171C2×C4×Dic17C2311yescharacteristic
172C2×C4×Dic17C2311yescharacteristic
173C2×C4×Dic17C2312yes—
174#10587576C2×C418yescomplemented
175#10587573C2×C418yescomplemented
176#10587565C2×C4116yescomplemented
177#10587563C2×C4116yescomplemented
178C17×#95C2312yes—
179C17×#95C2312yes—
180C17×#95C2312yes—
181C17×#95C2312yes—
182C17×#95C2312yes—
183#10587502C2312yes—
184#10587502C2312yes—
185#10587502C2312yes—
186#10587502C2312yes—
187#10587502C2312yes—
188#10587502C2312yes—
189#10587502C2312yes—
190#10587502C2312yes—
191#10587502C2312yes—
192#10587502C2312yes—
193#10587502C2312yes—
194#10587502C2312yes—
195#10587502C2312yes—
196#10587502C2312yes—
197#10587502C2312yes—
198#10587502C2312yes—
199#10587502C2312yes—
200#10587502C2312yes—
201#10587502C2312yes—
202#10587502C2312yes—
203#10587502C2312yes—
204#10587502C2312yes—
205#10587502C2312yes—
206C24×C17C2411yescharacteristic
207C24×C17C2412yes—
208C2×D4×C17—42no—
209C2×D4×C17—42no—
210C2×D4×C17—41no—
211C2×D4×C17—41no—
212C2×D4×C17C22×C414yes—
213C2×D4×C17C22×C418yes—
214C22×C4×C17—41no—
215C22×C4×C17—41no—
216C22×C4×C17—42no—
217C22×C4×C17—42no—
218C22×C4×C17—42no—
219C22×C4×C17C22×C414yes—
220C22×C4×C17C2412yes—
221C22×C4×C17C2412yes—
222C22×C4×C17C2412yes—
223C22×C4×C17C2412yes—
224C22×C4×C17C2411yescharacteristic
225C22×C4×C17C2411yescharacteristic
226C22×C4×C17C2412yes—
227C22×Dic17—42no—
228C22×Dic17—42no—
229C22×Dic17—42no—
230C22×Dic17—42no—
231C22×Dic17—42no—
232C22×Dic17—42no—
233C22×Dic17—42no—
234C22×Dic17C22×C418yes—
235C22×Dic17C22×C414yes—
236C22×Dic17C22×C414yes—
237C22×Dic17C2412yes—
238C22×Dic17C2412yes—
239C22×Dic17C2412yes—
240C22×Dic17C2412yes—
241C22×Dic17C2412yes—
242C22×Dic17C2411yescharacteristic
243C22×Dic17C2411yescharacteristic
244C22×Dic17C2411yescharacteristic
245C22×Dic17C2412yes—
246C22×Dic17C2411yescharacteristic
247C2×Dic34—41no—
248C2×Dic34—41no—
249C2×Dic34C22×C414yes—
250C4⋊C4×C17—42no—
251C4⋊C4×C17C22×C414yes—
252C22⋊C4×C17—42no—
253C22⋊C4×C17—42no—
254C22⋊C4×C17—42no—
255C22⋊C4×C17—41no—
256C22⋊C4×C17—42no—
257C22⋊C4×C17—41no—
258C22⋊C4×C17C22×C418yes—
259C42×C17—41no—
260C42×C17—41no—
261C42×C17—42no—
262C22⋊Dic17—42no—
263C22⋊Dic17—42no—
264C22⋊Dic17—41no—
265C22⋊Dic17—42no—
266C22⋊Dic17—42no—
267C22⋊Dic17—41no—
268C22⋊Dic17C22×C418yes—
269C22⋊Dic17C22×C418yes—
270C22⋊Dic17C22×C418yes—
271C22⋊Dic17C22×C418yes—
272C4⋊Dic17—42no—
273C4⋊Dic17C22×C418yes—
274C4⋊Dic17C22×C414yes—
275#63225—42no—
276#63225—42no—
277#63225—42no—
278#63225—42no—
279#63225—42no—
280#63225—42no—
281#63225—42no—
282#63225—42no—
283#63225C22×C418yes—
284#63225C22×C418yes—
285#63225C22×C418yes—
286C4×Dic17—42no—
287C4×Dic17—42no—
288C4×Dic17—42no—
289C4×Dic17—42no—
290C4×Dic17—42no—
291C4×Dic17—42no—
292C4×Dic17—41no—
293C4×Dic17—41no—
294C4×Dic17—42no—
295C4×Dic17C22×C414yes—
296C4×Dic17C22×C418yes—
297C4×Dic17C22×C414yes—
298C4×Dic17C22×C414yes—
299C4×Dic17C22×C414yes—
300#34405—171nomaximal, Sylow
301C23×C17—22no—
302C23×C17—21no—
303C23×C17—21no—
304C23×C17—22no—
305C23×C17—22no—
306C23×C17—22no—
307C23×C17—22no—
308C23×C17—22no—
309C23×C17—22no—
310C23×C17—22no—
311C23×C17C23×C414yes—
312C23×C17C23×C412yes—
313C23×C17C2511yescharacteristic
314D4×C17—44no—
315D4×C17—48no—
316C2×C4×C17—21no—
317C2×C4×C17—21no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—21no—
321C2×C4×C17—21no—
322C2×C4×C17—22no—
323C2×C4×C17—22no—
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—22no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—22no—
333C2×C4×C17—22no—
334C2×C4×C17—44no—
335C2×C4×C17—84no—
336C2×C4×C17C23×C412yes—
337C2×C4×C17C23×C414yes—
338C2×C4×C17C23×C412yes—
339C2×Dic17—22no—
340C2×Dic17—22no—
341C2×Dic17—22no—
342C2×Dic17—22no—
343C2×Dic17—22no—
344C2×Dic17—22no—
345C2×Dic17—22no—
346C2×Dic17—22no—
347C2×Dic17—22no—
348C2×Dic17—22no—
349C2×Dic17—22no—
350C2×Dic17—22no—
351C2×Dic17—22no—
352C2×Dic17—22no—
353C2×Dic17—22no—
354C2×Dic17—22no—
355C2×Dic17—22no—
356C2×Dic17—22no—
357C2×Dic17—22no—
358C2×Dic17—22no—
359C2×Dic17—48no—
360C2×Dic17—44no—
361C2×Dic17—44no—
362C2×Dic17—84no—
363C2×Dic17C23×C414yes—
364C2×Dic17C23×C412yes—
365C2×Dic17C23×C412yes—
366C2×Dic17C23×C412yes—
367C2×Dic17C23×C414yes—
368C2×Dic17C23×C412yes—
369Dic34—44no—
370C2×#529—171no—
371#2382—172no—
372#2379—172no—
373#2373—172no—
374#2373—172no—
375#2356—172no—
376#2353—172no—
377#2347—172no—
378#2343—172no—
379#2335—172no—
380#2335—172no—
381#2333—171no—
382#2333D1711yescharacteristic
383#2332—171no—
384#2332—171no—
385#2319—172no—
386#2318—172no—
387#2283—171no—
388#2283—171no—
389C22×C17—22no—
390C22×C17—22no—
391C22×C17—24no—
392C22×C17—22no—
393C22×C17—24no—
394C22×C17—24no—
395C22×C17—42no—
396C22×C17—42no—
397C22×C17—42no—
398C22×C17—42no—
399C22×C17—42no—
400C22×C17—42no—
401C22×C17C24×C411yescharacteristic
402C22×C17#58511yescharacteristic
403C22×C17#58512yes—
404C22×C17#58511yescharacteristic
405C22×C17#58512yes—
406C4×C17—22no—
407C4×C17—22no—
408C4×C17—24no—
409C4×C17—42no—
410C4×C17—42no—
411C4×C17—42no—
412C4×C17—42no—
413Dic17—24no—
414Dic17—22no—
415Dic17—22no—
416Dic17—22no—
417Dic17—24no—
418Dic17—22no—
419Dic17—42no—
420Dic17—42no—
421Dic17—42no—
422Dic17—42no—
423#529—1716no—
424C2×#126—172no—
425C2×#125—171no—
426C2×#124—171no—
427C2×#123—172no—
428C2×C22⋊Q8—171no—
429C2×#121C2×D1711yescharacteristic
430C2×C4×Q8—171no—
431C2×C4×D4—172no—
432C2×C4×D4—171no—
433C2×#117—172no—
434C22×C42—171no—
435#391—172no—
436#391—172no—
437#390—172no—
438#390C2×D1712yes—
439#389—172no—
440#389—172no—
441#389—172no—
442#389—172no—
443#388—172no—
444#388—172no—
445#388—172no—
446#388—172no—
447#388—172no—
448#388—172no—
449#388—172no—
450#388—172no—
451#388—172no—
452#388—172no—
453#388—172no—
454#388C2×D1712yes—
455#387—172no—
456#387—172no—
457#387—172no—
458#387—172no—
459#387—172no—
460#387—172no—
461#387—172no—
462#387—172no—
463#387—172no—
464#387—172no—
465#387—172no—
466#387C2×D1712yes—
467#386—172no—
468#386—172no—
469#386C2×D1712yes—
470#386C2×D1712yes—
471#385—172no—
472#385—172no—
473#385—172no—
474#385—172no—
475#383—172no—
476#383—172no—
477#383—172no—
478#382—172no—
479#382—172no—
480#382—172no—
481#381—171no—
482#381—172no—
483#381—172no—
484#381C2×D1711yescharacteristic
485#380—171no—
486#380—171no—
487#380—172no—
488#380—172no—
489C4×C4⋊C4—172no—
490C4×C4⋊C4—172no—
491C4×C4⋊C4—172no—
492C4×C4⋊C4—171no—
493C4×C4⋊C4—171no—
494C4×C4⋊C4—172no—
495C4×C4⋊C4—172no—
496C4×C4⋊C4—172no—
497C4×C22⋊C4—171no—
498C4×C22⋊C4—172no—
499C4×C22⋊C4—172no—
500C4×C22⋊C4—172no—
501C4×C22⋊C4—171no—
502C4×C22⋊C4—171no—
503C4×C22⋊C4—172no—
504C4×C22⋊C4C2×D1711yescharacteristic
505C4×C22⋊C4C2×D1712yes—
506#376—172no—
507#376—171no—
508#376—171no—
509#376—172no—
510C2×#95—172no—
511C2×C17—42no—
512C2×C17—44no—
513C2×C17#342811yescharacteristic
514C2×C17#342811yescharacteristic
515C2×C17#342811yescharacteristic
516C2×C17#356712yes—
517C2×C17#356812yes—
518C22×Q8—171no—
519C22×D4C22×D1712yes—
520C22×D4C22×D1711yescharacteristic
521C23×C4—172no—
522C23×C4—171no—
523C23×C4—171no—
524C23×C4—172no—
525C23×C4C22×D1712yes—
526C23×C4C22×D1711yescharacteristic
527#126—1716no—
528#125—178no—
529#124—178no—
530#123—1716no—
531C22⋊Q8—178no—
532#121C4×D1718yes—
533C4×Q8—178no—
534C4×D4—178no—
535C4×D4—1716no—
536#117—1716no—
537C2×C4⋊C4—172no—
538C2×C4⋊C4—172no—
539C2×C4⋊C4—171no—
540C2×C4⋊C4—172no—
541C2×C4⋊C4—172no—
542C2×C4⋊C4—172no—
543C2×C4⋊C4—172no—
544C2×C4⋊C4—172no—
545C2×C4⋊C4—172no—
546C2×C4⋊C4—172no—
547C2×C4⋊C4—172no—
548C2×C4⋊C4—172no—
549C2×C4⋊C4—172no—
550C2×C4⋊C4—172no—
551C2×C4⋊C4C22×D1712yes—
552C2×C4⋊C4C22×D1711yescharacteristic
553C2×C22⋊C4—172no—
554C2×C22⋊C4—172no—
555C2×C22⋊C4—172no—
556C2×C22⋊C4—172no—
557C2×C22⋊C4—171no—
558C2×C22⋊C4—172no—
559C2×C22⋊C4—171no—
560C2×C22⋊C4—172no—
561C2×C22⋊C4—172no—
562C2×C22⋊C4—172no—
563C2×C22⋊C4C22×D1711yescharacteristic
564C2×C22⋊C4C22×D1711yescharacteristic
565C2×C22⋊C4C22×D1712yes—
566C2×C22⋊C4C22×D1712yes—
567C2×C22⋊C4C22×D1712yes—
568C2×C22⋊C4C22×D1712yes—
569C2×C22⋊C4C22×D1712yes—
570C2×C42—178no—
571C2×C42—171no—
572C2×C42—172no—
573C2×C42—171no—
574C2×C42—171no—
575C2×C42—171no—
576C2×C42—171no—
577C2×C42—172no—
578C2×C42—172no—
579C2×C42—171no—
580C2×C42—172no—
581C2×C42—172no—
582C2×C42—172no—
583C2×C42—172no—
584C2×C42—172no—
585C2×C42C22×D1711yescharacteristic
586C2×C42C22×D1711yescharacteristic
587C2×C42C22×D1712yes—
588#95—172no—
589#95—172no—
590#95—172no—
591#95—172no—
592#95—172no—
593#95—172no—
594#95—172no—
595#95—172no—
596#95—172no—
597#95—172no—
598#95—172no—
599#95—172no—
600#95—172no—
601#95—172no—
602#95—172no—
603#95—172no—
604#95—172no—
605#95—172no—
606#95—172no—
607#95—172no—
608#95—172no—
609#95—172no—
610#95—172no—
611#95C22×D1712yes—
612#95C22×D1712yes—
613#95C22×D1712yes—
614#95C22×D1712yes—
615#95C22×D1712yes—
616C17#3440511yescharacteristic, complemented, Sylow
617C24C23×D1711yescharacteristic
618C24C23×D1712yes—
619C2×Q8—174no—
620C2×Q8—681no—
621C2×Q8—681no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4C2×C4×D1718yes—
627C2×D4C2×C4×D1714yes—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—171no—
634C22×C4—171no—
635C22×C4—172no—
636C22×C4—171no—
637C22×C4—171no—
638C22×C4—172no—
639C22×C4—174no—
640C22×C4—174no—
641C22×C4—178no—
642C22×C4—172no—
643C22×C4—172no—
644C22×C4—172no—
645C22×C4—172no—
646C22×C4—682no—
647C22×C4—682no—
648C22×C4—682no—
649C22×C4—682no—
650C22×C4—682no—
651C22×C4—682no—
652C22×C4—682no—
653C22×C4C2×C4×D1714yes—
654C22×C4C23×D1712yes—
655C22×C4C23×D1712yes—
656C22×C4C23×D1712yes—
657C22×C4C23×D1712yes—
658C22×C4C23×D1711yescharacteristic
659C22×C4C23×D1711yescharacteristic
660C22×C4C23×D1712yes—
661C4⋊C4—42no—
662C4⋊C4—178no—
663C4⋊C4—178no—
664C4⋊C4—174no—
665C4⋊C4—178no—
666C4⋊C4—178no—
667C4⋊C4—682no—
668C4⋊C4—682no—
669C4⋊C4—682no—
670C4⋊C4—682no—
671C4⋊C4—682no—
672C4⋊C4—682no—
673C4⋊C4—682no—
674C4⋊C4—682no—
675C4⋊C4—682no—
676C4⋊C4C2×C4×D1714yes—
677C22⋊C4—42no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—41no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—178no—
684C22⋊C4—178no—
685C22⋊C4—178no—
686C22⋊C4—178no—
687C22⋊C4—682no—
688C22⋊C4—681no—
689C22⋊C4—682no—
690C22⋊C4—681no—
691C22⋊C4—682no—
692C22⋊C4—682no—
693C22⋊C4C2×C4×D1718yes—
694C42—41no—
695C42—41no—
696C42—42no—
697C42—174no—
698C42—174no—
699C42—174no—
700C42—174no—
701C42—178no—
702C42—681no—
703C42—681no—
704C42—682no—
705C42—682no—
706C42—682no—
707C42—682no—
708C42—682no—
709C42—682no—
710C42—682no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23C22×C4×D1714yes—
722C23C22×C4×D1712yes—
723C23C24×D1711yescharacteristic
724Q8—684no—
725D4—44no—
726D4—48no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—44no—
746C2×C4—84no—
747C2×C4—172no—
748C2×C4—172no—
749C2×C4—172no—
750C2×C4—172no—
751C2×C4—174no—
752C2×C4—174no—
753C2×C4—342no—
754C2×C4—342no—
755C2×C4—342no—
756C2×C4—342no—
757C2×C4—342no—
758C2×C4—342no—
759C2×C4—342no—
760C2×C4—342no—
761C2×C4—342no—
762C2×C4—342no—
763C2×C4—342no—
764C2×C4—342no—
765C2×C4—342no—
766C2×C4—342no—
767C2×C4—342no—
768C2×C4—342no—
769C2×C4—342no—
770C2×C4—342no—
771C2×C4—342no—
772C2×C4—342no—
773C2×C4—684no—
774C2×C4—684no—
775C2×C4—688no—
776C2×C4—1364no—
777C2×C4C22×C4×D1712yes—
778C2×C4C22×C4×D1712yes—
779C2×C4C22×C4×D1714yes—
780C22—22no—
781C22—22no—
782C22—24no—
783C22—24no—
784C22—22no—
785C22—24no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C23×C4×D1711yescharacteristic
793C22#1176364411yescharacteristic
794C22#1176364412yes—
795C22#1176364411yescharacteristic
796C22#1176364512yes—
797C4—22no—
798C4—22no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—342no—
805C4—342no—
806C4—344no—
807C4—342no—
808C4—342no—
809C4—344no—
810C4—682no—
811C4—682no—
812C4—682no—
813C4—682no—
814C2—42no—
815C2—44no—
816C2#1454198211yescharacteristic
817C2#1454198211yescharacteristic
818C2#1454198311yescharacteristic
819C2#1454346912yes—
820C2#1454347712yes—
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2333C2
socle, cosocleC23×C17C25
prime radicalC2×C17×#121C22
hypercenter#2333D17
hypocenterC17#34405
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2333

Complements

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

NH ≅ G/Ntype
2. #14531967C2semidirect
3. #14531954C2semidirect
4. #14531905C2semidirect
5. #14531901C2semidirect
6. #14531746C2semidirect
7. #14531722C2semidirect
8. #14531674C2semidirect
9. #14531638C2semidirect
10. #14531575C2semidirect
11. #14531571C2semidirect
13. #14531540C2semidirect
14. #14531537C2semidirect
15. #14531421C2semidirect
16. #14531410C2semidirect
17. #14531178C2semidirect
18. #14531175C2semidirect
20. #11763340C4semidirect
141. #10587621C2×C4semidirect
143. D4×Dic17C2×C4semidirect
147. #10587610C2×C4semidirect
159. C2×C4×Dic17C2×C4semidirect
174. #10587576C2×C4semidirect
175. #10587573C2×C4semidirect
176. #10587565C2×C4semidirect
177. #10587563C2×C4semidirect
616. C17#34405semidirect

Maximal subgroups

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

subgroupindex
C2×#117633402
#145319672
#145319542
#145319052
#145319012
#145317462
#145317222
#145316742
#145316382
#145315752
#145315712
#145315512
#145315402
#145315372
#145314212
#145314102
#145311782
#145311752
C17×#23332
#3440517