Finite Group Databasebeta

← C2×#14538998 #17902587

Subgroups — C2×#14538998 #17902587

Order 4352.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763421C211yesmaximal, characteristic, complemented
2#14538998C2116yesmaximal, direct product factor
3C2×#11763144C211yesmaximal, characteristic, complemented
4C2×#11763139C211yesmaximal, characteristic, complemented
5C2×#11763116C211yesmaximal, characteristic, complemented
6C2×#11763109C211yesmaximal, characteristic, complemented
7C2×#11763019C211yesmaximal, characteristic, complemented
8C2×#11763014C211yesmaximal, characteristic, complemented
9C2×#11762971C211yesmaximal, characteristic
10C2×#11762971C211yesmaximal, characteristic
11C2×#11762914C211yesmaximal, characteristic, complemented
12C2×#11762909C211yesmaximal, characteristic, complemented
13C2×C4×#63231C211yesmaximal, characteristic, complemented
14C2×C4×#63229C211yesmaximal, characteristic, complemented
15C2×#11762870C211yesmaximal, characteristic, complemented
16C2×C17×#520C211yesmaximal, characteristic
17C22×#63231C2211yescharacteristic
18C22×#63231C2211yescharacteristic
19C22×#63229C2211yescharacteristic
20C22×#63229C2211yescharacteristic
21#11763421—24no—
22#11763421C2218yescomplemented
23C2×#10587555C2211yescharacteristic
24C2×#10587565—21no—
25C2×#10587565—21no—
26C2×#10587556C2211yescharacteristic
27C2×#10587575—21no—
28C2×#10587575—21no—
29C2×#10587610C2211yescharacteristic
30C2×#10587610C2211yescharacteristic
31C2×C4×Dic34C2211yescharacteristic
32C2×C4×Dic34C2211yescharacteristic
33#11763144C2218yescomplemented
34#11763139C2218yescomplemented
35#11763116C2218yescomplemented
36#11763109C2218yescomplemented
37#11763019C2218yescomplemented
38#11763014C2218yescomplemented
39#11762971C2218yes—
40#11762971C2218yes—
41#11762914C2218yescomplemented
42#11762909C2218yescomplemented
43C4×#63231C2218yescomplemented
44C4×#63229C2218yescomplemented
45#11762870C2218yescomplemented
46C2×#10587478C2211yescharacteristic
47C2×#10587478C2211yescharacteristic
48C2×#10587479C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×C4⋊#3622C2211yescharacteristic
51C2×C4⋊#3622C2211yescharacteristic
52C2×#10587506C2211yescharacteristic
53C2×#10587506C2211yescharacteristic
54C2×#10587481C2211yescharacteristic
55C2×#10587481C2211yescharacteristic
56C2×#10587481C2211yescharacteristic
57C2×#10587481C2211yescharacteristic
58C2×#10587503C2211yescharacteristic
59C2×#10587503C2211yescharacteristic
60C2×C22⋊#3622C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C22×#41×C17C2211yescharacteristic
65C17×#520—24no—
66C17×#520C2218yes—
67C2×C4×Q8×C17C2211yescharacteristic
68C2×C4×Q8×C17C2211yescharacteristic
69C2×C4×D4×C17—21no—
70C2×C4×D4×C17—21no—
71C2×C4×D4×C17C2211yescharacteristic
72C2×C4×D4×C17C2211yescharacteristic
73C2×C17×#117—21no—
74C2×C17×#117C2211yescharacteristic
75C22×C4⋊C4×C17—21no—
76C22×C4⋊C4×C17C2211yescharacteristic
77C2×#41×C17—24no—
78C2×#41×C17—24no—
79C2×#41×C17—22no—
80C2×#41×C17C2314yes—
81C22×Q8×C17C2311yescharacteristic
82C22×D4×C17—21no—
83C22×D4×C17C2311yescharacteristic
84C23×C4×C17—21no—
85C23×C4×C17—21no—
86C23×C4×C17—21no—
87C23×C4×C17—21no—
88C23×C4×C17C2311yescharacteristic
89C22×Dic34C2311yescharacteristic
90C22×Dic34C2311yescharacteristic
91C4×Q8×C17—22no—
92C4×Q8×C17—22no—
93C4×Q8×C17C2314yes—
94C4×Q8×C17C2314yes—
95C4×D4×C17—28no—
96C4×D4×C17—28no—
97C4×D4×C17—22no—
98C4×D4×C17—22no—
99C4×D4×C17C2314yes—
100C4×D4×C17C2314yes—
101C17×#117—28no—
102C17×#117D414yes—
103C17×#117C2314yes—
104C2×C4⋊C4×C17—21no—
105C2×C4⋊C4×C17—21no—
106C2×C4⋊C4×C17—21no—
107C2×C4⋊C4×C17—22no—
108C2×C4⋊C4×C17—28no—
109C2×C4⋊C4×C17D411yescharacteristic
110C2×C4⋊C4×C17D411yescharacteristic
111C2×C4⋊C4×C17C2311yescharacteristic
112C2×C4⋊C4×C17C2311yescharacteristic
113C2×C4⋊C4×C17C2314yes—
114C2×C22⋊C4×C17—21no—
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17D411yescharacteristic
117C2×C22⋊C4×C17D411yescharacteristic
118C2×C42×C17—21no—
119C2×C42×C17—21no—
120C2×C42×C17C2311yescharacteristic
121C2×C42×C17C2311yescharacteristic
122C2×C22⋊Dic17—21no—
123C2×C22⋊Dic17—21no—
124C2×#63231—24no—
125C2×#63231—24no—
126C2×#63231C2314yes—
127C2×#63231C2314yes—
128C2×#63229—24no—
129C2×#63229—24no—
130C2×#63229C2314yes—
131C2×#63229C2314yes—
132C2×C4⋊Dic17—21no—
133C2×C4⋊Dic17—21no—
134C2×C4⋊Dic17C2311yescharacteristic
135C2×C4⋊Dic17C2311yescharacteristic
136#10587610—22no—
137#10587610—22no—
138#10587610C2314yes—
139#10587610C2314yes—
140C2×#63225—21no—
141C2×#63225—21no—
142C2×#63225—21no—
143C2×#63225—21no—
144C2×#63225—21no—
145C2×#63225—21no—
146C2×C4×Dic17—21no—
147C2×C4×Dic17—21no—
148C22×#3622C2311yescharacteristic
149C22×#3622C2311yescharacteristic
150C22×#3622C2311yescharacteristic
151C22×#3622C2311yescharacteristic
152#10587575—28no—
153#10587575—28no—
154#10587565—28no—
155#10587565—28no—
156#10587556—22no—
157#10587556C2314yes—
158#10587555—22no—
159#10587555C2314yes—
160C4×Dic34—22no—
161C4×Dic34—22no—
162C4×Dic34C2314yes—
163C4×Dic34C2314yes—
164#10587506C2314yes—
165#10587506C2314yes—
166#10587503C2314yes—
167#10587503C2314yes—
168C22⋊#3622C2314yes—
169C22⋊#3622C2314yes—
170#10587481C2314yes—
171#10587481C2314yes—
172#10587481C2314yes—
173#10587481C2314yes—
174#10587479C2314yes—
175#10587479C2314yes—
176#10587478C2314yes—
177#10587478C2314yes—
178C4⋊#3622C2314yes—
179C4⋊#3622C2314yes—
180#10587474C2314yes—
181C4×#3622C2314yes—
182C24×C17—21no—
183C24×C17C2×D411yescharacteristic
184#41×C17—216no—
185#41×C17—28no—
186#41×C17—28no—
187C2×Q8×C17—21no—
188C2×Q8×C17—22no—
189C2×Q8×C17#4114yes—
190C2×Q8×C17C2412yes—
191C2×D4×C17—28no—
192C2×D4×C17—24no—
193C2×D4×C17—21no—
194C2×D4×C17—22no—
195C2×D4×C17#4114yes—
196C2×D4×C17C2412yes—
197C22×C4×C17—28no—
198C22×C4×C17—21no—
199C22×C4×C17—24no—
200C22×C4×C17—22no—
201C22×C4×C17—22no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—24no—
205C22×C4×C17—24no—
206C22×C4×C17—24no—
207C22×C4×C17—82no—
208C22×C4×C17—82no—
209C22×C4×C17—82no—
210C22×C4×C17C2×D411yescharacteristic
211C22×C4×C17C2×D411yescharacteristic
212C22×C4×C17C2×D411yescharacteristic
213C22×C4×C17C2×D412yes—
214C22×C4×C17C2×D411yescharacteristic
215C22×C4×C17C2×D411yescharacteristic
216C22×C4×C17C2412yes—
217C22×C4×C17C2411yescharacteristic
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C2×Dic34—22no—
223C2×Dic34—22no—
224C2×Dic34—22no—
225C2×Dic34—22no—
226C2×Dic34—21no—
227C2×Dic34—21no—
228C2×Dic34C2412yes—
229C2×Dic34C2412yes—
230C4⋊C4×C17—24no—
231C4⋊C4×C17—24no—
232C4⋊C4×C17—24no—
233C4⋊C4×C17—21no—
234C4⋊C4×C17—21no—
235C4⋊C4×C17C2×D414yes—
236C4⋊C4×C17C2×D414yes—
237C4⋊C4×C17C2412yes—
238C4⋊C4×C17C2412yes—
239C22⋊C4×C17—24no—
240C22⋊C4×C17—24no—
241C22⋊C4×C17C2×D414yes—
242C22⋊C4×C17C2×D414yes—
243C42×C17—24no—
244C42×C17—24no—
245C42×C17C2×D412yes—
246C42×C17C2×D412yes—
247C42×C17C2412yes—
248C42×C17C2412yes—
249C22⋊Dic17—24no—
250C22⋊Dic17—24no—
251#63231—28no—
252#63231—28no—
253#63229—28no—
254#63229—28no—
255C4⋊Dic17—21no—
256C4⋊Dic17—21no—
257C4⋊Dic17—24no—
258C4⋊Dic17—24no—
259C4⋊Dic17C2412yes—
260C4⋊Dic17C2412yes—
261#63225—24no—
262#63225—24no—
263#63225—24no—
264#63225—24no—
265#63225—24no—
266#63225—24no—
267C4×Dic17—24no—
268C4×Dic17—24no—
269C2×#3622—22no—
270C2×#3622—22no—
271C2×#3622—22no—
272C2×#3622—22no—
273C2×#3622C2412yes—
274C2×#3622C2412yes—
275C2×#3622C2412yes—
276C2×#3622C2412yes—
277C2×#3120—171nomaximal, Sylow
278C23×C17—22no—
279C23×C17—24no—
280C23×C17—22no—
281C23×C17—22no—
282C23×C17—22no—
283C23×C17—42no—
284C23×C17—42no—
285C23×C17C22×D412yes—
286C23×C17C22×D411yescharacteristic
287Q8×C17—24no—
288Q8×C17—22no—
289Q8×C17C2×#4114yes—
290D4×C17—216no—
291D4×C17—24no—
292D4×C17—22no—
293D4×C17C2×#4114yes—
294C2×C4×C17—216no—
295C2×C4×C17—22no—
296C2×C4×C17—24no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—24no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—42no—
308C2×C4×C17—42no—
309C2×C4×C17—84no—
310C2×C4×C17—84no—
311C2×C4×C17—84no—
312C2×C4×C17C22×D412yes—
313C2×C4×C17C22×D412yes—
314C2×C4×C17C22×D412yes—
315C2×C4×C17C22×D412yes—
316C2×C4×C17C22×D412yes—
317C2×C4×C17C22×D411yescharacteristic
318C2×C4×C17C2×#4112yes—
319C2×C4×C17C2×#4112yes—
320C2×C4×C17C2511yescharacteristic
321C2×Dic17—22no—
322C2×Dic17—22no—
323C2×Dic17—22no—
324C2×Dic17—22no—
325C2×Dic17—42no—
326C2×Dic17—42no—
327C2×Dic17—42no—
328C2×Dic17—42no—
329Dic34—22no—
330Dic34—22no—
331Dic34—22no—
332Dic34—22no—
333Dic34—42no—
334Dic34—42no—
335#3622—22no—
336#3622—22no—
337#3622—22no—
338#3622—22no—
339C2×#541—171no—
340C2×#520D1711yescharacteristic
341#3120—1716no—
342C2×#484—171no—
343C2×#483—171no—
344C2×#479—171no—
345C2×#478—171no—
346C2×#462—171no—
347C2×#461—171no—
348C2×#452—171no—
349C2×#452—171no—
350C2×#441—171no—
351C2×#440—171no—
352C2×C4×Q16—171no—
353C2×C4×SD16—171no—
354C2×#433—171no—
355C22×C17—22no—
356C22×C17—24no—
357C22×C17—22no—
358C22×C17—22no—
359C22×C17—44no—
360C22×C17—48no—
361C22×C17—42no—
362C22×C17—42no—
363C22×C17#52512yes—
364C22×C17#57712yes—
365C22×C17#57812yes—
366C22×C17C23×D411yescharacteristic
367C4×C17—22no—
368C4×C17—24no—
369C4×C17—22no—
370C4×C17—22no—
371C4×C17—22no—
372C4×C17—22no—
373C4×C17—42no—
374C4×C17—42no—
375C4×C17#52512yes—
376C4×C17C22×#4111yescharacteristic
377C4×C17C22×#4111yescharacteristic
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381Dic17—42no—
382C22×#41C2×D1711yescharacteristic
383C22×Q16—171no—
384C22×Q16—171no—
385C22×SD16—171no—
386C22×SD16—171no—
387#541—178no—
388#541—344no—
389C2×C4⋊Q8—171no—
390C2×#126—341no—
391C2×#126—341no—
392C2×#125—171no—
393C2×#125—341no—
394C2×#125—341no—
395C2×C22⋊Q8—171no—
396C2×C22⋊Q8—171no—
397#520—24no—
398#520C2×D1718yes—
399C2×C4×Q8—171no—
400C2×C4×Q8—171no—
401C2×C4×Q8C2×D1711yescharacteristic
402C2×C4×Q8C2×D1711yescharacteristic
403C2×C4×D4—21no—
404C2×C4×D4—21no—
405C2×C4×D4C2×D1711yescharacteristic
406C2×C4×D4C2×D1711yescharacteristic
407C2×#117—21no—
408C2×#117C2×D1711yescharacteristic
409C22×C4⋊C4—21no—
410C22×C4⋊C4C2×D1711yescharacteristic
411#484—178no—
412#483—178no—
413#479—178no—
414#478—178no—
415#462—178no—
416#461—178no—
417#452—178no—
418#452—178no—
419#441—178no—
420#440—178no—
421C4×Q16—178no—
422C4×SD16—178no—
423#433—178no—
424C2×#107—171no—
425C2×#107—171no—
426C2×#106—171no—
427C2×#106—171no—
428C2×C4⋊C8—171no—
429C2×C4⋊C8—171no—
430C2×#103—171no—
431C2×#103—171no—
432C2×#103—171no—
433C2×#103—171no—
434C2×#103—171no—
435C2×#103—171no—
436C2×#102—171no—
437C2×#102—171no—
438C2×C22⋊C8—171no—
439C2×C22⋊C8—171no—
440C2×#97—171no—
441C2×C4×C8—171no—
442C2×C17—42no—
443C2×C17—44no—
444C2×C17#312014yescomplemented
445C2×C17C2×#52511yescharacteristic
446C2×C17C2×#57711yescharacteristic
447C2×C17C2×#57811yescharacteristic
448C2×#41—24no—
449C2×#41—24no—
450C2×#41—22no—
451C2×#41C22×D1714yes—
452C22×Q8—171no—
453C22×Q8—171no—
454C22×Q8C22×D1711yescharacteristic
455C22×D4—21no—
456C22×D4C22×D1711yescharacteristic
457C23×C4—21no—
458C23×C4—21no—
459C23×C4—21no—
460C23×C4—21no—
461C23×C4C22×D1711yescharacteristic
462C2×Q16—174no—
463C2×Q16—174no—
464C2×Q16—344no—
465C2×Q16—344no—
466C2×SD16—174no—
467C2×SD16—174no—
468C2×SD16—344no—
469C2×SD16—344no—
470C22×C8—171no—
471C22×C8—171no—
472C22×C8—171no—
473C22×C8—171no—
474C4⋊Q8—174no—
475C4⋊Q8—342no—
476#126—348no—
477#126—348no—
478#125—174no—
479#125—348no—
480#125—348no—
481#125—342no—
482C22⋊Q8—174no—
483C22⋊Q8—174no—
484C22⋊Q8—342no—
485C22⋊Q8—342no—
486C4×Q8—22no—
487C4×Q8—22no—
488C4×Q8—174no—
489C4×Q8—174no—
490C4×Q8—342no—
491C4×Q8—342no—
492C4×Q8C22×D1714yes—
493C4×Q8C22×D1714yes—
494C4×D4—28no—
495C4×D4—28no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4C22×D1714yes—
499C4×D4C22×D1714yes—
500#117—28no—
501#117C22⋊D1714yes—
502#117C22×D1714yes—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—28no—
508C2×C4⋊C4—171no—
509C2×C4⋊C4—171no—
510C2×C4⋊C4—341no—
511C2×C4⋊C4—341no—
512C2×C4⋊C4—341no—
513C2×C4⋊C4—341no—
514C2×C4⋊C4—341no—
515C2×C4⋊C4—341no—
516C2×C4⋊C4—341no—
517C2×C4⋊C4—341no—
518C2×C4⋊C4C22⋊D1711yescharacteristic
519C2×C4⋊C4C22⋊D1711yescharacteristic
520C2×C4⋊C4C22×D1711yescharacteristic
521C2×C4⋊C4C22×D1711yescharacteristic
522C2×C4⋊C4C22×D1714yes—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—341no—
526C2×C22⋊C4—341no—
527C2×C22⋊C4C22⋊D1711yescharacteristic
528C2×C22⋊C4C22⋊D1711yescharacteristic
529C2×C42—21no—
530C2×C42—21no—
531C2×C42—341no—
532C2×C42—341no—
533C2×C42C22×D1711yescharacteristic
534C2×C42C22×D1711yescharacteristic
535#107—174no—
536#107—174no—
537#106—174no—
538#106—174no—
539C4⋊C8—174no—
540C4⋊C8—174no—
541#103—174no—
542#103—174no—
543#103—174no—
544#103—174no—
545#103—174no—
546#103—174no—
547#102—174no—
548#102—174no—
549C22⋊C8—174no—
550C22⋊C8—174no—
551#97—174no—
552C4×C8—174no—
553C17C2×#312011yescharacteristic, complemented, Sylow
554C24—21no—
555C24C2×C22⋊D1711yescharacteristic
556#41—216no—
557#41—28no—
558#41—28no—
559C2×Q8—22no—
560C2×Q8—21no—
561C2×Q8—172no—
562C2×Q8—172no—
563C2×Q8—341no—
564C2×Q8—341no—
565C2×Q8—342no—
566C2×Q8—342no—
567C2×Q8—342no—
568C2×Q8—342no—
569C2×Q8#6325214yes—
570C2×Q8C23×D1712yes—
571C2×D4—28no—
572C2×D4—24no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4#6325214yes—
576C2×D4C23×D1712yes—
577C22×C4—28no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—82no—
590C22×C4—341no—
591C22×C4—341no—
592C22×C4—341no—
593C22×C4—341no—
594C22×C4C2×C22⋊D1712yes—
595C22×C4C2×C22⋊D1711yescharacteristic
596C22×C4C2×C22⋊D1711yescharacteristic
597C22×C4C2×C22⋊D1711yescharacteristic
598C22×C4C2×C22⋊D1711yescharacteristic
599C22×C4C2×C22⋊D1711yescharacteristic
600C22×C4C23×D1712yes—
601C22×C4C23×D1711yescharacteristic
602Q16—348no—
603Q16—348no—
604SD16—348no—
605SD16—348no—
606C2×C8—172no—
607C2×C8—172no—
608C2×C8—172no—
609C2×C8—172no—
610C2×C8—342no—
611C2×C8—342no—
612C2×C8—342no—
613C2×C8—342no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—172no—
620C4⋊C4—172no—
621C4⋊C4—341no—
622C4⋊C4—341no—
623C4⋊C4—344no—
624C4⋊C4—344no—
625C4⋊C4—344no—
626C4⋊C4—344no—
627C4⋊C4—344no—
628C4⋊C4—344no—
629C4⋊C4—344no—
630C4⋊C4—344no—
631C4⋊C4C2×C22⋊D1714yes—
632C4⋊C4C2×C22⋊D1714yes—
633C4⋊C4C23×D1712yes—
634C4⋊C4C23×D1712yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—344no—
638C22⋊C4—344no—
639C22⋊C4C2×C22⋊D1714yes—
640C22⋊C4C2×C22⋊D1714yes—
641C42—24no—
642C42—24no—
643C42—344no—
644C42—344no—
645C42C2×C22⋊D1712yes—
646C42C2×C22⋊D1712yes—
647C42C23×D1712yes—
648C42C23×D1712yes—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23C22×C22⋊D1712yes—
657C23C22×C22⋊D1711yescharacteristic
658Q8—24no—
659Q8—22no—
660Q8—342no—
661Q8—342no—
662Q8—342no—
663Q8—342no—
664Q8—682no—
665Q8—682no—
666Q8C2×#6325214yes—
667D4—216no—
668D4—24no—
669D4—22no—
670D4C2×#6325214yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—84no—
687C2×C4—84no—
688C2×C4—84no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—342no—
693C2×C4—682no—
694C2×C4—682no—
695C2×C4—682no—
696C2×C4—682no—
697C2×C4C2×#6325212yes—
698C2×C4C2×#6325212yes—
699C2×C4C22×C22⋊D1712yes—
700C2×C4C22×C22⋊D1712yes—
701C2×C4C22×C22⋊D1712yes—
702C2×C4C22×C22⋊D1712yes—
703C2×C4C22×C22⋊D1712yes—
704C2×C4C22×C22⋊D1711yescharacteristic
705C2×C4C24×D1711yescharacteristic
706C8—342no—
707C8—342no—
708C8—342no—
709C8—342no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—24no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—48no—
718C22#1176332012yes—
719C22#1176362012yes—
720C22#1176362412yes—
721C22C23×C22⋊D1711yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—682no—
731C4—682no—
732C4—682no—
733C4—682no—
734C4#1176332012yes—
735C4C22×#6325211yescharacteristic
736C4C22×#6325211yescharacteristic
737C2—42no—
738C2—44no—
739C2#1453899814yesdirect product factor
740C2C2×#1176332011yescharacteristic
741C2C2×#1176362011yescharacteristic
742C2C2×#1176362411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#520C2
socleC23×C17C22×D4
prime radicalC22×#41×C17C22
hypercenterC2×#520D17
hypocenterC17C2×#3120
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#11763421C2semidirect
2. #14538998C2direct (N × H)
3. C2×#11763144C2semidirect
4. C2×#11763139C2semidirect
5. C2×#11763116C2semidirect
6. C2×#11763109C2semidirect
7. C2×#11763019C2semidirect
8. C2×#11763014C2semidirect
11. C2×#11762914C2semidirect
12. C2×#11762909C2semidirect
13. C2×C4×#63231C2semidirect
14. C2×C4×#63229C2semidirect
15. C2×#11762870C2semidirect
22. #11763421C22semidirect
33. #11763144C22semidirect
34. #11763139C22semidirect
35. #11763116C22semidirect
36. #11763109C22semidirect
37. #11763019C22semidirect
38. #11763014C22semidirect
41. #11762914C22semidirect
42. #11762909C22semidirect
43. C4×#63231C22semidirect
44. C4×#63229C22semidirect
45. #11762870C22semidirect
444. C2×C17#3120semidirect
553. C17C2×#3120semidirect
739. C2#14538998direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634212
#145389982
C2×#117631442
C2×#117631392
C2×#117631162
C2×#117631092
C2×#117630192
C2×#117630142
C2×#117629712
C2×#117629142
C2×#117629092
C2×C4×#632312
C2×C4×#632292
C2×#117628702
C2×C17×#5202
C2×#312017