Finite Group Databasebeta

← C2×#14538895 #17902506

Subgroups — C2×#14538895 #17902506

Order 4352.

2182 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763343C211yesmaximal, characteristic, complemented
2C2×C4×#63252C211yesmaximal, characteristic, complemented
3#14538895C2116yesmaximal, direct product factor
4C2×#11763151C211yesmaximal, characteristic, complemented
5C2×#11763134C211yesmaximal, characteristic, complemented
6C2×#11763117C211yesmaximal, characteristic, complemented
7C2×#11763110C211yesmaximal, characteristic, complemented
8C2×#11763032C211yesmaximal, characteristic, complemented
9C2×#11763025C211yesmaximal, characteristic, complemented
10C2×#11762973C211yesmaximal, characteristic, complemented
11C2×#11762956C211yesmaximal, characteristic
12C2×#11762922C211yesmaximal, characteristic, complemented
13C2×#11762917C211yesmaximal, characteristic, complemented
14C2×#11762911C211yesmaximal, characteristic, complemented
15C2×#11762911C211yesmaximal, characteristic, complemented
16C2×C17×#432C211yesmaximal, characteristic, complemented
17C22×#63252C2211yescharacteristic
18C22×Dic68C2211yescharacteristic
19C22×#63219C2211yescharacteristic
20C22×#63219C2211yescharacteristic
21C22×D136C2211yescharacteristic
22#11763343—24no—
23#11763343C2218yescomplemented
24C2×#10587562—21no—
25C2×#10587556C2211yescharacteristic
26C2×#10587561C2211yescharacteristic
27C2×#10587615—21no—
28C2×#10587610C2211yescharacteristic
29C2×#10587616C2211yescharacteristic
30C4×#63252—24no—
31C4×#63252C2218yescomplemented
32C2×C4×Dic34C2211yescharacteristic
33C2×C4×Dic34C2211yescharacteristic
34C2×C4×Dic34C2211yescharacteristic
35C2×C4×D68C2211yescharacteristic
36C2×C4×D68C2211yescharacteristic
37C2×C4×D68C2211yescharacteristic
38C2×C4×C22⋊D17—21no—
39C2×C4×C22⋊D17—21no—
40C2×C4×C22⋊D17—21no—
41C2×#10587612C2211yescharacteristic
42C2×#10587558—21no—
43C2×#10587558—21no—
44C2×C42×D17—21no—
45#11763151C2218yescomplemented
46#11763134C2218yescomplemented
47#11763117C2218yescomplemented
48#11763110C2218yescomplemented
49#11763032C2218yescomplemented
50#11763025C2218yescomplemented
51#11762973C2218yescomplemented
52#11762956C2218yes—
53#11762922C2218yescomplemented
54#11762917C2218yescomplemented
55#11762911C2218yescomplemented
56#11762911C2218yescomplemented
57C2×#10587489C2211yescharacteristic
58C2×#10587489C2211yescharacteristic
59C2×#10587488C2211yescharacteristic
60C2×#10587488C2211yescharacteristic
61C2×#10587487C2211yescharacteristic
62C2×#10587487C2211yescharacteristic
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587492C2211yescharacteristic
66C2×#10587492C2211yescharacteristic
67C2×#10587492C2211yescharacteristic
68C2×#10587492C2211yescharacteristic
69C22×C42×C17C2211yescharacteristic
70C17×#432C2218yescomplemented
71C2×C17×C4⋊C8C2211yescharacteristic
72C2×C17×C4⋊C8C2211yescharacteristic
73C2×C17×C22⋊C8C2211yescharacteristic
74C2×C17×C22⋊C8C2211yescharacteristic
75C2×C17×#97C2211yescharacteristic
76C2×C17×#97C2211yescharacteristic
77C23×C4×C17D411yescharacteristic
78C23×C4×C17D411yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C22×C22⋊D17—21no—
81C22×C22⋊D17—21no—
82C2×#63252—22no—
83C2×#63252—24no—
84C2×#63252—24no—
85C2×#63252C2314yes—
86C22×D68C2311yescharacteristic
87C22×D68C2311yescharacteristic
88C22×C4×D17—21no—
89C22×C4×D17—21no—
90C22×C4×D17—21no—
91C22×C4×D17—21no—
92C22×Dic34C2311yescharacteristic
93C22×Dic34C2311yescharacteristic
94C22×C8×C17C2311yescharacteristic
95C22×C8×C17C2311yescharacteristic
96C22×C8×C17C2311yescharacteristic
97C22×C8×C17C2311yescharacteristic
98C2×C42×C17D411yescharacteristic
99C2×C42×C17D411yescharacteristic
100C2×C42×C17D414yes—
101C2×C42×C17C2311yescharacteristic
102C2×C42×C17C2311yescharacteristic
103C2×C42×C17C2314yes—
104C2×C22⋊Dic17—21no—
105C2×C22⋊Dic17—21no—
106#10587616—22no—
107#10587616C2314yes—
108#10587615—28no—
109C4×C22⋊D17—28no—
110C4×C22⋊D17—28no—
111C4×C22⋊D17—28no—
112C2×#63227—21no—
113C2×#63227—21no—
114C2×#63227—21no—
115C2×#63227—21no—
116C2×#63227—21no—
117C2×#63227—21no—
118#10587612—22no—
119#10587612C2314yes—
120C2×C4⋊Dic17C2311yescharacteristic
121C2×C4⋊Dic17C2311yescharacteristic
122C2×C4⋊Dic17C2311yescharacteristic
123C2×C4⋊Dic17C2311yescharacteristic
124#10587610—22no—
125#10587610C2314yes—
126C2×#63225—21no—
127C2×#63225—21no—
128C2×#63225—21no—
129C2×#63225—21no—
130C2×#63225—21no—
131C2×#63225—21no—
132C2×C4×Dic17—21no—
133C2×C4×Dic17—21no—
134C2×C4×Dic17—21no—
135C2×C4×Dic17—21no—
136C2×Dic68—24no—
137C2×Dic68C2314yes—
138C2×D136—24no—
139C2×D136C2314yes—
140C2×#63219—24no—
141C2×#63219—24no—
142C2×#63219C2314yes—
143C2×#63219C2314yes—
144#10587562—28no—
145#10587561—22no—
146#10587561C2314yes—
147C4×D68—22no—
148C4×D68—22no—
149C4×D68—22no—
150C4×D68C2314yes—
151C4×D68C2314yes—
152C4×D68C2314yes—
153#10587558—28no—
154#10587558—28no—
155C42×D17—28no—
156#10587556—22no—
157#10587556C2314yes—
158C4×Dic34—22no—
159C4×Dic34—22no—
160C4×Dic34—22no—
161C4×Dic34C2314yes—
162C4×Dic34C2314yes—
163C4×Dic34C2314yes—
164C17×C4⋊C8C2314yes—
165C17×C4⋊C8C2314yes—
166C17×C22⋊C8C2314yes—
167C17×C22⋊C8C2314yes—
168C17×#97C2314yes—
169C17×#97C2314yes—
170#10587492C2314yes—
171#10587492C2314yes—
172#10587492C2314yes—
173#10587492C2314yes—
174#10587489C2314yes—
175#10587489C2314yes—
176#10587488C2314yes—
177#10587488C2314yes—
178#10587487C2314yes—
179#10587487C2314yes—
180#10587487C2314yes—
181#10587487C2314yes—
182C24×C17C2×D411yescharacteristic
183C23×D17—21no—
184C23×D17—21no—
185C22×C4×C17—22no—
186C22×C4×C17—22no—
187C22×C4×C17—42no—
188C22×C4×C17—42no—
189C22×C4×C17C2×D411yescharacteristic
190C22×C4×C17C2×D411yescharacteristic
191C22×C4×C17C2×D411yescharacteristic
192C22×C4×C17C2×D411yescharacteristic
193C22×C4×C17C2×D412yes—
194C22×C4×C17C2×D411yescharacteristic
195C22×C4×C17C2×D414yes—
196C22×C4×C17C2×D414yes—
197C22×C4×C17C2412yes—
198C22×C4×C17C2411yescharacteristic
199C2×C22⋊D17—28no—
200C2×C22⋊D17—24no—
201C2×C22⋊D17—24no—
202C2×C22⋊D17—44no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209#63252—216no—
210#63252—28no—
211#63252—28no—
212C2×D68—21no—
213C2×D68—22no—
214C2×D68—22no—
215C2×D68—22no—
216C2×D68—21no—
217C2×D68#4114yes—
218C2×D68C2412yes—
219C2×D68C2412yes—
220C2×C4×D17—28no—
221C2×C4×D17—24no—
222C2×C4×D17—24no—
223C2×C4×D17—24no—
224C2×C4×D17—24no—
225C2×C4×D17—44no—
226C2×C4×D17—44no—
227C2×C4×D17—44no—
228C2×Dic34—21no—
229C2×Dic34—22no—
230C2×Dic34—22no—
231C2×Dic34—22no—
232C2×Dic34—21no—
233C2×Dic34#4114yes—
234C2×Dic34C2412yes—
235C2×Dic34C2412yes—
236C2×C8×C17—22no—
237C2×C8×C17—22no—
238C2×C8×C17—22no—
239C2×C8×C17—22no—
240C2×C8×C17C2412yes—
241C2×C8×C17C2412yes—
242C2×C8×C17C2412yes—
243C2×C8×C17C2412yes—
244C42×C17C2×D412yes—
245C42×C17C2×D412yes—
246C42×C17C2×D414yes—
247C42×C17C2×D414yes—
248C42×C17C2412yes—
249C42×C17C2412yes—
250C22⋊Dic17—24no—
251C22⋊Dic17—24no—
252#63227—24no—
253#63227—24no—
254#63227—24no—
255#63227—24no—
256#63227—24no—
257#63227—24no—
258C4⋊Dic17—21no—
259C4⋊Dic17—21no—
260C4⋊Dic17—21no—
261C4⋊Dic17—21no—
262C4⋊Dic17C2412yes—
263C4⋊Dic17C2412yes—
264C4⋊Dic17C2412yes—
265C4⋊Dic17C2412yes—
266#63225—24no—
267#63225—24no—
268#63225—24no—
269#63225—24no—
270#63225—24no—
271#63225—24no—
272C4×Dic17—24no—
273C4×Dic17—24no—
274C4×Dic17—24no—
275C4×Dic17—24no—
276Dic68—28no—
277D136—28no—
278#63219—28no—
279#63219—28no—
280C2×#3111—171nomaximal, Sylow
281C23×C17—22no—
282C23×C17—22no—
283C23×C17—22no—
284C23×C17C22×D412yes—
285C23×C17C22×D411yescharacteristic
286C22×D17—24no—
287C22×D17—22no—
288C22×D17—22no—
289C22×D17—42no—
290C22×D17—42no—
291C22×D17—42no—
292C22×D17—42no—
293C22×D17—42no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—24no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—44no—
303C2×C4×C17—44no—
304C2×C4×C17C22×D412yes—
305C2×C4×C17C22×D412yes—
306C2×C4×C17C22×D412yes—
307C2×C4×C17C22×D412yes—
308C2×C4×C17C22×D412yes—
309C2×C4×C17C22×D411yescharacteristic
310C2×C4×C17C2×#4112yes—
311C2×C4×C17C2×#4112yes—
312C2×C4×C17C2511yescharacteristic
313C22⋊D17—216no—
314C22⋊D17—48no—
315C2×Dic17—24no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—22no—
321C2×Dic17—22no—
322C2×Dic17—42no—
323C2×Dic17—42no—
324C2×Dic17—42no—
325C2×Dic17—42no—
326C2×Dic17—42no—
327D68—24no—
328D68—22no—
329D68—22no—
330D68—22no—
331D68—42no—
332D68C2×#4114yes—
333C4×D17—216no—
334C4×D17—48no—
335C4×D17—48no—
336C4×D17—48no—
337Dic34—24no—
338Dic34—22no—
339Dic34—22no—
340Dic34—22no—
341Dic34—42no—
342Dic34C2×#4114yes—
343C8×C17—22no—
344C8×C17—22no—
345C8×C17—22no—
346C8×C17—22no—
347C2×#529—171no—
348C2×C4×#41—171no—
349#3111—1716no—
350C2×#485—171no—
351C2×#482—171no—
352C2×#479—171no—
353C2×#478—171no—
354C2×#464—171no—
355C2×#463—171no—
356C2×#452—171no—
357C2×#449—171no—
358C2×#442—171no—
359C2×#441—171no—
360C2×#440—171no—
361C2×#440—171no—
362C2×#432D1711yescharacteristic, complemented
363C22×C17—22no—
364C22×C17—22no—
365C22×C17—22no—
366C22×C17—44no—
367C22×C17#52512yes—
368C22×C17#57512yes—
369C22×C17#57512yes—
370C22×C17C23×D411yescharacteristic
371C2×D17—24no—
372C2×D17—48no—
373C2×D17—42no—
374C2×D17—42no—
375C2×D17—42no—
376C2×D17—42no—
377C2×D17—42no—
378C2×D17—84no—
379C4×C17—22no—
380C4×C17—22no—
381C4×C17—22no—
382C4×C17—22no—
383C4×C17—22no—
384C4×C17#52512yes—
385C4×C17C22×#4111yescharacteristic
386C4×C17C22×#4111yescharacteristic
387Dic17—24no—
388Dic17—42no—
389Dic17—42no—
390Dic17—42no—
391Dic17—42no—
392Dic17—42no—
393C22×#41—171no—
394C22×Q16—171no—
395C22×SD16—171no—
396C22×SD16—171no—
397C22×D8—171no—
398#529—178no—
399#529—344no—
400C2×#126—341no—
401C2×#125—171no—
402C2×#124—171no—
403C2×#123—341no—
404C2×C22⋊Q8—171no—
405C2×#121—171no—
406C4×#41—178no—
407C4×#41—344no—
408C2×C4×Q8—171no—
409C2×C4×Q8—171no—
410C2×C4×Q8—171no—
411C2×C4×D4—171no—
412C2×C4×D4—171no—
413C2×C4×D4—171no—
414C2×C4×D4—341no—
415C2×C4×D4—341no—
416C2×C4×D4—341no—
417C2×#117—171no—
418C2×#117—341no—
419C2×#117—341no—
420C22×C42—341no—
421C22×C42C2×D1711yescharacteristic
422#485—178no—
423#482—178no—
424#479—178no—
425#478—178no—
426#464—178no—
427#463—178no—
428#452—178no—
429#449—178no—
430#442—178no—
431#441—178no—
432#440—178no—
433#440—178no—
434#432C2×D1718yescomplemented
435C2×#107—171no—
436C2×#107—171no—
437C2×#106—171no—
438C2×#106—171no—
439C2×C4⋊C8C2×D1711yescharacteristic
440C2×C4⋊C8C2×D1711yescharacteristic
441C2×#103—171no—
442C2×#103—171no—
443C2×#103—171no—
444C2×#103—171no—
445C2×#102—171no—
446C2×#102—171no—
447C2×#102—171no—
448C2×#102—171no—
449C2×C22⋊C8C2×D1711yescharacteristic
450C2×C22⋊C8C2×D1711yescharacteristic
451C2×#97C2×D1711yescharacteristic
452C2×#97C2×D1711yescharacteristic
453C2×C17—42no—
454C2×C17#311114yescomplemented
455C2×C17C2×#52511yescharacteristic
456C2×C17C2×#57511yescharacteristic
457C2×C17C2×#57511yescharacteristic
458D17—44no—
459D17—82no—
460C2×#41—174no—
461C2×#41—344no—
462C2×#41—344no—
463C2×#41—342no—
464C22×Q8—171no—
465C22×Q8—171no—
466C22×D4—171no—
467C22×D4—171no—
468C22×D4—341no—
469C22×D4—341no—
470C23×C4—341no—
471C23×C4—341no—
472C23×C4—341no—
473C23×C4—341no—
474C23×C4D6811yescharacteristic
475C23×C4D6811yescharacteristic
476C23×C4C22×D1711yescharacteristic
477C2×Q16—174no—
478C2×Q16—344no—
479C2×SD16—174no—
480C2×SD16—174no—
481C2×SD16—344no—
482C2×SD16—344no—
483C2×D8—174no—
484C2×D8—344no—
485C22×C8C22×D1711yescharacteristic
486C22×C8C22×D1711yescharacteristic
487C22×C8C22×D1711yescharacteristic
488C22×C8C22×D1711yescharacteristic
489#126—348no—
490#125—174no—
491#125—342no—
492#124—174no—
493#124—342no—
494#123—348no—
495C22⋊Q8—174no—
496C22⋊Q8—342no—
497#121—174no—
498#121—342no—
499C4×Q8—174no—
500C4×Q8—174no—
501C4×Q8—174no—
502C4×Q8—342no—
503C4×Q8—342no—
504C4×Q8—342no—
505C4×D4—174no—
506C4×D4—174no—
507C4×D4—174no—
508C4×D4—348no—
509C4×D4—348no—
510C4×D4—348no—
511C4×D4—342no—
512C4×D4—342no—
513C4×D4—342no—
514#117—174no—
515#117—342no—
516#117—348no—
517#117—348no—
518C2×C4⋊C4—171no—
519C2×C4⋊C4—171no—
520C2×C4⋊C4—171no—
521C2×C4⋊C4—171no—
522C2×C4⋊C4—341no—
523C2×C4⋊C4—341no—
524C2×C4⋊C4—341no—
525C2×C4⋊C4—341no—
526C2×C4⋊C4—341no—
527C2×C4⋊C4—341no—
528C2×C22⋊C4—341no—
529C2×C22⋊C4—341no—
530C2×C22⋊C4—341no—
531C2×C22⋊C4—341no—
532C2×C22⋊C4—341no—
533C2×C22⋊C4—341no—
534C2×C22⋊C4—341no—
535C2×C22⋊C4—341no—
536C2×C42—341no—
537C2×C42—341no—
538C2×C42—341no—
539C2×C42—341no—
540C2×C42—348no—
541C2×C42D6811yescharacteristic
542C2×C42D6814yes—
543C2×C42D6811yescharacteristic
544C2×C42C22×D1711yescharacteristic
545C2×C42C22×D1711yescharacteristic
546C2×C42C22×D1714yes—
547#107—174no—
548#107—174no—
549#106—174no—
550#106—174no—
551C4⋊C8C22×D1714yes—
552C4⋊C8C22×D1714yes—
553#103—174no—
554#103—174no—
555#103—174no—
556#103—174no—
557#102—174no—
558#102—174no—
559#102—174no—
560#102—174no—
561C22⋊C8C22×D1714yes—
562C22⋊C8C22×D1714yes—
563#97C22×D1714yes—
564#97C22×D1714yes—
565C17C2×#311111yescharacteristic, complemented, Sylow
566C24—341no—
567C24—341no—
568C24C2×D6811yescharacteristic
569#41—348no—
570#41—348no—
571#41—3416no—
572C2×Q8—174no—
573C2×Q8—172no—
574C2×Q8—172no—
575C2×Q8—341no—
576C2×Q8—341no—
577C2×Q8—342no—
578C2×Q8—342no—
579C2×Q8—342no—
580C2×D4—174no—
581C2×D4—172no—
582C2×D4—172no—
583C2×D4—348no—
584C2×D4—344no—
585C2×D4—344no—
586C2×D4—341no—
587C2×D4—341no—
588C2×D4—342no—
589C2×D4—342no—
590C2×D4—342no—
591C2×D4—684no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—348no—
597C22×C4—341no—
598C22×C4—344no—
599C22×C4—341no—
600C22×C4—341no—
601C22×C4—341no—
602C22×C4—341no—
603C22×C4—341no—
604C22×C4—344no—
605C22×C4—344no—
606C22×C4—344no—
607C22×C4—684no—
608C22×C4—684no—
609C22×C4—684no—
610C22×C4C2×D6812yes—
611C22×C4C2×D6811yescharacteristic
612C22×C4C2×D6811yescharacteristic
613C22×C4C2×D6811yescharacteristic
614C22×C4C2×D6811yescharacteristic
615C22×C4C2×D6811yescharacteristic
616C22×C4C2×D6814yes—
617C22×C4C2×D6814yes—
618C22×C4C23×D1712yes—
619C22×C4C23×D1711yescharacteristic
620Q16—348no—
621SD16—348no—
622SD16—348no—
623D8—348no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8C23×D1712yes—
629C2×C8C23×D1712yes—
630C2×C8C23×D1712yes—
631C2×C8C23×D1712yes—
632C4⋊C4—172no—
633C4⋊C4—172no—
634C4⋊C4—172no—
635C4⋊C4—172no—
636C4⋊C4—341no—
637C4⋊C4—341no—
638C4⋊C4—341no—
639C4⋊C4—341no—
640C4⋊C4—344no—
641C4⋊C4—344no—
642C4⋊C4—344no—
643C4⋊C4—344no—
644C4⋊C4—344no—
645C4⋊C4—344no—
646C22⋊C4—344no—
647C22⋊C4—344no—
648C22⋊C4—344no—
649C22⋊C4—344no—
650C22⋊C4—344no—
651C22⋊C4—344no—
652C22⋊C4—344no—
653C22⋊C4—344no—
654C42—344no—
655C42—344no—
656C42—344no—
657C42—344no—
658C42C2×D6814yes—
659C42C2×D6814yes—
660C42C2×D6812yes—
661C42C2×D6812yes—
662C42C23×D1712yes—
663C42C23×D1712yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—344no—
668C23—342no—
669C23—342no—
670C23—682no—
671C23—682no—
672C23—682no—
673C23—682no—
674C23—682no—
675C23C22×D6812yes—
676C23C22×D6811yescharacteristic
677Q8—174no—
678Q8—344no—
679Q8—342no—
680Q8—342no—
681Q8—342no—
682Q8—682no—
683D4—174no—
684D4—3416no—
685D4—344no—
686D4—342no—
687D4—342no—
688D4—342no—
689D4—688no—
690D4—682no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—3416no—
702C2×C4—344no—
703C2×C4—342no—
704C2×C4—342no—
705C2×C4—342no—
706C2×C4—342no—
707C2×C4—342no—
708C2×C4—342no—
709C2×C4—688no—
710C2×C4—688no—
711C2×C4—688no—
712C2×C4—682no—
713C2×C4—682no—
714C2×C4—682no—
715C2×C4—682no—
716C2×C4—682no—
717C2×C4C22×D6812yes—
718C2×C4C22×D6812yes—
719C2×C4C22×D6812yes—
720C2×C4C22×D6812yes—
721C2×C4C22×D6812yes—
722C2×C4C22×D6811yescharacteristic
723C2×C4#41×D1712yes—
724C2×C4#41×D1712yes—
725C2×C4C24×D1711yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—344no—
735C22—688no—
736C22—682no—
737C22—682no—
738C22—682no—
739C22—682no—
740C22—682no—
741C22—1364no—
742C22#1176332112yes—
743C22#1176360912yes—
744C22#1176360912yes—
745C22C23×D6811yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—344no—
752C4—682no—
753C4—682no—
754C4—682no—
755C4—682no—
756C4—682no—
757C4#1176332112yes—
758C4C2×#41×D1711yescharacteristic
759C4C2×#41×D1711yescharacteristic
760C2—42no—
761C2—684no—
762C2—1362no—
763C2#1453889514yesdirect product factor
764C2C2×#1176332111yescharacteristic
765C2C2×#1176360911yescharacteristic
766C2C2×#1176360911yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#432C2
socleC23×C17C22×D4
prime radicalC2×#11762956C2
hypercenterC2×#432D17
hypocenterC17C2×#3111
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×#11763343C2semidirect
2. C2×C4×#63252C2semidirect
3. #14538895C2direct (N × H)
4. C2×#11763151C2semidirect
5. C2×#11763134C2semidirect
6. C2×#11763117C2semidirect
7. C2×#11763110C2semidirect
8. C2×#11763032C2semidirect
9. C2×#11763025C2semidirect
10. C2×#11762973C2semidirect
12. C2×#11762922C2semidirect
13. C2×#11762917C2semidirect
14. C2×#11762911C2semidirect
15. C2×#11762911C2semidirect
16. C2×C17×#432C2semidirect
23. #11763343C22semidirect
31. C4×#63252C22semidirect
45. #11763151C22semidirect
46. #11763134C22semidirect
47. #11763117C22semidirect
48. #11763110C22semidirect
49. #11763032C22semidirect
50. #11763025C22semidirect
51. #11762973C22semidirect
53. #11762922C22semidirect
54. #11762917C22semidirect
55. #11762911C22semidirect
56. #11762911C22semidirect
70. C17×#432C22semidirect
362. C2×#432D17semidirect
434. #432C2×D17semidirect
454. C2×C17#3111semidirect
565. C17C2×#3111semidirect
763. C2#14538895direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117633432
C2×C4×#632522
#145388952
C2×#117631512
C2×#117631342
C2×#117631172
C2×#117631102
C2×#117630322
C2×#117630252
C2×#117629732
C2×#117629562
C2×#117629222
C2×#117629172
C2×#117629112
C2×C17×#4322
C2×#311117