Finite Group Databasebeta

← #17050614

Subgroups — #17050614

Order 4352.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763499C211yesmaximal, characteristic
2D4×C4⋊Dic17C211yesmaximal, characteristic
3#14529753C211yesmaximal, characteristic, complemented
4#14529739C211yesmaximal, characteristic, complemented
5#14529217C211yesmaximal, characteristic, complemented
6#14529207C211yesmaximal, characteristic, complemented
7#14529089C211yesmaximal, characteristic, complemented
8#14529089C211yesmaximal, characteristic, complemented
9#14528880C211yesmaximal, characteristic, complemented
10#14528871C211yesmaximal, characteristic, complemented
11#14528790C211yesmaximal, characteristic, complemented
12#14528615C211yesmaximal, characteristic, complemented
13#14528504C211yesmaximal, characteristic, complemented
14C2×#11762572C211yesmaximal, characteristic, complemented
15C2×C17×#435C211yesmaximal, characteristic
16#11763499—24no—
17#11763499C418yescomplemented
18C2×#10587565—21no—
19C2×#10587556C2211yescharacteristic
20C2×#10587575—21no—
21C2×#10587621—21no—
22C2×#10587610C2211yescharacteristic
23C2×#10587610C2211yescharacteristic
24C2×C4×Dic34C2211yescharacteristic
25C2×D4×Dic17—21no—
26C2×#10587612C2211yescharacteristic
27C2×#10587563—21no—
28C22×C4⋊Dic17C2211yescharacteristic
29C22×C4⋊Dic17C2211yescharacteristic
30C22×C4⋊Dic17C2211yescharacteristic
31C2×#10587487C2211yescharacteristic
32C2×#10587487C2211yescharacteristic
33C2×#10587487C2211yescharacteristic
34C2×#10587487C2211yescharacteristic
35#11762708—21no—
36#11762684—21no—
37#11762684—21no—
38#11762679C2211yescharacteristic
39#11762669C2211yescharacteristic
40#11762669C2211yescharacteristic
41C4×C4⋊Dic17C2211yescharacteristic
42#11762572C2211yescharacteristic
43#11762572C2211yescharacteristic
44#11762572C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762572C2211yescharacteristic
51#11762572C2211yescharacteristic
52#11762572C2211yescharacteristic
53#11762572C2211yescharacteristic
54C22×M16×C17C2211yescharacteristic
55C23×C8×C17C2211yescharacteristic
56C2×C4×D4×C17C2211yescharacteristic
57C17×#435—24no—
58C2×C17×C4⋊C8C2211yescharacteristic
59C2×C17×C22⋊C8C2211yescharacteristic
60C2×C17×C22⋊C8C2211yescharacteristic
61C2×C17×#97C2211yescharacteristic
62C22×D4×C17D411yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×Dic17—21no—
66C23×Dic17—21no—
67C23×Dic17—21no—
68C22×Dic34C2311yescharacteristic
69C2×M16×C17—22no—
70C2×M16×C17—22no—
71C2×M16×C17—41no—
72C22×C8×C17—22no—
73C22×C8×C17—22no—
74C22×C8×C17—41no—
75C22×C8×C17C2311yescharacteristic
76C22×C8×C17C2311yescharacteristic
77C22×C8×C17C2311yescharacteristic
78C22×C8×C17C2311yescharacteristic
79C4×D4×C17C2×C414yes—
80C4×D4×C17D414yes—
81C2×C4⋊C4×C17D411yescharacteristic
82C2×C22⋊C4×C17D411yescharacteristic
83C2×C22⋊C4×C17D411yescharacteristic
84C2×C42×C17C2311yescharacteristic
85C2×C22⋊Dic17—21no—
86C2×C22⋊Dic17—21no—
87C2×C22⋊Dic17—21no—
88C2×C22⋊Dic17—21no—
89C2×C22⋊Dic17—21no—
90#10587621—28no—
91D4×Dic17—44no—
92#10587612—22no—
93#10587612C2×C414yescomplemented
94C2×C4⋊Dic17—22no—
95C2×C4⋊Dic17—21no—
96C2×C4⋊Dic17—21no—
97C2×C4⋊Dic17—21no—
98C2×C4⋊Dic17—21no—
99C2×C4⋊Dic17—21no—
100C2×C4⋊Dic17—22no—
101C2×C4⋊Dic17—22no—
102C2×C4⋊Dic17—41no—
103C2×C4⋊Dic17—41no—
104C2×C4⋊Dic17C2×C414yescomplemented
105C2×C4⋊Dic17C2311yescharacteristic
106C2×C4⋊Dic17C2311yescharacteristic
107C2×C4⋊Dic17C2311yescharacteristic
108C2×C4⋊Dic17C2311yescharacteristic
109C2×C4⋊Dic17C2311yescharacteristic
110C2×C4⋊Dic17C2311yescharacteristic
111C2×C4⋊Dic17C2311yescharacteristic
112#10587610—22no—
113#10587610—22no—
114#10587610C2×C414yescomplemented
115#10587610C2×C414yescomplemented
116C2×#63225—21no—
117C2×#63225—21no—
118C2×#63225—21no—
119C2×#63225—21no—
120C2×#63225—21no—
121C2×C4×Dic17—21no—
122C2×C4×Dic17—21no—
123C2×C4×Dic17—21no—
124#10587575—28no—
125#10587565—28no—
126#10587563—28no—
127#10587556—22no—
128#10587556C2×C414yescomplemented
129C4×Dic34—22no—
130C4×Dic34C2×C414yescomplemented
131C17×C4⋊C8—22no—
132C17×C22⋊C8—22no—
133C17×C22⋊C8—22no—
134C17×#97—22no—
135#10587502—21no—
136#10587502—21no—
137#10587502—21no—
138#10587487—22no—
139#10587487—22no—
140#10587487—41no—
141#10587487—41no—
142C24×C17C2×D411yescharacteristic
143C24×C17C2×D411yescharacteristic
144C2×D4×C17—22no—
145C2×D4×C17—22no—
146C2×D4×C17C22⋊C414yes—
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17C22×C412yes—
156C22×C4×C17C22×C412yes—
157C22×C4×C17C2×D411yescharacteristic
158C22×C4×C17C2×D411yescharacteristic
159C22×C4×C17C2×D411yescharacteristic
160C22×C4×C17C2×D411yescharacteristic
161C22×C4×C17C2×D412yes—
162C22×C4×C17C2×D412yes—
163C22×C4×C17C2411yescharacteristic
164C22×Dic17—24no—
165C22×Dic17—21no—
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17—21no—
169C22×Dic17—21no—
170C22×Dic17—21no—
171C22×Dic17—21no—
172C22×Dic17—21no—
173C22×Dic17—42no—
174C22×Dic17—42no—
175C22×Dic17—42no—
176C22×Dic17—42no—
177C22×Dic17—42no—
178C22×Dic17—42no—
179C22×Dic17—81no—
180C22×Dic17—81no—
181C2×Dic34—21no—
182C2×Dic34—21no—
183C2×Dic34—21no—
184C2×Dic34—21no—
185C2×Dic34—21no—
186C2×Dic34C22×C412yes—
187M16×C17—44no—
188C2×C8×C17—21no—
189C2×C8×C17—21no—
190C2×C8×C17—21no—
191C2×C8×C17—21no—
192C2×C8×C17—21no—
193C2×C8×C17—21no—
194C2×C8×C17—21no—
195C2×C8×C17—21no—
196C2×C8×C17—21no—
197C2×C8×C17—21no—
198C2×C8×C17—21no—
199C2×C8×C17—44no—
200C2×C8×C17#4112yes—
201C4⋊C4×C17C22⋊C414yes—
202C22⋊C4×C17C22⋊C414yes—
203C22⋊C4×C17C22⋊C414yes—
204C42×C17C22×C412yes—
205C42×C17C2×D412yes—
206C22⋊Dic17—24no—
207C22⋊Dic17—24no—
208C22⋊Dic17—24no—
209C22⋊Dic17—42no—
210C22⋊Dic17—42no—
211C4⋊Dic17—24no—
212C4⋊Dic17—21no—
213C4⋊Dic17—21no—
214C4⋊Dic17—21no—
215C4⋊Dic17—21no—
216C4⋊Dic17—21no—
217C4⋊Dic17—21no—
218C4⋊Dic17—21no—
219C4⋊Dic17—21no—
220C4⋊Dic17—21no—
221C4⋊Dic17—21no—
222C4⋊Dic17—42no—
223C4⋊Dic17—42no—
224C4⋊Dic17—42no—
225C4⋊Dic17—81no—
226C4⋊Dic17C22×C412yes—
227C4⋊Dic17C22×C412yes—
228C4⋊Dic17C22×C412yes—
229C4⋊Dic17#4112yes—
230#63225—24no—
231#63225—24no—
232#63225—24no—
233#63225—24no—
234#63225—24no—
235C4×Dic17—24no—
236C4×Dic17—24no—
237C4×Dic17—42no—
238#22491—171nomaximal, Sylow
239C23×C17—21no—
240C23×C17—21no—
241C23×C17—21no—
242C23×C17—21no—
243C23×C17—21no—
244C23×C17—21no—
245C23×C17—21no—
246C23×C17—21no—
247C23×C17—21no—
248C23×C17—21no—
249C23×C17C2×C22⋊C412yes—
250C23×C17C2×C22⋊C412yes—
251C23×C17AGL(1,ℤ/8)12yes—
252C23×C17#13712yes—
253C23×C17C22×D411yescharacteristic
254D4×C17—28no—
255C2×C4×C17—21no—
256C2×C4×C17—21no—
257C2×C4×C17—21no—
258C2×C4×C17—21no—
259C2×C4×C17—21no—
260C2×C4×C17—21no—
261C2×C4×C17—21no—
262C2×C4×C17—21no—
263C2×C4×C17—22no—
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17C2×C22⋊C412yes—
272C2×C4×C17C2×C22⋊C412yes—
273C2×C4×C17C2×C22⋊C412yes—
274C2×C4×C17C2×C22⋊C412yes—
275C2×C4×C17C23×C411yescharacteristic
276C2×C4×C17C22×D411yescharacteristic
277C2×C4×C17C2×#4111yescharacteristic
278C2×C4×C17C2×#4111yescharacteristic
279C2×C4×C17H(5,𝔽2)11yescharacteristic
280C2×C4×C172−1+411yescharacteristic
281C2×Dic17—22no—
282C2×Dic17—22no—
283C2×Dic17—22no—
284C2×Dic17—22no—
285C2×Dic17—22no—
286C2×Dic17—41no—
287C2×Dic17—41no—
288C2×Dic17—41no—
289C2×Dic17—41no—
290C2×Dic17—41no—
291C2×Dic17—41no—
292C2×Dic17—41no—
293C2×Dic17—41no—
294C2×Dic17—41no—
295C2×Dic17—41no—
296C2×Dic17—48no—
297C2×Dic17—41no—
298C2×Dic17—41no—
299C2×Dic17—41no—
300C2×Dic17—41no—
301C2×Dic17—41no—
302C2×Dic17—41no—
303C2×Dic17—41no—
304C2×Dic17—41no—
305C2×Dic17—41no—
306C2×Dic17—84no—
307C2×Dic17—84no—
308Dic34—22no—
309Dic34—22no—
310Dic34—41no—
311Dic34—41no—
312C8×C17—22no—
313C8×C17—41no—
314C8×C17—41no—
315C8×C17—41no—
316C2×#552—171no—
317C2×#435D1711yescharacteristic
318D4×C4⋊C4—171no—
319#1992—171no—
320#1989—171no—
321#1894—171no—
322#1892—171no—
323#1872—171no—
324#1872—171no—
325#1825—171no—
326#1823—171no—
327#1803—171no—
328#1763—171no—
329#1736—171no—
330C2×#340—171no—
331C22×C17—22no—
332C22×C17—22no—
333C22×C17—22no—
334C22×C17—22no—
335C22×C17—22no—
336C22×C17—22no—
337C22×C17—22no—
338C22×C17—22no—
339C22×C17—22no—
340C22×C17—41no—
341C22×C17—41no—
342C22×C17—41no—
343C22×C17—41no—
344C22×C17#41714yes—
345C22×C17C22×C22⋊C411yescharacteristic
346C22×C17#54611yescharacteristic
347C22×C17#54711yescharacteristic
348C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C17C2×#13711yescharacteristic
350C22×C17#57711yescharacteristic
351C22×C17#57811yescharacteristic
352C4×C17—22no—
353C4×C17—22no—
354C4×C17—22no—
355C4×C17—22no—
356C4×C17C4×#4111yescharacteristic
357C4×C17#52011yescharacteristic
358C4×C17#54611yescharacteristic
359C4×C17#54711yescharacteristic
360Dic17—42no—
361Dic17—42no—
362Dic17—42no—
363Dic17—42no—
364Dic17—42no—
365Dic17—81no—
366Dic17—81no—
367Dic17—81no—
368C22×M16C2×D1711yescharacteristic
369C23×C8C2×D1711yescharacteristic
370#552—178no—
371#552—344no—
372C2×#126—341no—
373C2×#125—171no—
374C2×#125—341no—
375C2×#123—341no—
376C2×C22⋊Q8—171no—
377C2×C22⋊Q8—171no—
378C2×C4×Q8—171no—
379C2×C4×D4—341no—
380C2×C4×D4C2×D1711yescharacteristic
381C2×#117—171no—
382C2×#117—341no—
383C22×C4⋊C4—171no—
384C22×C4⋊C4—171no—
385C22×C4⋊C4—171no—
386#435—24no—
387C2×C4⋊C8C2×D1711yescharacteristic
388C2×#103—171no—
389C2×#103—171no—
390C2×#103—171no—
391C2×#103—171no—
392C2×C22⋊C8C2×D1711yescharacteristic
393C2×C22⋊C8C2×D1711yescharacteristic
394C2×#97C2×D1711yescharacteristic
395#389—341no—
396#385—341no—
397#385—341no—
398#384—171no—
399#380—171no—
400#380—171no—
401C4×C4⋊C4—171no—
402#340—171no—
403#340—171no—
404#340—171no—
405#340—171no—
406#340—171no—
407#340—171no—
408#340—171no—
409#340—171no—
410#340—171no—
411#340—171no—
412#340—171no—
413#340—171no—
414C2×C17—24no—
415C2×C17—42no—
416C2×C17#233911yescharacteristic
417C2×C17C2×#41711yescharacteristic
418C2×C17#289811yescharacteristic
419C2×C17#331011yescharacteristic
420C2×C17#331211yescharacteristic
421C2×C17#334311yescharacteristic
422C2×C17#334411yescharacteristic
423C22×Q8—171no—
424C22×D4D6811yescharacteristic
425C23×C4—341no—
426C23×C4—341no—
427C23×C4—341no—
428C23×C4C22×D1711yescharacteristic
429C23×C4C22×D1711yescharacteristic
430C2×M16—22no—
431C2×M16—22no—
432C2×M16—41no—
433C22×C8—22no—
434C22×C8—22no—
435C22×C8—41no—
436C22×C8C22×D1711yescharacteristic
437C22×C8C22×D1711yescharacteristic
438C22×C8C22×D1711yescharacteristic
439C22×C8C22×D1711yescharacteristic
440#126—348no—
441#125—174no—
442#125—348no—
443#125—342no—
444#123—348no—
445C22⋊Q8—174no—
446C22⋊Q8—174no—
447C22⋊Q8—342no—
448C22⋊Q8—342no—
449C4×Q8—174no—
450C4×Q8—342no—
451C4×D4—684no—
452C4×D4C4×D1714yes—
453C4×D4C22⋊D1714yes—
454#117—174no—
455#117—342no—
456#117—348no—
457C2×C4⋊C4—174no—
458C2×C4⋊C4—171no—
459C2×C4⋊C4—171no—
460C2×C4⋊C4—171no—
461C2×C4⋊C4—171no—
462C2×C4⋊C4—171no—
463C2×C4⋊C4—171no—
464C2×C4⋊C4—171no—
465C2×C4⋊C4—342no—
466C2×C4⋊C4—342no—
467C2×C4⋊C4—341no—
468C2×C4⋊C4—341no—
469C2×C4⋊C4—341no—
470C2×C4⋊C4—341no—
471C2×C4⋊C4—341no—
472C2×C4⋊C4—341no—
473C2×C4⋊C4—342no—
474C2×C4⋊C4—341no—
475C2×C4⋊C4—341no—
476C2×C4⋊C4—341no—
477C2×C4⋊C4—341no—
478C2×C4⋊C4—681no—
479C2×C4⋊C4—681no—
480C2×C4⋊C4D6811yescharacteristic
481C2×C22⋊C4—341no—
482C2×C22⋊C4—341no—
483C2×C22⋊C4—341no—
484C2×C22⋊C4—341no—
485C2×C22⋊C4—341no—
486C2×C22⋊C4D6811yescharacteristic
487C2×C22⋊C4D6811yescharacteristic
488C2×C42—341no—
489C2×C42—341no—
490C2×C42—341no—
491C2×C42C22×D1711yescharacteristic
492C4⋊C8—22no—
493#103—342no—
494#103—342no—
495#103—681no—
496#103—681no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499#97—22no—
500#95—341no—
501#95—341no—
502#95—341no—
503C17#2249111yescharacteristic, complemented, Sylow
504C24C2×D6811yescharacteristic
505C24C2×D6811yescharacteristic
506C2×Q8—172no—
507C2×Q8—341no—
508C2×Q8—341no—
509C2×Q8—341no—
510C2×Q8—341no—
511C2×Q8—341no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4#6322714yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—341no—
524C22×C4—341no—
525C22×C4—341no—
526C22×C4—341no—
527C22×C4—341no—
528C22×C4—344no—
529C22×C4—341no—
530C22×C4—341no—
531C22×C4—341no—
532C22×C4—682no—
533C22×C4—682no—
534C22×C4—682no—
535C22×C4—682no—
536C22×C4—682no—
537C22×C4—682no—
538C22×C4—1361no—
539C22×C4—1361no—
540C22×C4C2×C4×D1712yes—
541C22×C4C2×C4×D1712yes—
542C22×C4C2×D6811yescharacteristic
543C22×C4C2×D6811yescharacteristic
544C22×C4C2×D6811yescharacteristic
545C22×C4C2×D6811yescharacteristic
546C22×C4C2×C22⋊D1712yes—
547C22×C4C2×C22⋊D1712yes—
548C22×C4C23×D1711yescharacteristic
549M16—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—44no—
562C2×C8#6325412yes—
563C4⋊C4—172no—
564C4⋊C4—172no—
565C4⋊C4—172no—
566C4⋊C4—172no—
567C4⋊C4—341no—
568C4⋊C4—341no—
569C4⋊C4—341no—
570C4⋊C4—341no—
571C4⋊C4—344no—
572C4⋊C4—344no—
573C4⋊C4—344no—
574C4⋊C4—344no—
575C4⋊C4—344no—
576C4⋊C4—344no—
577C4⋊C4—341no—
578C4⋊C4—341no—
579C4⋊C4—341no—
580C4⋊C4—341no—
581C4⋊C4—341no—
582C4⋊C4—341no—
583C4⋊C4—682no—
584C4⋊C4—682no—
585C4⋊C4—682no—
586C4⋊C4—1361no—
587C4⋊C4#6322714yes—
588C22⋊C4—344no—
589C22⋊C4—344no—
590C22⋊C4—344no—
591C22⋊C4—682no—
592C22⋊C4—682no—
593C22⋊C4#6322714yes—
594C22⋊C4#6322714yes—
595C42—344no—
596C42—344no—
597C42—682no—
598C42C2×C4×D1712yes—
599C42C2×C22⋊D1712yes—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23#1058759412yes—
611C23#1058759512yes—
612C23C2×#6322712yes—
613C23C2×#6322712yes—
614C23C22×D6811yescharacteristic
615Q8—342no—
616Q8—342no—
617Q8—681no—
618Q8—681no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—342no—
637C2×C4—342no—
638C2×C4—342no—
639C2×C4—342no—
640C2×C4—342no—
641C2×C4—681no—
642C2×C4—688no—
643C2×C4—681no—
644C2×C4—681no—
645C2×C4—681no—
646C2×C4—681no—
647C2×C4—681no—
648C2×C4—681no—
649C2×C4—681no—
650C2×C4—681no—
651C2×C4—681no—
652C2×C4—681no—
653C2×C4—681no—
654C2×C4—681no—
655C2×C4—681no—
656C2×C4—681no—
657C2×C4—681no—
658C2×C4—681no—
659C2×C4—681no—
660C2×C4—681no—
661C2×C4—1364no—
662C2×C4—1364no—
663C2×C4C2×#6322712yes—
664C2×C4C2×#6322712yes—
665C2×C4C2×#6322712yes—
666C2×C4C2×#6322712yes—
667C2×C4C22×C4×D1711yescharacteristic
668C2×C4C2×#6325411yescharacteristic
669C2×C4#1058769111yescharacteristic
670C2×C4#41×D1711yescharacteristic
671C2×C4#1058769711yescharacteristic
672C2×C4C22×C22⋊D1711yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1176281114yes—
691C22C22×#6322711yescharacteristic
692C22#1176345411yescharacteristic
693C22#1176346311yescharacteristic
694C22C2×#1058759411yescharacteristic
695C22C2×#1058759511yescharacteristic
696C22#1176362111yescharacteristic
697C22#1176362611yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—682no—
703C4—682no—
704C4—682no—
705C4—682no—
706C4—682no—
707C4—1361no—
708C4—1361no—
709C4—1361no—
710C4C4×#6325411yescharacteristic
711C4#1176328811yescharacteristic
712C4#1176345311yescharacteristic
713C4#1176345811yescharacteristic
714C2—24no—
715C2—42no—
716C2#1453160911yescharacteristic
717C2C2×#1176281111yescharacteristic
718C2#1453731811yescharacteristic
719C2#1454080711yescharacteristic
720C2#1454083711yescharacteristic
721C2#1454122611yescharacteristic
722C2#1454124111yescharacteristic
subgroupG/H
centerC23C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#435C2
socleC23×C17C22×D4
prime radicalC22×D4×C17D4
cosocleC22×C4×C17C24
hypercenterC2×#435D17
hypocenterC17#22491
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #14529753C2semidirect
4. #14529739C2semidirect
5. #14529217C2semidirect
6. #14529207C2semidirect
7. #14529089C2semidirect
8. #14529089C2semidirect
9. #14528880C2semidirect
10. #14528871C2semidirect
11. #14528790C2semidirect
12. #14528615C2semidirect
13. #14528504C2semidirect
14. C2×#11762572C2semidirect
17. #11763499C4semidirect
93. #10587612C2×C4semidirect
104. C2×C4⋊Dic17C2×C4semidirect
114. #10587610C2×C4semidirect
115. #10587610C2×C4semidirect
128. #10587556C2×C4semidirect
130. C4×Dic34C2×C4semidirect
503. C17#22491semidirect

Maximal subgroups

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

subgroupindex
C2×#117634992
D4×C4⋊Dic172
#145297532
#145297392
#145292172
#145292072
#145290892
#145288802
#145288712
#145287902
#145286152
#145285042
C2×#117625722
C2×C17×#4352
#2249117