Finite Group Databasebeta

← D17×#3497 #17942493

Subgroups — D17×#3497 #17942493

Order 4352.

11210 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D17C212yesmaximal, complemented
2#14542555C211yesmaximal, characteristic, complemented
3#14542554C214yesmaximal, complemented
4#14542553C216yesmaximal, complemented
5#14542552C218yesmaximal, complemented
6#14542551C212yesmaximal, complemented
7#14542550C216yesmaximal, complemented
8#14542549C214yesmaximal, complemented
9D17×#550C214yesmaximal, complemented
10D4×Q8×D17C214yesmaximal, complemented
11D17×#548C218yesmaximal, complemented
12D17×#537C216yesmaximal, complemented
13D17×#532C216yesmaximal, complemented
14C2×C4×Q8×D17C211yesmaximal, characteristic, complemented
15C17×#3497C211yesmaximal, characteristic, complemented
16C2×#10587694C2212yescomplemented
17C2×#10587694C2218yescomplemented
18C2×#10587697C2218yescomplemented
19C2×#10587697C22112yescomplemented
202−1+4×D17—232no—
21C2×#41×D17C22112yes—
22C2×#41×D17C2218yes—
23C22×Q8×D17C2218yes—
24C22×Q8×D17C2211yescharacteristic
25#11763481C2214yescomplemented
26#11763480C22112yescomplemented
27#11763479C22112yescomplemented
28#11763478C2218yescomplemented
29#11763477C22124yescomplemented
30Q8×D68C2214yescomplemented
31D4×Dic34C22112yescomplemented
32#11763474C22112yescomplemented
33Q8×C22⋊D17C2218yescomplemented
34#11763472C22124yescomplemented
35#11763471C2218yescomplemented
36#11763470C2218yescomplemented
37#11763469C22124yescomplemented
38#11763468C22124yescomplemented
39#11763467C22124yescomplemented
40#11763466C2218yescomplemented
41#11763465C22124yescomplemented
42#11763390C2216yescomplemented
43#11763389C22124yescomplemented
44#11763388C22124yescomplemented
45#11763387C22112yescomplemented
46#11763386C22124yescomplemented
47#11763360C2216yescomplemented
48#11763359C2216yescomplemented
49#11763358C22112yescomplemented
50#11763357C2216yescomplemented
51#11763356C22112yescomplemented
52#11763356C22112yescomplemented
53#11763355C22112yescomplemented
54#11763354C22112yescomplemented
55#11763354C22112yescomplemented
56C4⋊Q8×D17C2216yes—
57#127×D17C2216yes—
58#124×D17C22112yes—
59C22⋊Q8×D17C22124yes—
60#121×D17C22112yes—
61#121×D17C22124yes—
62#121×D17C2214yes—
63C2×Q8×Dic17C2211yescharacteristic, complemented
64C2×C4×Dic34C2213yescomplemented
65C2×#10587573C2213yescomplemented
66C4×Q8×D17C2214yes—
67C4×Q8×D17C2214yes—
68C4×Q8×D17C2214yescomplemented
69C4×Q8×D17C2214yescomplemented
70C4×D4×D17C22112yes—
71C4×D4×D17C22112yes—
72C2×C4⋊C4×D17C2213yes—
73C2×C42×D17C2213yes—
74C2×C17×2−1+4C2212yescomplemented
75C17×#550C2214yescomplemented
76D4×Q8×C17C2214yescomplemented
77C17×#548C2218yescomplemented
78C17×#537C2216yescomplemented
79C17×#532C2216yescomplemented
80C2×C4×Q8×C17C2211yescharacteristic, complemented
81C17×2−1+4—216no—
82C2×#41×C17C2318yes—
83C2×#41×C17C23112yes—
84C22×Q8×C17C2318yes—
85C22×Q8×C17C2311yescharacteristic
86#10587697—264no—
87#10587697—296no—
88#41×D17—264no—
89#41×D17—296no—
90#10587694—216no—
91#10587694—264no—
92C2×#63256C2318yes—
93C2×#63256C23112yes—
94C2×Q8×D17—264no—
95C2×Q8×D17D4116yescomplemented
96C2×Q8×D17C2318yes—
97C2×Q8×D17C23124yes—
98C2×Q8×D17C23112yes—
99C2×Q8×D17C2314yes—
100C2×Q8×D17C2314yes—
101C2×#63254C23124yes—
102C2×#63254C23124yes—
103C2×#63254C23112yes—
104C2×D4×D17C2314yes—
105C2×D4×D17C2318yes—
106C2×D4×D17C23112yes—
107C2×D4×D17C23112yes—
108C2×#63252C23124yes—
109C2×#63252C23112yes—
110C2×#63252C23124yes—
111C22×C4×D17C2311yescharacteristic
112C22×C4×D17C23124yes—
113C22×C4×D17C2313yes—
114C22×C4×D17C2313yes—
115C22×Dic34C23124yes—
116C22×Dic34C2313yes—
117C17×C4⋊Q8C2316yes—
118C17×#127C2316yes—
119C17×#124C23112yes—
120C17×C22⋊Q8C23124yes—
121C17×#121C23124yes—
122C17×#121C2314yes—
123C17×#121C23112yes—
124C4×Q8×C17C2314yes—
125C4×Q8×C17C2314yes—
126C4×D4×C17C23112yes—
127C4×D4×C17C23112yes—
128C2×C4⋊C4×C17C2313yes—
129C2×C42×C17C2313yes—
130#10587633C23112yes—
131#10587632C23124yes—
132Q8×Dic17C2314yes—
133Q8×Dic17C2314yes—
134#10587630C23112yes—
135#10587626C23112yes—
136#10587626C23112yes—
137#10587626C23112yes—
138#10587625C23148yes—
139#10587625C2318yes—
140#10587625C23124yes—
141#10587624C23124yes—
142#10587624C2314yes—
143#10587624C23112yes—
144#10587622C23112yes—
145D4×Dic17C23112yes—
146D4×Dic17C23112yes—
147#10587616C23124yes—
148#10587616C2314yes—
149#10587616C23112yes—
150C4×C22⋊D17C23124yes—
151C4×C22⋊D17C23124yes—
152C2×C4⋊Dic17C2313yes—
153#10587610C23124yes—
154C2×#63225C2316yes—
155C2×C4×Dic17C2313yes—
156C2×C4×Dic17C2313yes—
157C2×C4×Dic17C2313yes—
158#10587583C23124yes—
159#10587582C23148yes—
160#10587581C23124yes—
161#10587581C2314yes—
162#10587581C23112yes—
163#10587579C23112yes—
164#10587579C23112yes—
165C4⋊C4×D17C23112yes—
166C4⋊C4×D17C23112yes—
167C4⋊C4×D17C2314yes—
168C4⋊C4×D17C23112yes—
169#10587574C23112yes—
170#10587574C23112yes—
171#10587573C23112yes—
172#10587573C23112yes—
173#10587571C23124yes—
174#10587571C23124yes—
175#10587570C23148yes—
176#10587570C2318yes—
177#10587570C23124yes—
178#10587567C23124yes—
179#10587567C23124yes—
180C22⋊C4×D17C2318yes—
181C22⋊C4×D17C23124yes—
182#10587564C23148yes—
183#10587561C23112yes—
184#10587560C2316yes—
185C4×D68C23112yes—
186C4×D68C23112yes—
187C42×D17C2316yes—
188C42×D17C2316yes—
189C42×D17C2316yes—
190C42×D17C2316yes—
191#10587555C2316yes—
192C4×Dic34C23112yes—
193C4×Dic34C23112yes—
194C23×D17C2418yes—
195C23×D17C2411yescharacteristic
196#41×C17—232no—
197#41×C17—248no—
198C2×Q8×C17—232no—
199C2×Q8×C17C2×D418yescomplemented
200C2×Q8×C17C24112yes—
201C2×Q8×C17C2414yes—
202C2×D4×C17C24112yes—
203C2×D4×C17C2414yes—
204C2×D4×C17C2418yes—
205C2×D4×C17C24112yes—
206C22×C4×C17C24124yes—
207C22×C4×C17C2411yescharacteristic
208C22×C4×C17C2413yes—
209C22×C4×C17C2413yes—
210C2×C22⋊D17C2418yes—
211C2×C22⋊D17C24124yes—
212C2×C22⋊D17C2418yes—
213C2×C22⋊D17C2418yes—
214C2×C22⋊D17C24124yes—
215C22×Dic17C24124yes—
216C22×Dic17C2411yescharacteristic
217C22×Dic17C2413yes—
218C22×Dic17C2413yes—
219#63256—232no—
220#63256—248no—
221Q8×D17—232no—
222Q8×D17—248no—
223Q8×D17—296no—
224Q8×D17C2×D4132yes—
225Q8×D17C2×D4132yescomplemented
226#63254—296no—
227#63254—248no—
228#63254—296no—
229D4×D17—232no—
230D4×D17—248no—
231D4×D17—216no—
232D4×D17—424no—
233#63252—248no—
234#63252—296no—
235#63252—296no—
236C2×D68C24112yes—
237C2×D68C2418yes—
238C2×D68C2414yes—
239C2×D68C24112yes—
240C2×C4×D17—296no—
241C2×C4×D17—24no—
242C2×C4×D17—46no—
243C2×C4×D17C2×D4124yes—
244C2×C4×D17C2418yes—
245C2×C4×D17C24124yes—
246C2×C4×D17C24124yes—
247C2×C4×D17C2416yes—
248C2×C4×D17C2411yescharacteristic
249C2×C4×D17C2411yescharacteristic
250C2×C4×D17C2411yescharacteristic
251C2×C4×D17C2416yes—
252C2×C4×D17C2416yes—
253C2×C4×D17C2416yes—
254C2×C4×D17C2411yescharacteristic
255C2×Dic34—296no—
256C2×Dic34C2×D4124yescomplemented
257C2×Dic34C24112yes—
258C2×Dic34C24124yes—
259C2×Dic34C24112yes—
260C4⋊C4×C17C24112yes—
261C4⋊C4×C17C24112yes—
262C4⋊C4×C17C2414yes—
263C22⋊C4×C17C24124yes—
264C22⋊C4×C17C2418yes—
265C42×C17C2416yes—
266C42×C17C2416yes—
267C22⋊Dic17C24124yes—
268C22⋊Dic17C2418yes—
269#63227C2418yes—
270#63227C24124yes—
271#63227C24124yes—
272#63227C2418yes—
273C4⋊Dic17C24112yes—
274C4⋊Dic17C2414yes—
275C4⋊Dic17C24112yes—
276#63225C24124yes—
277#63225C24124yes—
278#63225C2418yes—
279C4×Dic17C2416yes—
280C4×Dic17C2416yes—
281C4×Dic17C2416yes—
282C4×Dic17C2416yes—
283C4×Dic17C2416yes—
284C4×Dic17C2416yes—
285C2×#3497—171nomaximal, Sylow
286C23×C17C2518yes—
287C23×C17C2511yescharacteristic
288C22×D17—22no—
289C22×D17—22no—
290C22×D17—216no—
291C22×D17—216no—
292C22×D17—216no—
293C22×D17C22×D414yes—
294C22×D17C2518yes—
295C22×D17C2511yescharacteristic
296C22×D17C2511yescharacteristic
297Q8×C17—224no—
298Q8×C17C22×D4116yes—
299D4×C17—216no—
300D4×C17—224no—
301D4×C17—28no—
302D4×C17—412no—
303C2×C4×C17—248no—
304C2×C4×C17—22no—
305C2×C4×C17—43no—
306C2×C4×C17C22×D4112yes—
307C2×C4×C17C2511yescharacteristic
308C2×C4×C17C2516yes—
309C2×C4×C17C2518yes—
310C2×C4×C17C2516yes—
311C2×C4×C17C2511yescharacteristic
312C22⋊D17—216no—
313C22⋊D17—216no—
314C22⋊D17—248no—
315C22⋊D17—216no—
316C22⋊D17—424no—
317C2×Dic17—248no—
318C2×Dic17—22no—
319C2×Dic17—43no—
320C2×Dic17C22×D4112yes—
321C2×Dic17C2511yescharacteristic
322C2×Dic17C2518yes—
323C2×Dic17C2516yes—
324C2×Dic17C2516yes—
325C2×Dic17C2511yescharacteristic
326D68—216no—
327D68—224no—
328D68—28no—
329D68—412no—
330C4×D17—216no—
331C4×D17—22no—
332C4×D17—212no—
333C4×D17—248no—
334C4×D17—22no—
335C4×D17—248no—
336C4×D17—22no—
337C4×D17—46no—
338C4×D17C22×D4124yes—
339C4×D17C22×D4124yes—
340C4×D172−1+414yescomplemented
341Dic34—224no—
342Dic34—248no—
343Dic34C22×D4148yes—
344C22×2−1+4—172no—
345#3497—172no—
346#3497—174no—
347#3497—174no—
348#3497—178no—
349#3497—176no—
350#3497—176no—
351#3497—171no—
352#3497D1711yescharacteristic, direct product factor
353C2×#550—174no—
354C2×D4×Q8—174no—
355C2×#548—178no—
356C2×#537—176no—
357C2×#532—176no—
358C22×C4×Q8—171no—
359C22×C17—21no—
360C22×C17—21no—
361C22×C17—28no—
362C22×C17—28no—
363C22×C17—28no—
364C22×C17C23×D412yes—
365C22×C17C2611yescharacteristic
366C2×D17—21no—
367C2×D17—21no—
368C2×D17—28no—
369C2×D17—28no—
370C2×D17—28no—
371C2×D17—28no—
372C2×D17—432no—
373C2×D17C23×D412yes—
374C2×D17C23×D412yes—
375C2×D17C2×2−1+412yes—
376C2×D17#58512yes—
377C4×C17—28no—
378C4×C17—21no—
379C4×C17—26no—
380C4×C17C23×D4112yes—
381C4×C17C2×2−1+412yescomplemented
382Dic17—28no—
383Dic17—21no—
384Dic17—26no—
385Dic17C23×D4112yes—
386Dic17C2×2−1+412yescomplemented
387C2×2−1+4—178no—
388C2×2−1+4—1712no—
389C2×2−1+4—178no—
390C2×2−1+4—172no—
391C2×2−1+4—3432no—
392C2×2−1+4C2×D1712yescomplemented
393C22×#41—1712no—
394C22×#41—178no—
395C23×Q8—171no—
396C23×Q8—178no—
397#550—178no—
398#550—1712no—
399#550—1724no—
400#550—174no—
401#550—1712no—
402#550C2×D1714yescomplemented
403D4×Q8—178no—
404D4×Q8—1712no—
405D4×Q8—1724no—
406D4×Q8—174no—
407D4×Q8—1712no—
408D4×Q8C2×D1714yescomplemented
409#548—178no—
410#548—178no—
411#548—1724no—
412#548—1724no—
413#548—1724no—
414#548—178no—
415#548—1724no—
416#548C2×D1718yescomplemented
417#537—1712no—
418#537—1724no—
419#537—1724no—
420#537—1724no—
421#537—176no—
422#537C2×D1716yescomplemented
423#532—1712no—
424#532—176no—
425#532—176no—
426#532—1712no—
427#532—1712no—
428#532—1712no—
429#532—1712no—
430#532—1712no—
431#532—176no—
432#532C2×D1716yescomplemented
433C2×C4⋊Q8—176no—
434C2×#127—176no—
435C2×#124—1712no—
436C2×C22⋊Q8—1724no—
437C2×#121—174no—
438C2×#121—1712no—
439C2×#121—1724no—
440C2×C4×Q8—171no—
441C2×C4×Q8—174no—
442C2×C4×Q8—174no—
443C2×C4×Q8—174no—
444C2×C4×Q8—174no—
445C2×C4×Q8—173no—
446C2×C4×Q8—173no—
447C2×C4×Q8C2×D1711yescharacteristic, complemented
448C2×C4×D4—1712no—
449C2×C4×D4—1712no—
450C22×C4⋊C4—173no—
451C22×C42—173no—
452C2×C17—22no—
453C2×C17—48no—
454C2×C17C24×D411yescharacteristic
455C2×C17C22×2−1+411yescharacteristic
456C2×C17C2×#58511yescharacteristic
457D17—22no—
458D17—48no—
459D17#349714yesdirect product factor
4602−1+4—216no—
4612−1+4—3464no—
4622−1+4—3464no—
4632−1+4—3496no—
4642−1+4—3416no—
465C2×#41—1712no—
466C2×#41—178no—
467C2×#41—1724no—
468C2×#41—1712no—
469C2×#41—1724no—
470C2×#41—1724no—
471C2×#41—1712no—
472C2×#41—1724no—
473C2×#41—3496no—
474C2×#41—3464no—
475C2×#41C22×D17112yes—
476C2×#41C22×D1718yes—
477C22×Q8—1716no—
478C22×Q8—174no—
479C22×Q8—174no—
480C22×Q8—1712no—
481C22×Q8—1724no—
482C22×Q8—178no—
483C22×Q8—173no—
484C22×Q8—1724no—
485C22×Q8—3464no—
486C22×Q8C22×D1718yes—
487C22×Q8C22×D1711yescharacteristic
488C22×D4—174no—
489C22×D4—178no—
490C22×D4—1712no—
491C22×D4—1712no—
492C23×C4—173no—
493C23×C4—1724no—
494C23×C4—171no—
495C23×C4—173no—
496C4⋊Q8—1712no—
497C4⋊Q8—1712no—
498C4⋊Q8—1712no—
499C4⋊Q8—176no—
500C4⋊Q8C22×D1716yes—
501#127—1712no—
502#127—1712no—
503#127—1712no—
504#127—176no—
505#127C22×D1716yes—
506#124—1712no—
507#124—1712no—
508#124—1724no—
509#124—1724no—
510#124—1712no—
511#124C22×D17112yes—
512C22⋊Q8—1724no—
513C22⋊Q8—1724no—
514C22⋊Q8—1748no—
515C22⋊Q8—1724no—
516C22⋊Q8—1748no—
517C22⋊Q8C22×D17124yes—
518#121—174no—
519#121—178no—
520#121—1712no—
521#121—1724no—
522#121—1724no—
523#121—1748no—
524#121—174no—
525#121—1712no—
526#121—1724no—
527#121—174no—
528#121—1712no—
529#121—1724no—
530#121—178no—
531#121—1724no—
532#121—1748no—
533#121C22×D1714yes—
534#121C22×D17112yes—
535#121C22×D17124yes—
536C4×Q8—174no—
537C4×Q8—174no—
538C4×Q8—1712no—
539C4×Q8—1712no—
540C4×Q8—1712no—
541C4×Q8—1712no—
542C4×Q8C22×D1714yes—
543C4×Q8C22×D1714yes—
544C4×D4—1712no—
545C4×D4—1712no—
546C4×D4—1724no—
547C4×D4—1724no—
548C4×D4—1712no—
549C4×D4—1712no—
550C4×D4—1724no—
551C4×D4—1724no—
552C4×D4—1712no—
553C4×D4—1712no—
554C4×D4C22×D17112yes—
555C4×D4C22×D17112yes—
556C2×C4⋊C4—176no—
557C2×C4⋊C4—173no—
558C2×C4⋊C4—1712no—
559C2×C4⋊C4—1712no—
560C2×C4⋊C4—174no—
561C2×C4⋊C4—1712no—
562C2×C4⋊C4C22×D1713yes—
563C2×C22⋊C4—178no—
564C2×C22⋊C4—1724no—
565C2×C42—173no—
566C2×C42—173no—
567C2×C42—173no—
568C2×C42—176no—
569C2×C42—176no—
570C2×C42—176no—
571C2×C42—176no—
572C2×C42C22×D1713yes—
573C17C2×#349711yescharacteristic, complemented, Sylow
574C24—171no—
575C24—178no—
576#41—232no—
577#41—248no—
578#41—3496no—
579#41—3496no—
580#41—3496no—
581#41—3448no—
582#41—3448no—
583#41—3496no—
584#41—3432no—
585#41—3448no—
586C2×Q8—232no—
587C2×Q8—1732no—
588C2×Q8—1732no—
589C2×Q8—1724no—
590C2×Q8—1712no—
591C2×Q8—1724no—
592C2×Q8—1712no—
593C2×Q8—3496no—
594C2×Q8—3448no—
595C2×Q8—3496no—
596C2×Q8—3432no—
597C2×Q8D4×D1718yescomplemented
598C2×Q8C23×D17112yes—
599C2×Q8C23×D1714yes—
600C2×D4—178no—
601C2×D4—178no—
602C2×D4—178no—
603C2×D4—1724no—
604C2×D4—1724no—
605C2×D4—174no—
606C2×D4—178no—
607C2×D4—1712no—
608C2×D4—1712no—
609C2×D4—3416no—
610C2×D4—3448no—
611C2×D4—3432no—
612C2×D4—6824no—
613C2×D4C23×D1714yes—
614C2×D4C23×D1718yes—
615C2×D4C23×D17112yes—
616C2×D4C23×D17112yes—
617C22×C4—173no—
618C22×C4—1724no—
619C22×C4—171no—
620C22×C4—176no—
621C22×C4—176no—
622C22×C4—171no—
623C22×C4—1724no—
624C22×C4—173no—
625C22×C4—171no—
626C22×C4—171no—
627C22×C4—171no—
628C22×C4—176no—
629C22×C4—178no—
630C22×C4—1724no—
631C22×C4—1724no—
632C22×C4—176no—
633C22×C4—344no—
634C22×C4—3496no—
635C22×C4—686no—
636C22×C4C23×D1711yescharacteristic
637C22×C4C23×D17124yes—
638C22×C4C23×D1713yes—
639C22×C4C23×D1713yes—
640C4⋊C4—1724no—
641C4⋊C4—1712no—
642C4⋊C4—178no—
643C4⋊C4—174no—
644C4⋊C4—1724no—
645C4⋊C4—1712no—
646C4⋊C4C23×D17112yes—
647C4⋊C4C23×D1714yes—
648C4⋊C4C23×D17112yes—
649C22⋊C4—178no—
650C22⋊C4—1724no—
651C22⋊C4—178no—
652C22⋊C4—178no—
653C22⋊C4—1724no—
654C22⋊C4—1724no—
655C22⋊C4C23×D1718yes—
656C22⋊C4C23×D17124yes—
657C42—176no—
658C42—176no—
659C42—176no—
660C42—176no—
661C42—176no—
662C42—176no—
663C42C23×D1716yes—
664C42C23×D1716yes—
665C23—171no—
666C23—174no—
667C23—171no—
668C23—178no—
669C23—342no—
670C23—342no—
671C23—3416no—
672C23—3416no—
673C23—3416no—
674C23C24×D1718yes—
675C23C24×D1711yescharacteristic
676Q8—224no—
677Q8—1748no—
678Q8—3448no—
679Q8—3424no—
680Q8C2×D4×D17116yes—
681D4—216no—
682D4—224no—
683D4—28no—
684D4—412no—
685D4—3416no—
686D4—3448no—
687D4—3416no—
688D4—3416no—
689D4—3416no—
690D4—3424no—
691D4—348no—
692D4—6812no—
693D4—6824no—
694C2×C4—248no—
695C2×C4—22no—
696C2×C4—43no—
697C2×C4—1712no—
698C2×C4—171no—
699C2×C4—176no—
700C2×C4—1724no—
701C2×C4—1724no—
702C2×C4—174no—
703C2×C4—171no—
704C2×C4—176no—
705C2×C4—178no—
706C2×C4—3448no—
707C2×C4—342no—
708C2×C4—3416no—
709C2×C4—342no—
710C2×C4—3412no—
711C2×C4—3448no—
712C2×C4—342no—
713C2×C4—3448no—
714C2×C4—342no—
715C2×C4—686no—
716C2×C4—683no—
717C2×C4C2×D4×D17112yes—
718C2×C4C24×D1711yescharacteristic
719C2×C4C24×D1716yes—
720C2×C4C24×D1718yes—
721C2×C4C24×D1716yes—
722C2×C4C24×D1711yescharacteristic
723C22—21no—
724C22—21no—
725C22—28no—
726C22—28no—
727C22—28no—
728C22—172no—
729C22—172no—
730C22—172no—
731C22—172no—
732C22—348no—
733C22—341no—
734C22—341no—
735C22—348no—
736C22—348no—
737C22—348no—
738C22—6832no—
739C22C22×D4×D1712yes—
740C22C25×D1711yescharacteristic
741C4—28no—
742C4—21no—
743C4—26no—
744C4—1712no—
745C4—172no—
746C4—348no—
747C4—341no—
748C4—346no—
749C4C22×D4×D17112yes—
750C42−1+4×D1712yescomplemented
751C2—22no—
752C2—48no—
753C2—174no—
754C2—342no—
755C2—688no—
756C2C23×D4×D1711yescharacteristic
757C2C2×2−1+4×D1711yescharacteristic
758C2D17×#58511yescharacteristic
subgroupG/H
center, FrattiniC22C25×D17
commutator, socle, cosocleC22×C17C26
FittingC17×#3497C2
hypercenter#3497D17
hypocenterC17C2×#3497
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D17C2semidirect
2. #14542555C2semidirect
3. #14542554C2semidirect
4. #14542553C2semidirect
5. #14542552C2semidirect
6. #14542551C2semidirect
7. #14542550C2semidirect
8. #14542549C2semidirect
9. D17×#550C2semidirect
10. D4×Q8×D17C2semidirect
11. D17×#548C2semidirect
12. D17×#537C2semidirect
13. D17×#532C2semidirect
14. C2×C4×Q8×D17C2semidirect
15. C17×#3497C2semidirect
16. C2×#10587694C22semidirect
17. C2×#10587694C22semidirect
18. C2×#10587697C22semidirect
19. C2×#10587697C22semidirect
25. #11763481C22semidirect
26. #11763480C22semidirect
27. #11763479C22semidirect
28. #11763478C22semidirect
29. #11763477C22semidirect
30. Q8×D68C22semidirect
31. D4×Dic34C22semidirect
32. #11763474C22semidirect
33. Q8×C22⋊D17C22semidirect
34. #11763472C22semidirect
35. #11763471C22semidirect
36. #11763470C22semidirect
37. #11763469C22semidirect
38. #11763468C22semidirect
39. #11763467C22semidirect
40. #11763466C22semidirect
41. #11763465C22semidirect
42. #11763390C22semidirect
43. #11763389C22semidirect
44. #11763388C22semidirect
45. #11763387C22semidirect
46. #11763386C22semidirect
47. #11763360C22semidirect
48. #11763359C22semidirect
49. #11763358C22semidirect
50. #11763357C22semidirect
51. #11763356C22semidirect
52. #11763356C22semidirect
53. #11763355C22semidirect
54. #11763354C22semidirect
55. #11763354C22semidirect
63. C2×Q8×Dic17C22semidirect
64. C2×C4×Dic34C22semidirect
65. C2×#10587573C22semidirect
68. C4×Q8×D17C22semidirect
69. C4×Q8×D17C22semidirect
74. C2×C17×2−1+4C22semidirect
75. C17×#550C22semidirect
76. D4×Q8×C17C22semidirect
77. C17×#548C22semidirect
78. C17×#537C22semidirect
79. C17×#532C22semidirect
80. C2×C4×Q8×C17C22semidirect
95. C2×Q8×D17D4semidirect
199. C2×Q8×C17C2×D4semidirect
225. Q8×D17C2×D4semidirect
256. C2×Dic34C2×D4semidirect
340. C4×D172−1+4semidirect
352. #3497D17direct (N × H)
381. C4×C17C2×2−1+4semidirect
386. Dic17C2×2−1+4semidirect
392. C2×2−1+4C2×D17semidirect
402. #550C2×D17semidirect
408. D4×Q8C2×D17semidirect
416. #548C2×D17semidirect
422. #537C2×D17semidirect
432. #532C2×D17semidirect
447. C2×C4×Q8C2×D17semidirect
459. D17#3497direct (N × H)
573. C17C2×#3497semidirect
597. C2×Q8D4×D17semidirect
750. C42−1+4×D17semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D172
#145425552
#145425542
#145425532
#145425522
#145425512
#145425502
#145425492
D17×#5502
D4×Q8×D172
D17×#5482
D17×#5372
D17×#5322
C2×C4×Q8×D172
C17×#34972
C2×#349717