Finite Group Databasebeta

← D17×#3523 #17942537

Subgroups — D17×#3523 #17942537

Order 4352.

7022 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542881C211yesmaximal, characteristic, complemented
2#14542880C211yesmaximal, characteristic, complemented
3#14542879C213yesmaximal, complemented
4#14542878C213yesmaximal, complemented
5#14542877C213yesmaximal, complemented
6#14542876C216yesmaximal, complemented
7#14542875C211yesmaximal, characteristic, complemented
8#14542874C212yesmaximal, complemented
9#14542873C216yesmaximal, complemented
10#14542872C213yesmaximal, complemented
11#14542871C212yesmaximal, complemented
12D17×#557C213yesmaximal, complemented
13D17×#557C211yesmaximal, characteristic, complemented
14D17×#556C213yesmaximal, complemented
15D17×#552C216yesmaximal, complemented
16D4×Q8×D17C212yesmaximal, complemented
17D4×Q8×D17C211yesmaximal, characteristic, complemented
18D17×#541C216yesmaximal, complemented
19D17×#533C213yesmaximal, complemented
20D17×#529C213yesmaximal
21D17×#519C212yesmaximal, complemented
22C2×C4×Q8×D17C211yesmaximal, characteristic, complemented
23C17×#3523C211yesmaximal, characteristic, complemented
24C22×Q8×D17C2211yescharacteristic
25C22×Q8×D17C2212yes—
26#11763538C2211yescharacteristic, complemented
27#11763538C2213yescomplemented
28#11763537C2216yescomplemented
29#11763537C2213yescomplemented
30#11763537C2213yescomplemented
31#11763536C22112yescomplemented
32#11763536C2216yescomplemented
33#11763536C2216yescomplemented
34#11763535C2212yescomplemented
35#11763535C2216yescomplemented
36#11763534C2216yescomplemented
37#11763534C2213yescomplemented
38#11763534C2213yescomplemented
39#11763533C2213yescomplemented
40#11763532C2213yescomplemented
41#11763531C2216yescomplemented
42#11763530C2216yescomplemented
43#11763529C2213yescomplemented
44#11763528C2216yescomplemented
45#11763527C2216yescomplemented
46#11763526C22112yescomplemented
47#11763501C2216yescomplemented
48#11763500C2216yescomplemented
49#11763499C2216yescomplemented
50#11763498C2216yescomplemented
51#11763497C2216yescomplemented
52#11763496C22112yescomplemented
53#11763495C22112yescomplemented
54#11763494C2216yescomplemented
55#11763493C2216yescomplemented
56#11763492C22112yescomplemented
57#11763491C22112yescomplemented
58Q8×D68C2212yescomplemented
59Q8×D68C2211yescharacteristic, complemented
60D4×Dic34C2216yescomplemented
61D4×Dic34C2213yescomplemented
62#11763474C2213yescomplemented
63#11763474C2216yescomplemented
64Q8×C22⋊D17C2212yescomplemented
65Q8×C22⋊D17C2212yescomplemented
66Q8×C22⋊D17C2212yescomplemented
67#11763472C2216yescomplemented
68#11763472C2216yescomplemented
69#11763472C2216yescomplemented
70#11763422C2216yescomplemented
71#11763421C2216yescomplemented
72#11763420C2216yescomplemented
73#11763419C2216yescomplemented
74#11763419C2216yescomplemented
75#11763418C22112yescomplemented
76#11763418C22112yescomplemented
77#11763417C2216yescomplemented
78#11763417C2216yescomplemented
79#11763416C22112yescomplemented
80#11763416C22112yescomplemented
81#11763366C2213yescomplemented
82#11763365C2216yescomplemented
83#11763364C2213yescomplemented
84#11763364C2213yescomplemented
85#11763363C2216yescomplemented
86#11763363C2216yescomplemented
87#11763362C2216yescomplemented
88#11763361C2216yescomplemented
89#11763361C2216yescomplemented
90C4⋊Q8×D17C2216yes—
91C4⋊Q8×D17C2213yes—
92C4⋊Q8×D17C2213yes—
93#11763346C2213yes—
94#11763345C2213yes—
95#11763344C2213yes—
96#11763343C2213yes—
97#11763342C2216yes—
98#11763341C2213yes—
99#11763340C2213yes—
100#11763339C2216yes—
101#11763338C2213yes—
102#11763337C2216yes—
103#11763336C2216yes—
104#126×D17C2216yes—
105#126×D17C22112yes—
106#125×D17C2213yes—
107#125×D17C22112yes—
108#125×D17C2216yes—
109#125×D17C2216yes—
110#124×D17C2213yes—
111#123×D17C2216yes—
112C22⋊Q8×D17C2216yes—
113C22⋊Q8×D17C2216yes—
114C22⋊Q8×D17C2216yes—
115C22⋊Q8×D17C2213yes—
116#121×D17C2211yescharacteristic
117#11763287C2212yescomplemented
118#11763286C2216yescomplemented
119#11763286C2216yescomplemented
120#11763285C2212yescomplemented
121#11763285C2216yescomplemented
122#11763285C2216yescomplemented
123#11763285C2212yescomplemented
124C2×Q8×Dic17C2211yescharacteristic, complemented
125C2×C4×Dic34C2213yescomplemented
126C2×#10587573C2213yescomplemented
127C4×Q8×D17C2213yes—
128C4×Q8×D17C2211yescharacteristic
129C4×Q8×D17C2213yes—
130C4×Q8×D17C2212yes—
131C4×Q8×D17C2216yes—
132C4×Q8×D17C2216yes—
133C4×Q8×D17C2213yes—
134C4×Q8×D17C2216yes—
135C4×Q8×D17C2211yescharacteristic
136C4×Q8×D17C2211yescharacteristic, complemented
137C4×Q8×D17C2211yescharacteristic, complemented
138C4×Q8×D17C2213yescomplemented
139C4×Q8×D17C2213yescomplemented
140C4×D4×D17C2216yes—
141C4×D4×D17C2213yes—
142#117×D17C2216yes—
143#117×D17C2216yes—
144#117×D17C2216yes—
145C2×C4⋊C4×D17C2213yes—
146C2×C42×D17C2213yes—
147C17×#557C2213yescomplemented
148C17×#557C2211yescharacteristic, complemented
149C17×#556C2213yescomplemented
150C17×#552C2216yescomplemented
151D4×Q8×C17C2212yescomplemented
152D4×Q8×C17C2211yescharacteristic, complemented
153C17×#541C2216yescomplemented
154C17×#533C2213yescomplemented
155C17×#529C2213yes—
156C17×#519C2212yescomplemented
157C2×C4×Q8×C17C2211yescharacteristic, complemented
158C22×Q8×C17C2311yescharacteristic
159C22×Q8×C17C2312yes—
160C2×Q8×D17—28no—
161C2×Q8×D17—216no—
162C2×Q8×D17C2313yes—
163C2×Q8×D17C2316yes—
164C2×Q8×D17C2311yescharacteristic
165C2×Q8×D17C2312yes—
166C2×Q8×D17C2313yes—
167C2×Q8×D17C2313yes—
168C2×Q8×D17C2316yes—
169C2×Q8×D17C2311yescharacteristic
170C2×D4×D17C2312yes—
171C2×D4×D17C2311yescharacteristic
172C22×C4×D17C2311yescharacteristic
173C22×C4×D17C2313yes—
174C22×C4×D17C2313yes—
175C22×C4×D17C2316yes—
176C22×Dic34C2313yes—
177C22×Dic34C2316yes—
178C17×C4⋊Q8C2313yes—
179C17×C4⋊Q8C2316yes—
180C17×C4⋊Q8C2313yes—
181C17×#126C2316yes—
182C17×#126C23112yes—
183C17×#125C23112yes—
184C17×#125C2313yes—
185C17×#125C2316yes—
186C17×#125C2316yes—
187C17×#124C2313yes—
188C17×#123C2316yes—
189C17×C22⋊Q8C2316yes—
190C17×C22⋊Q8C2316yes—
191C17×C22⋊Q8C2316yes—
192C17×C22⋊Q8C2313yes—
193C17×#121C2311yescharacteristic
194C4×Q8×C17C2311yescharacteristic
195C4×Q8×C17C2312yes—
196C4×Q8×C17C2311yescharacteristic
197C4×Q8×C17C2313yes—
198C4×Q8×C17C2313yes—
199C4×Q8×C17C2316yes—
200C4×Q8×C17C2316yes—
201C4×Q8×C17C2313yes—
202C4×Q8×C17C2316yes—
203C4×D4×C17C2316yes—
204C4×D4×C17C2313yes—
205C17×#117C2316yes—
206C17×#117C2316yes—
207C17×#117C2316yes—
208C2×C4⋊C4×C17C2313yes—
209C2×C42×C17C2313yes—
210#10587633C2313yes—
211#10587632C2316yes—
212#10587632C2316yes—
213#10587632C2316yes—
214#10587632C2313yes—
215Q8×Dic17C2311yescharacteristic
216Q8×Dic17C2312yes—
217Q8×Dic17C2316yes—
218Q8×Dic17C2313yes—
219Q8×Dic17C2311yescharacteristic
220Q8×Dic17C2313yes—
221Q8×Dic17C2316yes—
222Q8×Dic17C2313yes—
223Q8×Dic17C2316yes—
224#10587630C2316yes—
225#10587630C2316yes—
226#10587630C2316yes—
227#10587630C2316yes—
228#10587625C2312yes—
229#10587624C2311yescharacteristic
230#10587622C2313yes—
231#10587621C2316yes—
232D4×Dic17C2316yes—
233D4×Dic17C2313yes—
234#10587616C2311yescharacteristic
235#10587615C2316yes—
236C4×C22⋊D17C2316yes—
237C4×C22⋊D17C2316yes—
238C4×C22⋊D17C2316yes—
239#10587612C2316yes—
240#10587612C2316yes—
241#10587612C2316yes—
242C2×C4⋊Dic17C2313yes—
243#10587610C2316yes—
244#10587610C2316yes—
245#10587610C2316yes—
246#10587610C2313yes—
247C2×#63225C2316yes—
248C2×C4×Dic17C2313yes—
249C2×C4×Dic17C2313yes—
250C2×C4×Dic17C2313yes—
251#10587584C23112yes—
252#10587584C23112yes—
253#10587584C23112yes—
254#10587584C2316yes—
255#10587584C2316yes—
256#10587584C2316yes—
257#10587583C2316yes—
258#10587583C2316yes—
259#10587583C2316yes—
260#10587583C2313yes—
261#10587582C23112yes—
262#10587582C23112yes—
263#10587582C23112yes—
264#10587582C2316yes—
265#10587581C2311yescharacteristic
266#10587580C2316yes—
267#10587580C2316yes—
268#10587579C2316yes—
269#10587579C2313yes—
270#10587578C2316yes—
271#10587578C2316yes—
272#10587578C2316yes—
273#10587578C2316yes—
274#10587578C2316yes—
275#10587578C2316yes—
276C4⋊C4×D17C2316yes—
277C4⋊C4×D17C2313yes—
278C4⋊C4×D17C2313yes—
279C4⋊C4×D17C2313yes—
280C4⋊C4×D17C2313yes—
281C4⋊C4×D17C2316yes—
282C4⋊C4×D17C2316yes—
283C4⋊C4×D17C2316yes—
284C4⋊C4×D17C2316yes—
285C4⋊C4×D17C2316yes—
286C4⋊C4×D17C2316yes—
287C4⋊C4×D17C2313yes—
288C4⋊C4×D17C2316yes—
289C4⋊C4×D17C2311yescharacteristic
290C4⋊C4×D17C23112yes—
291C4⋊C4×D17C2316yes—
292#10587576C2316yes—
293#10587576C23112yes—
294#10587576C23112yes—
295#10587576C2316yes—
296#10587576C2313yes—
297#10587576C2313yes—
298#10587576C2316yes—
299#10587576C2316yes—
300#10587575C23112yes—
301#10587575C23112yes—
302#10587575C23112yes—
303#10587575C23112yes—
304#10587575C23112yes—
305#10587575C23112yes—
306#10587575C2316yes—
307#10587575C2316yes—
308#10587575C23112yes—
309#10587575C23112yes—
310#10587574C23112yes—
311#10587574C2316yes—
312#10587574C2316yes—
313#10587574C23112yes—
314#10587574C2316yes—
315#10587574C2316yes—
316#10587573C2313yes—
317#10587573C2316yes—
318#10587573C23112yes—
319#10587573C2316yes—
320#10587573C2316yes—
321#10587573C23112yes—
322#10587573C2313yes—
323#10587573C2313yes—
324#10587573C2316yes—
325#10587573C2313yes—
326#10587573C2316yes—
327#10587573C2316yes—
328#10587573C2313yes—
329#10587573C2316yes—
330#10587573C23112yes—
331#10587572C2316yes—
332#10587571C2316yes—
333#10587571C2316yes—
334#10587570C2312yes—
335#10587569C2316yes—
336#10587569C2316yes—
337#10587567C2316yes—
338#10587567C2316yes—
339#10587567C2316yes—
340C22⋊C4×D17C2312yes—
341C22⋊C4×D17C2316yes—
342C22⋊C4×D17C2316yes—
343C22⋊C4×D17C2316yes—
344C22⋊C4×D17C2316yes—
345#10587565C23112yes—
346#10587565C23112yes—
347#10587565C23112yes—
348#10587565C2316yes—
349#10587565C2316yes—
350#10587565C2316yes—
351#10587564C23112yes—
352#10587564C23112yes—
353#10587564C23112yes—
354#10587564C2316yes—
355#10587563C23112yes—
356#10587563C23112yes—
357#10587563C2316yes—
358#10587563C2316yes—
359#10587562C23112yes—
360#10587562C2316yes—
361#10587561C2313yes—
362C4×D68C2316yes—
363C4×D68C2313yes—
364#10587558C23112yes—
365#10587558C23112yes—
366#10587558C2316yes—
367#10587558C2316yes—
368C42×D17C2313yes—
369C42×D17C2313yes—
370C42×D17C2313yes—
371C42×D17C2313yes—
372C42×D17C2313yes—
373C42×D17C2313yes—
374C42×D17C2313yes—
375C42×D17C2313yes—
376C42×D17C23112yes—
377C42×D17C2316yes—
378#10587556C23112yes—
379#10587556C2316yes—
380#10587556C2313yes—
381#10587556C2316yes—
382#10587555C2313yes—
383#10587555C2316yes—
384#10587555C2313yes—
385C4×Dic34C2313yes—
386C4×Dic34C2316yes—
387C4×Dic34C23112yes—
388C4×Dic34C2316yes—
389C4×Dic34C23112yes—
390C4×Dic34C2316yes—
391C4×Dic34C2313yes—
392C4×Dic34C2313yes—
393C4×Dic34C2316yes—
394C4×Dic34C2313yes—
395C4×Dic34C2316yes—
396C4×Dic34C2313yes—
397C4×Dic34C2316yes—
398C4×Dic34C23112yes—
399C4×Dic34C2316yes—
400C23×D17C2412yes—
401C23×D17C2411yescharacteristic
402C2×Q8×C17—24no—
403C2×Q8×C17—28no—
404C2×Q8×C17C2416yes—
405C2×Q8×C17C2413yes—
406C2×Q8×C17C2413yes—
407C2×Q8×C17C2411yescharacteristic
408C2×D4×C17C2412yes—
409C2×D4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2413yes—
412C22×C4×C17C2416yes—
413C22×C4×C17C2413yes—
414C2×C22⋊D17C2412yes—
415C2×C22⋊D17C2412yes—
416C2×C22⋊D17C2412yes—
417C22×Dic17C2416yes—
418C22×Dic17C2413yes—
419C22×Dic17C2413yes—
420C22×Dic17C2411yescharacteristic
421Q8×D17—24no—
422Q8×D17—28no—
423Q8×D17—212no—
424Q8×D17—224no—
425Q8×D17—212no—
426Q8×D17—212no—
427Q8×D17—224no—
428Q8×D17#4118yes—
429D4×D17—28no—
430D4×D17—24no—
431C2×D68C2411yescharacteristic
432C2×D68C2412yes—
433C2×C4×D17—212no—
434C2×C4×D17—212no—
435C2×C4×D17—224no—
436C2×C4×D17—24no—
437C2×C4×D17C2413yes—
438C2×C4×D17C2413yes—
439C2×C4×D17C2416yes—
440C2×C4×D17C2413yes—
441C2×C4×D17C2416yes—
442C2×C4×D17C2416yes—
443C2×C4×D17C2411yescharacteristic
444C2×C4×D17C2413yes—
445C2×C4×D17C2411yescharacteristic
446C2×C4×D17C2411yescharacteristic
447C2×C4×D17C2413yes—
448C2×C4×D17C2413yes—
449C2×C4×D17C2413yes—
450C2×C4×D17C2412yes—
451C2×C4×D17C2416yes—
452C2×C4×D17C2413yes—
453C2×C4×D17C2411yescharacteristic
454C2×Dic34—212no—
455C2×Dic34—224no—
456C2×Dic34C2413yes—
457C2×Dic34C2416yes—
458C2×Dic34C2416yes—
459C2×Dic34C24112yes—
460C2×Dic34C2413yes—
461C2×Dic34C2416yes—
462C2×Dic34C2413yes—
463C4⋊C4×C17C2416yes—
464C4⋊C4×C17C24112yes—
465C4⋊C4×C17C2413yes—
466C4⋊C4×C17C2416yes—
467C4⋊C4×C17C2416yes—
468C4⋊C4×C17C2413yes—
469C4⋊C4×C17C2416yes—
470C4⋊C4×C17C2416yes—
471C4⋊C4×C17C2416yes—
472C4⋊C4×C17C2416yes—
473C4⋊C4×C17C2411yescharacteristic
474C4⋊C4×C17C2416yes—
475C4⋊C4×C17C2413yes—
476C22⋊C4×C17C2416yes—
477C22⋊C4×C17C2416yes—
478C22⋊C4×C17C2416yes—
479C22⋊C4×C17C2416yes—
480C22⋊C4×C17C2412yes—
481C42×C17C2413yes—
482C42×C17C2413yes—
483C42×C17C24112yes—
484C42×C17C2416yes—
485C42×C17C2413yes—
486C42×C17C2413yes—
487C22⋊Dic17C2412yes—
488C22⋊Dic17C2416yes—
489C22⋊Dic17C2416yes—
490C22⋊Dic17C2416yes—
491C22⋊Dic17C2416yes—
492#63227C2416yes—
493#63227C2412yes—
494#63227C2416yes—
495#63227C2412yes—
496#63227C2416yes—
497#63227C2416yes—
498#63227C2416yes—
499#63227C2416yes—
500#63227C2416yes—
501#63227C2416yes—
502C4⋊Dic17C2413yes—
503C4⋊Dic17C2411yescharacteristic
504C4⋊Dic17C2413yes—
505C4⋊Dic17C2416yes—
506C4⋊Dic17C2413yes—
507C4⋊Dic17C2416yes—
508C4⋊Dic17C2416yes—
509C4⋊Dic17C2416yes—
510C4⋊Dic17C24112yes—
511C4⋊Dic17C2416yes—
512C4⋊Dic17C2416yes—
513C4⋊Dic17C2416yes—
514C4⋊Dic17C2416yes—
515#63225C2416yes—
516#63225C2412yes—
517#63225C2416yes—
518#63225C2416yes—
519#63225C2416yes—
520#63225C24112yes—
521#63225C2416yes—
522#63225C2416yes—
523#63225C2416yes—
524#63225C2416yes—
525#63225C2416yes—
526#63225C2416yes—
527#63225C24112yes—
528#63225C24112yes—
529#63225C2416yes—
530#63225C2416yes—
531#63225C24112yes—
532#63225C24112yes—
533#63225C2416yes—
534C4×Dic17C2413yes—
535C4×Dic17C2413yes—
536C4×Dic17C2413yes—
537C4×Dic17C2413yes—
538C4×Dic17C2413yes—
539C4×Dic17C2413yes—
540C4×Dic17C24112yes—
541C4×Dic17C2413yes—
542C4×Dic17C2416yes—
543C4×Dic17C24112yes—
544C4×Dic17C2416yes—
545C4×Dic17C2416yes—
546C4×Dic17C2413yes—
547C4×Dic17C2413yes—
548C4×Dic17C2413yes—
549C4×Dic17C2413yes—
550C4×Dic17C2413yes—
551C4×Dic17C24112yes—
552C2×#3523—171nomaximal, Sylow
553C23×C17C2512yes—
554C23×C17C2511yescharacteristic
555C22×D17—22no—
556C22×D17—22no—
557C22×D17—24no—
558C22×D17—24no—
559C22×D17—24no—
560C22×D172−1+414yes—
561C22×D17C2512yes—
562C22×D17C2511yescharacteristic
563C22×D17C2511yescharacteristic
564Q8×C17—26no—
565Q8×C17—212no—
566Q8×C17—26no—
567Q8×C17C2×#4114yes—
568D4×C17—24no—
569D4×C17—22no—
570C2×C4×C17—26no—
571C2×C4×C17—26no—
572C2×C4×C17—212no—
573C2×C4×C17—22no—
574C2×C4×C17C2513yes—
575C2×C4×C17C2511yescharacteristic
576C2×C4×C17C2516yes—
577C2×C4×C17C2512yes—
578C2×C4×C17C2513yes—
579C2×C4×C17C2513yes—
580C2×C4×C17C2516yes—
581C2×C4×C17C2513yes—
582C2×C4×C17C2511yescharacteristic
583C22⋊D17—24no—
584C22⋊D17—24no—
585C22⋊D17—24no—
586C2×Dic17—26no—
587C2×Dic17—26no—
588C2×Dic17—212no—
589C2×Dic17—22no—
590C2×Dic17C2516yes—
591C2×Dic17C2516yes—
592C2×Dic17C2513yes—
593C2×Dic17C2511yescharacteristic
594C2×Dic17C2513yes—
595C2×Dic17C2513yes—
596C2×Dic17C2512yes—
597C2×Dic17C2513yes—
598C2×Dic17C2511yescharacteristic
599D68—24no—
600D68—22no—
601C4×D17—26no—
602C4×D17—212no—
603C4×D17—26no—
604C4×D17—26no—
605C4×D17—26no—
606C4×D17—26no—
607C4×D17—22no—
608C4×D17—24no—
609C4×D17—212no—
610C4×D17—26no—
611C4×D17—212no—
612C4×D17—22no—
613C4×D17—26no—
614C4×D17—212no—
615C4×D17—22no—
616C4×D17C2×#41112yes—
617C4×D172−1+414yes—
618Dic34—26no—
619Dic34—212no—
620Dic34—26no—
621Dic34—212no—
622Dic34—224no—
623Dic34—212no—
624Dic34C2×#41112yes—
625#3523—173no—
626#3523—171no—
627#3523—173no—
628#3523—176no—
629#3523—172no—
630#3523—171no—
631#3523—176no—
632#3523—173no—
633#3523—173no—
634#3523—172no—
635#3523—171no—
636#3523D1711yescharacteristic, direct product factor
637C2×#557—171no—
638C2×#557—173no—
639C2×#556—173no—
640C2×#552—176no—
641C2×D4×Q8—172no—
642C2×D4×Q8—171no—
643C2×#541—176no—
644C2×#533—173no—
645C2×#529—173no—
646C2×#519—172no—
647C22×C4×Q8—171no—
648C22×C17—21no—
649C22×C17—21no—
650C22×C17—22no—
651C22×C17—22no—
652C22×C17—22no—
653C22×C17C2×2−1+412yes—
654C22×C17C2611yescharacteristic
655C2×D17—21no—
656C2×D17—21no—
657C2×D17—28no—
658C2×D17—22no—
659C2×D17—22no—
660C2×D17—22no—
661C2×D17—48no—
662C2×D17C22×#4112yes—
663C2×D17C2×2−1+412yes—
664C2×D17C2×2−1+412yes—
665C2×D17C2×2−1+412yes—
666C4×C17—23no—
667C4×C17—26no—
668C4×C17—26no—
669C4×C17—23no—
670C4×C17—23no—
671C4×C17—21no—
672C4×C17—22no—
673C4×C17C22×#4116yes—
674C4×C17C2×2−1+412yes—
675Dic17—23no—
676Dic17—26no—
677Dic17—26no—
678Dic17—23no—
679Dic17—23no—
680Dic17—21no—
681Dic17—22no—
682Dic17C22×#4116yes—
683Dic17C2×2−1+412yes—
684C23×Q8—171no—
685C23×Q8—172no—
686#557—176no—
687#557—173no—
688#557—173no—
689#557—176no—
690#557—1712no—
691#557—176no—
692#557—172no—
693#557—176no—
694#557—176no—
695#557—173no—
696#557—173no—
697#557—171no—
698#557—173no—
699#557C2×D1711yescharacteristic, complemented
700#557C2×D1713yescomplemented
701#556—173no—
702#556—1712no—
703#556—176no—
704#556—176no—
705#556—176no—
706#556—173no—
707#556—173no—
708#556—176no—
709#556C2×D1713yescomplemented
710#552—1712no—
711#552—1712no—
712#552—176no—
713#552—1712no—
714#552—176no—
715#552—176no—
716#552—176no—
717#552—176no—
718#552—1712no—
719#552—176no—
720#552—176no—
721#552C2×D1716yescomplemented
722D4×Q8—172no—
723D4×Q8—172no—
724D4×Q8—172no—
725D4×Q8—176no—
726D4×Q8—173no—
727D4×Q8—176no—
728D4×Q8—176no—
729D4×Q8—176no—
730D4×Q8—172no—
731D4×Q8—171no—
732D4×Q8—176no—
733D4×Q8—173no—
734D4×Q8C2×D1712yescomplemented
735D4×Q8C2×D1711yescharacteristic, complemented
736#541—176no—
737#541—1712no—
738#541—1712no—
739#541—1712no—
740#541—1712no—
741#541—176no—
742#541—176no—
743#541—176no—
744#541—176no—
745#541—176no—
746#541—176no—
747#541C2×D1716yescomplemented
748#533—173no—
749#533—173no—
750#533—176no—
751#533—176no—
752#533—176no—
753#533—176no—
754#533—176no—
755#533—176no—
756#533—173no—
757#533C2×D1713yescomplemented
758C2×C4⋊Q8—173no—
759C2×C4⋊Q8—173no—
760C2×C4⋊Q8—176no—
761#529—176no—
762#529—173no—
763#529—173no—
764#529—176no—
765#529—173no—
766#529—173no—
767#529—173no—
768#529—176no—
769#529—173no—
770#529—176no—
771#529—173no—
772#529C2×D1713yes—
773C2×#126—176no—
774C2×#126—1712no—
775C2×#125—173no—
776C2×#125—176no—
777C2×#125—1712no—
778C2×#125—176no—
779C2×#124—173no—
780C2×#123—176no—
781C2×C22⋊Q8—173no—
782C2×C22⋊Q8—176no—
783C2×C22⋊Q8—176no—
784C2×C22⋊Q8—176no—
785C2×#121—171no—
786#519—172no—
787#519—176no—
788#519—176no—
789#519—172no—
790#519—172no—
791#519—176no—
792#519—176no—
793#519C2×D1712yescomplemented
794C2×C4×Q8—171no—
795C2×C4×Q8—171no—
796C2×C4×Q8—173no—
797C2×C4×Q8—171no—
798C2×C4×Q8—173no—
799C2×C4×Q8—176no—
800C2×C4×Q8—172no—
801C2×C4×Q8—176no—
802C2×C4×Q8—173no—
803C2×C4×Q8—176no—
804C2×C4×Q8—171no—
805C2×C4×Q8—173no—
806C2×C4×Q8—171no—
807C2×C4×Q8—173no—
808C2×C4×Q8—173no—
809C2×C4×Q8—173no—
810C2×C4×Q8C2×D1711yescharacteristic, complemented
811C2×C4×D4—176no—
812C2×C4×D4—173no—
813C2×#117—176no—
814C2×#117—176no—
815C2×#117—176no—
816C22×C4⋊C4—173no—
817C22×C42—173no—
818C2×C17—22no—
819C2×C17—42no—
820C2×C17C23×#4111yescharacteristic
821C2×C17C22×2−1+411yescharacteristic
822C2×C17C22×2−1+411yescharacteristic
823D17—22no—
824D17—42no—
825D17#352314yesdirect product factor
826C22×Q8—171no—
827C22×Q8—173no—
828C22×Q8—173no—
829C22×Q8—176no—
830C22×Q8—173no—
831C22×Q8—171no—
832C22×Q8—176no—
833C22×Q8—172no—
834C22×Q8—173no—
835C22×Q8—176no—
836C22×Q8—348no—
837C22×Q8—3416no—
838C22×Q8C22×D1711yescharacteristic
839C22×Q8C22×D1712yes—
840C22×D4—172no—
841C22×D4—171no—
842C23×C4—173no—
843C23×C4—173no—
844C23×C4—176no—
845C23×C4—171no—
846C4⋊Q8—176no—
847C4⋊Q8—176no—
848C4⋊Q8—176no—
849C4⋊Q8—176no—
850C4⋊Q8—176no—
851C4⋊Q8—176no—
852C4⋊Q8—176no—
853C4⋊Q8—176no—
854C4⋊Q8—1712no—
855C4⋊Q8—1712no—
856C4⋊Q8—173no—
857C4⋊Q8—173no—
858C4⋊Q8—176no—
859C4⋊Q8C22×D1713yes—
860C4⋊Q8C22×D1713yes—
861C4⋊Q8C22×D1716yes—
862#126—176no—
863#126—176no—
864#126—176no—
865#126—1712no—
866#126—1712no—
867#126—1712no—
868#126—176no—
869#126—176no—
870#126—176no—
871#126—1712no—
872#126—1712no—
873#126—1712no—
874#126—176no—
875#126—1712no—
876#126C22×D1716yes—
877#126C22×D17112yes—
878#125—176no—
879#125—176no—
880#125—173no—
881#125—173no—
882#125—1712no—
883#125—1712no—
884#125—176no—
885#125—176no—
886#125—1712no—
887#125—1712no—
888#125—1712no—
889#125—1712no—
890#125—1712no—
891#125—1712no—
892#125—1712no—
893#125—1712no—
894#125—176no—
895#125—176no—
896#125—173no—
897#125—176no—
898#125—1712no—
899#125—176no—
900#125C22×D1713yes—
901#125C22×D1716yes—
902#125C22×D17112yes—
903#125C22×D1716yes—
904#124—173no—
905#124—173no—
906#124—176no—
907#124—176no—
908#124—173no—
909#124C22×D1713yes—
910#123—176no—
911#123—176no—
912#123—176no—
913#123—176no—
914#123—176no—
915#123—176no—
916#123—176no—
917#123C22×D1716yes—
918C22⋊Q8—173no—
919C22⋊Q8—176no—
920C22⋊Q8—176no—
921C22⋊Q8—176no—
922C22⋊Q8—173no—
923C22⋊Q8—176no—
924C22⋊Q8—176no—
925C22⋊Q8—176no—
926C22⋊Q8—176no—
927C22⋊Q8—173no—
928C22⋊Q8—1712no—
929C22⋊Q8—176no—
930C22⋊Q8—1712no—
931C22⋊Q8—176no—
932C22⋊Q8—1712no—
933C22⋊Q8—176no—
934C22⋊Q8—176no—
935C22⋊Q8—1712no—
936C22⋊Q8—1712no—
937C22⋊Q8—1712no—
938C22⋊Q8C22×D1713yes—
939C22⋊Q8C22×D1716yes—
940C22⋊Q8C22×D1716yes—
941C22⋊Q8C22×D1716yes—
942#121—171no—
943#121—172no—
944#121—171no—
945#121—171no—
946#121—172no—
947#121C22×D1711yescharacteristic
948C4×Q8—171no—
949C4×Q8—173no—
950C4×Q8—171no—
951C4×Q8—173no—
952C4×Q8—176no—
953C4×Q8—172no—
954C4×Q8—176no—
955C4×Q8—173no—
956C4×Q8—176no—
957C4×Q8—173no—
958C4×Q8—176no—
959C4×Q8—173no—
960C4×Q8—173no—
961C4×Q8—176no—
962C4×Q8—173no—
963C4×Q8—1712no—
964C4×Q8—176no—
965C4×Q8—176no—
966C4×Q8—1712no—
967C4×Q8—176no—
968C4×Q8—176no—
969C4×Q8—173no—
970C4×Q8—1712no—
971C4×Q8—176no—
972C4×Q8—173no—
973C4×Q8—176no—
974C4×Q8—173no—
975C4×Q8—173no—
976C4×Q8—176no—
977C4×Q8—173no—
978C4×Q8—1712no—
979C4×Q8—176no—
980C4×Q8—176no—
981C4×Q8—176no—
982C4×Q8—1712no—
983C4×Q8—176no—
984C4×Q8—173no—
985C4×Q8—1712no—
986C4×Q8—176no—
987C4×Q8C22×D1711yescharacteristic
988C4×Q8C22×D1713yes—
989C4×Q8C22×D1711yescharacteristic
990C4×Q8C22×D1713yes—
991C4×Q8C22×D1716yes—
992C4×Q8C22×D1712yes—
993C4×Q8C22×D1716yes—
994C4×Q8C22×D1713yes—
995C4×Q8C22×D1716yes—
996C4×D4—176no—
997C4×D4—173no—
998C4×D4—176no—
999C4×D4—176no—
1000C4×D4—176no—
1001C4×D4—176no—
1002C4×D4—173no—
1003C4×D4—176no—
1004C4×D4—176no—
1005C4×D4—176no—
1006C4×D4—176no—
1007C4×D4—173no—
1008C4×D4C22×D1716yes—
1009C4×D4C22×D1713yes—
1010#117—176no—
1011#117—176no—
1012#117—176no—
1013#117—176no—
1014#117—176no—
1015#117—176no—
1016#117—176no—
1017#117—176no—
1018#117—176no—
1019#117—176no—
1020#117—176no—
1021#117—1712no—
1022#117—1712no—
1023#117—176no—
1024#117—176no—
1025#117—1712no—
1026#117—1712no—
1027#117C22×D1716yes—
1028#117C22×D1716yes—
1029#117C22×D1716yes—
1030C2×C4⋊C4—176no—
1031C2×C4⋊C4—173no—
1032C2×C4⋊C4—173no—
1033C2×C4⋊C4—173no—
1034C2×C4⋊C4—176no—
1035C2×C4⋊C4—176no—
1036C2×C4⋊C4—173no—
1037C2×C4⋊C4—173no—
1038C2×C4⋊C4—176no—
1039C2×C4⋊C4—176no—
1040C2×C4⋊C4—176no—
1041C2×C4⋊C4—176no—
1042C2×C4⋊C4—176no—
1043C2×C4⋊C4—173no—
1044C2×C4⋊C4—176no—
1045C2×C4⋊C4—171no—
1046C2×C4⋊C4—1712no—
1047C2×C4⋊C4—176no—
1048C2×C4⋊C4C22×D1713yes—
1049C2×C22⋊C4—172no—
1050C2×C22⋊C4—176no—
1051C2×C22⋊C4—176no—
1052C2×C22⋊C4—176no—
1053C2×C22⋊C4—176no—
1054C2×C42—173no—
1055C2×C42—173no—
1056C2×C42—173no—
1057C2×C42—173no—
1058C2×C42—1712no—
1059C2×C42—176no—
1060C2×C42—173no—
1061C2×C42—173no—
1062C2×C42—173no—
1063C2×C42—173no—
1064C2×C42—173no—
1065C2×C42—173no—
1066C2×C42—173no—
1067C2×C42C22×D1713yes—
1068C17C2×#352311yescharacteristic, complemented, Sylow
1069C24—171no—
1070C24—172no—
1071C2×Q8—24no—
1072C2×Q8—28no—
1073C2×Q8—178no—
1074C2×Q8—173no—
1075C2×Q8—176no—
1076C2×Q8—173no—
1077C2×Q8—176no—
1078C2×Q8—1712no—
1079C2×Q8—173no—
1080C2×Q8—176no—
1081C2×Q8—3412no—
1082C2×Q8—3424no—
1083C2×Q8—3412no—
1084C2×Q8—3412no—
1085C2×Q8—3424no—
1086C2×Q8—3412no—
1087C2×Q8—3424no—
1088C2×Q8—344no—
1089C2×Q8—348no—
1090C2×Q8C23×D1713yes—
1091C2×Q8C23×D1713yes—
1092C2×Q8C23×D1716yes—
1093C2×Q8C23×D1711yescharacteristic
1094C2×D4—172no—
1095C2×D4—172no—
1096C2×D4—172no—
1097C2×D4—172no—
1098C2×D4—171no—
1099C2×D4—344no—
1100C2×D4—348no—
1101C2×D4C23×D1712yes—
1102C2×D4C23×D1711yescharacteristic
1103C22×C4—171no—
1104C22×C4—173no—
1105C22×C4—171no—
1106C22×C4—173no—
1107C22×C4—173no—
1108C22×C4—176no—
1109C22×C4—171no—
1110C22×C4—173no—
1111C22×C4—171no—
1112C22×C4—171no—
1113C22×C4—176no—
1114C22×C4—172no—
1115C22×C4—173no—
1116C22×C4—176no—
1117C22×C4—173no—
1118C22×C4—173no—
1119C22×C4—173no—
1120C22×C4—173no—
1121C22×C4—173no—
1122C22×C4—176no—
1123C22×C4—176no—
1124C22×C4—344no—
1125C22×C4—3412no—
1126C22×C4—3424no—
1127C22×C4—3412no—
1128C22×C4C23×D1711yescharacteristic
1129C22×C4C23×D1713yes—
1130C22×C4C23×D1713yes—
1131C22×C4C23×D1716yes—
1132C4⋊C4—176no—
1133C4⋊C4—173no—
1134C4⋊C4—176no—
1135C4⋊C4—173no—
1136C4⋊C4—176no—
1137C4⋊C4—176no—
1138C4⋊C4—176no—
1139C4⋊C4—1712no—
1140C4⋊C4—176no—
1141C4⋊C4—176no—
1142C4⋊C4—176no—
1143C4⋊C4—176no—
1144C4⋊C4—176no—
1145C4⋊C4—176no—
1146C4⋊C4—176no—
1147C4⋊C4—1712no—
1148C4⋊C4—176no—
1149C4⋊C4—1712no—
1150C4⋊C4—176no—
1151C4⋊C4—176no—
1152C4⋊C4—173no—
1153C4⋊C4—176no—
1154C4⋊C4—176no—
1155C4⋊C4—176no—
1156C4⋊C4—172no—
1157C4⋊C4—171no—
1158C4⋊C4—1712no—
1159C4⋊C4—1712no—
1160C4⋊C4—1712no—
1161C4⋊C4—176no—
1162C4⋊C4—176no—
1163C4⋊C4—176no—
1164C4⋊C4C23×D1713yes—
1165C4⋊C4C23×D1713yes—
1166C4⋊C4C23×D1716yes—
1167C4⋊C4C23×D1716yes—
1168C4⋊C4C23×D1716yes—
1169C4⋊C4C23×D1716yes—
1170C4⋊C4C23×D1716yes—
1171C4⋊C4C23×D1716yes—
1172C4⋊C4C23×D1713yes—
1173C4⋊C4C23×D1716yes—
1174C4⋊C4C23×D1711yescharacteristic
1175C4⋊C4C23×D17112yes—
1176C4⋊C4C23×D1716yes—
1177C22⋊C4—172no—
1178C22⋊C4—176no—
1179C22⋊C4—176no—
1180C22⋊C4—176no—
1181C22⋊C4—176no—
1182C22⋊C4—172no—
1183C22⋊C4—172no—
1184C22⋊C4—176no—
1185C22⋊C4—176no—
1186C22⋊C4—176no—
1187C22⋊C4—176no—
1188C22⋊C4—176no—
1189C22⋊C4—176no—
1190C22⋊C4—176no—
1191C22⋊C4—176no—
1192C22⋊C4C23×D1712yes—
1193C22⋊C4C23×D1716yes—
1194C22⋊C4C23×D1716yes—
1195C22⋊C4C23×D1716yes—
1196C22⋊C4C23×D1716yes—
1197C42—173no—
1198C42—173no—
1199C42—173no—
1200C42—173no—
1201C42—173no—
1202C42—173no—
1203C42—173no—
1204C42—173no—
1205C42—173no—
1206C42—173no—
1207C42—173no—
1208C42—173no—
1209C42—1712no—
1210C42—1712no—
1211C42—1712no—
1212C42—176no—
1213C42—176no—
1214C42—176no—
1215C42C23×D1713yes—
1216C42C23×D1713yes—
1217C42C23×D1713yes—
1218C42C23×D1713yes—
1219C42C23×D17112yes—
1220C42C23×D1716yes—
1221C23—171no—
1222C23—174no—
1223C23—171no—
1224C23—172no—
1225C23—342no—
1226C23—342no—
1227C23—344no—
1228C23—344no—
1229C23—344no—
1230C23C24×D1712yes—
1231C23C24×D1711yescharacteristic
1232Q8—26no—
1233Q8—212no—
1234Q8—26no—
1235Q8—1712no—
1236Q8—3412no—
1237Q8—3424no—
1238Q8—3412no—
1239Q8—346no—
1240Q8—3412no—
1241Q8—346no—
1242Q8#41×D1714yes—
1243D4—24no—
1244D4—22no—
1245D4—344no—
1246D4—344no—
1247D4—344no—
1248D4—344no—
1249D4—342no—
1250C2×C4—26no—
1251C2×C4—26no—
1252C2×C4—212no—
1253C2×C4—22no—
1254C2×C4—171no—
1255C2×C4—173no—
1256C2×C4—1712no—
1257C2×C4—174no—
1258C2×C4—171no—
1259C2×C4—173no—
1260C2×C4—176no—
1261C2×C4—172no—
1262C2×C4—173no—
1263C2×C4—173no—
1264C2×C4—176no—
1265C2×C4—346no—
1266C2×C4—3412no—
1267C2×C4—342no—
1268C2×C4—3412no—
1269C2×C4—346no—
1270C2×C4—342no—
1271C2×C4—346no—
1272C2×C4—346no—
1273C2×C4—346no—
1274C2×C4—346no—
1275C2×C4—344no—
1276C2×C4—3412no—
1277C2×C4—346no—
1278C2×C4—3412no—
1279C2×C4—342no—
1280C2×C4—346no—
1281C2×C4—346no—
1282C2×C4—3412no—
1283C2×C4—342no—
1284C2×C4C24×D1711yescharacteristic
1285C2×C4C24×D1713yes—
1286C2×C4C24×D1716yes—
1287C2×C4C24×D1712yes—
1288C2×C4C24×D1713yes—
1289C2×C4C24×D1713yes—
1290C2×C4C24×D1716yes—
1291C2×C4C24×D1713yes—
1292C2×C4C24×D1711yescharacteristic
1293C22—21no—
1294C22—21no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—172no—
1299C22—172no—
1300C22—172no—
1301C22—172no—
1302C22—348no—
1303C22—341no—
1304C22—341no—
1305C22—342no—
1306C22—342no—
1307C22—342no—
1308C22—688no—
1309C222−1+4×D1712yes—
1310C22C25×D1711yescharacteristic
1311C4—23no—
1312C4—26no—
1313C4—23no—
1314C4—23no—
1315C4—21no—
1316C4—22no—
1317C4—26no—
1318C4—176no—
1319C4—172no—
1320C4—343no—
1321C4—346no—
1322C4—343no—
1323C4—343no—
1324C4—341no—
1325C4—342no—
1326C4—346no—
1327C4C2×#41×D1716yes—
1328C42−1+4×D1712yes—
1329C2—22no—
1330C2—42no—
1331C2—174no—
1332C2—342no—
1333C2—682no—
1334C2C22×#41×D1711yescharacteristic
1335C2C2×2−1+4×D1711yescharacteristic
1336C2C2×2−1+4×D1711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D17
commutator, socle, cosocleC22×C17C26
FittingC17×#3523C2
prime radical#121×D17C22
hypercenter#3523D17
hypocenterC17C2×#3523
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #3523

Complements

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

NH ≅ G/Ntype
1. #14542881C2semidirect
2. #14542880C2semidirect
3. #14542879C2semidirect
4. #14542878C2semidirect
5. #14542877C2semidirect
6. #14542876C2semidirect
7. #14542875C2semidirect
8. #14542874C2semidirect
9. #14542873C2semidirect
10. #14542872C2semidirect
11. #14542871C2semidirect
12. D17×#557C2semidirect
13. D17×#557C2semidirect
14. D17×#556C2semidirect
15. D17×#552C2semidirect
16. D4×Q8×D17C2semidirect
17. D4×Q8×D17C2semidirect
18. D17×#541C2semidirect
19. D17×#533C2semidirect
21. D17×#519C2semidirect
22. C2×C4×Q8×D17C2semidirect
23. C17×#3523C2semidirect
26. #11763538C22semidirect
27. #11763538C22semidirect
28. #11763537C22semidirect
29. #11763537C22semidirect
30. #11763537C22semidirect
31. #11763536C22semidirect
32. #11763536C22semidirect
33. #11763536C22semidirect
34. #11763535C22semidirect
35. #11763535C22semidirect
36. #11763534C22semidirect
37. #11763534C22semidirect
38. #11763534C22semidirect
39. #11763533C22semidirect
40. #11763532C22semidirect
41. #11763531C22semidirect
42. #11763530C22semidirect
43. #11763529C22semidirect
44. #11763528C22semidirect
45. #11763527C22semidirect
46. #11763526C22semidirect
47. #11763501C22semidirect
48. #11763500C22semidirect
49. #11763499C22semidirect
50. #11763498C22semidirect
51. #11763497C22semidirect
52. #11763496C22semidirect
53. #11763495C22semidirect
54. #11763494C22semidirect
55. #11763493C22semidirect
56. #11763492C22semidirect
57. #11763491C22semidirect
58. Q8×D68C22semidirect
59. Q8×D68C22semidirect
60. D4×Dic34C22semidirect
61. D4×Dic34C22semidirect
62. #11763474C22semidirect
63. #11763474C22semidirect
64. Q8×C22⋊D17C22semidirect
65. Q8×C22⋊D17C22semidirect
66. Q8×C22⋊D17C22semidirect
67. #11763472C22semidirect
68. #11763472C22semidirect
69. #11763472C22semidirect
70. #11763422C22semidirect
71. #11763421C22semidirect
72. #11763420C22semidirect
73. #11763419C22semidirect
74. #11763419C22semidirect
75. #11763418C22semidirect
76. #11763418C22semidirect
77. #11763417C22semidirect
78. #11763417C22semidirect
79. #11763416C22semidirect
80. #11763416C22semidirect
81. #11763366C22semidirect
82. #11763365C22semidirect
83. #11763364C22semidirect
84. #11763364C22semidirect
85. #11763363C22semidirect
86. #11763363C22semidirect
87. #11763362C22semidirect
88. #11763361C22semidirect
89. #11763361C22semidirect
117. #11763287C22semidirect
118. #11763286C22semidirect
119. #11763286C22semidirect
120. #11763285C22semidirect
121. #11763285C22semidirect
122. #11763285C22semidirect
123. #11763285C22semidirect
124. C2×Q8×Dic17C22semidirect
125. C2×C4×Dic34C22semidirect
126. C2×#10587573C22semidirect
136. C4×Q8×D17C22semidirect
137. C4×Q8×D17C22semidirect
138. C4×Q8×D17C22semidirect
139. C4×Q8×D17C22semidirect
147. C17×#557C22semidirect
148. C17×#557C22semidirect
149. C17×#556C22semidirect
150. C17×#552C22semidirect
151. D4×Q8×C17C22semidirect
152. D4×Q8×C17C22semidirect
153. C17×#541C22semidirect
154. C17×#533C22semidirect
156. C17×#519C22semidirect
157. C2×C4×Q8×C17C22semidirect
636. #3523D17direct (N × H)
699. #557C2×D17semidirect
700. #557C2×D17semidirect
709. #556C2×D17semidirect
721. #552C2×D17semidirect
734. D4×Q8C2×D17semidirect
735. D4×Q8C2×D17semidirect
747. #541C2×D17semidirect
757. #533C2×D17semidirect
793. #519C2×D17semidirect
810. C2×C4×Q8C2×D17semidirect
825. D17#3523direct (N × H)
1068. C17C2×#3523semidirect

Maximal subgroups

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

subgroupindex
#145428812
#145428802
#145428792
#145428782
#145428772
#145428762
#145428752
#145428742
#145428732
#145428722
#145428712
D17×#5572
D17×#5562
D17×#5522
D4×Q8×D172
D17×#5412
D17×#5332
D17×#5292
D17×#5192
C2×C4×Q8×D172
C17×#35232
C2×#352317