Finite Group Databasebeta

← D17×#3548 #17942113

Subgroups — D17×#3548 #17942113

Order 4352.

7810 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14543184C211yesmaximal, characteristic, complemented
2#14543183C214yesmaximal, complemented
3#14543182C212yesmaximal, complemented
4#14543181C214yesmaximal, complemented
5#14543180C214yesmaximal, complemented
6#14543179C218yesmaximal, complemented
7#14543178C214yesmaximal, complemented
8#14543177C214yesmaximal, complemented
9D17×#562C214yesmaximal, complemented
10D17×#554C214yesmaximal, complemented
11D17×#550C214yesmaximal, complemented
12D17×#547C214yesmaximal, complemented
13D17×#540C214yesmaximal, complemented
14D17×#537C218yesmaximal, complemented
15D17×#533C211yesmaximal, characteristic, complemented
16D17×#532C212yesmaximal, complemented
17C17×#3548C211yesmaximal, characteristic, complemented
18C2×#41×D17C2214yes—
19C2×#41×D17C2218yes—
20#11763557C2214yescomplemented
21#11763556C22116yescomplemented
22#11763555C22116yescomplemented
23#11763554C22116yescomplemented
24#11763553C2218yescomplemented
25#11763520C2214yescomplemented
26#11763519C2214yescomplemented
27#11763518C2218yescomplemented
28#11763517C2218yescomplemented
29#11763516C2214yescomplemented
30#11763515C2218yescomplemented
31#11763514C2218yescomplemented
32#11763513C22116yescomplemented
33#11763481C2214yescomplemented
34#11763480C2218yescomplemented
35#11763480C2214yescomplemented
36#11763479C2218yescomplemented
37#11763479C2214yescomplemented
38#11763478C2218yescomplemented
39#11763477C22116yescomplemented
40#11763477C2218yescomplemented
41#11763464C2214yescomplemented
42#11763463C2214yescomplemented
43#11763462C2214yescomplemented
44#11763461C2218yescomplemented
45#11763460C2218yescomplemented
46#11763459C2218yescomplemented
47#11763458C2218yescomplemented
48#11763457C22116yescomplemented
49#11763415C2214yescomplemented
50#11763414C2214yescomplemented
51#11763413C2214yescomplemented
52#11763412C2218yescomplemented
53#11763411C22116yescomplemented
54#11763410C2218yescomplemented
55#11763409C22116yescomplemented
56#11763390C2218yescomplemented
57#11763389C2218yescomplemented
58#11763389C22116yescomplemented
59#11763389C2218yescomplemented
60#11763388C2218yescomplemented
61#11763388C22116yescomplemented
62#11763388C2218yescomplemented
63#11763387C2218yescomplemented
64#11763387C2218yescomplemented
65#11763386C22116yescomplemented
66#11763386C22116yescomplemented
67#11763366C2211yescharacteristic, complemented
68#11763365C2212yescomplemented
69#11763364C2212yescomplemented
70#11763363C2214yescomplemented
71#11763362C2212yescomplemented
72#11763361C2214yescomplemented
73#11763360C2212yescomplemented
74#11763359C2212yescomplemented
75#11763358C2214yescomplemented
76#11763357C2212yescomplemented
77#11763356C2214yescomplemented
78#11763356C2214yescomplemented
79#11763355C2214yescomplemented
80#11763354C2214yescomplemented
81#11763354C2214yescomplemented
82C4⋊Q8×D17C2212yes—
83C4⋊Q8×D17C2212yes—
84#127×D17C2214yes—
85#127×D17C2212yes—
86#125×D17C2214yes—
87#125×D17C2212yes—
88#124×D17C2214yes—
89#123×D17C22116yes—
90C22⋊Q8×D17C2214yes—
91C22⋊Q8×D17C22116yes—
92C22⋊Q8×D17C2218yes—
93#121×D17C22116yes—
94#121×D17C2214yes—
95#121×D17C22116yes—
96#121×D17C2218yes—
97#121×D17C2214yes—
98C4×Q8×D17C2214yes—
99C4×D4×D17C2218yes—
100C4×D4×D17C2214yes—
101C4×D4×D17C2214yes—
102#117×D17C2212yes—
103C2×C4⋊C4×D17C2218yes—
104C2×C42×D17C2211yescharacteristic
105C17×#562C2214yescomplemented
106C17×#554C2214yescomplemented
107C17×#550C2214yescomplemented
108C17×#547C2214yescomplemented
109C17×#540C2214yescomplemented
110C17×#537C2218yescomplemented
111C17×#533C2211yescharacteristic, complemented
112C17×#532C2212yescomplemented
113C2×#41×C17C2318yes—
114C2×#41×C17C2314yes—
115#41×D17—416no—
116#41×D17—432no—
117C2×#63256C2318yes—
118C2×#63256C2314yes—
119C2×Q8×D17C2314yes—
120C2×Q8×D17C2314yes—
121C2×#63254C23116yes—
122C2×#63254C2318yes—
123C2×#63254C2318yes—
124C2×#63254C2314yes—
125C2×D4×D17C2314yes—
126C2×D4×D17C2314yes—
127C2×D4×D17C2318yes—
128C2×D4×D17C23116yes—
129C2×D4×D17C2314yes—
130C2×#63252C23116yes—
131C2×#63252C2318yes—
132C2×#63252C2314yes—
133C2×#63252C2318yes—
134C22×C4×D17C2311yescharacteristic
135C22×C4×D17C2312yes—
136C22×C4×D17C2318yes—
137C22×C4×D17C23116yes—
138C17×C4⋊Q8C2312yes—
139C17×C4⋊Q8C2312yes—
140C17×#127C2312yes—
141C17×#127C2314yes—
142C17×#125C2312yes—
143C17×#125C2314yes—
144C17×#124C2314yes—
145C17×#123C23116yes—
146C17×C22⋊Q8C2318yes—
147C17×C22⋊Q8C2314yes—
148C17×C22⋊Q8C23116yes—
149C17×#121C2318yes—
150C17×#121C23116yes—
151C17×#121C2314yes—
152C17×#121C2314yes—
153C17×#121C23116yes—
154C4×Q8×C17C2314yes—
155C4×D4×C17C2314yes—
156C4×D4×C17C2314yes—
157C4×D4×C17C2318yes—
158C17×#117C2312yes—
159C2×C4⋊C4×C17C2318yes—
160C2×C42×C17C2311yescharacteristic
161#10587633C2314yes—
162#10587632C2318yes—
163#10587632C23116yes—
164#10587632C2314yes—
165Q8×Dic17C2314yes—
166#10587630C2314yes—
167#10587630C2314yes—
168#10587626C2314yes—
169#10587626C23116yes—
170#10587626C2314yes—
171#10587626C2314yes—
172#10587626C2318yes—
173#10587625C23116yes—
174#10587625C23116yes—
175#10587625C23116yes—
176#10587625C2318yes—
177#10587625C2318yes—
178#10587625C23116yes—
179#10587625C23116yes—
180#10587624C2318yes—
181#10587624C23116yes—
182#10587624C2314yes—
183#10587624C2314yes—
184#10587624C23116yes—
185#10587622C2314yes—
186#10587621C23116yes—
187D4×Dic17C2314yes—
188D4×Dic17C2318yes—
189D4×Dic17C2314yes—
190#10587616C2318yes—
191#10587616C23116yes—
192#10587616C2314yes—
193#10587616C2314yes—
194#10587616C23116yes—
195#10587615C23116yes—
196C4×C22⋊D17C2318yes—
197C4×C22⋊D17C23116yes—
198C4×C22⋊D17C2318yes—
199#10587612C2312yes—
200C2×C4⋊Dic17C2318yes—
201#10587610C2318yes—
202#10587610C23116yes—
203#10587610C2314yes—
204C2×#63225C23116yes—
205C2×C4×Dic17C2311yescharacteristic
206C2×C4×Dic17C2312yes—
207#10587583C2318yes—
208#10587583C23116yes—
209#10587583C2314yes—
210#10587582C23116yes—
211#10587582C23116yes—
212#10587582C23116yes—
213#10587582C2318yes—
214#10587581C2318yes—
215#10587581C23116yes—
216#10587581C2314yes—
217#10587581C2314yes—
218#10587581C23116yes—
219#10587580C23116yes—
220#10587580C23116yes—
221#10587579C2314yes—
222#10587579C2314yes—
223#10587579C2318yes—
224#10587578C2314yes—
225C4⋊C4×D17C23116yes—
226C4⋊C4×D17C2318yes—
227C4⋊C4×D17C2318yes—
228C4⋊C4×D17C2314yes—
229C4⋊C4×D17C2314yes—
230C4⋊C4×D17C23116yes—
231C4⋊C4×D17C2314yes—
232C4⋊C4×D17C2314yes—
233C4⋊C4×D17C2318yes—
234#10587576C2318yes—
235#10587576C2314yes—
236#10587575C23116yes—
237#10587575C2318yes—
238#10587574C2314yes—
239#10587574C2314yes—
240#10587574C2314yes—
241#10587574C2314yes—
242#10587573C2318yes—
243#10587573C2314yes—
244#10587572C23116yes—
245#10587571C2318yes—
246#10587571C2318yes—
247#10587570C23116yes—
248#10587570C23116yes—
249#10587570C23116yes—
250#10587570C2318yes—
251#10587570C2318yes—
252#10587570C23116yes—
253#10587570C23116yes—
254#10587569C23116yes—
255#10587569C23116yes—
256#10587567C2318yes—
257#10587567C2318yes—
258#10587567C23116yes—
259C22⋊C4×D17C2314yes—
260C22⋊C4×D17C23116yes—
261C22⋊C4×D17C2318yes—
262C22⋊C4×D17C2318yes—
263#10587564C23116yes—
264#10587564C23116yes—
265#10587564C23116yes—
266#10587564C2318yes—
267#10587563C2314yes—
268#10587561C2314yes—
269#10587560C2312yes—
270#10587560C2314yes—
271C4×D68C2314yes—
272C4×D68C2318yes—
273C4×D68C2314yes—
274#10587558C2314yes—
275C42×D17C2311yescharacteristic
276C42×D17C2312yes—
277C42×D17C2311yescharacteristic
278C42×D17C2311yescharacteristic
279C42×D17C2312yes—
280C42×D17C2311yescharacteristic
281C42×D17C2314yes—
282#10587556C2314yes—
283#10587556C2312yes—
284#10587555C2312yes—
285#10587555C2312yes—
286C4×Dic34C2318yes—
287C4×Dic34C2314yes—
288C23×D17C2411yescharacteristic
289C23×D17C2418yes—
290#41×C17—48no—
291#41×C17—416no—
292C2×Q8×C17C2414yes—
293C2×Q8×C17C2414yes—
294C2×D4×C17C2414yes—
295C2×D4×C17C2414yes—
296C2×D4×C17C24116yes—
297C2×D4×C17C2414yes—
298C2×D4×C17C2418yes—
299C22×C4×C17C2412yes—
300C22×C4×C17C2418yes—
301C22×C4×C17C2411yescharacteristic
302C22×C4×C17C24116yes—
303C2×C22⋊D17C2418yes—
304C2×C22⋊D17C2418yes—
305C2×C22⋊D17C24116yes—
306C2×C22⋊D17C2418yes—
307C2×C22⋊D17C2418yes—
308C2×C22⋊D17C24116yes—
309C2×C22⋊D17C2418yes—
310C22×Dic17C2412yes—
311C22×Dic17C2418yes—
312C22×Dic17C2411yescharacteristic
313C22×Dic17C24116yes—
314#63256—48no—
315#63256—416no—
316Q8×D17—216no—
317Q8×D17—48no—
318#63254—416no—
319#63254—432no—
320#63254—416no—
321#63254—48no—
322D4×D17—216no—
323D4×D17—216no—
324D4×D17—416no—
325D4×D17—48no—
326D4×D17—432no—
327#63252—432no—
328#63252—416no—
329#63252—416no—
330#63252—48no—
331C2×D68C2414yes—
332C2×D68C2414yes—
333C2×D68C2414yes—
334C2×D68C24116yes—
335C2×D68C2418yes—
336C2×C4×D17—232no—
337C2×C4×D17—28no—
338C2×C4×D17—24no—
339C2×C4×D17—432no—
340C2×C4×D17C2418yes—
341C2×C4×D17C2418yes—
342C2×C4×D17C2412yes—
343C2×C4×D17C2418yes—
344C2×C4×D17C2418yes—
345C2×C4×D17C2412yes—
346C2×C4×D17C2412yes—
347C2×C4×D17C2411yescharacteristic
348C2×C4×D17C2411yescharacteristic
349C2×C4×D17C2411yescharacteristic
350C2×C4×D17C24116yes—
351C2×C4×D17C24116yes—
352C2×C4×D17C2412yes—
353C2×C4×D17C2411yescharacteristic
354C2×Dic34C2414yes—
355C2×Dic34C2418yes—
356C2×Dic34C2414yes—
357C2×Dic34C2418yes—
358C4⋊C4×C17C24116yes—
359C4⋊C4×C17C2418yes—
360C4⋊C4×C17C2414yes—
361C4⋊C4×C17C2414yes—
362C4⋊C4×C17C2414yes—
363C4⋊C4×C17C2414yes—
364C22⋊C4×C17C24116yes—
365C22⋊C4×C17C2418yes—
366C22⋊C4×C17C2414yes—
367C22⋊C4×C17C2418yes—
368C42×C17C2411yescharacteristic
369C42×C17C2414yes—
370C42×C17C2412yes—
371C42×C17C2411yescharacteristic
372C22⋊Dic17C2414yes—
373C22⋊Dic17C24116yes—
374C22⋊Dic17C2418yes—
375C22⋊Dic17C2418yes—
376#63227C2418yes—
377#63227C2418yes—
378#63227C2418yes—
379#63227C24116yes—
380#63227C2418yes—
381#63227C2418yes—
382#63227C24116yes—
383C4⋊Dic17C2414yes—
384C4⋊Dic17C2418yes—
385C4⋊Dic17C2414yes—
386C4⋊Dic17C2414yes—
387C4⋊Dic17C2414yes—
388C4⋊Dic17C24116yes—
389#63225C2418yes—
390#63225C2418yes—
391#63225C2418yes—
392#63225C24116yes—
393#63225C2418yes—
394#63225C2418yes—
395#63225C24116yes—
396#63225C2418yes—
397C4×Dic17C2412yes—
398C4×Dic17C2414yes—
399C4×Dic17C2411yescharacteristic
400C4×Dic17C2412yes—
401C4×Dic17C2411yescharacteristic
402C4×Dic17C2412yes—
403C4×Dic17C2412yes—
404C4×Dic17C2412yes—
405C4×Dic17C2418yes—
406C2×#3548—171nomaximal, Sylow
407C23×C17C2511yescharacteristic
408C23×C17C2518yes—
409C22×D17—24no—
410C22×D17—216no—
411C22×D17—216no—
412C22×D17—22no—
413C22×D17—216no—
414C22×D17C2511yescharacteristic
415C22×D17C2518yes—
416C22×D17C2511yescharacteristic
417Q8×C17—28no—
418Q8×C17—44no—
419D4×C17—28no—
420D4×C17—28no—
421D4×C17—416no—
422D4×C17—44no—
423D4×C17—48no—
424C2×C4×C17—24no—
425C2×C4×C17—216no—
426C2×C4×C17—22no—
427C2×C4×C17—416no—
428C2×C4×C17C2511yescharacteristic
429C2×C4×C17C2512yes—
430C2×C4×C17C2518yes—
431C2×C4×C17C2518yes—
432C2×C4×C17C2512yes—
433C2×C4×C17C2511yescharacteristic
434C22⋊D17—216no—
435C22⋊D17—216no—
436C22⋊D17—416no—
437C22⋊D17—416no—
438C22⋊D17—48no—
439C22⋊D17—48no—
440C22⋊D17—48no—
441C2×Dic17—24no—
442C2×Dic17—216no—
443C2×Dic17—22no—
444C2×Dic17—416no—
445C2×Dic17C2511yescharacteristic
446C2×Dic17C2512yes—
447C2×Dic17C2518yes—
448C2×Dic17C2518yes—
449C2×Dic17C2512yes—
450C2×Dic17C2511yescharacteristic
451D68—28no—
452D68—28no—
453D68—416no—
454D68—44no—
455D68—48no—
456C4×D17—216no—
457C4×D17—24no—
458C4×D17—216no—
459C4×D17—22no—
460C4×D17—24no—
461C4×D17—216no—
462C4×D17—22no—
463C4×D17—216no—
464C4×D17—24no—
465C4×D17—22no—
466C4×D17—416no—
467C4×D17—416no—
468C4×D17H(5,𝔽2)18yes—
469C4×D172−1+414yes—
470Dic34—28no—
471Dic34—216no—
472Dic34—48no—
473Dic34—44no—
474#3548—174no—
475#3548—174no—
476#3548—174no—
477#3548—174no—
478#3548—174no—
479#3548—178no—
480#3548—171no—
481#3548—172no—
482#3548D1711yescharacteristic, direct product factor
483C2×#562—174no—
484C2×#554—174no—
485C2×#550—174no—
486C2×#547—174no—
487C2×#540—174no—
488C2×#537—178no—
489C2×#533—171no—
490C2×#532—172no—
491C22×C17—22no—
492C22×C17—28no—
493C22×C17—28no—
494C22×C17—21no—
495C22×C17—28no—
496C22×C17C2611yescharacteristic
497C2×D17—22no—
498C2×D17—28no—
499C2×D17—28no—
500C2×D17—21no—
501C2×D17—28no—
502C2×D17—44no—
503C2×D17—432no—
504C2×D17C2×H(5,𝔽2)14yes—
505C2×D17C2×2−1+412yes—
506C4×C17—28no—
507C4×C17—22no—
508C4×C17—28no—
509C4×C17—21no—
510C4×C17C2×H(5,𝔽2)14yes—
511C4×C17C2×2−1+412yes—
512Dic17—28no—
513Dic17—22no—
514Dic17—28no—
515Dic17—21no—
516Dic17C2×H(5,𝔽2)14yes—
517Dic17C2×2−1+412yes—
518C22×#41—174no—
519C22×#41—178no—
520#562—174no—
521#562—178no—
522#562—1716no—
523#562—1716no—
524#562—1716no—
525#562C2×D1714yescomplemented
526#554—174no—
527#554—178no—
528#554—1716no—
529#554—178no—
530#554—174no—
531#554—174no—
532#554—178no—
533#554—178no—
534#554C2×D1714yescomplemented
535#550—178no—
536#550—178no—
537#550—174no—
538#550—178no—
539#550—1716no—
540#550—174no—
541#550—178no—
542#550—174no—
543#550C2×D1714yescomplemented
544#547—178no—
545#547—174no—
546#547—1716no—
547#547—178no—
548#547—178no—
549#547—174no—
550#547—174no—
551#547—178no—
552#547C2×D1714yescomplemented
553#540—174no—
554#540—174no—
555#540—1716no—
556#540—1716no—
557#540—178no—
558#540—178no—
559#540—174no—
560#540C2×D1714yescomplemented
561#537—178no—
562#537—178no—
563#537—178no—
564#537—1716no—
565#537—178no—
566#537—1716no—
567#537—1716no—
568#537—178no—
569#537—1716no—
570#537—178no—
571#537—178no—
572#537C2×D1718yescomplemented
573#533—172no—
574#533—172no—
575#533—174no—
576#533—174no—
577#533—172no—
578#533—171no—
579#533C2×D1711yescharacteristic, complemented
580#532—174no—
581#532—172no—
582#532—172no—
583#532—174no—
584#532—174no—
585#532—174no—
586#532—174no—
587#532—174no—
588#532—172no—
589#532C2×D1712yescomplemented
590C2×C4⋊Q8—172no—
591C2×C4⋊Q8—172no—
592C2×#127—172no—
593C2×#127—174no—
594C2×#125—172no—
595C2×#125—174no—
596C2×#124—174no—
597C2×#123—1716no—
598C2×C22⋊Q8—174no—
599C2×C22⋊Q8—178no—
600C2×C22⋊Q8—1716no—
601C2×#121—174no—
602C2×#121—174no—
603C2×#121—1716no—
604C2×#121—178no—
605C2×#121—1716no—
606C2×C4×Q8—174no—
607C2×C4×D4—174no—
608C2×C4×D4—174no—
609C2×C4×D4—178no—
610C2×#117—172no—
611C22×C4⋊C4—178no—
612C22×C42—171no—
613C2×C17—41no—
614C2×C17—48no—
615C2×C17C22×H(5,𝔽2)12yes—
616C2×C17C22×2−1+411yescharacteristic
617D17—41no—
618D17—48no—
619D17#354814yesdirect product factor
620C2×#41—174no—
621C2×#41—178no—
622C2×#41—178no—
623C2×#41—174no—
624C2×#41—1716no—
625C2×#41—178no—
626C2×#41—178no—
627C2×#41—174no—
628C2×#41—1716no—
629C2×#41—178no—
630C2×#41—6816no—
631C2×#41—6832no—
632C2×#41C22×D1714yes—
633C2×#41C22×D1718yes—
634C22×Q8—174no—
635C22×Q8—174no—
636C22×D4—174no—
637C22×D4—174no—
638C22×D4—178no—
639C22×D4—1716no—
640C22×D4—174no—
641C23×C4—178no—
642C23×C4—171no—
643C23×C4—172no—
644C23×C4—1716no—
645C4⋊Q8—174no—
646C4⋊Q8—174no—
647C4⋊Q8—174no—
648C4⋊Q8—174no—
649C4⋊Q8—174no—
650C4⋊Q8—174no—
651C4⋊Q8—172no—
652C4⋊Q8—172no—
653C4⋊Q8C22×D1712yes—
654C4⋊Q8C22×D1712yes—
655#127—174no—
656#127—174no—
657#127—174no—
658#127—1716no—
659#127—178no—
660#127—172no—
661#127—174no—
662#127C22×D1712yes—
663#127C22×D1714yes—
664#125—178no—
665#125—174no—
666#125—1716no—
667#125—178no—
668#125—172no—
669#125—174no—
670#125C22×D1712yes—
671#125C22×D1714yes—
672#124—174no—
673#124—174no—
674#124—178no—
675#124—178no—
676#124—174no—
677#124C22×D1714yes—
678#123—1716no—
679#123—1716no—
680#123—1716no—
681#123—1716no—
682#123—1716no—
683#123—1716no—
684#123—1716no—
685#123C22×D17116yes—
686C22⋊Q8—174no—
687C22⋊Q8—178no—
688C22⋊Q8—1716no—
689C22⋊Q8—174no—
690C22⋊Q8—178no—
691C22⋊Q8—1716no—
692C22⋊Q8—178no—
693C22⋊Q8—174no—
694C22⋊Q8—1716no—
695C22⋊Q8—178no—
696C22⋊Q8—1716no—
697C22⋊Q8—1716no—
698C22⋊Q8—1716no—
699C22⋊Q8—178no—
700C22⋊Q8—1716no—
701C22⋊Q8—1716no—
702C22⋊Q8—1716no—
703C22⋊Q8C22×D1714yes—
704C22⋊Q8C22×D1718yes—
705C22⋊Q8C22×D17116yes—
706#121—174no—
707#121—178no—
708#121—174no—
709#121—178no—
710#121—1716no—
711#121—1716no—
712#121—1716no—
713#121—178no—
714#121—1716no—
715#121—1716no—
716#121—1716no—
717#121—1716no—
718#121—174no—
719#121—174no—
720#121—1716no—
721#121—178no—
722#121—1716no—
723#121—174no—
724#121—174no—
725#121—1716no—
726#121—178no—
727#121—1716no—
728#121—178no—
729#121—178no—
730#121—1716no—
731#121—1716no—
732#121—1716no—
733#121—1716no—
734#121—1716no—
735#121C22×D1714yes—
736#121C22×D1714yes—
737#121C22×D17116yes—
738#121C22×D1718yes—
739#121C22×D17116yes—
740C4×Q8—174no—
741C4×Q8—178no—
742C4×Q8—174no—
743C4×Q8—178no—
744C4×Q8—174no—
745C4×Q8C22×D1714yes—
746C4×D4—174no—
747C4×D4—174no—
748C4×D4—178no—
749C4×D4—178no—
750C4×D4—178no—
751C4×D4—1716no—
752C4×D4—174no—
753C4×D4—174no—
754C4×D4—178no—
755C4×D4—178no—
756C4×D4—178no—
757C4×D4—1716no—
758C4×D4—174no—
759C4×D4—174no—
760C4×D4—178no—
761C4×D4C22×D1714yes—
762C4×D4C22×D1714yes—
763C4×D4C22×D1718yes—
764#117—172no—
765#117—174no—
766#117—174no—
767#117—174no—
768#117C22×D1712yes—
769C2×C4⋊C4—1716no—
770C2×C4⋊C4—178no—
771C2×C4⋊C4—174no—
772C2×C4⋊C4—174no—
773C2×C4⋊C4—1716no—
774C2×C4⋊C4—1716no—
775C2×C4⋊C4—178no—
776C2×C4⋊C4—178no—
777C2×C4⋊C4—174no—
778C2×C4⋊C4—174no—
779C2×C4⋊C4—178no—
780C2×C4⋊C4C22×D1718yes—
781C2×C22⋊C4—174no—
782C2×C22⋊C4—1716no—
783C2×C22⋊C4—178no—
784C2×C22⋊C4—178no—
785C2×C42—172no—
786C2×C42—171no—
787C2×C42—174no—
788C2×C42—171no—
789C2×C42—172no—
790C2×C42—171no—
791C2×C42—171no—
792C2×C42—172no—
793C2×C42—171no—
794C2×C42C22×D1711yescharacteristic
795C17C2×#354811yescharacteristic, complemented, Sylow
796C24—171no—
797C24—178no—
798#41—48no—
799#41—416no—
800#41—6816no—
801#41—688no—
802#41—6816no—
803#41—6832no—
804#41—6816no—
805#41—688no—
806#41—688no—
807#41—6816no—
808#41—6832no—
809#41—6816no—
810C2×Q8—178no—
811C2×Q8—174no—
812C2×Q8—178no—
813C2×Q8—174no—
814C2×Q8—3416no—
815C2×Q8—688no—
816C2×Q8C23×D1714yes—
817C2×Q8C23×D1714yes—
818C2×D4—178no—
819C2×D4—178no—
820C2×D4—178no—
821C2×D4—178no—
822C2×D4—1716no—
823C2×D4—1716no—
824C2×D4—178no—
825C2×D4—174no—
826C2×D4—174no—
827C2×D4—178no—
828C2×D4—1716no—
829C2×D4—174no—
830C2×D4—3416no—
831C2×D4—3416no—
832C2×D4—6816no—
833C2×D4—688no—
834C2×D4—6832no—
835C2×D4C23×D1714yes—
836C2×D4C23×D1714yes—
837C2×D4C23×D1718yes—
838C2×D4C23×D17116yes—
839C2×D4C23×D1714yes—
840C22×C4—171no—
841C22×C4—172no—
842C22×C4—171no—
843C22×C4—172no—
844C22×C4—178no—
845C22×C4—1716no—
846C22×C4—171no—
847C22×C4—172no—
848C22×C4—171no—
849C22×C4—171no—
850C22×C4—172no—
851C22×C4—172no—
852C22×C4—178no—
853C22×C4—178no—
854C22×C4—178no—
855C22×C4—178no—
856C22×C4—1716no—
857C22×C4—1716no—
858C22×C4—344no—
859C22×C4—3432no—
860C22×C4—348no—
861C22×C4—6832no—
862C22×C4C23×D1711yescharacteristic
863C22×C4C23×D1712yes—
864C22×C4C23×D1718yes—
865C22×C4C23×D17116yes—
866C4⋊C4—178no—
867C4⋊C4—174no—
868C4⋊C4—178no—
869C4⋊C4—174no—
870C4⋊C4—1716no—
871C4⋊C4—1716no—
872C4⋊C4—1716no—
873C4⋊C4—178no—
874C4⋊C4—174no—
875C4⋊C4—178no—
876C4⋊C4—174no—
877C4⋊C4—178no—
878C4⋊C4—178no—
879C4⋊C4—178no—
880C4⋊C4C23×D1714yes—
881C4⋊C4C23×D1714yes—
882C4⋊C4C23×D17116yes—
883C4⋊C4C23×D1714yes—
884C4⋊C4C23×D1714yes—
885C4⋊C4C23×D1718yes—
886C22⋊C4—174no—
887C22⋊C4—1716no—
888C22⋊C4—178no—
889C22⋊C4—178no—
890C22⋊C4—178no—
891C22⋊C4—1716no—
892C22⋊C4—1716no—
893C22⋊C4—178no—
894C22⋊C4—178no—
895C22⋊C4—178no—
896C22⋊C4—178no—
897C22⋊C4C23×D1714yes—
898C22⋊C4C23×D17116yes—
899C22⋊C4C23×D1718yes—
900C22⋊C4C23×D1718yes—
901C42—171no—
902C42—172no—
903C42—172no—
904C42—172no—
905C42—172no—
906C42—172no—
907C42—171no—
908C42—178no—
909C42—174no—
910C42C23×D1711yescharacteristic
911C42C23×D1712yes—
912C42C23×D1711yescharacteristic
913C42C23×D1714yes—
914C23—171no—
915C23—171no—
916C23—178no—
917C23—344no—
918C23—3416no—
919C23—342no—
920C23—3416no—
921C23—3416no—
922C23C24×D1711yescharacteristic
923C23C24×D1718yes—
924Q8—28no—
925Q8—44no—
926Q8—3416no—
927Q8—348no—
928Q8—688no—
929Q8—684no—
930D4—28no—
931D4—28no—
932D4—48no—
933D4—44no—
934D4—416no—
935D4—3416no—
936D4—3416no—
937D4—348no—
938D4—348no—
939D4—688no—
940D4—684no—
941D4—6816no—
942D4—688no—
943D4—688no—
944D4—688no—
945D4—6816no—
946D4—6816no—
947C2×C4—216no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—416no—
951C2×C4—171no—
952C2×C4—172no—
953C2×C4—178no—
954C2×C4—174no—
955C2×C4—171no—
956C2×C4—172no—
957C2×C4—178no—
958C2×C4—178no—
959C2×C4—3416no—
960C2×C4—344no—
961C2×C4—342no—
962C2×C4—3416no—
963C2×C4—344no—
964C2×C4—342no—
965C2×C4—3416no—
966C2×C4—3416no—
967C2×C4—344no—
968C2×C4—342no—
969C2×C4—3416no—
970C2×C4—344no—
971C2×C4—342no—
972C2×C4—6816no—
973C2×C4—6816no—
974C2×C4—6816no—
975C2×C4C24×D1711yescharacteristic
976C2×C4C24×D1712yes—
977C2×C4C24×D1718yes—
978C2×C4C24×D1718yes—
979C2×C4C24×D1712yes—
980C2×C4C24×D1711yescharacteristic
981C22—22no—
982C22—28no—
983C22—28no—
984C22—21no—
985C22—28no—
986C22—174no—
987C22—172no—
988C22—342no—
989C22—348no—
990C22—348no—
991C22—341no—
992C22—348no—
993C22—684no—
994C22—6832no—
995C22C25×D1711yescharacteristic
996C4—28no—
997C4—22no—
998C4—28no—
999C4—21no—
1000C4—174no—
1001C4—172no—
1002C4—348no—
1003C4—342no—
1004C4—348no—
1005C4—341no—
1006C4H(5,𝔽2)×D1714yes—
1007C42−1+4×D1712yes—
1008C2—41no—
1009C2—48no—
1010C2—174no—
1011C2—681no—
1012C2—688no—
1013C2C2×H(5,𝔽2)×D1712yes—
1014C2C2×2−1+4×D1711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D17
commutator, socle, cosocleC22×C17C26
FittingC17×#3548C2
hypercenter#3548D17
hypocenterC17C2×#3548
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #14543184C2semidirect
2. #14543183C2semidirect
3. #14543182C2semidirect
4. #14543181C2semidirect
5. #14543180C2semidirect
6. #14543179C2semidirect
7. #14543178C2semidirect
8. #14543177C2semidirect
9. D17×#562C2semidirect
10. D17×#554C2semidirect
11. D17×#550C2semidirect
12. D17×#547C2semidirect
13. D17×#540C2semidirect
14. D17×#537C2semidirect
15. D17×#533C2semidirect
16. D17×#532C2semidirect
17. C17×#3548C2semidirect
20. #11763557C22semidirect
21. #11763556C22semidirect
22. #11763555C22semidirect
23. #11763554C22semidirect
24. #11763553C22semidirect
25. #11763520C22semidirect
26. #11763519C22semidirect
27. #11763518C22semidirect
28. #11763517C22semidirect
29. #11763516C22semidirect
30. #11763515C22semidirect
31. #11763514C22semidirect
32. #11763513C22semidirect
33. #11763481C22semidirect
34. #11763480C22semidirect
35. #11763480C22semidirect
36. #11763479C22semidirect
37. #11763479C22semidirect
38. #11763478C22semidirect
39. #11763477C22semidirect
40. #11763477C22semidirect
41. #11763464C22semidirect
42. #11763463C22semidirect
43. #11763462C22semidirect
44. #11763461C22semidirect
45. #11763460C22semidirect
46. #11763459C22semidirect
47. #11763458C22semidirect
48. #11763457C22semidirect
49. #11763415C22semidirect
50. #11763414C22semidirect
51. #11763413C22semidirect
52. #11763412C22semidirect
53. #11763411C22semidirect
54. #11763410C22semidirect
55. #11763409C22semidirect
56. #11763390C22semidirect
57. #11763389C22semidirect
58. #11763389C22semidirect
59. #11763389C22semidirect
60. #11763388C22semidirect
61. #11763388C22semidirect
62. #11763388C22semidirect
63. #11763387C22semidirect
64. #11763387C22semidirect
65. #11763386C22semidirect
66. #11763386C22semidirect
67. #11763366C22semidirect
68. #11763365C22semidirect
69. #11763364C22semidirect
70. #11763363C22semidirect
71. #11763362C22semidirect
72. #11763361C22semidirect
73. #11763360C22semidirect
74. #11763359C22semidirect
75. #11763358C22semidirect
76. #11763357C22semidirect
77. #11763356C22semidirect
78. #11763356C22semidirect
79. #11763355C22semidirect
80. #11763354C22semidirect
81. #11763354C22semidirect
105. C17×#562C22semidirect
106. C17×#554C22semidirect
107. C17×#550C22semidirect
108. C17×#547C22semidirect
109. C17×#540C22semidirect
110. C17×#537C22semidirect
111. C17×#533C22semidirect
112. C17×#532C22semidirect
482. #3548D17direct (N × H)
525. #562C2×D17semidirect
534. #554C2×D17semidirect
543. #550C2×D17semidirect
552. #547C2×D17semidirect
560. #540C2×D17semidirect
572. #537C2×D17semidirect
579. #533C2×D17semidirect
589. #532C2×D17semidirect
619. D17#3548direct (N × H)
795. C17C2×#3548semidirect

Maximal subgroups

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

subgroupindex
#145431842
#145431832
#145431822
#145431812
#145431802
#145431792
#145431782
#145431772
D17×#5622
D17×#5542
D17×#5502
D17×#5472
D17×#5402
D17×#5372
D17×#5332
D17×#5322
C17×#35482
C2×#354817