Finite Group Databasebeta

← #17207284

Subgroups — #17207284

Order 4352.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763391C212yesmaximal, complemented
2#14537148C211yesmaximal, characteristic, complemented
3#14537138C211yesmaximal, characteristic, complemented
4#14537115C211yesmaximal, characteristic, complemented
5#14534925C212yesmaximal, complemented
6#14534913C212yesmaximal, complemented
7#14533857C212yesmaximal, complemented
8#14533849C212yesmaximal, complemented
9#14533366C211yesmaximal, characteristic, complemented
10#14533149C211yesmaximal, characteristic, complemented
11#14532916C212yesmaximal, complemented
12#14532545C211yesmaximal, characteristic, complemented
13#14532489C211yesmaximal, characteristic, complemented
14#14532418C211yesmaximal, characteristic, complemented
15#14532374C211yesmaximal, characteristic, complemented
16#14532317C212yesmaximal, complemented
17#14532220C211yesmaximal, characteristic, complemented
18#14532136C211yesmaximal, characteristic, complemented
19#14531443C212yesmaximal, complemented
20#14531300C211yesmaximal, characteristic, complemented
21D17×#390C211yesmaximal, characteristic, complemented
22C42×C22⋊D17C211yesmaximal, characteristic, complemented
23C17×#2856C211yesmaximal, characteristic, complemented
24C22×D4×D17C2211yescharacteristic
25#11763391—216no—
26C2×#10587574C2211yescharacteristic, complemented
27C2×#10587626C2211yescharacteristic
28C2×#10587584C2212yescomplemented
29C2×#10587565C2212yescomplemented
30C2×#10587622C2212yescomplemented
31C2×#10587571C2212yescomplemented
32C2×#10587571C2212yescomplemented
33C2×#10587615C2212yescomplemented
34C2×#10587621C2212yescomplemented
35C2×#10587582C2212yes—
36C2×#10587616C2211yescharacteristic
37C2×#10587625C2212yescomplemented
38C2×#10587624C2212yes—
39C2×#10587624C2211yescharacteristic
40C2×#10587623C2212yes—
41C2×#10587623C2212yes—
42C2×#10587623C2212yes—
43C2×D4×Dic17C2211yescharacteristic, complemented
44C2×C4×C22⋊D17C2211yescharacteristic
45C2×C4×C22⋊D17C2211yescharacteristic
46C2×C4×C22⋊D17C2211yescharacteristic
47C2×#10587567C2212yes—
48C2×C4⋊C4×D17C2211yescharacteristic
49C2×C22⋊C4×D17C2212yes—
50C2×C22⋊C4×D17C2212yes—
51C2×C42×D17C2211yescharacteristic
52#11762740C2212yescomplemented
53#11762735C2212yescomplemented
54#11762732C2212yescomplemented
55#11762731C2212yescomplemented
56#11762729C2212yescomplemented
57#11762724C2212yes—
58#11762724C2212yescomplemented
59#11762723C2212yescomplemented
60#11762723C2212yescomplemented
61#11762723C2212yescomplemented
62#11762723C2212yescomplemented
63#11762721C2212yescomplemented
64#11762717C2212yes—
65#11762717C2212yes—
66#11762717C2212yes—
67#11762717C2212yescomplemented
68#11762712C2211yescharacteristic
69#11762712C2211yescharacteristic
70#11762712C2211yescharacteristic
71#11762712C2211yescharacteristic, complemented
72#11762711C2211yescharacteristic
73#11762711C2211yescharacteristic
74#11762710C2211yescharacteristic
75#11762710C2211yescharacteristic
76#11762709C2212yes—
77#11762709C2212yes—
78#11762709C2212yescomplemented
79#11762709C2212yescomplemented
80#11762708C2211yescharacteristic, complemented
81#11762707C2211yescharacteristic, complemented
82#11762707C2211yescharacteristic, complemented
83#11762705C2211yescharacteristic, complemented
84#11762703C2212yescomplemented
85#11762703C2212yescomplemented
86#11762703C2212yescomplemented
87#11762702C2212yescomplemented
88#11762700C2212yescomplemented
89#11762700C2212yescomplemented
90#11762699C2212yescomplemented
91#11762697C2212yescomplemented
92#11762689C2212yescomplemented
93#11762688C2212yescomplemented
94#11762686C2212yescomplemented
95#11762685C2212yes—
96#11762685C2212yes—
97#11762680C2212yes—
98#11762669C2211yescharacteristic, complemented
99#11762666C2211yescharacteristic
100#11762664C2212yes—
101C4⋊C4×Dic17C2211yescharacteristic, complemented
102C4×#63225C2211yescharacteristic, complemented
103C4×#63225C2211yescharacteristic, complemented
104C4×#63225C2211yescharacteristic, complemented
105C22⋊C4×Dic17C2212yescomplemented
106C4×#63227C2211yescharacteristic
107C4×#63227C2211yescharacteristic
108C4×#63227C2211yescharacteristic
109C4×C22⋊Dic17C2211yescharacteristic, complemented
110C4×C22⋊Dic17C2211yescharacteristic, complemented
111C4×C22⋊Dic17C2211yescharacteristic, complemented
112C42×Dic17C2211yescharacteristic, complemented
113C2×C17×#127C2211yescharacteristic
114C2×C17×#121C2211yescharacteristic
115C2×C17×#121C2212yescomplemented
116C2×C17×#121C2211yescharacteristic, complemented
117C2×C17×#121C2212yescomplemented
118C22×C42×C17C2211yescharacteristic, complemented
119C17×#390C2211yescharacteristic
120C17×#390C2212yescomplemented
121C17×#390C2212yescomplemented
122C17×#390C2211yescharacteristic, complemented
123C17×#384C2211yescharacteristic, complemented
124C24×D17C2312yes—
125C22×D4×C17C2311yescharacteristic
126C22×D4×C17C2311yescharacteristic
127C22×D4×C17C2312yes—
128C22×D4×C17C2312yes—
129C22×D4×C17C2312yes—
130C22×D4×C17C2312yes—
131C23×C4×C17C2311yescharacteristic
132C23×C4×C17C2311yescharacteristic
133C23×C4×C17C2311yescharacteristic
134C22×C22⋊D17C2312yes—
135C22×C22⋊D17C2311yescharacteristic
136C22×C22⋊D17C2312yes—
137C22×C22⋊D17C2312yes—
138C22×C22⋊D17C2312yes—
139C22×C22⋊D17C2312yes—
140C23×Dic17C2312yes—
141C2×D4×D17—24no—
142C2×D4×D17—42no—
143C2×D4×D17—42no—
144C22×D68C2311yescharacteristic
145C22×C4×D17C2311yescharacteristic
146C22×C4×D17C2311yescharacteristic
147C22×C4×D17C2312yes—
148C22×C4×D17C2311yescharacteristic
149C22×Dic34C2312yes—
150C17×#127—42no—
151C17×#121—28no—
152C17×#121—44no—
153C17×#121—42no—
154C17×#121—42no—
155C2×C4⋊C4×C17C2311yescharacteristic
156C2×C4⋊C4×C17C2311yescharacteristic
157C2×C4⋊C4×C17C2312yes—
158C2×C4⋊C4×C17C2312yes—
159C2×C22⋊C4×C17C2312yes—
160C2×C22⋊C4×C17C2312yes—
161C2×C22⋊C4×C17C2312yes—
162C2×C22⋊C4×C17C2312yes—
163C2×C22⋊C4×C17C2312yes—
164C2×C22⋊C4×C17C2312yes—
165C2×C42×C17—42no—
166C2×C42×C17C2311yescharacteristic
167C2×C42×C17C2311yescharacteristic
168C2×C42×C17C2311yescharacteristic
169C2×C42×C17C2311yescharacteristic
170C2×C22⋊Dic17C2312yes—
171C2×C22⋊Dic17C2312yes—
172C2×C22⋊Dic17C2312yes—
173C2×C22⋊Dic17C2312yes—
174C2×C22⋊Dic17C2312yes—
175C2×C22⋊Dic17C2312yes—
176C2×C22⋊Dic17C2312yes—
177C2×C22⋊Dic17C2311yescharacteristic
178C2×C22⋊Dic17C2311yescharacteristic
179C2×C22⋊Dic17C2312yes—
180C2×C22⋊Dic17C2312yes—
181C2×C22⋊Dic17C2312yes—
182C2×C22⋊Dic17C2312yes—
183C2×C22⋊Dic17C2311yescharacteristic
184#10587626—42no—
185#10587625—28no—
186#10587624—28no—
187#10587624—24no—
188#10587623—28no—
189#10587623—28no—
190#10587623—28no—
191#10587622—28no—
192#10587621—28no—
193D4×Dic17—42no—
194#10587616—42no—
195#10587615—28no—
196C4×C22⋊D17—24no—
197C4×C22⋊D17—24no—
198C4×C22⋊D17D418yescomplemented
199C2×#63227C2312yes—
200C2×#63227C2312yes—
201C2×#63227C2312yes—
202C2×#63227C2312yes—
203C2×#63227C2312yes—
204C2×#63227C2312yes—
205C2×#63227C2312yes—
206C2×#63227C2311yescharacteristic
207C2×#63227C2312yes—
208C2×#63227C2312yes—
209C2×#63227C2312yes—
210C2×#63227C2311yescharacteristic
211C2×#63227C2311yescharacteristic
212C2×C4⋊Dic17C2312yes—
213C2×C4⋊Dic17C2311yescharacteristic
214C2×C4⋊Dic17C2311yescharacteristic
215C2×C4⋊Dic17C2311yescharacteristic
216C2×#63225C2312yes—
217C2×#63225C2312yes—
218C2×#63225C2312yes—
219C2×#63225C2311yescharacteristic
220C2×#63225C2311yescharacteristic
221C2×#63225C2312yes—
222C2×#63225C2312yes—
223C2×#63225C2311yescharacteristic
224C2×C4×Dic17C2311yescharacteristic
225C2×C4×Dic17C2312yes—
226C2×C4×Dic17C2311yescharacteristic
227C2×C4×Dic17C2311yescharacteristic
228C2×C4×Dic17C2311yescharacteristic
229C2×C4×Dic17C2311yescharacteristic
230C2×C4×Dic17C2311yescharacteristic
231C2×C4×Dic17C2311yescharacteristic
232C2×C4×Dic17C2311yescharacteristic
233C2×C4×Dic17C2311yescharacteristic
234#10587584—28no—
235#10587582—28no—
236C4⋊C4×D17—42no—
237#10587574—42no—
238#10587571—28no—
239#10587571—44no—
240#10587567—28no—
241C22⋊C4×D17—28no—
242C22⋊C4×D17—44no—
243#10587565—28no—
244C42×D17—42no—
245#10587502C2312yes—
246#10587502C2312yes—
247#10587502C2311yescharacteristic
248#10587502C2312yes—
249#10587502C2312yes—
250#10587502C2312yes—
251#10587502C2311yescharacteristic
252#10587502C2312yes—
253#10587502C2312yes—
254#10587502C2311yescharacteristic
255#10587502C2311yescharacteristic
256#10587502C2311yescharacteristic
257#10587502C2311yescharacteristic
258C24×C17C2412yes—
259C24×C17C2412yes—
260C24×C17C2411yescharacteristic
261C23×D17—24no—
262C23×D17—24no—
263C23×D17—24no—
264C23×D17—42no—
265C23×D17—42no—
266C23×D17—42no—
267C23×D17—42no—
268C23×D17C2412yes—
269C23×D17C2411yescharacteristic
270C2×D4×C17—24no—
271C2×D4×C17—24no—
272C2×D4×C17—24no—
273C2×D4×C17—22no—
274C2×D4×C17—22no—
275C2×D4×C17—24no—
276C2×D4×C17—22no—
277C2×D4×C17—22no—
278C2×D4×C17—22no—
279C2×D4×C17—22no—
280C2×D4×C17—42no—
281C2×D4×C17—42no—
282C2×D4×C17—42no—
283C2×D4×C17—42no—
284C2×D4×C17—42no—
285C2×D4×C17—42no—
286C2×D4×C17—42no—
287C2×D4×C17—42no—
288C22×C4×C17—22no—
289C22×C4×C17—22no—
290C22×C4×C17—22no—
291C22×C4×C17—22no—
292C22×C4×C17—22no—
293C22×C4×C17—41no—
294C22×C4×C17—41no—
295C22×C4×C17—41no—
296C22×C4×C17C2×D414yescomplemented
297C22×C4×C17C2412yes—
298C22×C4×C17C2412yes—
299C22×C4×C17C2411yescharacteristic
300C22×C4×C17C2411yescharacteristic
301C22×C4×C17C2411yescharacteristic
302C22×C4×C17C2411yescharacteristic
303C22×C4×C17C2411yescharacteristic
304C22×C4×C17C2411yescharacteristic
305C2×C22⋊D17—22no—
306C2×C22⋊D17—22no—
307C2×C22⋊D17—24no—
308C2×C22⋊D17—24no—
309C2×C22⋊D17—24no—
310C2×C22⋊D17—24no—
311C2×C22⋊D17—24no—
312C2×C22⋊D17—24no—
313C2×C22⋊D17—24no—
314C2×C22⋊D17—42no—
315C2×C22⋊D17—42no—
316C2×C22⋊D17—42no—
317C2×C22⋊D17—42no—
318C2×C22⋊D17—42no—
319C2×C22⋊D17—42no—
320C2×C22⋊D17—42no—
321C2×C22⋊D17—42no—
322C2×C22⋊D17C2×D414yes—
323C22×Dic17—24no—
324C22×Dic17—42no—
325C22×Dic17—42no—
326C22×Dic17C2412yes—
327C22×Dic17C2411yescharacteristic
328C22×Dic17C2412yes—
329C22×Dic17C2412yes—
330C22×Dic17C2411yescharacteristic
331C22×Dic17C2411yescharacteristic
332C22×Dic17C2411yescharacteristic
333C22×Dic17C2411yescharacteristic
334C22×Dic17C2411yescharacteristic
335C22×Dic17C2411yescharacteristic
336D4×D17—416no—
337C2×D68—22no—
338C2×D68—22no—
339C2×D68—22no—
340C2×C4×D17—22no—
341C2×C4×D17—22no—
342C2×C4×D17—22no—
343C2×C4×D17—22no—
344C2×C4×D17—24no—
345C2×C4×D17—41no—
346C2×C4×D17—41no—
347C2×C4×D17—41no—
348C2×C4×D17—42no—
349C2×C4×D17—42no—
350C2×C4×D17C2×D414yes—
351C2×C4×D17#4114yes—
352C2×Dic34—24no—
353C2×Dic34—42no—
354C2×Dic34—42no—
355C4⋊C4×C17—24no—
356C4⋊C4×C17—22no—
357C4⋊C4×C17—22no—
358C4⋊C4×C17—42no—
359C22⋊C4×C17—24no—
360C22⋊C4×C17—24no—
361C22⋊C4×C17—24no—
362C22⋊C4×C17—24no—
363C22⋊C4×C17—42no—
364C22⋊C4×C17—42no—
365C42×C17—22no—
366C42×C17—22no—
367C42×C17—41no—
368C42×C17—41no—
369C22⋊Dic17—24no—
370C22⋊Dic17—24no—
371C22⋊Dic17—24no—
372C22⋊Dic17—24no—
373C22⋊Dic17—24no—
374C22⋊Dic17—22no—
375C22⋊Dic17—22no—
376C22⋊Dic17—24no—
377C22⋊Dic17—24no—
378C22⋊Dic17—42no—
379C22⋊Dic17—42no—
380C22⋊Dic17—42no—
381C22⋊Dic17—42no—
382C22⋊Dic17C2×D414yescomplemented
383#63227—24no—
384#63227—22no—
385#63227—24no—
386#63227—24no—
387#63227—24no—
388#63227—24no—
389#63227—24no—
390#63227—24no—
391#63227—42no—
392#63227—42no—
393#63227—42no—
394#63227C2×D414yes—
395#63227#4114yes—
396C4⋊Dic17—22no—
397C4⋊Dic17—22no—
398C4⋊Dic17—22no—
399C4⋊Dic17—24no—
400#63225—24no—
401#63225—24no—
402#63225—22no—
403#63225—24no—
404#63225—22no—
405#63225—42no—
406#63225—42no—
407#63225C2×D414yescomplemented
408C4×Dic17—22no—
409C4×Dic17—22no—
410C4×Dic17—22no—
411C4×Dic17—22no—
412C4×Dic17—24no—
413C4×Dic17—22no—
414C4×Dic17—41no—
415C4×Dic17—41no—
416C4×Dic17—41no—
417C4×Dic17C2×D414yescomplemented
418#35007—171nomaximal, Sylow
419C23×C17—21no—
420C23×C17—21no—
421C23×C17—21no—
422C23×C17—21no—
423C23×C17—21no—
424C23×C17—21no—
425C23×C17—22no—
426C23×C17—22no—
427C23×C17—22no—
428C23×C17—22no—
429C23×C17—22no—
430C23×C17—22no—
431C23×C17—22no—
432C23×C17—22no—
433C23×C17—22no—
434C23×C17—22no—
435C23×C17—22no—
436C23×C17—22no—
437C23×C17—22no—
438C23×C17—22no—
439C23×C17C22×D412yes—
440C23×C17C2511yescharacteristic
441C22×D17—21no—
442C22×D17—21no—
443C22×D17—21no—
444C22×D17—21no—
445C22×D17—22no—
446C22×D17—22no—
447C22×D17—22no—
448C22×D17—22no—
449C22×D17—22no—
450C22×D17—22no—
451C22×D17—22no—
452C22×D17—48no—
453C22×D17—48no—
454C22×D17—48no—
455C22×D17—84no—
456C22×D17—84no—
457C22×D17—84no—
458C22×D17—84no—
459C22×D17C22×D412yes—
460C22×D17C2×#4112yes—
461C22×D17C2×#4112yes—
462D4×C17—44no—
463D4×C17—44no—
464D4×C17—84no—
465D4×C17—84no—
466D4×C17—84no—
467D4×C17—84no—
468C2×C4×C17—21no—
469C2×C4×C17—21no—
470C2×C4×C17—21no—
471C2×C4×C17—21no—
472C2×C4×C17—21no—
473C2×C4×C17—21no—
474C2×C4×C17—21no—
475C2×C4×C17—21no—
476C2×C4×C17—22no—
477C2×C4×C17—22no—
478C2×C4×C17—21no—
479C2×C4×C17—21no—
480C2×C4×C17—22no—
481C2×C4×C17—22no—
482C2×C4×C17—21no—
483C2×C4×C17—22no—
484C2×C4×C17—22no—
485C2×C4×C17—44no—
486C2×C4×C17—44no—
487C2×C4×C17—44no—
488C2×C4×C17C22×D412yes—
489C2×C4×C17C22×D412yes—
490C2×C4×C17C2×#4112yes—
491C2×C4×C17C2×#4112yes—
492C2×C4×C17H(5,𝔽2)12yes—
493C2×C4×C17H(5,𝔽2)12yes—
494C2×C4×C17H(5,𝔽2)12yes—
495C22⋊D17—28no—
496C22⋊D17—48no—
497C22⋊D17—48no—
498C22⋊D17—84no—
499C22⋊D17—84no—
500C22⋊D17—84no—
501C2×Dic17—21no—
502C2×Dic17—21no—
503C2×Dic17—21no—
504C2×Dic17—21no—
505C2×Dic17—21no—
506C2×Dic17—21no—
507C2×Dic17—21no—
508C2×Dic17—21no—
509C2×Dic17—21no—
510C2×Dic17—21no—
511C2×Dic17—22no—
512C2×Dic17—22no—
513C2×Dic17—22no—
514C2×Dic17—21no—
515C2×Dic17—22no—
516C2×Dic17—22no—
517C2×Dic17—21no—
518C2×Dic17—22no—
519C2×Dic17—21no—
520C2×Dic17—21no—
521C2×Dic17—21no—
522C2×Dic17—22no—
523C2×Dic17—22no—
524C2×Dic17—21no—
525C2×Dic17—22no—
526C2×Dic17—84no—
527C2×Dic17C22×D412yes—
528C2×Dic17C22×D412yes—
529C2×Dic17C22×D412yes—
530C2×Dic17C2×#4112yes—
531C2×Dic17C2×#4112yes—
532D68—44no—
533C4×D17—28no—
534C4×D17—44no—
535C4×D17—44no—
536C4×D17—84no—
537Dic34—84no—
538C2×#538—172no—
539#2860—171no—
540#2858—171no—
541#2856D1711yescharacteristic, complemented
542#2854—171no—
543#2662—172no—
544#2661—172no—
545#2555—172no—
546#2554—172no—
547#2512—171no—
548#2491—171no—
549#2472—172no—
550#2445—171no—
551#2440—171no—
552#2433—171no—
553#2428—171no—
554#2424—172no—
555#2416—171no—
556#2408—171no—
557#2321—172no—
558C4×#121—171no—
559C2×#390—171no—
560C42×D4—171no—
561C22×C17—22no—
562C22×C17—22no—
563C22×C17—22no—
564C22×C17—41no—
565C22×C17—41no—
566C22×C17—41no—
567C22×C17—41no—
568C22×C17—42no—
569C22×C17—42no—
570C22×C17—42no—
571C22×C17—42no—
572C22×C17—42no—
573C22×C17—42no—
574C22×C17—42no—
575C22×C17—42no—
576C22×C17—42no—
577C22×C17—42no—
578C22×C17—42no—
579C22×C17—42no—
580C22×C17—42no—
581C22×C17—42no—
582C22×C17C23×D411yescharacteristic
583C22×C17C22×#4111yescharacteristic
584C22×C17C22×#4111yescharacteristic
585C22×C17C2×H(5,𝔽2)11yescharacteristic
586C22×C17C2×H(5,𝔽2)11yescharacteristic
587C22×C17C2×H(5,𝔽2)11yescharacteristic
588C22×C17#58511yescharacteristic
589C2×D17—22no—
590C2×D17—22no—
591C2×D17—22no—
592C2×D17—22no—
593C2×D17—22no—
594C2×D17—22no—
595C2×D17—42no—
596C2×D17—42no—
597C2×D17—42no—
598C2×D17—42no—
599C2×D17—42no—
600C2×D17—42no—
601C2×D17—42no—
602C2×D17—816no—
603C2×D17#53214yes—
604C4×C17—22no—
605C4×C17—22no—
606C4×C17—22no—
607C4×C17—22no—
608C4×C17—41no—
609C4×C17—42no—
610C4×C17—42no—
611C4×C17#53814yescomplemented
612Dic17—22no—
613Dic17—22no—
614Dic17—22no—
615Dic17—22no—
616Dic17—22no—
617Dic17—42no—
618Dic17—41no—
619Dic17—42no—
620Dic17—42no—
621Dic17—41no—
622C23×D4—171no—
623#538—3416no—
624C2×C4⋊Q8—171no—
625C2×#127—171no—
626C2×#127C2×D1711yescharacteristic
627C2×#126—172no—
628C2×#126—172no—
629C2×#124—172no—
630C2×#124—172no—
631C2×#124—172no—
632C2×#123—172no—
633C2×#123—172no—
634C2×C22⋊Q8—172no—
635C2×#121—172no—
636C2×#121—171no—
637C2×#121—172no—
638C2×#121—171no—
639C2×#121C2×D1711yescharacteristic
640C2×#121C2×D1712yescomplemented
641C2×#121C2×D1711yescharacteristic, complemented
642C2×#121C2×D1712yescomplemented
643C2×#120—172no—
644C2×#120—172no—
645C2×#120—172no—
646C2×C4×D4—171no—
647C2×C4×D4—171no—
648C2×C4×D4—171no—
649C2×C4×D4—171no—
650C2×C4×D4—172no—
651C22×C4⋊C4—171no—
652C22×C22⋊C4—172no—
653C22×C22⋊C4—172no—
654C22×C42—171no—
655C22×C42C2×D1711yescharacteristic, complemented
656#398—172no—
657#397—172no—
658#396—172no—
659#396—172no—
660#395—172no—
661#394—172no—
662#394—172no—
663#394—172no—
664#394—172no—
665#394—172no—
666#394—172no—
667#393—172no—
668#392—172no—
669#392—172no—
670#392—172no—
671#392—172no—
672#390—171no—
673#390—171no—
674#390—171no—
675#390—171no—
676#390—171no—
677#390—171no—
678#390—172no—
679#390—172no—
680#390—172no—
681#390—172no—
682#390—171no—
683#390—171no—
684#390C2×D1711yescharacteristic
685#390C2×D1712yescomplemented
686#390C2×D1711yescharacteristic, complemented
687#390C2×D1712yescomplemented
688#389—171no—
689#389—171no—
690#389—171no—
691#389—171no—
692#388—172no—
693#388—172no—
694#388—172no—
695#388—172no—
696#388—172no—
697#388—172no—
698#388—172no—
699#388—172no—
700#386—172no—
701#386—172no—
702#386—172no—
703#386—172no—
704#386—172no—
705#385—172no—
706#384C2×D1711yescharacteristic, complemented
707#380—171no—
708#380—171no—
709#379—172no—
710C4×C4⋊C4—171no—
711C4×C4⋊C4—171no—
712C4×C4⋊C4—171no—
713C4×C4⋊C4—171no—
714C4×C22⋊C4—171no—
715C4×C22⋊C4—171no—
716C4×C22⋊C4—171no—
717C4×C22⋊C4—172no—
718C4×C22⋊C4—171no—
719C4×C22⋊C4—171no—
720C4×C22⋊C4—171no—
721C43—171no—
722C2×C17—42no—
723C2×C17—82no—
724C2×C17—82no—
725C2×C17C2×#53211yescharacteristic
726C2×C17C2×#53811yescharacteristic
727C2×C17#346011yescharacteristic
728C2×C17#349611yescharacteristic
729C2×C17#349811yescharacteristic
730C2×C17#351411yescharacteristic
731C2×C17#351911yescharacteristic
732D17—24no—
733D17—82no—
734C25—172no—
735C22×Q8—172no—
736C22×D4—171no—
737C22×D4—172no—
738C22×D4—172no—
739C22×D4—172no—
740C22×D4—172no—
741C22×D4—172no—
742C22×D4—171no—
743C22×D4—344no—
744C22×D4—682no—
745C22×D4—682no—
746C22×D4C22×D1711yescharacteristic
747C22×D4C22×D1711yescharacteristic
748C22×D4C22×D1712yes—
749C22×D4C22×D1712yes—
750C22×D4C22×D1712yes—
751C22×D4C22×D1712yes—
752C23×C4—171no—
753C23×C4—171no—
754C23×C4—172no—
755C23×C4—171no—
756C23×C4—172no—
757C23×C4C22×D1711yescharacteristic
758C23×C4C22×D1711yescharacteristic
759C23×C4C22×D1711yescharacteristic
760C4⋊Q8—682no—
761#127—42no—
762#127—682no—
763#126—348no—
764#126—348no—
765#124—348no—
766#124—348no—
767#124—684no—
768#123—348no—
769#123—348no—
770C22⋊Q8—348no—
771#121—28no—
772#121—44no—
773#121—42no—
774#121—42no—
775#121—348no—
776#121—344no—
777#121—348no—
778#121—682no—
779#120—348no—
780#120—348no—
781#120—348no—
782C4×D4—178no—
783C4×D4—348no—
784C4×D4—344no—
785C4×D4—344no—
786C4×D4—682no—
787C2×C4⋊C4—171no—
788C2×C4⋊C4—171no—
789C2×C4⋊C4—171no—
790C2×C4⋊C4—172no—
791C2×C4⋊C4—171no—
792C2×C4⋊C4—171no—
793C2×C4⋊C4—172no—
794C2×C4⋊C4—172no—
795C2×C4⋊C4—171no—
796C2×C4⋊C4—172no—
797C2×C4⋊C4—172no—
798C2×C4⋊C4—172no—
799C2×C4⋊C4—682no—
800C2×C4⋊C4C22×D1711yescharacteristic
801C2×C4⋊C4C22×D1711yescharacteristic
802C2×C4⋊C4C22×D1712yes—
803C2×C4⋊C4C22×D1712yes—
804C2×C22⋊C4—171no—
805C2×C22⋊C4—171no—
806C2×C22⋊C4—171no—
807C2×C22⋊C4—172no—
808C2×C22⋊C4—171no—
809C2×C22⋊C4—171no—
810C2×C22⋊C4—172no—
811C2×C22⋊C4—172no—
812C2×C22⋊C4—172no—
813C2×C22⋊C4—172no—
814C2×C22⋊C4—172no—
815C2×C22⋊C4—172no—
816C2×C22⋊C4—172no—
817C2×C22⋊C4—172no—
818C2×C22⋊C4—172no—
819C2×C22⋊C4—172no—
820C2×C22⋊C4—171no—
821C2×C22⋊C4—172no—
822C2×C22⋊C4—172no—
823C2×C22⋊C4—172no—
824C2×C22⋊C4—172no—
825C2×C22⋊C4—172no—
826C2×C22⋊C4—172no—
827C2×C22⋊C4—172no—
828C2×C22⋊C4—172no—
829C2×C22⋊C4—172no—
830C2×C22⋊C4—172no—
831C2×C22⋊C4—348no—
832C2×C22⋊C4—684no—
833C2×C22⋊C4C22×D1712yes—
834C2×C22⋊C4C22×D1712yes—
835C2×C22⋊C4C22×D1712yes—
836C2×C22⋊C4C22×D1712yes—
837C2×C22⋊C4C22×D1712yes—
838C2×C22⋊C4C22×D1712yes—
839C2×C42—42no—
840C2×C42—171no—
841C2×C42—172no—
842C2×C42—171no—
843C2×C42—171no—
844C2×C42—171no—
845C2×C42—171no—
846C2×C42—171no—
847C2×C42—171no—
848C2×C42—171no—
849C2×C42—171no—
850C2×C42—682no—
851C2×C42C22×D1711yescharacteristic
852C2×C42C22×D1711yescharacteristic
853C2×C42C22×D1711yescharacteristic
854C2×C42C22×D1711yescharacteristic
855#95—171no—
856#95—171no—
857#95—171no—
858#95—171no—
859#95—171no—
860#95—171no—
861#95—172no—
862#95—172no—
863#95—172no—
864#95—172no—
865#95—172no—
866#95—172no—
867#95—172no—
868C17#3500711yescharacteristic, complemented, Sylow
869C24—171no—
870C24—172no—
871C24—344no—
872C24—344no—
873C24—344no—
874C24—682no—
875C24—682no—
876C24—682no—
877C24—682no—
878C24C23×D1712yes—
879C24C23×D1712yes—
880C24C23×D1711yescharacteristic
881C2×Q8—344no—
882C2×Q8—682no—
883C2×Q8—682no—
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—24no—
887C2×D4—22no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—22no—
893C2×D4—24no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—174no—
903C2×D4—344no—
904C2×D4—344no—
905C2×D4—344no—
906C2×D4—342no—
907C2×D4—342no—
908C2×D4—344no—
909C2×D4—344no—
910C2×D4—344no—
911C2×D4—344no—
912C2×D4—342no—
913C2×D4—342no—
914C2×D4—342no—
915C2×D4—6816no—
916C2×D4—682no—
917C2×D4—682no—
918C2×D4—682no—
919C2×D4—682no—
920C2×D4—682no—
921C2×D4—682no—
922C2×D4—682no—
923C2×D4—682no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—41no—
932C22×C4—171no—
933C22×C4—171no—
934C22×C4—171no—
935C22×C4—171no—
936C22×C4—171no—
937C22×C4—174no—
938C22×C4—174no—
939C22×C4—171no—
940C22×C4—171no—
941C22×C4—172no—
942C22×C4—172no—
943C22×C4—172no—
944C22×C4—342no—
945C22×C4—344no—
946C22×C4—344no—
947C22×C4—342no—
948C22×C4—342no—
949C22×C4—342no—
950C22×C4—681no—
951C22×C4—681no—
952C22×C4—681no—
953C22×C4—682no—
954C22×C4—682no—
955C22×C4—682no—
956C22×C4—682no—
957C22×C4D4×D1714yescomplemented
958C22×C4C23×D1711yescharacteristic
959C22×C4C23×D1712yes—
960C22×C4C23×D1712yes—
961C22×C4C23×D1711yescharacteristic
962C22×C4C23×D1711yescharacteristic
963C22×C4C23×D1711yescharacteristic
964C22×C4C23×D1711yescharacteristic
965C22×C4C23×D1711yescharacteristic
966C4⋊C4—24no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—42no—
970C4⋊C4—174no—
971C4⋊C4—342no—
972C4⋊C4—344no—
973C4⋊C4—344no—
974C4⋊C4—344no—
975C4⋊C4—344no—
976C4⋊C4—342no—
977C4⋊C4—342no—
978C4⋊C4—342no—
979C4⋊C4—342no—
980C4⋊C4—682no—
981C4⋊C4—682no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—174no—
989C22⋊C4—174no—
990C22⋊C4—174no—
991C22⋊C4—344no—
992C22⋊C4—344no—
993C22⋊C4—344no—
994C22⋊C4—342no—
995C22⋊C4—344no—
996C22⋊C4—342no—
997C22⋊C4—342no—
998C22⋊C4—344no—
999C22⋊C4—344no—
1000C22⋊C4—344no—
1001C22⋊C4—344no—
1002C22⋊C4—344no—
1003C22⋊C4—344no—
1004C22⋊C4—344no—
1005C22⋊C4—344no—
1006C22⋊C4—344no—
1007C22⋊C4—344no—
1008C22⋊C4—682no—
1009C22⋊C4—682no—
1010C22⋊C4—682no—
1011C22⋊C4—682no—
1012C22⋊C4—682no—
1013C22⋊C4—682no—
1014C22⋊C4—682no—
1015C42—22no—
1016C42—22no—
1017C42—41no—
1018C42—41no—
1019C42—174no—
1020C42—344no—
1021C42—342no—
1022C42—342no—
1023C42—342no—
1024C42—342no—
1025C42—342no—
1026C42—681no—
1027C42—681no—
1028C42—681no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—172no—
1050C23—172no—
1051C23—172no—
1052C23—341no—
1053C23—341no—
1054C23—341no—
1055C23—341no—
1056C23—342no—
1057C23—342no—
1058C23—342no—
1059C23—342no—
1060C23—342no—
1061C23—342no—
1062C23—342no—
1063C23—688no—
1064C23—688no—
1065C23—688no—
1066C23—1364no—
1067C23—1364no—
1068C23—1364no—
1069C23—1364no—
1070C23C2×D4×D1712yes—
1071C23C24×D1711yescharacteristic
1072Q8—1364no—
1073D4—44no—
1074D4—44no—
1075D4—84no—
1076D4—84no—
1077D4—84no—
1078D4—84no—
1079D4—348no—
1080D4—688no—
1081D4—688no—
1082D4—684no—
1083D4—1364no—
1084D4—1364no—
1085D4—1364no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—44no—
1104C2×C4—44no—
1105C2×C4—44no—
1106C2×C4—172no—
1107C2×C4—172no—
1108C2×C4—172no—
1109C2×C4—172no—
1110C2×C4—172no—
1111C2×C4—341no—
1112C2×C4—341no—
1113C2×C4—341no—
1114C2×C4—341no—
1115C2×C4—341no—
1116C2×C4—341no—
1117C2×C4—341no—
1118C2×C4—341no—
1119C2×C4—341no—
1120C2×C4—341no—
1121C2×C4—348no—
1122C2×C4—342no—
1123C2×C4—342no—
1124C2×C4—342no—
1125C2×C4—341no—
1126C2×C4—342no—
1127C2×C4—341no—
1128C2×C4—342no—
1129C2×C4—341no—
1130C2×C4—341no—
1131C2×C4—342no—
1132C2×C4—341no—
1133C2×C4—342no—
1134C2×C4—342no—
1135C2×C4—341no—
1136C2×C4—342no—
1137C2×C4—684no—
1138C2×C4—684no—
1139C2×C4—1364no—
1140C2×C4—1364no—
1141C2×C4C2×D4×D1712yes—
1142C2×C4C2×D4×D1712yes—
1143C2×C4#1058769112yes—
1144C2×C4#1058769112yes—
1145C2×C4#1058769112yes—
1146C2×C4#41×D1712yes—
1147C2×C4#41×D1712yes—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—174no—
1170C22—342no—
1171C22—342no—
1172C22—342no—
1173C22—342no—
1174C22—342no—
1175C22—342no—
1176C22—682no—
1177C22—682no—
1178C22—682no—
1179C22—682no—
1180C22—682no—
1181C22—682no—
1182C22—682no—
1183C22—13616no—
1184C22C22×D4×D1711yescharacteristic
1185C22C2×#41×D1711yescharacteristic
1186C22C2×#41×D1711yescharacteristic
1187C22C2×#1058769111yescharacteristic
1188C22C2×#1058769111yescharacteristic
1189C22C2×#1058769111yescharacteristic
1190C22#1176364511yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—41no—
1196C4—42no—
1197C4—42no—
1198C4—342no—
1199C4—342no—
1200C4—342no—
1201C4—342no—
1202C4—342no—
1203C4—681no—
1204C4—682no—
1205C4—681no—
1206C4—682no—
1207C4—682no—
1208C4#1176339114yescomplemented
1209C2—42no—
1210C2—82no—
1211C2—82no—
1212C2—344no—
1213C2—1362no—
1214C2D17×#53211yescharacteristic
1215C2C2×#1176339111yescharacteristic
1216C2#1454219811yescharacteristic
1217C2#1454254111yescharacteristic
1218C2#1454256011yescharacteristic
1219C2#1454274011yescharacteristic
1220C2#1454281011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2856C2
hypercenter#2856D17
hypocenterC17#35007
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2856

Complements

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

NH ≅ G/Ntype
1. C2×#11763391C2semidirect
2. #14537148C2semidirect
3. #14537138C2semidirect
4. #14537115C2semidirect
5. #14534925C2semidirect
6. #14534913C2semidirect
7. #14533857C2semidirect
8. #14533849C2semidirect
9. #14533366C2semidirect
10. #14533149C2semidirect
11. #14532916C2semidirect
12. #14532545C2semidirect
13. #14532489C2semidirect
14. #14532418C2semidirect
15. #14532374C2semidirect
16. #14532317C2semidirect
17. #14532220C2semidirect
18. #14532136C2semidirect
19. #14531443C2semidirect
20. #14531300C2semidirect
21. D17×#390C2semidirect
22. C42×C22⋊D17C2semidirect
23. C17×#2856C2semidirect
26. C2×#10587574C22semidirect
28. C2×#10587584C22semidirect
29. C2×#10587565C22semidirect
30. C2×#10587622C22semidirect
31. C2×#10587571C22semidirect
32. C2×#10587571C22semidirect
33. C2×#10587615C22semidirect
34. C2×#10587621C22semidirect
37. C2×#10587625C22semidirect
43. C2×D4×Dic17C22semidirect
52. #11762740C22semidirect
53. #11762735C22semidirect
54. #11762732C22semidirect
55. #11762731C22semidirect
56. #11762729C22semidirect
58. #11762724C22semidirect
59. #11762723C22semidirect
60. #11762723C22semidirect
61. #11762723C22semidirect
62. #11762723C22semidirect
63. #11762721C22semidirect
67. #11762717C22semidirect
71. #11762712C22semidirect
78. #11762709C22semidirect
79. #11762709C22semidirect
80. #11762708C22semidirect
81. #11762707C22semidirect
82. #11762707C22semidirect
83. #11762705C22semidirect
84. #11762703C22semidirect
85. #11762703C22semidirect
86. #11762703C22semidirect
87. #11762702C22semidirect
88. #11762700C22semidirect
89. #11762700C22semidirect
90. #11762699C22semidirect
91. #11762697C22semidirect
92. #11762689C22semidirect
93. #11762688C22semidirect
94. #11762686C22semidirect
98. #11762669C22semidirect
101. C4⋊C4×Dic17C22semidirect
102. C4×#63225C22semidirect
103. C4×#63225C22semidirect
104. C4×#63225C22semidirect
105. C22⋊C4×Dic17C22semidirect
109. C4×C22⋊Dic17C22semidirect
110. C4×C22⋊Dic17C22semidirect
111. C4×C22⋊Dic17C22semidirect
112. C42×Dic17C22semidirect
115. C2×C17×#121C22semidirect
116. C2×C17×#121C22semidirect
117. C2×C17×#121C22semidirect
118. C22×C42×C17C22semidirect
120. C17×#390C22semidirect
121. C17×#390C22semidirect
122. C17×#390C22semidirect
123. C17×#384C22semidirect
198. C4×C22⋊D17D4semidirect
296. C22×C4×C17C2×D4semidirect
382. C22⋊Dic17C2×D4semidirect
407. #63225C2×D4semidirect
417. C4×Dic17C2×D4semidirect
541. #2856D17semidirect
611. C4×C17#538semidirect
640. C2×#121C2×D17semidirect
641. C2×#121C2×D17semidirect
642. C2×#121C2×D17semidirect
655. C22×C42C2×D17semidirect
685. #390C2×D17semidirect
686. #390C2×D17semidirect
687. #390C2×D17semidirect
706. #384C2×D17semidirect
868. C17#35007semidirect
957. C22×C4D4×D17semidirect
1208. C4#11763391semidirect

Maximal subgroups

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

subgroupindex
C2×#117633912
#145371482
#145371382
#145371152
#145349252
#145349132
#145338572
#145338492
#145333662
#145331492
#145329162
#145325452
#145324892
#145324182
#145323742
#145323172
#145322202
#145321362
#145314432
#145313002
D17×#3902
C42×C22⋊D172
C17×#28562
#3500717