Finite Group Databasebeta

← #17194705

Subgroups — #17194705

Order 4352.

3054 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763356C211yesmaximal, characteristic
2C2×#11763290C211yesmaximal, characteristic, complemented
3C2×#11763289C211yesmaximal, characteristic, complemented
4#14531835C212yesmaximal, complemented
5#14531833C212yesmaximal, complemented
6#14531830C212yesmaximal, complemented
7#14531828C212yesmaximal, complemented
8#14531716C211yesmaximal, characteristic, complemented
9#14531715C211yesmaximal, characteristic, complemented
10#14531714C211yesmaximal, characteristic, complemented
11#14531713C211yesmaximal, characteristic, complemented
12#14531710C211yesmaximal, characteristic, complemented
13#14531709C211yesmaximal, characteristic, complemented
14#14531706C211yesmaximal, characteristic, complemented
15#14531505C212yesmaximal, complemented
16#14531499C212yesmaximal, complemented
17#14531373C211yesmaximal, characteristic, complemented
18#14531373C211yesmaximal, characteristic, complemented
19#14531325C212yesmaximal, complemented
20C4×#10587571C212yesmaximal, complemented
21D17×#382C211yesmaximal, characteristic, complemented
22C4×#10587578C211yesmaximal, characteristic, complemented
23C17×#2352C211yesmaximal, characteristic, complemented
24C22×#63252C2211yescharacteristic
25C22×#63252C2211yescharacteristic
26#11763356C4116yescomplemented
27C2×#10587574C2211yescharacteristic
28C2×#10587626C2211yescharacteristic
29C2×#10587571C2211yescharacteristic
30C2×#10587571C2211yescharacteristic
31C2×#10587581C2211yescharacteristic
32C2×#10587570C2211yescharacteristic
33C2×#10587570C2211yescharacteristic
34C2×#10587624C2211yescharacteristic
35#11763290—28no—
36#11763289—28no—
37C2×C4×Dic34C2212yes—
38C2×#10587573C2212yes—
39C2×C4×D68C2212yes—
40C2×C4×D68C2211yescharacteristic
41C2×#10587579C2212yes—
42C2×C4×C22⋊D17C2212yes—
43C2×C4×C22⋊D17C2212yes—
44C2×C4×C22⋊D17C2211yescharacteristic
45C2×C4×C22⋊D17C2211yescharacteristic
46C2×#10587567C2212yes—
47C2×#10587567C2212yes—
48C2×#10587612C2211yescharacteristic
49C2×#10587578C2211yescharacteristic
50C2×#10587578C2211yescharacteristic
51C2×#10587578C2211yescharacteristic
52C2×#10587578C2211yescharacteristic
53C22×C4⋊Dic17C2211yescharacteristic
54C2×C4⋊C4×D17C2211yescharacteristic
55C2×C4⋊C4×D17C2211yescharacteristic
56C2×C4⋊C4×D17C2211yescharacteristic
57C2×C4⋊C4×D17C2211yescharacteristic
58C2×C42×D17C2211yescharacteristic
59#11762713C2212yes—
60#11762713C2212yes—
61#11762709C2212yes—
62#11762709C2212yes—
63#11762703C2212yes—
64#11762702C2212yes—
65#11762701C2212yes—
66#11762700C2212yes—
67#11762699C2212yes—
68#11762698C2212yes—
69#11762697C2212yes—
70#11762696C2212yes—
71#11762695C2212yes—
72#11762694C2212yes—
73#11762693C2212yes—
74#11762692C2212yes—
75#11762691C2212yes—
76#11762690C2212yes—
77#11762689C2212yes—
78#11762688C2212yes—
79#11762687C2212yes—
80#11762687C2212yes—
81#11762687C2212yes—
82#11762687C2212yes—
83#11762686C2212yes—
84#11762685C2212yes—
85#11762685C2212yes—
86#11762685C2212yes—
87#11762685C2212yes—
88#11762675C2211yescharacteristic
89#11762674C2211yescharacteristic
90#11762674C2211yescharacteristic
91#11762673C2212yes—
92#11762673C2212yes—
93#11762669C2211yescharacteristic
94#11762669C2211yescharacteristic
95#11762666C2211yescharacteristic
96#11762666C2211yescharacteristic
97#11762666C2211yescharacteristic
98#11762666C2211yescharacteristic
99C4⋊C4×Dic17C2211yescharacteristic
100C4⋊C4×Dic17C2211yescharacteristic
101C4×C4⋊Dic17C2211yescharacteristic
102C22⋊C4×Dic17C2212yes—
103C22⋊C4×Dic17C2212yes—
104C4×#63227C2212yes—
105C4×#63227C2212yes—
106C4×#63227C2212yes—
107C4×C22⋊Dic17C2212yes—
108#11762656C2212yes—
109#11762656C2212yes—
110#11762656C2212yes—
111#11762654C2212yes—
112#95×D17C2212yes—
113#95×D17C2212yes—
114C42×Dic17C2212yes—
115C2×C4×D4×C17C2211yescharacteristic
116C2×C17×#117C2211yescharacteristic
117C22×C4⋊C4×C17C2211yescharacteristic
118C17×#388C2212yes—
119C17×#387C2212yes—
120C17×#386C2212yes—
121C17×#382C2211yescharacteristic
122C17×#380C2211yescharacteristic
123C17×#380C2211yescharacteristic
124C4×C4⋊C4×C17C2211yescharacteristic
125C4×C22⋊C4×C17C2212yes—
126C22×D4×C17C2311yescharacteristic
127C23×C4×C17C2311yescharacteristic
128C23×C4×C17C2311yescharacteristic
129C23×C4×C17C2312yes—
130C22×C22⋊D17C2311yescharacteristic
131C22×C22⋊D17C2311yescharacteristic
132C22×C22⋊D17C2311yescharacteristic
133C22×C22⋊D17C2311yescharacteristic
134C22×C22⋊D17C2311yescharacteristic
135C22×C22⋊D17C2311yescharacteristic
136C23×Dic17C2312yes—
137C2×#63252—24no—
138C2×#63252—24no—
139C2×#63252—24no—
140C2×#63252—24no—
141C2×#63252C2×C418yescomplemented
142C2×#63252C2×C418yescomplemented
143C22×D68C2311yescharacteristic
144C22×D68C2311yescharacteristic
145C22×D68C2311yescharacteristic
146C22×C4×D17C2311yescharacteristic
147C22×C4×D17C2311yescharacteristic
148C22×C4×D17C2312yes—
149C22×C4×D17C2312yes—
150C22×C4×D17C2312yes—
151C22×C4×D17C2312yes—
152C22×C4×D17C2311yescharacteristic
153C22×C4×D17C2311yescharacteristic
154C22×C4×D17C2311yescharacteristic
155C22×Dic34C2311yescharacteristic
156C22×Dic34C2311yescharacteristic
157C4×D4×C17C2×C418yescomplemented
158C17×#117—24no—
159C2×C4⋊C4×C17—24no—
160C2×C4⋊C4×C17C2312yes—
161C2×C4⋊C4×C17C2311yescharacteristic
162C2×C4⋊C4×C17C2311yescharacteristic
163C2×C4⋊C4×C17C2311yescharacteristic
164C2×C4⋊C4×C17C2311yescharacteristic
165C2×C4⋊C4×C17C2311yescharacteristic
166C2×C22⋊C4×C17C2312yes—
167C2×C22⋊C4×C17C2312yes—
168C2×C22⋊C4×C17C2312yes—
169C2×C22⋊C4×C17C2311yescharacteristic
170C2×C22⋊C4×C17C2311yescharacteristic
171C2×C42×C17C2312yes—
172C2×C42×C17C2312yes—
173C2×C42×C17C2311yescharacteristic
174C2×C22⋊Dic17C2312yes—
175C2×C22⋊Dic17C2312yes—
176C2×C22⋊Dic17C2312yes—
177C2×C22⋊Dic17C2311yescharacteristic
178C2×C22⋊Dic17C2311yescharacteristic
179#10587626C2×C418yescomplemented
180#10587624C2×C418yescomplemented
181C4×C22⋊D17—28no—
182C4×C22⋊D17—28no—
183C4×C22⋊D17C2×C418yescomplemented
184C4×C22⋊D17C2×C418yescomplemented
185C2×#63227C2312yes—
186C2×#63227C2312yes—
187C2×#63227C2312yes—
188C2×#63227C2312yes—
189C2×#63227C2312yes—
190C2×#63227C2312yes—
191C2×#63227C2312yes—
192C2×#63227C2311yescharacteristic
193C2×#63227C2311yescharacteristic
194C2×#63227C2311yescharacteristic
195C2×#63227C2311yescharacteristic
196C2×#63227C2312yes—
197#10587612—24no—
198C2×C4⋊Dic17—24no—
199C2×C4⋊Dic17C2312yes—
200C2×C4⋊Dic17C2311yescharacteristic
201C2×C4⋊Dic17C2311yescharacteristic
202C2×C4⋊Dic17C2311yescharacteristic
203C2×C4⋊Dic17C2311yescharacteristic
204C2×C4⋊Dic17C2311yescharacteristic
205C2×#63225C2312yes—
206C2×#63225C2312yes—
207C2×#63225C2312yes—
208C2×#63225C2312yes—
209C2×#63225C2311yescharacteristic
210C2×#63225C2311yescharacteristic
211C2×C4×Dic17C2312yes—
212C2×C4×Dic17C2312yes—
213C2×C4×Dic17C2312yes—
214C2×C4×Dic17C2312yes—
215C2×C4×Dic17C2312yes—
216C2×C4×Dic17C2312yes—
217C2×C4×Dic17C2312yes—
218C2×C4×Dic17C2311yescharacteristic
219C2×C4×Dic17C2311yescharacteristic
220C2×C4×Dic17C2311yescharacteristic
221C2×C4×Dic17C2312yes—
222#10587581C2×C418yescomplemented
223#10587579—28no—
224#10587578—24no—
225#10587578—24no—
226#10587578—24no—
227#10587578D418yescomplemented
228C4⋊C4×D17—24no—
229C4⋊C4×D17—24no—
230C4⋊C4×D17—24no—
231C4⋊C4×D17—24no—
232#10587574C2×C418yescomplemented
233#10587573—28no—
234#10587571C2×C418yescomplemented
235#10587571C2×C418yescomplemented
236#10587570C2×C418yescomplemented
237#10587570C2×C418yescomplemented
238#10587567—28no—
239#10587567—28no—
240C4×D68—28no—
241C4×D68C2×C418yescomplemented
242C42×D17C2×C418yescomplemented
243C4×Dic34—28no—
244C17×#95C2312yes—
245C17×#95C2312yes—
246C17×#95C2312yes—
247C17×#95C2312yes—
248C17×#95C2312yes—
249#10587502C2312yes—
250#10587502C2312yes—
251#10587502C2312yes—
252#10587502C2312yes—
253#10587502C2312yes—
254#10587502C2312yes—
255#10587502C2312yes—
256#10587502C2312yes—
257#10587502C2312yes—
258#10587502C2312yes—
259#10587502C2312yes—
260#10587502C2312yes—
261#10587502C2312yes—
262#10587502C2312yes—
263#10587502C2312yes—
264C24×C17C2411yescharacteristic
265C24×C17C2411yescharacteristic
266C23×D17C2411yescharacteristic
267C23×D17C2411yescharacteristic
268C23×D17C2411yescharacteristic
269C2×D4×C17—41no—
270C2×D4×C17—41no—
271C2×D4×C17C22×C414yes—
272C22×C4×C17—22no—
273C22×C4×C17—22no—
274C22×C4×C17—22no—
275C22×C4×C17—22no—
276C22×C4×C17—24no—
277C22×C4×C17—42no—
278C22×C4×C17—42no—
279C22×C4×C17C22×C414yes—
280C22×C4×C17C22×C414yes—
281C22×C4×C17C2412yes—
282C22×C4×C17C2412yes—
283C22×C4×C17C2412yes—
284C22×C4×C17C2411yescharacteristic
285C22×C4×C17C2411yescharacteristic
286C22×C4×C17C2411yescharacteristic
287C22×C4×C17C2411yescharacteristic
288C22×C4×C17C2412yes—
289C22×C4×C17C2411yescharacteristic
290C2×C22⋊D17—22no—
291C2×C22⋊D17—22no—
292C2×C22⋊D17—22no—
293C2×C22⋊D17—22no—
294C2×C22⋊D17—22no—
295C2×C22⋊D17—22no—
296C2×C22⋊D17—22no—
297C2×C22⋊D17—22no—
298C2×C22⋊D17—41no—
299C2×C22⋊D17—41no—
300C2×C22⋊D17—41no—
301C2×C22⋊D17—41no—
302C2×C22⋊D17C22×C414yes—
303C2×C22⋊D17C22×C414yes—
304C2×C22⋊D17C22×C414yes—
305C2×C22⋊D17C22×C414yes—
306C2×C22⋊D17C22×C414yes—
307C2×C22⋊D17C22×C414yes—
308C22×Dic17—24no—
309C22×Dic17—42no—
310C22×Dic17—42no—
311C22×Dic17C2412yes—
312C22×Dic17C2412yes—
313C22×Dic17C2412yes—
314C22×Dic17C2411yescharacteristic
315C22×Dic17C2411yescharacteristic
316C22×Dic17C2411yescharacteristic
317C22×Dic17C2411yescharacteristic
318C22×Dic17C2412yes—
319C22×Dic17C2411yescharacteristic
320#63252—232no—
321#63252—232no—
322C2×D68—22no—
323C2×D68—22no—
324C2×D68—22no—
325C2×D68—22no—
326C2×D68—41no—
327C2×D68—41no—
328C2×D68C22×C414yes—
329C2×D68C22×C414yes—
330C2×D68C22×C414yes—
331C2×C4×D17—22no—
332C2×C4×D17—22no—
333C2×C4×D17—22no—
334C2×C4×D17—22no—
335C2×C4×D17—24no—
336C2×C4×D17—24no—
337C2×C4×D17—24no—
338C2×C4×D17—24no—
339C2×C4×D17—41no—
340C2×C4×D17—41no—
341C2×C4×D17—41no—
342C2×C4×D17—41no—
343C2×C4×D17—42no—
344C2×C4×D17—42no—
345C2×C4×D17—42no—
346C2×C4×D17—42no—
347C2×C4×D17—42no—
348C2×C4×D17—42no—
349C2×C4×D17—42no—
350C2×C4×D17—42no—
351C2×C4×D17C22×C414yes—
352C2×C4×D17C22×C414yes—
353C2×C4×D17C22×C414yes—
354C2×C4×D17C22×C414yes—
355C2×C4×D17C22×C414yes—
356C2×C4×D17C2×D414yes—
357C2×C4×D17#4114yes—
358C2×Dic34—22no—
359C2×Dic34—22no—
360C2×Dic34—22no—
361C2×Dic34—22no—
362C2×Dic34C22×C414yes—
363C2×Dic34C22×C414yes—
364C4⋊C4×C17—24no—
365C4⋊C4×C17—22no—
366C4⋊C4×C17—22no—
367C4⋊C4×C17—22no—
368C4⋊C4×C17C22×C414yes—
369C4⋊C4×C17C2×D414yes—
370C22⋊C4×C17—24no—
371C22⋊C4×C17—42no—
372C22⋊C4×C17—42no—
373C22⋊C4×C17C22×C414yes—
374C22⋊C4×C17C22×C414yes—
375C42×C17—24no—
376C42×C17—42no—
377C42×C17C22×C414yes—
378C22⋊Dic17—24no—
379C22⋊Dic17—42no—
380C22⋊Dic17—42no—
381C22⋊Dic17C22×C414yes—
382C22⋊Dic17C22×C414yes—
383#63227—24no—
384#63227—24no—
385#63227—24no—
386#63227—42no—
387#63227—42no—
388#63227—42no—
389#63227—42no—
390#63227C22×C414yes—
391#63227C22×C414yes—
392#63227C22×C414yes—
393#63227C22×C414yes—
394#63227C2×D418yes—
395C4⋊Dic17—22no—
396C4⋊Dic17—22no—
397C4⋊Dic17—22no—
398C4⋊Dic17—24no—
399C4⋊Dic17C22×C414yes—
400C4⋊Dic17C2×D414yes—
401#63225—24no—
402#63225—24no—
403#63225—24no—
404#63225—24no—
405#63225C22×C414yes—
406#63225C22×C414yes—
407C4×Dic17—24no—
408C4×Dic17—24no—
409C4×Dic17—24no—
410C4×Dic17—24no—
411C4×Dic17—42no—
412C4×Dic17—42no—
413C4×Dic17—42no—
414C4×Dic17C22×C414yes—
415C4×Dic17C22×C414yes—
416C4×Dic17C22×C414yes—
417C4×Dic17C2×D418yes—
418#34208—171nomaximal, Sylow
419C23×C17—21no—
420C23×C17—21no—
421C23×C17—21no—
422C23×C17—21no—
423C23×C17—21no—
424C23×C17—21no—
425C23×C17—21no—
426C23×C17—21no—
427C23×C17—21no—
428C23×C17—21no—
429C23×C17—21no—
430C23×C17—21no—
431C23×C17C23×C412yes—
432C23×C17C23×C412yes—
433C23×C17C2511yescharacteristic
434C22×D17—21no—
435C22×D17—21no—
436C22×D17—21no—
437C22×D17—21no—
438C22×D17—21no—
439C22×D17—21no—
440C22×D17—21no—
441C22×D17—21no—
442C22×D17—21no—
443C22×D17—21no—
444C22×D17—21no—
445C22×D17—21no—
446C22×D17—21no—
447C22×D17—21no—
448C22×D17—21no—
449C22×D17—21no—
450C22×D17C23×C412yes—
451C22×D17C23×C412yes—
452C22×D17C23×C412yes—
453C22×D17C22×D412yes—
454C22×D17C2×#4112yes—
455D4×C17—44no—
456C2×C4×C17—21no—
457C2×C4×C17—21no—
458C2×C4×C17—21no—
459C2×C4×C17—21no—
460C2×C4×C17—21no—
461C2×C4×C17—22no—
462C2×C4×C17—21no—
463C2×C4×C17—21no—
464C2×C4×C17—22no—
465C2×C4×C17—21no—
466C2×C4×C17—28no—
467C2×C4×C17—28no—
468C2×C4×C17—22no—
469C2×C4×C17—22no—
470C2×C4×C17—22no—
471C2×C4×C17—22no—
472C2×C4×C17—22no—
473C2×C4×C17—22no—
474C2×C4×C17—22no—
475C2×C4×C17—22no—
476C2×C4×C17—22no—
477C2×C4×C17—84no—
478C2×C4×C17C23×C412yes—
479C2×C4×C17C23×C412yes—
480C2×C4×C17C23×C412yes—
481C2×C4×C17C23×C412yes—
482C2×C4×C17C23×C412yes—
483C2×C4×C17C22×D414yes—
484C2×C4×C17C22×D412yes—
485C2×C4×C17C2×#4112yes—
486C22⋊D17—28no—
487C22⋊D17—28no—
488C22⋊D17—28no—
489C22⋊D17—28no—
490C22⋊D17—44no—
491C22⋊D17—44no—
492C2×Dic17—21no—
493C2×Dic17—21no—
494C2×Dic17—21no—
495C2×Dic17—21no—
496C2×Dic17—22no—
497C2×Dic17—22no—
498C2×Dic17—21no—
499C2×Dic17—21no—
500C2×Dic17—21no—
501C2×Dic17—21no—
502C2×Dic17—22no—
503C2×Dic17—22no—
504C2×Dic17—22no—
505C2×Dic17—22no—
506C2×Dic17—22no—
507C2×Dic17—22no—
508C2×Dic17—22no—
509C2×Dic17—22no—
510C2×Dic17—22no—
511C2×Dic17—84no—
512C2×Dic17C23×C412yes—
513C2×Dic17C23×C412yes—
514C2×Dic17C23×C412yes—
515C2×Dic17C23×C412yes—
516C2×Dic17C23×C412yes—
517C2×Dic17C22×D414yes—
518C2×Dic17C22×D412yes—
519C2×Dic17C2×#4112yes—
520D68—28no—
521D68—28no—
522D68—44no—
523C4×D17—28no—
524C4×D17—28no—
525C4×D17—44no—
526C4×D17—44no—
527C4×D17—84no—
528C4×D17—84no—
529C4×D17—84no—
530C4×D17—84no—
531C4×D17C4×D4116yes—
532Dic34—28no—
533Dic34—28no—
534C2×#532—171no—
535C2×#520—171no—
536C2×#520—171no—
537#2364—172no—
538#2364—172no—
539#2364—172no—
540#2364—172no—
541#2352—171no—
542#2352—171no—
543#2352—171no—
544#2352—171no—
545#2352—171no—
546#2352—171no—
547#2352—171no—
548#2352D1711yescharacteristic, complemented
549#2328—172no—
550#2327—172no—
551#2311—171no—
552#2311—171no—
553C4×#124—172no—
554C4×#124—172no—
555C2×#382—171no—
556C4×#117—171no—
557C22×C17—22no—
558C22×C17—22no—
559C22×C17—22no—
560C22×C17—22no—
561C22×C17—22no—
562C22×C17—22no—
563C22×C17—41no—
564C22×C17—41no—
565C22×C17—41no—
566C22×C17—41no—
567C22×C17—41no—
568C22×C17—41no—
569C22×C17—41no—
570C22×C17—41no—
571C22×C17C24×C411yescharacteristic
572C22×C17C23×D411yescharacteristic
573C22×C17C22×#4111yescharacteristic
574C22×C17#58511yescharacteristic
575C22×C17#58511yescharacteristic
576C22×C17#58511yescharacteristic
577C22×C17#58511yescharacteristic
578C2×D17—22no—
579C2×D17—22no—
580C2×D17—22no—
581C2×D17—22no—
582C2×D17—22no—
583C2×D17—22no—
584C2×D17—22no—
585C2×D17—22no—
586C2×D17—22no—
587C2×D17—22no—
588C2×D17—22no—
589C2×D17—22no—
590C2×D17—41no—
591C2×D17—41no—
592C2×D17—41no—
593C2×D17—41no—
594C2×D17—41no—
595C2×D17—41no—
596C2×D17—41no—
597C2×D17—41no—
598C2×D17C2×C4×D414yes—
599C4×C17—22no—
600C4×C17—22no—
601C4×C17—22no—
602C4×C17—22no—
603C4×C17—24no—
604C4×C17—42no—
605C4×C17—42no—
606C4×C17—42no—
607C4×C17C2×C4×D414yes—
608Dic17—22no—
609Dic17—22no—
610Dic17—22no—
611Dic17—22no—
612Dic17—24no—
613Dic17—42no—
614Dic17—42no—
615Dic17—42no—
616Dic17C2×C4×D414yes—
617C22×#41—171no—
618C22×#41—171no—
619#532—1716no—
620C2×C4⋊Q8—171no—
621C2×#127—171no—
622C2×#124—171no—
623C2×#124—171no—
624C2×#121—171no—
625C2×#121—171no—
626C2×#121—171no—
627C2×#121—171no—
628#520—348no—
629#520—348no—
630C2×C4×Q8—172no—
631C2×C4×Q8—172no—
632C2×C4×D4—171no—
633C2×C4×D4—171no—
634C2×C4×D4—172no—
635C2×C4×D4—172no—
636C2×C4×D4—172no—
637C2×C4×D4—172no—
638C2×C4×D4—172no—
639C2×C4×D4—171no—
640C2×C4×D4—172no—
641C2×C4×D4C2×D1711yescharacteristic
642C2×#117—171no—
643C2×#117—171no—
644C2×#117—171no—
645C2×#117—171no—
646C2×#117—171no—
647C2×#117C2×D1711yescharacteristic
648C22×C4⋊C4—171no—
649C22×C4⋊C4—171no—
650C22×C4⋊C4—171no—
651C22×C4⋊C4—171no—
652C22×C4⋊C4—171no—
653C22×C4⋊C4C2×D1711yescharacteristic
654C22×C42—171no—
655#391—172no—
656#391—172no—
657#390—172no—
658#390—172no—
659#388—172no—
660#388—172no—
661#388—172no—
662#388—172no—
663#388—172no—
664#388—172no—
665#388—172no—
666#388C2×D1712yes—
667#387—172no—
668#387—172no—
669#387—172no—
670#387—172no—
671#387—172no—
672#387—172no—
673#387—172no—
674#387C2×D1712yes—
675#386—172no—
676#386—172no—
677#386—172no—
678#386—172no—
679#386—172no—
680#386—172no—
681#386—172no—
682#386—172no—
683#386—172no—
684#386—172no—
685#386—172no—
686#386C2×D1712yes—
687#382—171no—
688#382—171no—
689#382—171no—
690#382—172no—
691#382—172no—
692#382C2×D1711yescharacteristic
693#380—171no—
694#380—171no—
695#380—171no—
696#380—171no—
697#380—171no—
698#380—171no—
699#380C2×D1711yescharacteristic
700#380C2×D1711yescharacteristic
701C4×C4⋊C4—171no—
702C4×C4⋊C4—171no—
703C4×C4⋊C4—171no—
704C4×C4⋊C4C2×D1711yescharacteristic
705C4×C22⋊C4—172no—
706C4×C22⋊C4—172no—
707C4×C22⋊C4—172no—
708C4×C22⋊C4—172no—
709C4×C22⋊C4—172no—
710C4×C22⋊C4—172no—
711C4×C22⋊C4—172no—
712C4×C22⋊C4—172no—
713C4×C22⋊C4—172no—
714C4×C22⋊C4C2×D1712yes—
715#376—172no—
716C2×#95—172no—
717C2×#95—172no—
718C43—172no—
719C2×C17—42no—
720C2×C17—42no—
721C2×C17C22×C4×D411yescharacteristic
722C2×C17#342811yescharacteristic
723C2×C17#342811yescharacteristic
724C2×C17#350011yescharacteristic
725C2×C17#350011yescharacteristic
726C2×C17#351211yescharacteristic
727C2×C17#351211yescharacteristic
728D17—24no—
729D17—42no—
730D17—42no—
731C2×#41—178no—
732C2×#41—178no—
733C2×#41—344no—
734C2×#41—344no—
735C2×#41—344no—
736C2×#41—344no—
737C22×Q8—171no—
738C22×Q8—171no—
739C22×D4—171no—
740C22×D4—171no—
741C22×D4—171no—
742C22×D4—171no—
743C22×D4—171no—
744C22×D4—171no—
745C22×D4—171no—
746C22×D4—171no—
747C22×D4—171no—
748C22×D4C22×D1711yescharacteristic
749C23×C4—171no—
750C23×C4—171no—
751C23×C4—171no—
752C23×C4—171no—
753C23×C4—171no—
754C23×C4—172no—
755C23×C4—172no—
756C23×C4—172no—
757C23×C4—172no—
758C23×C4—172no—
759C23×C4C22×D1711yescharacteristic
760C23×C4C22×D1711yescharacteristic
761C23×C4C22×D1712yes—
762C4⋊Q8—178no—
763#127—178no—
764#124—178no—
765#124—178no—
766#121—178no—
767#121—178no—
768#121—178no—
769#121—178no—
770C4×Q8—348no—
771C4×Q8—348no—
772C4×D4—178no—
773C4×D4—178no—
774C4×D4—178no—
775C4×D4—348no—
776C4×D4—348no—
777C4×D4—348no—
778C4×D4—348no—
779C4×D4—348no—
780C4×D4—348no—
781C4×D4C4×D1718yescomplemented
782#117—24no—
783#117—178no—
784#117—344no—
785#117—344no—
786#117—344no—
787#117—344no—
788C2×C4⋊C4—24no—
789C2×C4⋊C4—171no—
790C2×C4⋊C4—171no—
791C2×C4⋊C4—171no—
792C2×C4⋊C4—171no—
793C2×C4⋊C4—171no—
794C2×C4⋊C4—171no—
795C2×C4⋊C4—172no—
796C2×C4⋊C4—172no—
797C2×C4⋊C4—172no—
798C2×C4⋊C4—172no—
799C2×C4⋊C4—172no—
800C2×C4⋊C4—171no—
801C2×C4⋊C4—344no—
802C2×C4⋊C4—344no—
803C2×C4⋊C4—344no—
804C2×C4⋊C4—344no—
805C2×C4⋊C4—344no—
806C2×C4⋊C4C22×D1711yescharacteristic
807C2×C4⋊C4C22×D1711yescharacteristic
808C2×C4⋊C4C22×D1712yes—
809C2×C4⋊C4C22×D1711yescharacteristic
810C2×C4⋊C4C22×D1711yescharacteristic
811C2×C4⋊C4C22×D1711yescharacteristic
812C2×C22⋊C4—171no—
813C2×C22⋊C4—171no—
814C2×C22⋊C4—172no—
815C2×C22⋊C4—171no—
816C2×C22⋊C4—171no—
817C2×C22⋊C4—171no—
818C2×C22⋊C4—171no—
819C2×C22⋊C4—172no—
820C2×C22⋊C4—172no—
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⋊C4C22×D1712yes—
830C2×C22⋊C4C22×D1712yes—
831C2×C22⋊C4C22×D1712yes—
832C2×C22⋊C4C22×D1711yescharacteristic
833C2×C22⋊C4C22×D1711yescharacteristic
834C2×C42—172no—
835C2×C42—171no—
836C2×C42—171no—
837C2×C42—171no—
838C2×C42—178no—
839C2×C42—172no—
840C2×C42—172no—
841C2×C42—172no—
842C2×C42—172no—
843C2×C42—172no—
844C2×C42—172no—
845C2×C42—172no—
846C2×C42C22×D1712yes—
847C2×C42C22×D1712yes—
848C2×C42C22×D1711yescharacteristic
849#95—172no—
850#95—172no—
851#95—172no—
852#95—172no—
853#95—172no—
854#95—172no—
855#95—172no—
856#95—172no—
857#95—172no—
858#95—172no—
859#95—172no—
860#95—172no—
861#95—172no—
862#95—172no—
863#95—172no—
864#95C22×D1712yes—
865#95C22×D1712yes—
866#95C22×D1712yes—
867#95C22×D1712yes—
868#95C22×D1712yes—
869C17#3420811yescharacteristic, complemented, Sylow
870C24—171no—
871C24—171no—
872C24—171no—
873C24C23×D1711yescharacteristic
874C24C23×D1711yescharacteristic
875#41—3432no—
876#41—3432no—
877C2×Q8—174no—
878C2×Q8—174no—
879C2×Q8—342no—
880C2×Q8—342no—
881C2×Q8—342no—
882C2×Q8—342no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—174no—
886C2×D4—174no—
887C2×D4—174no—
888C2×D4—174no—
889C2×D4—174no—
890C2×D4—174no—
891C2×D4—174no—
892C2×D4—174no—
893C2×D4—174no—
894C2×D4—342no—
895C2×D4—342no—
896C2×D4—342no—
897C2×D4—342no—
898C2×D4—342no—
899C2×D4—342no—
900C2×D4—342no—
901C2×D4—342no—
902C2×D4—342no—
903C2×D4—342no—
904C2×D4—342no—
905C2×D4—342no—
906C2×D4—681no—
907C2×D4—681no—
908C2×D4—681no—
909C2×D4—681no—
910C2×D4—681no—
911C2×D4—681no—
912C2×D4C2×C4×D1714yes—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—24no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—171no—
921C22×C4—174no—
922C22×C4—174no—
923C22×C4—174no—
924C22×C4—171no—
925C22×C4—171no—
926C22×C4—171no—
927C22×C4—171no—
928C22×C4—172no—
929C22×C4—174no—
930C22×C4—174no—
931C22×C4—174no—
932C22×C4—174no—
933C22×C4—172no—
934C22×C4—172no—
935C22×C4—172no—
936C22×C4—344no—
937C22×C4—344no—
938C22×C4—344no—
939C22×C4—344no—
940C22×C4—342no—
941C22×C4—342no—
942C22×C4—342no—
943C22×C4—342no—
944C22×C4—344no—
945C22×C4—681no—
946C22×C4—681no—
947C22×C4—681no—
948C22×C4—681no—
949C22×C4—682no—
950C22×C4—682no—
951C22×C4—682no—
952C22×C4—682no—
953C22×C4—682no—
954C22×C4—682no—
955C22×C4—682no—
956C22×C4—682no—
957C22×C4—682no—
958C22×C4—682no—
959C22×C4C2×C4×D1714yes—
960C22×C4C2×C4×D1714yes—
961C22×C4C23×D1712yes—
962C22×C4C23×D1712yes—
963C22×C4C23×D1712yes—
964C22×C4C23×D1711yescharacteristic
965C22×C4C23×D1711yescharacteristic
966C22×C4C23×D1711yescharacteristic
967C22×C4C23×D1711yescharacteristic
968C22×C4C23×D1712yes—
969C22×C4C23×D1711yescharacteristic
970C4⋊C4—22no—
971C4⋊C4—24no—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—174no—
975C4⋊C4—174no—
976C4⋊C4—174no—
977C4⋊C4—174no—
978C4⋊C4—344no—
979C4⋊C4—344no—
980C4⋊C4—344no—
981C4⋊C4—344no—
982C4⋊C4—342no—
983C4⋊C4—342no—
984C4⋊C4—344no—
985C4⋊C4—342no—
986C4⋊C4C2×C4×D1714yes—
987C4⋊C4D4×D1714yes—
988C22⋊C4—24no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—174no—
992C22⋊C4—174no—
993C22⋊C4—174no—
994C22⋊C4—174no—
995C22⋊C4—174no—
996C22⋊C4—174no—
997C22⋊C4—178no—
998C22⋊C4—344no—
999C22⋊C4—344no—
1000C22⋊C4—344no—
1001C22⋊C4—344no—
1002C22⋊C4—682no—
1003C22⋊C4—682no—
1004C22⋊C4—682no—
1005C22⋊C4—682no—
1006C22⋊C4—682no—
1007C22⋊C4—682no—
1008C22⋊C4C2×C4×D1714yes—
1009C22⋊C4C2×C4×D1714yes—
1010C42—24no—
1011C42—42no—
1012C42—174no—
1013C42—174no—
1014C42—174no—
1015C42—178no—
1016C42—344no—
1017C42—344no—
1018C42—344no—
1019C42—344no—
1020C42—682no—
1021C42—682no—
1022C42—682no—
1023C42C2×C4×D1714yes—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—172no—
1037C23—172no—
1038C23—172no—
1039C23—172no—
1040C23—172no—
1041C23—341no—
1042C23—341no—
1043C23—341no—
1044C23—341no—
1045C23—341no—
1046C23—341no—
1047C23—341no—
1048C23—341no—
1049C23—341no—
1050C23—341no—
1051C23—341no—
1052C23—341no—
1053C23—341no—
1054C23—341no—
1055C23—341no—
1056C23—341no—
1057C23C22×C4×D1712yes—
1058C23C22×C4×D1712yes—
1059C23C24×D1711yescharacteristic
1060Q8—348no—
1061Q8—348no—
1062D4—44no—
1063D4—348no—
1064D4—348no—
1065D4—348no—
1066D4—348no—
1067D4—348no—
1068D4—348no—
1069D4—684no—
1070D4—684no—
1071D4—684no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—28no—
1083C2×C4—28no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—84no—
1094C2×C4—172no—
1095C2×C4—172no—
1096C2×C4—172no—
1097C2×C4—1716no—
1098C2×C4—172no—
1099C2×C4—172no—
1100C2×C4—172no—
1101C2×C4—172no—
1102C2×C4—174no—
1103C2×C4—341no—
1104C2×C4—341no—
1105C2×C4—341no—
1106C2×C4—341no—
1107C2×C4—341no—
1108C2×C4—341no—
1109C2×C4—341no—
1110C2×C4—342no—
1111C2×C4—342no—
1112C2×C4—341no—
1113C2×C4—348no—
1114C2×C4—348no—
1115C2×C4—342no—
1116C2×C4—342no—
1117C2×C4—342no—
1118C2×C4—342no—
1119C2×C4—342no—
1120C2×C4—342no—
1121C2×C4—342no—
1122C2×C4—342no—
1123C2×C4—342no—
1124C2×C4—684no—
1125C2×C4—684no—
1126C2×C4—1364no—
1127C2×C4—1364no—
1128C2×C4—1364no—
1129C2×C4—1364no—
1130C2×C4—1364no—
1131C2×C4C22×C4×D1712yes—
1132C2×C4C22×C4×D1712yes—
1133C2×C4C22×C4×D1712yes—
1134C2×C4C22×C4×D1712yes—
1135C2×C4C22×C4×D1712yes—
1136C2×C4C2×D4×D1714yes—
1137C2×C4C2×D4×D1712yes—
1138C2×C4#41×D1712yes—
1139C22—22no—
1140C22—22no—
1141C22—22no—
1142C22—22no—
1143C22—22no—
1144C22—22no—
1145C22—41no—
1146C22—41no—
1147C22—41no—
1148C22—41no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—174no—
1154C22—342no—
1155C22—342no—
1156C22—342no—
1157C22—342no—
1158C22—342no—
1159C22—342no—
1160C22—342no—
1161C22—342no—
1162C22—342no—
1163C22—342no—
1164C22—342no—
1165C22—342no—
1166C22—681no—
1167C22—681no—
1168C22—681no—
1169C22—681no—
1170C22—681no—
1171C22—681no—
1172C22—681no—
1173C22—681no—
1174C22C23×C4×D1711yescharacteristic
1175C22C22×D4×D1711yescharacteristic
1176C22C2×#41×D1711yescharacteristic
1177C22#1176364411yescharacteristic
1178C22#1176364511yescharacteristic
1179C22#1176364511yescharacteristic
1180C22#1176364611yescharacteristic
1181C4—22no—
1182C4—22no—
1183C4—22no—
1184C4—22no—
1185C4—24no—
1186C4—42no—
1187C4—42no—
1188C4—42no—
1189C4—174no—
1190C4—342no—
1191C4—342no—
1192C4—342no—
1193C4—342no—
1194C4—344no—
1195C4—682no—
1196C4—682no—
1197C4—682no—
1198C4C4×D4×D1714yes—
1199C2—42no—
1200C2—42no—
1201C2—344no—
1202C2—682no—
1203C2—682no—
1204C2C2×C4×D4×D1711yescharacteristic
1205C2#1454198411yescharacteristic
1206C2#1454198511yescharacteristic
1207C2#1454257011yescharacteristic
1208C2#1454257511yescharacteristic
1209C2#1454269811yescharacteristic
1210C2#1454270211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2352C2
socle, cosocleC23×C17C25
prime radicalC2×#11763356C2
hypercenter#2352D17
hypocenterC17#34208
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#11763290C2semidirect
3. C2×#11763289C2semidirect
4. #14531835C2semidirect
5. #14531833C2semidirect
6. #14531830C2semidirect
7. #14531828C2semidirect
8. #14531716C2semidirect
9. #14531715C2semidirect
10. #14531714C2semidirect
11. #14531713C2semidirect
12. #14531710C2semidirect
13. #14531709C2semidirect
14. #14531706C2semidirect
15. #14531505C2semidirect
16. #14531499C2semidirect
17. #14531373C2semidirect
18. #14531373C2semidirect
19. #14531325C2semidirect
20. C4×#10587571C2semidirect
21. D17×#382C2semidirect
22. C4×#10587578C2semidirect
23. C17×#2352C2semidirect
26. #11763356C4semidirect
141. C2×#63252C2×C4semidirect
142. C2×#63252C2×C4semidirect
157. C4×D4×C17C2×C4semidirect
179. #10587626C2×C4semidirect
180. #10587624C2×C4semidirect
183. C4×C22⋊D17C2×C4semidirect
184. C4×C22⋊D17C2×C4semidirect
222. #10587581C2×C4semidirect
227. #10587578D4semidirect
232. #10587574C2×C4semidirect
234. #10587571C2×C4semidirect
235. #10587571C2×C4semidirect
236. #10587570C2×C4semidirect
237. #10587570C2×C4semidirect
241. C4×D68C2×C4semidirect
242. C42×D17C2×C4semidirect
548. #2352D17semidirect
781. C4×D4C4×D17semidirect
869. C17#34208semidirect

Maximal subgroups

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

subgroupindex
C2×#117633562
C2×#117632902
C2×#117632892
#145318352
#145318332
#145318302
#145318282
#145317162
#145317152
#145317142
#145317132
#145317102
#145317092
#145317062
#145315052
#145314992
#145313732
#145313252
C4×#105875712
D17×#3822
C4×#105875782
C17×#23522
#3420817