Finite Group Databasebeta

← #17195224

Subgroups — #17195224

Order 4352.

3194 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587570C211yesmaximal, characteristic
2#14531835C214yesmaximal, complemented
3#14531823C214yesmaximal, complemented
4#14531662C212yesmaximal, complemented
5C22⋊C4×D68C212yesmaximal, complemented
6C22⋊C4×C22⋊D17C212yesmaximal, complemented
7C22⋊C4×C22⋊D17C212yesmaximal, complemented
8#14531544C214yesmaximal, complemented
9#14531382C211yesmaximal, characteristic, complemented
10#14531379C211yesmaximal, characteristic, complemented
11C4×#10587570C214yesmaximal, complemented
12#14531165C211yesmaximal, characteristic, complemented
13#14531136C211yesmaximal, characteristic, complemented
14C4×C22⋊C4×D17C211yesmaximal, characteristic, complemented
15C17×#2273C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C22⋊D17C2211yescharacteristic
18C23×C22⋊D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C2×#10587570C4116yescomplemented
21C2×#10587570C2212yes—
22C2×#10587570C2212yes—
23C2×#10587570C2212yes—
24C2×#10587570C2212yes—
25C2×C4×D68C2214yescomplemented
26C2×C4×C22⋊D17C2214yescomplemented
27C2×C4×C22⋊D17C2214yescomplemented
28C2×#10587558C2212yescomplemented
29C22×#63225C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C2×C22⋊C4×D17C2212yes—
32C2×C22⋊C4×D17C2212yes—
33C2×C42×D17C2212yescomplemented
34#11762711C2214yescomplemented
35#11762709C2214yescomplemented
36#11762709C2214yescomplemented
37#11762706C2214yescomplemented
38#11762702C2214yescomplemented
39#11762702C2214yescomplemented
40#11762700C2214yescomplemented
41#11762698C2214yescomplemented
42#11762696C2214yescomplemented
43#11762693C2214yescomplemented
44#11762688C2214yescomplemented
45#11762688C2214yescomplemented
46#11762687C2214yescomplemented
47#11762687C2214yescomplemented
48#11762685C2214yescomplemented
49#11762685C2214yescomplemented
50#11762671C2212yescomplemented
51#11762669C2212yes—
52#11762668C2212yescomplemented
53#11762667C2212yes—
54#11762667C2212yes—
55#11762665C2212yes—
56#11762664C2212yes—
57#11762664C2212yes—
58C4×#63225C2214yescomplemented
59C22⋊C4×Dic17C2212yes—
60C22⋊C4×Dic17C2212yes—
61C4×#63227C2212yescomplemented
62C4×#63227C2214yescomplemented
63C4×#63227C2212yescomplemented
64C4×C22⋊Dic17C2211yescharacteristic
65C4×C22⋊Dic17C2211yescharacteristic
66#11762656C2212yescomplemented
67#11762656C2214yescomplemented
68#95×D17C2212yescomplemented
69C22×C22⋊C4×C17C2212yes—
70C22×C22⋊C4×C17C2211yescharacteristic
71C4×C22⋊C4×C17C2212yes—
72C4×C22⋊C4×C17C2211yescharacteristic
73C4×C22⋊C4×C17C2211yescharacteristic
74C4×C22⋊C4×C17C2214yescomplemented
75C4×C22⋊C4×C17C2214yescomplemented
76C25×C17C2311yescharacteristic
77C24×D17C2311yescharacteristic
78C24×D17C2311yescharacteristic
79C23×C4×C17C2314yes—
80C23×C4×C17C2311yescharacteristic
81C23×C4×C17C2311yescharacteristic
82C22×C22⋊D17—44no—
83C22×C22⋊D17—44no—
84C22×C22⋊D17C2×C418yescomplemented
85C22×C22⋊D17C2×C418yescomplemented
86C22×C22⋊D17C2312yes—
87C22×C22⋊D17C2312yes—
88C22×C22⋊D17C2312yes—
89C22×C22⋊D17C2312yes—
90C23×Dic17C2311yescharacteristic
91C23×Dic17C2311yescharacteristic
92C22×D68—44no—
93C22×D68C2×C418yescomplemented
94C22×D68C2312yes—
95C22×D68C2312yes—
96C22×C4×D17—44no—
97C22×C4×D17C2×C418yescomplemented
98C22×C4×D17C2314yes—
99C22×C4×D17C2311yescharacteristic
100C22×C4×D17C2311yescharacteristic
101C22×C4×D17C2314yes—
102C22×C4×D17C2311yescharacteristic
103C22×C4×D17C2311yescharacteristic
104C2×C22⋊C4×C17—28no—
105C2×C22⋊C4×C17C2×C418yescomplemented
106C2×C22⋊C4×C17C2314yes—
107C2×C22⋊C4×C17C2312yes—
108C2×C22⋊C4×C17C2312yes—
109C2×C22⋊C4×C17C2312yes—
110C2×C22⋊C4×C17C2312yes—
111C2×C42×C17C2314yes—
112C2×C42×C17C2312yes—
113C2×C42×C17C2312yes—
114C2×C22⋊Dic17C2312yes—
115C2×C22⋊Dic17C2312yes—
116C2×C22⋊Dic17C2314yes—
117C2×C22⋊Dic17C2314yes—
118C4×C22⋊D17—48no—
119C4×C22⋊D17—48no—
120C2×#63227C2×C418yescomplemented
121C2×#63227C2314yes—
122C2×#63227C2314yes—
123C2×#63227C2314yes—
124C2×#63227C2314yes—
125C2×#63227C2314yes—
126C2×#63227C2314yes—
127C2×#63227C2312yes—
128C2×#63227C2312yes—
129C2×C4⋊Dic17C2314yes—
130C2×#63225C2×C418yescomplemented
131C2×#63225C2314yes—
132C2×#63225C2314yes—
133C2×#63225C2312yes—
134C2×#63225C2312yes—
135C2×C4×Dic17C2314yes—
136C2×C4×Dic17C2314yes—
137C2×C4×Dic17C2312yes—
138C2×C4×Dic17C2312yes—
139#10587570C2×C4116yescomplemented
140#10587570C2×C4116yescomplemented
141#10587570C2×C4116yescomplemented
142#10587570C2×C4116yescomplemented
143C22⋊C4×D17—28no—
144C22⋊C4×D17—28no—
145C4×D68—48no—
146#10587558—44no—
147C42×D17—44no—
148C17×#95C2314yes—
149C17×#95C2312yes—
150C17×#95C2312yes—
151#10587502C2314yes—
152#10587502C2314yes—
153#10587502C2314yes—
154#10587502C2314yes—
155#10587502C2314yes—
156#10587502C2312yes—
157#10587502C2312yes—
158C24×C17—24no—
159C24×C17—42no—
160C24×C17—42no—
161C24×C17C22×C414yes—
162C24×C17C2412yes—
163C24×C17C2411yescharacteristic
164C23×D17—24no—
165C23×D17—24no—
166C23×D17—24no—
167C23×D17—42no—
168C23×D17—42no—
169C23×D17—42no—
170C23×D17C22×C414yes—
171C23×D17C22×C414yes—
172C23×D17C2412yes—
173C23×D17C2411yescharacteristic
174C23×D17C2411yescharacteristic
175C22×C4×C17—28no—
176C22×C4×C17—42no—
177C22×C4×C17—42no—
178C22×C4×C17—44no—
179C22×C4×C17—44no—
180C22×C4×C17C22×C414yes—
181C22×C4×C17C22×C414yes—
182C22×C4×C17C2414yes—
183C22×C4×C17C2411yescharacteristic
184C22×C4×C17C2411yescharacteristic
185C22×C4×C17C2412yes—
186C22×C4×C17C2414yes—
187C2×C22⋊D17—28no—
188C2×C22⋊D17—28no—
189C2×C22⋊D17—416no—
190C2×C22⋊D17—44no—
191C2×C22⋊D17—44no—
192C2×C22⋊D17—416no—
193C2×C22⋊D17C22×C418yes—
194C2×C22⋊D17C22×C418yes—
195C2×C22⋊D17C22×C418yes—
196C2×C22⋊D17C22×C418yes—
197C22×Dic17—24no—
198C22×Dic17—42no—
199C22×Dic17C22×C414yes—
200C22×Dic17C22×C414yes—
201C22×Dic17C2414yes—
202C22×Dic17C2414yes—
203C22×Dic17C2411yescharacteristic
204C22×Dic17C2412yes—
205C22×Dic17C2411yescharacteristic
206C2×D68—28no—
207C2×D68—416no—
208C2×D68—44no—
209C2×D68C22×C418yes—
210C2×D68C22×C418yes—
211C2×C4×D17—24no—
212C2×C4×D17—24no—
213C2×C4×D17—28no—
214C2×C4×D17—28no—
215C2×C4×D17—28no—
216C2×C4×D17—416no—
217C2×C4×D17—42no—
218C2×C4×D17—42no—
219C2×C4×D17—44no—
220C2×C4×D17—44no—
221C2×C4×D17—44no—
222C2×C4×D17C22×C414yes—
223C2×C4×D17C22×C414yes—
224C2×C4×D17C22×C414yes—
225C2×C4×D17C22×C414yes—
226C22⋊C4×C17—24no—
227C22⋊C4×C17—28no—
228C22⋊C4×C17C22×C418yes—
229C22⋊C4×C17C22×C418yes—
230C22⋊C4×C17#4118yes—
231C42×C17—42no—
232C42×C17—42no—
233C42×C17—44no—
234C22⋊Dic17—24no—
235C22⋊Dic17—24no—
236C22⋊Dic17—44no—
237C22⋊Dic17—44no—
238#63227—28no—
239#63227—28no—
240#63227—28no—
241#63227—44no—
242#63227—44no—
243#63227—44no—
244#63227C22×C418yes—
245#63227C22×C418yes—
246C4⋊Dic17—44no—
247#63225—28no—
248#63225—44no—
249#63225C22×C418yes—
250#63225C22×C418yes—
251C4×Dic17—28no—
252C4×Dic17—42no—
253C4×Dic17—42no—
254C4×Dic17—44no—
255#34246—171nomaximal, Sylow
256C23×C17—22no—
257C23×C17—22no—
258C23×C17—22no—
259C23×C17—22no—
260C23×C17—24no—
261C23×C17—24no—
262C23×C17—28no—
263C23×C17—44no—
264C23×C17—44no—
265C23×C17—88no—
266C23×C17C23×C414yes—
267C23×C17C23×C412yes—
268C23×C17C2×#4114yes—
269C23×C17C2511yescharacteristic
270C22×D17—22no—
271C22×D17—22no—
272C22×D17—28no—
273C22×D17—22no—
274C22×D17—22no—
275C22×D17—22no—
276C22×D17—22no—
277C22×D17—24no—
278C22×D17—24no—
279C22×D17—22no—
280C22×D17—28no—
281C22×D17—28no—
282C22×D17—44no—
283C22×D17—44no—
284C22×D17—44no—
285C22×D17—416no—
286C22×D17—88no—
287C22×D17C23×C412yes—
288C22×D17C23×C414yes—
289C22×D17C23×C412yes—
290C22×D17H(5,𝔽2)14yes—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—24no—
294C2×C4×C17—24no—
295C2×C4×C17—24no—
296C2×C4×C17—24no—
297C2×C4×C17—24no—
298C2×C4×C17—24no—
299C2×C4×C17—44no—
300C2×C4×C17—44no—
301C2×C4×C17—88no—
302C2×C4×C17C23×C412yes—
303C2×C4×C17C23×C412yes—
304C2×C4×C17C23×C414yes—
305C2×C4×C17C2×#4118yes—
306C22⋊D17—216no—
307C22⋊D17—216no—
308C22⋊D17—48no—
309C22⋊D17—48no—
310C2×Dic17—22no—
311C2×Dic17—24no—
312C2×Dic17—28no—
313C2×Dic17—24no—
314C2×Dic17—24no—
315C2×Dic17—24no—
316C2×Dic17—24no—
317C2×Dic17—24no—
318C2×Dic17—24no—
319C2×Dic17—44no—
320C2×Dic17C23×C412yes—
321C2×Dic17C23×C414yes—
322C2×Dic17C23×C412yes—
323C2×Dic17H(5,𝔽2)14yes—
324D68—216no—
325D68—48no—
326C4×D17—28no—
327C4×D17—28no—
328C4×D17—44no—
329C4×D17—44no—
330C4×D17—416no—
331C4×D17—88no—
332C22×#121—171no—
333#2364—174no—
334#2363—174no—
335#2345—172no—
336D4×C22⋊C4—172no—
337D4×C22⋊C4—172no—
338D4×C22⋊C4—172no—
339#2333—174no—
340#2312—171no—
341#2312—171no—
342C4×#121—174no—
343#2280—171no—
344#2273—171no—
345#2273D1711yescharacteristic, complemented
346C2×C4×C22⋊C4—171no—
347C22×C17—22no—
348C22×C17—22no—
349C22×C17—28no—
350C22×C17—24no—
351C22×C17—24no—
352C22×C17—24no—
353C22×C17—44no—
354C22×C17—44no—
355C22×C17—88no—
356C22×C17C4×#4114yes—
357C22×C17C24×C411yescharacteristic
358C22×C17C22×#4112yes—
359C22×C17C2×H(5,𝔽2)12yes—
360C22×C17C2×H(5,𝔽2)12yes—
361C2×D17—22no—
362C2×D17—22no—
363C2×D17—28no—
364C2×D17—22no—
365C2×D17—24no—
366C2×D17—22no—
367C2×D17—24no—
368C2×D17—22no—
369C2×D17—24no—
370C2×D17—416no—
371C2×D17—44no—
372C2×D17—44no—
373C2×D17—44no—
374C2×D17—88no—
375C2×D17#51814yes—
376C4×C17—22no—
377C4×C17—22no—
378C4×C17—24no—
379C4×C17—28no—
380C4×C17—44no—
381Dic17—22no—
382Dic17—24no—
383Dic17—44no—
384Dic17—44no—
385Dic17#51814yes—
386C23×D4—171no—
387C23×D4—171no—
388C23×D4—171no—
389C24×C4—171no—
390C2×#121—1716no—
391C2×#121—172no—
392C2×#121—172no—
393C2×#121—172no—
394C2×#121—172no—
395C2×C4×D4—174no—
396C2×C4×D4—174no—
397C2×C4×D4—174no—
398C2×#117—172no—
399C22×C4⋊C4—171no—
400C22×C22⋊C4—171no—
401C22×C22⋊C4—172no—
402C22×C22⋊C4—172no—
403C22×C22⋊C4C2×D1712yes—
404C22×C22⋊C4C2×D1711yescharacteristic
405C22×C42—172no—
406#390—174no—
407#390—174no—
408#390—174no—
409#389—174no—
410#388—174no—
411#388—174no—
412#388—174no—
413#388—174no—
414#387—174no—
415#387—174no—
416#386—174no—
417#386—174no—
418#386—174no—
419#386—174no—
420#386—174no—
421#386—174no—
422#381—172no—
423#380—172no—
424#380—172no—
425#380—172no—
426#380—172no—
427#379—172no—
428#379—172no—
429#379—172no—
430C4×C4⋊C4—174no—
431C4×C22⋊C4—171no—
432C4×C22⋊C4—171no—
433C4×C22⋊C4—172no—
434C4×C22⋊C4—172no—
435C4×C22⋊C4—172no—
436C4×C22⋊C4—174no—
437C4×C22⋊C4—172no—
438C4×C22⋊C4—172no—
439C4×C22⋊C4—174no—
440C4×C22⋊C4C2×D1711yescharacteristic
441C4×C22⋊C4C2×D1712yes—
442C4×C22⋊C4C2×D1711yescharacteristic
443C4×C22⋊C4C2×D1714yescomplemented
444C4×C22⋊C4C2×D1714yescomplemented
445C2×#95—172no—
446C2×C17—24no—
447C2×C17—44no—
448C2×C17C2×C4×#4111yescharacteristic
449C2×C17C2×#51811yescharacteristic
450C2×C17C2×#51811yescharacteristic
451C2×C17#351914yes—
452D17—24no—
453D17—42no—
454D17—44no—
455C25—171no—
456C25—171no—
457C25C22×D1711yescharacteristic
458C22×D4—172no—
459C22×D4—172no—
460C22×D4—178no—
461C22×D4—178no—
462C22×D4—172no—
463C22×D4—172no—
464C22×D4—178no—
465C22×D4—172no—
466C22×D4—172no—
467C22×D4—684no—
468C22×D4—684no—
469C22×D4—684no—
470C23×C4—171no—
471C23×C4—171no—
472C23×C4—171no—
473C23×C4—171no—
474C23×C4—178no—
475C23×C4—171no—
476C23×C4—171no—
477C23×C4—174no—
478C23×C4—174no—
479C23×C4—684no—
480C23×C4C22×D1714yes—
481C23×C4C22×D1711yescharacteristic
482C23×C4C22×D1711yescharacteristic
483#121—1716no—
484#121—1716no—
485#121—1716no—
486#121—1716no—
487C4×D4—688no—
488C4×D4—688no—
489C4×D4—688no—
490#117—684no—
491C2×C4⋊C4—178no—
492C2×C4⋊C4—172no—
493C2×C4⋊C4—172no—
494C2×C4⋊C4—174no—
495C2×C4⋊C4—174no—
496C2×C4⋊C4—174no—
497C2×C22⋊C4—28no—
498C2×C22⋊C4—178no—
499C2×C22⋊C4—172no—
500C2×C22⋊C4—172no—
501C2×C22⋊C4—172no—
502C2×C22⋊C4—172no—
503C2×C22⋊C4—174no—
504C2×C22⋊C4—174no—
505C2×C22⋊C4—174no—
506C2×C22⋊C4—174no—
507C2×C22⋊C4—174no—
508C2×C22⋊C4—174no—
509C2×C22⋊C4—174no—
510C2×C22⋊C4—174no—
511C2×C22⋊C4—348no—
512C2×C22⋊C4—348no—
513C2×C22⋊C4C4×D1718yescomplemented
514C2×C22⋊C4C22×D1712yes—
515C2×C22⋊C4C22×D1714yes—
516C2×C22⋊C4C22×D1712yes—
517C2×C22⋊C4C22×D1712yes—
518C2×C22⋊C4C22×D1712yes—
519C2×C42—174no—
520C2×C42—172no—
521C2×C42—174no—
522C2×C42—172no—
523C2×C42—684no—
524C2×C42C22×D1712yes—
525C2×C42C22×D1714yes—
526C2×C42C22×D1712yes—
527#95—174no—
528#95—172no—
529#95—172no—
530#95—174no—
531#95—174no—
532#95—174no—
533#95—174no—
534#95C22×D1712yes—
535#95C22×D1712yes—
536#95C22×D1714yes—
537C17#3424611yescharacteristic, complemented, Sylow
538C24—24no—
539C24—42no—
540C24—42no—
541C24—171no—
542C24—172no—
543C24—171no—
544C24—174no—
545C24—174no—
546C24—344no—
547C24—344no—
548C24—344no—
549C24—682no—
550C24—682no—
551C24—682no—
552C24C2×C4×D1714yes—
553C24C23×D1712yes—
554C24C23×D1711yescharacteristic
555C2×D4—178no—
556C2×D4—178no—
557C2×D4—178no—
558C2×D4—178no—
559C2×D4—178no—
560C2×D4—178no—
561C2×D4—348no—
562C2×D4—348no—
563C2×D4—348no—
564C2×D4—684no—
565C2×D4—6816no—
566C2×D4—6816no—
567C2×D4—684no—
568C2×D4—684no—
569C2×D4—6816no—
570C22×C4—28no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—171no—
576C22×C4—174no—
577C22×C4—171no—
578C22×C4—172no—
579C22×C4—174no—
580C22×C4—174no—
581C22×C4—174no—
582C22×C4—174no—
583C22×C4—174no—
584C22×C4—174no—
585C22×C4—174no—
586C22×C4—344no—
587C22×C4—344no—
588C22×C4—348no—
589C22×C4—344no—
590C22×C4—348no—
591C22×C4—348no—
592C22×C4—684no—
593C22×C4—682no—
594C22×C4—682no—
595C22×C4—684no—
596C22×C4—684no—
597C22×C4—6816no—
598C22×C4—682no—
599C22×C4C2×C4×D1714yes—
600C22×C4C2×C4×D1714yes—
601C22×C4C23×D1714yes—
602C22×C4C23×D1711yescharacteristic
603C22×C4C23×D1711yescharacteristic
604C22×C4C23×D1712yes—
605C22×C4C23×D1714yes—
606C4⋊C4—178no—
607C4⋊C4—178no—
608C4⋊C4—348no—
609C4⋊C4—684no—
610C4⋊C4—684no—
611C22⋊C4—24no—
612C22⋊C4—28no—
613C22⋊C4—178no—
614C22⋊C4—178no—
615C22⋊C4—348no—
616C22⋊C4—344no—
617C22⋊C4—344no—
618C22⋊C4—348no—
619C22⋊C4—348no—
620C22⋊C4—684no—
621C22⋊C4—684no—
622C22⋊C4—684no—
623C22⋊C4—684no—
624C22⋊C4—684no—
625C22⋊C4C2×C4×D1718yes—
626C22⋊C4C2×C4×D1718yes—
627C22⋊C4#6325218yes—
628C42—42no—
629C42—42no—
630C42—44no—
631C42—348no—
632C42—682no—
633C42—682no—
634C42—684no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—28no—
642C23—44no—
643C23—44no—
644C23—88no—
645C23—172no—
646C23—174no—
647C23—174no—
648C23—172no—
649C23—348no—
650C23—342no—
651C23—342no—
652C23—348no—
653C23—342no—
654C23—342no—
655C23—342no—
656C23—342no—
657C23—344no—
658C23—344no—
659C23—342no—
660C23—348no—
661C23—684no—
662C23—684no—
663C23—684no—
664C23—6816no—
665C23—1368no—
666C23C22×C4×D1714yes—
667C23C22×C4×D1712yes—
668C23C2×#6325214yes—
669C23C24×D1711yescharacteristic
670D4—3416no—
671D4—3416no—
672D4—3416no—
673D4—688no—
674D4—688no—
675D4—688no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—88no—
687C2×C4—172no—
688C2×C4—174no—
689C2×C4—174no—
690C2×C4—172no—
691C2×C4—348no—
692C2×C4—348no—
693C2×C4—348no—
694C2×C4—344no—
695C2×C4—342no—
696C2×C4—344no—
697C2×C4—344no—
698C2×C4—344no—
699C2×C4—344no—
700C2×C4—344no—
701C2×C4—344no—
702C2×C4—684no—
703C2×C4—684no—
704C2×C4—6816no—
705C2×C4—684no—
706C2×C4—1368no—
707C2×C4C22×C4×D1712yes—
708C2×C4C22×C4×D1712yes—
709C2×C4C22×C4×D1714yes—
710C2×C4C2×#6325218yes—
711C22—22no—
712C22—22no—
713C22—28no—
714C22—24no—
715C22—24no—
716C22—24no—
717C22—44no—
718C22—44no—
719C22—88no—
720C22—174no—
721C22—342no—
722C22—342no—
723C22—348no—
724C22—342no—
725C22—344no—
726C22—342no—
727C22—344no—
728C22—344no—
729C22—342no—
730C22—6816no—
731C22—684no—
732C22—684no—
733C22—684no—
734C22—1368no—
735C22C4×#6325214yes—
736C22C23×C4×D1711yescharacteristic
737C22C22×#6325212yes—
738C22H(5,𝔽2)×D1712yes—
739C22H(5,𝔽2)×D1712yes—
740C4—22no—
741C4—22no—
742C4—24no—
743C4—28no—
744C4—44no—
745C4—174no—
746C4—342no—
747C4—344no—
748C4—684no—
749C4—684no—
750C2—24no—
751C2—44no—
752C2—344no—
753C2—682no—
754C2—684no—
755C2C2×C4×#6325211yescharacteristic
756C2D17×#51811yescharacteristic
757C2D17×#51811yescharacteristic
758C2#1454280614yes—
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2273C2
socle, cosocleC23×C17C25
prime radicalC22×#10587570C2
hypercenter#2273D17
hypocenterC17#34246
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2273

Complements

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

NH ≅ G/Ntype
2. #14531835C2semidirect
3. #14531823C2semidirect
4. #14531662C2semidirect
5. C22⋊C4×D68C2semidirect
6. C22⋊C4×C22⋊D17C2semidirect
7. C22⋊C4×C22⋊D17C2semidirect
8. #14531544C2semidirect
9. #14531382C2semidirect
10. #14531379C2semidirect
11. C4×#10587570C2semidirect
12. #14531165C2semidirect
13. #14531136C2semidirect
14. C4×C22⋊C4×D17C2semidirect
15. C17×#2273C2semidirect
20. C2×#10587570C4semidirect
25. C2×C4×D68C22semidirect
26. C2×C4×C22⋊D17C22semidirect
27. C2×C4×C22⋊D17C22semidirect
28. C2×#10587558C22semidirect
33. C2×C42×D17C22semidirect
34. #11762711C22semidirect
35. #11762709C22semidirect
36. #11762709C22semidirect
37. #11762706C22semidirect
38. #11762702C22semidirect
39. #11762702C22semidirect
40. #11762700C22semidirect
41. #11762698C22semidirect
42. #11762696C22semidirect
43. #11762693C22semidirect
44. #11762688C22semidirect
45. #11762688C22semidirect
46. #11762687C22semidirect
47. #11762687C22semidirect
48. #11762685C22semidirect
49. #11762685C22semidirect
50. #11762671C22semidirect
52. #11762668C22semidirect
58. C4×#63225C22semidirect
61. C4×#63227C22semidirect
62. C4×#63227C22semidirect
63. C4×#63227C22semidirect
66. #11762656C22semidirect
67. #11762656C22semidirect
68. #95×D17C22semidirect
74. C4×C22⋊C4×C17C22semidirect
75. C4×C22⋊C4×C17C22semidirect
84. C22×C22⋊D17C2×C4semidirect
85. C22×C22⋊D17C2×C4semidirect
93. C22×D68C2×C4semidirect
97. C22×C4×D17C2×C4semidirect
105. C2×C22⋊C4×C17C2×C4semidirect
120. C2×#63227C2×C4semidirect
130. C2×#63225C2×C4semidirect
139. #10587570C2×C4semidirect
140. #10587570C2×C4semidirect
141. #10587570C2×C4semidirect
142. #10587570C2×C4semidirect
345. #2273D17semidirect
443. C4×C22⋊C4C2×D17semidirect
444. C4×C22⋊C4C2×D17semidirect
513. C2×C22⋊C4C4×D17semidirect
537. C17#34246semidirect

Maximal subgroups

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

subgroupindex
C22×#105875702
#145318352
#145318232
#145316622
C22⋊C4×D682
C22⋊C4×C22⋊D172
#145315442
#145313822
#145313792
C4×#105875702
#145311652
#145311362
C4×C22⋊C4×D172
C17×#22732
#3424617