Finite Group Databasebeta

← #16957770

Subgroups — #16957770

Order 4352.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587625C211yesmaximal, characteristic
2C2×#11762689C211yesmaximal, characteristic, complemented
3C2×#11762688C211yesmaximal, characteristic, complemented
4C2×#11762688C211yesmaximal, characteristic, complemented
5C2×#11762686C211yesmaximal, characteristic, complemented
6C22×#10587502C211yesmaximal, characteristic, complemented
7#14527034C211yesmaximal, characteristic, complemented
8#14527031C211yesmaximal, characteristic, complemented
9#14527026C211yesmaximal, characteristic, complemented
10#14527023C211yesmaximal, characteristic, complemented
11#14527022C211yesmaximal, characteristic, complemented
12#14527017C211yesmaximal, characteristic, complemented
13#14527007C211yesmaximal, characteristic, complemented
14#14527006C211yesmaximal, characteristic, complemented
15C22×C4×D4×C17C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C22⋊D17C2211yescharacteristic
18C24×Dic17C2211yescharacteristic
19C24×Dic17C2211yescharacteristic
20C2×#10587625—24no—
21C2×#10587625—24no—
22C2×#10587625C418yescomplemented
23C22×#63225C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33#11762689—24no—
34#11762688—24no—
35#11762688—24no—
36#11762686—24no—
37C2×#10587502—24no—
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C23×D4×C17C2211yescharacteristic
53C24×C4×C17C2211yescharacteristic
54C24×C4×C17C2211yescharacteristic
55C2×C4×D4×C17—24no—
56C2×C4×D4×C17—24no—
57C2×C4×D4×C17—24no—
58C22×C4⋊C4×C17C2211yescharacteristic
59C22×C22⋊C4×C17C2211yescharacteristic
60C22×C22⋊C4×C17C2211yescharacteristic
61C22×C42×C17C2211yescharacteristic
62C25×C17C2311yescharacteristic
63C25×C17C2311yescharacteristic
64C24×D17C2311yescharacteristic
65C22×D4×C17—22no—
66C22×D4×C17—22no—
67C22×D4×C17—22no—
68C22×D4×C17—22no—
69C22×D4×C17C2×C414yes—
70C22×D4×C17D414yes—
71C22×D4×C17D414yes—
72C23×C4×C17—22no—
73C23×C4×C17—22no—
74C23×C4×C17—22no—
75C23×C4×C17—22no—
76C23×C4×C17—22no—
77C23×C4×C17—22no—
78C23×C4×C17—22no—
79C23×C4×C17—22no—
80C23×C4×C17—22no—
81C23×C4×C17—41no—
82C23×C4×C17—41no—
83C23×C4×C17—41no—
84C23×C4×C17—41no—
85C23×C4×C17D414yescomplemented
86C23×C4×C17C2311yescharacteristic
87C23×C4×C17C2311yescharacteristic
88C23×C4×C17C2311yescharacteristic
89C23×C4×C17C2311yescharacteristic
90C23×C4×C17C2311yescharacteristic
91C22×C22⋊D17—22no—
92C22×C22⋊D17—22no—
93C22×C22⋊D17—22no—
94C22×C22⋊D17—22no—
95C22×C22⋊D17—22no—
96C22×C22⋊D17—22no—
97C22×C22⋊D17—22no—
98C22×C22⋊D17—22no—
99C22×C22⋊D17—22no—
100C22×C22⋊D17—22no—
101C22×C22⋊D17—41no—
102C22×C22⋊D17—41no—
103C22×C22⋊D17C2×C414yescomplemented
104C22×C22⋊D17C2×C414yescomplemented
105C23×Dic17—22no—
106C23×Dic17—22no—
107C23×Dic17—22no—
108C23×Dic17—22no—
109C23×Dic17—22no—
110C23×Dic17—22no—
111C23×Dic17—22no—
112C23×Dic17—22no—
113C23×Dic17—22no—
114C23×Dic17—41no—
115C23×Dic17—41no—
116C23×Dic17—41no—
117C23×Dic17—41no—
118C23×Dic17C2×C414yescomplemented
119C23×Dic17C2311yescharacteristic
120C23×Dic17C2311yescharacteristic
121C23×Dic17C2311yescharacteristic
122C23×Dic17C2311yescharacteristic
123C23×Dic17C2311yescharacteristic
124C23×Dic17C2311yescharacteristic
125C23×Dic17C2311yescharacteristic
126C4×D4×C17—232no—
127C2×C4⋊C4×C17—22no—
128C2×C4⋊C4×C17—22no—
129C2×C4⋊C4×C17—22no—
130C2×C22⋊C4×C17—22no—
131C2×C22⋊C4×C17—22no—
132C2×C22⋊C4×C17—22no—
133C2×C22⋊C4×C17—22no—
134C2×C22⋊C4×C17—22no—
135C2×C22⋊C4×C17D414yescomplemented
136C2×C42×C17—22no—
137C2×C42×C17—22no—
138C2×C42×C17—22no—
139C2×C22⋊Dic17—22no—
140C2×C22⋊Dic17—22no—
141C2×C22⋊Dic17—22no—
142C2×C22⋊Dic17—22no—
143C2×C22⋊Dic17—22no—
144C2×C22⋊Dic17—22no—
145C2×C22⋊Dic17—22no—
146C2×C22⋊Dic17—22no—
147C2×C22⋊Dic17—22no—
148C2×C22⋊Dic17—41no—
149C2×C22⋊Dic17—41no—
150C2×C22⋊Dic17C2×C414yescomplemented
151#10587625—232no—
152C2×#63227—22no—
153C2×#63227—22no—
154C2×#63227—22no—
155C2×#63227—22no—
156C2×#63227—22no—
157C2×#63227—22no—
158C2×#63227—22no—
159C2×#63227—22no—
160C2×#63227—22no—
161C2×#63227—22no—
162C2×#63227—41no—
163C2×#63227—41no—
164C2×#63227—41no—
165C2×#63227—41no—
166C2×#63227C2×C414yescomplemented
167C2×#63225—22no—
168C2×#63225—22no—
169C2×#63225C2×C414yescomplemented
170#10587502—22no—
171#10587502—22no—
172#10587502—22no—
173#10587502—22no—
174#10587502—22no—
175#10587502—22no—
176#10587502—22no—
177#10587502—22no—
178#10587502—22no—
179#10587502—22no—
180#10587502—22no—
181#10587502—41no—
182#10587502—41no—
183#10587502D414yescomplemented
184C24×C17—21no—
185C24×C17—21no—
186C24×C17—21no—
187C24×C17—21no—
188C24×C17—21no—
189C24×C17—21no—
190C24×C17—21no—
191C24×C17—21no—
192C24×C17—21no—
193C24×C17—21no—
194C24×C17—21no—
195C24×C17—21no—
196C24×C17—21no—
197C24×C17—21no—
198C24×C17—21no—
199C24×C17—21no—
200C24×C17—21no—
201C24×C17—21no—
202C24×C17—21no—
203C24×C17—21no—
204C24×C17C22×C412yes—
205C24×C17C22×C412yes—
206C24×C17C2×D412yes—
207C24×C17C2×D412yes—
208C24×C17C2×D412yes—
209C24×C17C2×D412yes—
210C24×C17C2×D412yes—
211C24×C17C2×D412yes—
212C24×C17#4112yes—
213C24×C17#4112yes—
214C24×C17C2411yescharacteristic
215C23×D17—21no—
216C23×D17—21no—
217C23×D17—21no—
218C23×D17—21no—
219C23×D17—21no—
220C23×D17—21no—
221C23×D17—21no—
222C23×D17—21no—
223C23×D17—21no—
224C23×D17—21no—
225C23×D17—21no—
226C23×D17—21no—
227C23×D17—21no—
228C23×D17—21no—
229C23×D17C22×C412yes—
230C2×D4×C17—28no—
231C2×D4×C17—28no—
232C2×D4×C17—28no—
233C2×D4×C17—28no—
234C2×D4×C17—28no—
235C2×D4×C17—28no—
236C2×D4×C17C22⋊C4116yescomplemented
237C22×C4×C17—21no—
238C22×C4×C17—21no—
239C22×C4×C17—21no—
240C22×C4×C17—21no—
241C22×C4×C17—21no—
242C22×C4×C17—21no—
243C22×C4×C17—21no—
244C22×C4×C17—21no—
245C22×C4×C17—28no—
246C22×C4×C17—28no—
247C22×C4×C17—21no—
248C22×C4×C17—21no—
249C22×C4×C17—21no—
250C22×C4×C17—21no—
251C22×C4×C17—21no—
252C22×C4×C17—21no—
253C22×C4×C17—21no—
254C22×C4×C17—21no—
255C22×C4×C17—21no—
256C22×C4×C17—21no—
257C22×C4×C17—21no—
258C22×C4×C17—21no—
259C22×C4×C17—21no—
260C22×C4×C17—21no—
261C22×C4×C17—21no—
262C22×C4×C17—21no—
263C22×C4×C17—21no—
264C22×C4×C17—21no—
265C22×C4×C17—28no—
266C22×C4×C17—44no—
267C22×C4×C17—44no—
268C22×C4×C17—44no—
269C22×C4×C17—44no—
270C22×C4×C17—44no—
271C22×C4×C17—44no—
272C22×C4×C17—44no—
273C22×C4×C17—44no—
274C22×C4×C17—44no—
275C22×C4×C17—44no—
276C22×C4×C17—44no—
277C22×C4×C17C22×C412yes—
278C22×C4×C17C2×D412yes—
279C22×C4×C17C2×D412yes—
280C22×C4×C17C2×D412yes—
281C22×C4×C17C2×D412yes—
282C22×C4×C17C2×D412yes—
283C22×C4×C17C2×D412yes—
284C22×C4×C17C2×D412yes—
285C22×C4×C17#4112yes—
286C2×C22⋊D17—28no—
287C2×C22⋊D17—28no—
288C2×C22⋊D17—28no—
289C2×C22⋊D17—28no—
290C2×C22⋊D17—28no—
291C2×C22⋊D17—44no—
292C2×C22⋊D17—44no—
293C2×C22⋊D17—44no—
294C2×C22⋊D17—44no—
295C2×C22⋊D17—44no—
296C2×C22⋊D17—44no—
297C2×C22⋊D17—44no—
298C2×C22⋊D17—44no—
299C2×C22⋊D17—44no—
300C22×Dic17—21no—
301C22×Dic17—21no—
302C22×Dic17—21no—
303C22×Dic17—21no—
304C22×Dic17—28no—
305C22×Dic17—28no—
306C22×Dic17—21no—
307C22×Dic17—21no—
308C22×Dic17—21no—
309C22×Dic17—21no—
310C22×Dic17—21no—
311C22×Dic17—21no—
312C22×Dic17—21no—
313C22×Dic17—21no—
314C22×Dic17—21no—
315C22×Dic17—21no—
316C22×Dic17—21no—
317C22×Dic17—21no—
318C22×Dic17—21no—
319C22×Dic17—21no—
320C22×Dic17—21no—
321C22×Dic17—21no—
322C22×Dic17—21no—
323C22×Dic17—21no—
324C22×Dic17—21no—
325C22×Dic17—21no—
326C22×Dic17—21no—
327C22×Dic17—21no—
328C22×Dic17—21no—
329C22×Dic17—21no—
330C22×Dic17—28no—
331C22×Dic17—21no—
332C22×Dic17—21no—
333C22×Dic17—21no—
334C22×Dic17—21no—
335C22×Dic17—21no—
336C22×Dic17—21no—
337C22×Dic17—21no—
338C22×Dic17—21no—
339C22×Dic17—21no—
340C22×Dic17—21no—
341C22×Dic17—21no—
342C22×Dic17—21no—
343C22×Dic17—21no—
344C22×Dic17—21no—
345C22×Dic17—44no—
346C22×Dic17—44no—
347C22×Dic17—44no—
348C22×Dic17—44no—
349C22×Dic17—44no—
350C22×Dic17—44no—
351C22×Dic17—44no—
352C22×Dic17—44no—
353C22×Dic17—44no—
354C22×Dic17—44no—
355C22×Dic17—44no—
356C22×Dic17C22×C412yes—
357C22×Dic17C22×C412yes—
358C22×Dic17C22×C412yes—
359C22×Dic17C2×D412yes—
360C22×Dic17C2×D412yes—
361C22×Dic17#4112yes—
362C22×Dic17#4112yes—
363C4⋊C4×C17—28no—
364C22⋊C4×C17—28no—
365C22⋊C4×C17—28no—
366C42×C17—28no—
367C22⋊Dic17—28no—
368C22⋊Dic17—44no—
369C22⋊Dic17—44no—
370C22⋊Dic17—44no—
371#63227—28no—
372#63227—44no—
373#63227—44no—
374#63227—44no—
375#63227—44no—
376#63225—28no—
377#14023—171nomaximal, Sylow
378C23×C17—22no—
379C23×C17—22no—
380C23×C17—22no—
381C23×C17—22no—
382C23×C17—22no—
383C23×C17—22no—
384C23×C17—22no—
385C23×C17—22no—
386C23×C17—22no—
387C23×C17—22no—
388C23×C17—22no—
389C23×C17—22no—
390C23×C17—22no—
391C23×C17—22no—
392C23×C17—22no—
393C23×C17—22no—
394C23×C17—22no—
395C23×C17—22no—
396C23×C17—22no—
397C23×C17—22no—
398C23×C17—22no—
399C23×C17—22no—
400C23×C17—22no—
401C23×C17—22no—
402C23×C17—22no—
403C23×C17—22no—
404C23×C17—22no—
405C23×C17—22no—
406C23×C17—22no—
407C23×C17—22no—
408C23×C17—22no—
409C23×C17—22no—
410C23×C17—22no—
411C23×C17—22no—
412C23×C17—22no—
413C23×C17—22no—
414C23×C17—22no—
415C23×C17—22no—
416C23×C17—22no—
417C23×C17—22no—
418C23×C17—22no—
419C23×C17—22no—
420C23×C17—22no—
421C23×C17—22no—
422C23×C17—22no—
423C23×C17—22no—
424C23×C17—41no—
425C23×C17—41no—
426C23×C17—41no—
427C23×C17—41no—
428C23×C17—41no—
429C23×C17—41no—
430C23×C17—41no—
431C23×C17—41no—
432C23×C17—41no—
433C23×C17—41no—
434C23×C17—41no—
435C23×C17—41no—
436C23×C17—41no—
437C23×C17—41no—
438C23×C17—41no—
439C23×C17—41no—
440C23×C17C2×C22⋊C414yes—
441C23×C17C2×C22⋊C414yes—
442C23×C17C4×D414yes—
443C23×C17C4×D414yes—
444C23×C17#12014yes—
445C23×C17#12114yes—
446C23×C17#12114yes—
447C23×C17#12314yes—
448C23×C17C23×C411yescharacteristic
449C23×C17C22×D411yescharacteristic
450C23×C17C22×D411yescharacteristic
451C23×C17C22×D411yescharacteristic
452C23×C17C22×D411yescharacteristic
453C23×C17C22×D411yescharacteristic
454C23×C17C2×#4111yescharacteristic
455C23×C17C2×#4111yescharacteristic
456C23×C17C2×#4111yescharacteristic
457C23×C17C2×#4111yescharacteristic
458C23×C17C2×#4111yescharacteristic
459C23×C17H(5,𝔽2)11yescharacteristic
460C23×C17H(5,𝔽2)11yescharacteristic
461C23×C17H(5,𝔽2)11yescharacteristic
462C23×C172−1+411yescharacteristic
463C22×D17—22no—
464C22×D17—22no—
465C22×D17—22no—
466C22×D17—22no—
467C22×D17—22no—
468C22×D17—22no—
469C22×D17—22no—
470C22×D17—41no—
471C22×D17—41no—
472C22×D17—41no—
473C22×D17—41no—
474C22×D17—41no—
475C22×D17—41no—
476C22×D17—41no—
477C22×D17—41no—
478C22×D17—41no—
479C22×D17—41no—
480C22×D17—41no—
481C22×D17—41no—
482C22×D17—41no—
483C22×D17—41no—
484C22×D17—41no—
485C22×D17—41no—
486C22×D17—41no—
487C22×D17—41no—
488C22×D17—41no—
489C22×D17—41no—
490C22×D17—41no—
491C22×D17—41no—
492C22×D17—41no—
493C22×D17—41no—
494C22×D17—41no—
495C22×D17—41no—
496C22×D17—41no—
497C22×D17—41no—
498D4×C17—232no—
499C2×C4×C17—22no—
500C2×C4×C17—22no—
501C2×C4×C17—22no—
502C2×C4×C17—22no—
503C2×C4×C17—22no—
504C2×C4×C17—22no—
505C2×C4×C17—22no—
506C2×C4×C17—22no—
507C2×C4×C17—22no—
508C2×C4×C17—22no—
509C2×C4×C17—22no—
510C2×C4×C17—22no—
511C2×C4×C17—22no—
512C2×C4×C17—22no—
513C2×C4×C17—22no—
514C2×C4×C17—22no—
515C2×C4×C17—22no—
516C2×C4×C17—22no—
517C2×C4×C17—22no—
518C2×C4×C17—22no—
519C2×C4×C17—22no—
520C2×C4×C17—416no—
521C2×C4×C17—416no—
522C2×C4×C17—41no—
523C2×C4×C17—41no—
524C2×C4×C17—41no—
525C2×C4×C17—41no—
526C2×C4×C17—41no—
527C2×C4×C17—41no—
528C2×C4×C17—41no—
529C2×C4×C17—41no—
530C2×C4×C17—41no—
531C2×C4×C17—41no—
532C2×C4×C17—41no—
533C2×C4×C17—41no—
534C2×C4×C17C2×C22⋊C414yes—
535C2×C4×C17#12114yescomplemented
536C22⋊D17—416no—
537C22⋊D17—416no—
538C2×Dic17—22no—
539C2×Dic17—22no—
540C2×Dic17—22no—
541C2×Dic17—22no—
542C2×Dic17—22no—
543C2×Dic17—22no—
544C2×Dic17—22no—
545C2×Dic17—22no—
546C2×Dic17—22no—
547C2×Dic17—22no—
548C2×Dic17—22no—
549C2×Dic17—22no—
550C2×Dic17—22no—
551C2×Dic17—22no—
552C2×Dic17—22no—
553C2×Dic17—22no—
554C2×Dic17—22no—
555C2×Dic17—22no—
556C2×Dic17—416no—
557C2×Dic17—416no—
558C2×Dic17—41no—
559C2×Dic17—41no—
560C2×Dic17—41no—
561C2×Dic17—41no—
562C2×Dic17—41no—
563C2×Dic17—41no—
564C2×Dic17—41no—
565C2×Dic17—41no—
566C2×Dic17—41no—
567C2×Dic17—41no—
568C2×Dic17—41no—
569C2×Dic17—41no—
570C2×Dic17—41no—
571C2×Dic17—41no—
572C2×Dic17—41no—
573C2×Dic17—41no—
574C2×Dic17—41no—
575C2×Dic17—41no—
576C2×Dic17—41no—
577C2×Dic17—41no—
578C2×Dic17—41no—
579C2×Dic17—41no—
580C2×Dic17—41no—
581C2×Dic17—41no—
582C2×Dic17—41no—
583C2×Dic17—41no—
584C2×Dic17—41no—
585C2×Dic17—41no—
586C2×Dic17—41no—
587C2×Dic17—41no—
588C2×Dic17C4×D414yescomplemented
589C22×#121—171no—
590C22×C4×D4D1711yescharacteristic, complemented
591C2×#386—171no—
592C2×#386—171no—
593C2×#386—171no—
594C2×#386—171no—
595C22×#95—171no—
596#1441—171no—
597#1440—171no—
598#1439—171no—
599#1438—171no—
600#1437—171no—
601#1436—171no—
602C22⋊#95—171no—
603C22⋊#95—171no—
604C22×C17—24no—
605C22×C17—24no—
606C22×C17—24no—
607C22×C17—24no—
608C22×C17—24no—
609C22×C17—24no—
610C22×C17—24no—
611C22×C17—24no—
612C22×C17—24no—
613C22×C17—24no—
614C22×C17—24no—
615C22×C17—24no—
616C22×C17—24no—
617C22×C17—24no—
618C22×C17—24no—
619C22×C17—24no—
620C22×C17—24no—
621C22×C17—42no—
622C22×C17—42no—
623C22×C17—42no—
624C22×C17—42no—
625C22×C17—42no—
626C22×C17—42no—
627C22×C17—42no—
628C22×C17—42no—
629C22×C17—42no—
630C22×C17—42no—
631C22×C17—42no—
632C22×C17—42no—
633C22×C17#38618yescomplemented
634C22×C17C22×C22⋊C411yescharacteristic
635C22×C17C2×C4×D411yescharacteristic
636C22×C17C2×C4×D411yescharacteristic
637C22×C17C2×C4×D411yescharacteristic
638C22×C17C4×#4111yescharacteristic
639C22×C17#51811yescharacteristic
640C22×C17#52011yescharacteristic
641C22×C17C2×#12011yescharacteristic
642C22×C17C2×#12111yescharacteristic
643C22×C17C2×#12111yescharacteristic
644C22×C17C2×#12111yescharacteristic
645C22×C17C2×#12311yescharacteristic
646C22×C17#52511yescharacteristic
647C22×C17#52911yescharacteristic
648C22×C17#53211yescharacteristic
649C22×C17#53411yescharacteristic
650C22×C17#53711yescharacteristic
651C22×C17#53811yescharacteristic
652C22×C17#53911yescharacteristic
653C22×C17D4211yescharacteristic
654C22×C17D4211yescharacteristic
655C22×C17D4211yescharacteristic
656C22×C17#54611yescharacteristic
657C22×C17#54611yescharacteristic
658C22×C17#54611yescharacteristic
659C22×C17#54611yescharacteristic
660C22×C17#54611yescharacteristic
661C22×C17#54611yescharacteristic
662C22×C17#54711yescharacteristic
663C22×C17#54711yescharacteristic
664C22×C17#54711yescharacteristic
665C22×C17#54811yescharacteristic
666C22×C17#55311yescharacteristic
667C22×C17#55311yescharacteristic
668C22×C17#55311yescharacteristic
669C2×D17—42no—
670C2×D17—42no—
671C2×D17—42no—
672C2×D17—42no—
673C2×D17—42no—
674C2×D17—42no—
675C2×D17—42no—
676C2×D17—81no—
677C2×D17—81no—
678C2×D17—81no—
679C2×D17—81no—
680C2×D17—81no—
681C2×D17—81no—
682C2×D17—81no—
683C2×D17—81no—
684C4×C17—24no—
685C4×C17—24no—
686C4×C17—42no—
687C4×C17—42no—
688C4×C17—42no—
689Dic17—24no—
690Dic17—42no—
691Dic17—42no—
692Dic17—42no—
693Dic17—42no—
694Dic17—81no—
695Dic17—81no—
696C23×D4—171no—
697C23×D4—171no—
698C23×D4C2×D1711yescharacteristic
699C24×C4—171no—
700C24×C4—171no—
701C24×C4C2×D1711yescharacteristic
702C24×C4C2×D1711yescharacteristic
703C2×#121—178no—
704C2×#121—344no—
705C2×#121—344no—
706C2×C4×D4—24no—
707C2×C4×D4—24no—
708C2×C4×D4—24no—
709C22×C4⋊C4—171no—
710C22×C4⋊C4C2×D1711yescharacteristic
711C22×C22⋊C4—171no—
712C22×C22⋊C4—171no—
713C22×C22⋊C4—171no—
714C22×C22⋊C4—171no—
715C22×C22⋊C4—171no—
716C22×C22⋊C4—171no—
717C22×C22⋊C4—171no—
718C22×C22⋊C4—171no—
719C22×C22⋊C4—171no—
720C22×C22⋊C4C2×D1711yescharacteristic
721C22×C22⋊C4C2×D1711yescharacteristic
722C22×C42C2×D1711yescharacteristic
723#386—344no—
724#386—344no—
725#386—344no—
726#386—344no—
727C2×#95—171no—
728C2×#95—171no—
729C2×#95—171no—
730C2×#95—171no—
731C2×#95—171no—
732C2×#95—171no—
733C2×#95—171no—
734C2×#95—171no—
735C2×#95—171no—
736C2×#95—171no—
737C2×#95—171no—
738C2×#95—171no—
739C2×#95—171no—
740C2×#95—171no—
741C2×#95—344no—
742C2×C17—28no—
743C2×C17—44no—
744C2×C17C2×#38611yescharacteristic
745C2×C17C4×#12111yescharacteristic
746C2×C17#232511yescharacteristic
747C2×C17D4×C22⋊C411yescharacteristic
748C2×C17#233911yescharacteristic
749C2×C17#236111yescharacteristic
750C2×C17#236411yescharacteristic
751C2×C17#241011yescharacteristic
752C2×C17#241611yescharacteristic
753C2×C17#242411yescharacteristic
754C2×C17#242511yescharacteristic
755C2×C17#243011yescharacteristic
756C2×C17#244311yescharacteristic
757C2×C17#244411yescharacteristic
758C2×C17#254311yescharacteristic
759D17—82no—
760C25—171no—
761C25C22×D1711yescharacteristic
762C25C22×D1711yescharacteristic
763C22×D4—22no—
764C22×D4—22no—
765C22×D4—22no—
766C22×D4—22no—
767C22×D4—174no—
768C22×D4—174no—
769C22×D4—342no—
770C22×D4—342no—
771C22×D4—342no—
772C22×D4—342no—
773C22×D4—342no—
774C22×D4—342no—
775C22×D4—342no—
776C22×D4—342no—
777C22×D4—342no—
778C22×D4—342no—
779C22×D4—681no—
780C22×D4—681no—
781C22×D4C4×D1714yes—
782C22×D4D6814yes—
783C22×D4C22⋊D1714yes—
784C23×C4—22no—
785C23×C4—22no—
786C23×C4—22no—
787C23×C4—22no—
788C23×C4—22no—
789C23×C4—22no—
790C23×C4—22no—
791C23×C4—22no—
792C23×C4—22no—
793C23×C4—41no—
794C23×C4—41no—
795C23×C4—41no—
796C23×C4—41no—
797C23×C4—171no—
798C23×C4—171no—
799C23×C4—171no—
800C23×C4—171no—
801C23×C4—171no—
802C23×C4—174no—
803C23×C4—171no—
804C23×C4—171no—
805C23×C4—342no—
806C23×C4—342no—
807C23×C4—342no—
808C23×C4—342no—
809C23×C4—342no—
810C23×C4—342no—
811C23×C4—342no—
812C23×C4—342no—
813C23×C4—342no—
814C23×C4—681no—
815C23×C4—681no—
816C23×C4—681no—
817C23×C4—681no—
818C23×C4C22⋊D1714yescomplemented
819C23×C4C22×D1711yescharacteristic
820C23×C4C22×D1711yescharacteristic
821C23×C4C22×D1711yescharacteristic
822C23×C4C22×D1711yescharacteristic
823C23×C4C22×D1711yescharacteristic
824#121—3432no—
825C4×D4—232no—
826C2×C4⋊C4—22no—
827C2×C4⋊C4—22no—
828C2×C4⋊C4—22no—
829C2×C4⋊C4—174no—
830C2×C4⋊C4—342no—
831C2×C4⋊C4—342no—
832C2×C22⋊C4—22no—
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—174no—
838C2×C22⋊C4—174no—
839C2×C22⋊C4—342no—
840C2×C22⋊C4—342no—
841C2×C22⋊C4—342no—
842C2×C22⋊C4—342no—
843C2×C22⋊C4—342no—
844C2×C22⋊C4—342no—
845C2×C22⋊C4—342no—
846C2×C22⋊C4—342no—
847C2×C22⋊C4—342no—
848C2×C22⋊C4—342no—
849C2×C22⋊C4—342no—
850C2×C22⋊C4—342no—
851C2×C22⋊C4—342no—
852C2×C22⋊C4—342no—
853C2×C22⋊C4—342no—
854C2×C22⋊C4—342no—
855C2×C22⋊C4—342no—
856C2×C22⋊C4—342no—
857C2×C22⋊C4—342no—
858C2×C22⋊C4—681no—
859C2×C22⋊C4—681no—
860C2×C22⋊C4—681no—
861C2×C22⋊C4—681no—
862C2×C22⋊C4—681no—
863C2×C22⋊C4—681no—
864C2×C22⋊C4C22⋊D1714yescomplemented
865C2×C42—22no—
866C2×C42—22no—
867C2×C42—22no—
868#95—174no—
869#95—342no—
870#95—342no—
871#95—342no—
872#95—342no—
873#95—342no—
874#95—342no—
875#95—342no—
876#95—342no—
877#95—342no—
878#95—342no—
879#95—342no—
880#95—681no—
881#95—681no—
882C17#1402311yescharacteristic, complemented, Sylow
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901C24—21no—
902C24—21no—
903C24—172no—
904C24—341no—
905C24—341no—
906C24—341no—
907C24—341no—
908C24—341no—
909C24—341no—
910C24—341no—
911C24—341no—
912C24—341no—
913C24—341no—
914C24—341no—
915C24—341no—
916C24—341no—
917C24—341no—
918C24C2×C4×D1712yes—
919C24C2×C4×D1712yes—
920C24C2×D6812yes—
921C24C2×D6812yes—
922C24#6325212yes—
923C24#6325212yes—
924C24C2×C22⋊D1712yes—
925C24C2×C22⋊D1712yes—
926C24C2×C22⋊D1712yes—
927C24C2×C22⋊D1712yes—
928C24C23×D1711yescharacteristic
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—28no—
932C2×D4—28no—
933C2×D4—28no—
934C2×D4—28no—
935C2×D4—348no—
936C2×D4—348no—
937C2×D4—348no—
938C2×D4—348no—
939C2×D4—348no—
940C2×D4—684no—
941C2×D4—684no—
942C2×D4—684no—
943C2×D4—684no—
944C2×D4—684no—
945C2×D4—684no—
946C2×D4—684no—
947C2×D4—684no—
948C2×D4—684no—
949C2×D4#63227116yescomplemented
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—28no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—28no—
978C22×C4—28no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—172no—
991C22×C4—172no—
992C22×C4—172no—
993C22×C4—172no—
994C22×C4—172no—
995C22×C4—172no—
996C22×C4—172no—
997C22×C4—348no—
998C22×C4—341no—
999C22×C4—341no—
1000C22×C4—341no—
1001C22×C4—341no—
1002C22×C4—348no—
1003C22×C4—341no—
1004C22×C4—341no—
1005C22×C4—341no—
1006C22×C4—341no—
1007C22×C4—341no—
1008C22×C4—341no—
1009C22×C4—341no—
1010C22×C4—341no—
1011C22×C4—341no—
1012C22×C4—341no—
1013C22×C4—341no—
1014C22×C4—341no—
1015C22×C4—341no—
1016C22×C4—341no—
1017C22×C4—341no—
1018C22×C4—341no—
1019C22×C4—341no—
1020C22×C4—341no—
1021C22×C4—341no—
1022C22×C4—341no—
1023C22×C4—341no—
1024C22×C4—341no—
1025C22×C4—341no—
1026C22×C4—341no—
1027C22×C4—348no—
1028C22×C4—341no—
1029C22×C4—341no—
1030C22×C4—341no—
1031C22×C4—341no—
1032C22×C4—341no—
1033C22×C4—341no—
1034C22×C4—341no—
1035C22×C4—341no—
1036C22×C4—341no—
1037C22×C4—341no—
1038C22×C4—341no—
1039C22×C4—341no—
1040C22×C4—341no—
1041C22×C4—341no—
1042C22×C4—684no—
1043C22×C4—684no—
1044C22×C4—684no—
1045C22×C4—684no—
1046C22×C4—684no—
1047C22×C4—684no—
1048C22×C4—684no—
1049C22×C4—684no—
1050C22×C4—684no—
1051C22×C4—684no—
1052C22×C4—684no—
1053C22×C4C2×C4×D1712yes—
1054C22×C4C2×D6812yes—
1055C22×C4D4×D1712yes—
1056C22×C4#6325412yes—
1057C22×C4C2×C22⋊D1712yes—
1058C22×C4C2×C22⋊D1712yes—
1059C22×C4C2×C22⋊D1712yes—
1060C22×C4C2×C22⋊D1712yes—
1061C22×C4C2×C22⋊D1712yes—
1062C4⋊C4—28no—
1063C4⋊C4—348no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—348no—
1067C22⋊C4—348no—
1068C22⋊C4—684no—
1069C22⋊C4—684no—
1070C22⋊C4—684no—
1071C22⋊C4—684no—
1072C22⋊C4—684no—
1073C22⋊C4—684no—
1074C22⋊C4—684no—
1075C42—28no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—342no—
1139C23—342no—
1140C23—342no—
1141C23—342no—
1142C23—342no—
1143C23—342no—
1144C23—342no—
1145C23—681no—
1146C23—681no—
1147C23—681no—
1148C23—681no—
1149C23—681no—
1150C23—681no—
1151C23—681no—
1152C23—681no—
1153C23—681no—
1154C23—681no—
1155C23—681no—
1156C23—681no—
1157C23—681no—
1158C23—681no—
1159C23—681no—
1160C23—681no—
1161C23—681no—
1162C23—681no—
1163C23—681no—
1164C23—681no—
1165C23—681no—
1166C23—681no—
1167C23—681no—
1168C23—681no—
1169C23—681no—
1170C23—681no—
1171C23—681no—
1172C23—681no—
1173C23C2×#6322714yes—
1174C23C2×#6322714yes—
1175C23C4×C22⋊D1714yes—
1176C23C4×C22⋊D1714yes—
1177C23#1058761514yes—
1178C23#1058761614yes—
1179C23#1058761614yes—
1180C23#1058763914yes—
1181C23C22×C4×D1711yescharacteristic
1182C23C22×D6811yescharacteristic
1183C23C2×#6325211yescharacteristic
1184C23C2×#6325211yescharacteristic
1185C23C2×D4×D1711yescharacteristic
1186C23C2×#6325411yescharacteristic
1187C23#1058769111yescharacteristic
1188C23#1058769111yescharacteristic
1189C23#41×D1711yescharacteristic
1190C23#41×D1711yescharacteristic
1191C23#1058769611yescharacteristic
1192C23#1058769711yescharacteristic
1193C23C22×C22⋊D1711yescharacteristic
1194C23C22×C22⋊D1711yescharacteristic
1195C23C22×C22⋊D1711yescharacteristic
1196D4—232no—
1197D4—6816no—
1198D4—6816no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—416no—
1221C2×C4—416no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—174no—
1235C2×C4—342no—
1236C2×C4—342no—
1237C2×C4—342no—
1238C2×C4—342no—
1239C2×C4—342no—
1240C2×C4—342no—
1241C2×C4—342no—
1242C2×C4—342no—
1243C2×C4—342no—
1244C2×C4—342no—
1245C2×C4—342no—
1246C2×C4—342no—
1247C2×C4—342no—
1248C2×C4—342no—
1249C2×C4—342no—
1250C2×C4—342no—
1251C2×C4—342no—
1252C2×C4—342no—
1253C2×C4—6816no—
1254C2×C4—6816no—
1255C2×C4—681no—
1256C2×C4—681no—
1257C2×C4—681no—
1258C2×C4—681no—
1259C2×C4—681no—
1260C2×C4—681no—
1261C2×C4—681no—
1262C2×C4—681no—
1263C2×C4—681no—
1264C2×C4—681no—
1265C2×C4—681no—
1266C2×C4—681no—
1267C2×C4—681no—
1268C2×C4—681no—
1269C2×C4—681no—
1270C2×C4—681no—
1271C2×C4—681no—
1272C2×C4—681no—
1273C2×C4—681no—
1274C2×C4—681no—
1275C2×C4—681no—
1276C2×C4—681no—
1277C2×C4—681no—
1278C2×C4—681no—
1279C2×C4—681no—
1280C2×C4—681no—
1281C2×C4—681no—
1282C2×C4—681no—
1283C2×C4—681no—
1284C2×C4—681no—
1285C2×C4C2×#6322714yes—
1286C2×C4#1058762514yescomplemented
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—24no—
1300C22—24no—
1301C22—24no—
1302C22—24no—
1303C22—24no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—682no—
1317C22—682no—
1318C22—682no—
1319C22—682no—
1320C22—682no—
1321C22—682no—
1322C22—682no—
1323C22—1361no—
1324C22—1361no—
1325C22—1361no—
1326C22—1361no—
1327C22—1361no—
1328C22—1361no—
1329C22—1361no—
1330C22—1361no—
1331C22#1176268818yescomplemented
1332C22C22×#6322711yescharacteristic
1333C22C4×D4×D1711yescharacteristic
1334C22C2×C4×C22⋊D1711yescharacteristic
1335C22C2×C4×C22⋊D1711yescharacteristic
1336C22C4×#6325411yescharacteristic
1337C22#1176328111yescharacteristic
1338C22#1176328811yescharacteristic
1339C22C2×#1058763911yescharacteristic
1340C22C2×#1058762511yescharacteristic
1341C22C2×#1058761611yescharacteristic
1342C22C2×#1058761611yescharacteristic
1343C22C2×#1058761511yescharacteristic
1344C22#1176331811yescharacteristic
1345C22#1176333911yescharacteristic
1346C22#1176335511yescharacteristic
1347C22#1176336811yescharacteristic
1348C22#1176338711yescharacteristic
1349C22#1176339211yescharacteristic
1350C22#1176340111yescharacteristic
1351C22D4×C22⋊D1711yescharacteristic
1352C22D4×C22⋊D1711yescharacteristic
1353C22D4×D6811yescharacteristic
1354C22#1176344711yescharacteristic
1355C22#1176344711yescharacteristic
1356C22#1176345311yescharacteristic
1357C22#1176345311yescharacteristic
1358C22#1176345411yescharacteristic
1359C22#1176345411yescharacteristic
1360C22#1176345811yescharacteristic
1361C22#1176345811yescharacteristic
1362C22#1176346311yescharacteristic
1363C22#1176346811yescharacteristic
1364C22#1176350511yescharacteristic
1365C22#1176350811yescharacteristic
1366C22#1176350811yescharacteristic
1367C4—24no—
1368C4—24no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—344no—
1373C4—682no—
1374C4—682no—
1375C4—682no—
1376C4—682no—
1377C4—1361no—
1378C4—1361no—
1379C2—28no—
1380C2—44no—
1381C2—1362no—
1382C2C2×#1176268811yescharacteristic
1383C2C4×#1058762511yescharacteristic
1384C2#1453148211yescharacteristic
1385C2D4×#6322711yescharacteristic
1386C2#1453160911yescharacteristic
1387C2#1453180111yescharacteristic
1388C2#1453182911yescharacteristic
1389C2#1453215811yescharacteristic
1390C2#1453222411yescharacteristic
1391C2#1453231411yescharacteristic
1392C2#1453232911yescharacteristic
1393C2#1453238811yescharacteristic
1394C2#1453251311yescharacteristic
1395C2#1453252811yescharacteristic
1396C2#1453374011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC22×C4×D4×C17C2
socle, cosocleC24×C17C24
prime radicalC22×#10587625C2
hypercenterC22×C4×D4D17
hypocenterC17#14023
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#11762689C2semidirect
3. C2×#11762688C2semidirect
4. C2×#11762688C2semidirect
5. C2×#11762686C2semidirect
6. C22×#10587502C2semidirect
7. #14527034C2semidirect
8. #14527031C2semidirect
9. #14527026C2semidirect
10. #14527023C2semidirect
11. #14527022C2semidirect
12. #14527017C2semidirect
13. #14527007C2semidirect
14. #14527006C2semidirect
15. C22×C4×D4×C17C2semidirect
22. C2×#10587625C4semidirect
85. C23×C4×C17D4semidirect
103. C22×C22⋊D17C2×C4semidirect
104. C22×C22⋊D17C2×C4semidirect
118. C23×Dic17C2×C4semidirect
135. C2×C22⋊C4×C17D4semidirect
150. C2×C22⋊Dic17C2×C4semidirect
166. C2×#63227C2×C4semidirect
169. C2×#63225C2×C4semidirect
183. #10587502D4semidirect
236. C2×D4×C17C22⋊C4semidirect
535. C2×C4×C17#121semidirect
588. C2×Dic17C4×D4semidirect
590. C22×C4×D4D17semidirect
633. C22×C17#386semidirect
818. C23×C4C22⋊D17semidirect
864. C2×C22⋊C4C22⋊D17semidirect
882. C17#14023semidirect
949. C2×D4#63227semidirect
1286. C2×C4#10587625semidirect
1331. C22#11762688semidirect

Maximal subgroups

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

subgroupindex
C22×#105876252
C2×#117626892
C2×#117626882
C2×#117626862
C22×#105875022
#145270342
#145270312
#145270262
#145270232
#145270222
#145270172
#145270072
#145270062
C22×C4×D4×C172
#1402317