Finite Group Databasebeta

← #16958754

Subgroups — #16958754

Order 4352.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587580C211yesmaximal, characteristic
2C2×#11762711C211yesmaximal, characteristic
3C2×#11762695C211yesmaximal, characteristic, complemented
4C2×C4×#63227C211yesmaximal, characteristic, complemented
5#14527038C211yesmaximal, characteristic, complemented
6#14527026C211yesmaximal, characteristic, complemented
7#14527026C211yesmaximal, characteristic, complemented
8#14527024C211yesmaximal, characteristic
9#14527022C211yesmaximal, characteristic, complemented
10#14527022C211yesmaximal, characteristic, complemented
11#14527022C211yesmaximal, characteristic, complemented
12#14527020C211yesmaximal, characteristic, complemented
13#14527017C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C2×C4×C4⋊C4×C17C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C2×#10587580—24no—
19C2×#10587580—24no—
20C2×#10587580C418yescomplemented
21C22×C4⋊Dic17C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35#11762711—24no—
36#11762695—24no—
37C4×#63227—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
50C22×C4⋊C4×C17C2211yescharacteristic
51C22×C4⋊C4×C17C2211yescharacteristic
52C22×C42×C17C2211yescharacteristic
53C22×C42×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C4×C4⋊C4×C17—24no—
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C24×D17C2311yescharacteristic
59C24×D17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C22×D68—22no—
74C22×D68—22no—
75C22×D68—22no—
76C22×D68—22no—
77C22×D68—41no—
78C22×D68—41no—
79C22×D68C2×C414yes—
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—22no—
83C22×C4×D17—22no—
84C22×C4×D17—41no—
85C22×C4×D17—41no—
86C22×C4×D17C2×C414yes—
87C2×C4⋊C4×C17—22no—
88C2×C4⋊C4×C17—22no—
89C2×C4⋊C4×C17—22no—
90C2×C4⋊C4×C17C2×C414yes—
91C2×C4⋊C4×C17D414yes—
92C2×C4⋊C4×C17D414yes—
93C2×C42×C17—22no—
94C2×C42×C17—22no—
95C2×C42×C17—22no—
96C2×C42×C17—22no—
97C2×C42×C17—22no—
98C2×C42×C17—22no—
99C2×C42×C17—22no—
100C2×C42×C17—41no—
101C2×C42×C17—41no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—22no—
105C2×#63227—22no—
106C2×#63227—22no—
107C2×#63227—22no—
108C2×#63227—22no—
109C2×#63227—22no—
110C2×#63227—22no—
111C2×#63227—22no—
112C2×#63227—22no—
113C2×#63227—22no—
114C2×#63227—22no—
115C2×#63227—22no—
116C2×#63227—22no—
117C2×#63227—22no—
118C2×#63227—22no—
119C2×#63227—22no—
120C2×#63227—22no—
121C2×#63227—22no—
122C2×#63227—22no—
123C2×#63227—22no—
124C2×#63227—22no—
125C2×#63227—41no—
126C2×#63227—41no—
127C2×#63227—41no—
128C2×#63227—41no—
129C2×#63227—41no—
130C2×#63227—41no—
131C2×#63227C2×C414yes—
132C2×#63227C2×C414yes—
133C2×#63227C2×C414yes—
134C2×#63227D414yes—
135C2×C4⋊Dic17—22no—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17—41no—
138C2×#63225—22no—
139C2×#63225—22no—
140C2×#63225C2×C414yes—
141C2×C4×Dic17—22no—
142C2×C4×Dic17—22no—
143C2×C4×Dic17—41no—
144#10587580—232no—
145C17×#95—22no—
146C17×#95—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—22no—
150#10587502—22no—
151#10587502—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—22no—
155#10587502—41no—
156#10587502—41no—
157#10587502—41no—
158#10587502—41no—
159C24×C17C2411yescharacteristic
160C23×D17—21no—
161C23×D17—21no—
162C23×D17—21no—
163C23×D17—21no—
164C23×D17—21no—
165C23×D17—21no—
166C23×D17—21no—
167C23×D17—21no—
168C23×D17—21no—
169C23×D17—21no—
170C23×D17—21no—
171C23×D17—21no—
172C23×D17—21no—
173C23×D17—21no—
174C23×D17—21no—
175C23×D17—21no—
176C23×D17—21no—
177C23×D17—21no—
178C23×D17—21no—
179C23×D17—21no—
180C23×D17—21no—
181C23×D17—21no—
182C23×D17—21no—
183C23×D17—21no—
184C23×D17—21no—
185C23×D17—21no—
186C23×D17C22×C412yes—
187C23×D17C22×C412yes—
188C23×D17C2×D412yes—
189C23×D17#4112yes—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17C22×C412yes—
225C22×C4×C17C22×C412yes—
226C22×C4×C17C22×C412yes—
227C22×C4×C17C2×D412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17C2×D412yes—
230C22×C4×C17C2×D412yes—
231C22×C4×C17C2×D412yes—
232C22×C4×C17C2×D412yes—
233C22×C4×C17C2×D412yes—
234C22×C4×C17#4112yes—
235C22×C4×C17#4112yes—
236C22×C4×C17#4112yes—
237C22×C4×C17#4112yes—
238C22×C4×C17#4112yes—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17C22×C412yes—
278C22×Dic17C22×C412yes—
279C22×Dic17C2×D412yes—
280C22×Dic17#4112yes—
281C2×D68—28no—
282C2×D68—28no—
283C2×D68—44no—
284C2×D68—44no—
285C2×D68—44no—
286C2×D68—44no—
287C2×D68—44no—
288C2×C4×D17—28no—
289C2×C4×D17—28no—
290C2×C4×D17—44no—
291C2×C4×D17—44no—
292C2×C4×D17—44no—
293C2×C4×D17—44no—
294C2×C4×D17—44no—
295C4⋊C4×C17—28no—
296C4⋊C4×C17C22⋊C4116yescomplemented
297C42×C17—28no—
298C42×C17—44no—
299C42×C17—44no—
300#63227—28no—
301#63227—28no—
302#63227—28no—
303#63227—28no—
304#63227—28no—
305#63227—44no—
306#63227—44no—
307#63227—44no—
308#63227—44no—
309#63227—44no—
310#63227—44no—
311C4⋊Dic17—44no—
312#63225—28no—
313C4×Dic17—44no—
314#14095—171nomaximal, Sylow
315C23×C17C23×C411yescharacteristic
316C23×C17C22×D411yescharacteristic
317C23×C17C22×D411yescharacteristic
318C23×C17C22×D411yescharacteristic
319C23×C17C2×#4111yescharacteristic
320C23×C17C2×#4111yescharacteristic
321C23×C17C2×#4111yescharacteristic
322C23×C17C2×#4111yescharacteristic
323C23×C17C2×#4111yescharacteristic
324C23×C17C2×#4111yescharacteristic
325C23×C17C2×#4111yescharacteristic
326C23×C17H(5,𝔽2)11yescharacteristic
327C23×C17H(5,𝔽2)11yescharacteristic
328C23×C17H(5,𝔽2)11yescharacteristic
329C23×C172−1+411yescharacteristic
330C22×D17—22no—
331C22×D17—22no—
332C22×D17—22no—
333C22×D17—22no—
334C22×D17—22no—
335C22×D17—22no—
336C22×D17—22no—
337C22×D17—22no—
338C22×D17—22no—
339C22×D17—22no—
340C22×D17—22no—
341C22×D17—22no—
342C22×D17—22no—
343C22×D17—22no—
344C22×D17—22no—
345C22×D17—22no—
346C22×D17—22no—
347C22×D17—22no—
348C22×D17—22no—
349C22×D17—22no—
350C22×D17—22no—
351C22×D17—22no—
352C22×D17—22no—
353C22×D17—22no—
354C22×D17—22no—
355C22×D17—41no—
356C22×D17—41no—
357C22×D17—41no—
358C22×D17—41no—
359C22×D17—41no—
360C22×D17—41no—
361C22×D17—41no—
362C22×D17—41no—
363C22×D17—41no—
364C22×D17—41no—
365C22×D17—41no—
366C22×D17—41no—
367C22×D17—41no—
368C22×D17—41no—
369C22×D17—41no—
370C22×D17—41no—
371C22×D17—41no—
372C22×D17—41no—
373C22×D17—41no—
374C22×D17—41no—
375C22×D17—41no—
376C22×D17—41no—
377C22×D17—41no—
378C22×D17—41no—
379C22×D17—41no—
380C22×D17—41no—
381C22×D17—41no—
382C22×D17—41no—
383C22×D17—41no—
384C22×D17—41no—
385C22×D17—41no—
386C22×D17—41no—
387C22×D17—41no—
388C22×D17—41no—
389C22×D17—41no—
390C22×D17—41no—
391C22×D17—41no—
392C22×D17—41no—
393C22×D17—41no—
394C22×D17—41no—
395C22×D17—41no—
396C22×D17—41no—
397C22×D17—41no—
398C22×D17—41no—
399C22×D17C4×D414yes—
400C2×C4×C17—22no—
401C2×C4×C17—22no—
402C2×C4×C17—22no—
403C2×C4×C17—22no—
404C2×C4×C17—22no—
405C2×C4×C17—22no—
406C2×C4×C17—22no—
407C2×C4×C17—22no—
408C2×C4×C17—22no—
409C2×C4×C17—22no—
410C2×C4×C17—22no—
411C2×C4×C17—22no—
412C2×C4×C17—22no—
413C2×C4×C17—22no—
414C2×C4×C17—22no—
415C2×C4×C17—22no—
416C2×C4×C17—22no—
417C2×C4×C17—22no—
418C2×C4×C17—22no—
419C2×C4×C17—22no—
420C2×C4×C17—22no—
421C2×C4×C17—22no—
422C2×C4×C17—22no—
423C2×C4×C17—22no—
424C2×C4×C17—22no—
425C2×C4×C17—22no—
426C2×C4×C17—22no—
427C2×C4×C17—22no—
428C2×C4×C17—22no—
429C2×C4×C17—22no—
430C2×C4×C17—22no—
431C2×C4×C17—22no—
432C2×C4×C17—22no—
433C2×C4×C17—41no—
434C2×C4×C17—41no—
435C2×C4×C17—41no—
436C2×C4×C17—41no—
437C2×C4×C17—41no—
438C2×C4×C17—41no—
439C2×C4×C17—41no—
440C2×C4×C17—41no—
441C2×C4×C17—41no—
442C2×C4×C17—41no—
443C2×C4×C17—41no—
444C2×C4×C17—41no—
445C2×C4×C17C2×C22⋊C414yes—
446C2×C4×C17C2×C22⋊C414yes—
447C2×C4×C17C2×C22⋊C414yes—
448C2×C4×C17#12314yescomplemented
449C2×Dic17—22no—
450C2×Dic17—22no—
451C2×Dic17—22no—
452C2×Dic17—22no—
453C2×Dic17—22no—
454C2×Dic17—22no—
455C2×Dic17—22no—
456C2×Dic17—22no—
457C2×Dic17—22no—
458C2×Dic17—22no—
459C2×Dic17—22no—
460C2×Dic17—22no—
461C2×Dic17—41no—
462C2×Dic17—41no—
463C2×Dic17—41no—
464C2×Dic17—41no—
465C2×Dic17—41no—
466C2×Dic17—41no—
467C2×Dic17—41no—
468C2×Dic17—41no—
469C2×Dic17—41no—
470C2×Dic17—41no—
471C2×Dic17—41no—
472C2×Dic17—41no—
473C2×Dic17—41no—
474C2×Dic17—41no—
475C2×Dic17—41no—
476C2×Dic17—41no—
477C2×Dic17—41no—
478C2×Dic17—41no—
479C2×Dic17—41no—
480C2×Dic17—41no—
481C2×Dic17—41no—
482C2×Dic17—41no—
483C2×Dic17—41no—
484C2×Dic17—41no—
485C2×Dic17—41no—
486C2×Dic17—41no—
487C2×Dic17—41no—
488C2×Dic17—41no—
489C2×Dic17—41no—
490C2×Dic17—41no—
491D68—416no—
492C4×D17—416no—
493C22×#123—171no—
494C2×#390—171no—
495C2×#387—171no—
496C2×C4×C4⋊C4D1711yescharacteristic, complemented
497C2×C4×C22⋊C4—171no—
498#1441—171no—
499#1439—171no—
500#1439—171no—
501#1438—171no—
502#1437—171no—
503#1437—171no—
504#1437—171no—
505#1437—171no—
506#1436—171no—
507C22⋊#95—171no—
508C22×C17C22×C22⋊C411yescharacteristic
509C22×C17C2×C4×D411yescharacteristic
510C22×C17C4×#4111yescharacteristic
511C22×C17C4×#4111yescharacteristic
512C22×C17C4×#4111yescharacteristic
513C22×C17#51811yescharacteristic
514C22×C17#52011yescharacteristic
515C22×C17C2×#12311yescharacteristic
516C22×C17#52511yescharacteristic
517C22×C17#52511yescharacteristic
518C22×C17#52511yescharacteristic
519C22×C17#52911yescharacteristic
520C22×C17#52911yescharacteristic
521C22×C17#53211yescharacteristic
522C22×C17#53211yescharacteristic
523C22×C17#53811yescharacteristic
524C22×C17#53911yescharacteristic
525C22×C17#54011yescharacteristic
526C22×C17#54211yescharacteristic
527C22×C17D4211yescharacteristic
528C22×C17D4211yescharacteristic
529C22×C17#54611yescharacteristic
530C22×C17#54611yescharacteristic
531C22×C17#54611yescharacteristic
532C22×C17#54711yescharacteristic
533C22×C17#54811yescharacteristic
534C22×C17#54811yescharacteristic
535C22×C17#55011yescharacteristic
536C22×C17#55011yescharacteristic
537C22×C17#55111yescharacteristic
538C22×C17#55111yescharacteristic
539C22×C17#55211yescharacteristic
540C22×C17#55311yescharacteristic
541C22×C17#55311yescharacteristic
542C22×C17#55911yescharacteristic
543C2×D17—24no—
544C2×D17—24no—
545C2×D17—24no—
546C2×D17—42no—
547C2×D17—42no—
548C2×D17—42no—
549C2×D17—42no—
550C2×D17—42no—
551C2×D17—42no—
552C2×D17—42no—
553C2×D17—42no—
554C2×D17—42no—
555C2×D17—42no—
556C2×D17—42no—
557C2×D17—42no—
558C2×D17—42no—
559C2×D17—42no—
560C2×D17—42no—
561C2×D17—42no—
562C2×D17—42no—
563C2×D17—42no—
564C2×D17—42no—
565C2×D17—81no—
566C2×D17—81no—
567C2×D17—81no—
568C2×D17—81no—
569C2×D17—81no—
570C2×D17—81no—
571C2×D17—81no—
572C2×D17—81no—
573C4×C17—24no—
574C4×C17—24no—
575C4×C17—24no—
576C4×C17—24no—
577C4×C17—42no—
578C4×C17—42no—
579C4×C17—42no—
580Dic17—42no—
581Dic17—42no—
582Dic17—42no—
583Dic17—42no—
584Dic17—81no—
585Dic17—81no—
586C23×D4—171no—
587C24×C4—171no—
588C2×#123—178no—
589C2×#123—344no—
590C2×#123—344no—
591C22×C4⋊C4—171no—
592C22×C4⋊C4—171no—
593C22×C4⋊C4C2×D1711yescharacteristic
594C22×C4⋊C4C2×D1711yescharacteristic
595C22×C22⋊C4—171no—
596C22×C22⋊C4—171no—
597C22×C22⋊C4—171no—
598C22×C22⋊C4—171no—
599C22×C22⋊C4—171no—
600C22×C22⋊C4—171no—
601C22×C22⋊C4—171no—
602C22×C22⋊C4—171no—
603C22×C22⋊C4—171no—
604C22×C22⋊C4—171no—
605C22×C22⋊C4—171no—
606C22×C42—171no—
607C22×C42C2×D1711yescharacteristic
608C22×C42C2×D1711yescharacteristic
609C22×C42C2×D1711yescharacteristic
610#390—344no—
611#387—344no—
612C4×C4⋊C4—24no—
613C4×C22⋊C4—344no—
614C2×#95—171no—
615C2×#95—171no—
616C2×#95—171no—
617C2×#95—171no—
618C2×#95—171no—
619C2×#95—171no—
620C2×#95—171no—
621C2×#95—171no—
622C2×#95—171no—
623C2×#95—171no—
624C2×#95—171no—
625C2×#95—171no—
626C2×#95C2×D1711yescharacteristic
627C2×#95C2×D1711yescharacteristic
628C2×C17#229711yescharacteristic
629C2×C17C4×#12311yescharacteristic
630C2×C17#233511yescharacteristic
631C2×C17D4×C22⋊C411yescharacteristic
632C2×C17#234111yescharacteristic
633C2×C17#235911yescharacteristic
634C2×C17#237411yescharacteristic
635C2×C17#244311yescharacteristic
636C2×C17#244511yescharacteristic
637C2×C17#245611yescharacteristic
638C2×C17#245811yescharacteristic
639C2×C17#246111yescharacteristic
640C2×C17#247111yescharacteristic
641C2×C17#255411yescharacteristic
642C2×C17#255811yescharacteristic
643D17—44no—
644D17—82no—
645C25—171no—
646C25—171no—
647C22×D4—174no—
648C22×D4—342no—
649C22×D4—342no—
650C22×D4—342no—
651C22×D4—342no—
652C22×D4—681no—
653C22×D4—681no—
654C23×C4—171no—
655C23×C4—171no—
656C23×C4—171no—
657C23×C4—171no—
658C23×C4—174no—
659C23×C4—171no—
660C23×C4—171no—
661C23×C4—342no—
662C23×C4—342no—
663C23×C4—342no—
664C23×C4—342no—
665C23×C4—681no—
666C23×C4—681no—
667C23×C4C22×D1711yescharacteristic
668C23×C4C22×D1711yescharacteristic
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C23×C4C22×D1711yescharacteristic
672C23×C4C22×D1711yescharacteristic
673C23×C4C22×D1711yescharacteristic
674#123—3432no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—174no—
679C2×C4⋊C4—342no—
680C2×C4⋊C4—342no—
681C2×C4⋊C4—342no—
682C2×C4⋊C4—342no—
683C2×C4⋊C4—681no—
684C2×C4⋊C4C4×D1714yes—
685C2×C4⋊C4D6814yes—
686C2×C4⋊C4C22⋊D1714yes—
687C2×C22⋊C4—174no—
688C2×C22⋊C4—174no—
689C2×C22⋊C4—174no—
690C2×C22⋊C4—174no—
691C2×C22⋊C4—342no—
692C2×C22⋊C4—342no—
693C2×C22⋊C4—342no—
694C2×C22⋊C4—342no—
695C2×C22⋊C4—342no—
696C2×C22⋊C4—342no—
697C2×C22⋊C4—342no—
698C2×C22⋊C4—342no—
699C2×C22⋊C4—342no—
700C2×C22⋊C4—342no—
701C2×C22⋊C4—342no—
702C2×C22⋊C4—342no—
703C2×C22⋊C4—342no—
704C2×C22⋊C4—342no—
705C2×C22⋊C4—342no—
706C2×C22⋊C4—342no—
707C2×C22⋊C4—342no—
708C2×C22⋊C4—342no—
709C2×C22⋊C4—342no—
710C2×C22⋊C4—342no—
711C2×C22⋊C4—342no—
712C2×C22⋊C4—342no—
713C2×C22⋊C4—342no—
714C2×C22⋊C4—681no—
715C2×C22⋊C4—681no—
716C2×C22⋊C4—681no—
717C2×C22⋊C4—681no—
718C2×C22⋊C4—681no—
719C2×C22⋊C4—681no—
720C2×C42—22no—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—41no—
728C2×C42—41no—
729C2×C42—342no—
730C2×C42—342no—
731C2×C42—681no—
732#95—22no—
733#95—22no—
734#95—342no—
735#95—342no—
736#95—342no—
737#95—342no—
738#95—342no—
739#95—342no—
740#95—342no—
741#95—342no—
742#95—681no—
743#95—681no—
744#95—681no—
745#95—681no—
746C17#1409511yescharacteristic, complemented, Sylow
747C24—172no—
748C24—172no—
749C24—172no—
750C24—172no—
751C24—341no—
752C24—341no—
753C24—341no—
754C24—341no—
755C24—341no—
756C24—341no—
757C24—341no—
758C24—341no—
759C24—341no—
760C24—341no—
761C24—341no—
762C24—341no—
763C24—341no—
764C24—341no—
765C24—341no—
766C24—341no—
767C24—341no—
768C24—341no—
769C24—341no—
770C24—341no—
771C24—341no—
772C24—341no—
773C24—341no—
774C24—341no—
775C24—341no—
776C24—341no—
777C24C23×D1711yescharacteristic
778C2×D4—348no—
779C2×D4—348no—
780C2×D4—684no—
781C2×D4—684no—
782C2×D4—684no—
783C2×D4—684no—
784C2×D4—684no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—172no—
820C22×C4—172no—
821C22×C4—172no—
822C22×C4—172no—
823C22×C4—348no—
824C22×C4—341no—
825C22×C4—341no—
826C22×C4—341no—
827C22×C4—341no—
828C22×C4—341no—
829C22×C4—341no—
830C22×C4—341no—
831C22×C4—341no—
832C22×C4—341no—
833C22×C4—341no—
834C22×C4—341no—
835C22×C4—341no—
836C22×C4—341no—
837C22×C4—341no—
838C22×C4—341no—
839C22×C4—341no—
840C22×C4—341no—
841C22×C4—341no—
842C22×C4—341no—
843C22×C4—341no—
844C22×C4—341no—
845C22×C4—341no—
846C22×C4—341no—
847C22×C4—341no—
848C22×C4—348no—
849C22×C4—341no—
850C22×C4—341no—
851C22×C4—341no—
852C22×C4—341no—
853C22×C4—341no—
854C22×C4—341no—
855C22×C4—341no—
856C22×C4—341no—
857C22×C4—341no—
858C22×C4—341no—
859C22×C4—341no—
860C22×C4—341no—
861C22×C4—341no—
862C22×C4—341no—
863C22×C4—684no—
864C22×C4—684no—
865C22×C4—684no—
866C22×C4—684no—
867C22×C4—684no—
868C22×C4C2×C4×D1712yes—
869C22×C4C2×C4×D1712yes—
870C22×C4C2×C4×D1712yes—
871C22×C4C2×D6812yes—
872C22×C4C2×D6812yes—
873C22×C4C2×D6812yes—
874C22×C4#6325212yes—
875C22×C4#6325212yes—
876C22×C4#6325212yes—
877C22×C4#6325212yes—
878C22×C4D4×D1712yes—
879C22×C4#6325612yes—
880C22×C4C2×C22⋊D1712yes—
881C22×C4C2×C22⋊D1712yes—
882C22×C4C2×C22⋊D1712yes—
883C4⋊C4—28no—
884C4⋊C4—348no—
885C4⋊C4—684no—
886C4⋊C4#63227116yescomplemented
887C22⋊C4—348no—
888C22⋊C4—348no—
889C22⋊C4—348no—
890C22⋊C4—348no—
891C22⋊C4—348no—
892C22⋊C4—684no—
893C22⋊C4—684no—
894C22⋊C4—684no—
895C22⋊C4—684no—
896C22⋊C4—684no—
897C22⋊C4—684no—
898C42—28no—
899C42—44no—
900C42—44no—
901C42—684no—
902C23—174no—
903C23—342no—
904C23—342no—
905C23—342no—
906C23—342no—
907C23—342no—
908C23—342no—
909C23—342no—
910C23—342no—
911C23—342no—
912C23—342no—
913C23—342no—
914C23—342no—
915C23—342no—
916C23—342no—
917C23—342no—
918C23—342no—
919C23—342no—
920C23—342no—
921C23—342no—
922C23—342no—
923C23—342no—
924C23—342no—
925C23—342no—
926C23—342no—
927C23—342no—
928C23—681no—
929C23—681no—
930C23—681no—
931C23—681no—
932C23—681no—
933C23—681no—
934C23—681no—
935C23—681no—
936C23—681no—
937C23—681no—
938C23—681no—
939C23—681no—
940C23—681no—
941C23—681no—
942C23—681no—
943C23—681no—
944C23—681no—
945C23—681no—
946C23—681no—
947C23—681no—
948C23—681no—
949C23—681no—
950C23—681no—
951C23—681no—
952C23—681no—
953C23—681no—
954C23—681no—
955C23—681no—
956C23—681no—
957C23—681no—
958C23—681no—
959C23—681no—
960C23—681no—
961C23—681no—
962C23—681no—
963C23—681no—
964C23—681no—
965C23—681no—
966C23—681no—
967C23—681no—
968C23—681no—
969C23—681no—
970C23—681no—
971C23—681no—
972C23C22×C4×D1711yescharacteristic
973C23C22×D6811yescharacteristic
974C23C2×#6325211yescharacteristic
975C23C2×#6325211yescharacteristic
976C23C2×#6325211yescharacteristic
977C23C2×#6325211yescharacteristic
978C23C2×D4×D1711yescharacteristic
979C23#1058769111yescharacteristic
980C23C2×#6325611yescharacteristic
981C23#1058769411yescharacteristic
982C23#41×D1711yescharacteristic
983C23#41×D1711yescharacteristic
984C23#1058769611yescharacteristic
985C23#1058769611yescharacteristic
986C23C22×C22⋊D1711yescharacteristic
987D4—6816no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—342no—
1034C2×C4—342no—
1035C2×C4—342no—
1036C2×C4—342no—
1037C2×C4—342no—
1038C2×C4—342no—
1039C2×C4—342no—
1040C2×C4—342no—
1041C2×C4—342no—
1042C2×C4—342no—
1043C2×C4—342no—
1044C2×C4—342no—
1045C2×C4—6816no—
1046C2×C4—681no—
1047C2×C4—681no—
1048C2×C4—681no—
1049C2×C4—681no—
1050C2×C4—681no—
1051C2×C4—681no—
1052C2×C4—681no—
1053C2×C4—681no—
1054C2×C4—681no—
1055C2×C4—681no—
1056C2×C4—681no—
1057C2×C4—681no—
1058C2×C4—681no—
1059C2×C4—681no—
1060C2×C4—681no—
1061C2×C4—681no—
1062C2×C4—681no—
1063C2×C4—681no—
1064C2×C4—681no—
1065C2×C4—681no—
1066C2×C4—681no—
1067C2×C4—681no—
1068C2×C4—681no—
1069C2×C4—681no—
1070C2×C4—681no—
1071C2×C4—681no—
1072C2×C4—681no—
1073C2×C4—681no—
1074C2×C4—681no—
1075C2×C4—681no—
1076C2×C4#1058758014yescomplemented
1077C2×C4C2×#6322714yes—
1078C2×C4C2×#6322714yes—
1079C2×C4C2×#6322714yes—
1080C22—344no—
1081C22—344no—
1082C22—344no—
1083C22—682no—
1084C22—682no—
1085C22—682no—
1086C22—682no—
1087C22—682no—
1088C22—682no—
1089C22—682no—
1090C22—682no—
1091C22—682no—
1092C22—682no—
1093C22—682no—
1094C22—682no—
1095C22—682no—
1096C22—682no—
1097C22—682no—
1098C22—682no—
1099C22—682no—
1100C22—682no—
1101C22—682no—
1102C22—1361no—
1103C22—1361no—
1104C22—1361no—
1105C22—1361no—
1106C22—1361no—
1107C22—1361no—
1108C22—1361no—
1109C22—1361no—
1110C22C22×#6322711yescharacteristic
1111C22C4×D4×D1711yescharacteristic
1112C22C4×#6325211yescharacteristic
1113C22C4×#6325211yescharacteristic
1114C22C4×#6325611yescharacteristic
1115C22#1176328111yescharacteristic
1116C22#1176329111yescharacteristic
1117C22C2×#1058758011yescharacteristic
1118C22#1176331811yescharacteristic
1119C22#1176332011yescharacteristic
1120C22#1176332011yescharacteristic
1121C22#1176333711yescharacteristic
1122C22#1176334611yescharacteristic
1123C22#1176335911yescharacteristic
1124C22#1176335911yescharacteristic
1125C22#1176339211yescharacteristic
1126C22#1176340611yescharacteristic
1127C22#1176341411yescharacteristic
1128C22#1176343111yescharacteristic
1129C22D4×C22⋊D1711yescharacteristic
1130C22D4×D6811yescharacteristic
1131C22#1176344711yescharacteristic
1132C22#1176345411yescharacteristic
1133C22#1176345511yescharacteristic
1134C22#1176346011yescharacteristic
1135C22#1176347011yescharacteristic
1136C22#1176347111yescharacteristic
1137C22#1176347811yescharacteristic
1138C22#1176348111yescharacteristic
1139C22#1176348311yescharacteristic
1140C22#1176348311yescharacteristic
1141C22#1176350011yescharacteristic
1142C22#1176350711yescharacteristic
1143C22#1176350811yescharacteristic
1144C22#1176354411yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—682no—
1153C4—682no—
1154C4—682no—
1155C4—682no—
1156C4—1361no—
1157C4—1361no—
1158C2—684no—
1159C2—1362no—
1160C2#1453127411yescharacteristic
1161C2C4×#1058758011yescharacteristic
1162C2#1453156811yescharacteristic
1163C2D4×#6322711yescharacteristic
1164C2#1453162211yescharacteristic
1165C2#1453178111yescharacteristic
1166C2#1453191311yescharacteristic
1167C2#1453251911yescharacteristic
1168C2#1453254911yescharacteristic
1169C2#1453267011yescharacteristic
1170C2#1453270011yescharacteristic
1171C2#1453275111yescharacteristic
1172C2#1453288911yescharacteristic
1173C2#1453383811yescharacteristic
1174C2#1453389211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C4×C4⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenterC2×C4×C4⋊C4D17
hypocenterC17#14095
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#11762695C2semidirect
4. C2×C4×#63227C2semidirect
5. #14527038C2semidirect
6. #14527026C2semidirect
7. #14527026C2semidirect
9. #14527022C2semidirect
10. #14527022C2semidirect
11. #14527022C2semidirect
12. #14527020C2semidirect
13. #14527017C2semidirect
14. #14527005C2semidirect
15. C2×C4×C4⋊C4×C17C2semidirect
20. C2×#10587580C4semidirect
296. C4⋊C4×C17C22⋊C4semidirect
448. C2×C4×C17#123semidirect
496. C2×C4×C4⋊C4D17semidirect
746. C17#14095semidirect
886. C4⋊C4#63227semidirect
1076. C2×C4#10587580semidirect

Maximal subgroups

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

subgroupindex
C22×#105875802
C2×#117627112
C2×#117626952
C2×C4×#632272
#145270382
#145270262
#145270242
#145270222
#145270202
#145270172
#145270052
C2×C4×C4⋊C4×C172
#1409517