Finite Group Databasebeta

← #16957293

Subgroups — #16957293

Order 4352.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762686C211yesmaximal, characteristic
2C2×#11762685C211yesmaximal, characteristic
3C2×#11762671C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
5C2×C4×#63227C211yesmaximal, characteristic, complemented
6#14527044C211yesmaximal, characteristic, complemented
7#14527028C211yesmaximal, characteristic, complemented
8#14527027C211yesmaximal, characteristic, complemented
9#14527023C211yesmaximal, characteristic
10#14527020C211yesmaximal, characteristic, complemented
11#14527015C211yesmaximal, characteristic, complemented
12#14527011C211yesmaximal, characteristic, complemented
13#14527009C211yesmaximal, characteristic, complemented
14#14527006C211yesmaximal, characteristic, complemented
15C17×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29#11762686—24no—
30#11762685C418yescomplemented
31#11762671—24no—
32C22⋊C4×Dic17—24no—
33C4×#63227—24no—
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C22×C22⋊C4×C17C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C22×C42×C17C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C25×C17C2311yescharacteristic
57C24×D17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C22×C22⋊D17—22no—
65C22×C22⋊D17—22no—
66C22×C22⋊D17—22no—
67C22×C22⋊D17—22no—
68C22×C22⋊D17—41no—
69C22×C22⋊D17—41no—
70C22×C22⋊D17C2×C414yes—
71C23×Dic17—22no—
72C23×Dic17—22no—
73C23×Dic17—22no—
74C23×Dic17—22no—
75C23×Dic17—22no—
76C23×Dic17—41no—
77C23×Dic17—41no—
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C22×C4×D17—22no—
86C22×C4×D17—22no—
87C22×C4×D17—22no—
88C22×C4×D17—22no—
89C22×C4×D17—41no—
90C22×C4×D17—41no—
91C22×C4×D17C2×C414yescomplemented
92C2×C22⋊C4×C17—22no—
93C2×C22⋊C4×C17—22no—
94C2×C22⋊C4×C17—22no—
95C2×C22⋊C4×C17—22no—
96C2×C22⋊C4×C17—22no—
97C2×C22⋊C4×C17—22no—
98C2×C22⋊C4×C17—41no—
99C2×C22⋊C4×C17—41no—
100C2×C22⋊C4×C17C2×C414yes—
101C2×C42×C17—22no—
102C2×C42×C17—22no—
103C2×C42×C17—41no—
104C2×C22⋊Dic17—22no—
105C2×C22⋊Dic17—22no—
106C2×C22⋊Dic17—22no—
107C2×C22⋊Dic17—41no—
108C2×C22⋊Dic17—41no—
109C2×C22⋊Dic17C2×C414yes—
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—41no—
120C2×#63227—41no—
121C2×#63227—41no—
122C2×#63227—41no—
123C2×#63227C2×C414yescomplemented
124C2×#63227D414yes—
125C2×#63225—22no—
126C2×#63225—41no—
127C2×#63225—41no—
128C2×C4×Dic17—22no—
129C2×C4×Dic17—22no—
130C2×C4×Dic17—22no—
131C2×C4×Dic17—22no—
132C2×C4×Dic17—41no—
133C2×C4×Dic17—41no—
134C17×#95—22no—
135C17×#95—22no—
136C17×#95—41no—
137#10587502—22no—
138#10587502—22no—
139#10587502—22no—
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—41no—
146#10587502—41no—
147#10587502—41no—
148#10587502—41no—
149#10587502C2×C414yescomplemented
150#10587502C2×C414yescomplemented
151#10587502D414yescomplemented
152C24×C17—21no—
153C24×C17—21no—
154C24×C17—21no—
155C24×C17—21no—
156C24×C17—21no—
157C24×C17—21no—
158C24×C17—21no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17C22×C412yes—
165C24×C17#4112yes—
166C24×C17#4112yes—
167C24×C17C2411yescharacteristic
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×D17C22×C412yes—
181C23×D17C2×D412yes—
182C23×D17#4112yes—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
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×C17C22×C412yes—
220C22×C4×C17C22×C412yes—
221C22×C4×C17C2×D412yes—
222C22×C4×C17C2×D412yes—
223C22×C4×C17#4112yes—
224C22×C4×C17#4112yes—
225C2×C22⋊D17—28no—
226C2×C22⋊D17—28no—
227C2×C22⋊D17—44no—
228C2×C22⋊D17—44no—
229C2×C22⋊D17—44no—
230C2×C22⋊D17—44no—
231C2×C22⋊D17—44no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—28no—
237C22×Dic17—21no—
238C22×Dic17—21no—
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—44no—
274C22×Dic17—44no—
275C22×Dic17—44no—
276C22×Dic17—44no—
277C22×Dic17—44no—
278C22×Dic17—44no—
279C22×Dic17C22×C412yes—
280C22×Dic17C22×C412yes—
281C22×Dic17C22×C412yes—
282C22×Dic17C2×D412yes—
283C22×Dic17C2×D412yes—
284C22×Dic17C2×D412yes—
285C22×Dic17#4112yes—
286C22×Dic17#4112yes—
287C22×Dic17#4112yes—
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—
295C22⋊C4×C17—28no—
296C22⋊C4×C17—44no—
297C22⋊C4×C17—44no—
298C42×C17—44no—
299C22⋊Dic17—28no—
300C22⋊Dic17—44no—
301#63227—28no—
302#63227—28no—
303#63227—44no—
304#63227—44no—
305#63227—44no—
306#63225—44no—
307C4×Dic17—44no—
308C4×Dic17—44no—
309#13984—171nomaximal, Sylow
310C23×C17—22no—
311C23×C17—22no—
312C23×C17—22no—
313C23×C17—22no—
314C23×C17—22no—
315C23×C17—22no—
316C23×C17—22no—
317C23×C17—22no—
318C23×C17—22no—
319C23×C17—22no—
320C23×C17—22no—
321C23×C17—22no—
322C23×C17—22no—
323C23×C17—22no—
324C23×C17—22no—
325C23×C17—22no—
326C23×C17—22no—
327C23×C17—22no—
328C23×C17—41no—
329C23×C17—41no—
330C23×C17—41no—
331C23×C17—41no—
332C23×C17—41no—
333C23×C17—41no—
334C23×C17—41no—
335C23×C17—41no—
336C23×C17—41no—
337C23×C17—41no—
338C23×C17—41no—
339C23×C17—41no—
340C23×C17—41no—
341C23×C17—41no—
342C23×C17—41no—
343C23×C17—41no—
344C23×C17#11714yes—
345C23×C17C23×C411yescharacteristic
346C23×C17C22×D411yescharacteristic
347C23×C17C22×D411yescharacteristic
348C23×C17C2×#4111yescharacteristic
349C23×C17C2×#4111yescharacteristic
350C23×C17C2×#4111yescharacteristic
351C23×C17C2×#4111yescharacteristic
352C23×C17C2×#4111yescharacteristic
353C23×C17C2×#4111yescharacteristic
354C23×C17C2×#4111yescharacteristic
355C23×C17C2×#4111yescharacteristic
356C23×C17H(5,𝔽2)11yescharacteristic
357C23×C17H(5,𝔽2)11yescharacteristic
358C23×C17H(5,𝔽2)11yescharacteristic
359C23×C17H(5,𝔽2)11yescharacteristic
360C22×D17—22no—
361C22×D17—22no—
362C22×D17—22no—
363C22×D17—22no—
364C22×D17—22no—
365C22×D17—22no—
366C22×D17—22no—
367C22×D17—22no—
368C22×D17—22no—
369C22×D17—22no—
370C22×D17—22no—
371C22×D17—22no—
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—22no—
375C22×D17—22no—
376C22×D17—22no—
377C22×D17—22no—
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×D17C4×D414yes—
395C2×C4×C17—22no—
396C2×C4×C17—22no—
397C2×C4×C17—22no—
398C2×C4×C17—22no—
399C2×C4×C17—22no—
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—41no—
411C2×C4×C17—41no—
412C2×C4×C17—41no—
413C2×C4×C17—41no—
414C2×C4×C17—41no—
415C2×C4×C17—41no—
416C2×C4×C17—41no—
417C2×C4×C17—41no—
418C2×C4×C17—41no—
419C2×C4×C17—41no—
420C2×C4×C17—41no—
421C2×C4×C17—41no—
422C2×C4×C17—41no—
423C2×C4×C17—41no—
424C2×C4×C17—41no—
425C2×C4×C17—41no—
426C2×C4×C17—41no—
427C2×C4×C17—41no—
428C2×C4×C17—41no—
429C2×C4×C17—41no—
430C2×C4×C17—41no—
431C2×C4×C17—41no—
432C2×C4×C17—41no—
433C2×C4×C17—41no—
434C2×C4×C17—41no—
435C2×C4×C17—41no—
436C2×C4×C17C4×D414yes—
437C22⋊D17—416no—
438C2×Dic17—22no—
439C2×Dic17—22no—
440C2×Dic17—22no—
441C2×Dic17—22no—
442C2×Dic17—22no—
443C2×Dic17—22no—
444C2×Dic17—22no—
445C2×Dic17—22no—
446C2×Dic17—22no—
447C2×Dic17—22no—
448C2×Dic17—22no—
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—22no—
462C2×Dic17—416no—
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#12314yes—
488C4×D17—416no—
489C2×#386—171no—
490C2×#386—171no—
491C2×#381—171no—
492C2×C4×C22⋊C4—171no—
493C2×C4×C22⋊C4—171no—
494#1443—171no—
495#1439—171no—
496#1439—171no—
497#1438—171no—
498#1437—171no—
499#1437D1711yescharacteristic, complemented
500#1436—171no—
501#1434—171no—
502#1434—171no—
503C22⋊#95—171no—
504C22×C17—24no—
505C22×C17—24no—
506C22×C17—24no—
507C22×C17—42no—
508C22×C17—42no—
509C22×C17—42no—
510C22×C17—42no—
511C22×C17—42no—
512C22×C17—42no—
513C22×C17—42no—
514C22×C17—42no—
515C22×C17—42no—
516C22×C17—42no—
517C22×C17—42no—
518C22×C17—42no—
519C22×C17C2×#11711yescharacteristic
520C22×C17C2×C4×D411yescharacteristic
521C22×C17C2×C4×D411yescharacteristic
522C22×C17C4×#4111yescharacteristic
523C22×C17C4×#4111yescharacteristic
524C22×C17#51811yescharacteristic
525C22×C17#51811yescharacteristic
526C22×C17C2×#12311yescharacteristic
527C22×C17#52511yescharacteristic
528C22×C17#52511yescharacteristic
529C22×C17#52511yescharacteristic
530C22×C17#52911yescharacteristic
531C22×C17#52911yescharacteristic
532C22×C17#52911yescharacteristic
533C22×C17#52911yescharacteristic
534C22×C17#53811yescharacteristic
535C22×C17#53811yescharacteristic
536C22×C17#54011yescharacteristic
537C22×C17#54011yescharacteristic
538C22×C17D4211yescharacteristic
539C22×C17#54611yescharacteristic
540C22×C17#54611yescharacteristic
541C22×C17#54611yescharacteristic
542C22×C17#54611yescharacteristic
543C22×C17#54611yescharacteristic
544C22×C17#55011yescharacteristic
545C22×C17#55111yescharacteristic
546C22×C17#55111yescharacteristic
547C22×C17#55111yescharacteristic
548C22×C17#55111yescharacteristic
549C22×C17#55111yescharacteristic
550C22×C17#55311yescharacteristic
551C22×C17#55311yescharacteristic
552C22×C17#55311yescharacteristic
553C22×C17#55511yescharacteristic
554C2×D17—24no—
555C2×D17—24no—
556C2×D17—24no—
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—42no—
566C2×D17—42no—
567C2×D17—42no—
568C2×D17—42no—
569C4×C17—24no—
570C4×C17—42no—
571C4×C17—42no—
572C4×C17—42no—
573C4×C17—81no—
574C4×C17—81no—
575Dic17—24no—
576Dic17—42no—
577Dic17—42no—
578Dic17—42no—
579Dic17—42no—
580Dic17—42no—
581Dic17—42no—
582C23×D4—171no—
583C24×C4—171no—
584C24×C4—171no—
585C22×C4⋊C4—171no—
586C22×C22⋊C4—171no—
587C22×C22⋊C4—171no—
588C22×C22⋊C4—171no—
589C22×C22⋊C4—171no—
590C22×C22⋊C4—171no—
591C22×C22⋊C4—171no—
592C22×C22⋊C4—171no—
593C22×C22⋊C4C2×D1711yescharacteristic
594C22×C22⋊C4C2×D1711yescharacteristic
595C22×C22⋊C4C2×D1711yescharacteristic
596C22×C42—171no—
597C22×C42—171no—
598C22×C42C2×D1711yescharacteristic
599#386—178no—
600#386—344no—
601#381—344no—
602C4×C22⋊C4—344no—
603C4×C22⋊C4—344no—
604C2×#95—171no—
605C2×#95—171no—
606C2×#95—171no—
607C2×#95—171no—
608C2×#95—171no—
609C2×#95—171no—
610C2×#95—171no—
611C2×#95—171no—
612C2×#95—171no—
613C2×#95—171no—
614C2×#95—171no—
615C2×#95—171no—
616C2×#95—171no—
617C2×#95—171no—
618C2×#95—171no—
619C2×#95C2×D1711yescharacteristic
620C2×#95C2×D1711yescharacteristic
621C2×#95C2×D1711yescharacteristic
622C2×C17—44no—
623C2×C17#229011yescharacteristic
624C2×C17C4×#12311yescharacteristic
625C2×C17#233311yescharacteristic
626C2×C17#234211yescharacteristic
627C2×C17#235311yescharacteristic
628C2×C17#235811yescharacteristic
629C2×C17#236311yescharacteristic
630C2×C17#241811yescharacteristic
631C2×C17#242011yescharacteristic
632C2×C17#245611yescharacteristic
633C2×C17#245711yescharacteristic
634C2×C17#245711yescharacteristic
635C2×C17#247111yescharacteristic
636C2×C17#257211yescharacteristic
637C2×C17#257611yescharacteristic
638D17—44no—
639C25—171no—
640C25C22×D1711yescharacteristic
641C22×D4—174no—
642C22×D4—342no—
643C22×D4—342no—
644C22×D4—342no—
645C22×D4—342no—
646C22×D4—681no—
647C22×D4—681no—
648C23×C4—171no—
649C23×C4—171no—
650C23×C4—171no—
651C23×C4—171no—
652C23×C4—171no—
653C23×C4—171no—
654C23×C4—171no—
655C23×C4—174no—
656C23×C4—342no—
657C23×C4—342no—
658C23×C4—342no—
659C23×C4—342no—
660C23×C4—342no—
661C23×C4—342no—
662C23×C4—342no—
663C23×C4—342no—
664C23×C4—342no—
665C23×C4—681no—
666C23×C4—681no—
667C23×C4—681no—
668C23×C4—681no—
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C23×C4C22×D1711yescharacteristic
672C23×C4C22×D1711yescharacteristic
673C23×C4C22×D1711yescharacteristic
674C23×C4C22×D1711yescharacteristic
675C2×C4⋊C4—342no—
676C2×C4⋊C4—681no—
677C2×C4⋊C4—681no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—174no—
687C2×C22⋊C4—174no—
688C2×C22⋊C4—174no—
689C2×C22⋊C4—342no—
690C2×C22⋊C4—342no—
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—681no—
702C2×C22⋊C4—681no—
703C2×C22⋊C4—681no—
704C2×C22⋊C4—681no—
705C2×C22⋊C4—681no—
706C2×C22⋊C4—681no—
707C2×C22⋊C4C4×D1714yes—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—41no—
711C2×C42—342no—
712C2×C42—342no—
713C2×C42—342no—
714C2×C42—342no—
715C2×C42—681no—
716C2×C42—681no—
717#95—22no—
718#95—22no—
719#95—41no—
720#95—174no—
721#95—174no—
722#95—174no—
723#95—342no—
724#95—342no—
725#95—342no—
726#95—342no—
727#95—342no—
728#95—342no—
729#95—342no—
730#95—342no—
731#95—681no—
732#95—681no—
733#95—681no—
734#95—681no—
735C17#1398411yescharacteristic, complemented, Sylow
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
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—
763C24C2×C4×D1712yes—
764C24#6325212yes—
765C24#6325212yes—
766C24C23×D1711yescharacteristic
767C2×D4—348no—
768C2×D4—348no—
769C2×D4—684no—
770C2×D4—684no—
771C2×D4—684no—
772C2×D4—684no—
773C2×D4—684no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
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—172no—
811C22×C4—172no—
812C22×C4—172no—
813C22×C4—172no—
814C22×C4—172no—
815C22×C4—172no—
816C22×C4—172no—
817C22×C4—172no—
818C22×C4—172no—
819C22×C4—348no—
820C22×C4—341no—
821C22×C4—341no—
822C22×C4—341no—
823C22×C4—341no—
824C22×C4—348no—
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—341no—
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—348no—
862C22×C4—684no—
863C22×C4—684no—
864C22×C4—684no—
865C22×C4—684no—
866C22×C4—684no—
867C22×C4—684no—
868C22×C4—684no—
869C22×C4—684no—
870C22×C4—684no—
871C22×C4—684no—
872C22×C4—684no—
873C22×C4C2×C4×D1712yes—
874C22×C4C2×C4×D1712yes—
875C22×C4D4×D1712yes—
876C22×C4D4×D1712yes—
877C22×C4#6325412yes—
878C22×C4#6325412yes—
879C4⋊C4—684no—
880C22⋊C4—28no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—348no—
884C22⋊C4—348no—
885C22⋊C4—348no—
886C22⋊C4—684no—
887C22⋊C4—684no—
888C22⋊C4—684no—
889C22⋊C4—684no—
890C42—44no—
891C42—684no—
892C42—684no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—174no—
928C23—342no—
929C23—342no—
930C23—342no—
931C23—342no—
932C23—342no—
933C23—342no—
934C23—342no—
935C23—342no—
936C23—342no—
937C23—342no—
938C23—342no—
939C23—342no—
940C23—342no—
941C23—342no—
942C23—342no—
943C23—342no—
944C23—342no—
945C23—342no—
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#1058755814yes—
963C23C22×C4×D1711yescharacteristic
964C23C2×#6325211yescharacteristic
965C23C2×#6325211yescharacteristic
966C23C2×D4×D1711yescharacteristic
967C23C2×D4×D1711yescharacteristic
968C23C2×#6325411yescharacteristic
969C23C2×#6325411yescharacteristic
970C23#1058769111yescharacteristic
971C23#1058769111yescharacteristic
972C23#41×D1711yescharacteristic
973C23#41×D1711yescharacteristic
974C23#41×D1711yescharacteristic
975C23#41×D1711yescharacteristic
976C23#1058769611yescharacteristic
977C23#1058769611yescharacteristic
978D4—6816no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—174no—
1021C2×C4—342no—
1022C2×C4—342no—
1023C2×C4—342no—
1024C2×C4—342no—
1025C2×C4—342no—
1026C2×C4—342no—
1027C2×C4—342no—
1028C2×C4—342no—
1029C2×C4—342no—
1030C2×C4—342no—
1031C2×C4—342no—
1032C2×C4—342no—
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—6816no—
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#1058756714yes—
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—344no—
1088C22—344no—
1089C22—344no—
1090C22—682no—
1091C22—682no—
1092C22—682no—
1093C22—682no—
1094C22—682no—
1095C22—682no—
1096C22—682no—
1097C22—682no—
1098C22—682no—
1099C22—682no—
1100C22—682no—
1101C22—682no—
1102C22C2×#1058755811yescharacteristic
1103C22C4×D4×D1711yescharacteristic
1104C22C2×#1058756711yescharacteristic
1105C22C4×#6325411yescharacteristic
1106C22#1176327711yescharacteristic
1107C22#1176328111yescharacteristic
1108C22#1176328111yescharacteristic
1109C22#123×D1711yescharacteristic
1110C22#1176331811yescharacteristic
1111C22#1176331811yescharacteristic
1112C22#1176331911yescharacteristic
1113C22#1176333811yescharacteristic
1114C22#1176333911yescharacteristic
1115C22#1176333911yescharacteristic
1116C22#1176334211yescharacteristic
1117C22#1176339311yescharacteristic
1118C22#1176339811yescharacteristic
1119C22#1176340911yescharacteristic
1120C22#1176341111yescharacteristic
1121C22#1176344311yescharacteristic
1122C22#1176344611yescharacteristic
1123C22#1176344811yescharacteristic
1124C22#1176344911yescharacteristic
1125C22#1176345211yescharacteristic
1126C22#1176345511yescharacteristic
1127C22#1176347911yescharacteristic
1128C22#1176348211yescharacteristic
1129C22#1176348311yescharacteristic
1130C22#1176348311yescharacteristic
1131C22#1176348511yescharacteristic
1132C22#1176348811yescharacteristic
1133C22#1176350511yescharacteristic
1134C22#1176350811yescharacteristic
1135C22#1176351111yescharacteristic
1136C22#1176352311yescharacteristic
1137C4—24no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—81no—
1142C4—81no—
1143C4—344no—
1144C4—682no—
1145C4—682no—
1146C4—682no—
1147C4—682no—
1148C4—682no—
1149C4—682no—
1150C2—44no—
1151C2—684no—
1152C2#1453122311yescharacteristic
1153C2#1453131111yescharacteristic
1154C2#1453154711yescharacteristic
1155C2#1453162711yescharacteristic
1156C2#1453171811yescharacteristic
1157C2#1453176411yescharacteristic
1158C2#1453182711yescharacteristic
1159C2#1453225311yescharacteristic
1160C2#1453227311yescharacteristic
1161C2#1453268211yescharacteristic
1162C2#1453269611yescharacteristic
1163C2#1453269711yescharacteristic
1164C2#1453290111yescharacteristic
1165C2#1453403111yescharacteristic
1166C2#1453409411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1437C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1437D17
hypocenterC17#13984
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×#11762671C2semidirect
4. C2×C22⋊C4×Dic17C2semidirect
5. C2×C4×#63227C2semidirect
6. #14527044C2semidirect
7. #14527028C2semidirect
8. #14527027C2semidirect
10. #14527020C2semidirect
11. #14527015C2semidirect
12. #14527011C2semidirect
13. #14527009C2semidirect
14. #14527006C2semidirect
15. C17×#1437C2semidirect
30. #11762685C4semidirect
91. C22×C4×D17C2×C4semidirect
123. C2×#63227C2×C4semidirect
149. #10587502C2×C4semidirect
150. #10587502C2×C4semidirect
151. #10587502D4semidirect
499. #1437D17semidirect
735. C17#13984semidirect

Maximal subgroups

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

subgroupindex
C2×#117626862
C2×#117626852
C2×#117626712
C2×C22⋊C4×Dic172
C2×C4×#632272
#145270442
#145270282
#145270272
#145270232
#145270202
#145270152
#145270112
#145270092
#145270062
C17×#14372
#1398417