Finite Group Databasebeta

← #16957764

Subgroups — #16957764

Order 4352.

1954 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762709C211yesmaximal, characteristic
2C2×#11762709C211yesmaximal, characteristic
3C2×#11762709C211yesmaximal, characteristic
4C2×#11762703C211yesmaximal, characteristic, complemented
5C2×#11762700C211yesmaximal, characteristic, complemented
6C2×C4×#63225C211yesmaximal, characteristic, complemented
7C2×#11762660C211yesmaximal, characteristic, complemented
8#14527033C211yesmaximal, characteristic, complemented
9#14527032C211yesmaximal, characteristic, complemented
10#14527028C211yesmaximal, characteristic, complemented
11#14527027C211yesmaximal, characteristic, complemented
12#14527020C211yesmaximal, characteristic, complemented
13#14527012C211yesmaximal, characteristic, complemented
14#14527012C211yesmaximal, characteristic, complemented
15C17×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35#11762709—24no—
36#11762709—24no—
37#11762709C418yescomplemented
38#11762703—24no—
39#11762700—24no—
40C4×#63225—24no—
41#11762660—24no—
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C24×D17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C22×C22⋊D17—22no—
67C22×C22⋊D17—22no—
68C22×C22⋊D17—22no—
69C22×C22⋊D17—22no—
70C22×C22⋊D17—22no—
71C22×C22⋊D17—22no—
72C22×C22⋊D17C2×C414yes—
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C2×C22⋊C4×C17—22no—
81C2×C22⋊C4×C17—22no—
82C2×C22⋊C4×C17—22no—
83C2×C22⋊C4×C17—22no—
84C2×C22⋊C4×C17—22no—
85C2×C22⋊C4×C17—41no—
86C2×C22⋊C4×C17—41no—
87C2×C22⋊C4×C17—41no—
88C2×C22⋊C4×C17C2×C414yes—
89C2×C42×C17—22no—
90C2×C42×C17—22no—
91C2×C42×C17—41no—
92C2×C22⋊Dic17—22no—
93C2×C22⋊Dic17—22no—
94C2×C22⋊Dic17—22no—
95C2×C22⋊Dic17—22no—
96C2×C22⋊Dic17—22no—
97C2×C22⋊Dic17—41no—
98C2×C22⋊Dic17—41no—
99C2×C22⋊Dic17—41no—
100C2×C22⋊Dic17C2×C414yes—
101C2×#63227—22no—
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—41no—
112C2×#63227—41no—
113C2×#63227—41no—
114C2×#63227—41no—
115C2×#63227—41no—
116C2×#63227—41no—
117C2×#63227C2×C414yes—
118C2×#63227C2×C414yes—
119C2×#63225—22no—
120C2×#63225—22no—
121C2×#63225—22no—
122C2×#63225—22no—
123C2×#63225—22no—
124C2×#63225—22no—
125C2×#63225—22no—
126C2×#63225—22no—
127C2×#63225—22no—
128C2×#63225—22no—
129C2×#63225—22no—
130C2×#63225—22no—
131C2×#63225C2×C414yes—
132C2×#63225D414yes—
133C2×#63225D414yescomplemented
134C2×C4×Dic17—22no—
135C2×C4×Dic17—22no—
136C2×C4×Dic17—22no—
137C2×C4×Dic17—22no—
138C2×C4×Dic17—22no—
139C2×C4×Dic17—22no—
140C2×C4×Dic17—22no—
141C2×C4×Dic17—22no—
142C2×C4×Dic17—22no—
143C2×C4×Dic17—41no—
144C2×C4×Dic17C2×C414yes—
145C2×C4×Dic17D414yes—
146C17×#95—22no—
147C17×#95—41no—
148C17×#95—41no—
149#10587502—22no—
150#10587502—22no—
151#10587502—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—22no—
155#10587502—22no—
156#10587502—41no—
157#10587502—41no—
158C24×C17—21no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17—21no—
165C24×C17—21no—
166C24×C17—21no—
167C24×C17—21no—
168C24×C17—21no—
169C24×C17—21no—
170C24×C17—21no—
171C24×C17—21no—
172C24×C17C22×C412yes—
173C24×C17C2411yescharacteristic
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×D17—21no—
187C23×D17—21no—
188C23×D17C22×C412yes—
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×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×C17C2×D412yes—
227C22×C4×C17C2×D412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17#4112yes—
230C22×C4×C17#4112yes—
231C2×C22⋊D17—28no—
232C2×C22⋊D17—28no—
233C2×C22⋊D17—28no—
234C2×C22⋊D17—44no—
235C2×C22⋊D17—44no—
236C2×C22⋊D17—44no—
237C2×C22⋊D17—44no—
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×Dic17C22×C412yes—
274C22×Dic17C22×C412yes—
275C22×Dic17C22×C412yes—
276C22×Dic17C2×D412yes—
277C22×Dic17C2×D412yes—
278C22×Dic17C2×D412yes—
279C22×Dic17C2×D412yes—
280C22×Dic17C2×D412yes—
281C22×Dic17C2×D412yes—
282C22×Dic17#4112yes—
283C22×Dic17#4112yes—
284C22×Dic17#4112yes—
285C22×Dic17#4112yes—
286C22×Dic17#4112yes—
287C22⋊C4×C17—44no—
288C22⋊C4×C17—44no—
289C22⋊C4×C17—44no—
290C42×C17—44no—
291C22⋊Dic17—28no—
292C22⋊Dic17—44no—
293C22⋊Dic17—44no—
294#63227—28no—
295#63227—44no—
296#63227—44no—
297#63227—44no—
298#63227—44no—
299#63227—44no—
300#63225—28no—
301#63225—28no—
302#63225—28no—
303#63225—28no—
304#63225—44no—
305C4×Dic17—28no—
306C4×Dic17—28no—
307C4×Dic17—44no—
308C4×Dic17—44no—
309#14022—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—41no—
318C23×C17—41no—
319C23×C17—41no—
320C23×C17—41no—
321C23×C17—41no—
322C23×C17—41no—
323C23×C17—41no—
324C23×C17—41no—
325C23×C17—41no—
326C23×C17—41no—
327C23×C17—41no—
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—41no—
345C23×C17C23×C411yescharacteristic
346C23×C17C22×D411yescharacteristic
347C23×C17C22×D411yescharacteristic
348C23×C17C22×D411yescharacteristic
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×C172−1+411yescharacteristic
360C22×D17—22no—
361C22×D17—22no—
362C22×D17—22no—
363C22×D17—22no—
364C22×D17—22no—
365C22×D17—22no—
366C22×D17—22no—
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—
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—22no—
411C2×C4×C17—22no—
412C2×C4×C17—22no—
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×C17#12114yes—
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—41no—
457C2×Dic17—41no—
458C2×Dic17—41no—
459C2×Dic17—41no—
460C2×Dic17—41no—
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#11714yes—
480C2×Dic17C4×D414yes—
481C2×Dic17C4×D414yes—
482C2×Dic17C4×D414yes—
483C2×Dic17#12114yes—
484C2×Dic17#12314yes—
485C2×Dic17#12414yes—
486C2×Dic17#12614yes—
487C2×#390—171no—
488C2×#390—171no—
489C2×#390—171no—
490C2×#388—171no—
491C2×#388—171no—
492C2×C4×C4⋊C4—171no—
493C2×C4×C4⋊C4—171no—
494#1440—171no—
495#1440—171no—
496#1439—171no—
497#1439—171no—
498#1437—171no—
499#1437D1711yescharacteristic, complemented
500C4⋊#95—171no—
501C4⋊#95—171no—
502C22×C17—42no—
503C22×C17—42no—
504C22×C17—42no—
505C22×C17—42no—
506C22×C17—42no—
507C22×C17—42no—
508C22×C17—42no—
509C22×C17—81no—
510C22×C17—81no—
511C22×C17—81no—
512C22×C17—81no—
513C22×C17—81no—
514C22×C17—81no—
515C22×C17—81no—
516C22×C17—81no—
517C22×C17C2×#11711yescharacteristic
518C22×C17C2×C4×D411yescharacteristic
519C22×C17C2×C4×D411yescharacteristic
520C22×C17C2×C4×D411yescharacteristic
521C22×C17C4×#4111yescharacteristic
522C22×C17#51811yescharacteristic
523C22×C17#52011yescharacteristic
524C22×C17C2×#12111yescharacteristic
525C22×C17C2×#12111yescharacteristic
526C22×C17C2×#12311yescharacteristic
527C22×C17#52511yescharacteristic
528C22×C17C2×#12411yescharacteristic
529C22×C17C2×#12611yescharacteristic
530C22×C17#52911yescharacteristic
531C22×C17#53211yescharacteristic
532C22×C17#53511yescharacteristic
533C22×C17#53711yescharacteristic
534C22×C17#54011yescharacteristic
535C22×C17#54211yescharacteristic
536C22×C17D4211yescharacteristic
537C22×C17#54611yescharacteristic
538C22×C17#54711yescharacteristic
539C22×C17#54811yescharacteristic
540C22×C17#55011yescharacteristic
541C22×C17#55011yescharacteristic
542C22×C17#55011yescharacteristic
543C22×C17#55311yescharacteristic
544C22×C17#55311yescharacteristic
545C22×C17#55511yescharacteristic
546C22×C17#55611yescharacteristic
547C22×C17#55611yescharacteristic
548C22×C17#55911yescharacteristic
549C22×C17#55911yescharacteristic
550C22×C17#55911yescharacteristic
551C22×C17#55911yescharacteristic
552C2×D17—42no—
553C2×D17—42no—
554C2×D17—42no—
555C2×D17—42no—
556C2×D17—42no—
557C2×D17—42no—
558C2×D17—42no—
559C2×D17—81no—
560C2×D17—81no—
561C2×D17—81no—
562C2×D17—81no—
563C2×D17—81no—
564C2×D17—81no—
565C2×D17—81no—
566C2×D17—81no—
567C4×C17—24no—
568C4×C17—42no—
569C4×C17—42no—
570C4×C17—42no—
571C4×C17—42no—
572C4×C17—81no—
573Dic17—24no—
574Dic17—42no—
575Dic17—42no—
576Dic17—42no—
577Dic17—42no—
578Dic17—81no—
579Dic17#38818yescomplemented
580C23×D4—171no—
581C22×C4⋊C4—171no—
582C22×C4⋊C4—171no—
583C22×C4⋊C4—171no—
584C22×C4⋊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⋊C4—171no—
594C22×C22⋊C4—171no—
595C22×C22⋊C4C2×D1711yescharacteristic
596C22×C22⋊C4C2×D1711yescharacteristic
597C22×C22⋊C4C2×D1711yescharacteristic
598C22×C42—171no—
599C22×C42—171no—
600C22×C42—171no—
601C22×C42—171no—
602C22×C42C2×D1711yescharacteristic
603#390—178no—
604#390—344no—
605#390—344no—
606#388—344no—
607#388—344no—
608C4×C4⋊C4—344no—
609C4×C4⋊C4—344no—
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—82no—
623C2×C17C2×#38811yescharacteristic
624C2×C17C4×#12111yescharacteristic
625C2×C17#232411yescharacteristic
626C2×C17#235411yescharacteristic
627C2×C17#235711yescharacteristic
628C2×C17#236611yescharacteristic
629C2×C17#236711yescharacteristic
630C2×C17#241411yescharacteristic
631C2×C17#241611yescharacteristic
632C2×C17#244511yescharacteristic
633C2×C17#244811yescharacteristic
634C2×C17#251211yescharacteristic
635C2×C17#251311yescharacteristic
636C2×C17#254811yescharacteristic
637C2×C17#259211yescharacteristic
638D17—82no—
639C25—171no—
640C25C22×D1711yescharacteristic
641C22×D4—174no—
642C22×D4—342no—
643C22×D4—342no—
644C22×D4—342no—
645C22×D4—342no—
646C22×D4—342no—
647C22×D4—342no—
648C23×C4—171no—
649C23×C4—171no—
650C23×C4—171no—
651C23×C4—171no—
652C23×C4—171no—
653C23×C4—171no—
654C23×C4—171no—
655C23×C4C22×D1711yescharacteristic
656C23×C4C22×D1711yescharacteristic
657C23×C4C22×D1711yescharacteristic
658C23×C4C22×D1711yescharacteristic
659C23×C4C22×D1711yescharacteristic
660C23×C4C22×D1711yescharacteristic
661C2×C4⋊C4—174no—
662C2×C4⋊C4—174no—
663C2×C4⋊C4—174no—
664C2×C4⋊C4—342no—
665C2×C4⋊C4—342no—
666C2×C4⋊C4—342no—
667C2×C4⋊C4—342no—
668C2×C4⋊C4—342no—
669C2×C4⋊C4—342no—
670C2×C4⋊C4—342no—
671C2×C4⋊C4—342no—
672C2×C4⋊C4—342no—
673C2×C4⋊C4—342no—
674C2×C4⋊C4—342no—
675C2×C4⋊C4—342no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—174no—
685C2×C22⋊C4—174no—
686C2×C22⋊C4—174no—
687C2×C22⋊C4—342no—
688C2×C22⋊C4—342no—
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—342no—
702C2×C22⋊C4—681no—
703C2×C22⋊C4—681no—
704C2×C22⋊C4—681no—
705C2×C22⋊C4—681no—
706C2×C22⋊C4—681no—
707C2×C22⋊C4—681no—
708C2×C22⋊C4—681no—
709C2×C22⋊C4—681no—
710C2×C22⋊C4—681no—
711C2×C22⋊C4C4×D1714yes—
712C2×C42—22no—
713C2×C42—22no—
714C2×C42—41no—
715C2×C42—174no—
716C2×C42—174no—
717C2×C42—342no—
718C2×C42—342no—
719C2×C42—342no—
720C2×C42—342no—
721C2×C42—342no—
722C2×C42—342no—
723C2×C42—342no—
724C2×C42—342no—
725C2×C42—342no—
726C2×C42—681no—
727#95—22no—
728#95—41no—
729#95—41no—
730#95—342no—
731#95—342no—
732#95—342no—
733#95—342no—
734#95—342no—
735#95—342no—
736#95—342no—
737#95—681no—
738#95—681no—
739C17#1402211yescharacteristic, complemented, Sylow
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—172no—
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—
769C24C2×C4×D1712yes—
770C24C23×D1711yescharacteristic
771C2×D4—348no—
772C2×D4—348no—
773C2×D4—348no—
774C2×D4—684no—
775C2×D4—684no—
776C2×D4—684no—
777C2×D4—684no—
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—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—172no—
814C22×C4—172no—
815C22×C4—172no—
816C22×C4—172no—
817C22×C4—172no—
818C22×C4—172no—
819C22×C4—172no—
820C22×C4—172no—
821C22×C4—172no—
822C22×C4—172no—
823C22×C4—172no—
824C22×C4—172no—
825C22×C4—172no—
826C22×C4—172no—
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—341no—
862C22×C4C2×C4×D1712yes—
863C22×C4C2×C4×D1712yes—
864C22×C4#6325212yes—
865C22×C4#6325212yes—
866C22×C4D4×D1712yes—
867C22×C4D4×D1712yes—
868C22×C4D4×D1712yes—
869C4⋊C4—348no—
870C4⋊C4—348no—
871C4⋊C4—348no—
872C4⋊C4—348no—
873C4⋊C4—684no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—348no—
878C22⋊C4—348no—
879C22⋊C4—684no—
880C22⋊C4—684no—
881C22⋊C4—684no—
882C22⋊C4—684no—
883C22⋊C4—684no—
884C22⋊C4—684no—
885C22⋊C4—684no—
886C42—44no—
887C42—348no—
888C42—348no—
889C42—684no—
890C42—684no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
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—342no—
927C23—342no—
928C23—342no—
929C23—342no—
930C23—342no—
931C23—342no—
932C23—342no—
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—
961C23C22×C4×D1711yescharacteristic
962C23C2×#6325211yescharacteristic
963C23C2×#6325211yescharacteristic
964C23C2×D4×D1711yescharacteristic
965C23C2×D4×D1711yescharacteristic
966C23C2×D4×D1711yescharacteristic
967C23#1058769111yescharacteristic
968C23#1058769111yescharacteristic
969C23#1058769111yescharacteristic
970C23#41×D1711yescharacteristic
971C23#41×D1711yescharacteristic
972C23#41×D1711yescharacteristic
973C23#41×D1711yescharacteristic
974C23#41×D1711yescharacteristic
975C23#1058769711yescharacteristic
976D4—6816no—
977C2×C4—22no—
978C2×C4—22no—
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—22no—
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—174no—
1019C2×C4—174no—
1020C2×C4—174no—
1021C2×C4—174no—
1022C2×C4—174no—
1023C2×C4—174no—
1024C2×C4—174no—
1025C2×C4—174no—
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—681no—
1045C2×C4—681no—
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#1058757014yes—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—682no—
1084C22—682no—
1085C22—682no—
1086C22—682no—
1087C22—682no—
1088C22—682no—
1089C22—682no—
1090C22—1361no—
1091C22—1361no—
1092C22—1361no—
1093C22—1361no—
1094C22—1361no—
1095C22—1361no—
1096C22—1361no—
1097C22—1361no—
1098C22#117×D1711yescharacteristic
1099C22C4×D4×D1711yescharacteristic
1100C22C4×D4×D1711yescharacteristic
1101C22C4×D4×D1711yescharacteristic
1102C22C4×#6325211yescharacteristic
1103C22#1176328211yescharacteristic
1104C22#1176328811yescharacteristic
1105C22#121×D1711yescharacteristic
1106C22C2×#1058757011yescharacteristic
1107C22#123×D1711yescharacteristic
1108C22#1176331811yescharacteristic
1109C22#124×D1711yescharacteristic
1110C22#126×D1711yescharacteristic
1111C22#1176333711yescharacteristic
1112C22#1176335611yescharacteristic
1113C22#1176337211yescharacteristic
1114C22#1176338611yescharacteristic
1115C22#1176340911yescharacteristic
1116C22#1176342311yescharacteristic
1117C22#1176344111yescharacteristic
1118C22#1176344911yescharacteristic
1119C22#1176345711yescharacteristic
1120C22#1176346811yescharacteristic
1121C22#1176347711yescharacteristic
1122C22#1176347711yescharacteristic
1123C22#1176347711yescharacteristic
1124C22#1176350811yescharacteristic
1125C22#1176350811yescharacteristic
1126C22#1176352111yescharacteristic
1127C22#1176352611yescharacteristic
1128C22#1176352711yescharacteristic
1129C22#1176354211yescharacteristic
1130C22#1176354211yescharacteristic
1131C22#1176354211yescharacteristic
1132C22#1176354311yescharacteristic
1133C4—24no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—81no—
1139C4—178no—
1140C4—344no—
1141C4—682no—
1142C4—682no—
1143C4—682no—
1144C4—682no—
1145C4—1361no—
1146C2—82no—
1147C2—1362no—
1148C2D17×#38811yescharacteristic
1149C2C4×#1058757011yescharacteristic
1150C2#1453147011yescharacteristic
1151C2#1453173011yescharacteristic
1152C2#1453175811yescharacteristic
1153C2#1453184711yescharacteristic
1154C2#1453185611yescharacteristic
1155C2#1453219911yescharacteristic
1156C2#1453222311yescharacteristic
1157C2#1453254611yescharacteristic
1158C2#1453258111yescharacteristic
1159C2#1453336711yescharacteristic
1160C2#1453338011yescharacteristic
1161C2#1453378811yescharacteristic
1162C2#1453427011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1437C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1437D17
hypocenterC17#14022
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×#11762703C2semidirect
5. C2×#11762700C2semidirect
6. C2×C4×#63225C2semidirect
7. C2×#11762660C2semidirect
8. #14527033C2semidirect
9. #14527032C2semidirect
10. #14527028C2semidirect
11. #14527027C2semidirect
12. #14527020C2semidirect
13. #14527012C2semidirect
14. #14527012C2semidirect
15. C17×#1437C2semidirect
37. #11762709C4semidirect
133. C2×#63225D4semidirect
499. #1437D17semidirect
579. Dic17#388semidirect
739. C17#14022semidirect

Maximal subgroups

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

subgroupindex
C2×#117627092
C2×#117627032
C2×#117627002
C2×C4×#632252
C2×#117626602
#145270332
#145270322
#145270282
#145270272
#145270202
#145270122
C17×#14372
#1402217