Finite Group Databasebeta

← #16959993

Subgroups — #16959993

Order 4352.

1954 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762726C211yesmaximal, characteristic
2C2×#11762699C211yesmaximal, characteristic, complemented
3C2×#11762687C211yesmaximal, characteristic
4C2×C4×#63227C211yesmaximal, characteristic, complemented
5C2×#11762656C211yesmaximal, characteristic, complemented
6#14527032C211yesmaximal, characteristic, complemented
7#14527026C211yesmaximal, characteristic, complemented
8#14527024C211yesmaximal, characteristic
9#14527022C211yesmaximal, characteristic, complemented
10#14527020C211yesmaximal, characteristic, complemented
11#14527020C211yesmaximal, characteristic, complemented
12#14527016C211yesmaximal, characteristic, complemented
13#14527010C211yesmaximal, characteristic, complemented
14#14527010C211yesmaximal, characteristic, complemented
15C17×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×#63227C2211yescharacteristic
19C22×#63227C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762726C418yescomplemented
33#11762699—24no—
34#11762687—24no—
35C4×#63227—24no—
36#11762656—24no—
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×C4⋊C4×C17C2211yescharacteristic
50C22×C4⋊C4×C17C2211yescharacteristic
51C22×C42×C17C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C24×D17C2311yescharacteristic
57C24×D17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C22×D68—22no—
72C22×D68—22no—
73C22×D68—41no—
74C22×D68—41no—
75C22×D68—41no—
76C22×D68—41no—
77C22×D68C2×C414yes—
78C22×C4×D17—22no—
79C22×C4×D17—22no—
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—41no—
83C22×C4×D17—41no—
84C22×C4×D17D414yes—
85C2×C4⋊C4×C17—22no—
86C2×C4⋊C4×C17—22no—
87C2×C4⋊C4×C17—41no—
88C2×C4⋊C4×C17—41no—
89C2×C4⋊C4×C17—41no—
90C2×C4⋊C4×C17C2×C414yescomplemented
91C2×C42×C17—22no—
92C2×C42×C17—22no—
93C2×C42×C17—41no—
94C2×#63227—22no—
95C2×#63227—22no—
96C2×#63227—22no—
97C2×#63227—22no—
98C2×#63227—22no—
99C2×#63227—22no—
100C2×#63227—22no—
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—22no—
112C2×#63227—22no—
113C2×#63227—22no—
114C2×#63227—22no—
115C2×#63227—22no—
116C2×#63227—22no—
117C2×#63227—41no—
118C2×#63227—41no—
119C2×#63227—41no—
120C2×#63227—41no—
121C2×#63227—41no—
122C2×#63227—41no—
123C2×#63227C2×C414yes—
124C2×#63227C2×C414yes—
125C2×#63227C2×C414yescomplemented
126C2×#63227C2×C414yescomplemented
127C2×C4×Dic17—22no—
128C2×C4×Dic17—22no—
129C2×C4×Dic17—22no—
130C2×C4×Dic17—22no—
131C2×C4×Dic17—22no—
132C2×C4×Dic17—22no—
133C2×C4×Dic17—41no—
134C2×C4×Dic17—41no—
135C2×C4×Dic17—41no—
136C17×#95—22no—
137C17×#95—22no—
138C17×#95—41no—
139C17×#95—41no—
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—41no—
148#10587502—41no—
149#10587502—41no—
150#10587502C2×C414yescomplemented
151#10587502D414yescomplemented
152C24×C17C2411yescharacteristic
153C23×D17—21no—
154C23×D17—21no—
155C23×D17—21no—
156C23×D17—21no—
157C23×D17—21no—
158C23×D17—21no—
159C23×D17—21no—
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×D17C22×C412yes—
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×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17C22×C412yes—
223C22×C4×C17C22×C412yes—
224C22×C4×C17C22×C412yes—
225C22×C4×C17C2×D412yes—
226C22×C4×C17C2×D412yes—
227C22×C4×C17#4112yes—
228C22×C4×C17#4112yes—
229C22×C4×C17#4112yes—
230C22×C4×C17#4112yes—
231C22×C4×C17#4112yes—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
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×Dic17C22×C412yes—
268C22×Dic17C22×C412yes—
269C22×Dic17C2×D412yes—
270C22×Dic17C2×D412yes—
271C22×Dic17C2×D412yes—
272C22×Dic17#4112yes—
273C22×Dic17#4112yes—
274C2×D68—28no—
275C2×D68—44no—
276C2×D68—44no—
277C2×D68—44no—
278C2×D68—44no—
279C2×D68—44no—
280C2×D68—44no—
281C2×C4×D17—28no—
282C2×C4×D17—28no—
283C2×C4×D17—44no—
284C2×C4×D17—44no—
285C2×C4×D17—44no—
286C2×C4×D17—44no—
287C2×C4×D17—44no—
288C4⋊C4×C17—44no—
289C4⋊C4×C17—44no—
290C42×C17—44no—
291#63227—28no—
292#63227—28no—
293#63227—28no—
294#63227—28no—
295#63227—28no—
296#63227—44no—
297#63227—44no—
298#63227—44no—
299#63227—44no—
300#63227—44no—
301#63227—44no—
302C4×Dic17—44no—
303C4×Dic17—44no—
304C4×Dic17—44no—
305#14199—171nomaximal, Sylow
306C23×C17C23×C411yescharacteristic
307C23×C17C22×D411yescharacteristic
308C23×C17C22×D411yescharacteristic
309C23×C17C2×#4111yescharacteristic
310C23×C17C2×#4111yescharacteristic
311C23×C17C2×#4111yescharacteristic
312C23×C17C2×#4111yescharacteristic
313C23×C17C2×#4111yescharacteristic
314C23×C17C2×#4111yescharacteristic
315C23×C17C2×#4111yescharacteristic
316C23×C17C2×#4111yescharacteristic
317C23×C17H(5,𝔽2)11yescharacteristic
318C23×C17H(5,𝔽2)11yescharacteristic
319C23×C17H(5,𝔽2)11yescharacteristic
320C23×C17H(5,𝔽2)11yescharacteristic
321C22×D17—22no—
322C22×D17—22no—
323C22×D17—22no—
324C22×D17—22no—
325C22×D17—22no—
326C22×D17—22no—
327C22×D17—22no—
328C22×D17—22no—
329C22×D17—22no—
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—41no—
347C22×D17—41no—
348C22×D17—41no—
349C22×D17—41no—
350C22×D17—41no—
351C22×D17—41no—
352C22×D17—41no—
353C22×D17—41no—
354C22×D17—41no—
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×D17C4×D414yes—
391C2×C4×C17—22no—
392C2×C4×C17—22no—
393C2×C4×C17—22no—
394C2×C4×C17—22no—
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—22no—
414C2×C4×C17—22no—
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—41no—
437C2×C4×C17—41no—
438C2×C4×C17C4×D414yes—
439C2×C4×C17#12314yes—
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—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—41no—
480C2×Dic17—41no—
481C2×Dic17#12114yes—
482D68—416no—
483C4×D17—416no—
484C2×#394—171no—
485C2×#388—171no—
486C2×#386—171no—
487C2×C4×C22⋊C4—171no—
488C2×C4×C22⋊C4—171no—
489#1440—171no—
490#1439—171no—
491#1438—171no—
492#1437—171no—
493#1437—171no—
494#1437—171no—
495#1436—171no—
496C4⋊#95D1711yescharacteristic, complemented
497#1434—171no—
498#1434—171no—
499C22×C17C2×C4×D411yescharacteristic
500C22×C17C2×C4×D411yescharacteristic
501C22×C17C4×#4111yescharacteristic
502C22×C17C4×#4111yescharacteristic
503C22×C17C4×#4111yescharacteristic
504C22×C17#51811yescharacteristic
505C22×C17#51811yescharacteristic
506C22×C17C2×#12111yescharacteristic
507C22×C17C2×#12311yescharacteristic
508C22×C17#52511yescharacteristic
509C22×C17#52511yescharacteristic
510C22×C17#52911yescharacteristic
511C22×C17#52911yescharacteristic
512C22×C17#52911yescharacteristic
513C22×C17#53211yescharacteristic
514C22×C17#53411yescharacteristic
515C22×C17#53511yescharacteristic
516C22×C17#53811yescharacteristic
517C22×C17#53811yescharacteristic
518C22×C17#54611yescharacteristic
519C22×C17#54611yescharacteristic
520C22×C17#54611yescharacteristic
521C22×C17#55011yescharacteristic
522C22×C17#55111yescharacteristic
523C22×C17#55111yescharacteristic
524C22×C17#55111yescharacteristic
525C22×C17#55311yescharacteristic
526C22×C17#55311yescharacteristic
527C22×C17#55311yescharacteristic
528C22×C17#55311yescharacteristic
529C22×C17#55311yescharacteristic
530C22×C17#55511yescharacteristic
531C22×C17#55511yescharacteristic
532C22×C17#55511yescharacteristic
533C22×C17#55911yescharacteristic
534C2×D17—24no—
535C2×D17—24no—
536C2×D17—24no—
537C2×D17—42no—
538C2×D17—42no—
539C2×D17—42no—
540C2×D17—42no—
541C2×D17—42no—
542C2×D17—42no—
543C2×D17—42no—
544C2×D17—42no—
545C2×D17—42no—
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—81no—
557C2×D17—81no—
558C2×D17—81no—
559C2×D17—81no—
560C2×D17—81no—
561C2×D17—81no—
562C2×D17—81no—
563C2×D17—81no—
564C4×C17—24no—
565C4×C17—24no—
566C4×C17—42no—
567C4×C17—42no—
568C4×C17—42no—
569C4×C17—42no—
570C4×C17—81no—
571Dic17—24no—
572Dic17—42no—
573Dic17—42no—
574Dic17—42no—
575Dic17—42no—
576Dic17—81no—
577C23×D4—171no—
578C24×C4—171no—
579C22×C4⋊C4C2×D1711yescharacteristic
580C22×C4⋊C4C2×D1711yescharacteristic
581C22×C22⋊C4—171no—
582C22×C22⋊C4—171no—
583C22×C22⋊C4—171no—
584C22×C22⋊C4—171no—
585C22×C22⋊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×C42—171no—
593C22×C42—171no—
594C22×C42—171no—
595C22×C42C2×D1711yescharacteristic
596#394—178no—
597#388—344no—
598#386—344no—
599C4×C22⋊C4—344no—
600C4×C22⋊C4—344no—
601C2×#95—171no—
602C2×#95—171no—
603C2×#95—171no—
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×#95C2×D1711yescharacteristic
614C2×#95C2×D1711yescharacteristic
615C2×#95C2×D1711yescharacteristic
616C2×#95C2×D1711yescharacteristic
617C2×C17C4×#12111yescharacteristic
618C2×C17C4×#12311yescharacteristic
619C2×C17#232111yescharacteristic
620C2×C17#236311yescharacteristic
621C2×C17#236411yescharacteristic
622C2×C17#237211yescharacteristic
623C2×C17#237411yescharacteristic
624C2×C17#241211yescharacteristic
625C2×C17#241411yescharacteristic
626C2×C17#245911yescharacteristic
627C2×C17#246711yescharacteristic
628C2×C17#250011yescharacteristic
629C2×C17#251811yescharacteristic
630C2×C17#251811yescharacteristic
631C2×C17#260211yescharacteristic
632D17—44no—
633D17—82no—
634C25—171no—
635C25—171no—
636C22×D4—174no—
637C22×D4—342no—
638C22×D4—342no—
639C22×D4—681no—
640C22×D4—681no—
641C22×D4—681no—
642C22×D4—681no—
643C23×C4—171no—
644C23×C4—171no—
645C23×C4—171no—
646C23×C4—171no—
647C23×C4—171no—
648C23×C4—174no—
649C23×C4—171no—
650C23×C4—342no—
651C23×C4—342no—
652C23×C4—342no—
653C23×C4—342no—
654C23×C4—681no—
655C23×C4—681no—
656C23×C4C22×D1711yescharacteristic
657C23×C4C22×D1711yescharacteristic
658C23×C4C22×D1711yescharacteristic
659C23×C4C22×D1711yescharacteristic
660C23×C4C22×D1711yescharacteristic
661C23×C4C22×D1711yescharacteristic
662C23×C4C22×D1711yescharacteristic
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—41no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4C4×D1714yescomplemented
669C2×C22⋊C4—174no—
670C2×C22⋊C4—174no—
671C2×C22⋊C4—174no—
672C2×C22⋊C4—174no—
673C2×C22⋊C4—342no—
674C2×C22⋊C4—342no—
675C2×C22⋊C4—342no—
676C2×C22⋊C4—342no—
677C2×C22⋊C4—342no—
678C2×C22⋊C4—342no—
679C2×C22⋊C4—342no—
680C2×C22⋊C4—342no—
681C2×C22⋊C4—342no—
682C2×C22⋊C4—342no—
683C2×C22⋊C4—342no—
684C2×C22⋊C4—342no—
685C2×C22⋊C4—342no—
686C2×C22⋊C4—342no—
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—681no—
697C2×C22⋊C4—681no—
698C2×C22⋊C4—681no—
699C2×C22⋊C4—681no—
700C2×C22⋊C4—681no—
701C2×C22⋊C4—681no—
702C2×C42—22no—
703C2×C42—22no—
704C2×C42—41no—
705C2×C42—342no—
706C2×C42—342no—
707C2×C42—342no—
708C2×C42—342no—
709C2×C42—342no—
710C2×C42—342no—
711C2×C42—681no—
712C2×C42—681no—
713C2×C42—681no—
714#95—22no—
715#95—22no—
716#95—41no—
717#95—41no—
718#95—174no—
719#95—174no—
720#95—342no—
721#95—342no—
722#95—342no—
723#95—342no—
724#95—342no—
725#95—342no—
726#95—342no—
727#95—681no—
728#95—681no—
729#95—681no—
730C17#1419911yescharacteristic, complemented, Sylow
731C24—172no—
732C24—172no—
733C24—172no—
734C24—172no—
735C24—341no—
736C24—341no—
737C24—341no—
738C24—341no—
739C24—341no—
740C24—341no—
741C24—341no—
742C24—341no—
743C24—341no—
744C24—341no—
745C24—341no—
746C24—341no—
747C24—341no—
748C24—341no—
749C24—341no—
750C24—341no—
751C24—341no—
752C24—341no—
753C24—341no—
754C24—341no—
755C24—341no—
756C24—341no—
757C24—341no—
758C24—341no—
759C24—341no—
760C24—341no—
761C24C23×D1711yescharacteristic
762C2×D4—348no—
763C2×D4—684no—
764C2×D4—684no—
765C2×D4—684no—
766C2×D4—684no—
767C2×D4—684no—
768C2×D4—684no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
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—172no—
809C22×C4—172no—
810C22×C4—172no—
811C22×C4—172no—
812C22×C4—172no—
813C22×C4—172no—
814C22×C4—172no—
815C22×C4—348no—
816C22×C4—341no—
817C22×C4—341no—
818C22×C4—341no—
819C22×C4—341no—
820C22×C4—341no—
821C22×C4—341no—
822C22×C4—341no—
823C22×C4—341no—
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—348no—
845C22×C4—341no—
846C22×C4—341no—
847C22×C4—341no—
848C22×C4—341no—
849C22×C4—341no—
850C22×C4—341no—
851C22×C4—341no—
852C22×C4—684no—
853C22×C4—684no—
854C22×C4—684no—
855C22×C4—684no—
856C22×C4—684no—
857C22×C4C2×C4×D1712yes—
858C22×C4C2×C4×D1712yes—
859C22×C4C2×C4×D1712yes—
860C22×C4#6325212yes—
861C22×C4#6325212yes—
862C22×C4D4×D1712yes—
863C22×C4D4×D1712yes—
864C22×C4#6325612yes—
865C22×C4#6325612yes—
866C22×C4#6325612yes—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C22⋊C4—348no—
870C22⋊C4—348no—
871C22⋊C4—348no—
872C22⋊C4—348no—
873C22⋊C4—348no—
874C22⋊C4—684no—
875C22⋊C4—684no—
876C22⋊C4—684no—
877C22⋊C4—684no—
878C22⋊C4—684no—
879C22⋊C4—684no—
880C42—44no—
881C42—684no—
882C42—684no—
883C42—684no—
884C23—174no—
885C23—342no—
886C23—342no—
887C23—342no—
888C23—342no—
889C23—342no—
890C23—342no—
891C23—342no—
892C23—342no—
893C23—342no—
894C23—342no—
895C23—342no—
896C23—342no—
897C23—342no—
898C23—342no—
899C23—342no—
900C23—342no—
901C23—342no—
902C23—342no—
903C23—342no—
904C23—342no—
905C23—342no—
906C23—342no—
907C23—342no—
908C23—342no—
909C23—342no—
910C23—681no—
911C23—681no—
912C23—681no—
913C23—681no—
914C23—681no—
915C23—681no—
916C23—681no—
917C23—681no—
918C23—681no—
919C23—681no—
920C23—681no—
921C23—681no—
922C23—681no—
923C23—681no—
924C23—681no—
925C23—681no—
926C23—681no—
927C23—681no—
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—
954C23C22×C4×D1711yescharacteristic
955C23C2×#6325211yescharacteristic
956C23C2×#6325211yescharacteristic
957C23C2×D4×D1711yescharacteristic
958C23C2×D4×D1711yescharacteristic
959C23#1058769111yescharacteristic
960C23#1058769111yescharacteristic
961C23#1058769111yescharacteristic
962C23C2×#6325611yescharacteristic
963C23C2×#6325611yescharacteristic
964C23C2×#6325611yescharacteristic
965C23#41×D1711yescharacteristic
966C23#41×D1711yescharacteristic
967C23#41×D1711yescharacteristic
968C23#1058769611yescharacteristic
969D4—6816no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
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—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—174no—
1018C2×C4—342no—
1019C2×C4—342no—
1020C2×C4—342no—
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—6816no—
1037C2×C4—681no—
1038C2×C4—681no—
1039C2×C4—681no—
1040C2×C4—681no—
1041C2×C4—681no—
1042C2×C4—681no—
1043C2×C4—681no—
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#1058757914yes—
1061C2×C4#1058758014yes—
1062C22—344no—
1063C22—344no—
1064C22—344no—
1065C22—682no—
1066C22—682no—
1067C22—682no—
1068C22—682no—
1069C22—682no—
1070C22—682no—
1071C22—682no—
1072C22—682no—
1073C22—682no—
1074C22—682no—
1075C22—682no—
1076C22—682no—
1077C22—682no—
1078C22—682no—
1079C22—682no—
1080C22—682no—
1081C22—682no—
1082C22—682no—
1083C22—682no—
1084C22—1361no—
1085C22—1361no—
1086C22—1361no—
1087C22—1361no—
1088C22—1361no—
1089C22—1361no—
1090C22—1361no—
1091C22—1361no—
1092C22C4×D4×D1711yescharacteristic
1093C22C2×#1058757911yescharacteristic
1094C22C4×#6325211yescharacteristic
1095C22C4×#6325611yescharacteristic
1096C22C4×#6325611yescharacteristic
1097C22#1176328111yescharacteristic
1098C22#1176328211yescharacteristic
1099C22#121×D1711yescharacteristic
1100C22C2×#1058758011yescharacteristic
1101C22#1176331811yescharacteristic
1102C22#1176332211yescharacteristic
1103C22#1176333711yescharacteristic
1104C22#1176334411yescharacteristic
1105C22#1176334611yescharacteristic
1106C22#1176336011yescharacteristic
1107C22#1176336711yescharacteristic
1108C22#1176337211yescharacteristic
1109C22#1176339111yescharacteristic
1110C22#1176339311yescharacteristic
1111C22#1176344911yescharacteristic
1112C22#1176344911yescharacteristic
1113C22#1176345011yescharacteristic
1114C22#1176347711yescharacteristic
1115C22#1176348311yescharacteristic
1116C22#1176348611yescharacteristic
1117C22#1176348611yescharacteristic
1118C22#1176350711yescharacteristic
1119C22#1176350711yescharacteristic
1120C22#1176350711yescharacteristic
1121C22#1176350811yescharacteristic
1122C22#1176351211yescharacteristic
1123C22#1176352111yescharacteristic
1124C22#1176352511yescharacteristic
1125C22#1176352511yescharacteristic
1126C22#1176354411yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—81no—
1134C4—344no—
1135C4—682no—
1136C4—682no—
1137C4—682no—
1138C4—682no—
1139C4—1361no—
1140C2—684no—
1141C2—1362no—
1142C2#1453129211yescharacteristic
1143C2C4×#1058758011yescharacteristic
1144C2#1453144311yescharacteristic
1145C2#1453182111yescharacteristic
1146C2#1453183111yescharacteristic
1147C2#1453189511yescharacteristic
1148C2#1453191311yescharacteristic
1149C2#1453217711yescharacteristic
1150C2#1453219911yescharacteristic
1151C2#1453272811yescharacteristic
1152C2#1453284211yescharacteristic
1153C2#1453324311yescharacteristic
1154C2#1453343811yescharacteristic
1155C2#1453344111yescharacteristic
1156C2#1453439511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C4⋊#95C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenterC4⋊#95D17
hypocenterC17#14199
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#11762699C2semidirect
4. C2×C4×#63227C2semidirect
5. C2×#11762656C2semidirect
6. #14527032C2semidirect
7. #14527026C2semidirect
9. #14527022C2semidirect
10. #14527020C2semidirect
11. #14527020C2semidirect
12. #14527016C2semidirect
13. #14527010C2semidirect
14. #14527010C2semidirect
15. C17×C4⋊#95C2semidirect
32. #11762726C4semidirect
90. C2×C4⋊C4×C17C2×C4semidirect
125. C2×#63227C2×C4semidirect
126. C2×#63227C2×C4semidirect
150. #10587502C2×C4semidirect
151. #10587502D4semidirect
496. C4⋊#95D17semidirect
668. C2×C4⋊C4C4×D17semidirect
730. C17#14199semidirect

Maximal subgroups

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

subgroupindex
C2×#117627262
C2×#117626992
C2×#117626872
C2×C4×#632272
C2×#117626562
#145270322
#145270262
#145270242
#145270222
#145270202
#145270162
#145270102
C17×C4⋊#952
#1419917