Finite Group Databasebeta

← #16957641

Subgroups — #16957641

Order 4352.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762709C211yesmaximal, characteristic
2C2×#11762703C211yesmaximal, characteristic, complemented
3C2×#11762699C211yesmaximal, characteristic, complemented
4C2×#11762685C211yesmaximal, characteristic
5C2×#11762668C211yesmaximal, characteristic, complemented
6C2×C4×#63227C211yesmaximal, characteristic, complemented
7#14527047C211yesmaximal, characteristic, complemented
8#14527032C211yesmaximal, characteristic, complemented
9#14527027C211yesmaximal, characteristic, complemented
10#14527023C211yesmaximal, characteristic
11#14527021C211yesmaximal, characteristic, complemented
12#14527019C211yesmaximal, characteristic, complemented
13#14527017C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762709—24no—
33#11762703—24no—
34#11762699—24no—
35#11762685C418yescomplemented
36#11762668—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×C22⋊C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C17×#388—24no—
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—41no—
71C22×C22⋊D17—41no—
72C22×C22⋊D17C2×C414yes—
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
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—41no—
90C2×C22⋊C4×C17—22no—
91C2×C22⋊C4×C17—22no—
92C2×C22⋊C4×C17—22no—
93C2×C22⋊C4×C17—22no—
94C2×C22⋊C4×C17—22no—
95C2×C22⋊C4×C17—22no—
96C2×C22⋊C4×C17—41no—
97C2×C22⋊C4×C17—41no—
98C2×C22⋊C4×C17C2×C414yes—
99C2×C42×C17—22no—
100C2×C42×C17—22no—
101C2×C42×C17—41no—
102C2×C22⋊Dic17—22no—
103C2×C22⋊Dic17—22no—
104C2×C22⋊Dic17—22no—
105C2×C22⋊Dic17—22no—
106C2×C22⋊Dic17—22no—
107C2×C22⋊Dic17—22no—
108C2×C22⋊Dic17—41no—
109C2×C22⋊Dic17—41no—
110C2×C22⋊Dic17C2×C414yes—
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—41no—
123C2×#63227—41no—
124C2×#63227C2×C414yes—
125C2×#63227D414yes—
126C2×#63225—22no—
127C2×#63225—22no—
128C2×#63225—22no—
129C2×#63225—22no—
130C2×#63225—22no—
131C2×#63225—22no—
132C2×#63225—41no—
133C2×#63225—41no—
134C2×#63225—41no—
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—41no—
143C2×C4×Dic17—41no—
144C17×#95—22no—
145C17×#95D414yescomplemented
146#10587502—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—22no—
150#10587502—22no—
151#10587502—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—41no—
155#10587502C2×C414yes—
156#10587502C2×C414yes—
157#10587502D414yescomplemented
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×D17C22×C412yes—
187C23×D17C2×D412yes—
188C23×D17#4112yes—
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×C17C22×C412yes—
224C22×C4×C17C22×C412yes—
225C22×C4×C17C2×D412yes—
226C22×C4×C17C2×D412yes—
227C22×C4×C17C2×D412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17C2×D412yes—
230C22×C4×C17#4112yes—
231C2×C22⋊D17—28no—
232C2×C22⋊D17—28no—
233C2×C22⋊D17—44no—
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×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17C22×C412yes—
277C22×Dic17C22×C412yes—
278C22×Dic17C22×C412yes—
279C22×Dic17C2×D412yes—
280C22×Dic17C2×D412yes—
281C22×Dic17C2×D412yes—
282C22×Dic17#4112yes—
283C22×Dic17#4112yes—
284C22×Dic17#4112yes—
285C22×Dic17#4112yes—
286C22×Dic17#4112yes—
287C2×C4×D17—28no—
288C2×C4×D17—28no—
289C2×C4×D17—44no—
290C2×C4×D17—44no—
291C2×C4×D17—44no—
292C2×C4×D17—44no—
293C2×C4×D17—44no—
294C4⋊C4×C17—44no—
295C22⋊C4×C17—28no—
296C22⋊C4×C17—44no—
297C22⋊C4×C17—44no—
298C42×C17—44no—
299C22⋊Dic17—28no—
300C22⋊Dic17—44no—
301C22⋊Dic17—44no—
302#63227—28no—
303#63227—28no—
304#63227—28no—
305#63227—44no—
306#63227—44no—
307#63225—44no—
308#63225—44no—
309#63225—44no—
310C4×Dic17—44no—
311C4×Dic17—44no—
312C4×Dic17—44no—
313#14012—171nomaximal, Sylow
314C23×C17—22no—
315C23×C17—22no—
316C23×C17—22no—
317C23×C17—22no—
318C23×C17—22no—
319C23×C17—22no—
320C23×C17—22no—
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×C17—41no—
346C23×C17—41no—
347C23×C17—41no—
348C23×C17—41no—
349C23×C17C23×C411yescharacteristic
350C23×C17C22×D411yescharacteristic
351C23×C17C22×D411yescharacteristic
352C23×C17C22×D411yescharacteristic
353C23×C17C2×#4111yescharacteristic
354C23×C17C2×#4111yescharacteristic
355C23×C17C2×#4111yescharacteristic
356C23×C17C2×#4111yescharacteristic
357C23×C17C2×#4111yescharacteristic
358C23×C17C2×#4111yescharacteristic
359C23×C17C2×#4111yescharacteristic
360C23×C17H(5,𝔽2)11yescharacteristic
361C23×C17H(5,𝔽2)11yescharacteristic
362C23×C17H(5,𝔽2)11yescharacteristic
363C23×C172−1+411yescharacteristic
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—22no—
379C22×D17—22no—
380C22×D17—22no—
381C22×D17—22no—
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×D17C4×D414yes—
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—22no—
416C2×C4×C17—22no—
417C2×C4×C17—22no—
418C2×C4×C17—22no—
419C2×C4×C17—22no—
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×C17—41no—
439C2×C4×C17—41no—
440C2×C4×C17C4×D414yes—
441C22⋊D17—416no—
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—22no—
463C2×Dic17—22no—
464C2×Dic17—22no—
465C2×Dic17—22no—
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#11714yes—
489C2×Dic17C4×D414yes—
490C2×Dic17#12114yes—
491C4×D17—416no—
492C2×#390—171no—
493C2×#388—171no—
494C2×#388—171no—
495C2×#388D1711yescharacteristic, complemented
496C2×#386—171no—
497C2×#380—171no—
498C2×C4×C22⋊C4—171no—
499#1444—171no—
500#1440—171no—
501#1439—171no—
502#1438—171no—
503#1437—171no—
504#1436—171no—
505#1436—171no—
506C4×#95—171no—
507C22×C17—42no—
508C22×C17—42no—
509C22×C17—42no—
510C22×C17—42no—
511C22×C17—42no—
512C22×C17—42no—
513C22×C17—42no—
514C22×C17—81no—
515C22×C17—81no—
516C22×C17—81no—
517C22×C17—81no—
518C22×C17—81no—
519C22×C17—81no—
520C22×C17—81no—
521C22×C17—81no—
522C22×C17C2×#11711yescharacteristic
523C22×C17C2×C4×D411yescharacteristic
524C22×C17C2×C4×D411yescharacteristic
525C22×C17C2×C4×D411yescharacteristic
526C22×C17C4×#4111yescharacteristic
527C22×C17#51811yescharacteristic
528C22×C17#52011yescharacteristic
529C22×C17C2×#12111yescharacteristic
530C22×C17#52511yescharacteristic
531C22×C17#52911yescharacteristic
532C22×C17#52911yescharacteristic
533C22×C17#52911yescharacteristic
534C22×C17#53211yescharacteristic
535C22×C17#53211yescharacteristic
536C22×C17#53211yescharacteristic
537C22×C17#53811yescharacteristic
538C22×C17#53911yescharacteristic
539C22×C17#54011yescharacteristic
540C22×C17#54211yescharacteristic
541C22×C17D4211yescharacteristic
542C22×C17D4211yescharacteristic
543C22×C17#54611yescharacteristic
544C22×C17#54611yescharacteristic
545C22×C17#54611yescharacteristic
546C22×C17#54611yescharacteristic
547C22×C17#54711yescharacteristic
548C22×C17#54711yescharacteristic
549C22×C17#54811yescharacteristic
550C22×C17#55011yescharacteristic
551C22×C17#55111yescharacteristic
552C22×C17#55111yescharacteristic
553C22×C17#55111yescharacteristic
554C22×C17#55311yescharacteristic
555C22×C17#55511yescharacteristic
556C22×C17#55611yescharacteristic
557C2×D17—24no—
558C2×D17—24no—
559C2×D17—24no—
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—
569C2×D17—42no—
570C2×D17—42no—
571C2×D17—42no—
572C4×C17—24no—
573C4×C17—42no—
574C4×C17—42no—
575C4×C17—42no—
576C4×C17—42no—
577C4×C17—42no—
578Dic17—24no—
579Dic17—24no—
580Dic17—24no—
581Dic17—42no—
582Dic17—42no—
583Dic17—81no—
584Dic17—81no—
585C23×D4—171no—
586C24×C4—171no—
587C22×C4⋊C4—171no—
588C22×C4⋊C4—171no—
589C22×C4⋊C4—171no—
590C22×C4⋊C4C2×D1711yescharacteristic
591C22×C22⋊C4—171no—
592C22×C22⋊C4—171no—
593C22×C22⋊C4—171no—
594C22×C22⋊C4—171no—
595C22×C22⋊C4—171no—
596C22×C22⋊C4—171no—
597C22×C22⋊C4—171no—
598C22×C22⋊C4—171no—
599C22×C22⋊C4C2×D1711yescharacteristic
600C22×C22⋊C4C2×D1711yescharacteristic
601C22×C22⋊C4C2×D1711yescharacteristic
602C22×C42—171no—
603C22×C42—171no—
604C22×C42—171no—
605C22×C42C2×D1711yescharacteristic
606#390—344no—
607#388—24no—
608#388—344no—
609#388—344no—
610#386—178no—
611#380—344no—
612C4×C22⋊C4—344no—
613C2×#95—171no—
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×#95C2×D1711yescharacteristic
626C2×#95C2×D1711yescharacteristic
627C2×C17—82no—
628C2×C17#229311yescharacteristic
629C2×C17C4×#12111yescharacteristic
630C2×C17#233511yescharacteristic
631C2×C17#234211yescharacteristic
632C2×C17#235411yescharacteristic
633C2×C17#235811yescharacteristic
634C2×C17#236111yescharacteristic
635C2×C17#242511yescharacteristic
636C2×C17#242811yescharacteristic
637C2×C17#246111yescharacteristic
638C2×C17#246711yescharacteristic
639C2×C17#252111yescharacteristic
640C2×C17#253111yescharacteristic
641C2×C17#255511yescharacteristic
642C2×C17#256011yescharacteristic
643D17—44no—
644C25—171no—
645C25C22×D1711yescharacteristic
646C22×D4—174no—
647C22×D4—342no—
648C22×D4—342no—
649C22×D4—342no—
650C22×D4—342no—
651C22×D4—681no—
652C22×D4—681no—
653C23×C4—171no—
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
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—41no—
676C2×C4⋊C4—342no—
677C2×C4⋊C4—342no—
678C2×C4⋊C4—342no—
679C2×C4⋊C4—342no—
680C2×C4⋊C4—342no—
681C2×C4⋊C4—342no—
682C2×C4⋊C4—681no—
683C2×C4⋊C4—681no—
684C2×C4⋊C4—681no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—174no—
694C2×C22⋊C4—174no—
695C2×C22⋊C4—174no—
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—681no—
714C2×C22⋊C4—681no—
715C2×C22⋊C4—681no—
716C2×C22⋊C4—681no—
717C2×C22⋊C4C4×D1714yes—
718C2×C42—22no—
719C2×C42—22no—
720C2×C42—41no—
721C2×C42—342no—
722C2×C42—342no—
723C2×C42—342no—
724C2×C42—342no—
725C2×C42—342no—
726C2×C42—342no—
727C2×C42—342no—
728C2×C42—681no—
729C2×C42—681no—
730#95—22no—
731#95—174no—
732#95—174no—
733#95—174no—
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#95C22⋊D1714yescomplemented
744C17#1401211yescharacteristic, complemented, Sylow
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—172no—
760C24—172no—
761C24—172no—
762C24—341no—
763C24—341no—
764C24—341no—
765C24—341no—
766C24—341no—
767C24—341no—
768C24—341no—
769C24—341no—
770C24—341no—
771C24—341no—
772C24—341no—
773C24—341no—
774C24C2×C4×D1712yes—
775C24C23×D1711yescharacteristic
776C2×D4—348no—
777C2×D4—348no—
778C2×D4—684no—
779C2×D4—684no—
780C2×D4—684no—
781C2×D4—684no—
782C2×D4—684no—
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—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
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—172no—
828C22×C4—348no—
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—348no—
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—341no—
864C22×C4—341no—
865C22×C4—341no—
866C22×C4—341no—
867C22×C4—341no—
868C22×C4—684no—
869C22×C4—684no—
870C22×C4—684no—
871C22×C4—684no—
872C22×C4—684no—
873C22×C4C2×C4×D1712yes—
874C22×C4C2×C4×D1712yes—
875C22×C4#6325212yes—
876C22×C4D4×D1712yes—
877C22×C4D4×D1712yes—
878C22×C4C2×C22⋊D1712yes—
879C22×C4C2×C22⋊D1712yes—
880C22×C4C2×C22⋊D1712yes—
881C4⋊C4—44no—
882C4⋊C4—684no—
883C4⋊C4—684no—
884C4⋊C4—684no—
885C22⋊C4—28no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—348no—
889C22⋊C4—348no—
890C22⋊C4—348no—
891C22⋊C4—348no—
892C22⋊C4—684no—
893C22⋊C4—684no—
894C22⋊C4—684no—
895C22⋊C4—684no—
896C42—44no—
897C42—684no—
898C42—684no—
899C42—684no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
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—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—174no—
936C23—342no—
937C23—342no—
938C23—342no—
939C23—342no—
940C23—342no—
941C23—342no—
942C23—342no—
943C23—342no—
944C23—342no—
945C23—342no—
946C23—342no—
947C23—342no—
948C23—342no—
949C23—342no—
950C23—342no—
951C23—342no—
952C23—342no—
953C23—342no—
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—
970C23C22×C4×D1711yescharacteristic
971C23C2×#6325211yescharacteristic
972C23C2×D4×D1711yescharacteristic
973C23C2×D4×D1711yescharacteristic
974C23#1058769111yescharacteristic
975C23#1058769111yescharacteristic
976C23#41×D1711yescharacteristic
977C23#41×D1711yescharacteristic
978C23#41×D1711yescharacteristic
979C23#41×D1711yescharacteristic
980C23#41×D1711yescharacteristic
981C23#41×D1711yescharacteristic
982C23#1058769611yescharacteristic
983C23#1058769711yescharacteristic
984C23C22×C22⋊D1711yescharacteristic
985D4—6816no—
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—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—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—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—174no—
1028C2×C4—174no—
1029C2×C4—174no—
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—342no—
1046C2×C4—342no—
1047C2×C4—342no—
1048C2×C4—342no—
1049C2×C4—342no—
1050C2×C4—342no—
1051C2×C4—342no—
1052C2×C4—342no—
1053C2×C4—342no—
1054C2×C4—6816no—
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—681no—
1077C2×C4C4×C22⋊D1714yes—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—344no—
1094C22—344no—
1095C22—344no—
1096C22—682no—
1097C22—682no—
1098C22—682no—
1099C22—682no—
1100C22—682no—
1101C22—682no—
1102C22—682no—
1103C22—682no—
1104C22—682no—
1105C22—682no—
1106C22—682no—
1107C22—682no—
1108C22#117×D1711yescharacteristic
1109C22C4×D4×D1711yescharacteristic
1110C22C4×D4×D1711yescharacteristic
1111C22C2×C4×C22⋊D1711yescharacteristic
1112C22#1176327711yescharacteristic
1113C22#1176328111yescharacteristic
1114C22#1176328811yescharacteristic
1115C22#121×D1711yescharacteristic
1116C22#1176331711yescharacteristic
1117C22#1176333711yescharacteristic
1118C22#1176333711yescharacteristic
1119C22#1176334211yescharacteristic
1120C22#1176335511yescharacteristic
1121C22#1176335511yescharacteristic
1122C22#1176335811yescharacteristic
1123C22#1176339311yescharacteristic
1124C22#1176340011yescharacteristic
1125C22#1176340911yescharacteristic
1126C22#1176342711yescharacteristic
1127C22D4×C22⋊D1711yescharacteristic
1128C22D4×C22⋊D1711yescharacteristic
1129C22#1176344711yescharacteristic
1130C22#1176344811yescharacteristic
1131C22#1176345211yescharacteristic
1132C22#1176345511yescharacteristic
1133C22#1176345711yescharacteristic
1134C22#1176346411yescharacteristic
1135C22#1176346611yescharacteristic
1136C22#1176347711yescharacteristic
1137C22#1176348411yescharacteristic
1138C22#1176348711yescharacteristic
1139C22#1176348811yescharacteristic
1140C22#1176350911yescharacteristic
1141C22#1176352111yescharacteristic
1142C22#1176352611yescharacteristic
1143C4—24no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—344no—
1150C4—344no—
1151C4—344no—
1152C4—682no—
1153C4—682no—
1154C4—1361no—
1155C4—1361no—
1156C2—82no—
1157C2—684no—
1158C2#1453124311yescharacteristic
1159C2#1453129611yescharacteristic
1160C2#1453157211yescharacteristic
1161C2#1453163211yescharacteristic
1162C2#1453173011yescharacteristic
1163C2#1453176111yescharacteristic
1164C2#1453179611yescharacteristic
1165C2#1453234011yescharacteristic
1166C2#1453236911yescharacteristic
1167C2#1453275011yescharacteristic
1168C2#1453283411yescharacteristic
1169C2#1453348511yescharacteristic
1170C2#1453362911yescharacteristic
1171C2#1453385511yescharacteristic
1172C2#1453392611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×#388D17
hypocenterC17#14012
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#11762703C2semidirect
3. C2×#11762699C2semidirect
5. C2×#11762668C2semidirect
6. C2×C4×#63227C2semidirect
7. #14527047C2semidirect
8. #14527032C2semidirect
9. #14527027C2semidirect
11. #14527021C2semidirect
12. #14527019C2semidirect
13. #14527017C2semidirect
14. #95×Dic17C2semidirect
15. C2×C17×#388C2semidirect
35. #11762685C4semidirect
145. C17×#95D4semidirect
157. #10587502D4semidirect
495. C2×#388D17semidirect
743. #95C22⋊D17semidirect
744. C17#14012semidirect

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×#117626992
C2×#117626852
C2×#117626682
C2×C4×#632272
#145270472
#145270322
#145270272
#145270232
#145270212
#145270192
#145270172
#95×Dic172
C2×C17×#3882
#1401217