Finite Group Databasebeta

← #16958760

Subgroups — #16958760

Order 4352.

2158 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587615C211yesmaximal, characteristic
2C2×#11762709C211yesmaximal, characteristic
3C2×#11762693C211yesmaximal, characteristic, complemented
4C2×C4×#63225C211yesmaximal, characteristic, complemented
5#14527035C211yesmaximal, characteristic, complemented
6#14527028C211yesmaximal, characteristic, complemented
7#14527027C211yesmaximal, characteristic, complemented
8#14527023C211yesmaximal, characteristic
9#14527022C211yesmaximal, characteristic, complemented
10#14527022C211yesmaximal, characteristic, complemented
11#14527021C211yesmaximal, characteristic, complemented
12#14527020C211yesmaximal, characteristic, complemented
13#14527015C211yesmaximal, characteristic, complemented
14#14527007C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C17C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C2×#10587615—24no—
18C2×#10587615—24no—
19C2×#10587615C418yescomplemented
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35#11762709—24no—
36#11762693—24no—
37C4×#63225—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
50C24×C4×C17C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C42×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C4×C22⋊C4×C17—24no—
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C24×D17C2311yescharacteristic
60C23×C4×C17—22no—
61C23×C4×C17—22no—
62C23×C4×C17—22no—
63C23×C4×C17—22no—
64C23×C4×C17—41no—
65C23×C4×C17—41no—
66C23×C4×C17C2×C414yes—
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C22×C22⋊D17—22no—
74C22×C22⋊D17—22no—
75C22×C22⋊D17—22no—
76C22×C22⋊D17—22no—
77C22×C22⋊D17—41no—
78C22×C22⋊D17—41no—
79C22×C22⋊D17C2×C414yes—
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C2×C22⋊C4×C17—22no—
88C2×C22⋊C4×C17—22no—
89C2×C22⋊C4×C17—22no—
90C2×C22⋊C4×C17—22no—
91C2×C22⋊C4×C17—22no—
92C2×C22⋊C4×C17D414yes—
93C2×C42×C17—22no—
94C2×C42×C17—22no—
95C2×C42×C17—22no—
96C2×C42×C17—22no—
97C2×C42×C17—41no—
98C2×C42×C17—41no—
99C2×C22⋊Dic17—22no—
100C2×C22⋊Dic17—22no—
101C2×C22⋊Dic17—22no—
102C2×C22⋊Dic17—22no—
103C2×C22⋊Dic17—22no—
104C2×C22⋊Dic17—22no—
105C2×C22⋊Dic17—41no—
106C2×C22⋊Dic17—41no—
107C2×C22⋊Dic17C2×C414yes—
108#10587615—232no—
109C2×#63227—22no—
110C2×#63227—22no—
111C2×#63227—22no—
112C2×#63227—22no—
113C2×#63227—22no—
114C2×#63227—22no—
115C2×#63227—22no—
116C2×#63227—22no—
117C2×#63227—22no—
118C2×#63227—22no—
119C2×#63227—22no—
120C2×#63227—22no—
121C2×#63227—41no—
122C2×#63227—41no—
123C2×#63227—41no—
124C2×#63227—41no—
125C2×#63227C2×C414yes—
126C2×#63227C2×C414yes—
127C2×#63225—22no—
128C2×#63225—22no—
129C2×#63225—22no—
130C2×#63225—22no—
131C2×#63225—22no—
132C2×#63225—22no—
133C2×#63225—22no—
134C2×#63225—41no—
135C2×#63225C2×C414yes—
136C2×#63225C2×C414yes—
137C2×#63225D414yes—
138C2×#63225D414yes—
139C2×C4×Dic17—22no—
140C2×C4×Dic17—22no—
141C2×C4×Dic17—22no—
142C2×C4×Dic17—22no—
143C2×C4×Dic17—22no—
144C2×C4×Dic17—41no—
145C17×#95—22no—
146C17×#95—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—22no—
150#10587502—22no—
151#10587502—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—22no—
155#10587502—41no—
156#10587502—41no—
157#10587502—41no—
158#10587502—41no—
159C24×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×C17C22×C412yes—
172C24×C17C2×D412yes—
173C24×C17#4112yes—
174C24×C17C2411yescharacteristic
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×D17—21no—
189C23×D17C22×C412yes—
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—28no—
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—28no—
224C22×C4×C17—44no—
225C22×C4×C17—44no—
226C22×C4×C17—44no—
227C22×C4×C17—44no—
228C22×C4×C17—44no—
229C22×C4×C17C22×C412yes—
230C22×C4×C17C22×C412yes—
231C22×C4×C17C2×D412yes—
232C22×C4×C17C2×D412yes—
233C22×C4×C17C2×D412yes—
234C22×C4×C17C2×D412yes—
235C22×C4×C17#4112yes—
236C22×C4×C17#4112yes—
237C22×C4×C17#4112yes—
238C22×C4×C17#4112yes—
239C2×C22⋊D17—28no—
240C2×C22⋊D17—28no—
241C2×C22⋊D17—44no—
242C2×C22⋊D17—44no—
243C2×C22⋊D17—44no—
244C2×C22⋊D17—44no—
245C2×C22⋊D17—44no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17—21no—
280C22×Dic17—21no—
281C22×Dic17—21no—
282C22×Dic17—21no—
283C22×Dic17—21no—
284C22×Dic17—21no—
285C22×Dic17—21no—
286C22×Dic17C22×C412yes—
287C22×Dic17C22×C412yes—
288C22×Dic17C22×C412yes—
289C22×Dic17C2×D412yes—
290C22×Dic17C2×D412yes—
291C22×Dic17C2×D412yes—
292C22×Dic17C2×D412yes—
293C22×Dic17#4112yes—
294C22×Dic17#4112yes—
295C22⋊C4×C17—28no—
296C22⋊C4×C17—28no—
297C42×C17—44no—
298C42×C17—44no—
299C22⋊Dic17—28no—
300C22⋊Dic17—44no—
301C22⋊Dic17—44no—
302#63227—28no—
303#63227—28no—
304#63227—44no—
305#63227—44no—
306#63227—44no—
307#63227—44no—
308#63225—28no—
309#63225—28no—
310#63225—44no—
311#63225C22⋊C4116yescomplemented
312C4×Dic17—28no—
313C4×Dic17—44no—
314#14095—171nomaximal, Sylow
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—22no—
329C23×C17—22no—
330C23×C17—22no—
331C23×C17—22no—
332C23×C17—22no—
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×C17C4×D414yes—
350C23×C17C23×C411yescharacteristic
351C23×C17C22×D411yescharacteristic
352C23×C17C22×D411yescharacteristic
353C23×C17C22×D411yescharacteristic
354C23×C17C2×#4111yescharacteristic
355C23×C17C2×#4111yescharacteristic
356C23×C17C2×#4111yescharacteristic
357C23×C17C2×#4111yescharacteristic
358C23×C17C2×#4111yescharacteristic
359C23×C17C2×#4111yescharacteristic
360C23×C17C2×#4111yescharacteristic
361C23×C17H(5,𝔽2)11yescharacteristic
362C23×C17H(5,𝔽2)11yescharacteristic
363C23×C17H(5,𝔽2)11yescharacteristic
364C23×C172−1+411yescharacteristic
365C22×D17—22no—
366C22×D17—22no—
367C22×D17—22no—
368C22×D17—22no—
369C22×D17—22no—
370C22×D17—22no—
371C22×D17—22no—
372C22×D17—41no—
373C22×D17—41no—
374C22×D17—41no—
375C22×D17—41no—
376C22×D17—41no—
377C22×D17—41no—
378C22×D17—41no—
379C22×D17—41no—
380C22×D17—41no—
381C22×D17—41no—
382C22×D17—41no—
383C22×D17—41no—
384C22×D17—41no—
385C22×D17—41no—
386C22×D17—41no—
387C22×D17—41no—
388C22×D17—41no—
389C22×D17—41no—
390C22×D17—41no—
391C22×D17—41no—
392C22×D17—41no—
393C22×D17—41no—
394C22×D17—41no—
395C22×D17—41no—
396C22×D17—41no—
397C22×D17—41no—
398C22×D17—41no—
399C22×D17—41no—
400C2×C4×C17—22no—
401C2×C4×C17—22no—
402C2×C4×C17—22no—
403C2×C4×C17—22no—
404C2×C4×C17—22no—
405C2×C4×C17—22no—
406C2×C4×C17—22no—
407C2×C4×C17—22no—
408C2×C4×C17—22no—
409C2×C4×C17—22no—
410C2×C4×C17—22no—
411C2×C4×C17—22no—
412C2×C4×C17—22no—
413C2×C4×C17—22no—
414C2×C4×C17—22no—
415C2×C4×C17—22no—
416C2×C4×C17—22no—
417C2×C4×C17—22no—
418C2×C4×C17—22no—
419C2×C4×C17—22no—
420C2×C4×C17—22no—
421C2×C4×C17—22no—
422C2×C4×C17—22no—
423C2×C4×C17—22no—
424C2×C4×C17—416no—
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×C17—41no—
441C2×C4×C17C2×C22⋊C414yes—
442C2×C4×C17#12314yescomplemented
443C22⋊D17—416no—
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—41no—
466C2×Dic17—41no—
467C2×Dic17—41no—
468C2×Dic17—41no—
469C2×Dic17—41no—
470C2×Dic17—41no—
471C2×Dic17—41no—
472C2×Dic17—41no—
473C2×Dic17—41no—
474C2×Dic17—41no—
475C2×Dic17—41no—
476C2×Dic17—41no—
477C2×Dic17—41no—
478C2×Dic17—41no—
479C2×Dic17—41no—
480C2×Dic17—41no—
481C2×Dic17—41no—
482C2×Dic17—41no—
483C2×Dic17—41no—
484C2×Dic17—41no—
485C2×Dic17—41no—
486C2×Dic17—41no—
487C2×Dic17—41no—
488C2×Dic17—41no—
489C2×Dic17—41no—
490C2×Dic17—41no—
491C2×Dic17C2×C22⋊C414yes—
492C2×Dic17C2×C22⋊C414yes—
493C22×#123—171no—
494C2×#390—171no—
495C2×#387—171no—
496C2×C4×C4⋊C4—171no—
497C2×C4×C22⋊C4D1711yescharacteristic, complemented
498#1441—171no—
499#1439—171no—
500#1439—171no—
501#1438—171no—
502#1437—171no—
503#1437—171no—
504#1437—171no—
505#1437—171no—
506#1436—171no—
507C22⋊#95—171no—
508C22×C17—24no—
509C22×C17—24no—
510C22×C17—24no—
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×C17—42no—
520C22×C17—42no—
521C22×C17—42no—
522C22×C17—42no—
523C22×C17C22×C22⋊C411yescharacteristic
524C22×C17C2×C4×D411yescharacteristic
525C22×C17C4×#4111yescharacteristic
526C22×C17C4×#4111yescharacteristic
527C22×C17C4×#4111yescharacteristic
528C22×C17#51811yescharacteristic
529C22×C17#52011yescharacteristic
530C22×C17C2×#12311yescharacteristic
531C22×C17#52511yescharacteristic
532C22×C17#52511yescharacteristic
533C22×C17#52511yescharacteristic
534C22×C17#52911yescharacteristic
535C22×C17#52911yescharacteristic
536C22×C17#53211yescharacteristic
537C22×C17#53211yescharacteristic
538C22×C17#53811yescharacteristic
539C22×C17#53911yescharacteristic
540C22×C17#54011yescharacteristic
541C22×C17#54211yescharacteristic
542C22×C17D4211yescharacteristic
543C22×C17D4211yescharacteristic
544C22×C17#54611yescharacteristic
545C22×C17#54611yescharacteristic
546C22×C17#54611yescharacteristic
547C22×C17#54711yescharacteristic
548C22×C17#54811yescharacteristic
549C22×C17#54811yescharacteristic
550C22×C17#55011yescharacteristic
551C22×C17#55011yescharacteristic
552C22×C17#55111yescharacteristic
553C22×C17#55111yescharacteristic
554C22×C17#55211yescharacteristic
555C22×C17#55311yescharacteristic
556C22×C17#55311yescharacteristic
557C22×C17#55911yescharacteristic
558C2×D17—42no—
559C2×D17—42no—
560C2×D17—42no—
561C2×D17—42no—
562C2×D17—42no—
563C2×D17—42no—
564C2×D17—42no—
565C2×D17—81no—
566C2×D17—81no—
567C2×D17—81no—
568C2×D17—81no—
569C2×D17—81no—
570C2×D17—81no—
571C2×D17—81no—
572C2×D17—81no—
573C4×C17—24no—
574C4×C17—24no—
575C4×C17—42no—
576C4×C17—42no—
577C4×C17—42no—
578C4×C17—42no—
579Dic17—24no—
580Dic17—24no—
581Dic17—42no—
582Dic17—42no—
583Dic17—42no—
584Dic17—81no—
585Dic17—81no—
586C23×D4—171no—
587C24×C4C2×D1711yescharacteristic
588C2×#123—178no—
589C2×#123—344no—
590C2×#123—344no—
591C22×C4⋊C4—171no—
592C22×C4⋊C4—171no—
593C22×C4⋊C4—171no—
594C22×C4⋊C4—171no—
595C22×C22⋊C4—171no—
596C22×C22⋊C4—171no—
597C22×C22⋊C4—171no—
598C22×C22⋊C4—171no—
599C22×C22⋊C4—171no—
600C22×C22⋊C4—171no—
601C22×C22⋊C4—171no—
602C22×C22⋊C4—171no—
603C22×C22⋊C4—171no—
604C22×C22⋊C4C2×D1711yescharacteristic
605C22×C22⋊C4C2×D1711yescharacteristic
606C22×C42—171no—
607C22×C42—171no—
608C22×C42C2×D1711yescharacteristic
609C22×C42C2×D1711yescharacteristic
610#390—344no—
611#387—344no—
612C4×C4⋊C4—344no—
613C4×C22⋊C4—24no—
614C2×#95—171no—
615C2×#95—171no—
616C2×#95—171no—
617C2×#95—171no—
618C2×#95—171no—
619C2×#95—171no—
620C2×#95—171no—
621C2×#95—171no—
622C2×#95—171no—
623C2×#95—171no—
624C2×#95—171no—
625C2×#95—171no—
626C2×#95C2×D1711yescharacteristic
627C2×#95C2×D1711yescharacteristic
628C2×C17—44no—
629C2×C17#229711yescharacteristic
630C2×C17C4×#12311yescharacteristic
631C2×C17#233511yescharacteristic
632C2×C17D4×C22⋊C411yescharacteristic
633C2×C17#234111yescharacteristic
634C2×C17#235911yescharacteristic
635C2×C17#237411yescharacteristic
636C2×C17#244311yescharacteristic
637C2×C17#244511yescharacteristic
638C2×C17#245611yescharacteristic
639C2×C17#245811yescharacteristic
640C2×C17#246111yescharacteristic
641C2×C17#247111yescharacteristic
642C2×C17#255411yescharacteristic
643C2×C17#255811yescharacteristic
644D17—82no—
645C25—171no—
646C25C22×D1711yescharacteristic
647C22×D4—174no—
648C22×D4—342no—
649C22×D4—342no—
650C22×D4—342no—
651C22×D4—342no—
652C22×D4—681no—
653C22×D4—681no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—41no—
659C23×C4—41no—
660C23×C4—171no—
661C23×C4—171no—
662C23×C4—171no—
663C23×C4—171no—
664C23×C4—171no—
665C23×C4—171no—
666C23×C4—171no—
667C23×C4C4×D1714yes—
668C23×C4C22×D1711yescharacteristic
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C23×C4C22×D1711yescharacteristic
672C23×C4C22×D1711yescharacteristic
673C23×C4C22×D1711yescharacteristic
674#123—3432no—
675C2×C4⋊C4—174no—
676C2×C4⋊C4—174no—
677C2×C4⋊C4—174no—
678C2×C4⋊C4—174no—
679C2×C4⋊C4—342no—
680C2×C4⋊C4—342no—
681C2×C4⋊C4—342no—
682C2×C4⋊C4—342no—
683C2×C4⋊C4—342no—
684C2×C4⋊C4—342no—
685C2×C4⋊C4—342no—
686C2×C4⋊C4—681no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—174no—
693C2×C22⋊C4—174no—
694C2×C22⋊C4—174no—
695C2×C22⋊C4—342no—
696C2×C22⋊C4—342no—
697C2×C22⋊C4—342no—
698C2×C22⋊C4—342no—
699C2×C22⋊C4—342no—
700C2×C22⋊C4—342no—
701C2×C22⋊C4—342no—
702C2×C22⋊C4—342no—
703C2×C22⋊C4—342no—
704C2×C22⋊C4—342no—
705C2×C22⋊C4—342no—
706C2×C22⋊C4—342no—
707C2×C22⋊C4—342no—
708C2×C22⋊C4—342no—
709C2×C22⋊C4—342no—
710C2×C22⋊C4—342no—
711C2×C22⋊C4—342no—
712C2×C22⋊C4—342no—
713C2×C22⋊C4—681no—
714C2×C22⋊C4—681no—
715C2×C22⋊C4—681no—
716C2×C22⋊C4—681no—
717C2×C22⋊C4—681no—
718C2×C22⋊C4—681no—
719C2×C22⋊C4C22⋊D1714yes—
720C2×C42—22no—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—41no—
725C2×C42—41no—
726C2×C42—342no—
727C2×C42—342no—
728C2×C42—342no—
729C2×C42—342no—
730C2×C42—342no—
731C2×C42—681no—
732#95—22no—
733#95—22no—
734#95—342no—
735#95—342no—
736#95—342no—
737#95—342no—
738#95—342no—
739#95—342no—
740#95—342no—
741#95—342no—
742#95—681no—
743#95—681no—
744#95—681no—
745#95—681no—
746C17#1409511yescharacteristic, complemented, Sylow
747C24—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—341no—
761C24—341no—
762C24—341no—
763C24—341no—
764C24—341no—
765C24—341no—
766C24—341no—
767C24—341no—
768C24—341no—
769C24—341no—
770C24—341no—
771C24—341no—
772C24—341no—
773C24—341no—
774C24C2×C4×D1712yes—
775C24#6325212yes—
776C24C2×C22⋊D1712yes—
777C24C23×D1711yescharacteristic
778C2×D4—348no—
779C2×D4—348no—
780C2×D4—684no—
781C2×D4—684no—
782C2×D4—684no—
783C2×D4—684no—
784C2×D4—684no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—28no—
818C22×C4—28no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—172no—
825C22×C4—172no—
826C22×C4—172no—
827C22×C4—172no—
828C22×C4—172no—
829C22×C4—172no—
830C22×C4—172no—
831C22×C4—172no—
832C22×C4—172no—
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×C4—341no—
863C22×C4—341no—
864C22×C4—341no—
865C22×C4—341no—
866C22×C4—341no—
867C22×C4—341no—
868C22×C4—341no—
869C22×C4—341no—
870C22×C4—341no—
871C22×C4—341no—
872C22×C4—341no—
873C22×C4C2×C4×D1712yes—
874C22×C4C2×C4×D1712yes—
875C22×C4#6325212yes—
876C22×C4#6325212yes—
877C22×C4#6325212yes—
878C22×C4#6325212yes—
879C22×C4D4×D1712yes—
880C22×C4D4×D1712yes—
881C22×C4C2×C22⋊D1712yes—
882C22×C4C2×C22⋊D1712yes—
883C4⋊C4—1716no—
884C4⋊C4—348no—
885C4⋊C4—348no—
886C4⋊C4—684no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—348no—
890C22⋊C4—348no—
891C22⋊C4—348no—
892C22⋊C4—684no—
893C22⋊C4—684no—
894C22⋊C4—684no—
895C22⋊C4—684no—
896C22⋊C4—684no—
897C22⋊C4—684no—
898C42—44no—
899C42—44no—
900C42—348no—
901C42—684no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
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—41no—
936C23—342no—
937C23—342no—
938C23—342no—
939C23—342no—
940C23—342no—
941C23—342no—
942C23—342no—
943C23—681no—
944C23—681no—
945C23—681no—
946C23—681no—
947C23—681no—
948C23—681no—
949C23—681no—
950C23—681no—
951C23—681no—
952C23—681no—
953C23—681no—
954C23—681no—
955C23—681no—
956C23—681no—
957C23—681no—
958C23—681no—
959C23—681no—
960C23—681no—
961C23—681no—
962C23—681no—
963C23—681no—
964C23—681no—
965C23—681no—
966C23—681no—
967C23—681no—
968C23—681no—
969C23—681no—
970C23—681no—
971C23C4×C22⋊D1714yes—
972C23C22×C4×D1711yescharacteristic
973C23C2×#6325211yescharacteristic
974C23C2×#6325211yescharacteristic
975C23C2×#6325211yescharacteristic
976C23C2×#6325211yescharacteristic
977C23C2×#6325211yescharacteristic
978C23C2×D4×D1711yescharacteristic
979C23C2×D4×D1711yescharacteristic
980C23#1058769111yescharacteristic
981C23#1058769111yescharacteristic
982C23#41×D1711yescharacteristic
983C23#41×D1711yescharacteristic
984C23#1058769611yescharacteristic
985C23#1058769711yescharacteristic
986C23C22×C22⋊D1711yescharacteristic
987D4—6816no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—416no—
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—41no—
1028C2×C4—41no—
1029C2×C4—174no—
1030C2×C4—174no—
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—681no—
1053C2×C4—681no—
1054C2×C4—681no—
1055C2×C4—681no—
1056C2×C4—681no—
1057C2×C4—681no—
1058C2×C4—681no—
1059C2×C4—681no—
1060C2×C4—681no—
1061C2×C4—681no—
1062C2×C4—681no—
1063C2×C4—681no—
1064C2×C4—681no—
1065C2×C4—681no—
1066C2×C4—681no—
1067C2×C4—681no—
1068C2×C4—681no—
1069C2×C4—681no—
1070C2×C4—681no—
1071C2×C4—681no—
1072C2×C4—681no—
1073C2×C4—681no—
1074C2×C4—681no—
1075C2×C4—681no—
1076C2×C4—681no—
1077C2×C4—681no—
1078C2×C4C22⋊C4×D1714yes—
1079C2×C4#1058761514yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—682no—
1096C22—682no—
1097C22—682no—
1098C22—682no—
1099C22—682no—
1100C22—682no—
1101C22—682no—
1102C22—1361no—
1103C22—1361no—
1104C22—1361no—
1105C22—1361no—
1106C22—1361no—
1107C22—1361no—
1108C22—1361no—
1109C22—1361no—
1110C22C2×C22⋊C4×D1711yescharacteristic
1111C22C2×C4×C22⋊D1711yescharacteristic
1112C22#1176327711yescharacteristic
1113C22C4×#6325211yescharacteristic
1114C22C4×#6325211yescharacteristic
1115C22#1176328211yescharacteristic
1116C22#1176328911yescharacteristic
1117C22C2×#1058761511yescharacteristic
1118C22#1176331811yescharacteristic
1119C22#1176331811yescharacteristic
1120C22#1176332011yescharacteristic
1121C22#1176334311yescharacteristic
1122C22#1176334311yescharacteristic
1123C22#1176335611yescharacteristic
1124C22#1176335611yescharacteristic
1125C22#1176339211yescharacteristic
1126C22#1176340111yescharacteristic
1127C22#1176341011yescharacteristic
1128C22#1176342411yescharacteristic
1129C22D4×C22⋊D1711yescharacteristic
1130C22D4×C22⋊D1711yescharacteristic
1131C22#1176344711yescharacteristic
1132C22#1176344911yescharacteristic
1133C22#1176344911yescharacteristic
1134C22#1176345811yescharacteristic
1135C22#1176346811yescharacteristic
1136C22#1176346811yescharacteristic
1137C22#1176348011yescharacteristic
1138C22#1176348011yescharacteristic
1139C22#1176348311yescharacteristic
1140C22#1176348811yescharacteristic
1141C22#1176349211yescharacteristic
1142C22#1176350811yescharacteristic
1143C22#1176350911yescharacteristic
1144C22#1176354211yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—344no—
1152C4—344no—
1153C4—682no—
1154C4—682no—
1155C4—682no—
1156C4—1361no—
1157C4—1361no—
1158C2—44no—
1159C2—1362no—
1160C2#1453127011yescharacteristic
1161C2C4×#1058761511yescharacteristic
1162C2#1453157411yescharacteristic
1163C2C22⋊C4×C22⋊D1711yescharacteristic
1164C2#1453162411yescharacteristic
1165C2#1453177611yescharacteristic
1166C2#1453191511yescharacteristic
1167C2#1453251311yescharacteristic
1168C2#1453254311yescharacteristic
1169C2#1453267611yescharacteristic
1170C2#1453270611yescharacteristic
1171C2#1453274511yescharacteristic
1172C2#1453289511yescharacteristic
1173C2#1453384411yescharacteristic
1174C2#1453389811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C4×C22⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×C4×C22⋊C4D17
hypocenterC17#14095
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#11762693C2semidirect
4. C2×C4×#63225C2semidirect
5. #14527035C2semidirect
6. #14527028C2semidirect
7. #14527027C2semidirect
9. #14527022C2semidirect
10. #14527022C2semidirect
11. #14527021C2semidirect
12. #14527020C2semidirect
13. #14527015C2semidirect
14. #14527007C2semidirect
15. C2×C4×C22⋊C4×C17C2semidirect
19. C2×#10587615C4semidirect
311. #63225C22⋊C4semidirect
442. C2×C4×C17#123semidirect
497. C2×C4×C22⋊C4D17semidirect
746. C17#14095semidirect
1079. C2×C4#10587615semidirect

Maximal subgroups

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

subgroupindex
C22×#105876152
C2×#117627092
C2×#117626932
C2×C4×#632252
#145270352
#145270282
#145270272
#145270232
#145270222
#145270212
#145270202
#145270152
#145270072
C2×C4×C22⋊C4×C172
#1409517