Finite Group Databasebeta

← #16957686

Subgroups — #16957686

Order 4352.

2950 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D17C211yesmaximal, characteristic
2C2×#11762688C211yesmaximal, characteristic
3C2×#11762688C211yesmaximal, characteristic
4C2×#11762682C211yesmaximal, characteristic, complemented
5C2×#11762680C212yesmaximal, complemented
6#14527047C212yesmaximal, complemented
7#14527026C212yesmaximal, complemented
8#14527016C212yesmaximal, complemented
9#14527007C211yesmaximal, characteristic, complemented
10#14527007C211yesmaximal, characteristic, complemented
11C23×C4⋊C4×C17C211yesmaximal, characteristic, complemented
12C23×C22⋊D17C2211yescharacteristic
13C23×C4×D17C2211yescharacteristic
14C2×C4×C22⋊D17—24no—
15C2×C4×C22⋊D17—24no—
16C2×C4×C22⋊D17—24no—
17C22×#63225C2211yescharacteristic
18C22×#63225C2212yes—
19C22×C22⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2212yes—
24C22×#63227C2212yes—
25C22×C4×Dic17C2211yescharacteristic
26#11762688—24no—
27#11762688C418yescomplemented
28#11762682—24no—
29#11762680—28no—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C2×#10587502C2212yes—
37C24×C4×C17C2211yescharacteristic
38C24×C4×C17C2211yescharacteristic
39C24×C4×C17C2211yescharacteristic
40C22×C4⋊C4×C17—28no—
41C22×C4⋊C4×C17—24no—
42C22×C4⋊C4×C17C2212yes—
43C22×C4⋊C4×C17C2212yes—
44C25×C17C2311yescharacteristic
45C24×D17C2311yescharacteristic
46C23×C4×C17—22no—
47C23×C4×C17—22no—
48C23×C4×C17—24no—
49C23×C4×C17—24no—
50C23×C4×C17—22no—
51C23×C4×C17—22no—
52C23×C4×C17—22no—
53C23×C4×C17—24no—
54C23×C4×C17—24no—
55C23×C4×C17—22no—
56C23×C4×C17—22no—
57C23×C4×C17—42no—
58C23×C4×C17—42no—
59C23×C4×C17C2×C414yescomplemented
60C23×C4×C17D414yes—
61C23×C4×C17C2312yes—
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2312yes—
64C23×C4×C17C2311yescharacteristic
65C22×C22⋊D17—22no—
66C22×C22⋊D17—22no—
67C22×C22⋊D17—22no—
68C22×C22⋊D17—22no—
69C22×C22⋊D17C2×C414yes—
70C22×C22⋊D17D414yes—
71C22×C22⋊D17Q814yes—
72C23×Dic17C2312yes—
73C23×Dic17C2312yes—
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C22×C4×D17—22no—
78C22×C4×D17—22no—
79C22×C4×D17—22no—
80C22×C4×D17—24no—
81C22×C4×D17—42no—
82C2×C4⋊C4×C17—232no—
83C2×C4⋊C4×C17—24no—
84C2×C4⋊C4×C17—24no—
85C2×C4⋊C4×C17—24no—
86C2×C4⋊C4×C17—24no—
87C2×C4⋊C4×C17—24no—
88C2×C4⋊C4×C17D418yescomplemented
89C2×C22⋊Dic17—22no—
90C2×C22⋊Dic17—22no—
91C2×C22⋊Dic17—22no—
92C2×C22⋊Dic17—22no—
93C2×C22⋊Dic17—22no—
94C2×C22⋊Dic17—22no—
95C2×C22⋊Dic17—22no—
96C2×C22⋊Dic17C2×C414yescomplemented
97C2×C22⋊Dic17D414yes—
98C4×C22⋊D17—232no—
99C2×#63227—22no—
100C2×#63227—24no—
101C2×#63227—22no—
102C2×#63227—24no—
103C2×#63227—24no—
104C2×#63227—24no—
105C2×#63227—22no—
106C2×#63227—42no—
107C2×#63227C2×C418yescomplemented
108C2×#63225—22no—
109C2×#63225—24no—
110C2×#63225—22no—
111C2×#63225—22no—
112C2×#63225—24no—
113C2×#63225—42no—
114C2×C4×Dic17—22no—
115C2×C4×Dic17—22no—
116C2×C4×Dic17—22no—
117#10587502—24no—
118#10587502—24no—
119#10587502—24no—
120#10587502—24no—
121#10587502—24no—
122#10587502—42no—
123#10587502C2×C418yescomplemented
124C24×C17—22no—
125C24×C17—22no—
126C24×C17—22no—
127C24×C17—22no—
128C24×C17C22×C412yes—
129C24×C17C2×D412yes—
130C24×C17C2×D412yes—
131C24×C17C2×D412yes—
132C24×C17C2×Q812yes—
133C24×C17#4112yes—
134C24×C17#4112yes—
135C24×C17C2411yescharacteristic
136C23×D17—21no—
137C23×D17—21no—
138C23×D17—22no—
139C23×D17—21no—
140C23×D17—21no—
141C23×D17—22no—
142C23×D17—22no—
143C23×D17—22no—
144C23×D17C22×C412yes—
145C23×D17C2×D412yes—
146C23×D17C2×Q812yes—
147C22×C4×C17—216no—
148C22×C4×C17—28no—
149C22×C4×C17—28no—
150C22×C4×C17—28no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—22no—
154C22×C4×C17—22no—
155C22×C4×C17—22no—
156C22×C4×C17—22no—
157C22×C4×C17—22no—
158C22×C4×C17—216no—
159C22×C4×C17—28no—
160C22×C4×C17—28no—
161C22×C4×C17—22no—
162C22×C4×C17—22no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—22no—
166C22×C4×C17—22no—
167C22×C4×C17—22no—
168C22×C4×C17—22no—
169C22×C4×C17—22no—
170C22×C4×C17—22no—
171C22×C4×C17—28no—
172C22×C4×C17—44no—
173C22×C4×C17—48no—
174C22×C4×C17—48no—
175C22×C4×C17—48no—
176C22×C4×C17—48no—
177C22×C4×C17—44no—
178C22×C4×C17—44no—
179C22×C4×C17C22×C414yes—
180C22×C4×C17C2×D414yes—
181C22×C4×C17C2×D412yes—
182C22×C4×C17C2×D414yes—
183C22×C4×C17C2×D414yes—
184C22×C4×C17C2×D412yes—
185C22×C4×C17#4114yes—
186C2×C22⋊D17—28no—
187C2×C22⋊D17—28no—
188C2×C22⋊D17—28no—
189C2×C22⋊D17—28no—
190C2×C22⋊D17—28no—
191C2×C22⋊D17—28no—
192C2×C22⋊D17C4⋊C4116yescomplemented
193C22×Dic17—21no—
194C22×Dic17—21no—
195C22×Dic17—21no—
196C22×Dic17—21no—
197C22×Dic17—22no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—22no—
201C22×Dic17—22no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—22no—
205C22×Dic17—22no—
206C22×Dic17—22no—
207C22×Dic17—22no—
208C22×Dic17—22no—
209C22×Dic17—22no—
210C22×Dic17—22no—
211C22×Dic17—22no—
212C22×Dic17—22no—
213C22×Dic17—22no—
214C22×Dic17—22no—
215C22×Dic17—22no—
216C22×Dic17—22no—
217C22×Dic17—22no—
218C22×Dic17C22×C414yes—
219C22×Dic17C22×C412yes—
220C22×Dic17C2×D412yes—
221C22×Dic17C2×D412yes—
222C22×Dic17C2×D412yes—
223C22×Dic17C2×Q812yes—
224C2×C4×D17—28no—
225C2×C4×D17—48no—
226C2×C4×D17—48no—
227C2×C4×D17—44no—
228C2×C4×D17—44no—
229C4⋊C4×C17—216no—
230C4⋊C4×C17—216no—
231C22⋊Dic17—28no—
232C22⋊Dic17—28no—
233C22⋊Dic17—44no—
234#63227—28no—
235#63227—216no—
236#63227—48no—
237#63225—28no—
238#63225—48no—
239C4×Dic17—28no—
240#14015—171nomaximal, Sylow
241C23×C17—24no—
242C23×C17—24no—
243C23×C17—22no—
244C23×C17—22no—
245C23×C17—24no—
246C23×C17—22no—
247C23×C17—22no—
248C23×C17—24no—
249C23×C17—24no—
250C23×C17—24no—
251C23×C17—24no—
252C23×C17—24no—
253C23×C17—24no—
254C23×C17—24no—
255C23×C17—24no—
256C23×C17—24no—
257C23×C17C2×C4⋊C414yes—
258C23×C17C4×D414yes—
259C23×C17C4×D414yes—
260C23×C17#12014yes—
261C23×C17C22⋊Q814yes—
262C23×C17C22⋊Q814yes—
263C23×C17#12314yes—
264C23×C17C23×C411yescharacteristic
265C23×C17C22×D411yescharacteristic
266C23×C17C22×D411yescharacteristic
267C23×C17C22×D411yescharacteristic
268C23×C17C22×D412yes—
269C23×C17C22×Q811yescharacteristic
270C23×C17C2×#4111yescharacteristic
271C23×C17C2×#4112yes—
272C23×C17C2×#4111yescharacteristic
273C23×C17H(5,𝔽2)12yes—
274C23×C172−1+412yes—
275C22×D17—22no—
276C22×D17—22no—
277C22×D17—24no—
278C22×D17—24no—
279C22×D17—22no—
280C22×D17—22no—
281C22×D17—22no—
282C22×D17—22no—
283C22×D17—24no—
284C22×D17—24no—
285C22×D17—24no—
286C22×D17—24no—
287C22×D17—41no—
288C22×D17—41no—
289C22×D17—42no—
290C22×D17—41no—
291C22×D17—41no—
292C22×D17—42no—
293C22×D17—42no—
294C22×D17—42no—
295C22×D17—42no—
296C22×D17—42no—
297C22×D17C2×C4⋊C414yescomplemented
298C2×C4×C17—232no—
299C2×C4×C17—24no—
300C2×C4×C17—24no—
301C2×C4×C17—24no—
302C2×C4×C17—22no—
303C2×C4×C17—24no—
304C2×C4×C17—24no—
305C2×C4×C17—24no—
306C2×C4×C17—22no—
307C2×C4×C17—24no—
308C2×C4×C17—24no—
309C2×C4×C17—22no—
310C2×C4×C17—24no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—24no—
314C2×C4×C17—24no—
315C2×C4×C17—416no—
316C2×C4×C17—416no—
317C2×C4×C17—42no—
318C2×C4×C17—42no—
319C2×C4×C17—42no—
320C2×C4×C17—42no—
321C2×C4×C17—42no—
322C2×C4×C17—42no—
323C2×C4×C17C4×D418yescomplemented
324C2×C4×C17#12014yes—
325C22⋊D17—232no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—22no—
329C2×Dic17—22no—
330C2×Dic17—22no—
331C2×Dic17—22no—
332C2×Dic17—24no—
333C2×Dic17—24no—
334C2×Dic17—24no—
335C2×Dic17—22no—
336C2×Dic17—22no—
337C2×Dic17—24no—
338C2×Dic17—24no—
339C2×Dic17—41no—
340C2×Dic17—41no—
341C2×Dic17—41no—
342C2×Dic17—41no—
343C2×Dic17—42no—
344C2×Dic17—42no—
345C2×Dic17—42no—
346C2×Dic17—42no—
347C2×Dic17—42no—
348C2×Dic17—42no—
349C2×Dic17—42no—
350C2×Dic17—42no—
351C2×Dic17—42no—
352C2×Dic17—42no—
353C2×Dic17—42no—
354C2×Dic17—42no—
355C2×Dic17—42no—
356C2×Dic17C2×C4⋊C414yescomplemented
357C4×D17—416no—
358C22×C4×D4—171no—
359C23×C4⋊C4D1711yescharacteristic, complemented
360C2×#386—171no—
361C2×#386—171no—
362C2×#385—171no—
363C2×#385—172no—
364#1444—172no—
365#1439—172no—
366#1436—172no—
367C22⋊#95—171no—
368C22⋊#95—171no—
369C22×C17—24no—
370C22×C17—24no—
371C22×C17—28no—
372C22×C17—28no—
373C22×C17—24no—
374C22×C17—24no—
375C22×C17—24no—
376C22×C17—28no—
377C22×C17—28no—
378C22×C17—24no—
379C22×C17#38518yescomplemented
380C22×C17C22×C4⋊C411yescharacteristic
381C22×C17C2×C4×D411yescharacteristic
382C22×C17C2×C4×D412yes—
383C22×C17C2×C4×D411yescharacteristic
384C22×C17#52012yes—
385C22×C17C2×#12011yescharacteristic
386C22×C17C2×#12011yescharacteristic
387C22×C17C2×C22⋊Q811yescharacteristic
388C22×C17C2×C22⋊Q811yescharacteristic
389C22×C17C2×#12311yescharacteristic
390C22×C17#52511yescharacteristic
391C22×C17#52512yes—
392C22×C17#53411yescharacteristic
393C22×C17#53611yescharacteristic
394C22×C17#53912yes—
395C22×C17D4212yes—
396C22×C17D4212yes—
397C22×C17#54712yes—
398C22×C17#54712yes—
399C22×C17#54812yes—
400C22×C17D4×Q812yes—
401C22×C17#55312yes—
402C22×C17#55412yes—
403C2×D17—28no—
404C2×D17—24no—
405C2×D17—42no—
406C2×D17—42no—
407C2×D17—44no—
408C2×D17—42no—
409C2×D17—42no—
410C2×D17—42no—
411C2×D17—44no—
412C2×D17—44no—
413C2×D17—42no—
414C4×C17—24no—
415C4×C17—28no—
416C4×C17—42no—
417C4×C17—44no—
418Dic17—24no—
419Dic17—44no—
420Dic17—42no—
421Dic17—42no—
422Dic17—82no—
423C23×D4—171no—
424C24×C4—171no—
425C24×C4C2×D1711yescharacteristic
426C24×C4C2×D1711yescharacteristic
427C24×C4C2×D1711yescharacteristic
428C2×C4×D4—344no—
429C2×C4×D4—344no—
430C2×C4×D4—344no—
431C22×C4⋊C4—24no—
432C22×C4⋊C4—28no—
433C22×C4⋊C4—171no—
434C22×C4⋊C4—172no—
435C22×C4⋊C4C2×D1712yes—
436C22×C4⋊C4C2×D1712yes—
437C22×C22⋊C4—171no—
438C22×C22⋊C4—171no—
439C22×C22⋊C4—172no—
440C22×C22⋊C4—171no—
441C22×C22⋊C4—171no—
442C22×C22⋊C4—172no—
443C22×C42—171no—
444#386—178no—
445#386—344no—
446#385—344no—
447#385—348no—
448C2×#95—172no—
449C2×#95—172no—
450C2×#95—172no—
451C2×#95—172no—
452C2×#95—172no—
453C2×#95—172no—
454C2×#95—172no—
455C2×C17—28no—
456C2×C17C2×#38511yescharacteristic
457C2×C17C4×#12011yescharacteristic
458C2×C17#232211yescharacteristic
459C2×C17D4×C4⋊C412yes—
460C2×C17#236112yes—
461C2×C17#240311yescharacteristic
462C2×C17#240611yescharacteristic
463C2×C17#240911yescharacteristic
464C2×C17#244312yes—
465C2×C17#244912yes—
466C2×C17#257911yescharacteristic
467D17—44no—
468C25—171no—
469C25C22×D1711yescharacteristic
470C22×D4—174no—
471C22×D4—174no—
472C22×D4—174no—
473C22×D4—342no—
474C22×D4—342no—
475C22×D4—342no—
476C22×D4—342no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—24no—
485C23×C4—24no—
486C23×C4—22no—
487C23×C4—22no—
488C23×C4—42no—
489C23×C4—42no—
490C23×C4—171no—
491C23×C4—172no—
492C23×C4—171no—
493C23×C4—171no—
494C23×C4—172no—
495C23×C4—342no—
496C23×C4—342no—
497C23×C4—342no—
498C23×C4—344no—
499C23×C4—682no—
500C23×C4C4×D1714yescomplemented
501C23×C4C22⋊D1714yes—
502C23×C4C22×D1712yes—
503C23×C4C22×D1711yescharacteristic
504C23×C4C22×D1712yes—
505C23×C4C22×D1711yescharacteristic
506C4×D4—3432no—
507C2×C4⋊C4—232no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—24no—
513C2×C4⋊C4—342no—
514C2×C4⋊C4—342no—
515C2×C4⋊C4—342no—
516C2×C4⋊C4—344no—
517C2×C4⋊C4—344no—
518C2×C4⋊C4—682no—
519C2×C4⋊C4C22⋊D1718yescomplemented
520C2×C22⋊C4—174no—
521C2×C22⋊C4—174no—
522C2×C22⋊C4—178no—
523C2×C22⋊C4—342no—
524C2×C22⋊C4—342no—
525C2×C22⋊C4—342no—
526C2×C22⋊C4—342no—
527C2×C22⋊C4—342no—
528C2×C22⋊C4—342no—
529C2×C22⋊C4—344no—
530C2×C22⋊C4—342no—
531C2×C22⋊C4—344no—
532C2×C22⋊C4—344no—
533C2×C22⋊C4—342no—
534C2×C22⋊C4—342no—
535C2×C22⋊C4—342no—
536C2×C22⋊C4—344no—
537C2×C22⋊C4—682no—
538C2×C42—342no—
539C2×C42—342no—
540C2×C42—342no—
541#95—178no—
542#95—344no—
543#95—344no—
544#95—344no—
545#95—344no—
546#95—344no—
547#95—682no—
548C17#1401511yescharacteristic, complemented, Sylow
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—172no—
554C24—172no—
555C24—172no—
556C24—342no—
557C24—341no—
558C24—341no—
559C24—342no—
560C24—341no—
561C24—342no—
562C24—342no—
563C24—341no—
564C24C2×C4×D1712yes—
565C24#6325212yes—
566C24D4×D1712yes—
567C24D4×D1712yes—
568C24Q8×D1712yes—
569C24#6325612yes—
570C24C2×C22⋊D1712yes—
571C24C23×D1711yescharacteristic
572C2×D4—1716no—
573C2×D4—348no—
574C2×D4—348no—
575C2×D4—348no—
576C2×D4—348no—
577C2×D4—348no—
578C2×D4—348no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—216no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—28no—
590C22×C4—216no—
591C22×C4—28no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—28no—
603C22×C4—28no—
604C22×C4—44no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—172no—
612C22×C4—172no—
613C22×C4—172no—
614C22×C4—174no—
615C22×C4—172no—
616C22×C4—172no—
617C22×C4—348no—
618C22×C4—341no—
619C22×C4—341no—
620C22×C4—341no—
621C22×C4—341no—
622C22×C4—342no—
623C22×C4—342no—
624C22×C4—342no—
625C22×C4—341no—
626C22×C4—341no—
627C22×C4—342no—
628C22×C4—342no—
629C22×C4—342no—
630C22×C4—342no—
631C22×C4—342no—
632C22×C4—342no—
633C22×C4—342no—
634C22×C4—341no—
635C22×C4—341no—
636C22×C4—342no—
637C22×C4—342no—
638C22×C4—342no—
639C22×C4—342no—
640C22×C4—342no—
641C22×C4—342no—
642C22×C4—342no—
643C22×C4—688no—
644C22×C4—688no—
645C22×C4—684no—
646C22×C4—684no—
647C22×C4C2×C4×D1714yes—
648C22×C4#6325214yes—
649C22×C4C2×C22⋊D1712yes—
650C22×C4C2×C22⋊D1714yes—
651C22×C4C2×C22⋊D1714yes—
652C22×C4C2×C22⋊D1714yes—
653C22×C4C2×C22⋊D1712yes—
654C4⋊C4—216no—
655C4⋊C4—216no—
656C4⋊C4—348no—
657C4⋊C4—688no—
658C22⋊C4—348no—
659C22⋊C4—348no—
660C22⋊C4—348no—
661C22⋊C4—3416no—
662C22⋊C4—688no—
663C22⋊C4—684no—
664C42—348no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—22no—
674C23—24no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—174no—
682C23—344no—
683C23—344no—
684C23—344no—
685C23—344no—
686C23—342no—
687C23—342no—
688C23—344no—
689C23—342no—
690C23—342no—
691C23—342no—
692C23—342no—
693C23—344no—
694C23—682no—
695C23—682no—
696C23—682no—
697C23—681no—
698C23—681no—
699C23—682no—
700C23—681no—
701C23—681no—
702C23—682no—
703C23—682no—
704C23C4⋊C4×D1714yes—
705C23#1058757914yes—
706C23#1058758014yes—
707C23#1058758214yes—
708C23C4×C22⋊D1714yes—
709C23#1058762314yes—
710C23#1058763214yes—
711C23C22×C4×D1711yescharacteristic
712C23C2×#6325212yes—
713C23C2×#6325211yescharacteristic
714C23C2×D4×D1711yescharacteristic
715C23C2×D4×D1711yescharacteristic
716C23#1058769112yes—
717C23C2×Q8×D1711yescharacteristic
718C23C2×#6325611yescharacteristic
719C23#1058769412yes—
720C23C22×C22⋊D1712yes—
721C23C22×C22⋊D1711yescharacteristic
722D4—3432no—
723C2×C4—232no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—416no—
741C2×C4—416no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—174no—
749C2×C4—342no—
750C2×C4—342no—
751C2×C4—342no—
752C2×C4—342no—
753C2×C4—342no—
754C2×C4—342no—
755C2×C4—344no—
756C2×C4—344no—
757C2×C4—344no—
758C2×C4—344no—
759C2×C4—342no—
760C2×C4—342no—
761C2×C4—344no—
762C2×C4—6816no—
763C2×C4—682no—
764C2×C4—682no—
765C2×C4—682no—
766C2×C4—682no—
767C2×C4—681no—
768C2×C4—681no—
769C2×C4—681no—
770C2×C4—681no—
771C2×C4—682no—
772C2×C4—682no—
773C2×C4—682no—
774C2×C4—682no—
775C2×C4—682no—
776C2×C4—682no—
777C2×C4—682no—
778C2×C4—682no—
779C2×C4—682no—
780C2×C4C4×C22⋊D1718yescomplemented
781C2×C4#1058763914yes—
782C22—24no—
783C22—24no—
784C22—28no—
785C22—24no—
786C22—28no—
787C22—24no—
788C22—28no—
789C22—28no—
790C22—24no—
791C22—24no—
792C22—348no—
793C22—344no—
794C22—682no—
795C22—682no—
796C22—682no—
797C22—684no—
798C22—682no—
799C22—684no—
800C22—684no—
801C22—682no—
802C22—682no—
803C22#1176268018yescomplemented
804C22C2×C4⋊C4×D1711yescharacteristic
805C22C2×C4×C22⋊D1712yes—
806C22C2×C4×C22⋊D1711yescharacteristic
807C22C2×#1058757911yescharacteristic
808C22#1176329012yes—
809C22C2×#1058762311yescharacteristic
810C22C2×#1058763911yescharacteristic
811C22C2×#1058763211yescharacteristic
812C22C2×#1058758211yescharacteristic
813C22C2×#1058758011yescharacteristic
814C22#1176332011yescharacteristic
815C22#1176332012yes—
816C22#1176336811yescharacteristic
817C22#1176338311yescharacteristic
818C22#1176340612yes—
819C22D4×C22⋊D1712yes—
820C22D4×C22⋊D1712yes—
821C22#1176346012yes—
822C22#1176346012yes—
823C22#1176347012yes—
824C22Q8×C22⋊D1712yes—
825C22#1176350712yes—
826C22#1176351412yes—
827C4—28no—
828C4—24no—
829C4—42no—
830C4—44no—
831C4—344no—
832C4—682no—
833C4—684no—
834C4—682no—
835C4—1362no—
836C2—28no—
837C2—684no—
838C2C2×#1176268011yescharacteristic
839C2C4×#1058763911yescharacteristic
840C2#1453145311yescharacteristic
841C2C4⋊C4×C22⋊D1712yes—
842C2#1453180012yes—
843C2#1453209411yescharacteristic
844C2#1453211911yescharacteristic
845C2#1453214311yescharacteristic
846C2#1453251912yes—
847C2#1453259312yes—
848C2#1453413111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC23×C4⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC23×C4⋊C4D17
hypocenterC17#14015
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#11762682C2semidirect
5. C2×#11762680C2semidirect
6. #14527047C2semidirect
7. #14527026C2semidirect
8. #14527016C2semidirect
9. #14527007C2semidirect
10. #14527007C2semidirect
11. C23×C4⋊C4×C17C2semidirect
27. #11762688C4semidirect
59. C23×C4×C17C2×C4semidirect
88. C2×C4⋊C4×C17D4semidirect
96. C2×C22⋊Dic17C2×C4semidirect
107. C2×#63227C2×C4semidirect
123. #10587502C2×C4semidirect
192. C2×C22⋊D17C4⋊C4semidirect
297. C22×D17C2×C4⋊C4semidirect
323. C2×C4×C17C4×D4semidirect
356. C2×Dic17C2×C4⋊C4semidirect
359. C23×C4⋊C4D17semidirect
379. C22×C17#385semidirect
500. C23×C4C4×D17semidirect
519. C2×C4⋊C4C22⋊D17semidirect
548. C17#14015semidirect
780. C2×C4C4×C22⋊D17semidirect
803. C22#11762680semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D172
C2×#117626882
C2×#117626822
C2×#117626802
#145270472
#145270262
#145270162
#145270072
C23×C4⋊C4×C172
#1401517