Finite Group Databasebeta

← #17963692

Subgroups — #17963692

Order 4352.

1390 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763760C212yesmaximal
2C2×#11763758C212yesmaximal
3#14543972C212yesmaximal
4#14543969C212yesmaximal
5#14543969C212yesmaximal
6#14543964C212yesmaximal
7#14543962C211yesmaximal, characteristic
8#14543962C211yesmaximal, characteristic
9D17×#389C211yesmaximal, characteristic
10C22×C4⋊#595C2212yes—
11C22×C4⋊#595C2212yes—
12C22×C4⋊#595C2211yescharacteristic
13C22×C4⋊#595C2211yescharacteristic
14C22×C4⋊#595C2211yescharacteristic
15C22×C4⋊#595C2211yescharacteristic
16C22×C4×#595C2212yes—
17#11763760—28no—
18#11763758—28no—
19C2×(C2×#595)⋊C4C2212yes—
20C2×(C2×#595)⋊C4C2212yes—
21C2×(C2×#595)⋊C4C2212yes—
22C2×(C2×#595)⋊C4C2212yes—
23C2×(C2×#595)⋊C4C2212yes—
24C2×(C2×#595)⋊C4C2212yes—
25C2×(C2×#595)⋊C4C2212yes—
26C2×(C2×#595)⋊C4C2212yes—
27C2×(C2×#595)⋊C4C2212yes—
28C2×C4⋊C4×D17C2212yes—
29C2×C4⋊C4×D17C2211yescharacteristic
30C2×C4⋊C4×D17C2211yescharacteristic
31C2×C42×D17C2211yescharacteristic
32#11762708C411yescharacteristic, complemented
33#11762707C411yescharacteristic, complemented
34#11762706C412yescomplemented
35#11762705C411yescharacteristic, complemented
36#11762704C412yescomplemented
37#95×D17C2212yes—
38C17×#389C411yescharacteristic, complemented
39C23×#595C2312yes—
40C23×#595C2312yes—
41C23×#595C2312yes—
42C23×#595C2312yes—
43C22×C4×D17C2312yes—
44C22×C4×D17C2311yescharacteristic
45C22×C4×D17C2312yes—
46C22×C4×D17C2311yescharacteristic
47C22×C4×D17C2311yescharacteristic
48C2×C4⋊#595—24no—
49C2×C4⋊#595—24no—
50C2×C4⋊#595—24no—
51C2×C4⋊#595—22no—
52C2×C4⋊#595—22no—
53C2×C4⋊#595—41no—
54C2×C4⋊#595—41no—
55C2×C4⋊#595—41no—
56C2×C4⋊#595—41no—
57C2×C4⋊#595—42no—
58C2×C4⋊#595—41no—
59C2×C4⋊#595—41no—
60C2×C4⋊#595—41no—
61C2×C4⋊#595—41no—
62C2×C4⋊#595—42no—
63C2×C4⋊#595—42no—
64C2×C4⋊#595D414yes—
65C2×C4⋊#595Q814yes—
66C2×C4×#595—24no—
67C2×C4×#595—24no—
68C2×C4×#595—42no—
69C2×C4⋊C4×C17C2×C412yes—
70C2×C4⋊C4×C17C2×C411yescharacteristic
71C2×C4⋊C4×C17C2×C411yescharacteristic
72C2×C42×C17C2×C411yescharacteristic
73C2×C4⋊Dic17C2×C412yes—
74C2×C4⋊Dic17C2×C411yescharacteristic
75C2×C4⋊Dic17C2×C411yescharacteristic
76C2×#63225C2×C412yes—
77C2×#63225C2×C412yes—
78C2×#63225C2×C412yes—
79C2×#63225C2×C412yes—
80C2×C4×Dic17C2×C411yescharacteristic
81C2×C4×Dic17C2×C411yescharacteristic
82C2×C4×Dic17C2×C411yescharacteristic
83C4⋊C4×D17—24no—
84C4⋊C4×D17—24no—
85C4⋊C4×D17—41no—
86C4⋊C4×D17—41no—
87C4⋊C4×D17D414yes—
88C4⋊C4×D17Q814yes—
89C42×D17—41no—
90C42×D17—41no—
91(C2×#595)⋊C4—24no—
92(C2×#595)⋊C4—24no—
93(C2×#595)⋊C4—24no—
94(C2×#595)⋊C4—24no—
95(C2×#595)⋊C4—24no—
96(C2×#595)⋊C4—24no—
97(C2×#595)⋊C4—24no—
98(C2×#595)⋊C4—42no—
99(C2×#595)⋊C4—42no—
100C17×#95C2×C412yes—
101#10587502C2×C412yes—
102#10587502C2×C412yes—
103#10587502C2×C412yes—
104C23×D17C2411yescharacteristic
105C22×#595—22no—
106C22×#595—22no—
107C22×#595—22no—
108C22×#595—22no—
109C22×#595—22no—
110C22×#595—22no—
111C22×#595—22no—
112C22×#595—22no—
113C22×#595—22no—
114C22×#595—22no—
115C22×#595—22no—
116C22×#595—22no—
117C22×#595—22no—
118C22×#595—22no—
119C22×#595—22no—
120C22×#595—22no—
121C22×#595—22no—
122C22×#595—22no—
123C22×#595—22no—
124C22×#595—22no—
125C22×#595—22no—
126C22×#595—22no—
127C22×#595—22no—
128C22×#595—22no—
129C22×#595—22no—
130C22×#595—22no—
131C22×#595C2×D414yes—
132C22×#595C2×Q814yes—
133C22×C4×C17C22×C412yes—
134C22×C4×C17C22×C412yes—
135C22×C4×C17C22×C411yescharacteristic
136C22×C4×C17C22×C411yescharacteristic
137C22×C4×C17C22×C411yescharacteristic
138C22×Dic17C22×C412yes—
139C22×Dic17C22×C412yes—
140C22×Dic17C22×C411yescharacteristic
141C22×Dic17C22×C411yescharacteristic
142C22×Dic17C22×C411yescharacteristic
143C2×C4×D17—22no—
144C2×C4×D17—22no—
145C2×C4×D17—22no—
146C2×C4×D17—21no—
147C2×C4×D17—21no—
148C2×C4×D17—21no—
149C2×C4×D17—21no—
150C2×C4×D17—21no—
151C2×C4×D17—21no—
152C2×C4×D17—21no—
153C2×C4×D17—21no—
154C2×C4×D17—21no—
155C2×C4×D17—21no—
156C2×C4×D17—21no—
157C2×C4×D17—21no—
158C2×C4×D17—22no—
159C2×C4×D17—22no—
160C2×C4×D17—22no—
161C2×C4×D17—22no—
162C2×C4×D17—22no—
163C2×C4×D17—22no—
164C2×C4×D17—22no—
165C2×C4×D17C2×D414yes—
166C2×C4×D17C2×D412yes—
167C2×C4×D17C2×D412yes—
168C2×C4×D17C2×Q812yes—
169C2×C4×D17C2×Q814yes—
170C2×C4×D17C2×Q812yes—
171C2×C4×D17#4112yes—
172C2×C4×D17#4112yes—
173C4⋊#595—44no—
174C4⋊#595—44no—
175C4⋊#595—48no—
176C4⋊#595—44no—
177C4⋊#595—44no—
178C4⋊#595—48no—
179C4×#595—48no—
180C4⋊C4×C17—24no—
181C4⋊C4×C17—41no—
182C4⋊C4×C17C4⋊C414yescomplemented
183C42×C17—41no—
184C4⋊Dic17—24no—
185C4⋊Dic17—41no—
186C4⋊Dic17C4⋊C414yescomplemented
187#63225—24no—
188#63225—24no—
189#63225—42no—
190#63225C4⋊C418yescomplemented
191C4×Dic17—41no—
192C4×Dic17—41no—
193C4×Dic17—41no—
194#14441—171nomaximal, Sylow
195C23×C17C23×C411yescharacteristic
196C22×D17C22×D411yescharacteristic
197C22×D17C22×D411yescharacteristic
198C22×D17C22×Q811yescharacteristic
199C22×D17C22×Q811yescharacteristic
200C22×D17C2×#4111yescharacteristic
201C22×D17C2×#4111yescharacteristic
202C22×D17H(5,𝔽2)11yescharacteristic
203C22×D17H(5,𝔽2)11yescharacteristic
204C22×D17H(5,𝔽2)11yescharacteristic
205C22×D17H(5,𝔽2)11yescharacteristic
206C22×D172−1+411yescharacteristic
207C22×D172−1+411yescharacteristic
208C22×D172−1+411yescharacteristic
209C22×D172−1+411yescharacteristic
210C2×#595—24no—
211C2×#595—24no—
212C2×#595—24no—
213C2×#595—24no—
214C2×#595—24no—
215C2×#595—24no—
216C2×#595—42no—
217C2×#595—42no—
218C2×#595—42no—
219C2×#595—42no—
220C2×#595—42no—
221C2×#595—42no—
222C2×#595—42no—
223C2×#595—42no—
224C2×#595—42no—
225C2×#595—42no—
226C2×#595—42no—
227C2×#595—42no—
228C2×#595—42no—
229C2×#595—42no—
230C2×#595—42no—
231C2×#595—42no—
232C2×#595—42no—
233C2×#595—42no—
234C2×#595—42no—
235C2×#595—42no—
236C2×#595—42no—
237C2×#595—42no—
238C2×C4×C17—22no—
239C2×C4×C17—21no—
240C2×C4×C17—21no—
241C2×C4×C17—21no—
242C2×C4×C17—21no—
243C2×C4×C17—21no—
244C2×C4×C17—21no—
245C2×C4×C17—22no—
246C2×C4×C17—22no—
247C2×C4×C17—22no—
248C2×C4×C17—22no—
249C2×C4×C17C2×C4⋊C414yes—
250C2×C4×C17C2×C4⋊C412yes—
251C2×C4×C17C4×D412yes—
252C2×C4×C17C4×Q812yes—
253C2×Dic17—22no—
254C2×Dic17—21no—
255C2×Dic17—21no—
256C2×Dic17—21no—
257C2×Dic17—21no—
258C2×Dic17—21no—
259C2×Dic17—21no—
260C2×Dic17—22no—
261C2×Dic17—22no—
262C2×Dic17—22no—
263C2×Dic17—22no—
264C2×Dic17C2×C4⋊C412yes—
265C2×Dic17C2×C4⋊C414yes—
266C2×Dic17C4×D412yes—
267C2×Dic17C4×Q812yes—
268C4×D17—22no—
269C4×D17—22no—
270C4×D17—22no—
271C4×D17—22no—
272C4×D17—22no—
273C4×D17—22no—
274C4×D17—22no—
275C4×D17—22no—
276C4×D17—22no—
277C4×D17—22no—
278C4×D17—22no—
279C4×D17—22no—
280C4×D17—24no—
281C4×D17—24no—
282C4×D17—24no—
283C4×D17—24no—
284C4×D17—42no—
285C4×D17—42no—
286C4×D17—42no—
287C4×D17—42no—
288C2×#389—171no—
289C2×#389—172no—
290C2×#387—172no—
291#1444—172no—
292#1441—172no—
293#1441—172no—
294#1436—172no—
295C4⋊#95—171no—
296C4⋊#95—171no—
297C22×C17C22×C4⋊C411yescharacteristic
298C22×C17C2×C4×D411yescharacteristic
299C22×C17C2×C4×Q811yescharacteristic
300C22×C17#51811yescharacteristic
301C22×C17#51911yescharacteristic
302C22×C17#52011yescharacteristic
303C22×C17#52011yescharacteristic
304C2×D17#53411yescharacteristic
305C2×D17#53711yescharacteristic
306C2×D17#53711yescharacteristic
307C2×D17#53711yescharacteristic
308C2×D17#53811yescharacteristic
309C2×D17#53811yescharacteristic
310C2×D17#53911yescharacteristic
311C2×D17#53911yescharacteristic
312C2×D17#54311yescharacteristic
313C2×D17#54411yescharacteristic
314C2×D17#54411yescharacteristic
315C2×D17#54411yescharacteristic
316C2×D17D4211yescharacteristic
317C2×D17#54711yescharacteristic
318C2×D17#54711yescharacteristic
319C2×D17D4×Q811yescharacteristic
320C2×D17D4×Q811yescharacteristic
321C2×D17D4×Q811yescharacteristic
322C2×D17#55011yescharacteristic
323C2×D17#55411yescharacteristic
324C2×D17#55611yescharacteristic
325C2×D17#55711yescharacteristic
326C2×D17#55711yescharacteristic
327C2×D17Q8211yescharacteristic
328C2×D17#56211yescharacteristic
329C2×D17#56311yescharacteristic
330C2×D17#56311yescharacteristic
331C2×D17#56411yescharacteristic
332#595—44no—
333#595—44no—
334#595—82no—
335#595—82no—
336C4×C17—22no—
337C4×C17—22no—
338C4×C17—22no—
339C4×C17—24no—
340C4×C17—42no—
341Dic17—22no—
342Dic17—22no—
343Dic17—22no—
344Dic17—24no—
345Dic17—42no—
346C22×C4⋊C4—171no—
347C22×C4⋊C4—171no—
348C22×C4⋊C4—171no—
349C22×C4⋊C4—172no—
350C22×C4⋊C4—171no—
351C22×C4⋊C4—172no—
352C22×C4⋊C4—171no—
353C22×C4⋊C4—171no—
354C22×C4⋊C4—172no—
355C22×C42—171no—
356C22×C42—172no—
357#389—172no—
358#389—171no—
359#389—171no—
360#389—171no—
361#389—172no—
362#389—348no—
363#389#59511yescharacteristic, complemented
364#387—348no—
365C2×#95—172no—
366C2×#95—172no—
367C2×#95—172no—
368C2×#95—172no—
369C2×#95—172no—
370C2×#95—172no—
371C2×#95—172no—
372C2×#95—172no—
373C2×#95—172no—
374C2×#95—172no—
375C2×C17#231611yescharacteristic
376C2×C17#232511yescharacteristic
377C2×C17#232911yescharacteristic
378C2×C17D4×C4⋊C411yescharacteristic
379C2×C17Q8×C4⋊C411yescharacteristic
380C2×C17#236511yescharacteristic
381C2×C17#238211yescharacteristic
382D17#268211yescharacteristic
383D17#268311yescharacteristic
384D17#272611yescharacteristic
385D17#272611yescharacteristic
386D17#272711yescharacteristic
387D17#273411yescharacteristic
388D17#280511yescharacteristic
389D17#280611yescharacteristic
390C23×C4—171no—
391C23×C4—172no—
392C23×C4—171no—
393C23×C4—171no—
394C23×C4—172no—
395C23×C4—172no—
396C23×C4—172no—
397C23×C4—172no—
398C23×C4—172no—
399C2×C4⋊C4—172no—
400C2×C4⋊C4—171no—
401C2×C4⋊C4—174no—
402C2×C4⋊C4—174no—
403C2×C4⋊C4—172no—
404C2×C4⋊C4—172no—
405C2×C4⋊C4—172no—
406C2×C4⋊C4—174no—
407C2×C4⋊C4—174no—
408C2×C4⋊C4—172no—
409C2×C4⋊C4—171no—
410C2×C4⋊C4—344no—
411C2×C4⋊C4—344no—
412C2×C4⋊C4—342no—
413C2×C4⋊C4—342no—
414C2×C4⋊C4—344no—
415C2×C4⋊C4—344no—
416C2×C4⋊C4—344no—
417C2×C4⋊C4—681no—
418C2×C4⋊C4—681no—
419C2×C4⋊C4—681no—
420C2×C4⋊C4—681no—
421C2×C4⋊C4—681no—
422C2×C4⋊C4—681no—
423C2×C4⋊C4—682no—
424C2×C4⋊C4—681no—
425C2×C4⋊C4—681no—
426C2×C4⋊C4—681no—
427C2×C4⋊C4—681no—
428C2×C4⋊C4—682no—
429C2×C4⋊C4—682no—
430C2×C4⋊C4C2×#59512yes—
431C2×C4⋊C4C2×#59511yescharacteristic
432C2×C4⋊C4C2×#59511yescharacteristic
433C2×C42—171no—
434C2×C42—171no—
435C2×C42—171no—
436C2×C42—344no—
437C2×C42—344no—
438C2×C42—681no—
439C2×C42—681no—
440C2×C42—682no—
441C2×C42C2×#59511yescharacteristic
442#95—172no—
443#95—172no—
444#95—172no—
445#95—344no—
446#95—344no—
447#95—344no—
448#95—344no—
449#95—344no—
450#95—344no—
451#95—344no—
452#95—682no—
453#95—682no—
454#95C2×#59512yes—
455C17#1444111yescharacteristic, complemented, Sylow
456C24—171no—
457C22×C4—171no—
458C22×C4—172no—
459C22×C4—171no—
460C22×C4—171no—
461C22×C4—172no—
462C22×C4—174no—
463C22×C4—174no—
464C22×C4—172no—
465C22×C4—172no—
466C22×C4—172no—
467C22×C4—172no—
468C22×C4—172no—
469C22×C4—174no—
470C22×C4—174no—
471C22×C4—172no—
472C22×C4—342no—
473C22×C4—341no—
474C22×C4—341no—
475C22×C4—341no—
476C22×C4—341no—
477C22×C4—341no—
478C22×C4—341no—
479C22×C4—342no—
480C22×C4—342no—
481C22×C4—341no—
482C22×C4—341no—
483C22×C4—341no—
484C22×C4—341no—
485C22×C4—341no—
486C22×C4—342no—
487C22×C4—341no—
488C22×C4—342no—
489C22×C4—342no—
490C22×C4—342no—
491C22×C4—342no—
492C22×C4—342no—
493C22×C4—342no—
494C22×C4—342no—
495C22×C4—342no—
496C22×C4—342no—
497C22×C4—342no—
498C22×C4—342no—
499C22×C4—342no—
500C22×C4—342no—
501C22×C4—342no—
502C22×C4—342no—
503C22×C4—342no—
504C22×C4—342no—
505C22×C4—342no—
506C22×C4—342no—
507C22×C4—342no—
508C22×C4—342no—
509C22×C4—342no—
510C22×C4—342no—
511C22×C4—342no—
512C22×C4—342no—
513C22×C4—342no—
514C22×C4—342no—
515C22×C4—342no—
516C22×C4—342no—
517C22×C4—342no—
518C22×C4—342no—
519C22×C4—342no—
520C22×C4C22×#59512yes—
521C22×C4C22×#59512yes—
522C22×C4C22×#59511yescharacteristic
523C22×C4C22×#59511yescharacteristic
524C22×C4C22×#59511yescharacteristic
525C4⋊C4—24no—
526C4⋊C4—41no—
527C4⋊C4—178no—
528C4⋊C4—174no—
529C4⋊C4—344no—
530C4⋊C4—344no—
531C4⋊C4—344no—
532C4⋊C4—682no—
533C4⋊C4—681no—
534C4⋊C4—684no—
535C4⋊C4—684no—
536C4⋊C4—688no—
537C4⋊C4—684no—
538C4⋊C4—684no—
539C4⋊C4—688no—
540C4⋊C4C4⋊#59514yescomplemented
541C42—41no—
542C42—681no—
543C42—681no—
544C42—681no—
545C42—688no—
546C23—171no—
547C23—171no—
548C23—171no—
549C23—171no—
550C23—171no—
551C23—171no—
552C23—171no—
553C23—171no—
554C23—171no—
555C23—171no—
556C23—171no—
557C23—171no—
558C23—171no—
559C23—171no—
560C23C23×#59511yescharacteristic
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—172no—
573C2×C4—174no—
574C2×C4—172no—
575C2×C4—172no—
576C2×C4—344no—
577C2×C4—342no—
578C2×C4—342no—
579C2×C4—342no—
580C2×C4—342no—
581C2×C4—342no—
582C2×C4—342no—
583C2×C4—342no—
584C2×C4—342no—
585C2×C4—342no—
586C2×C4—342no—
587C2×C4—342no—
588C2×C4—342no—
589C2×C4—344no—
590C2×C4—344no—
591C2×C4—344no—
592C2×C4—342no—
593C2×C4—341no—
594C2×C4—341no—
595C2×C4—341no—
596C2×C4—341no—
597C2×C4—341no—
598C2×C4—341no—
599C2×C4—342no—
600C2×C4—344no—
601C2×C4—344no—
602C2×C4—344no—
603C2×C4—344no—
604C2×C4—344no—
605C2×C4—344no—
606C2×C4—342no—
607C2×C4—342no—
608C2×C4—342no—
609C2×C4—682no—
610C2×C4—682no—
611C2×C4—682no—
612C2×C4—682no—
613C2×C4—682no—
614C2×C4—682no—
615C2×C4—682no—
616C2×C4—682no—
617C2×C4—682no—
618C2×C4—682no—
619C2×C4—682no—
620C2×C4—682no—
621C2×C4—682no—
622C2×C4—682no—
623C2×C4—682no—
624C2×C4—682no—
625C2×C4—682no—
626C2×C4—682no—
627C2×C4—682no—
628C2×C4—682no—
629C2×C4—682no—
630C2×C4—682no—
631C2×C4—682no—
632C2×C4—682no—
633C2×C4—682no—
634C2×C4—682no—
635C2×C4C2×C4⋊#59512yes—
636C2×C4C2×C4⋊#59514yes—
637C2×C4D4×#59512yes—
638C2×C4Q8×#59512yes—
639C22—171no—
640C22—171no—
641C22—171no—
642C22—171no—
643C22—171no—
644C22—171no—
645C22—171no—
646C22—171no—
647C22—171no—
648C22—171no—
649C22—171no—
650C22—171no—
651C22—171no—
652C22—171no—
653C22—171no—
654C22—171no—
655C22—171no—
656C22—171no—
657C22—171no—
658C22—171no—
659C22—171no—
660C22—171no—
661C22—171no—
662C22—171no—
663C22—171no—
664C22—171no—
665C22—171no—
666C22—171no—
667C22C22×C4⋊#59511yescharacteristic
668C22C2×D4×#59511yescharacteristic
669C22C2×Q8×#59511yescharacteristic
670C22#1176387611yescharacteristic
671C22#1176387711yescharacteristic
672C22#1176387811yescharacteristic
673C22#1176387811yescharacteristic
674C4—22no—
675C4—22no—
676C4—22no—
677C4—24no—
678C4—42no—
679C4—342no—
680C4—342no—
681C4—342no—
682C4—344no—
683C4—684no—
684C4—684no—
685C4—682no—
686C4—1362no—
687C4—1362no—
688C2—171no—
689C2—171no—
690C2—171no—
691C2—171no—
692C2—171no—
693C2—171no—
694C2—171no—
695C2—171no—
696C2#1454526411yescharacteristic
697C2#1454527311yescharacteristic
698C2#1454527711yescharacteristic
699C2D4×C4⋊#59511yescharacteristic
700C2Q8×C4⋊#59511yescharacteristic
701C2#1454531311yescharacteristic
702C2#1454533011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutator, socleC23×C17C23×C4
FittingC17×#389C4
prime radical, cosocleC23×D17C24
hypercenter#389#595
hypocenterC17#14441
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
32. #11762708C4semidirect
33. #11762707C4semidirect
34. #11762706C4semidirect
35. #11762705C4semidirect
36. #11762704C4semidirect
38. C17×#389C4semidirect
182. C4⋊C4×C17C4⋊C4semidirect
186. C4⋊Dic17C4⋊C4semidirect
190. #63225C4⋊C4semidirect
363. #389#595semidirect
455. C17#14441semidirect
540. C4⋊C4C4⋊#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637602
C2×#117637582
#145439722
#145439692
#145439642
#145439622
D17×#3892
#1444117