Finite Group Databasebeta

← #16960767

Subgroups — #16960767

Order 4352.

1262 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762707C211yesmaximal, characteristic
2C2×#11762707C211yesmaximal, characteristic
3#14527050C212yesmaximal
4#14527045C212yesmaximal
5#14527042C212yesmaximal
6#14527035C212yesmaximal
7#14527014C211yesmaximal, characteristic
8#14527014C211yesmaximal, characteristic
9#14527014C211yesmaximal, characteristic
10#14527014C211yesmaximal, characteristic
11C2×C17×#376C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×C4⋊Dic17C2211yescharacteristic
15C22×C4⋊Dic17C2211yescharacteristic
16C22×#63225C2212yes—
17C22×#63225C2212yes—
18#11762707—24no—
19#11762707C418yescomplemented
20C2×#10587502C2212yes—
21C2×#10587502C2212yes—
22C2×#10587502C2212yes—
23C2×#10587502C2212yes—
24C2×#10587502C2212yes—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C22×C42×C17C2211yescharacteristic
31C22×C42×C17C2211yescharacteristic
32C22×C42×C17C2211yescharacteristic
33C17×#376—24no—
34C2×C17×#95C2211yescharacteristic
35C2×C17×#95C2211yescharacteristic
36C2×C17×#95C2211yescharacteristic
37C2×C17×#95C2211yescharacteristic
38C23×C4×C17C2311yescharacteristic
39C23×C4×C17C2311yescharacteristic
40C23×C4×C17C2311yescharacteristic
41C23×C4×C17C2311yescharacteristic
42C23×C4×C17C2311yescharacteristic
43C23×C4×C17C2311yescharacteristic
44C23×C4×C17C2311yescharacteristic
45C23×Dic17C2312yes—
46C23×Dic17C2312yes—
47C23×Dic17C2312yes—
48C23×Dic17C2312yes—
49C2×C42×C17—22no—
50C2×C42×C17—22no—
51C2×C42×C17—22no—
52C2×C42×C17—22no—
53C2×C42×C17—22no—
54C2×C42×C17—22no—
55C2×C42×C17C2×C414yes—
56C2×C42×C17D414yes—
57C2×C42×C17Q814yes—
58C2×C4⋊Dic17—22no—
59C2×C4⋊Dic17—22no—
60C2×C4⋊Dic17—22no—
61C2×C4⋊Dic17—22no—
62C2×C4⋊Dic17—22no—
63C2×C4⋊Dic17—22no—
64C2×C4⋊Dic17—22no—
65C2×C4⋊Dic17—22no—
66C2×C4⋊Dic17—22no—
67C2×C4⋊Dic17—22no—
68C2×C4⋊Dic17C2×C414yes—
69C2×C4⋊Dic17C2×C414yes—
70C2×#63225—24no—
71C2×#63225—42no—
72C2×#63225—42no—
73C2×#63225—42no—
74C2×#63225—42no—
75C2×#63225C2×C418yes—
76C17×#95—22no—
77C17×#95—22no—
78C17×#95—22no—
79C17×#95—22no—
80#10587502—24no—
81#10587502—42no—
82#10587502—42no—
83#10587502—42no—
84#10587502—42no—
85#10587502—42no—
86#10587502—42no—
87#10587502—42no—
88#10587502—42no—
89#10587502C2×C418yes—
90C24×C17C2411yescharacteristic
91C22×C4×C17—21no—
92C22×C4×C17—21no—
93C22×C4×C17—21no—
94C22×C4×C17—21no—
95C22×C4×C17—21no—
96C22×C4×C17—21no—
97C22×C4×C17—21no—
98C22×C4×C17—21no—
99C22×C4×C17—21no—
100C22×C4×C17—21no—
101C22×C4×C17—21no—
102C22×C4×C17—21no—
103C22×C4×C17—21no—
104C22×C4×C17—21no—
105C22×C4×C17—21no—
106C22×C4×C17—21no—
107C22×C4×C17—21no—
108C22×C4×C17—21no—
109C22×C4×C17—21no—
110C22×C4×C17—21no—
111C22×C4×C17—21no—
112C22×C4×C17—21no—
113C22×C4×C17—21no—
114C22×C4×C17—21no—
115C22×C4×C17—21no—
116C22×C4×C17—21no—
117C22×C4×C17—21no—
118C22×C4×C17—21no—
119C22×C4×C17—21no—
120C22×C4×C17—21no—
121C22×C4×C17—21no—
122C22×C4×C17—21no—
123C22×C4×C17—21no—
124C22×C4×C17—21no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17C22×C412yes—
128C22×C4×C17C22×C412yes—
129C22×C4×C17C22×C412yes—
130C22×C4×C17C2×D412yes—
131C22×C4×C17C2×D412yes—
132C22×C4×C17C2×D412yes—
133C22×C4×C17C2×Q812yes—
134C22×C4×C17C2×Q812yes—
135C22×C4×C17C2×Q812yes—
136C22×C4×C17#4112yes—
137C22×C4×C17#4112yes—
138C22×C4×C17#4112yes—
139C22×C4×C17#4112yes—
140C22×Dic17—22no—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—22no—
144C22×Dic17—22no—
145C22×Dic17—22no—
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—22no—
151C22×Dic17—22no—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17—22no—
155C22×Dic17—22no—
156C22×Dic17—22no—
157C22×Dic17—22no—
158C22×Dic17—22no—
159C22×Dic17—22no—
160C22×Dic17—22no—
161C22×Dic17—22no—
162C22×Dic17—22no—
163C22×Dic17—22no—
164C22×Dic17—22no—
165C22×Dic17—22no—
166C22×Dic17C22×C414yes—
167C22×Dic17C22×C414yes—
168C42×C17—28no—
169C42×C17—28no—
170C42×C17—28no—
171C4⋊Dic17—28no—
172C4⋊Dic17—28no—
173C4⋊Dic17—44no—
174C4⋊Dic17—44no—
175#63225—48no—
176#63225—48no—
177#14266—171nomaximal, Sylow
178C23×C17C23×C411yescharacteristic
179C23×C17C22×D411yescharacteristic
180C23×C17C22×Q811yescharacteristic
181C23×C17C2×#4111yescharacteristic
182C23×C17C2×#4111yescharacteristic
183C23×C17C2×#4111yescharacteristic
184C23×C17C2×#4111yescharacteristic
185C23×C17H(5,𝔽2)11yescharacteristic
186C23×C17H(5,𝔽2)11yescharacteristic
187C23×C17H(5,𝔽2)11yescharacteristic
188C23×C17H(5,𝔽2)11yescharacteristic
189C23×C172−1+411yescharacteristic
190C23×C172−1+411yescharacteristic
191C23×C172−1+411yescharacteristic
192C23×C172−1+411yescharacteristic
193C2×C4×C17—22no—
194C2×C4×C17—22no—
195C2×C4×C17—22no—
196C2×C4×C17—22no—
197C2×C4×C17—22no—
198C2×C4×C17—22no—
199C2×C4×C17—22no—
200C2×C4×C17—22no—
201C2×C4×C17—22no—
202C2×C4×C17—22no—
203C2×C4×C17—22no—
204C2×C4×C17—22no—
205C2×C4×C17—22no—
206C2×C4×C17—22no—
207C2×C4×C17—22no—
208C2×C4×C17—22no—
209C2×C4×C17—22no—
210C2×C4×C17—22no—
211C2×C4×C17—41no—
212C2×C4×C17—41no—
213C2×C4×C17—41no—
214C2×C4×C17—41no—
215C2×C4×C17—41no—
216C2×C4×C17—41no—
217C2×C4×C17—41no—
218C2×C4×C17—41no—
219C2×C4×C17—41no—
220C2×C4×C17—41no—
221C2×C4×C17—41no—
222C2×C4×C17—41no—
223C2×C4×C17—41no—
224C2×C4×C17—41no—
225C2×C4×C17—41no—
226C2×C4×C17—41no—
227C2×C4×C17—41no—
228C2×C4×C17—41no—
229C2×C4×C17—41no—
230C2×C4×C17—41no—
231C2×C4×C17—41no—
232C2×C4×C17—41no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17#11714yes—
236C2×C4×C17C4×D414yes—
237C2×C4×C17C4×Q814yes—
238C2×C4×C17C22⋊Q814yes—
239C2×C4×C17#12314yes—
240C2×C4×C17#12514yes—
241C2×C4×C17#12614yes—
242C2×Dic17—24no—
243C2×Dic17—24no—
244C2×Dic17—24no—
245C2×Dic17—24no—
246C2×Dic17—24no—
247C2×Dic17—24no—
248C2×Dic17—42no—
249C2×Dic17—42no—
250C2×Dic17—42no—
251C2×Dic17—42no—
252C2×Dic17—42no—
253C2×Dic17—42no—
254C2×Dic17—42no—
255C2×Dic17—42no—
256C2×Dic17—42no—
257C2×Dic17—42no—
258C2×Dic17—42no—
259C2×Dic17—42no—
260C2×Dic17—42no—
261C2×Dic17—42no—
262C2×Dic17—42no—
263C2×Dic17—42no—
264C2×Dic17—42no—
265C2×Dic17—42no—
266C2×Dic17—42no—
267C2×Dic17—42no—
268C2×Dic17—42no—
269C2×Dic17—42no—
270C2×#389—171no—
271C2×#389—171no—
272C2×#376D1711yescharacteristic
273#1445—172no—
274#1443—172no—
275#1442—172no—
276#1441—172no—
277C4⋊#95—171no—
278C4⋊#95—171no—
279C4⋊#95—171no—
280C4⋊#95—171no—
281C22×C17C2×#11711yescharacteristic
282C22×C17C2×C4×D411yescharacteristic
283C22×C17C2×C4×Q811yescharacteristic
284C22×C17#51811yescharacteristic
285C22×C17#51911yescharacteristic
286C22×C17#52011yescharacteristic
287C22×C17#52011yescharacteristic
288C22×C17C2×C22⋊Q811yescharacteristic
289C22×C17C2×#12311yescharacteristic
290C22×C17C2×#12511yescharacteristic
291C22×C17C2×#12611yescharacteristic
292C22×C17#53511yescharacteristic
293C22×C17#53611yescharacteristic
294C22×C17#53711yescharacteristic
295C22×C17#53711yescharacteristic
296C22×C17#54011yescharacteristic
297C22×C17#54011yescharacteristic
298C22×C17#54011yescharacteristic
299C22×C17#54011yescharacteristic
300C22×C17#54111yescharacteristic
301C22×C17#54111yescharacteristic
302C22×C17#54111yescharacteristic
303C22×C17#54111yescharacteristic
304C22×C17#54211yescharacteristic
305C22×C17#54211yescharacteristic
306C22×C17#54211yescharacteristic
307C22×C17#54211yescharacteristic
308C22×C17#54211yescharacteristic
309C22×C17#54211yescharacteristic
310C22×C17#54211yescharacteristic
311C22×C17#54211yescharacteristic
312C22×C17#54411yescharacteristic
313C22×C17#54411yescharacteristic
314C22×C17#54411yescharacteristic
315C22×C17#54411yescharacteristic
316C4×C17—42no—
317C4×C17—42no—
318C4×C17—42no—
319C4×C17—42no—
320C4×C17—42no—
321C4×C17—42no—
322C4×C17#38718yes—
323Dic17—44no—
324Dic17—44no—
325Dic17—82no—
326Dic17—82no—
327C22×C4⋊C4—171no—
328C22×C4⋊C4—171no—
329C22×C4⋊C4—172no—
330C22×C4⋊C4—171no—
331C22×C4⋊C4—171no—
332C22×C4⋊C4—172no—
333C22×C42C2×D1711yescharacteristic
334C22×C42C2×D1711yescharacteristic
335C22×C42C2×D1711yescharacteristic
336#389—178no—
337#389—344no—
338#376—24no—
339C2×#95—172no—
340C2×#95—172no—
341C2×#95—172no—
342C2×#95—172no—
343C2×#95—172no—
344C2×#95—172no—
345C2×#95—172no—
346C2×#95—172no—
347C2×#95—172no—
348C2×#95—172no—
349C2×#95C2×D1711yescharacteristic
350C2×#95C2×D1711yescharacteristic
351C2×#95C2×D1711yescharacteristic
352C2×#95C2×D1711yescharacteristic
353C2×C17C2×#38711yescharacteristic
354C2×C17#231911yescharacteristic
355C2×C17#232011yescharacteristic
356C2×C17#232311yescharacteristic
357C2×C17#232411yescharacteristic
358C2×C17#233011yescharacteristic
359C2×C17#233111yescharacteristic
360C2×C17#262411yescharacteristic
361C2×C17#262511yescharacteristic
362C2×C17#262811yescharacteristic
363C2×C17#262911yescharacteristic
364C2×C17#264411yescharacteristic
365C2×C17#264511yescharacteristic
366C2×C17#264711yescharacteristic
367C2×C17#264711yescharacteristic
368C23×C4—172no—
369C23×C4—172no—
370C23×C4—172no—
371C23×C4—172no—
372C23×C4C22×D1711yescharacteristic
373C23×C4C22×D1711yescharacteristic
374C23×C4C22×D1711yescharacteristic
375C23×C4C22×D1711yescharacteristic
376C23×C4C22×D1711yescharacteristic
377C23×C4C22×D1711yescharacteristic
378C23×C4C22×D1711yescharacteristic
379C2×C4⋊C4—174no—
380C2×C4⋊C4—174no—
381C2×C4⋊C4—178no—
382C2×C4⋊C4—342no—
383C2×C4⋊C4—342no—
384C2×C4⋊C4—342no—
385C2×C4⋊C4—342no—
386C2×C4⋊C4—342no—
387C2×C4⋊C4—342no—
388C2×C4⋊C4—342no—
389C2×C4⋊C4—342no—
390C2×C4⋊C4—342no—
391C2×C4⋊C4—344no—
392C2×C4⋊C4—342no—
393C2×C4⋊C4—682no—
394C2×C4⋊C4—682no—
395C2×C4⋊C4—682no—
396C2×C4⋊C4—682no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42Dic3414yes—
404C2×C42C4×D1714yes—
405C2×C42C22⋊D1714yes—
406#95—22no—
407#95—22no—
408#95—22no—
409#95—22no—
410#95—178no—
411#95—344no—
412#95—682no—
413#95—682no—
414#95—682no—
415#95—682no—
416#95—682no—
417#95—682no—
418#95—682no—
419#95—682no—
420C17#1426611yescharacteristic, complemented, Sylow
421C24C23×D1711yescharacteristic
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—174no—
459C22×C4—174no—
460C22×C4—342no—
461C22×C4—342no—
462C22×C4—342no—
463C22×C4—342no—
464C22×C4—342no—
465C22×C4—342no—
466C22×C4—342no—
467C22×C4—342no—
468C22×C4—342no—
469C22×C4—342no—
470C22×C4—342no—
471C22×C4—342no—
472C22×C4—342no—
473C22×C4—342no—
474C22×C4—342no—
475C22×C4—342no—
476C22×C4—342no—
477C22×C4—342no—
478C22×C4—342no—
479C22×C4—342no—
480C22×C4—342no—
481C22×C4—342no—
482C22×C4—342no—
483C22×C4—342no—
484C22×C4—342no—
485C22×C4—342no—
486C22×C4C2×Dic3412yes—
487C22×C4C2×Dic3412yes—
488C22×C4C2×Dic3412yes—
489C22×C4C2×C4×D1712yes—
490C22×C4C2×C4×D1712yes—
491C22×C4C2×C4×D1712yes—
492C22×C4#6325212yes—
493C22×C4#6325212yes—
494C22×C4#6325212yes—
495C22×C4#6325212yes—
496C22×C4C2×C22⋊D1712yes—
497C22×C4C2×C22⋊D1712yes—
498C22×C4C2×C22⋊D1712yes—
499C4⋊C4—348no—
500C4⋊C4—348no—
501C4⋊C4—688no—
502C4⋊C4—688no—
503C4⋊C4—684no—
504C4⋊C4—684no—
505C42—28no—
506C42—28no—
507C42—28no—
508C23C22×Dic3411yescharacteristic
509C23C22×C4×D1711yescharacteristic
510C23C2×#6325211yescharacteristic
511C23C2×#6325211yescharacteristic
512C23C2×#6325211yescharacteristic
513C23C2×#6325211yescharacteristic
514C23#1058769611yescharacteristic
515C23#1058769611yescharacteristic
516C23#1058769611yescharacteristic
517C23#1058769611yescharacteristic
518C23#1058769711yescharacteristic
519C23#1058769711yescharacteristic
520C23#1058769711yescharacteristic
521C23#1058769711yescharacteristic
522C23C22×C22⋊D1711yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—344no—
566C2×C4—344no—
567C2×C4—344no—
568C2×C4—344no—
569C2×C4—344no—
570C2×C4—344no—
571C2×C4—682no—
572C2×C4—682no—
573C2×C4—682no—
574C2×C4—682no—
575C2×C4—682no—
576C2×C4—682no—
577C2×C4—682no—
578C2×C4—682no—
579C2×C4—682no—
580C2×C4—682no—
581C2×C4—682no—
582C2×C4—682no—
583C2×C4—682no—
584C2×C4—682no—
585C2×C4—682no—
586C2×C4—682no—
587C2×C4—682no—
588C2×C4—682no—
589C2×C4—682no—
590C2×C4—682no—
591C2×C4—682no—
592C2×C4—682no—
593C2×C4C4×Dic3414yes—
594C2×C4#1058755614yes—
595C2×C4#1058755814yes—
596C2×C4#1058756214yes—
597C2×C4#1058761014yes—
598C2×C4C4×C22⋊D1714yes—
599C2×C4#1058761514yes—
600C22C2×#1058755811yescharacteristic
601C22C2×C4×C22⋊D1711yescharacteristic
602C22C2×C4×Dic3411yescharacteristic
603C22#1176328311yescharacteristic
604C22#1176328611yescharacteristic
605C22#1176328911yescharacteristic
606C22#1176328911yescharacteristic
607C22C2×#1058761011yescharacteristic
608C22C2×#1058761511yescharacteristic
609C22C2×#1058755611yescharacteristic
610C22C2×#1058756211yescharacteristic
611C22#1176337311yescharacteristic
612C22#1176338011yescharacteristic
613C22#1176338711yescharacteristic
614C22#1176338711yescharacteristic
615C22#1176341411yescharacteristic
616C22#1176341411yescharacteristic
617C22#1176341411yescharacteristic
618C22#1176341411yescharacteristic
619C22#1176342111yescharacteristic
620C22#1176342111yescharacteristic
621C22#1176342111yescharacteristic
622C22#1176342111yescharacteristic
623C22#1176343011yescharacteristic
624C22#1176343011yescharacteristic
625C22#1176343011yescharacteristic
626C22#1176343011yescharacteristic
627C22#1176343011yescharacteristic
628C22#1176343011yescharacteristic
629C22#1176343011yescharacteristic
630C22#1176343011yescharacteristic
631C22#1176343711yescharacteristic
632C22#1176343711yescharacteristic
633C22#1176343711yescharacteristic
634C22#1176343711yescharacteristic
635C4—42no—
636C4—42no—
637C4—42no—
638C4—42no—
639C4—42no—
640C4—42no—
641C4—684no—
642C4—684no—
643C4—1362no—
644C4—1362no—
645C4#1176269318yes—
646C2C2×#1176269311yescharacteristic
647C2#1453142811yescharacteristic
648C2#1453143611yescharacteristic
649C2#1453146611yescharacteristic
650C2#1453147711yescharacteristic
651C2#1453152511yescharacteristic
652C2#1453153211yescharacteristic
653C2#1453457311yescharacteristic
654C2#1453458111yescharacteristic
655C2#1453460511yescharacteristic
656C2#1453461411yescharacteristic
657C2#1453474411yescharacteristic
658C2#1453474911yescharacteristic
659C2#1453475911yescharacteristic
660C2#1453475911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#376C2
socle, prime radical, cosocleC24×C17C24
hypercenterC2×#376D17
hypocenterC17#14266
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
19. #11762707C4semidirect
420. C17#14266semidirect

Maximal subgroups

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

subgroupindex
C2×#117627072
#145270502
#145270452
#145270422
#145270352
#145270142
C2×C17×#3762
#1426617