Finite Group Databasebeta

← #16965117

Subgroups — #16965117

Order 4352.

1378 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762745C211yesmaximal, characteristic
2#14527045C212yesmaximal, complemented
3#14527038C212yesmaximal, complemented
4#14527036C212yesmaximal, complemented
5#14527035C212yesmaximal, complemented
6#14527029C211yesmaximal, characteristic
7#14527027C212yesmaximal
8#14527007C212yesmaximal
9C17×C22⋊#95C211yesmaximal, characteristic
10C22×C4⋊Dic17C2211yescharacteristic
11C22×C4⋊Dic17C2211yescharacteristic
12C22×#63225C2212yes—
13C22×#63225C2212yes—
14C22×C22⋊Dic17C2212yes—
15C22×C22⋊Dic17C2212yes—
16#11762745C418yescomplemented
17C2×#10587502C2212yes—
18C2×#10587502C2212yes—
19C2×#10587502C2212yes—
20C2×#10587502C2212yes—
21C2×#10587502C2212yes—
22C2×#10587502C2212yes—
23C2×#10587502C2212yes—
24C2×#10587502C2211yescharacteristic
25C2×#10587502C2212yes—
26C2×#10587502C2211yescharacteristic
27C24×C4×C17C2211yescharacteristic
28C22×C22⋊C4×C17C2211yescharacteristic
29C22×C22⋊C4×C17C2211yescharacteristic
30C2×C17×#95C2212yes—
31C2×C17×#95C2212yes—
32C25×C17C2311yescharacteristic
33C23×C4×C17—41no—
34C23×C4×C17—41no—
35C23×C4×C17—42no—
36C23×C4×C17—42no—
37C23×C4×C17Q814yes—
38C23×C4×C17C2312yes—
39C23×C4×C17C2311yescharacteristic
40C23×C4×C17C2311yescharacteristic
41C23×C4×C17C2312yes—
42C23×Dic17C2312yes—
43C23×Dic17C2312yes—
44C23×Dic17C2312yes—
45C23×Dic17C2312yes—
46C2×C22⋊C4×C17—22no—
47C2×C22⋊C4×C17—41no—
48C2×C22⋊C4×C17—41no—
49C2×C22⋊C4×C17—41no—
50C2×C22⋊C4×C17—41no—
51C2×C22⋊C4×C17C2×C414yes—
52C2×C22⋊Dic17—24no—
53C2×C22⋊Dic17—42no—
54C2×C22⋊Dic17—42no—
55C2×C22⋊Dic17—42no—
56C2×C22⋊Dic17—42no—
57C2×C22⋊Dic17C2×C418yes—
58C2×C4⋊Dic17—41no—
59C2×C4⋊Dic17—41no—
60C2×C4⋊Dic17—41no—
61C2×C4⋊Dic17—42no—
62C2×C4⋊Dic17C2×C414yescomplemented
63C2×#63225—42no—
64C2×#63225—42no—
65C2×#63225—42no—
66C2×#63225—42no—
67C2×#63225—42no—
68C2×#63225C2×C418yescomplemented
69C17×#95—42no—
70C17×#95—42no—
71#10587502—42no—
72#10587502—42no—
73#10587502—42no—
74#10587502—42no—
75#10587502—42no—
76#10587502—42no—
77#10587502—42no—
78#10587502—42no—
79#10587502—41no—
80#10587502C2×C414yescomplemented
81C24×C17—22no—
82C24×C17—22no—
83C24×C17—21no—
84C24×C17—21no—
85C24×C17—22no—
86C24×C17—21no—
87C24×C17—21no—
88C24×C17—22no—
89C24×C17C22×C412yes—
90C24×C17C2×Q812yes—
91C24×C17#4112yes—
92C24×C17C2411yescharacteristic
93C22×C4×C17—22no—
94C22×C4×C17—22no—
95C22×C4×C17—22no—
96C22×C4×C17—22no—
97C22×C4×C17—22no—
98C22×C4×C17—22no—
99C22×C4×C17—22no—
100C22×C4×C17—21no—
101C22×C4×C17—22no—
102C22×C4×C17—22no—
103C22×C4×C17—21no—
104C22×C4×C17—21no—
105C22×C4×C17—21no—
106C22×C4×C17—22no—
107C22×C4×C17—22no—
108C22×C4×C17—22no—
109C22×C4×C17—22no—
110C22×C4×C17—22no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—44no—
115C22×C4×C17—48no—
116C22×C4×C17—44no—
117C22×C4×C17—48no—
118C22×C4×C17—44no—
119C22×C4×C17C22×C412yes—
120C22×C4×C17C22×C412yes—
121C22×C4×C17C2×Q814yes—
122C22×Dic17—22no—
123C22×Dic17—22no—
124C22×Dic17—22no—
125C22×Dic17—22no—
126C22×Dic17—22no—
127C22×Dic17—22no—
128C22×Dic17—22no—
129C22×Dic17—22no—
130C22×Dic17—22no—
131C22×Dic17—22no—
132C22×Dic17—22no—
133C22×Dic17—22no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—22no—
138C22×Dic17—22no—
139C22×Dic17—22no—
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×Dic17C22×C414yes—
149C22×Dic17C22×C414yes—
150C22⋊C4×C17—44no—
151C22⋊C4×C17—44no—
152C22⋊Dic17—48no—
153C22⋊Dic17—48no—
154C4⋊Dic17—44no—
155C4⋊Dic17—44no—
156#63225—48no—
157#63225—48no—
158#14636—171nomaximal, Sylow
159C23×C17—24no—
160C23×C17—22no—
161C23×C17—24no—
162C23×C17—22no—
163C23×C17—24no—
164C23×C17—22no—
165C23×C17—24no—
166C23×C17—22no—
167C23×C17—24no—
168C23×C17—22no—
169C23×C17—24no—
170C23×C17—22no—
171C23×C17—41no—
172C23×C17—42no—
173C23×C17—41no—
174C23×C17—42no—
175C23×C17—41no—
176C23×C17—42no—
177C23×C17—42no—
178C23×C17—42no—
179C23×C17—42no—
180C23×C17—41no—
181C23×C17C4×Q814yes—
182C23×C17C23×C411yescharacteristic
183C23×C17C22×Q811yescharacteristic
184C23×C17C2×#4111yescharacteristic
185C23×C17H(5,𝔽2)11yescharacteristic
186C23×C17H(5,𝔽2)12yes—
187C23×C17H(5,𝔽2)11yescharacteristic
188C23×C17H(5,𝔽2)12yes—
189C23×C17H(5,𝔽2)11yescharacteristic
190C23×C17H(5,𝔽2)12yes—
191C23×C172−1+411yescharacteristic
192C23×C172−1+412yes—
193C2×C4×C17—22no—
194C2×C4×C17—22no—
195C2×C4×C17—24no—
196C2×C4×C17—24no—
197C2×C4×C17—24no—
198C2×C4×C17—24no—
199C2×C4×C17—24no—
200C2×C4×C17—416no—
201C2×C4×C17—42no—
202C2×C4×C17—41no—
203C2×C4×C17—41no—
204C2×C4×C17—42no—
205C2×C4×C17—42no—
206C2×C4×C17—42no—
207C2×C4×C17—42no—
208C2×C4×C17—41no—
209C2×C4×C17—42no—
210C2×C4×C17—41no—
211C2×C4×C17—42no—
212C2×C4×C17—42no—
213C2×C4×C17—42no—
214C2×C4×C17—42no—
215C2×C4×C17—42no—
216C2×C4×C17—42no—
217C2×C4×C17—42no—
218C2×Dic17—24no—
219C2×Dic17—24no—
220C2×Dic17—24no—
221C2×Dic17—24no—
222C2×Dic17—24no—
223C2×Dic17—24no—
224C2×Dic17—42no—
225C2×Dic17—42no—
226C2×Dic17—42no—
227C2×Dic17—42no—
228C2×Dic17—42no—
229C2×Dic17—42no—
230C2×Dic17—42no—
231C2×Dic17—42no—
232C2×Dic17—42no—
233C2×Dic17—42no—
234C2×Dic17—42no—
235C2×Dic17—42no—
236C2×Dic17—42no—
237C2×Dic17—42no—
238C2×Dic17—42no—
239C2×Dic17—42no—
240C2×Dic17—42no—
241C2×Dic17—42no—
242C2×Dic17—42no—
243C2×Dic17—42no—
244C2×Dic17—42no—
245C2×Dic17—42no—
246C2×#399—171no—
247#1443—172no—
248#1441—172no—
249#1441—172no—
250#1441—172no—
251#1439—172no—
252#1439—171no—
253C22⋊#95—172no—
254C22⋊#95D1711yescharacteristic
255C22×C17—28no—
256C22×C17—24no—
257C22×C17—42no—
258C22×C17—44no—
259C22×C17—42no—
260C22×C17—44no—
261C22×C17—42no—
262C22×C17—42no—
263C22×C17—42no—
264C22×C17—44no—
265C22×C17—42no—
266C22×C17C2×C4×Q811yescharacteristic
267C22×C17#51812yes—
268C22×C17#51811yescharacteristic
269C22×C17#52012yes—
270C22×C17#52011yescharacteristic
271C22×C17#53812yes—
272C22×C17#53811yescharacteristic
273C22×C17#53912yes—
274C22×C17#53911yescharacteristic
275C22×C17#54312yes—
276C22×C17#54311yescharacteristic
277C22×C17#54412yes—
278C22×C17#54411yescharacteristic
279C22×C17#56012yes—
280C22×C17#56011yescharacteristic
281C22×C17#56012yes—
282C22×C17#56011yescharacteristic
283C22×C17#56011yescharacteristic
284C22×C17#56212yes—
285C22×C17#56212yes—
286C22×C17#56212yes—
287C22×C17#56312yes—
288C22×C17#56311yescharacteristic
289C4×C17—44no—
290C4×C17—42no—
291C4×C17—42no—
292C4×C17—82no—
293Dic17—44no—
294Dic17—44no—
295Dic17—82no—
296Dic17—82no—
297C24×C4C2×D1711yescharacteristic
298C22×C4⋊C4—172no—
299C22×C4⋊C4—171no—
300C22×C4⋊C4—172no—
301C22×C4⋊C4—171no—
302C22×C22⋊C4—172no—
303C22×C22⋊C4—172no—
304C22×C22⋊C4C2×D1711yescharacteristic
305C22×C22⋊C4C2×D1711yescharacteristic
306#399—178no—
307C2×#95—171no—
308C2×#95—172no—
309C2×#95—172no—
310C2×#95—172no—
311C2×#95—172no—
312C2×#95—172no—
313C2×#95—171no—
314C2×#95—172no—
315C2×#95—172no—
316C2×#95—172no—
317C2×#95C2×D1712yes—
318C2×#95C2×D1712yes—
319C2×C17—44no—
320C2×C17#232912yes—
321C2×C17#232911yescharacteristic
322C2×C17#237611yescharacteristic
323C2×C17#237612yes—
324C2×C17#238011yescharacteristic
325C2×C17#282611yescharacteristic
326C2×C17#282612yes—
327C2×C17#283411yescharacteristic
328C2×C17#284112yes—
329C2×C17#284111yescharacteristic
330C2×C17#284211yescharacteristic
331C25C22×D1711yescharacteristic
332C23×C4—42no—
333C23×C4—42no—
334C23×C4—41no—
335C23×C4—41no—
336C23×C4—172no—
337C23×C4—172no—
338C23×C4—172no—
339C23×C4—172no—
340C23×C4Dic3414yes—
341C23×C4C22×D1712yes—
342C23×C4C22×D1712yes—
343C23×C4C22×D1711yescharacteristic
344C23×C4C22×D1711yescharacteristic
345C2×C4⋊C4—178no—
346C2×C4⋊C4—174no—
347C2×C4⋊C4—682no—
348C2×C4⋊C4—682no—
349C2×C4⋊C4—682no—
350C2×C4⋊C4—682no—
351C2×C4⋊C4—682no—
352C2×C4⋊C4—681no—
353C2×C4⋊C4—681no—
354C2×C4⋊C4—681no—
355C2×C4⋊C4—682no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—178no—
362C2×C22⋊C4—344no—
363C2×C22⋊C4—682no—
364C2×C22⋊C4—682no—
365C2×C22⋊C4—682no—
366C2×C22⋊C4—682no—
367C2×C22⋊C4C4×D1714yes—
368#95—42no—
369#95—42no—
370#95—174no—
371#95—682no—
372#95—681no—
373#95—682no—
374#95—682no—
375#95—682no—
376#95—682no—
377#95—682no—
378#95—682no—
379#95—682no—
380C17#1463611yescharacteristic, complemented, Sylow
381C24—21no—
382C24—21no—
383C24—21no—
384C24—22no—
385C24—22no—
386C24—21no—
387C24—22no—
388C24—22no—
389C24C2×Dic3412yes—
390C24C2×C4×D1712yes—
391C24#6325212yes—
392C24C23×D1711yescharacteristic
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—48no—
415C22×C4—44no—
416C22×C4—44no—
417C22×C4—44no—
418C22×C4—48no—
419C22×C4—174no—
420C22×C4—174no—
421C22×C4—342no—
422C22×C4—342no—
423C22×C4—342no—
424C22×C4—342no—
425C22×C4—342no—
426C22×C4—342no—
427C22×C4—342no—
428C22×C4—342no—
429C22×C4—342no—
430C22×C4—342no—
431C22×C4—342no—
432C22×C4—342no—
433C22×C4—342no—
434C22×C4—342no—
435C22×C4—342no—
436C22×C4—342no—
437C22×C4—342no—
438C22×C4—342no—
439C22×C4—342no—
440C22×C4—342no—
441C22×C4—342no—
442C22×C4—342no—
443C22×C4—342no—
444C22×C4—342no—
445C22×C4—342no—
446C22×C4—342no—
447C22×C4C2×Dic3414yes—
448C22×C4C2×C4×D1712yes—
449C22×C4C2×C4×D1712yes—
450C4⋊C4—688no—
451C4⋊C4—684no—
452C4⋊C4—688no—
453C4⋊C4—684no—
454C22⋊C4—44no—
455C22⋊C4—44no—
456C22⋊C4—688no—
457C22⋊C4—688no—
458C23—24no—
459C23—22no—
460C23—24no—
461C23—22no—
462C23—24no—
463C23—22no—
464C23—24no—
465C23—22no—
466C23—24no—
467C23—22no—
468C23—24no—
469C23—22no—
470C23—42no—
471C23—41no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23C4×Dic3414yes—
481C23C22×Dic3411yescharacteristic
482C23C22×C4×D1711yescharacteristic
483C23C2×#6325211yescharacteristic
484C23#1058769112yes—
485C23#1058769111yescharacteristic
486C23#1058769111yescharacteristic
487C23#1058769112yes—
488C23#1058769111yescharacteristic
489C23#1058769411yescharacteristic
490C23#1058769612yes—
491C23#1058769712yes—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—416no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—344no—
518C2×C4—344no—
519C2×C4—344no—
520C2×C4—344no—
521C2×C4—344no—
522C2×C4—344no—
523C2×C4—682no—
524C2×C4—682no—
525C2×C4—682no—
526C2×C4—682no—
527C2×C4—682no—
528C2×C4—682no—
529C2×C4—682no—
530C2×C4—682no—
531C2×C4—682no—
532C2×C4—682no—
533C2×C4—682no—
534C2×C4—682no—
535C2×C4—682no—
536C2×C4—682no—
537C2×C4—682no—
538C2×C4—682no—
539C2×C4—682no—
540C2×C4—682no—
541C2×C4—682no—
542C2×C4—682no—
543C2×C4—682no—
544C2×C4—682no—
545C22—28no—
546C22—24no—
547C22—42no—
548C22—44no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—44no—
553C22—42no—
554C22—42no—
555C22—44no—
556C22C2×C4×Dic3411yescharacteristic
557C22#1176328112yes—
558C22#1176328211yescharacteristic
559C22#1176328812yes—
560C22#1176329011yescharacteristic
561C22#1176339212yes—
562C22#1176339711yescharacteristic
563C22#1176340112yes—
564C22#1176340611yescharacteristic
565C22#1176343512yes—
566C22#1176343511yescharacteristic
567C22#1176343712yes—
568C22#1176344011yescharacteristic
569C22#1176354712yes—
570C22#1176354811yescharacteristic
571C22#1176354811yescharacteristic
572C22#1176354812yes—
573C22#1176354911yescharacteristic
574C22#1176355412yes—
575C22#1176355512yes—
576C22#1176355612yes—
577C22#1176356012yes—
578C22#1176356211yescharacteristic
579C4—42no—
580C4—44no—
581C4—42no—
582C4—82no—
583C4—684no—
584C4—684no—
585C4—1362no—
586C4—1362no—
587C2—44no—
588C2#1453151212yes—
589C2#1453151711yescharacteristic
590C2#1453192711yescharacteristic
591C2#1453193312yes—
592C2#1453195911yescharacteristic
593C2#1453687711yescharacteristic
594C2#1453687912yes—
595C2#1453696711yescharacteristic
596C2#1453703912yes—
597C2#1453704111yescharacteristic
598C2#1453704811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C22⋊#95C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC22⋊#95D17
hypocenterC17#14636
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. #14527045C2semidirect
3. #14527038C2semidirect
4. #14527036C2semidirect
5. #14527035C2semidirect
16. #11762745C4semidirect
62. C2×C4⋊Dic17C2×C4semidirect
68. C2×#63225C2×C4semidirect
80. #10587502C2×C4semidirect
380. C17#14636semidirect

Maximal subgroups

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

subgroupindex
C2×#117627452
#145270452
#145270382
#145270362
#145270352
#145270292
#145270272
#145270072
C17×C22⋊#952
#1463617