Finite Group Databasebeta

← #17005467

Subgroups — #17005467

Order 4352.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537804C211yesmaximal, characteristic
2#14537733C211yesmaximal, characteristic, complemented
3#14527687C211yesmaximal, characteristic, complemented
4#14527675C211yesmaximal, characteristic, complemented
5#14527663C211yesmaximal, characteristic, complemented
6#14527656C211yesmaximal, characteristic, complemented
7#14527635C211yesmaximal, characteristic, complemented
8#14527628C211yesmaximal, characteristic, complemented
9#14527603C211yesmaximal, characteristic, complemented
10Q16×#3622C211yesmaximal, characteristic, complemented
11#14527569C211yesmaximal, characteristic, complemented
12#14527257C211yesmaximal, characteristic, complemented
13#14527171C211yesmaximal, characteristic
14#14527079C211yesmaximal, characteristic, complemented
15C17×#3107C211yesmaximal, characteristic
16#11762940—21no—
17#11762940—21no—
18#11762940C2211yescharacteristic
19#11762940C2211yescharacteristic
20Q8×#3622C2211yescharacteristic
21Q8×#3622C2211yescharacteristic
22Q8×#3622C2211yescharacteristic
23Q8×#3622C2211yescharacteristic
24#11762887—21no—
25#11762887—21no—
26#11762887C2211yescharacteristic
27#11762887C2211yescharacteristic
28#11762866—21no—
29#11762866C2211yescharacteristic
30#11762862C2211yescharacteristic
31#11762836—21no—
32C2×C4⋊#3622C2211yescharacteristic
33#11762765—21no—
34C4×#63223—21no—
35C4×#63223C2211yescharacteristic
36#11762562C2211yescharacteristic
37#11762562C2211yescharacteristic
38#11762560C2211yescharacteristic
39#11762560C2211yescharacteristic
40Q8⋊#3622C2211yescharacteristic
41Q8⋊#3622C2211yescharacteristic
42Q8⋊#3622C2211yescharacteristic
43Q8⋊#3622C2211yescharacteristic
44Q8⋊#3622C2211yescharacteristic
45Q8⋊#3622C2211yescharacteristic
46D4⋊#3622C2211yescharacteristic
47D4⋊#3622C2211yescharacteristic
48#11762531C2211yescharacteristic
49#11762531C2211yescharacteristic
50#11762530C2211yescharacteristic
51C8×#3622C2211yescharacteristic
52C17×#533C2211yescharacteristic
53C4×#41×C17C2211yescharacteristic
54C17×#485C411yescharacteristic
55C17×#485C411yescharacteristic
56C17×#475C411yescharacteristic
57C17×#474C411yescharacteristic
58C17×#462C411yescharacteristic
59C17×#461C411yescharacteristic
60C17×#452C411yescharacteristic
61C17×#452C411yescharacteristic
62C4×Q16×C17C2211yescharacteristic
63C4×Q16×C17C2211yescharacteristic
64C4×SD16×C17C2211yescharacteristic
65C4×SD16×C17C2211yescharacteristic
66C17×#431C2211yescharacteristic
67C2×#41×C17C2×C411yescharacteristic
68C2×Q16×C17C2×C411yescharacteristic
69C2×Q16×C17C2×C411yescharacteristic
70C2×SD16×C17C2×C411yescharacteristic
71C2×SD16×C17C2×C411yescharacteristic
72C17×C4⋊Q8C2×C411yescharacteristic
73C17×C4⋊Q8C2×C411yescharacteristic
74C17×#125—21no—
75C17×C22⋊Q8—21no—
76C17×C22⋊Q8C2×C411yescharacteristic
77C17×C22⋊Q8C2×C411yescharacteristic
78C4×Q8×C17—21no—
79C4×Q8×C17C2×C411yescharacteristic
80C4×Q8×C17C2311yescharacteristic
81C4×Q8×C17C2311yescharacteristic
82C4×Q8×C17C2311yescharacteristic
83C4×D4×C17—21no—
84C4×D4×C17—21no—
85C4×D4×C17C2×C411yescharacteristic
86C4×D4×C17C2311yescharacteristic
87C17×#117—21no—
88C17×#117—21no—
89C17×#117C2×C411yescharacteristic
90C2×C42×C17—21no—
91C2×C42×C17C2311yescharacteristic
92C2×#63223—21no—
93C2×#63223—21no—
94C2×#63223D411yescharacteristic
95C2×#63223D411yescharacteristic
96C22×#3622—21no—
97C17×#107C2×C411yescharacteristic
98C17×#107C2×C411yescharacteristic
99C17×#106C2×C411yescharacteristic
100C17×#106C2×C411yescharacteristic
101C17×C4⋊C8C2×C411yescharacteristic
102C17×C4⋊C8C2×C411yescharacteristic
103C17×#103C2×C411yescharacteristic
104C17×#103C2×C411yescharacteristic
105C17×#103C2×C411yescharacteristic
106C17×#103C2×C411yescharacteristic
107C17×#103C2×C411yescharacteristic
108C17×#103C2×C411yescharacteristic
109C17×#102C2×C411yescharacteristic
110C17×#102C2×C411yescharacteristic
111C17×C22⋊C8C2×C411yescharacteristic
112C17×C22⋊C8C2×C411yescharacteristic
113C4×C8×C17C2311yescharacteristic
114C4×C8×C17C2311yescharacteristic
115C22⋊#3622—21no—
116C22⋊#3622—21no—
117C22⋊#3622—21no—
118C22⋊#3622—21no—
119C4⋊#3622—21no—
120C4⋊#3622—21no—
121C4⋊#3622—21no—
122C4⋊#3622—21no—
123C4⋊#3622—21no—
124C4⋊#3622—21no—
125C4⋊#3622—21no—
126C4⋊#3622—21no—
127C4⋊#3622C2311yescharacteristic
128C4⋊#3622C2311yescharacteristic
129C4⋊#3622C2311yescharacteristic
130C4⋊#3622C2311yescharacteristic
131#10587474—21no—
132#10587474—21no—
133#10587474—21no—
134#10587474D411yescharacteristic
135#10587474D411yescharacteristic
136C4×#3622—21no—
137C4×#3622—21no—
138C4×#3622—21no—
139C4×#3622—21no—
140C4×#3622C2311yescharacteristic
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144#41×C17—22no—
145#41×C17—41no—
146C2×Q8×C17—21no—
147C2×Q8×C17C22×C411yescharacteristic
148C2×Q8×C17C22×C411yescharacteristic
149C2×Q8×C17C22×C411yescharacteristic
150C2×D4×C17—21no—
151C2×D4×C17C22×C411yescharacteristic
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17C22×C411yescharacteristic
156C22×C4×C17C2×D411yescharacteristic
157C22×C4×C17#4111yescharacteristic
158Q16×C17—22no—
159Q16×C17—22no—
160SD16×C17—41no—
161SD16×C17—41no—
162C2×C8×C17C22×C411yescharacteristic
163C2×C8×C17C22×C411yescharacteristic
164C2×C8×C17C22×C411yescharacteristic
165C2×C8×C17C22×C411yescharacteristic
166C4⋊C4×C17—21no—
167C4⋊C4×C17—21no—
168C4⋊C4×C17—21no—
169C4⋊C4×C17—21no—
170C4⋊C4×C17—21no—
171C4⋊C4×C17—21no—
172C4⋊C4×C17—21no—
173C4⋊C4×C17—21no—
174C4⋊C4×C17—21no—
175C4⋊C4×C17C22×C411yescharacteristic
176C4⋊C4×C17C22×C411yescharacteristic
177C4⋊C4×C17C22×C411yescharacteristic
178C4⋊C4×C17C22×C411yescharacteristic
179C22⋊C4×C17—21no—
180C22⋊C4×C17—21no—
181C22⋊C4×C17—21no—
182C22⋊C4×C17—21no—
183C22⋊C4×C17—21no—
184C42×C17—21no—
185C42×C17—21no—
186C42×C17—21no—
187C42×C17—21no—
188C42×C17—21no—
189C42×C17C22×C411yescharacteristic
190C42×C17C2×D411yescharacteristic
191C42×C17#4111yescharacteristic
192C42×C17C2411yescharacteristic
193#63223—22no—
194#63223—41no—
195#63223—42no—
196#63223—42no—
197C2×#3622—21no—
198C2×#3622—21no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—21no—
202C2×#3622—21no—
203C2×#3622—42no—
204C2×#3622C2×D411yescharacteristic
205C2×#3622C2×D411yescharacteristic
206C2×#3622C2×D411yescharacteristic
207C2×#3622C2×D411yescharacteristic
208#18013—171nomaximal, Sylow
209C23×C17—21no—
210C23×C17C4×D411yescharacteristic
211Q8×C17—21no—
212Q8×C17—21no—
213Q8×C17—21no—
214Q8×C17—21no—
215Q8×C17—21no—
216Q8×C17—81no—
217Q8×C17#13112yes—
218D4×C17—21no—
219D4×C17—21no—
220D4×C17—42no—
221C2×C4×C17—21no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17—21no—
227C2×C4×C17—21no—
228C2×C4×C17—21no—
229C2×C4×C17—21no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—41no—
233C2×C4×C17—42no—
234C2×C4×C17—41no—
235C2×C4×C17—41no—
236C2×C4×C17—81no—
237C2×C4×C17C4×D411yescharacteristic
238C2×C4×C17C4×D411yescharacteristic
239C2×C4×C17C4×D411yescharacteristic
240C2×C4×C17C23×C411yescharacteristic
241C2×C4×C17C22×D411yescharacteristic
242C2×C4×C17C2×#4111yescharacteristic
243C8×C17—21no—
244C8×C17—21no—
245C8×C17—21no—
246C8×C17—21no—
247#3622—21no—
248#3622—21no—
249#3622—21no—
250#3622—41no—
251#3622—41no—
252#3622—41no—
253#3622—41no—
254#3622—41no—
255#3622—41no—
256#3622#13712yes—
257#3107D1711yescharacteristic
258#2971—171no—
259#2962—171no—
260#1592—171no—
261#1590—171no—
262#1588—171no—
263#1587—171no—
264#1584—171no—
265#1583—171no—
266#1579—171no—
267C8×Q16—171no—
268#1573—171no—
269#1497—171no—
270#1477—171no—
271#1453—171no—
272C22×C17—21no—
273C22×C17—21no—
274C22×C17—21no—
275C22×C17—41no—
276C22×C17—41no—
277C22×C17—41no—
278C22×C17C2×C4×D411yescharacteristic
279C4×C17—21no—
280C4×C17—22no—
281C4×C17—21no—
282C4×C17—21no—
283C4×C17—21no—
284C4×C17—41no—
285C4×C17—41no—
286C4×C17—41no—
287C4×C17—41no—
288C4×C17—41no—
289C4×C17—41no—
290C4×C17C2×#13111yescharacteristic
291C4×C17#56811yescharacteristic
292C4×C17C2×#13711yescharacteristic
293C4×C17#57511yescharacteristic
294#533C2×D1711yescharacteristic
295C4×#41C2×D1711yescharacteristic
296#485Dic1711yescharacteristic
297#485Dic1711yescharacteristic
298#475Dic1711yescharacteristic
299#474Dic1711yescharacteristic
300#462Dic1711yescharacteristic
301#461Dic1711yescharacteristic
302#452Dic1711yescharacteristic
303#452Dic1711yescharacteristic
304#446—171no—
305#446—171no—
306#446—341no—
307#446—341no—
308C8×Q8—171no—
309C8×Q8—171no—
310C8×Q8—171no—
311C8×Q8—171no—
312C4×Q16C2×D1711yescharacteristic
313C4×Q16C2×D1711yescharacteristic
314C4×SD16C2×D1711yescharacteristic
315C4×SD16C2×D1711yescharacteristic
316#436—171no—
317#436—171no—
318#436—341no—
319#436—341no—
320#432—171no—
321#432—341no—
322#431—171no—
323#431C2×D1711yescharacteristic
324#424—341no—
325C2×C4⋊C8—171no—
326#405—341no—
327C4×M16—171no—
328C4×M16—341no—
329#335—171no—
330#335—171no—
331#334—171no—
332#334—171no—
333Q8⋊C8—171no—
334Q8⋊C8—171no—
335Q8⋊C8—171no—
336Q8⋊C8—171no—
337Q8⋊C8—171no—
338Q8⋊C8—171no—
339D4⋊C8—171no—
340D4⋊C8—171no—
341#322—171no—
342#322—171no—
343#322—171no—
344C82—171no—
345C2×C17—41no—
346C2×C17—81no—
347C2×C17#293311yescharacteristic
348C2×C17C4×#13711yescharacteristic
349C2×C17#295711yescharacteristic
350C2×#41C2×Dic1711yescharacteristic
351C2×Q16C2×Dic1711yescharacteristic
352C2×Q16C2×Dic1711yescharacteristic
353C2×SD16C2×Dic1711yescharacteristic
354C2×SD16C2×Dic1711yescharacteristic
355C2×M16—171no—
356C2×M16—171no—
357C2×M16—341no—
358C2×M16—341no—
359C22×C8—341no—
360C4⋊Q8C2×Dic1711yescharacteristic
361C4⋊Q8C2×Dic1711yescharacteristic
362#125—21no—
363C22⋊Q8—21no—
364C22⋊Q8C2×Dic1711yescharacteristic
365C22⋊Q8C2×Dic1711yescharacteristic
366C4×Q8—21no—
367C4×Q8C2×Dic1711yescharacteristic
368C4×Q8C22×D1711yescharacteristic
369C4×Q8C22×D1711yescharacteristic
370C4×Q8C22×D1711yescharacteristic
371C4×D4—21no—
372C4×D4—21no—
373C4×D4C2×Dic1711yescharacteristic
374C4×D4C22×D1711yescharacteristic
375#117—21no—
376#117—21no—
377#117C2×Dic1711yescharacteristic
378C2×C42—21no—
379C2×C42C22×D1711yescharacteristic
380#107C2×Dic1711yescharacteristic
381#107C2×Dic1711yescharacteristic
382#106C2×Dic1711yescharacteristic
383#106C2×Dic1711yescharacteristic
384C4⋊C8—171no—
385C4⋊C8—171no—
386C4⋊C8—171no—
387C4⋊C8—171no—
388C4⋊C8—341no—
389C4⋊C8—341no—
390C4⋊C8—341no—
391C4⋊C8—341no—
392C4⋊C8—341no—
393C4⋊C8—341no—
394C4⋊C8—341no—
395C4⋊C8—341no—
396C4⋊C8C2×Dic1711yescharacteristic
397C4⋊C8C2×Dic1711yescharacteristic
398#103C2×Dic1711yescharacteristic
399#103C2×Dic1711yescharacteristic
400#103C2×Dic1711yescharacteristic
401#103C2×Dic1711yescharacteristic
402#103C2×Dic1711yescharacteristic
403#103C2×Dic1711yescharacteristic
404#102C2×Dic1711yescharacteristic
405#102C2×Dic1711yescharacteristic
406C22⋊C8—341no—
407C22⋊C8—341no—
408C22⋊C8—341no—
409C22⋊C8—341no—
410C22⋊C8C2×Dic1711yescharacteristic
411C22⋊C8C2×Dic1711yescharacteristic
412#97—171no—
413#97—171no—
414#97—341no—
415#97—341no—
416#97—341no—
417C4×C8—171no—
418C4×C8—171no—
419C4×C8—171no—
420C4×C8—171no—
421C4×C8—341no—
422C4×C8—341no—
423C4×C8—341no—
424C4×C8—341no—
425C4×C8C22×D1711yescharacteristic
426C4×C8C22×D1711yescharacteristic
427C17#1801311yescharacteristic, complemented, Sylow
428#41—22no—
429#41—41no—
430C2×Q8—21no—
431C2×Q8C22×Dic1711yescharacteristic
432C2×Q8C22×Dic1711yescharacteristic
433C2×Q8C22×Dic1711yescharacteristic
434C2×D4—21no—
435C2×D4C22×Dic1711yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4D4×D1711yescharacteristic
440C22×C4#6325411yescharacteristic
441C22×C4C22×Dic1711yescharacteristic
442Q16—22no—
443Q16—22no—
444SD16—41no—
445SD16—41no—
446M16—342no—
447M16—682no—
448M16—681no—
449M16—682no—
450C2×C8—171no—
451C2×C8—171no—
452C2×C8—171no—
453C2×C8—171no—
454C2×C8—341no—
455C2×C8—341no—
456C2×C8—341no—
457C2×C8—341no—
458C2×C8—341no—
459C2×C8—341no—
460C2×C8—682no—
461C2×C8C22×Dic1711yescharacteristic
462C2×C8C22×Dic1711yescharacteristic
463C2×C8C22×Dic1711yescharacteristic
464C2×C8C22×Dic1711yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4C22×Dic1711yescharacteristic
475C4⋊C4C22×Dic1711yescharacteristic
476C4⋊C4C22×Dic1711yescharacteristic
477C4⋊C4C22×Dic1711yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42D4×D1711yescharacteristic
489C42#6325411yescharacteristic
490C42C22×Dic1711yescharacteristic
491C42C23×D1711yescharacteristic
492C23—21no—
493C23D4×Dic1711yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—81no—
500Q8#1058763412yes—
501D4—21no—
502D4—21no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—81no—
520C2×C4D4×Dic1711yescharacteristic
521C2×C4D4×Dic1711yescharacteristic
522C2×C4D4×Dic1711yescharacteristic
523C2×C4C2×D4×D1711yescharacteristic
524C2×C4C2×#6325411yescharacteristic
525C2×C4C23×Dic1711yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—172no—
531C8—341no—
532C8—341no—
533C8—341no—
534C8—681no—
535C8—681no—
536C8—681no—
537C8—681no—
538C8—681no—
539C8—681no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×D4×Dic1711yescharacteristic
547C4—21no—
548C4—22no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4C2×#1058763411yescharacteristic
559C4#1176357611yescharacteristic
560C4#137×D1711yescharacteristic
561C4#1176360811yescharacteristic
562C2—41no—
563C2—81no—
564C2#1453751111yescharacteristic
565C2#137×Dic1711yescharacteristic
566C2#1453770111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#3107C2
socleC22×C17C2×C4×D4
prime radicalC2×#41×C17C2×C4
cosocleC42×C17C24
hypercenter#3107D17
hypocenterC17#18013
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
2. #14537733C2semidirect
3. #14527687C2semidirect
4. #14527675C2semidirect
5. #14527663C2semidirect
6. #14527656C2semidirect
7. #14527635C2semidirect
8. #14527628C2semidirect
9. #14527603C2semidirect
10. Q16×#3622C2semidirect
11. #14527569C2semidirect
12. #14527257C2semidirect
14. #14527079C2semidirect
427. C17#18013semidirect

Maximal subgroups

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

subgroupindex
#145378042
#145377332
#145276872
#145276752
#145276632
#145276562
#145276352
#145276282
#145276032
Q16×#36222
#145275692
#145272572
#145271712
#145270792
C17×#31072
#1801317