Finite Group Databasebeta

← #17056413

Subgroups — #17056413

Order 4352.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538574C211yesmaximal, characteristic
2#14537731C211yesmaximal, characteristic, complemented
3#14537353C211yesmaximal, characteristic
4#14529764C211yesmaximal, characteristic, complemented
5#14529535C211yesmaximal, characteristic, complemented
6#14529530C211yesmaximal, characteristic, complemented
7#14529382C211yesmaximal, characteristic, complemented
8#14529382C211yesmaximal, characteristic, complemented
9#14529056C211yesmaximal, characteristic
10#14529056C211yesmaximal, characteristic
11#14528643C211yesmaximal, characteristic, complemented
12#14528627C211yesmaximal, characteristic
13#14528620C211yesmaximal, characteristic
14#14528597C211yesmaximal, characteristic
15C17×#1950C211yesmaximal, characteristic, complemented
16C2×#10587593C2211yescharacteristic
17C2×#10587593C2211yescharacteristic
18#11763366C2211yescharacteristic
19C4×#63252C2211yescharacteristic
20#11763117C411yescharacteristic, complemented
21#11763117C411yescharacteristic, complemented
22#11763110C411yescharacteristic, complemented
23#11763110C411yescharacteristic, complemented
24#11763105C411yescharacteristic, complemented
25#11763100C411yescharacteristic, complemented
26#11763095C411yescharacteristic, complemented
27#11763090C411yescharacteristic, complemented
28#11762939—21no—
29#11762937—21no—
30#11762937—21no—
31C8×Dic34—21no—
32#11762847C2211yescharacteristic
33#11762847C2211yescharacteristic
34#11762837C2211yescharacteristic
35#11762837C2211yescharacteristic
36#11762837C2211yescharacteristic
37#11762837C2211yescharacteristic
38#11762834—21no—
39#11762834—21no—
40#11762831—21no—
41C2×C4⋊#3622C2211yescharacteristic
42C4⋊C8×D17—21no—
43C2×#10587496C2211yescharacteristic
44C2×#10587496C2211yescharacteristic
45#11762806C2211yescharacteristic
46#11762806C2211yescharacteristic
47#11762767C2211yescharacteristic
48#11762767C2211yescharacteristic
49C2×#10587486C2211yescharacteristic
50C2×C8×Dic17C2211yescharacteristic
51#11762655C2211yescharacteristic
52#11762570C2211yescharacteristic
53#11762570C2211yescharacteristic
54#11762570C2211yescharacteristic
55#11762570C2211yescharacteristic
56#11762570C2211yescharacteristic
57#11762570C2211yescharacteristic
58#11762563C2211yescharacteristic
59#11762563C2211yescharacteristic
60C2×C17×#108C2211yescharacteristic
61C2×C17×#108C2211yescharacteristic
62C17×#423C2211yescharacteristic
63C2×C17×C4⋊C8C2211yescharacteristic
64C4×M16×C17C2211yescharacteristic
65C17×#341C2211yescharacteristic
66C17×#341C2211yescharacteristic
67C2×#63252C2311yescharacteristic
68C2×M16×C17C2311yescharacteristic
69C2×M16×C17C2311yescharacteristic
70C2×M16×C17C2311yescharacteristic
71C2×M16×C17C2311yescharacteristic
72C22×C8×C17C2311yescharacteristic
73C22×C8×C17C2311yescharacteristic
74C2×C42×C17C2311yescharacteristic
75C4×C22⋊D17—21no—
76C4×C22⋊D17—21no—
77#10587612C2311yescharacteristic
78#10587612C2311yescharacteristic
79#10587612C2311yescharacteristic
80#10587610—21no—
81#10587610—21no—
82C2×C4×Dic17C2311yescharacteristic
83C2×C4×Dic17C2311yescharacteristic
84C22×#3622C2311yescharacteristic
85C22×#3622C2311yescharacteristic
86#10587593—22no—
87#10587593—22no—
88#10587593—41no—
89#10587593—41no—
90C2×#63218—21no—
91C2×#63218—21no—
92C2×C8×D17—21no—
93C2×C8×D17—21no—
94C4×D68C2×C411yescharacteristic
95C4×D68C2×C411yescharacteristic
96#10587558—21no—
97C42×D17—21no—
98#10587556C2×C411yescharacteristic
99#10587556C2×C411yescharacteristic
100#10587555C2×C411yescharacteristic
101#10587555C2×C411yescharacteristic
102C4×Dic34—21no—
103C4×Dic34—21no—
104C4×Dic34C2×C411yescharacteristic
105C4×Dic34C2×C411yescharacteristic
106C17×#108—41no—
107C17×#108—41no—
108C17×C4⋊C8—21no—
109C17×C4⋊C8—21no—
110C17×C4⋊C8C2×C411yescharacteristic
111C17×C4⋊C8C2×C411yescharacteristic
112C17×C4⋊C8C2×C411yescharacteristic
113C17×C4⋊C8C2×C411yescharacteristic
114C17×#97—21no—
115C4×C8×C17—21no—
116#10587502—21no—
117#10587502—21no—
118#10587496—22no—
119#10587496Q814yescomplemented
120#10587492C2×C411yescharacteristic
121#10587492C2×C411yescharacteristic
122#10587492C2×C411yescharacteristic
123#10587492C2×C411yescharacteristic
124#10587489C2×C411yescharacteristic
125#10587489C2×C411yescharacteristic
126#10587489C2×C411yescharacteristic
127#10587489C2×C411yescharacteristic
128#10587488C2×C411yescharacteristic
129#10587488C2×C411yescharacteristic
130#10587488C2×C411yescharacteristic
131#10587488C2×C411yescharacteristic
132#10587487C2×C411yescharacteristic
133#10587487C2×C411yescharacteristic
134#10587487C2×C411yescharacteristic
135#10587487C2×C411yescharacteristic
136#10587486—21no—
137#10587486—21no—
138#10587486—41no—
139#10587485—21no—
140#10587485—21no—
141#10587485—21no—
142#10587485—21no—
143#10587485—21no—
144#10587485—21no—
145#10587485—21no—
146#10587485—21no—
147C8×Dic17—21no—
148C8×Dic17—21no—
149C8×Dic17—41no—
150C4⋊#3622D411yescharacteristic
151C4⋊#3622D411yescharacteristic
152C4⋊#3622D411yescharacteristic
153C4⋊#3622D411yescharacteristic
154C22×C4×C17#4111yescharacteristic
155C22×C4×C17#4111yescharacteristic
156C22×C4×C17C2411yescharacteristic
157C2×C22⋊D17—21no—
158C22×Dic17—21no—
159C22×Dic17—21no—
160#63252—21no—
161#63252—21no—
162#63252C2×Q812yes—
163#63252#4112yes—
164C2×D68C22×C411yescharacteristic
165C2×C4×D17—21no—
166C2×C4×D17—21no—
167C2×C4×D17—21no—
168C2×Dic34—21no—
169C2×Dic34—21no—
170C2×Dic34C22×C411yescharacteristic
171M16×C17—21no—
172M16×C17—21no—
173M16×C17—21no—
174M16×C17—21no—
175M16×C17—21no—
176M16×C17—21no—
177M16×C17—21no—
178M16×C17C2×Q812yes—
179C2×C8×C17—21no—
180C2×C8×C17—21no—
181C2×C8×C17—21no—
182C2×C8×C17—21no—
183C2×C8×C17—21no—
184C2×C8×C17—21no—
185C2×C8×C17—21no—
186C2×C8×C17—21no—
187C2×C8×C17C22×C411yescharacteristic
188C2×C8×C17C22×C411yescharacteristic
189C2×C8×C17C22×C411yescharacteristic
190C2×C8×C17C22×C411yescharacteristic
191C42×C17C22×C411yescharacteristic
192C42×C17C22×C411yescharacteristic
193C42×C17C2×D411yescharacteristic
194C42×C17C2×D411yescharacteristic
195C22⋊Dic17—21no—
196C22⋊Dic17—21no—
197C22⋊Dic17—21no—
198#63227—21no—
199#63227—21no—
200C4⋊Dic17—21no—
201C4⋊Dic17—21no—
202C4⋊Dic17C22×C411yescharacteristic
203C4⋊Dic17C22×C411yescharacteristic
204C4⋊Dic17C22×C411yescharacteristic
205C4⋊Dic17C22×C411yescharacteristic
206C4⋊Dic17C22×C411yescharacteristic
207C4⋊Dic17C22×C411yescharacteristic
208#63225—21no—
209#63225—21no—
210#63225—21no—
211#63225—21no—
212#63225—21no—
213#63225—21no—
214C4×Dic17—21no—
215C4×Dic17—21no—
216C4×Dic17—21no—
217C4×Dic17—21no—
218C4×Dic17—21no—
219C4×Dic17—21no—
220C4×Dic17—21no—
221C4×Dic17—21no—
222C4×Dic17C2×Q812yes—
223C2×#3622—21no—
224C2×#3622—21no—
225C2×#3622—21no—
226C2×#3622—21no—
227C2×#3622C2×D411yescharacteristic
228C2×#3622C2×D411yescharacteristic
229C2×#3622C2×D411yescharacteristic
230C2×#3622C2×D411yescharacteristic
231#63218—42no—
232#63218—42no—
233C8×D17—42no—
234C8×D17—42no—
235#22984—171nomaximal, Sylow
236C23×C17C2×#4111yescharacteristic
237C22×D17—21no—
238C2×C4×C17—41no—
239C2×C4×C17—41no—
240C2×C4×C17C4×D411yescharacteristic
241C2×C4×C17C4×D411yescharacteristic
242C2×C4×C17C4×D411yescharacteristic
243C2×C4×C17C4×D411yescharacteristic
244C2×C4×C17C23×C411yescharacteristic
245C2×C4×C17C22×D411yescharacteristic
246C2×C4×C17C22×Q811yescharacteristic
247C2×C4×C17C2×#4111yescharacteristic
248C2×C4×C17H(5,𝔽2)11yescharacteristic
249C2×C4×C172−1+411yescharacteristic
250C22⋊D17—22no—
251C22⋊D17—22no—
252C2×Dic17—21no—
253C2×Dic17—21no—
254C2×Dic17—21no—
255C2×Dic17—21no—
256C2×Dic17—21no—
257C2×Dic17—21no—
258C2×Dic17—21no—
259C2×Dic17—22no—
260C2×Dic17—41no—
261C2×Dic17—41no—
262C2×Dic17—41no—
263C2×Dic17—41no—
264C2×Dic17—41no—
265D68—21no—
266D68C4×Q812yes—
267C4×D17—22no—
268C4×D17—22no—
269C4×D17—42no—
270C4×D17—81no—
271Dic34—21no—
272Dic34—42no—
273Dic34—81no—
274Dic34C4×Q812yes—
275C8×C17—21no—
276C8×C17—21no—
277C8×C17—21no—
278C8×C17—21no—
279C8×C17—22no—
280C8×C17—41no—
281C8×C17—41no—
282C8×C17—41no—
283#3622—21no—
284#3622—21no—
285#3622—21no—
286#3622—21no—
287#3076—171no—
288#2962—171no—
289#2906—171no—
290#1995—171no—
291#1950D1711yescharacteristic, complemented
292#1946—171no—
293#1945—171no—
294#1922—171no—
295#1922—171no—
296#1866—171no—
297#1866—171no—
298#1768—171no—
299#1765—171no—
300#1764—171no—
301#1759—171no—
302C22×C17—21no—
303C22×C17—21no—
304C22×C17C2×C4×D411yescharacteristic
305C22×C17#55211yescharacteristic
306C22×C17#55411yescharacteristic
307C2×D17—22no—
308C2×D17—41no—
309C2×D17—41no—
310C4×C17—21no—
311C4×C17—21no—
312C4×C17—21no—
313C4×C17—21no—
314C4×C17C2×C4×Q811yescharacteristic
315C4×C17#52011yescharacteristic
316C4×C17#54611yescharacteristic
317C4×C17D4×Q811yescharacteristic
318Dic17—22no—
319Dic17—42no—
320Dic17—41no—
321Dic17—41no—
322Dic17—41no—
323Dic17—41no—
324Dic17—41no—
325Dic17—41no—
326Dic17—81no—
327C2×#131—171no—
328C2×#131—171no—
329#533—171no—
330C4×#41—171no—
331#479—171no—
332#479—171no—
333#478—171no—
334#478—171no—
335#477—171no—
336#476—171no—
337#475—171no—
338#474—171no—
339#446—341no—
340#446—341no—
341#446—341no—
342C8×Q8—341no—
343C2×#108C2×D1711yescharacteristic
344C2×#108C2×D1711yescharacteristic
345#427—171no—
346#427—171no—
347#424—171no—
348#424—171no—
349#424—171no—
350#424—171no—
351#424—341no—
352#424—341no—
353#423—341no—
354#423C2×D1711yescharacteristic
355C2×C4⋊C8—171no—
356C2×C4⋊C8—341no—
357C2×C4⋊C8C2×D1711yescharacteristic
358C2×#104—171no—
359C2×#104—171no—
360#416—171no—
361#416—171no—
362#405—171no—
363#405—171no—
364C4×M16C2×D1711yescharacteristic
365C2×#97—171no—
366C2×C4×C8—171no—
367#376—171no—
368#341C2×D1711yescharacteristic
369#341C2×D1711yescharacteristic
370#339—171no—
371#339—171no—
372#339—171no—
373#339—171no—
374#339—171no—
375#339—171no—
376#336—171no—
377#336—171no—
378C2×C17—21no—
379C2×C17—21no—
380C2×C17#236011yescharacteristic
381C2×C17#295511yescharacteristic
382C2×C17#295711yescharacteristic
383D17—42no—
384C2×#41—171no—
385#131—342no—
386#131—342no—
387#131—681no—
388#131—681no—
389C2×M16—341no—
390C2×M16—341no—
391C2×M16C22×D1711yescharacteristic
392C2×M16C22×D1711yescharacteristic
393C2×M16C22×D1711yescharacteristic
394C2×M16C22×D1711yescharacteristic
395C22×C8—171no—
396C22×C8—171no—
397C22×C8—341no—
398C22×C8—341no—
399C22×C8C22×D1711yescharacteristic
400C22×C8C22×D1711yescharacteristic
401C4⋊Q8—171no—
402C4⋊Q8—171no—
403#125—171no—
404#125—171no—
405C22⋊Q8—341no—
406C22⋊Q8—341no—
407C4×Q8—171no—
408C4×Q8—171no—
409C4×Q8—341no—
410C4×Q8—341no—
411C4×D4—171no—
412C4×D4—171no—
413C4×D4—341no—
414C4×D4—341no—
415#117—171no—
416#117—171no—
417#117—171no—
418#117—341no—
419C2×C42—171no—
420C2×C42—171no—
421C2×C42—341no—
422C2×C42C22×D1711yescharacteristic
423#108—41no—
424#108—41no—
425#107—171no—
426#107—171no—
427#107—171no—
428#107—171no—
429#106—171no—
430#106—171no—
431#106—171no—
432#106—171no—
433C4⋊C8—21no—
434C4⋊C8—21no—
435C4⋊C8—171no—
436C4⋊C8—171no—
437C4⋊C8—171no—
438C4⋊C8—171no—
439C4⋊C8—341no—
440C4⋊C8—341no—
441C4⋊C8—341no—
442C4⋊C8—341no—
443C4⋊C8—341no—
444C4⋊C8—341no—
445C4⋊C8—341no—
446C4⋊C8—341no—
447C4⋊C8C4×D1711yescharacteristic
448C4⋊C8C4×D1711yescharacteristic
449C4⋊C8C4×D1711yescharacteristic
450C4⋊C8C4×D1711yescharacteristic
451#104—174no—
452#104—342no—
453#103—171no—
454#103—171no—
455#103—171no—
456#103—171no—
457#102—171no—
458#102—171no—
459#102—171no—
460#102—171no—
461#97—21no—
462#97—341no—
463#97—341no—
464#97—681no—
465C4×C8—21no—
466C4×C8—341no—
467C4×C8—341no—
468C4×C8—681no—
469#95—341no—
470#95—341no—
471C17#2298411yescharacteristic, complemented, Sylow
472#41—172no—
473#41—172no—
474#41—341no—
475#41—341no—
476C2×Q8—171no—
477C2×Q8—341no—
478C2×Q8—341no—
479C2×D4—171no—
480C2×D4—341no—
481C22×C4—341no—
482C22×C4—341no—
483C22×C4—341no—
484C22×C4—341no—
485C22×C4—341no—
486C22×C4#6325611yescharacteristic
487C22×C4#6325611yescharacteristic
488C22×C4C23×D1711yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—21no—
496M16—682no—
497M16—682no—
498M16Q8×D1712yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—171no—
508C2×C8—171no—
509C2×C8—171no—
510C2×C8—171no—
511C2×C8—341no—
512C2×C8—341no—
513C2×C8—341no—
514C2×C8—341no—
515C2×C8—682no—
516C2×C8—682no—
517C2×C8C2×C4×D1711yescharacteristic
518C2×C8C2×C4×D1711yescharacteristic
519C2×C8C2×C4×D1711yescharacteristic
520C2×C8C2×C4×D1711yescharacteristic
521C4⋊C4—171no—
522C4⋊C4—171no—
523C4⋊C4—171no—
524C4⋊C4—171no—
525C4⋊C4—171no—
526C4⋊C4—171no—
527C4⋊C4—341no—
528C4⋊C4—341no—
529C4⋊C4—341no—
530C4⋊C4—341no—
531C4⋊C4—341no—
532C4⋊C4—341no—
533C4⋊C4—341no—
534C4⋊C4—341no—
535C22⋊C4—341no—
536C22⋊C4—341no—
537C22⋊C4—341no—
538C22⋊C4—341no—
539C22⋊C4—341no—
540C42—172no—
541C42—341no—
542C42—341no—
543C42—341no—
544C42—341no—
545C42—341no—
546C42—341no—
547C42—341no—
548C42—341no—
549C42C2×C4×D1711yescharacteristic
550C42C2×C4×D1711yescharacteristic
551C42D4×D1711yescharacteristic
552C42D4×D1711yescharacteristic
553C23—341no—
554C23C2×#6325611yescharacteristic
555Q8—172no—
556Q8—341no—
557Q8—682no—
558Q8—1361no—
559D4—172no—
560D4—342no—
561D4—342no—
562D4—341no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—341no—
566C2×C4—342no—
567C2×C4—342no—
568C2×C4—342no—
569C2×C4—341no—
570C2×C4—341no—
571C2×C4—341no—
572C2×C4—341no—
573C2×C4—341no—
574C2×C4—341no—
575C2×C4—682no—
576C2×C4—681no—
577C2×C4—681no—
578C2×C4—681no—
579C2×C4—681no—
580C2×C4—681no—
581C2×C4—1361no—
582C2×C4#1058757911yescharacteristic
583C2×C4#1058757911yescharacteristic
584C2×C4#1058757911yescharacteristic
585C2×C4#1058757911yescharacteristic
586C2×C4C22×C4×D1711yescharacteristic
587C2×C4C2×D4×D1711yescharacteristic
588C2×C4#1058769111yescharacteristic
589C2×C4C2×Q8×D1711yescharacteristic
590C2×C4#41×D1711yescharacteristic
591C2×C4#1058769711yescharacteristic
592C8—22no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—41no—
599C8—41no—
600C8—341no—
601C8—341no—
602C8—341no—
603C8—341no—
604C22—21no—
605C22—21no—
606C22—342no—
607C22—681no—
608C22—681no—
609C22C2×#1058757911yescharacteristic
610C22#1176349711yescharacteristic
611C22#1176352011yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—342no—
617C4—682no—
618C4—681no—
619C4—681no—
620C4—681no—
621C4—681no—
622C4—681no—
623C4—681no—
624C4—1361no—
625C4C4×Q8×D1711yescharacteristic
626C4#1176328811yescharacteristic
627C4#1176345611yescharacteristic
628C4#1176347211yescharacteristic
629C2—21no—
630C2—21no—
631C2—682no—
632C2#1453178811yescharacteristic
633C2#1453768611yescharacteristic
634C2#1453770011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1950C2
socleC22×C17C2×C4×D4
prime radicalC2×#63252C23
cosocleC22×C4×C17C24
hypercenter#1950D17
hypocenterC17#22984
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
2. #14537731C2semidirect
4. #14529764C2semidirect
5. #14529535C2semidirect
6. #14529530C2semidirect
7. #14529382C2semidirect
8. #14529382C2semidirect
11. #14528643C2semidirect
15. C17×#1950C2semidirect
20. #11763117C4semidirect
21. #11763117C4semidirect
22. #11763110C4semidirect
23. #11763110C4semidirect
24. #11763105C4semidirect
25. #11763100C4semidirect
26. #11763095C4semidirect
27. #11763090C4semidirect
119. #10587496Q8semidirect
291. #1950D17semidirect
471. C17#22984semidirect

Maximal subgroups

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

subgroupindex
#145385742
#145377312
#145373532
#145297642
#145295352
#145295302
#145293822
#145290562
#145286432
#145286272
#145286202
#145285972
C17×#19502
#2298417