Finite Group Databasebeta

← #17056411

Subgroups — #17056411

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#14538572C211yesmaximal, characteristic
2#14537731C211yesmaximal, characteristic, complemented
3#14537352C211yesmaximal, characteristic
4#14529765C211yesmaximal, characteristic, complemented
5#14529559C211yesmaximal, characteristic, complemented
6#14529536C211yesmaximal, characteristic, complemented
7#14529531C211yesmaximal, characteristic, complemented
8#14529386C211yesmaximal, characteristic, complemented
9#14529386C211yesmaximal, characteristic, complemented
10#14529057C211yesmaximal, characteristic
11#14529057C211yesmaximal, characteristic
12#14528641C211yesmaximal, characteristic, complemented
13#14528629C211yesmaximal, characteristic
14#14528622C211yesmaximal, characteristic
15C17×#1759C211yesmaximal, characteristic
16C2×#10587634C2211yescharacteristic
17C2×#10587634C2211yescharacteristic
18#11763366C2211yescharacteristic
19#11763116C411yescharacteristic, complemented
20#11763116C411yescharacteristic, complemented
21#11763109C411yescharacteristic, complemented
22#11763109C411yescharacteristic, complemented
23#11763104C411yescharacteristic, complemented
24#11763099C411yescharacteristic, complemented
25#11763094C411yescharacteristic, complemented
26#11763089C411yescharacteristic, complemented
27#11762939—21no—
28#11762937—21no—
29#11762937—21no—
30C8×Dic34—21no—
31C2×#10587493C2211yescharacteristic
32C2×#10587493C2211yescharacteristic
33#11762845C2211yescharacteristic
34#11762845C2211yescharacteristic
35#11762837C2211yescharacteristic
36#11762837C2211yescharacteristic
37#11762836—21no—
38#11762836—21no—
39#11762836C2211yescharacteristic
40#11762836C2211yescharacteristic
41#11762833—21no—
42#11762833C2211yescharacteristic
43C2×C4⋊#3622—21no—
44C2×C4⋊#3622C2211yescharacteristic
45C2×C4⋊#3622C2211yescharacteristic
46#11762805C2211yescharacteristic
47#11762805C2211yescharacteristic
48#11762767C2211yescharacteristic
49#11762767C2211yescharacteristic
50C2×#10587474C2211yescharacteristic
51C2×C4×#3622C2211yescharacteristic
52#11762573C2211yescharacteristic
53#11762573C2211yescharacteristic
54#11762569C2211yescharacteristic
55#11762569C2211yescharacteristic
56#11762569C2211yescharacteristic
57#11762569C2211yescharacteristic
58#11762564C2211yescharacteristic
59#11762564C2211yescharacteristic
60C4×#41×C17C2211yescharacteristic
61C2×C17×#104C2211yescharacteristic
62C2×C17×#104C2211yescharacteristic
63C4×M16×C17C2211yescharacteristic
64C17×#376C2211yescharacteristic
65C17×#339C2211yescharacteristic
66C17×#339C2211yescharacteristic
67C2×#41×C17C2311yescharacteristic
68C2×M16×C17C2311yescharacteristic
69C2×M16×C17C2311yescharacteristic
70C4×Q8×C17C2×C411yescharacteristic
71C4×Q8×C17C2×C411yescharacteristic
72C4×D4×C17—21no—
73C4×D4×C17—21no—
74C4×D4×C17C2×C411yescharacteristic
75C4×D4×C17C2×C411yescharacteristic
76C17×#117—21no—
77C17×#117C2311yescharacteristic
78C2×C42×C17—21no—
79C2×C42×C17C2311yescharacteristic
80C2×C42×C17C2311yescharacteristic
81C2×C42×C17C2311yescharacteristic
82#10587634—22no—
83#10587634—22no—
84#10587634—41no—
85#10587634—41no—
86#10587612C2311yescharacteristic
87#10587612C2311yescharacteristic
88#10587610—21no—
89#10587610—21no—
90C2×#63223—21no—
91C2×#63223—21no—
92C2×#63223C2311yescharacteristic
93C2×#63223C2311yescharacteristic
94C22×#3622—21no—
95C22×#3622—21no—
96C22×#3622C2311yescharacteristic
97C22×#3622C2311yescharacteristic
98C22×#3622C2311yescharacteristic
99C22×#3622C2311yescharacteristic
100#10587556C2×C411yescharacteristic
101#10587556C2×C411yescharacteristic
102#10587555C2×C411yescharacteristic
103#10587555C2×C411yescharacteristic
104C4×Dic34—21no—
105C4×Dic34—21no—
106C17×#104—22no—
107C17×#104Q814yescomplemented
108C17×#97—21no—
109C4×C8×C17—21no—
110C17×#95—21no—
111C17×#95—21no—
112#10587506C2×C411yescharacteristic
113#10587506C2×C411yescharacteristic
114#10587506C2×C411yescharacteristic
115#10587506C2×C411yescharacteristic
116#10587503C2×C411yescharacteristic
117#10587503C2×C411yescharacteristic
118#10587503C2×C411yescharacteristic
119#10587503C2×C411yescharacteristic
120#10587493—41no—
121#10587493—41no—
122#10587486—21no—
123#10587486—21no—
124#10587485—21no—
125#10587485—21no—
126#10587485—21no—
127#10587485—21no—
128C8×Dic17—21no—
129C8×Dic17—21no—
130#10587479C2×C411yescharacteristic
131#10587479C2×C411yescharacteristic
132#10587479C2×C411yescharacteristic
133#10587479C2×C411yescharacteristic
134#10587478C2×C411yescharacteristic
135#10587478C2×C411yescharacteristic
136#10587478C2×C411yescharacteristic
137#10587478C2×C411yescharacteristic
138C4⋊#3622—21no—
139C4⋊#3622—21no—
140C4⋊#3622—21no—
141C4⋊#3622—21no—
142C4⋊#3622—21no—
143C4⋊#3622—21no—
144C4⋊#3622C2×C411yescharacteristic
145C4⋊#3622C2×C411yescharacteristic
146C4⋊#3622C2×C411yescharacteristic
147C4⋊#3622C2×C411yescharacteristic
148C4⋊#3622D411yescharacteristic
149C4⋊#3622D411yescharacteristic
150C4⋊#3622D411yescharacteristic
151C4⋊#3622D411yescharacteristic
152#10587474—41no—
153C4×#3622—41no—
154#41×C17—21no—
155#41×C17—21no—
156#41×C17C2×Q812yes—
157#41×C17#4112yes—
158C2×Q8×C17C22×C411yescharacteristic
159C2×D4×C17—21no—
160C2×D4×C17C22×C411yescharacteristic
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17#4111yescharacteristic
167C22×C4×C17#4111yescharacteristic
168C22×C4×C17C2411yescharacteristic
169C2×Dic34—21no—
170C2×Dic34—21no—
171M16×C17—21no—
172M16×C17—21no—
173M16×C17—21no—
174M16×C17C2×Q812yes—
175C2×C8×C17—21no—
176C2×C8×C17—21no—
177C4⋊C4×C17—21no—
178C4⋊C4×C17—21no—
179C4⋊C4×C17C22×C411yescharacteristic
180C4⋊C4×C17C22×C411yescharacteristic
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×C17—21no—
190C42×C17C22×C411yescharacteristic
191C42×C17C22×C411yescharacteristic
192C42×C17C2×D411yescharacteristic
193C42×C17C2×D411yescharacteristic
194C42×C17C2×Q812yes—
195C22⋊Dic17—21no—
196C22⋊Dic17—21no—
197C4⋊Dic17—21no—
198C4⋊Dic17—21no—
199C4⋊Dic17C22×C411yescharacteristic
200C4⋊Dic17C22×C411yescharacteristic
201C4⋊Dic17C22×C411yescharacteristic
202C4⋊Dic17C22×C411yescharacteristic
203#63225—21no—
204#63225—21no—
205#63225—21no—
206#63225—21no—
207C4×Dic17—21no—
208C4×Dic17—21no—
209#63223—21no—
210#63223—21no—
211#63223—21no—
212#63223—21no—
213#63223—42no—
214#63223—42no—
215C2×#3622—21no—
216C2×#3622—21no—
217C2×#3622—21no—
218C2×#3622—21no—
219C2×#3622—21no—
220C2×#3622—21no—
221C2×#3622—21no—
222C2×#3622—21no—
223C2×#3622—21no—
224C2×#3622—21no—
225C2×#3622—42no—
226C2×#3622—42no—
227C2×#3622C22×C411yescharacteristic
228C2×#3622C22×C411yescharacteristic
229C2×#3622C22×C411yescharacteristic
230C2×#3622C22×C411yescharacteristic
231C2×#3622C2×D411yescharacteristic
232C2×#3622C2×D411yescharacteristic
233C2×#3622C2×D411yescharacteristic
234C2×#3622C2×D411yescharacteristic
235#22984—171nomaximal, Sylow
236C23×C17—21no—
237C23×C17C2×#4111yescharacteristic
238Q8×C17—21no—
239Q8×C17C4×Q812yes—
240D4×C17—22no—
241D4×C17—22no—
242D4×C17—21no—
243D4×C17C4×Q812yes—
244C2×C4×C17—21no—
245C2×C4×C17—22no—
246C2×C4×C17—22no—
247C2×C4×C17—21no—
248C2×C4×C17—21no—
249C2×C4×C17—22no—
250C2×C4×C17—41no—
251C2×C4×C17—41no—
252C2×C4×C17—42no—
253C2×C4×C17—41no—
254C2×C4×C17—41no—
255C2×C4×C17—41no—
256C2×C4×C17—41no—
257C2×C4×C17—41no—
258C2×C4×C17—81no—
259C2×C4×C17C4×D411yescharacteristic
260C2×C4×C17C4×D411yescharacteristic
261C2×C4×C17C4×D411yescharacteristic
262C2×C4×C17C4×D411yescharacteristic
263C2×C4×C17C23×C411yescharacteristic
264C2×C4×C17C22×D411yescharacteristic
265C2×C4×C17C22×Q811yescharacteristic
266C2×C4×C17C2×#4111yescharacteristic
267C2×C4×C17H(5,𝔽2)11yescharacteristic
268C2×C4×C172−1+411yescharacteristic
269C2×Dic17—21no—
270C2×Dic17—21no—
271C2×Dic17—21no—
272C2×Dic17—21no—
273Dic34—42no—
274Dic34—81no—
275C8×C17—22no—
276C8×C17—41no—
277#3622—21no—
278#3622—21no—
279#3622—21no—
280#3622—21no—
281#3622—21no—
282#3622—21no—
283#3622—21no—
284#3622—21no—
285#3622—41no—
286#3622—41no—
287#3076—171no—
288#2962—171no—
289#2906—171no—
290#1995—171no—
291#1950—171no—
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#1759D1711yescharacteristic
302C22×C17—21no—
303C22×C17—21no—
304C22×C17—22no—
305C22×C17—41no—
306C22×C17—41no—
307C22×C17C2×C4×D411yescharacteristic
308C22×C17#55211yescharacteristic
309C22×C17#55411yescharacteristic
310C4×C17—22no—
311C4×C17—21no—
312C4×C17—21no—
313C4×C17—21no—
314C4×C17—21no—
315C4×C17—42no—
316C4×C17—41no—
317C4×C17—41no—
318C4×C17—81no—
319C4×C17C2×C4×Q811yescharacteristic
320C4×C17#52011yescharacteristic
321C4×C17#54611yescharacteristic
322C4×C17D4×Q811yescharacteristic
323Dic17—41no—
324Dic17—41no—
325Dic17—41no—
326Dic17—41no—
327C2×#131—171no—
328C2×#131—171no—
329#533—171no—
330C4×#41C2×D1711yescharacteristic
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×#108—171no—
344C2×#108—171no—
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—171no—
354#423—341no—
355C2×C4⋊C8—171no—
356C2×C4⋊C8—171no—
357C2×C4⋊C8—341no—
358C2×#104C2×D1711yescharacteristic
359C2×#104C2×D1711yescharacteristic
360#416—171no—
361#416—171no—
362#405—171no—
363#405—171no—
364C4×M16C2×D1711yescharacteristic
365C2×#97—171no—
366C2×C4×C8—171no—
367#376C2×D1711yescharacteristic
368#341—171no—
369#341—171no—
370#339—171no—
371#339—171no—
372#339—171no—
373#339—171no—
374#339C2×D1711yescharacteristic
375#339C2×D1711yescharacteristic
376#336—171no—
377#336—171no—
378C2×C17—21no—
379C2×C17—21no—
380C2×C17—42no—
381C2×C17#236011yescharacteristic
382C2×C17#295511yescharacteristic
383C2×C17#295711yescharacteristic
384C2×#41C22×D1711yescharacteristic
385#131—342no—
386#131—342no—
387#131—681no—
388#131—681no—
389C2×M16—171no—
390C2×M16—171no—
391C2×M16—341no—
392C2×M16—341no—
393C2×M16C22×D1711yescharacteristic
394C2×M16C22×D1711yescharacteristic
395C22×C8—171no—
396C22×C8—171no—
397C22×C8—171no—
398C22×C8—171no—
399C22×C8—341no—
400C22×C8—341no—
401C4⋊Q8—171no—
402C4⋊Q8—171no—
403#125—171no—
404#125—171no—
405C22⋊Q8—341no—
406C22⋊Q8—341no—
407C4×Q8—341no—
408C4×Q8—341no—
409C4×Q8C4×D1711yescharacteristic
410C4×Q8C4×D1711yescharacteristic
411C4×D4—21no—
412C4×D4—21no—
413C4×D4C4×D1711yescharacteristic
414C4×D4C4×D1711yescharacteristic
415#117—21no—
416#117—171no—
417#117—171no—
418#117C22×D1711yescharacteristic
419C2×C42—21no—
420C2×C42C22×D1711yescharacteristic
421C2×C42C22×D1711yescharacteristic
422C2×C42C22×D1711yescharacteristic
423#108—681no—
424#108—681no—
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—171no—
434C4⋊C8—171no—
435C4⋊C8—171no—
436C4⋊C8—171no—
437C4⋊C8—171no—
438C4⋊C8—171no—
439C4⋊C8—171no—
440C4⋊C8—171no—
441C4⋊C8—341no—
442C4⋊C8—341no—
443C4⋊C8—341no—
444C4⋊C8—341no—
445C4⋊C8—341no—
446C4⋊C8—341no—
447C4⋊C8—341no—
448C4⋊C8—341no—
449C4⋊C8—341no—
450C4⋊C8—341no—
451#104—22no—
452#104Dic3414yescomplemented
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—21no—
470#95—21no—
471C17#2298411yescharacteristic, complemented, Sylow
472#41—21no—
473#41—21no—
474#41C2×Dic3412yes—
475#41#6325212yes—
476C2×Q8—341no—
477C2×Q8—341no—
478C2×Q8C2×C4×D1711yescharacteristic
479C2×D4—21no—
480C2×D4C2×C4×D1711yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4#6325411yescharacteristic
487C22×C4#6325411yescharacteristic
488C22×C4C23×D1711yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—341no—
493M16—341no—
494M16—341no—
495M16—341no—
496M16—682no—
497M16—682no—
498M16C2×Dic3412yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—171no—
502C2×C8—171no—
503C2×C8—171no—
504C2×C8—171no—
505C2×C8—171no—
506C2×C8—171no—
507C2×C8—171no—
508C2×C8—171no—
509C2×C8—341no—
510C2×C8—341no—
511C2×C8—341no—
512C2×C8—341no—
513C2×C8—341no—
514C2×C8—341no—
515C2×C8—341no—
516C2×C8—341no—
517C2×C8—341no—
518C2×C8—341no—
519C2×C8—682no—
520C2×C8—682no—
521C4⋊C4—21no—
522C4⋊C4—21no—
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⋊C4C2×C4×D1711yescharacteristic
534C4⋊C4C2×C4×D1711yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—341no—
539C22⋊C4—341no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—341no—
547C42—341no—
548C42C2×Dic3412yes—
549C42C2×C4×D1711yescharacteristic
550C42C2×C4×D1711yescharacteristic
551C42D4×D1711yescharacteristic
552C42D4×D1711yescharacteristic
553C23—21no—
554C23C2×#6325411yescharacteristic
555Q8—21no—
556Q8—682no—
557Q8—1361no—
558Q8C4×Dic3412yes—
559D4—22no—
560D4—22no—
561D4—21no—
562D4C4×Dic3412yes—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—81no—
578C2×C4—341no—
579C2×C4—341no—
580C2×C4—341no—
581C2×C4—341no—
582C2×C4#1058756711yescharacteristic
583C2×C4#1058756711yescharacteristic
584C2×C4#1058756711yescharacteristic
585C2×C4#1058756711yescharacteristic
586C2×C4C22×Dic3411yescharacteristic
587C2×C4C22×C4×D1711yescharacteristic
588C2×C4C2×#6325211yescharacteristic
589C2×C4C2×D4×D1711yescharacteristic
590C2×C4#1058769611yescharacteristic
591C2×C4#1058769711yescharacteristic
592C8—22no—
593C8—41no—
594C8—341no—
595C8—341no—
596C8—341no—
597C8—341no—
598C8—341no—
599C8—341no—
600C8—341no—
601C8—341no—
602C8—681no—
603C8—681no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22C2×#1058756711yescharacteristic
610C22#1176349911yescharacteristic
611C22#1176351611yescharacteristic
612C4—22no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—42no—
618C4—41no—
619C4—41no—
620C4—81no—
621C4—681no—
622C4—681no—
623C4—681no—
624C4—681no—
625C4C2×C4×Dic3411yescharacteristic
626C4#1176328911yescharacteristic
627C4#1176345511yescharacteristic
628C4D4×Dic3411yescharacteristic
629C2—21no—
630C2—21no—
631C2—42no—
632C2#1453178711yescharacteristic
633C2#1453768311yescharacteristic
634C2#1453769711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1759C2
socleC22×C17C2×C4×D4
prime radicalC2×#41×C17C23
cosocleC22×C4×C17C24
hypercenter#1759D17
hypocenterC17#22984
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. #14537731C2semidirect
4. #14529765C2semidirect
5. #14529559C2semidirect
6. #14529536C2semidirect
7. #14529531C2semidirect
8. #14529386C2semidirect
9. #14529386C2semidirect
12. #14528641C2semidirect
19. #11763116C4semidirect
20. #11763116C4semidirect
21. #11763109C4semidirect
22. #11763109C4semidirect
23. #11763104C4semidirect
24. #11763099C4semidirect
25. #11763094C4semidirect
26. #11763089C4semidirect
107. C17×#104Q8semidirect
452. #104Dic34semidirect
471. C17#22984semidirect

Maximal subgroups

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

subgroupindex
#145385722
#145377312
#145373522
#145297652
#145295592
#145295362
#145295312
#145293862
#145290572
#145286412
#145286292
#145286222
C17×#17592
#2298417