Finite Group Databasebeta

← #17056421

Subgroups — #17056421

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#14538566C211yesmaximal, characteristic
2#14537733C211yesmaximal, characteristic, complemented
3#14537353C211yesmaximal, characteristic
4#14529557C211yesmaximal, characteristic, complemented
5#14529536C211yesmaximal, characteristic, complemented
6#14529531C211yesmaximal, characteristic, complemented
7#14529381C211yesmaximal, characteristic, complemented
8#14529381C211yesmaximal, characteristic, complemented
9#14529060C211yesmaximal, characteristic
10#14529060C211yesmaximal, characteristic
11#14528641C211yesmaximal, characteristic, complemented
12#14528625C211yesmaximal, characteristic
13#14528618C211yesmaximal, characteristic
14#14528595C211yesmaximal, characteristic
15C17×#1995C211yesmaximal, characteristic, complemented
16C2×#10587593C2211yescharacteristic
17C2×#10587593C2211yescharacteristic
18C4×#63252C2211yescharacteristic
19#11763113C411yescharacteristic, complemented
20#11763113C411yescharacteristic, complemented
21#11763106C411yescharacteristic, complemented
22#11763106C411yescharacteristic, complemented
23#11763101C411yescharacteristic, complemented
24#11763096C411yescharacteristic, complemented
25#11763091C411yescharacteristic, complemented
26#11763086C411yescharacteristic, complemented
27#11762940—21no—
28#11762940—21no—
29#11762940—21no—
30Q8×#3622—21no—
31C2×#10587493C2211yescharacteristic
32C2×#10587493C2211yescharacteristic
33#11762845C2211yescharacteristic
34#11762845C2211yescharacteristic
35#11762837C2211yescharacteristic
36#11762837C2211yescharacteristic
37#11762836C2211yescharacteristic
38#11762836C2211yescharacteristic
39#11762834—21no—
40#11762834—21no—
41#11762831—21no—
42C2×C4⋊#3622C2211yescharacteristic
43C2×C4⋊#3622C2211yescharacteristic
44C4⋊C8×D17—21no—
45C2×#10587476C2211yescharacteristic
46C2×#10587476C2211yescharacteristic
47#11762803C2211yescharacteristic
48#11762803C2211yescharacteristic
49#11762765C2211yescharacteristic
50#11762765C2211yescharacteristic
51C4×#63223C2211yescharacteristic
52C2×#10587474C2211yescharacteristic
53C2×C4×#3622C2211yescharacteristic
54#11762573C2211yescharacteristic
55#11762573C2211yescharacteristic
56#11762569C2211yescharacteristic
57#11762569C2211yescharacteristic
58#11762564C2211yescharacteristic
59#11762564C2211yescharacteristic
60C17×#533C2211yescharacteristic
61C17×#423C2211yescharacteristic
62C17×#376C2211yescharacteristic
63C17×#339C2211yescharacteristic
64C17×#339C2211yescharacteristic
65C17×#339C2211yescharacteristic
66C17×#339C2211yescharacteristic
67C2×#63252C2311yescharacteristic
68C2×M16×C17C2311yescharacteristic
69C2×M16×C17C2311yescharacteristic
70C17×C4⋊Q8C2×C411yescharacteristic
71C17×C4⋊Q8C2×C411yescharacteristic
72C17×#125C2×C411yescharacteristic
73C17×#125C2×C411yescharacteristic
74C17×C22⋊Q8—21no—
75C17×C22⋊Q8—21no—
76C4×Q8×C17—21no—
77C4×Q8×C17—21no—
78C17×#117C2311yescharacteristic
79C17×#117C2311yescharacteristic
80C2×C42×C17C2311yescharacteristic
81C2×C42×C17C2311yescharacteristic
82C2×C42×C17C2311yescharacteristic
83C4×C22⋊D17—21no—
84C4×C22⋊D17—21no—
85#10587612C2311yescharacteristic
86C2×#63223C2311yescharacteristic
87C2×#63223C2311yescharacteristic
88C22×#3622C2311yescharacteristic
89C22×#3622C2311yescharacteristic
90C22×#3622C2311yescharacteristic
91C22×#3622C2311yescharacteristic
92#10587593—22no—
93#10587593—22no—
94#10587593—41no—
95#10587593—41no—
96C2×#63218—21no—
97C2×#63218—21no—
98C2×C8×D17—21no—
99C2×C8×D17—21no—
100C4×D68C2×C411yescharacteristic
101C4×D68C2×C411yescharacteristic
102#10587558—21no—
103C42×D17—21no—
104C4×Dic34C2×C411yescharacteristic
105C4×Dic34C2×C411yescharacteristic
106C17×C4⋊C8—21no—
107C17×C4⋊C8—21no—
108C17×#95—21no—
109C17×#95—21no—
110#10587493—41no—
111#10587493—41no—
112#10587485—21no—
113#10587485—21no—
114#10587485—21no—
115#10587485—21no—
116#10587481C2×C411yescharacteristic
117#10587481C2×C411yescharacteristic
118#10587481C2×C411yescharacteristic
119#10587481C2×C411yescharacteristic
120#10587480C2×C411yescharacteristic
121#10587480C2×C411yescharacteristic
122#10587480C2×C411yescharacteristic
123#10587480C2×C411yescharacteristic
124#10587479C2×C411yescharacteristic
125#10587479C2×C411yescharacteristic
126#10587479C2×C411yescharacteristic
127#10587479C2×C411yescharacteristic
128#10587478C2×C411yescharacteristic
129#10587478C2×C411yescharacteristic
130#10587478C2×C411yescharacteristic
131#10587478C2×C411yescharacteristic
132#10587476—22no—
133#10587476Q814yescomplemented
134C4⋊#3622—21no—
135C4⋊#3622—21no—
136C4⋊#3622—21no—
137C4⋊#3622—21no—
138C4⋊#3622C2×C411yescharacteristic
139C4⋊#3622C2×C411yescharacteristic
140C4⋊#3622C2×C411yescharacteristic
141C4⋊#3622C2×C411yescharacteristic
142C4⋊#3622D411yescharacteristic
143C4⋊#3622D411yescharacteristic
144C4⋊#3622D411yescharacteristic
145C4⋊#3622D411yescharacteristic
146#10587474—21no—
147#10587474—21no—
148#10587474—21no—
149#10587474—41no—
150C4×#3622—21no—
151C4×#3622—21no—
152C4×#3622—21no—
153C4×#3622—41no—
154C2×Q8×C17—21no—
155C2×Q8×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17#4111yescharacteristic
159C22×C4×C17#4111yescharacteristic
160C22×C4×C17C2411yescharacteristic
161C2×C22⋊D17—21no—
162#63252—21no—
163#63252—21no—
164#63252C2×Q812yes—
165#63252#4112yes—
166C2×D68C22×C411yescharacteristic
167C2×C4×D17—21no—
168C2×C4×D17—21no—
169C2×C4×D17—21no—
170C2×Dic34C22×C411yescharacteristic
171M16×C17—21no—
172M16×C17—21no—
173M16×C17—21no—
174M16×C17—21no—
175C2×C8×C17—21no—
176C2×C8×C17—21no—
177C4⋊C4×C17—21no—
178C4⋊C4×C17—21no—
179C4⋊C4×C17—21no—
180C4⋊C4×C17—21no—
181C4⋊C4×C17—21no—
182C4⋊C4×C17—21no—
183C4⋊C4×C17C22×C411yescharacteristic
184C4⋊C4×C17C22×C411yescharacteristic
185C4⋊C4×C17C22×C411yescharacteristic
186C4⋊C4×C17C22×C411yescharacteristic
187C22⋊C4×C17—21no—
188C22⋊C4×C17—21no—
189C42×C17—21no—
190C42×C17—21no—
191C42×C17—21no—
192C42×C17—21no—
193C42×C17—21no—
194C42×C17C22×C411yescharacteristic
195C42×C17C22×C411yescharacteristic
196C42×C17C2×D411yescharacteristic
197C42×C17C2×D411yescharacteristic
198C42×C17C2×Q812yes—
199C22⋊Dic17—21no—
200#63227—21no—
201#63227—21no—
202C4⋊Dic17C22×C411yescharacteristic
203C4⋊Dic17C22×C411yescharacteristic
204#63225—21no—
205#63225—21no—
206C4×Dic17—21no—
207C4×Dic17—21no—
208C4×Dic17—21no—
209#63223—21no—
210#63223—21no—
211#63223—21no—
212#63223C2×Q812yes—
213C2×#3622—21no—
214C2×#3622—21no—
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×#3622C22×C411yescharacteristic
224C2×#3622C22×C411yescharacteristic
225C2×#3622C22×C411yescharacteristic
226C2×#3622C22×C411yescharacteristic
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—
238Q8×C17—42no—
239Q8×C17—81no—
240C2×C4×C17—21no—
241C2×C4×C17—21no—
242C2×C4×C17—21no—
243C2×C4×C17—21no—
244C2×C4×C17—22no—
245C2×C4×C17—41no—
246C2×C4×C17—41no—
247C2×C4×C17—41no—
248C2×C4×C17—41no—
249C2×C4×C17—41no—
250C2×C4×C17—41no—
251C2×C4×C17—41no—
252C2×C4×C17C4×D411yescharacteristic
253C2×C4×C17C4×D411yescharacteristic
254C2×C4×C17C4×D411yescharacteristic
255C2×C4×C17C4×D411yescharacteristic
256C2×C4×C17C23×C411yescharacteristic
257C2×C4×C17C22×D411yescharacteristic
258C2×C4×C17C22×Q811yescharacteristic
259C2×C4×C17C2×#4111yescharacteristic
260C2×C4×C17H(5,𝔽2)11yescharacteristic
261C2×C4×C172−1+411yescharacteristic
262C22⋊D17—22no—
263C22⋊D17—22no—
264C2×Dic17—21no—
265C2×Dic17—21no—
266C2×Dic17—21no—
267D68—21no—
268D68C4×Q812yes—
269C4×D17—22no—
270C4×D17—22no—
271C4×D17—42no—
272C4×D17—81no—
273Dic34—21no—
274Dic34C4×Q812yes—
275C8×C17—41no—
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—22no—
286#3622—41no—
287#3076—171no—
288#2962—171no—
289#2906—171no—
290#1995D1711yescharacteristic, complemented
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#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×C17—42no—
315C4×C17—41no—
316C4×C17—41no—
317C4×C17—41no—
318C4×C17—41no—
319C4×C17—81no—
320C4×C17C2×C4×Q811yescharacteristic
321C4×C17#52011yescharacteristic
322C4×C17#54611yescharacteristic
323C4×C17D4×Q811yescharacteristic
324Dic17—22no—
325Dic17—41no—
326Dic17—41no—
327C2×#131—171no—
328C2×#131—171no—
329#533C2×D1711yescharacteristic
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×#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—341no—
354#423C2×D1711yescharacteristic
355C2×C4⋊C8—171no—
356C2×C4⋊C8—171no—
357C2×C4⋊C8—341no—
358C2×#104—171no—
359C2×#104—171no—
360#416—171no—
361#416—171no—
362#405—171no—
363#405—171no—
364C4×M16—171no—
365C2×#97—171no—
366C2×C4×C8—171no—
367#376C2×D1711yescharacteristic
368#341—171no—
369#341—171no—
370#339—171no—
371#339—171no—
372#339C2×D1711yescharacteristic
373#339C2×D1711yescharacteristic
374#339C2×D1711yescharacteristic
375#339C2×D1711yescharacteristic
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—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⋊Q8C4×D1711yescharacteristic
402C4⋊Q8C4×D1711yescharacteristic
403#125C4×D1711yescharacteristic
404#125C4×D1711yescharacteristic
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8—171no—
410C4×Q8—171no—
411C4×D4—171no—
412C4×D4—171no—
413C4×D4—341no—
414C4×D4—341no—
415#117—171no—
416#117—341no—
417#117C22×D1711yescharacteristic
418#117C22×D1711yescharacteristic
419C2×C42—341no—
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—21no—
434C4⋊C8—21no—
435C4⋊C8—171no—
436C4⋊C8—171no—
437C4⋊C8—171no—
438C4⋊C8—171no—
439C4⋊C8—171no—
440C4⋊C8—171no—
441C4⋊C8—171no—
442C4⋊C8—171no—
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—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—341no—
462#97—341no—
463#97—341no—
464#97—681no—
465C4×C8—341no—
466C4×C8—341no—
467C4×C8—341no—
468C4×C8—681no—
469#95—21no—
470#95—21no—
471C17#2298411yescharacteristic, complemented, Sylow
472#41—172no—
473#41—172no—
474#41—341no—
475#41—341no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—171no—
479C2×D4—171no—
480C2×D4—341no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—341no—
484C22×C4—341no—
485C22×C4—341no—
486C22×C4#6325411yescharacteristic
487C22×C4#6325411yescharacteristic
488C22×C4C23×D1711yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—172no—
494M16—341no—
495M16—341no—
496M16—341no—
497M16—682no—
498M16—682no—
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—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—171no—
528C4⋊C4—171no—
529C4⋊C4—341no—
530C4⋊C4—341no—
531C4⋊C4C2×C4×D1711yescharacteristic
532C4⋊C4C2×C4×D1711yescharacteristic
533C4⋊C4C2×C4×D1711yescharacteristic
534C4⋊C4C2×C4×D1711yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—341no—
538C22⋊C4—341no—
539C22⋊C4—341no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—341no—
546C42—341no—
547C42—341no—
548C42C2×C4×D1711yescharacteristic
549C42C2×C4×D1711yescharacteristic
550C42D4×D1711yescharacteristic
551C42D4×D1711yescharacteristic
552C42Q8×D1712yes—
553C23—341no—
554C23C2×#6325411yescharacteristic
555Q8—42no—
556Q8—81no—
557Q8—172no—
558Q8—341no—
559D4—172no—
560D4—342no—
561D4—342no—
562D4—341no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—341no—
576C2×C4—342no—
577C2×C4—342no—
578C2×C4—341no—
579C2×C4—341no—
580C2×C4—682no—
581C2×C4—1361no—
582C2×C4#1058756711yescharacteristic
583C2×C4#1058756711yescharacteristic
584C2×C4#1058756711yescharacteristic
585C2×C4#1058756711yescharacteristic
586C2×C4C22×C4×D1711yescharacteristic
587C2×C4C2×D4×D1711yescharacteristic
588C2×C4C2×Q8×D1711yescharacteristic
589C2×C4#1058769411yescharacteristic
590C2×C4#41×D1711yescharacteristic
591C2×C4#1058769611yescharacteristic
592C8—41no—
593C8—41no—
594C8—342no—
595C8—341no—
596C8—341no—
597C8—341no—
598C8—341no—
599C8—341no—
600C8—341no—
601C8—341no—
602C8—341no—
603C8—681no—
604C22—21no—
605C22—21no—
606C22—342no—
607C22—681no—
608C22—681no—
609C22C2×#1058756711yescharacteristic
610C22#1176349311yescharacteristic
611C22#1176351711yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—42no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—81no—
622C4—342no—
623C4—681no—
624C4—681no—
625C4C4×Q8×D1711yescharacteristic
626C4#1176329111yescharacteristic
627C4#1176345211yescharacteristic
628C4#1176347411yescharacteristic
629C2—21no—
630C2—21no—
631C2—682no—
632C2#1453179411yescharacteristic
633C2#1453768311yescharacteristic
634C2#1453769711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1995C2
socleC22×C17C2×C4×D4
prime radicalC2×#63252C23
cosocleC22×C4×C17C24
hypercenter#1995D17
hypocenterC17#22984
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
2. #14537733C2semidirect
4. #14529557C2semidirect
5. #14529536C2semidirect
6. #14529531C2semidirect
7. #14529381C2semidirect
8. #14529381C2semidirect
11. #14528641C2semidirect
15. C17×#1995C2semidirect
19. #11763113C4semidirect
20. #11763113C4semidirect
21. #11763106C4semidirect
22. #11763106C4semidirect
23. #11763101C4semidirect
24. #11763096C4semidirect
25. #11763091C4semidirect
26. #11763086C4semidirect
133. #10587476Q8semidirect
290. #1995D17semidirect
471. C17#22984semidirect

Maximal subgroups

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

subgroupindex
#145385662
#145377332
#145373532
#145295572
#145295362
#145295312
#145293812
#145290602
#145286412
#145286252
#145286182
#145285952
C17×#19952
#2298417