Finite Group Databasebeta

← #17042179

Subgroups — #17042179

Order 4352.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538566C211yesmaximal, characteristic
2#14537725C211yesmaximal, characteristic, complemented
3#14537213C211yesmaximal, characteristic
4#14529559C211yesmaximal, characteristic, complemented
5#14529386C211yesmaximal, characteristic, complemented
6#14529386C211yesmaximal, characteristic, complemented
7#14529060C211yesmaximal, characteristic
8#14529060C211yesmaximal, characteristic
9#14528805C211yesmaximal, characteristic
10#14528667C211yesmaximal, characteristic, complemented
11#14528662C211yesmaximal, characteristic, complemented
12#14528659C211yesmaximal, characteristic, complemented
13#14528625C211yesmaximal, characteristic
14#14528618C211yesmaximal, characteristic
15C17×#1986C211yesmaximal, 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—
30#11762940—21no—
31C2×#10587493C2211yescharacteristic
32C2×#10587493C2211yescharacteristic
33#11762845C2211yescharacteristic
34#11762845C2211yescharacteristic
35#11762836C2211yescharacteristic
36#11762836C2211yescharacteristic
37#11762833C2211yescharacteristic
38C2×C4⋊#3622C2211yescharacteristic
39C2×#10587476C2211yescharacteristic
40C2×#10587476C2211yescharacteristic
41#11762803C2211yescharacteristic
42#11762803C2211yescharacteristic
43#11762767C2211yescharacteristic
44#11762767C2211yescharacteristic
45#11762765C2211yescharacteristic
46#11762765C2211yescharacteristic
47#11762763—21no—
48#11762763—21no—
49#11762761—21no—
50C2×#10587474C2211yescharacteristic
51C2×#10587474C2211yescharacteristic
52#97×D17—21no—
53C2×C4×#3622C2211yescharacteristic
54#11762573C2211yescharacteristic
55#11762573C2211yescharacteristic
56#11762569C2211yescharacteristic
57#11762569C2211yescharacteristic
58#11762564C2211yescharacteristic
59#11762564C2211yescharacteristic
60C17×#533C2211yescharacteristic
61C4×M16×C17C2211yescharacteristic
62C4×C4⋊C4×C17C2211yescharacteristic
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×C4⋊C4×C17—21no—
81C2×C42×C17C2311yescharacteristic
82C2×C42×C17C2311yescharacteristic
83C2×C42×C17C2311yescharacteristic
84C4×C22⋊D17—21no—
85C4×C22⋊D17—21no—
86#10587612C2311yescharacteristic
87C2×#63223C2311yescharacteristic
88C2×#63223C2311yescharacteristic
89C22×#3622C2311yescharacteristic
90C22×#3622C2311yescharacteristic
91C22×#3622C2311yescharacteristic
92C22×#3622C2311yescharacteristic
93#10587593—22no—
94#10587593—22no—
95#10587593—22no—
96#10587593Q814yescomplemented
97C2×#63218—21no—
98C2×#63218—21no—
99C2×C8×D17—21no—
100C2×C8×D17—21no—
101C4×D68C2×C411yescharacteristic
102C4×D68C2×C411yescharacteristic
103#10587558—21no—
104C42×D17—21no—
105C4×Dic34C2×C411yescharacteristic
106C4×Dic34C2×C411yescharacteristic
107C17×#97—21no—
108C4×C8×C17—21no—
109C17×#95—21no—
110#10587493—22no—
111#10587493—22no—
112#10587486—21no—
113#10587486—21no—
114C8×Dic17—21no—
115C8×Dic17—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#10587476—22no—
134C4⋊#3622—21no—
135C4⋊#3622—21no—
136C4⋊#3622—21no—
137C4⋊#3622—21no—
138C4⋊#3622—21no—
139C4⋊#3622—21no—
140C4⋊#3622C2×C411yescharacteristic
141C4⋊#3622C2×C411yescharacteristic
142C4⋊#3622C2×C411yescharacteristic
143C4⋊#3622C2×C411yescharacteristic
144#10587474—21no—
145#10587474—21no—
146#10587474—22no—
147#10587474D411yescharacteristic
148#10587474D411yescharacteristic
149#10587474D411yescharacteristic
150#10587474D411yescharacteristic
151C4×#3622—21no—
152C4×#3622—21no—
153C4×#3622—22no—
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×C17C2×Q812yes—
174M16×C17#4112yes—
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×C17—42no—
184C4⋊C4×C17C22×C411yescharacteristic
185C4⋊C4×C17C22×C411yescharacteristic
186C4⋊C4×C17C22×C411yescharacteristic
187C4⋊C4×C17C22×C411yescharacteristic
188C22⋊C4×C17—21no—
189C22⋊C4×C17—21no—
190C42×C17—21no—
191C42×C17—21no—
192C42×C17—21no—
193C42×C17—21no—
194C42×C17—21no—
195C42×C17—21no—
196C42×C17C22×C411yescharacteristic
197C42×C17C22×C411yescharacteristic
198C42×C17C2×D411yescharacteristic
199C42×C17C2×D411yescharacteristic
200C22⋊Dic17—21no—
201#63227—21no—
202#63227—21no—
203C4⋊Dic17C22×C411yescharacteristic
204C4⋊Dic17C22×C411yescharacteristic
205#63225—21no—
206#63225—21no—
207C4×Dic17—21no—
208C4×Dic17—21no—
209C4×Dic17—21no—
210#63223—21no—
211#63223—21no—
212#63223—21no—
213#63223—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×#3622C22×C411yescharacteristic
223C2×#3622C22×C411yescharacteristic
224C2×#3622C22×C411yescharacteristic
225C2×#3622C22×C411yescharacteristic
226C2×#3622C2×D411yescharacteristic
227C2×#3622C2×D411yescharacteristic
228C2×#3622C2×D411yescharacteristic
229C2×#3622C2×D411yescharacteristic
230C2×#3622C2×Q812yes—
231C2×#3622#4112yes—
232#63218—24no—
233#63218—24no—
234C8×D17—24no—
235C8×D17—24no—
236#21629—171nomaximal, Sylow
237C23×C17C2×#4111yescharacteristic
238C22×D17—21no—
239Q8×C17—81no—
240Q8×C17—81no—
241C2×C4×C17—22no—
242C2×C4×C17—21no—
243C2×C4×C17—21no—
244C2×C4×C17—21no—
245C2×C4×C17—21no—
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×C17—41no—
253C2×C4×C17C4×D411yescharacteristic
254C2×C4×C17C4×D411yescharacteristic
255C2×C4×C17C4×D411yescharacteristic
256C2×C4×C17C4×D411yescharacteristic
257C2×C4×C17C23×C411yescharacteristic
258C2×C4×C17C22×D411yescharacteristic
259C2×C4×C17C22×Q811yescharacteristic
260C2×C4×C17C2×#4111yescharacteristic
261C2×C4×C17C2×#4111yescharacteristic
262C2×C4×C17C2×#4111yescharacteristic
263C22⋊D17—22no—
264C22⋊D17—22no—
265C2×Dic17—21no—
266C2×Dic17—21no—
267C2×Dic17—21no—
268D68—21no—
269D68C4×Q812yes—
270C4×D17—22no—
271C4×D17—22no—
272C4×D17—81no—
273C4×D17—81no—
274Dic34—21no—
275Dic34C4×Q812yes—
276C8×C17—22no—
277C8×C17—22no—
278#3622—21no—
279#3622—21no—
280#3622—21no—
281#3622—21no—
282#3622—21no—
283#3622—21no—
284#3622—41no—
285#3622—41no—
286#3622C22⋊Q812yes—
287#3622C22⋊Q812yes—
288#3076—171no—
289#2961—171no—
290#2875—171no—
291#1986D1711yescharacteristic, complemented
292#1950—171no—
293#1922—171no—
294#1922—171no—
295#1866—171no—
296#1866—171no—
297#1806—171no—
298#1773—171no—
299#1772—171no—
300#1771—171no—
301#1765—171no—
302#1764—171no—
303C22×C17—21no—
304C22×C17—21no—
305C22×C17C2×C4×D411yescharacteristic
306C22×C17#52911yescharacteristic
307C22×C17#53311yescharacteristic
308C2×D17—22no—
309C2×D17—41no—
310C2×D17—41no—
311C4×C17—21no—
312C4×C17—21no—
313C4×C17—21no—
314C4×C17—21no—
315C4×C17—42no—
316C4×C17—41no—
317C4×C17—41no—
318C4×C17—41no—
319C4×C17—41no—
320C4×C17—81no—
321C4×C17C2×C4×Q811yescharacteristic
322C4×C17C4×#4111yescharacteristic
323C4×C17C2×C22⋊Q811yescharacteristic
324C4×C17#52511yescharacteristic
325Dic17—22no—
326Dic17—41no—
327Dic17—41no—
328C2×#131—171no—
329C2×#131—171no—
330#533C2×D1711yescharacteristic
331C4×#41—171no—
332#479—171no—
333#479—171no—
334#478—171no—
335#478—171no—
336#477—171no—
337#476—171no—
338#475—171no—
339#474—171no—
340#446—341no—
341#446—341no—
342#446—341no—
343#446—341no—
344C2×#108—171no—
345C2×#108—171no—
346#427—171no—
347#427—171no—
348#424—171no—
349#424—171no—
350#423—171no—
351C2×C4⋊C8—171no—
352C2×#104—171no—
353C2×#104—171no—
354#416—171no—
355#416—171no—
356#405—171no—
357#405—171no—
358#405—171no—
359#405—171no—
360#405—341no—
361#405—341no—
362C4×M16—341no—
363C4×M16C2×D1711yescharacteristic
364C2×#97—171no—
365C2×#97—171no—
366C2×#97—341no—
367C2×C4×C8—171no—
368C4×C4⋊C4C2×D1711yescharacteristic
369#341—171no—
370#341—171no—
371#339—171no—
372#339—171no—
373#339C2×D1711yescharacteristic
374#339C2×D1711yescharacteristic
375#339C2×D1711yescharacteristic
376#339C2×D1711yescharacteristic
377#336—171no—
378#336—171no—
379C2×C17—21no—
380C2×C17—21no—
381C2×C17C4×C22⋊Q811yescharacteristic
382C2×C17#295611yescharacteristic
383C2×C17#295711yescharacteristic
384D17—42no—
385C2×#41—171no—
386#131—174no—
387#131—342no—
388#131—342no—
389#131—342no—
390C2×M16—171no—
391C2×M16—171no—
392C2×M16—341no—
393C2×M16—341no—
394C2×M16C22×D1711yescharacteristic
395C2×M16C22×D1711yescharacteristic
396C22×C8—171no—
397C22×C8—171no—
398C22×C8—171no—
399C22×C8—171no—
400C22×C8—341no—
401C22×C8—341no—
402C4⋊Q8C4×D1711yescharacteristic
403C4⋊Q8C4×D1711yescharacteristic
404#125C4×D1711yescharacteristic
405#125C4×D1711yescharacteristic
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—171no—
411C4×Q8—171no—
412C4×D4—171no—
413C4×D4—171no—
414C4×D4—341no—
415C4×D4—341no—
416#117—171no—
417#117—341no—
418#117C22×D1711yescharacteristic
419#117C22×D1711yescharacteristic
420C2×C4⋊C4—21no—
421C2×C42—341no—
422C2×C42C22×D1711yescharacteristic
423C2×C42C22×D1711yescharacteristic
424C2×C42C22×D1711yescharacteristic
425#108—342no—
426#108—342no—
427#107—171no—
428#107—171no—
429#107—171no—
430#107—171no—
431#106—171no—
432#106—171no—
433#106—171no—
434#106—171no—
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—
445#104—342no—
446#104—342no—
447#103—171no—
448#103—171no—
449#103—171no—
450#103—171no—
451#102—171no—
452#102—171no—
453#102—171no—
454#102—171no—
455#97—21no—
456#97—171no—
457#97—171no—
458#97—171no—
459#97—171no—
460#97—342no—
461#97—341no—
462#97—341no—
463#97—341no—
464#97—341no—
465C4×C8—21no—
466C4×C8—342no—
467C4×C8—341no—
468C4×C8—341no—
469C4×C8—341no—
470C4×C8—341no—
471#95—21no—
472C17#2162911yescharacteristic, complemented, Sylow
473#41—172no—
474#41—172no—
475#41—341no—
476#41—341no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—171no—
480C2×D4—171no—
481C2×D4—341no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—341no—
485C22×C4—341no—
486C22×C4—341no—
487C22×C4#6325411yescharacteristic
488C22×C4#6325411yescharacteristic
489C22×C4C23×D1711yescharacteristic
490M16—21no—
491M16—21no—
492M16—344no—
493M16—344no—
494M16—341no—
495M16—341no—
496M16—341no—
497M16—341no—
498M16Q8×D1712yes—
499M16#6325612yes—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—171no—
503C2×C8—171no—
504C2×C8—172no—
505C2×C8—172no—
506C2×C8—171no—
507C2×C8—171no—
508C2×C8—171no—
509C2×C8—171no—
510C2×C8—171no—
511C2×C8—171no—
512C2×C8—344no—
513C2×C8—344no—
514C2×C8—341no—
515C2×C8—341no—
516C2×C8—341no—
517C2×C8—341no—
518C2×C8—341no—
519C2×C8—341no—
520C2×C8—341no—
521C2×C8—341no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—171no—
530C4⋊C4—171no—
531C4⋊C4—341no—
532C4⋊C4—341no—
533C4⋊C4C2×C4×D1711yescharacteristic
534C4⋊C4C2×C4×D1711yescharacteristic
535C4⋊C4C2×C4×D1711yescharacteristic
536C4⋊C4C2×C4×D1711yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—341no—
540C22⋊C4—341no—
541C22⋊C4—341no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—341no—
549C42—341no—
550C42—341no—
551C42C2×C4×D1711yescharacteristic
552C42C2×C4×D1711yescharacteristic
553C42D4×D1711yescharacteristic
554C42D4×D1711yescharacteristic
555C23—341no—
556C23C2×#6325411yescharacteristic
557Q8—81no—
558Q8—81no—
559Q8—172no—
560Q8—341no—
561D4—172no—
562D4—342no—
563D4—342no—
564D4—341no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—341no—
578C2×C4—342no—
579C2×C4—342no—
580C2×C4—341no—
581C2×C4—341no—
582C2×C4—1361no—
583C2×C4—1361no—
584C2×C4#1058756711yescharacteristic
585C2×C4#1058756711yescharacteristic
586C2×C4#1058756711yescharacteristic
587C2×C4#1058756711yescharacteristic
588C2×C4C22×C4×D1711yescharacteristic
589C2×C4C2×D4×D1711yescharacteristic
590C2×C4C2×Q8×D1711yescharacteristic
591C2×C4C2×#6325611yescharacteristic
592C2×C4#41×D1711yescharacteristic
593C2×C4#41×D1711yescharacteristic
594C8—22no—
595C8—22no—
596C8—172no—
597C8—172no—
598C8—341no—
599C8—341no—
600C8—341no—
601C8—341no—
602C8—341no—
603C8—341no—
604C8—681no—
605C8—681no—
606C22—21no—
607C22—21no—
608C22—342no—
609C22—681no—
610C22—681no—
611C22C2×#1058756711yescharacteristic
612C22#1176333811yescharacteristic
613C22#1176336411yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—42no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—342no—
625C4—681no—
626C4—681no—
627C4C4×Q8×D1711yescharacteristic
628C4C4×#6325611yescharacteristic
629C4C22⋊Q8×D1711yescharacteristic
630C4#1176332211yescharacteristic
631C2—21no—
632C2—21no—
633C2—682no—
634C2#1453132211yescharacteristic
635C2#1453769011yescharacteristic
636C2#1453769711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1986C2
socleC22×C17C2×C4×D4
prime radicalC2×#63252C23
cosocleC22×C4×C17C24
hypercenter#1986D17
hypocenterC17#21629
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. #14537725C2semidirect
4. #14529559C2semidirect
5. #14529386C2semidirect
6. #14529386C2semidirect
10. #14528667C2semidirect
11. #14528662C2semidirect
12. #14528659C2semidirect
15. C17×#1986C2semidirect
19. #11763113C4semidirect
20. #11763113C4semidirect
21. #11763106C4semidirect
22. #11763106C4semidirect
23. #11763101C4semidirect
24. #11763096C4semidirect
25. #11763091C4semidirect
26. #11763086C4semidirect
96. #10587593Q8semidirect
291. #1986D17semidirect
472. C17#21629semidirect

Maximal subgroups

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

subgroupindex
#145385662
#145377252
#145372132
#145295592
#145293862
#145290602
#145288052
#145286672
#145286622
#145286592
#145286252
#145286182
C17×#19862
#2162917