Finite Group Databasebeta

← #17004384

Subgroups — #17004384

Order 4352.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538831C211yesmaximal, characteristic
2#14537935C211yesmaximal, characteristic, complemented
3#14527648C211yesmaximal, characteristic, complemented
4#14527641C211yesmaximal, characteristic, complemented
5#14527620C211yesmaximal, characteristic, complemented
6#14527613C211yesmaximal, characteristic, complemented
7#14527606C211yesmaximal, characteristic, complemented
8#14527596C211yesmaximal, characteristic, complemented
9C8×#63229C211yesmaximal, characteristic, complemented
10C8×#63228C211yesmaximal, characteristic, complemented
11#14527572C211yesmaximal, characteristic, complemented
12#14527209C211yesmaximal, characteristic, complemented
13#14527190C211yesmaximal, characteristic, complemented
14#14527084C211yesmaximal, characteristic, complemented
15C17×#2972C211yesmaximal, characteristic, complemented
16#11763343C2211yescharacteristic
17#11763144C411yescharacteristic
18#11763127C411yescharacteristic
19#11763109C411yescharacteristic
20#11763109C411yescharacteristic
21#11763024C411yescharacteristic
22#11763024C411yescharacteristic
23#11762960C411yescharacteristic
24#11762943C411yescharacteristic
25#11762939C2211yescharacteristic, complemented
26C8×Dic34C2211yescharacteristic, complemented
27C4×#63229C2211yescharacteristic
28C4×#63229C2211yescharacteristic
29C4×#63228C2211yescharacteristic
30C4×#63228C2211yescharacteristic
31#11762888C2211yescharacteristic, complemented
32#11762884—21no—
33#11762883—21no—
34C8×D68C2211yescharacteristic, complemented
35#11762869—21no—
36#11762862C2211yescharacteristic
37#11762862C2211yescharacteristic
38#11762834—21no—
39#11762833C2211yescharacteristic
40#11762561C2211yescharacteristic, complemented
41#11762561C2211yescharacteristic, complemented
42#11762559C2211yescharacteristic, complemented
43#11762559C2211yescharacteristic, complemented
44#11762539C2211yescharacteristic, complemented
45#11762539C2211yescharacteristic, complemented
46D4⋊#3622C2211yescharacteristic
47D4⋊#3622C2211yescharacteristic
48D4⋊#3622C2211yescharacteristic
49D4⋊#3622C2211yescharacteristic
50#11762536C2211yescharacteristic, complemented
51#11762536C2211yescharacteristic, complemented
52#11762531C2211yescharacteristic, complemented
53#11762531C2211yescharacteristic, complemented
54#11762530C2211yescharacteristic, complemented
55C8×#3622C2211yescharacteristic, complemented
56C2×C4×D4×C17C2211yescharacteristic
57C8×D4×C17—21no—
58C8×D4×C17—21no—
59C8×D4×C17C2211yescharacteristic
60C8×D4×C17C2211yescharacteristic
61C8×D4×C17C2211yescharacteristic
62C8×D4×C17C2211yescharacteristic
63C17×#431C2211yescharacteristic
64C17×#431C2211yescharacteristic
65C2×C17×C22⋊C8—21no—
66C2×C17×C22⋊C8—21no—
67C22×D4×C17C2×C411yescharacteristic
68C23×C4×C17—21no—
69C22×C8×C17—21no—
70C22×C8×C17—21no—
71C22×C8×C17—21no—
72C22×C8×C17—21no—
73C4×D4×C17—21no—
74C4×D4×C17—21no—
75C4×D4×C17C2×C411yescharacteristic
76C4×D4×C17C2×C411yescharacteristic
77C4×D4×C17C2311yescharacteristic
78C4×D4×C17C2311yescharacteristic
79C2×C4⋊C4×C17C2×C411yescharacteristic
80C2×C22⋊C4×C17—21no—
81C2×C42×C17C2311yescharacteristic
82C2×#63229C2×C411yescharacteristic
83C2×#63229C2×C411yescharacteristic
84C2×#63228C2×C411yescharacteristic
85C2×#63228C2×C411yescharacteristic
86#10587616C2×C411yescharacteristic
87#10587615—21no—
88C4×C22⋊D17—21no—
89#10587610C2×C411yescharacteristic
90C2×#63223—21no—
91C2×#63218—21no—
92C2×C8×D17—21no—
93#10587562—21no—
94#10587561C2×C411yescharacteristic
95C4×D68C2311yescharacteristic
96#10587558—21no—
97#10587556C2×C411yescharacteristic
98C4×Dic34C2311yescharacteristic
99C17×C4⋊C8D411yescharacteristic
100C17×C4⋊C8D411yescharacteristic
101C17×C4⋊C8C2311yescharacteristic
102C17×C4⋊C8C2311yescharacteristic
103C17×C22⋊C8—21no—
104C17×C22⋊C8—21no—
105C17×C22⋊C8—21no—
106C17×C22⋊C8—21no—
107C17×C22⋊C8—21no—
108C17×C22⋊C8D411yescharacteristic
109C17×C22⋊C8D411yescharacteristic
110C4×C8×C17—21no—
111C4×C8×C17C2311yescharacteristic
112C4×C8×C17C2311yescharacteristic
113#10587503C2×C411yescharacteristic
114#10587503C2×C411yescharacteristic
115#10587503C2×C411yescharacteristic
116#10587503C2×C411yescharacteristic
117C22⋊#3622—21no—
118C22⋊#3622C2×C411yescharacteristic
119C22⋊#3622C2×C411yescharacteristic
120#10587491—21no—
121#10587491—21no—
122#10587486—21no—
123#10587485—21no—
124#10587485—21no—
125C8×Dic17—21no—
126#10587481C2×C411yescharacteristic
127#10587481C2×C411yescharacteristic
128#10587480C2×C411yescharacteristic
129#10587480C2×C411yescharacteristic
130#10587479C2×C411yescharacteristic
131#10587479C2×C411yescharacteristic
132#10587478C2×C411yescharacteristic
133#10587478C2×C411yescharacteristic
134C4⋊#3622—21no—
135C4⋊#3622—21no—
136C4⋊#3622C2×C411yescharacteristic
137C4⋊#3622C2×C411yescharacteristic
138C4⋊#3622C2311yescharacteristic
139C4⋊#3622C2311yescharacteristic
140C4×#3622C2311yescharacteristic
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144C24×C17—21no—
145C2×D4×C17—22no—
146C2×D4×C17—22no—
147C2×D4×C17—21no—
148C2×D4×C17C22×C411yescharacteristic
149C2×D4×C17C22×C411yescharacteristic
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—81no—
156C22×C4×C17—81no—
157C22×C4×C17C22×C411yescharacteristic
158C22×C4×C17C2×D411yescharacteristic
159C22×C4×C17#4111yescharacteristic
160C2×C22⋊D17—21no—
161C2×D68C22×C411yescharacteristic
162C2×C4×D17—21no—
163C2×Dic34C22×C411yescharacteristic
164C2×C8×C17—21no—
165C2×C8×C17—21no—
166C2×C8×C17—81no—
167C2×C8×C17—81no—
168C2×C8×C17—81no—
169C2×C8×C17—81no—
170C2×C8×C17C2×D411yescharacteristic
171C2×C8×C17C2×D411yescharacteristic
172C2×C8×C17C2×D411yescharacteristic
173C2×C8×C17C2×D411yescharacteristic
174C4⋊C4×C17—21no—
175C4⋊C4×C17C22×C411yescharacteristic
176C4⋊C4×C17C22×C411yescharacteristic
177C22⋊C4×C17—21no—
178C22⋊C4×C17—21no—
179C22⋊C4×C17—21no—
180C22⋊C4×C17—21no—
181C42×C17C22×C411yescharacteristic
182C42×C17C2×D411yescharacteristic
183C42×C17#4111yescharacteristic
184C42×C17C2411yescharacteristic
185C22⋊Dic17—21no—
186#63229—22no—
187#63229—22no—
188#63228—22no—
189#63228—22no—
190#63227—21no—
191#63227—21no—
192#63227—21no—
193#63227—21no—
194C4⋊Dic17C22×C411yescharacteristic
195C4⋊Dic17C22×C411yescharacteristic
196#63225—21no—
197#63225—21no—
198#63225—21no—
199#63225—21no—
200C4×Dic17—21no—
201#63223—81no—
202C2×#3622—21no—
203C2×#3622—21no—
204C2×#3622—21no—
205C2×#3622—21no—
206C2×#3622C22×C411yescharacteristic
207C2×#3622C22×C411yescharacteristic
208C2×#3622C22×C411yescharacteristic
209C2×#3622C22×C411yescharacteristic
210#63218—81no—
211C8×D17—81no—
212#17918—171nomaximal, Sylow
213C23×C17—24no—
214C23×C17—21no—
215C23×C17—21no—
216C23×C17—81no—
217C23×C17—81no—
218C23×C17C4×D411yescharacteristic
219C22×D17—21no—
220D4×C17—24no—
221D4×C17—21no—
222D4×C17—21no—
223D4×C17#13112yes—
224D4×C17#13112yes—
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—41no—
232C2×C4×C17—41no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17—41no—
236C2×C4×C17—81no—
237C2×C4×C17—81no—
238C2×C4×C17—81no—
239C2×C4×C17C4×D411yescharacteristic
240C2×C4×C17C4×D411yescharacteristic
241C2×C4×C17C4×D411yescharacteristic
242C2×C4×C17C23×C411yescharacteristic
243C2×C4×C17C22×D411yescharacteristic
244C2×C4×C17C2×#4111yescharacteristic
245C22⋊D17—81no—
246C2×Dic17—21no—
247C2×Dic17—21no—
248C2×Dic17—21no—
249D68—21no—
250D68—21no—
251C4×D17—41no—
252C4×D17—41no—
253Dic34—21no—
254Dic34—21no—
255C8×C17—21no—
256C8×C17—21no—
257C8×C17—21no—
258C8×C17—21no—
259C8×C17—41no—
260C8×C17—41no—
261#3622—21no—
262#3622—21no—
263#3622—21no—
264#3622—21no—
265#3622—41no—
266#3622—41no—
267#3622—41no—
268#3622—41no—
269#3105—171no—
270#2993—171no—
271#2972D1711yescharacteristic, complemented
272#1586—171no—
273#1585—171no—
274#1582—171no—
275#1581—171no—
276#1580—171no—
277SD16⋊C8—171no—
278C8×SD16—171no—
279C8×D8—171no—
280#1574—171no—
281#1486—171no—
282#1482—171no—
283#1454—171no—
284C22×C17—21no—
285C22×C17—22no—
286C22×C17—22no—
287C22×C17—21no—
288C22×C17—21no—
289C22×C17—41no—
290C22×C17—41no—
291C22×C17—41no—
292C22×C17—41no—
293C22×C17—84no—
294C22×C17C2×C4×D411yescharacteristic
295C2×D17—41no—
296C2×D17—41no—
297C2×D17—41no—
298C4×C17—21no—
299C4×C17—21no—
300C4×C17—21no—
301C4×C17—21no—
302C4×C17—41no—
303C4×C17—41no—
304C4×C17C2×#13111yescharacteristic
305C4×C17C2×#13111yescharacteristic
306C4×C17#57611yescharacteristic
307C4×C17#57711yescharacteristic
308Dic17—41no—
309Dic17—41no—
310Dic17—41no—
311#529—171no—
312C2×C4×D4C2×D1711yescharacteristic
313#484—171no—
314#481—171no—
315#478—171no—
316#478—171no—
317#463—171no—
318#463—171no—
319#450—171no—
320#447—171no—
321#446—171no—
322C8×Q8—171no—
323C4×SD16—171no—
324C4×SD16—171no—
325C4×D8—171no—
326C4×D8—171no—
327#436—171no—
328#436—341no—
329#435—341no—
330C8×D4—21no—
331C8×D4—21no—
332C8×D4—171no—
333C8×D4C2×D1711yescharacteristic
334C8×D4C2×D1711yescharacteristic
335C8×D4C2×D1711yescharacteristic
336C8×D4C2×D1711yescharacteristic
337#433—341no—
338#431—171no—
339#431—171no—
340#431C2×D1711yescharacteristic
341#431C2×D1711yescharacteristic
342#424—341no—
343#423—171no—
344C2×C22⋊C8—21no—
345C2×C22⋊C8—21no—
346#335—171no—
347#335—171no—
348#334—171no—
349#334—171no—
350Q8⋊C8—171no—
351Q8⋊C8—171no—
352D4⋊C8—171no—
353D4⋊C8—171no—
354D4⋊C8—171no—
355D4⋊C8—171no—
356D4⋊C8—171no—
357D4⋊C8—171no—
358#322—171no—
359#322—171no—
360#322—171no—
361C82—171no—
362C2×C17—41no—
363C2×C17—42no—
364C2×C17—42no—
365C2×C17#292911yescharacteristic
366C2×C17#294611yescharacteristic
367C2×C17#295711yescharacteristic
368D17—81no—
369C22×D4C4×D1711yescharacteristic
370C23×C4—21no—
371C2×SD16—171no—
372C2×SD16—171no—
373C2×D8—171no—
374C2×D8—171no—
375C2×M16—341no—
376C2×M16—341no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—341no—
382#126—341no—
383#125—171no—
384#124—171no—
385#123—341no—
386C22⋊Q8—171no—
387#121—171no—
388C4×Q8—171no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—171no—
392C4×D4—341no—
393C4×D4C4×D1711yescharacteristic
394C4×D4C4×D1711yescharacteristic
395C4×D4C22×D1711yescharacteristic
396C4×D4C22×D1711yescharacteristic
397#117—341no—
398C2×C4⋊C4C4×D1711yescharacteristic
399C2×C22⋊C4—21no—
400C2×C42C22×D1711yescharacteristic
401#107—171no—
402#107—171no—
403#106—171no—
404#106—171no—
405C4⋊C8—171no—
406C4⋊C8—171no—
407C4⋊C8—171no—
408C4⋊C8—171no—
409C4⋊C8—341no—
410C4⋊C8—341no—
411C4⋊C8—341no—
412C4⋊C8—341no—
413C4⋊C8C22⋊D1711yescharacteristic
414C4⋊C8C22⋊D1711yescharacteristic
415C4⋊C8C22×D1711yescharacteristic
416C4⋊C8C22×D1711yescharacteristic
417#103—171no—
418#103—171no—
419#102—171no—
420#102—171no—
421#102—171no—
422#102—171no—
423#102—171no—
424#102—171no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—171no—
431C22⋊C8—171no—
432C22⋊C8—341no—
433C22⋊C8—341no—
434C22⋊C8—341no—
435C22⋊C8C22⋊D1711yescharacteristic
436C22⋊C8C22⋊D1711yescharacteristic
437#97—341no—
438C4×C8—21no—
439C4×C8—171no—
440C4×C8—171no—
441C4×C8—171no—
442C4×C8—171no—
443C4×C8—341no—
444C4×C8C22×D1711yescharacteristic
445C4×C8C22×D1711yescharacteristic
446C17#1791811yescharacteristic, complemented, Sylow
447C24—21no—
448C2×Q8—171no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—171no—
453C2×D4—341no—
454C2×D4C2×C4×D1711yescharacteristic
455C2×D4C2×C4×D1711yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—81no—
462C22×C4—81no—
463C22×C4—341no—
464C22×C4C2×C4×D1711yescharacteristic
465C22×C4#6325211yescharacteristic
466C22×C4C2×C22⋊D1711yescharacteristic
467SD16—342no—
468SD16—342no—
469D8—342no—
470D8—342no—
471M16—1361no—
472M16—1361no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—81no—
479C2×C8—171no—
480C2×C8—171no—
481C2×C8—171no—
482C2×C8—171no—
483C2×C8—341no—
484C2×C8—341no—
485C2×C8—341no—
486C2×C8—341no—
487C2×C8—1361no—
488C2×C8C2×C22⋊D1711yescharacteristic
489C2×C8C2×C22⋊D1711yescharacteristic
490C2×C8C2×C22⋊D1711yescharacteristic
491C2×C8C2×C22⋊D1711yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—171no—
494C4⋊C4—171no—
495C4⋊C4—341no—
496C4⋊C4—341no—
497C4⋊C4—341no—
498C4⋊C4—341no—
499C4⋊C4C2×C4×D1711yescharacteristic
500C4⋊C4C2×C4×D1711yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—341no—
506C22⋊C4—341no—
507C22⋊C4—341no—
508C22⋊C4—341no—
509C22⋊C4—341no—
510C42—341no—
511C42C2×C4×D1711yescharacteristic
512C42#6325211yescharacteristic
513C42C2×C22⋊D1711yescharacteristic
514C42C23×D1711yescharacteristic
515C23—24no—
516C23—21no—
517C23—21no—
518C23—81no—
519C23—81no—
520C23—341no—
521C23C4×C22⋊D1711yescharacteristic
522Q8—341no—
523Q8—341no—
524D4—24no—
525D4—21no—
526D4—21no—
527D4—341no—
528D4—341no—
529D4—1361no—
530D4#1058758712yes—
531D4#1058758712yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—341no—
547C2×C4—341no—
548C2×C4—341no—
549C2×C4—681no—
550C2×C4—681no—
551C2×C4C4×C22⋊D1711yescharacteristic
552C2×C4C4×C22⋊D1711yescharacteristic
553C2×C4C4×C22⋊D1711yescharacteristic
554C2×C4C22×C4×D1711yescharacteristic
555C2×C4C2×#6325211yescharacteristic
556C2×C4C22×C22⋊D1711yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—341no—
564C8—341no—
565C8—341no—
566C8—341no—
567C8—681no—
568C8—681no—
569C8—681no—
570C8—681no—
571C22—21no—
572C22—22no—
573C22—22no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—84no—
581C22—681no—
582C22—681no—
583C22—681no—
584C22C2×C4×C22⋊D1711yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—681no—
592C4—681no—
593C4—681no—
594C4C2×#1058758711yescharacteristic
595C4C2×#1058758711yescharacteristic
596C4#1176361211yescharacteristic
597C4#1176362011yescharacteristic
598C2—41no—
599C2—42no—
600C2—42no—
601C2—1361no—
602C2#1453747811yescharacteristic
603C2#1453761611yescharacteristic
604C2#1453769911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#2972C2
socleC22×C17C2×C4×D4
prime radical#11762943C4
cosocleC42×C17C24
hypercenter#2972D17
hypocenterC17#17918
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #14537935C2semidirect
3. #14527648C2semidirect
4. #14527641C2semidirect
5. #14527620C2semidirect
6. #14527613C2semidirect
7. #14527606C2semidirect
8. #14527596C2semidirect
9. C8×#63229C2semidirect
10. C8×#63228C2semidirect
11. #14527572C2semidirect
12. #14527209C2semidirect
13. #14527190C2semidirect
14. #14527084C2semidirect
15. C17×#2972C2semidirect
25. #11762939C22semidirect
26. C8×Dic34C22semidirect
31. #11762888C22semidirect
34. C8×D68C22semidirect
40. #11762561C22semidirect
41. #11762561C22semidirect
42. #11762559C22semidirect
43. #11762559C22semidirect
44. #11762539C22semidirect
45. #11762539C22semidirect
50. #11762536C22semidirect
51. #11762536C22semidirect
52. #11762531C22semidirect
53. #11762531C22semidirect
54. #11762530C22semidirect
55. C8×#3622C22semidirect
271. #2972D17semidirect
446. C17#17918semidirect

Maximal subgroups

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

subgroupindex
#145388312
#145379352
#145276482
#145276412
#145276202
#145276132
#145276062
#145275962
C8×#632292
C8×#632282
#145275722
#145272092
#145271902
#145270842
C17×#29722
#1791817