Finite Group Databasebeta

← #17054038

Subgroups — #17054038

Order 4352.

710 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537582C211yesmaximal, characteristic
2#14537449C211yesmaximal, characteristic, complemented
3#14529676C211yesmaximal, characteristic
4#14529671C211yesmaximal, characteristic
5#14529432C211yesmaximal, characteristic, complemented
6#14529432C211yesmaximal, characteristic, complemented
7#14529429C211yesmaximal, characteristic, complemented
8#14529429C211yesmaximal, characteristic, complemented
9#14528958C211yesmaximal, characteristic, complemented
10#14528804C211yesmaximal, characteristic, complemented
11#14528801C211yesmaximal, characteristic, complemented
12#14528669C211yesmaximal, characteristic, complemented
13#14528664C211yesmaximal, characteristic, complemented
14#14528661C211yesmaximal, characteristic, complemented
15C17×#2925C211yesmaximal, characteristic, complemented
16C2×#10587636C2211yescharacteristic
17C4×#63252C2211yescharacteristic
18#11762919C411yescharacteristic, complemented
19#11762919C411yescharacteristic, complemented
20#11762914C411yescharacteristic, complemented
21#11762914C411yescharacteristic, complemented
22#11762909C411yescharacteristic, complemented
23#11762909C411yescharacteristic, complemented
24#11762907C411yescharacteristic, complemented
25#11762907C411yescharacteristic, complemented
26#11762869—21no—
27#11762869—21no—
28#11762865—21no—
29#11762861—21no—
30C2×#10587493C2211yescharacteristic
31C2×#10587493C2211yescharacteristic
32C2×#10587493C2211yescharacteristic
33C2×#10587493C2211yescharacteristic
34#11762845C2211yescharacteristic
35#11762833C2211yescharacteristic
36C2×#10587508C2211yescharacteristic
37C2×#10587508C2211yescharacteristic
38C2×#10587496C2211yescharacteristic
39C2×#10587496C2211yescharacteristic
40#11762805C2211yescharacteristic
41#11762803C2211yescharacteristic
42#11762775C2211yescharacteristic
43#11762775C2211yescharacteristic
44#11762764C2211yescharacteristic
45#11762764C2211yescharacteristic
46C2×#10587474C2211yescharacteristic
47C2×#10587486C2211yescharacteristic
48C2×C8×Dic17C2211yescharacteristic
49C4×C4⋊Dic17C2211yescharacteristic
50#11762570C2211yescharacteristic
51#11762570C2211yescharacteristic
52#11762568C2211yescharacteristic
53#11762568C2211yescharacteristic
54#11762563C2211yescharacteristic
55#11762563C2211yescharacteristic
56C4×#41×C17C2211yescharacteristic
57C17×#433—21no—
58C17×#433—21no—
59C17×#432—21no—
60C17×#431—21no—
61C17×#423C2211yescharacteristic
62C2×C17×C4⋊C8C2211yescharacteristic
63C17×#408C2211yescharacteristic
64C17×#408C2211yescharacteristic
65C17×#405C2211yescharacteristic
66C17×#405C2211yescharacteristic
67C2×#41×C17C2311yescharacteristic
68C2×#63252C2311yescharacteristic
69C2×M16×C17C2311yescharacteristic
70C2×M16×C17C2311yescharacteristic
71C22×C8×C17C2311yescharacteristic
72C22×C8×C17C2311yescharacteristic
73C4×Q8×C17C2×C411yescharacteristic
74C4×Q8×C17C2×C411yescharacteristic
75C4×D4×C17—21no—
76C4×D4×C17—21no—
77C4×D4×C17C2×C411yescharacteristic
78C4×D4×C17C2×C411yescharacteristic
79C17×#117—21no—
80C17×#117C2311yescharacteristic
81C2×C42×C17—21no—
82C2×C42×C17C2311yescharacteristic
83#10587636—22no—
84#10587636—22no—
85C2×#63231C2×C411yescharacteristic
86C2×#63230C2×C411yescharacteristic
87C2×#63229C2×C411yescharacteristic
88C2×#63228C2×C411yescharacteristic
89C4×C22⋊D17—21no—
90C4×C22⋊D17—21no—
91#10587612C2311yescharacteristic
92C2×C4⋊Dic17—21no—
93C2×C4×Dic17C2311yescharacteristic
94C2×C4×Dic17C2311yescharacteristic
95C2×#63223C2311yescharacteristic
96C2×#63223C2311yescharacteristic
97C22×#3622C2311yescharacteristic
98C22×#3622C2311yescharacteristic
99C4×D68C2×C411yescharacteristic
100C4×D68C2×C411yescharacteristic
101#10587558—21no—
102C42×D17—21no—
103C4×Dic34C2×C411yescharacteristic
104C4×Dic34C2×C411yescharacteristic
105C17×C4⋊C8—21no—
106C17×C4⋊C8—21no—
107C17×C4⋊C8D411yescharacteristic
108C17×C4⋊C8D411yescharacteristic
109C17×C4⋊C8D411yescharacteristic
110C17×C4⋊C8D411yescharacteristic
111C17×C22⋊C8—21no—
112C17×C22⋊C8—21no—
113C17×C22⋊C8—21no—
114C17×C22⋊C8—21no—
115C17×#97—21no—
116C17×#97—21no—
117C4×C8×C17—21no—
118C4×C8×C17—21no—
119#10587508—41no—
120#10587508—41no—
121#10587506C2×C411yescharacteristic
122#10587506C2×C411yescharacteristic
123#10587503C2×C411yescharacteristic
124#10587503C2×C411yescharacteristic
125#10587502—21no—
126#10587496—41no—
127#10587496—41no—
128#10587493—22no—
129#10587493—22no—
130#10587493—41no—
131#10587493—41no—
132#10587491—21no—
133#10587491—21no—
134#10587491—21no—
135#10587491—21no—
136#10587486—22no—
137#10587486—21no—
138#10587486—21no—
139C8×Dic17—22no—
140C8×Dic17—21no—
141C8×Dic17—21no—
142#10587481C2×C411yescharacteristic
143#10587481C2×C411yescharacteristic
144#10587480C2×C411yescharacteristic
145#10587480C2×C411yescharacteristic
146#10587479C2×C411yescharacteristic
147#10587479C2×C411yescharacteristic
148#10587478C2×C411yescharacteristic
149#10587478C2×C411yescharacteristic
150C4⋊#3622—21no—
151C4⋊#3622—21no—
152#10587474C2×C411yescharacteristic
153#10587474C2×C411yescharacteristic
154#10587474C2×C411yescharacteristic
155#10587474C2×C411yescharacteristic
156#41×C17—21no—
157#41×C17—21no—
158#41×C17—21no—
159#41×C17—21no—
160C2×Q8×C17C22×C411yescharacteristic
161C2×D4×C17—21no—
162C2×D4×C17C22×C411yescharacteristic
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17#4111yescharacteristic
167C22×C4×C17#4111yescharacteristic
168C22×C4×C17C2411yescharacteristic
169C2×C22⋊D17—21no—
170C22×Dic17—21no—
171C22×Dic17—21no—
172#63252—21no—
173#63252—21no—
174#63252—21no—
175#63252—21no—
176C2×D68C22×C411yescharacteristic
177C2×C4×D17—21no—
178C2×C4×D17—21no—
179C2×C4×D17—21no—
180C2×Dic34C22×C411yescharacteristic
181M16×C17—21no—
182M16×C17—21no—
183M16×C17—21no—
184M16×C17—21no—
185C2×C8×C17—21no—
186C2×C8×C17—21no—
187C2×C8×C17—21no—
188C2×C8×C17—21no—
189C2×C8×C17—21no—
190C2×C8×C17—21no—
191C2×C8×C17C2×D411yescharacteristic
192C2×C8×C17C2×D411yescharacteristic
193C2×C8×C17C2×D411yescharacteristic
194C2×C8×C17C2×D411yescharacteristic
195C4⋊C4×C17—21no—
196C4⋊C4×C17—21no—
197C4⋊C4×C17C22×C411yescharacteristic
198C4⋊C4×C17C22×C411yescharacteristic
199C22⋊C4×C17—21no—
200C22⋊C4×C17—21no—
201C22⋊C4×C17—21no—
202C42×C17—21no—
203C42×C17—21no—
204C42×C17—21no—
205C42×C17C22×C411yescharacteristic
206C42×C17C22×C411yescharacteristic
207C42×C17C2×D411yescharacteristic
208C42×C17C2×D411yescharacteristic
209C22⋊Dic17—21no—
210#63231—22no—
211#63230—22no—
212#63229—22no—
213#63228—22no—
214#63227—21no—
215#63227—21no—
216C4⋊Dic17—42no—
217C4⋊Dic17C22×C411yescharacteristic
218C4⋊Dic17C22×C411yescharacteristic
219#63225—21no—
220#63225—21no—
221C4×Dic17—21no—
222C4×Dic17—21no—
223C4×Dic17—21no—
224C4×Dic17—21no—
225C4×Dic17—21no—
226C4×Dic17—21no—
227C4×Dic17—21no—
228#63223—21no—
229#63223—21no—
230#63223—21no—
231#63223—21no—
232C2×#3622—21no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622C22×C411yescharacteristic
237C2×#3622C22×C411yescharacteristic
238C2×#3622C22×C411yescharacteristic
239C2×#3622C22×C411yescharacteristic
240C2×#3622#4112yes—
241C2×#3622#4112yes—
242#22804—171nomaximal, Sylow
243C23×C17—21no—
244C23×C17C2×#4111yescharacteristic
245C22×D17—21no—
246Q8×C17—21no—
247Q8×C17—21no—
248D4×C17—21no—
249D4×C17—21no—
250D4×C17—41no—
251D4×C17—41no—
252C2×C4×C17—21no—
253C2×C4×C17—21no—
254C2×C4×C17—21no—
255C2×C4×C17—41no—
256C2×C4×C17—41no—
257C2×C4×C17—42no—
258C2×C4×C17—41no—
259C2×C4×C17—41no—
260C2×C4×C17—81no—
261C2×C4×C17C4×D411yescharacteristic
262C2×C4×C17C4×D411yescharacteristic
263C2×C4×C17C4×D411yescharacteristic
264C2×C4×C17C4×D411yescharacteristic
265C2×C4×C17C23×C411yescharacteristic
266C2×C4×C17C22×D411yescharacteristic
267C2×C4×C17C2×#4111yescharacteristic
268C2×C4×C17C2×#4111yescharacteristic
269C2×C4×C17H(5,𝔽2)11yescharacteristic
270C2×C4×C172−1+411yescharacteristic
271C22⋊D17—41no—
272C22⋊D17—41no—
273C2×Dic17—22no—
274C2×Dic17—21no—
275C2×Dic17—21no—
276C2×Dic17—21no—
277C2×Dic17—41no—
278C2×Dic17—41no—
279C2×Dic17—41no—
280C2×Dic17—41no—
281C2×Dic17—41no—
282D68—21no—
283D68—21no—
284C4×D17—42no—
285C4×D17—41no—
286C4×D17—41no—
287C4×D17—81no—
288Dic34—21no—
289Dic34—21no—
290C8×C17—21no—
291C8×C17—21no—
292C8×C17—21no—
293C8×C17—21no—
294C8×C17—41no—
295C8×C17—41no—
296#3622—21no—
297#3622—21no—
298#3622—41no—
299#3622—41no—
300#3622#11712yes—
301#3622#11712yes—
302#2943—171no—
303#2925—171no—
304#2925D1711yescharacteristic, complemented
305#1975—171no—
306#1974—171no—
307#1929—171no—
308#1929—171no—
309#1929—171no—
310#1929—171no—
311#1849—171no—
312#1806—171no—
313#1806—171no—
314#1773—171no—
315#1772—171no—
316#1771—171no—
317C22×C17—21no—
318C22×C17—21no—
319C22×C17—41no—
320C22×C17—41no—
321C22×C17—41no—
322C22×C17C2×C4×D411yescharacteristic
323C22×C17#55511yescharacteristic
324C22×C17#55611yescharacteristic
325C2×D17—41no—
326C2×D17—41no—
327C2×D17—41no—
328C4×C17—21no—
329C4×C17—21no—
330C4×C17—21no—
331C4×C17—21no—
332C4×C17—41no—
333C4×C17—41no—
334C4×C17—41no—
335C4×C17C2×#11711yescharacteristic
336C4×C17#52011yescharacteristic
337C4×C17#54711yescharacteristic
338C4×C17#55011yescharacteristic
339Dic17—42no—
340Dic17—41no—
341Dic17—41no—
342Dic17—41no—
343Dic17—81no—
344C2×#135—171no—
345C4×#41—171no—
346C4×#41C2×D1711yescharacteristic
347#442—171no—
348#442—171no—
349#441—171no—
350#441—171no—
351#440—171no—
352#440—171no—
353#440—171no—
354#440—171no—
355#433—21no—
356#433—21no—
357#433—341no—
358#433—341no—
359#432—21no—
360#432—341no—
361#431—21no—
362#431—341no—
363C2×#108—171no—
364C2×#108—171no—
365C2×#108—171no—
366C2×#108—171no—
367#427—171no—
368#423—171no—
369#423C2×D1711yescharacteristic
370C2×C4⋊C8C2×D1711yescharacteristic
371C2×#104—171no—
372C2×#104—171no—
373C2×#104—171no—
374C2×#104—171no—
375#416—171no—
376#416—171no—
377#408—171no—
378#408—171no—
379#408C2×D1711yescharacteristic
380#408C2×D1711yescharacteristic
381#405—171no—
382#405—171no—
383#405C2×D1711yescharacteristic
384#405C2×D1711yescharacteristic
385C2×#97—171no—
386C2×#97—171no—
387C2×C4×C8—171no—
388C4×C4⋊C4—171no—
389#339—171no—
390#339—171no—
391#339—171no—
392#339—171no—
393#336—171no—
394#336—171no—
395C2×C17—21no—
396C2×C17—21no—
397C2×C17—81no—
398C2×C17#235411yescharacteristic
399C2×C17#295511yescharacteristic
400C2×C17#295611yescharacteristic
401D17—81no—
402C2×#41—171no—
403C2×#41C22×D1711yescharacteristic
404#135—342no—
405#135—342no—
406C2×Q16—171no—
407C2×SD16—171no—
408C2×SD16—171no—
409C2×D8—171no—
410C2×M16—171no—
411C2×M16—171no—
412C2×M16C22×D1711yescharacteristic
413C2×M16C22×D1711yescharacteristic
414C22×C8—171no—
415C22×C8—171no—
416C22×C8C22×D1711yescharacteristic
417C22×C8C22×D1711yescharacteristic
418C4×Q8—171no—
419C4×Q8—171no—
420C4×Q8C4×D1711yescharacteristic
421C4×Q8C4×D1711yescharacteristic
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—171no—
425C4×D4—171no—
426C4×D4—341no—
427C4×D4—341no—
428C4×D4C4×D1711yescharacteristic
429C4×D4C4×D1711yescharacteristic
430#117—21no—
431#117—171no—
432#117—341no—
433#117C22×D1711yescharacteristic
434C2×C4⋊C4—341no—
435C2×C42—21no—
436C2×C42—171no—
437C2×C42—171no—
438C2×C42—341no—
439C2×C42C22×D1711yescharacteristic
440#108—342no—
441#108—342no—
442#108—681no—
443#108—681no—
444#107—171no—
445#107—171no—
446#106—171no—
447#106—171no—
448C4⋊C8—21no—
449C4⋊C8—21no—
450C4⋊C8—341no—
451C4⋊C8—341no—
452C4⋊C8C22⋊D1711yescharacteristic
453C4⋊C8C22⋊D1711yescharacteristic
454C4⋊C8C22⋊D1711yescharacteristic
455C4⋊C8C22⋊D1711yescharacteristic
456#104—681no—
457#104—681no—
458#104—681no—
459#104—681no—
460#103—171no—
461#103—171no—
462#103—171no—
463#103—171no—
464#102—171no—
465#102—171no—
466#102—171no—
467#102—171no—
468C22⋊C8—21no—
469C22⋊C8—21no—
470C22⋊C8—21no—
471C22⋊C8—21no—
472C22⋊C8—341no—
473C22⋊C8—341no—
474C22⋊C8—341no—
475C22⋊C8—341no—
476#97—21no—
477#97—21no—
478#97—171no—
479#97—171no—
480#97—171no—
481#97—171no—
482#97—342no—
483#97—341no—
484#97—341no—
485C4×C8—21no—
486C4×C8—21no—
487C4×C8—342no—
488C4×C8—341no—
489C4×C8—341no—
490#95—341no—
491C17#2280411yescharacteristic, complemented, Sylow
492#41—21no—
493#41—21no—
494#41—21no—
495#41—21no—
496#41—341no—
497#41—341no—
498#41—341no—
499#41—341no—
500C2×Q8—171no—
501C2×Q8C2×C4×D1711yescharacteristic
502C2×D4—21no—
503C2×D4—171no—
504C2×D4—341no—
505C2×D4C2×C4×D1711yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—341no—
510C22×C4—341no—
511C22×C4—341no—
512C22×C4—341no—
513C22×C4—341no—
514C22×C4#6325211yescharacteristic
515C22×C4#6325211yescharacteristic
516C22×C4C23×D1711yescharacteristic
517Q16—342no—
518SD16—342no—
519SD16—342no—
520D8—342no—
521M16—21no—
522M16—21no—
523M16—21no—
524M16—21no—
525M16—341no—
526M16—341no—
527M16—341no—
528M16—341no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—171no—
536C2×C8—171no—
537C2×C8—172no—
538C2×C8—172no—
539C2×C8—171no—
540C2×C8—171no—
541C2×C8—341no—
542C2×C8—341no—
543C2×C8—341no—
544C2×C8—341no—
545C2×C8C2×C22⋊D1711yescharacteristic
546C2×C8C2×C22⋊D1711yescharacteristic
547C2×C8C2×C22⋊D1711yescharacteristic
548C2×C8C2×C22⋊D1711yescharacteristic
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—171no—
552C4⋊C4—171no—
553C4⋊C4—341no—
554C4⋊C4—341no—
555C4⋊C4—682no—
556C4⋊C4C2×C4×D1711yescharacteristic
557C4⋊C4C2×C4×D1711yescharacteristic
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—341no—
562C22⋊C4—341no—
563C22⋊C4—341no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—341no—
568C42—341no—
569C42—341no—
570C42—341no—
571C42—341no—
572C42—341no—
573C42—341no—
574C42C2×C4×D1711yescharacteristic
575C42C2×C4×D1711yescharacteristic
576C42C2×C22⋊D1711yescharacteristic
577C42C2×C22⋊D1711yescharacteristic
578C23—21no—
579C23—341no—
580C23C2×#6325211yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—341no—
584Q8—341no—
585D4—21no—
586D4—21no—
587D4—41no—
588D4—41no—
589D4—341no—
590D4—341no—
591D4—681no—
592D4—681no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—81no—
602C2×C4—342no—
603C2×C4—341no—
604C2×C4—341no—
605C2×C4—341no—
606C2×C4—682no—
607C2×C4—681no—
608C2×C4—681no—
609C2×C4—681no—
610C2×C4—681no—
611C2×C4—681no—
612C2×C4—681no—
613C2×C4—681no—
614C2×C4—1361no—
615C2×C4C4×C22⋊D1711yescharacteristic
616C2×C4C4×C22⋊D1711yescharacteristic
617C2×C4C4×C22⋊D1711yescharacteristic
618C2×C4C4×C22⋊D1711yescharacteristic
619C2×C4C22×C4×D1711yescharacteristic
620C2×C4#41×D1711yescharacteristic
621C2×C4#41×D1711yescharacteristic
622C2×C4#1058769611yescharacteristic
623C2×C4#1058769711yescharacteristic
624C2×C4C22×C22⋊D1711yescharacteristic
625C8—21no—
626C8—21no—
627C8—21no—
628C8—21no—
629C8—41no—
630C8—41no—
631C8—172no—
632C8—172no—
633C8—341no—
634C8—341no—
635C8—681no—
636C8—681no—
637C22—21no—
638C22—21no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—681no—
643C22—681no—
644C22—681no—
645C22C2×C4×C22⋊D1711yescharacteristic
646C22#1176352211yescharacteristic
647C22#1176352711yescharacteristic
648C4—21no—
649C4—21no—
650C4—21no—
651C4—21no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—682no—
656C4—681no—
657C4—681no—
658C4—681no—
659C4—1361no—
660C4#117×D1711yescharacteristic
661C4#1176328911yescharacteristic
662C4#1176345811yescharacteristic
663C4#1176347811yescharacteristic
664C2—21no—
665C2—21no—
666C2—81no—
667C2—1361no—
668C2#1453173411yescharacteristic
669C2#1453768511yescharacteristic
670C2#1453769111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2925C2
socleC22×C17C2×C4×D4
prime radicalC2×#10587636C22
cosocleC22×C4×C17C24
hypercenter#2925D17
hypocenterC17#22804
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #14537449C2semidirect
5. #14529432C2semidirect
6. #14529432C2semidirect
7. #14529429C2semidirect
8. #14529429C2semidirect
9. #14528958C2semidirect
10. #14528804C2semidirect
11. #14528801C2semidirect
12. #14528669C2semidirect
13. #14528664C2semidirect
14. #14528661C2semidirect
15. C17×#2925C2semidirect
18. #11762919C4semidirect
19. #11762919C4semidirect
20. #11762914C4semidirect
21. #11762914C4semidirect
22. #11762909C4semidirect
23. #11762909C4semidirect
24. #11762907C4semidirect
25. #11762907C4semidirect
304. #2925D17semidirect
491. C17#22804semidirect

Maximal subgroups

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

subgroupindex
#145375822
#145374492
#145296762
#145296712
#145294322
#145294292
#145289582
#145288042
#145288012
#145286692
#145286642
#145286612
C17×#29252
#2280417