Finite Group Databasebeta

← #17106977

Subgroups — #17106977

Order 4352.

812 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531798C211yesmaximal, characteristic
2#14530188C211yesmaximal, characteristic, complemented
3#14530169C211yesmaximal, characteristic, complemented
4#14529966C211yesmaximal, characteristic
5#14529966C211yesmaximal, characteristic
6#14529540C211yesmaximal, characteristic, complemented
7#14529514C211yesmaximal, characteristic, complemented
8#14529392C211yesmaximal, characteristic, complemented
9#14529355C211yesmaximal, characteristic, complemented
10#14529352C211yesmaximal, characteristic, complemented
11#14529030C211yesmaximal, characteristic, complemented
12#14528971C211yesmaximal, characteristic, complemented
13#14528868C211yesmaximal, characteristic, complemented
14C4×#10587480C211yesmaximal, characteristic, complemented
15C17×#2496C211yesmaximal, characteristic, complemented
16C2×#10587616C2211yescharacteristic
17C2×C4×D68C2211yescharacteristic
18C2×#10587567—21no—
19C22×C4⋊Dic17C2211yescharacteristic
20C2×#10587478C2211yescharacteristic
21C2×#10587478C2211yescharacteristic
22C2×#10587478C2211yescharacteristic
23C2×#10587478C2211yescharacteristic
24C2×C4⋊#3622C2211yescharacteristic
25C2×#10587480C2211yescharacteristic
26C2×#10587480C2211yescharacteristic
27C2×#10587480C2211yescharacteristic
28C2×#10587480C2211yescharacteristic
29C2×C22⋊#3622C2211yescharacteristic
30C2×C22⋊#3622C2211yescharacteristic
31C2×C4×#3622C2211yescharacteristic
32#11762711C2211yescharacteristic
33#11762707C2211yescharacteristic
34#11762701—21no—
35#11762686—21no—
36#11762683—21no—
37C4×C4⋊Dic17C2211yescharacteristic
38#11762571C2211yescharacteristic
39#11762571C2211yescharacteristic
40#11762571C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762564C2211yescharacteristic
47#11762564C2211yescharacteristic
48C2×C17×#126—21no—
49C17×#400—21no—
50C17×#397—21no—
51C17×#389C2211yescharacteristic
52C17×#389C2211yescharacteristic
53C17×#387—21no—
54C17×#384C2211yescharacteristic
55C17×#380C2211yescharacteristic
56C17×#380C2211yescharacteristic
57C4×C4⋊C4×C17C2211yescharacteristic
58C4×C22⋊C4×C17C2211yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C22×C22⋊D17—21no—
61C23×Dic17—21no—
62C22×D68C2311yescharacteristic
63C22×C4×D17—21no—
64C17×#126—44no—
65C2×C4⋊C4×C17—21no—
66C2×C4⋊C4×C17—21no—
67C2×C4⋊C4×C17—21no—
68C2×C4⋊C4×C17—21no—
69C2×C4⋊C4×C17C2311yescharacteristic
70C2×C4⋊C4×C17C2311yescharacteristic
71C2×C4⋊C4×C17C2311yescharacteristic
72C2×C4⋊C4×C17C2311yescharacteristic
73C2×C22⋊C4×C17—21no—
74C2×C22⋊C4×C17—21no—
75C2×C22⋊C4×C17D411yescharacteristic
76C2×C22⋊C4×C17D411yescharacteristic
77C2×C42×C17—21no—
78C2×C42×C17C2311yescharacteristic
79C2×C42×C17C2311yescharacteristic
80#10587616—22no—
81#10587616—22no—
82C2×#63227—21no—
83C2×#63227—21no—
84C2×#63227—21no—
85C2×#63227—21no—
86C2×C4⋊Dic17—21no—
87C2×C4⋊Dic17—22no—
88C2×C4⋊Dic17—41no—
89C2×C4⋊Dic17C2311yescharacteristic
90C2×C4⋊Dic17C2311yescharacteristic
91C2×C4⋊Dic17C2311yescharacteristic
92C2×#63225—21no—
93C2×C4×Dic17—21no—
94C22×#3622C2311yescharacteristic
95C22×#3622C2311yescharacteristic
96C22×#3622C2311yescharacteristic
97C22×#3622C2311yescharacteristic
98#10587567—44no—
99C4×D68—22no—
100C4×D68—41no—
101C17×#95—21no—
102C17×#95—21no—
103C17×#95—21no—
104C17×#95—21no—
105C17×#95—21no—
106C17×#95D411yescharacteristic
107C17×#95D411yescharacteristic
108#10587502—21no—
109#10587502—21no—
110C22⋊#3622—22no—
111C22⋊#3622—41no—
112#10587480—22no—
113#10587480—22no—
114#10587480—22no—
115#10587480—41no—
116#10587478—22no—
117#10587478—22no—
118#10587478—22no—
119#10587478—41no—
120C4⋊#3622—22no—
121C4×#3622—41no—
122C24×C17C2×D411yescharacteristic
123C23×D17—21no—
124C22×C4×C17—21no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—21no—
128C22×C4×C17—21no—
129C22×C4×C17—21no—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17C2×D411yescharacteristic
135C22×C4×C17C2×D411yescharacteristic
136C22×C4×C17C2×D411yescharacteristic
137C22×C4×C17C2×D411yescharacteristic
138C22×C4×C17C2×D411yescharacteristic
139C22×C4×C17C2411yescharacteristic
140C2×C22⋊D17—24no—
141C2×C22⋊D17—42no—
142C2×C22⋊D17—42no—
143C22×Dic17—21no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17—42no—
147C22×Dic17—42no—
148C22×Dic17—81no—
149C2×D68—21no—
150C2×D68—21no—
151C2×D68—21no—
152C2×D68—21no—
153C2×D68—21no—
154C2×D68#4112yes—
155C2×C4×D17—42no—
156C2×C4×D17—42no—
157C2×C4×D17—81no—
158C4⋊C4×C17—21no—
159C4⋊C4×C17—21no—
160C4⋊C4×C17—21no—
161C4⋊C4×C17—21no—
162C4⋊C4×C17—21no—
163C4⋊C4×C17—21no—
164C4⋊C4×C17—21no—
165C4⋊C4×C17—21no—
166C4⋊C4×C17—42no—
167C4⋊C4×C17—42no—
168C4⋊C4×C17—42no—
169C4⋊C4×C17—42no—
170C22⋊C4×C17—41no—
171C22⋊C4×C17—42no—
172C22⋊C4×C17—42no—
173C22⋊C4×C17D814yes—
174C42×C17—21no—
175C42×C17—21no—
176C42×C17—21no—
177C42×C17—21no—
178C42×C17—42no—
179#63227—24no—
180#63227—42no—
181#63227—42no—
182#63227—81no—
183C4⋊Dic17—21no—
184C4⋊Dic17—21no—
185C4⋊Dic17—21no—
186C4⋊Dic17—21no—
187C4⋊Dic17—42no—
188C4⋊Dic17#4112yes—
189C4⋊Dic17#4112yes—
190#63225—42no—
191C4×Dic17—42no—
192C2×#3622—21no—
193C2×#3622—21no—
194C2×#3622—21no—
195C2×#3622—21no—
196C2×#3622—21no—
197C2×#3622—21no—
198C2×#3622—21no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—21no—
202C2×#3622—21no—
203C2×#3622#4112yes—
204#27030—171nomaximal, Sylow
205C23×C17—21no—
206C23×C17—21no—
207C23×C17—21no—
208C23×C17—21no—
209C23×C17—21no—
210C23×C17—21no—
211C23×C17C2×D812yes—
212C23×C17C22×D411yescharacteristic
213C22×D17—22no—
214C22×D17—41no—
215C22×D17—41no—
216C22×D17—41no—
217C22×D17—41no—
218C22×D17—41no—
219C22×D17—41no—
220C2×C4×C17—21no—
221C2×C4×C17—21no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—21no—
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—21no—
232C2×C4×C17—21no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17—41no—
236C2×C4×C17—41no—
237C2×C4×C17—41no—
238C2×C4×C17—41no—
239C2×C4×C17—41no—
240C2×C4×C17—41no—
241C2×C4×C17—41no—
242C2×C4×C17—41no—
243C2×C4×C17—41no—
244C2×C4×C17—41no—
245C2×C4×C17—41no—
246C2×C4×C17—41no—
247C2×C4×C17—41no—
248C2×C4×C17—41no—
249C2×C4×C17C2×D812yes—
250C2×C4×C17C2×D812yes—
251C2×C4×C17C2×#4111yescharacteristic
252C2×C4×C17C2×#4111yescharacteristic
253C2×C4×C17C2×#4111yescharacteristic
254C2×C4×C17C2×#4111yescharacteristic
255C2×C4×C17H(5,𝔽2)11yescharacteristic
256C2×C4×C172−1+411yescharacteristic
257C22⋊D17—48no—
258C2×Dic17—22no—
259C2×Dic17—22no—
260C2×Dic17—41no—
261C2×Dic17—41no—
262C2×Dic17—41no—
263C2×Dic17—41no—
264C2×Dic17—41no—
265C2×Dic17—41no—
266C2×Dic17—41no—
267C2×Dic17—84no—
268D68—22no—
269D68—22no—
270D68—41no—
271D68—41no—
272C4×D17—84no—
273#3622—22no—
274#3622—41no—
275#3622—41no—
276#3622—41no—
277#2496D1711yescharacteristic, complemented
278#2361—171no—
279#2071—171no—
280#2067—171no—
281#2033—171no—
282#2033—171no—
283#1947—171no—
284#1942—171no—
285#1923—171no—
286#1918—171no—
287#1918—171no—
288#1862—171no—
289#1852—171no—
290#1823—171no—
291C4×#102—171no—
292C22×C17—22no—
293C22×C17—22no—
294C22×C17—22no—
295C22×C17—41no—
296C22×C17—41no—
297C22×C17—41no—
298C22×C17—41no—
299C22×C17#52511yescharacteristic
300C22×C17#54611yescharacteristic
301C22×C17#54711yescharacteristic
302C22×C17C22×D811yescharacteristic
303C22×C17#57511yescharacteristic
304C22×C17#57711yescharacteristic
305C22×C17#57811yescharacteristic
306C2×D17—42no—
307C2×D17—42no—
308C2×D17—42no—
309C2×D17—81no—
310C2×D17—81no—
311C2×D17—81no—
312C2×D17—81no—
313C4×C17—22no—
314C4×C17—22no—
315C4×C17—41no—
316C4×C17—41no—
317C4×C17—41no—
318C4×C17—81no—
319C4×C17—81no—
320C4×C17—81no—
321C4×C17—81no—
322C4×C17#52911yescharacteristic
323C4×C17#53911yescharacteristic
324C4×C17#55311yescharacteristic
325C4×C17#55611yescharacteristic
326Dic17—42no—
327Dic17—42no—
328Dic17—81no—
329C2×#126—21no—
330C2×#121—171no—
331C2×C4×D4—171no—
332C2×C4×D4—341no—
333C22×C4⋊C4—171no—
334C2×#107—171no—
335C2×#107—171no—
336C2×#107—171no—
337C2×#107—171no—
338C2×C4⋊C8—171no—
339C2×#102—171no—
340C2×#102—171no—
341C2×#102—171no—
342C2×#102—171no—
343C2×C22⋊C8—171no—
344C2×C22⋊C8—171no—
345C2×C4×C8—171no—
346#400—21no—
347#397—21no—
348#390—171no—
349#389—171no—
350#389C2×D1711yescharacteristic
351#389C2×D1711yescharacteristic
352#388—341no—
353#387—21no—
354#386—341no—
355#385—341no—
356#384C2×D1711yescharacteristic
357#380C2×D1711yescharacteristic
358#380C2×D1711yescharacteristic
359C4×C4⋊C4—171no—
360C4×C4⋊C4C2×D1711yescharacteristic
361C4×C22⋊C4C2×D1711yescharacteristic
362#340—171no—
363#340—171no—
364#340—171no—
365#340—171no—
366#340—171no—
367#340—171no—
368#340—171no—
369#340—171no—
370#336—171no—
371#336—171no—
372C2×C17—42no—
373C2×C17#246611yescharacteristic
374C2×C17#310011yescharacteristic
375C2×C17#312011yescharacteristic
376C2×C17#329411yescharacteristic
377C2×C17#331311yescharacteristic
378C2×C17#333411yescharacteristic
379C2×C17#335111yescharacteristic
380D17—82no—
381C22×D4—171no—
382C22×D4—341no—
383C23×C4—341no—
384C23×C4—341no—
385C23×C4C22×D1711yescharacteristic
386C22×C8—171no—
387C22×C8—171no—
388C22×C8—171no—
389C22×C8—171no—
390#126—44no—
391#121—342no—
392#121—342no—
393C4×D4—342no—
394C4×D4—681no—
395C4×D4—684no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—171no—
401C2×C4⋊C4—171no—
402C2×C4⋊C4—171no—
403C2×C4⋊C4—342no—
404C2×C4⋊C4—341no—
405C2×C4⋊C4—341no—
406C2×C4⋊C4—681no—
407C2×C4⋊C4C22×D1711yescharacteristic
408C2×C4⋊C4C22×D1711yescharacteristic
409C2×C4⋊C4C22×D1711yescharacteristic
410C2×C4⋊C4C22×D1711yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—341no—
414C2×C22⋊C4—341no—
415C2×C22⋊C4—341no—
416C2×C22⋊C4—341no—
417C2×C22⋊C4C22⋊D1711yescharacteristic
418C2×C22⋊C4C22⋊D1711yescharacteristic
419C2×C42—21no—
420C2×C42—341no—
421C2×C42C22×D1711yescharacteristic
422C2×C42C22×D1711yescharacteristic
423#107—342no—
424#107—342no—
425#107—342no—
426#107—681no—
427C4⋊C8—342no—
428#102—342no—
429#102—342no—
430#102—342no—
431#102—681no—
432C22⋊C8—342no—
433C22⋊C8—681no—
434C4×C8—681no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—341no—
441#95—341no—
442#95C22⋊D1711yescharacteristic
443#95C22⋊D1711yescharacteristic
444C17#2703011yescharacteristic, complemented, Sylow
445C24—341no—
446C24C2×C22⋊D1711yescharacteristic
447C2×D4—172no—
448C2×D4—344no—
449C2×D4—341no—
450C2×D4—341no—
451C2×D4—341no—
452C2×D4—341no—
453C2×D4—341no—
454C2×D4—682no—
455C2×D4—682no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—341no—
467C22×C4—341no—
468C22×C4—341no—
469C22×C4—682no—
470C22×C4—682no—
471C22×C4—682no—
472C22×C4—682no—
473C22×C4—1361no—
474C22×C4—1361no—
475C22×C4C2×C22⋊D1711yescharacteristic
476C22×C4C2×C22⋊D1711yescharacteristic
477C22×C4C2×C22⋊D1711yescharacteristic
478C22×C4C2×C22⋊D1711yescharacteristic
479C22×C4C2×C22⋊D1711yescharacteristic
480C22×C4C23×D1711yescharacteristic
481C2×C8—172no—
482C2×C8—341no—
483C2×C8—341no—
484C2×C8—341no—
485C2×C8—341no—
486C2×C8—341no—
487C2×C8—341no—
488C2×C8—341no—
489C2×C8—341no—
490C2×C8—341no—
491C2×C8—341no—
492C2×C8—341no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—172no—
506C4⋊C4—172no—
507C4⋊C4—341no—
508C4⋊C4—341no—
509C4⋊C4—341no—
510C4⋊C4—341no—
511C4⋊C4—682no—
512C4⋊C4—682no—
513C22⋊C4—41no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—344no—
517C22⋊C4—682no—
518C22⋊C4—682no—
519C22⋊C4—1361no—
520C22⋊C4#6322814yes—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—42no—
526C42—682no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—342no—
534C23—681no—
535C23—681no—
536C23—681no—
537C23—681no—
538C23—681no—
539C23—681no—
540C23C2×#6322812yes—
541C23C22×C22⋊D1711yescharacteristic
542D4—342no—
543D4—342no—
544D4—688no—
545D4—681no—
546D4—681no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—342no—
577C2×C4—342no—
578C2×C4—681no—
579C2×C4—681no—
580C2×C4—681no—
581C2×C4—681no—
582C2×C4—681no—
583C2×C4—681no—
584C2×C4—681no—
585C2×C4—1364no—
586C2×C4—1364no—
587C2×C4C2×#6322812yes—
588C2×C4C2×#6322812yes—
589C2×C4#41×D1711yescharacteristic
590C2×C4#41×D1711yescharacteristic
591C2×C4#41×D1711yescharacteristic
592C2×C4#41×D1711yescharacteristic
593C2×C4#1058769611yescharacteristic
594C2×C4#1058769711yescharacteristic
595C8—342no—
596C8—681no—
597C8—681no—
598C8—681no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—682no—
607C22—682no—
608C22—682no—
609C22—1361no—
610C22—1361no—
611C22—1361no—
612C22—1361no—
613C22#1176331611yescharacteristic
614C22#1176344711yescharacteristic
615C22#1176345811yescharacteristic
616C22C22×#6322811yescharacteristic
617C22#1176360711yescharacteristic
618C22#1176361711yescharacteristic
619C22#1176362411yescharacteristic
620C4—22no—
621C4—22no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—81no—
626C4—81no—
627C4—81no—
628C4—81no—
629C4—682no—
630C4—682no—
631C4—1361no—
632C4#1176334211yescharacteristic
633C4#1176340011yescharacteristic
634C4#1176351011yescharacteristic
635C4#1176352611yescharacteristic
636C2—42no—
637C2—1362no—
638C2#1453281611yescharacteristic
639C2#1453878011yescharacteristic
640C2#1453899211yescharacteristic
641C2#1454059111yescharacteristic
642C2#1454084411yescharacteristic
643C2#1454112711yescharacteristic
644C2#1454134411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2496C2
socleC23×C17C22×D4
prime radicalC2×#10587616C22
hypercenter#2496D17
hypocenterC17#27030
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2496

Complements

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

NH ≅ G/Ntype
2. #14530188C2semidirect
3. #14530169C2semidirect
6. #14529540C2semidirect
7. #14529514C2semidirect
8. #14529392C2semidirect
9. #14529355C2semidirect
10. #14529352C2semidirect
11. #14529030C2semidirect
12. #14528971C2semidirect
13. #14528868C2semidirect
14. C4×#10587480C2semidirect
15. C17×#2496C2semidirect
277. #2496D17semidirect
444. C17#27030semidirect

Maximal subgroups

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

subgroupindex
#145317982
#145301882
#145301692
#145299662
#145295402
#145295142
#145293922
#145293552
#145293522
#145290302
#145289712
#145288682
C4×#105874802
C17×#24962
#2703017