Finite Group Databasebeta

← #17107024

Subgroups — #17107024

Order 4352.

784 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533184C211yesmaximal, characteristic, complemented
2#14531798C211yesmaximal, characteristic
3#14530199C211yesmaximal, characteristic, complemented
4#14530171C211yesmaximal, characteristic, complemented
5#14529974C211yesmaximal, characteristic
6#14529967C211yesmaximal, characteristic
7#14529554C211yesmaximal, characteristic, complemented
8#14529517C211yesmaximal, characteristic, complemented
9#14529377C211yesmaximal, characteristic, complemented
10#14529363C211yesmaximal, characteristic, complemented
11#14529034C211yesmaximal, characteristic, complemented
12#14528974C211yesmaximal, characteristic, complemented
13#14528875C211yesmaximal, characteristic, complemented
14C4×#10587492C211yesmaximal, characteristic, complemented
15C17×#1923C211yesmaximal, characteristic, complemented
16C2×#10587616C2211yescharacteristic
17C2×C4×D68C2211yescharacteristic
18C2×#10587567—21no—
19C22×C4⋊Dic17C2211yescharacteristic
20C2×#10587489C2211yescharacteristic
21C2×#10587489C2211yescharacteristic
22C2×#10587489C2211yescharacteristic
23C2×#10587488C2211yescharacteristic
24C2×#10587492C2211yescharacteristic
25C2×#10587492C2211yescharacteristic
26C2×#10587492C2211yescharacteristic
27C2×#10587492C2211yescharacteristic
28C17⋊#401—21no—
29#11762737—21no—
30#11762711C2211yescharacteristic
31#11762707C2211yescharacteristic
32#11762707C2211yescharacteristic
33#11762707C2211yescharacteristic
34#11762703—21no—
35#11762701—21no—
36#11762691—21no—
37#11762686—21no—
38#11762683—21no—
39#11762675C2211yescharacteristic
40#11762669C2211yescharacteristic
41#11762669C2211yescharacteristic
42C4×C4⋊Dic17C2211yescharacteristic
43C4×C4⋊Dic17C2211yescharacteristic
44#11762572C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762572C2211yescharacteristic
51#11762572C2211yescharacteristic
52C2×C17×C4⋊C8C2211yescharacteristic
53C2×C17×C22⋊C8C2211yescharacteristic
54C2×C17×C22⋊C8C2211yescharacteristic
55C2×C4×C8×C17C2211yescharacteristic
56C4×C22⋊C4×C17C2211yescharacteristic
57C17×#336C2211yescharacteristic
58C17×#336C2211yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C22×C22⋊D17—21no—
61C23×Dic17—21no—
62C22×D68C2311yescharacteristic
63C22×C4×D17—21no—
64C22×C8×C17C2311yescharacteristic
65C22×C8×C17C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C2×C22⋊C4×C17D411yescharacteristic
69C2×C22⋊C4×C17D411yescharacteristic
70C2×C42×C17C2311yescharacteristic
71C2×C42×C17C2311yescharacteristic
72C2×C22⋊Dic17—21no—
73C2×C22⋊Dic17—21no—
74#10587616—22no—
75#10587616—22no—
76C2×#63227—21no—
77C2×#63227—21no—
78C2×#63227—21no—
79C2×#63227—21no—
80C2×C4⋊Dic17—21no—
81C2×C4⋊Dic17—22no—
82C2×C4⋊Dic17—41no—
83C2×C4⋊Dic17C2311yescharacteristic
84C2×C4⋊Dic17C2311yescharacteristic
85C2×C4⋊Dic17C2311yescharacteristic
86C2×C4⋊Dic17C2311yescharacteristic
87C2×C4⋊Dic17C2311yescharacteristic
88C2×C4⋊Dic17C2311yescharacteristic
89C2×C4⋊Dic17C2311yescharacteristic
90C2×#63225—21no—
91C2×#63225—21no—
92C2×#63225—21no—
93C2×C4×Dic17—21no—
94C2×C4×Dic17—21no—
95#10587567—44no—
96C4×D68—22no—
97C4×D68—41no—
98C17×C4⋊C8—22no—
99C17×C22⋊C8—22no—
100C17×C22⋊C8—41no—
101C4×C8×C17—41no—
102C17×#95D411yescharacteristic
103C17×#95D411yescharacteristic
104#10587502—21no—
105#10587502—21no—
106#10587502—21no—
107#10587502—21no—
108#10587502—21no—
109#10587502—21no—
110#10587502—21no—
111#10587502—21no—
112#10587502—21no—
113#10587492—22no—
114#10587492—22no—
115#10587492—22no—
116#10587492—41no—
117#10587489—22no—
118#10587489—22no—
119#10587489—41no—
120#10587488—22no—
121C24×C17C2×D411yescharacteristic
122C23×D17—21no—
123C22×C4×C17—21no—
124C22×C4×C17—21no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—21no—
128C22×C4×C17—21no—
129C22×C4×C17C2×D411yescharacteristic
130C22×C4×C17C2×D411yescharacteristic
131C22×C4×C17C2×D411yescharacteristic
132C22×C4×C17C2×D411yescharacteristic
133C22×C4×C17C2×D411yescharacteristic
134C22×C4×C17C2411yescharacteristic
135C2×C22⋊D17—24no—
136C2×C22⋊D17—42no—
137C2×C22⋊D17—42no—
138C22×Dic17—21no—
139C22×Dic17—21no—
140C22×Dic17—21no—
141C22×Dic17—21no—
142C22×Dic17—21no—
143C22×Dic17—21no—
144C22×Dic17—21no—
145C22×Dic17—42no—
146C22×Dic17—42no—
147C22×Dic17—81no—
148C2×D68—21no—
149C2×D68—21no—
150C2×D68—21no—
151C2×D68—21no—
152C2×D68—21no—
153C2×D68#4112yes—
154C2×C4×D17—42no—
155C2×C4×D17—42no—
156C2×C4×D17—81no—
157C2×C8×C17—21no—
158C2×C8×C17—21no—
159C2×C8×C17—21no—
160C2×C8×C17—21no—
161C2×C8×C17—21no—
162C2×C8×C17—21no—
163C2×C8×C17—21no—
164C2×C8×C17—21no—
165C2×C8×C17—21no—
166C2×C8×C17—21no—
167C2×C8×C17—21no—
168C2×C8×C17#4112yes—
169C22⋊C4×C17—22no—
170C22⋊C4×C17—22no—
171C42×C17—21no—
172C42×C17—21no—
173C42×C17—21no—
174C42×C17—21no—
175C22⋊Dic17—42no—
176C22⋊Dic17—81no—
177#63227—24no—
178#63227—42no—
179#63227—42no—
180#63227—81no—
181C4⋊Dic17—21no—
182C4⋊Dic17—21no—
183C4⋊Dic17—21no—
184C4⋊Dic17—21no—
185C4⋊Dic17—21no—
186C4⋊Dic17—21no—
187C4⋊Dic17—21no—
188C4⋊Dic17—21no—
189C4⋊Dic17—21no—
190C4⋊Dic17—21no—
191C4⋊Dic17—21no—
192C4⋊Dic17—21no—
193C4⋊Dic17—42no—
194C4⋊Dic17#4112yes—
195C4⋊Dic17#4112yes—
196#63225—42no—
197#63225—42no—
198#63225—81no—
199C4×Dic17—42no—
200C4×Dic17—81no—
201#27033—171nomaximal, Sylow
202C23×C17—21no—
203C23×C17—21no—
204C23×C17—21no—
205C23×C17—21no—
206C23×C17—21no—
207C23×C17—21no—
208C23×C17#13512yes—
209C23×C17C22×D411yescharacteristic
210C22×D17—22no—
211C22×D17—41no—
212C22×D17—41no—
213C22×D17—41no—
214C22×D17—41no—
215C22×D17—41no—
216C22×D17—41no—
217C2×C4×C17—21no—
218C2×C4×C17—21no—
219C2×C4×C17—21no—
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—41no—
232C2×C4×C17—41no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17AGL(1,ℤ/8)12yes—
236C2×C4×C17C2×#4111yescharacteristic
237C2×C4×C17C2×#4111yescharacteristic
238C2×C4×C17C2×#4111yescharacteristic
239C2×C4×C17C2×#4111yescharacteristic
240C2×C4×C17H(5,𝔽2)11yescharacteristic
241C2×C4×C172−1+411yescharacteristic
242C22⋊D17—48no—
243C2×Dic17—22no—
244C2×Dic17—22no—
245C2×Dic17—41no—
246C2×Dic17—41no—
247C2×Dic17—41no—
248C2×Dic17—41no—
249C2×Dic17—41no—
250C2×Dic17—41no—
251C2×Dic17—41no—
252C2×Dic17—41no—
253C2×Dic17—41no—
254C2×Dic17—41no—
255C2×Dic17—41no—
256C2×Dic17—41no—
257C2×Dic17—41no—
258C2×Dic17—41no—
259C2×Dic17—41no—
260C2×Dic17—41no—
261C2×Dic17—41no—
262C2×Dic17—41no—
263C2×Dic17—41no—
264C2×Dic17—84no—
265D68—22no—
266D68—22no—
267D68—41no—
268D68—41no—
269C4×D17—84no—
270C8×C17—22no—
271C8×C17—41no—
272C8×C17—41no—
273C8×C17—41no—
274#2494—171no—
275#2361—171no—
276#2073—171no—
277#2067—171no—
278#2034—171no—
279#2033—171no—
280#1949—171no—
281#1942—171no—
282#1923D1711yescharacteristic, complemented
283#1921—171no—
284#1919—171no—
285#1862—171no—
286#1852—171no—
287#1824—171no—
288C4×#102—171no—
289C22×C17—22no—
290C22×C17—22no—
291C22×C17—22no—
292C22×C17—41no—
293C22×C17—41no—
294C22×C17—41no—
295C22×C17—41no—
296C22×C17#52511yescharacteristic
297C22×C17#54611yescharacteristic
298C22×C17#54711yescharacteristic
299C22×C17C2×#13511yescharacteristic
300C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C17#57611yescharacteristic
302C22×C17#57811yescharacteristic
303C2×D17—42no—
304C2×D17—42no—
305C2×D17—42no—
306C2×D17—81no—
307C2×D17—81no—
308C2×D17—81no—
309C2×D17—81no—
310C4×C17—22no—
311C4×C17—41no—
312C4×C17—41no—
313C4×C17—41no—
314C4×C17—41no—
315C4×C17#52911yescharacteristic
316C4×C17#53911yescharacteristic
317C4×C17#55311yescharacteristic
318C4×C17#55611yescharacteristic
319Dic17—42no—
320Dic17—42no—
321Dic17—81no—
322Dic17—81no—
323Dic17—81no—
324Dic17—81no—
325Dic17—81no—
326C2×#121—171no—
327C2×C4×D4—171no—
328C2×C4×D4—341no—
329C22×C4⋊C4—171no—
330C2×#107—171no—
331C2×#107—171no—
332C2×#107—171no—
333C2×#106—171no—
334C2×C4⋊C8C2×D1711yescharacteristic
335C2×#102—171no—
336C2×#102—171no—
337C2×#102—171no—
338C2×#102—171no—
339C2×C22⋊C8C2×D1711yescharacteristic
340C2×C22⋊C8C2×D1711yescharacteristic
341C2×C4×C8C2×D1711yescharacteristic
342#401—341no—
343#397—341no—
344#390—171no—
345#389—171no—
346#389—171no—
347#389—171no—
348#388—341no—
349#388—341no—
350#387—341no—
351#386—341no—
352#385—341no—
353#382—171no—
354#380—171no—
355#380—171no—
356C4×C4⋊C4—171no—
357C4×C4⋊C4—171no—
358C4×C22⋊C4C2×D1711yescharacteristic
359#340—171no—
360#340—171no—
361#340—171no—
362#340—171no—
363#340—171no—
364#340—171no—
365#340—171no—
366#340—171no—
367#336C2×D1711yescharacteristic
368#336C2×D1711yescharacteristic
369C2×C17—42no—
370C2×C17#246611yescharacteristic
371C2×C17#310511yescharacteristic
372C2×C17#312411yescharacteristic
373C2×C17#330011yescharacteristic
374C2×C17#331811yescharacteristic
375C2×C17#333911yescharacteristic
376C2×C17#335311yescharacteristic
377D17—82no—
378C22×D4—171no—
379C22×D4—341no—
380C23×C4—341no—
381C23×C4—341no—
382C23×C4C22×D1711yescharacteristic
383C22×C8C22×D1711yescharacteristic
384C22×C8C22×D1711yescharacteristic
385C22×C8C22×D1711yescharacteristic
386C22×C8C22×D1711yescharacteristic
387#121—342no—
388#121—342no—
389C4×D4—342no—
390C4×D4—681no—
391C4×D4—684no—
392C2×C4⋊C4—171no—
393C2×C4⋊C4—171no—
394C2×C4⋊C4—171no—
395C2×C4⋊C4—171no—
396C2×C4⋊C4—171no—
397C2×C4⋊C4—171no—
398C2×C4⋊C4—171no—
399C2×C4⋊C4—342no—
400C2×C4⋊C4—341no—
401C2×C4⋊C4—341no—
402C2×C4⋊C4—341no—
403C2×C4⋊C4—341no—
404C2×C4⋊C4—681no—
405C2×C22⋊C4—341no—
406C2×C22⋊C4—341no—
407C2×C22⋊C4—341no—
408C2×C22⋊C4—341no—
409C2×C22⋊C4—341no—
410C2×C22⋊C4—341no—
411C2×C22⋊C4D6811yescharacteristic
412C2×C22⋊C4D6811yescharacteristic
413C2×C42—341no—
414C2×C42—341no—
415C2×C42C22×D1711yescharacteristic
416C2×C42C22×D1711yescharacteristic
417#107—342no—
418#107—342no—
419#107—681no—
420#106—342no—
421C4⋊C8—22no—
422#102—342no—
423#102—342no—
424#102—342no—
425#102—681no—
426C22⋊C8—22no—
427C22⋊C8—41no—
428C4×C8—41no—
429#95—341no—
430#95—341no—
431#95—341no—
432#95—341no—
433#95—341no—
434#95—341no—
435#95—341no—
436#95—341no—
437#95—341no—
438#95D6811yescharacteristic
439#95D6811yescharacteristic
440C17#2703311yescharacteristic, complemented, Sylow
441C24—341no—
442C24C2×D6811yescharacteristic
443C2×D4—172no—
444C2×D4—344no—
445C2×D4—341no—
446C2×D4—341no—
447C2×D4—341no—
448C2×D4—341no—
449C2×D4—341no—
450C2×D4—682no—
451C2×D4—682no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—341no—
459C22×C4—341no—
460C22×C4—341no—
461C22×C4—341no—
462C22×C4—341no—
463C22×C4—341no—
464C22×C4—341no—
465C22×C4—682no—
466C22×C4—682no—
467C22×C4—682no—
468C22×C4—682no—
469C22×C4—1361no—
470C22×C4—1361no—
471C22×C4C2×D6811yescharacteristic
472C22×C4C2×D6811yescharacteristic
473C22×C4C2×D6811yescharacteristic
474C22×C4C2×D6811yescharacteristic
475C22×C4C2×D6811yescharacteristic
476C22×C4C23×D1711yescharacteristic
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8#6325412yes—
489C4⋊C4—172no—
490C4⋊C4—172no—
491C4⋊C4—341no—
492C4⋊C4—341no—
493C4⋊C4—341no—
494C4⋊C4—341no—
495C4⋊C4—341no—
496C4⋊C4—341no—
497C4⋊C4—341no—
498C4⋊C4—341no—
499C4⋊C4—341no—
500C4⋊C4—341no—
501C4⋊C4—341no—
502C4⋊C4—341no—
503C4⋊C4—682no—
504C4⋊C4—682no—
505C4⋊C4—682no—
506C4⋊C4—1361no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—344no—
510C22⋊C4—682no—
511C22⋊C4—682no—
512C22⋊C4—682no—
513C22⋊C4—1361no—
514C22⋊C4—1361no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—682no—
520C42—1361no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—342no—
528C23—681no—
529C23—681no—
530C23—681no—
531C23—681no—
532C23—681no—
533C23—681no—
534C23#1058759012yes—
535C23C22×D6811yescharacteristic
536D4—342no—
537D4—342no—
538D4—688no—
539D4—681no—
540D4—681no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
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—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—342no—
560C2×C4—342no—
561C2×C4—681no—
562C2×C4—681no—
563C2×C4—681no—
564C2×C4—681no—
565C2×C4—681no—
566C2×C4—681no—
567C2×C4—681no—
568C2×C4—681no—
569C2×C4—681no—
570C2×C4—681no—
571C2×C4—681no—
572C2×C4—681no—
573C2×C4—681no—
574C2×C4—681no—
575C2×C4—681no—
576C2×C4—681no—
577C2×C4—681no—
578C2×C4—681no—
579C2×C4—681no—
580C2×C4—1364no—
581C2×C4—1364no—
582C2×C4#1058759412yes—
583C2×C4C2×#6325411yescharacteristic
584C2×C4#1058769111yescharacteristic
585C2×C4#41×D1711yescharacteristic
586C2×C4#41×D1711yescharacteristic
587C2×C4#41×D1711yescharacteristic
588C2×C4#1058769711yescharacteristic
589C8—22no—
590C8—41no—
591C8—41no—
592C8—41no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—682no—
601C22—682no—
602C22—682no—
603C22—1361no—
604C22—1361no—
605C22—1361no—
606C22—1361no—
607C22#1176332111yescharacteristic
608C22#1176345411yescharacteristic
609C22#1176346311yescharacteristic
610C22C2×#1058759011yescharacteristic
611C22C2×#1058759411yescharacteristic
612C22#1176361411yescharacteristic
613C22#1176362611yescharacteristic
614C4—22no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—682no—
620C4—682no—
621C4—1361no—
622C4—1361no—
623C4—1361no—
624C4—1361no—
625C4—1361no—
626C4#1176333811yescharacteristic
627C4#1176340211yescharacteristic
628C4#1176350211yescharacteristic
629C4#1176352611yescharacteristic
630C2—42no—
631C2—1362no—
632C2#1453281811yescharacteristic
633C2#1453883311yescharacteristic
634C2#1453904811yescharacteristic
635C2#1454067311yescharacteristic
636C2#1454092711yescharacteristic
637C2#1454118711yescharacteristic
638C2#1454136911yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#1923C2
socleC23×C17C22×D4
prime radicalC2×#10587616C22
hypercenter#1923D17
hypocenterC17#27033
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. #14533184C2semidirect
3. #14530199C2semidirect
4. #14530171C2semidirect
7. #14529554C2semidirect
8. #14529517C2semidirect
9. #14529377C2semidirect
10. #14529363C2semidirect
11. #14529034C2semidirect
12. #14528974C2semidirect
13. #14528875C2semidirect
14. C4×#10587492C2semidirect
15. C17×#1923C2semidirect
282. #1923D17semidirect
440. C17#27033semidirect

Maximal subgroups

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

subgroupindex
#145331842
#145317982
#145301992
#145301712
#145299742
#145299672
#145295542
#145295172
#145293772
#145293632
#145290342
#145289742
#145288752
C4×#105874922
C17×#19232
#2703317