Finite Group Databasebeta

← #17102443

Subgroups — #17102443

Order 4352.

764 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#14533158C211yesmaximal, characteristic
2#14531787C211yesmaximal, characteristic
3#14530107C211yesmaximal, characteristic, complemented
4#14529988C211yesmaximal, characteristic
5#14529926C211yesmaximal, characteristic, complemented
6#14529794C211yesmaximal, characteristic
7#14529731C211yesmaximal, characteristic, complemented
8#14529460C211yesmaximal, characteristic, complemented
9#14529426C211yesmaximal, characteristic, complemented
10#14529377C211yesmaximal, characteristic, complemented
11#14529124C211yesmaximal, characteristic, complemented
12#14529089C211yesmaximal, characteristic
13#14528875C211yesmaximal, characteristic
14C4×#10587487C211yesmaximal, characteristic, complemented
15C17×#1923C211yesmaximal, characteristic
16C22×Dic68C2211yescharacteristic
17C2×#10587555C2211yescharacteristic
18C2×#10587610C2211yescharacteristic
19C2×#10587610C2211yescharacteristic
20C2×C4×Dic34C2211yescharacteristic
21C22×C4⋊Dic17C2211yescharacteristic
22C2×#10587489C2211yescharacteristic
23C2×#10587487C2211yescharacteristic
24C2×#10587487C2211yescharacteristic
25C2×#10587487C2211yescharacteristic
26C2×#10587487C2211yescharacteristic
27C2×#10587487C2211yescharacteristic
28C2×#10587487C2211yescharacteristic
29#11762751—21no—
30#11762721—21no—
31#11762715C2211yescharacteristic
32#11762715C2211yescharacteristic
33#11762715C2211yescharacteristic
34#11762713—21no—
35#11762707C2211yescharacteristic
36#11762706—21no—
37#11762702—21no—
38#11762696—21no—
39#11762681—21no—
40#11762669C2211yescharacteristic
41C4×C4⋊Dic17C2211yescharacteristic
42C4×C4⋊Dic17C2211yescharacteristic
43C22⋊C4×Dic17—21no—
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
60C23×Dic17—21no—
61C22×Dic34—21no—
62C22×Dic34C2311yescharacteristic
63C22×Dic34C2311yescharacteristic
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—
74C2×C22⋊Dic17—21no—
75C2×C4⋊Dic17—21no—
76C2×C4⋊Dic17—21no—
77C2×C4⋊Dic17—22no—
78C2×C4⋊Dic17—41no—
79C2×C4⋊Dic17C2311yescharacteristic
80C2×C4⋊Dic17C2311yescharacteristic
81C2×C4⋊Dic17C2311yescharacteristic
82C2×C4⋊Dic17C2311yescharacteristic
83C2×C4⋊Dic17C2311yescharacteristic
84C2×C4⋊Dic17C2311yescharacteristic
85#10587610—22no—
86#10587610—22no—
87#10587610—22no—
88#10587610—41no—
89C2×#63225—21no—
90C2×#63225—21no—
91C2×#63225—21no—
92C2×#63225—21no—
93C2×C4×Dic17—21no—
94C2×C4×Dic17—21no—
95C2×C4×Dic17—21no—
96C2×Dic68—22no—
97C2×Dic68—41no—
98C2×Dic68—41no—
99#10587555—22no—
100#10587555—41no—
101C4×Dic34—22no—
102C4×Dic34—41no—
103C17×C4⋊C8—41no—
104C17×C22⋊C8—41no—
105C17×C22⋊C8—41no—
106C4×C8×C17—41no—
107C17×#95D411yescharacteristic
108C17×#95D411yescharacteristic
109#10587502—21no—
110#10587502—21no—
111#10587502—21no—
112#10587502—21no—
113#10587502—21no—
114#10587502—21no—
115#10587502—21no—
116#10587502—21no—
117#10587502—21no—
118#10587502—21no—
119#10587489—22no—
120#10587487—22no—
121#10587487—22no—
122#10587487—22no—
123#10587487—22no—
124#10587487—41no—
125#10587487—41no—
126C24×C17C2×D411yescharacteristic
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×C17C2×D411yescharacteristic
134C22×C4×C17C2×D411yescharacteristic
135C22×C4×C17C2×D411yescharacteristic
136C22×C4×C17C2×D411yescharacteristic
137C22×C4×C17C2×D411yescharacteristic
138C22×C4×C17C2411yescharacteristic
139C22×Dic17—21no—
140C22×Dic17—21no—
141C22×Dic17—21no—
142C22×Dic17—21no—
143C22×Dic17—21no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17—21no—
147C22×Dic17—42no—
148C22×Dic17—42no—
149C22×Dic17—81no—
150C2×Dic34—21no—
151C2×Dic34—21no—
152C2×Dic34—21no—
153C2×Dic34—21no—
154C2×Dic34—21no—
155C2×Dic34—21no—
156C2×Dic34—21no—
157C2×Dic34—21no—
158C2×Dic34—21no—
159C2×Dic34—21no—
160C2×Dic34—21no—
161C2×Dic34—42no—
162C2×Dic34—42no—
163C2×Dic34—81no—
164C2×Dic34#4112yes—
165C2×C8×C17—21no—
166C2×C8×C17—21no—
167C2×C8×C17—21no—
168C2×C8×C17—21no—
169C2×C8×C17—21no—
170C2×C8×C17—21no—
171C2×C8×C17—21no—
172C2×C8×C17—21no—
173C2×C8×C17—21no—
174C2×C8×C17—21no—
175C2×C8×C17—21no—
176C2×C8×C17—21no—
177C22⋊C4×C17—41no—
178C22⋊C4×C17Q1614yescomplemented
179C42×C17—21no—
180C42×C17—21no—
181C42×C17—21no—
182C42×C17—21no—
183C22⋊Dic17—24no—
184C22⋊Dic17—42no—
185C22⋊Dic17—81no—
186C4⋊Dic17—21no—
187C4⋊Dic17—21no—
188C4⋊Dic17—21no—
189C4⋊Dic17—21no—
190C4⋊Dic17—21no—
191C4⋊Dic17—21no—
192C4⋊Dic17—21no—
193C4⋊Dic17—21no—
194C4⋊Dic17—21no—
195C4⋊Dic17—42no—
196C4⋊Dic17—42no—
197C4⋊Dic17#4112yes—
198C4⋊Dic17#4112yes—
199C4⋊Dic17#4112yes—
200#63225—24no—
201#63225—42no—
202#63225—42no—
203#63225—81no—
204C4×Dic17—42no—
205C4×Dic17—81no—
206C4×Dic17—81no—
207Dic68—44no—
208#26726—171nomaximal, Sylow
209C23×C17—21no—
210C23×C17—21no—
211C23×C17—21no—
212C23×C17—21no—
213C23×C17—21no—
214C23×C17—21no—
215C23×C17C2×Q1612yes—
216C23×C17C22×D411yescharacteristic
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—41no—
231C2×C4×C17—41no—
232C2×C4×C17—41no—
233C2×C4×C17—41no—
234C2×C4×C17C2×Q1612yes—
235C2×C4×C17C2×Q1612yes—
236C2×C4×C17C2×#4111yescharacteristic
237C2×C4×C17C2×#4111yescharacteristic
238C2×C4×C17C2×#4111yescharacteristic
239C2×C4×C17C2×#4111yescharacteristic
240C2×C4×C17H(5,𝔽2)11yescharacteristic
241C2×C4×C17H(5,𝔽2)11yescharacteristic
242C2×Dic17—22no—
243C2×Dic17—22no—
244C2×Dic17—22no—
245C2×Dic17—22no—
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—41no—
265C2×Dic17—41no—
266C2×Dic17—84no—
267Dic34—22no—
268Dic34—22no—
269Dic34—41no—
270Dic34—41no—
271Dic34—41no—
272Dic34—41no—
273Dic34—41no—
274Dic34—41no—
275Dic34—84no—
276C8×C17—41no—
277C8×C17—41no—
278C8×C17—41no—
279C8×C17—41no—
280#2492—171no—
281#2360—171no—
282#2056—171no—
283#2036—171no—
284#2024—171no—
285#2001—171no—
286#1987—171no—
287#1933—171no—
288#1928—171no—
289#1923D1711yescharacteristic
290#1921—171no—
291#1878—171no—
292#1872—171no—
293#1824—171no—
294C4×#103—171no—
295C22×C17—22no—
296C22×C17—22no—
297C22×C17—22no—
298C22×C17—41no—
299C22×C17—41no—
300C22×C17—41no—
301C22×C17—41no—
302C22×C17#52511yescharacteristic
303C22×C17#54611yescharacteristic
304C22×C17#54611yescharacteristic
305C22×C17C22×Q1611yescharacteristic
306C22×C17#57511yescharacteristic
307C22×C17#57711yescharacteristic
308C22×C17#57711yescharacteristic
309C4×C17—22no—
310C4×C17—22no—
311C4×C17—41no—
312C4×C17—41no—
313C4×C17—41no—
314C4×C17#52911yescharacteristic
315C4×C17#53811yescharacteristic
316C4×C17#55511yescharacteristic
317C4×C17#55911yescharacteristic
318Dic17—42no—
319Dic17—42no—
320Dic17—42no—
321Dic17—42no—
322Dic17—81no—
323Dic17—81no—
324Dic17—81no—
325Dic17—81no—
326C22×Q16—171no—
327C2×C4⋊Q8—171no—
328C2×C22⋊Q8—171no—
329C2×C22⋊Q8—171no—
330C2×C4×Q8—171no—
331C22×C4⋊C4—171no—
332C2×#107—171no—
333C2×C4⋊C8C2×D1711yescharacteristic
334C2×#103—171no—
335C2×#103—171no—
336C2×#103—171no—
337C2×#103—171no—
338C2×#103—171no—
339C2×#103—171no—
340C2×C22⋊C8C2×D1711yescharacteristic
341C2×C22⋊C8C2×D1711yescharacteristic
342C2×C4×C8C2×D1711yescharacteristic
343#400—341no—
344#393—341no—
345#391—171no—
346#391—171no—
347#391—171no—
348#391—341no—
349#389—171no—
350#389—341no—
351#388—341no—
352#387—341no—
353#385—341no—
354#380—171no—
355C4×C4⋊C4—171no—
356C4×C4⋊C4—171no—
357C4×C22⋊C4—341no—
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#245911yescharacteristic
371C2×C17#310411yescharacteristic
372C2×C17#312511yescharacteristic
373C2×C17#329911yescharacteristic
374C2×C17#329911yescharacteristic
375C2×C17#331111yescharacteristic
376C2×C17#332311yescharacteristic
377C22×Q8—171no—
378C22×Q8—171no—
379C22×Q8—341no—
380C23×C4—341no—
381C23×C4C22×D1711yescharacteristic
382C2×Q16—342no—
383C2×Q16—681no—
384C2×Q16—681no—
385C22×C8C22×D1711yescharacteristic
386C22×C8C22×D1711yescharacteristic
387C22×C8C22×D1711yescharacteristic
388C22×C8C22×D1711yescharacteristic
389C4⋊Q8—342no—
390C4⋊Q8—681no—
391C22⋊Q8—342no—
392C22⋊Q8—342no—
393C22⋊Q8—342no—
394C22⋊Q8—681no—
395C4×Q8—342no—
396C4×Q8—681no—
397C2×C4⋊C4—171no—
398C2×C4⋊C4—171no—
399C2×C4⋊C4—171no—
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—341no—
407C2×C4⋊C4—341no—
408C2×C4⋊C4—341no—
409C2×C4⋊C4—341no—
410C2×C4⋊C4—681no—
411C2×C22⋊C4—341no—
412C2×C22⋊C4—341no—
413C2×C22⋊C4—341no—
414C2×C22⋊C4D6811yescharacteristic
415C2×C22⋊C4D6811yescharacteristic
416C2×C42—341no—
417C2×C42—341no—
418C2×C42—341no—
419C2×C42C22×D1711yescharacteristic
420C2×C42C22×D1711yescharacteristic
421#107—342no—
422C4⋊C8—41no—
423#103—342no—
424#103—342no—
425#103—342no—
426#103—342no—
427#103—681no—
428#103—681no—
429C22⋊C8—41no—
430C22⋊C8—41no—
431C4×C8—41no—
432#95—341no—
433#95—341no—
434#95—341no—
435#95—341no—
436#95—341no—
437#95—341no—
438#95—341no—
439#95—341no—
440#95—341no—
441#95—341no—
442#95D6811yescharacteristic
443#95D6811yescharacteristic
444C17#2672611yescharacteristic, complemented, Sylow
445C24C2×D6811yescharacteristic
446C2×Q8—172no—
447C2×Q8—341no—
448C2×Q8—341no—
449C2×Q8—341no—
450C2×Q8—341no—
451C2×Q8—341no—
452C2×Q8—341no—
453C2×Q8—341no—
454C2×Q8—341no—
455C2×Q8—341no—
456C2×Q8—341no—
457C2×Q8—341no—
458C2×Q8—682no—
459C2×Q8—682no—
460C2×Q8—1361no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—341no—
468C22×C4—341no—
469C22×C4—341no—
470C22×C4—341no—
471C22×C4—341no—
472C22×C4—341no—
473C22×C4—341no—
474C22×C4—341no—
475C22×C4—682no—
476C22×C4—682no—
477C22×C4—1361no—
478C22×C4C2×D6811yescharacteristic
479C22×C4C2×D6811yescharacteristic
480C22×C4C2×D6811yescharacteristic
481C22×C4C2×D6811yescharacteristic
482C22×C4C2×D6811yescharacteristic
483C22×C4C23×D1711yescharacteristic
484Q16—684no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C4⋊C4—172no—
498C4⋊C4—172no—
499C4⋊C4—172no—
500C4⋊C4—344no—
501C4⋊C4—341no—
502C4⋊C4—341no—
503C4⋊C4—341no—
504C4⋊C4—341no—
505C4⋊C4—341no—
506C4⋊C4—341no—
507C4⋊C4—341no—
508C4⋊C4—341no—
509C4⋊C4—341no—
510C4⋊C4—682no—
511C4⋊C4—682no—
512C4⋊C4—682no—
513C4⋊C4—682no—
514C4⋊C4—1361no—
515C22⋊C4—41no—
516C22⋊C4—344no—
517C22⋊C4—682no—
518C22⋊C4—1361no—
519C22⋊C4Dic6814yescomplemented
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—682no—
525C42—1361no—
526C42—1361no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23C2×Dic6812yes—
534C23C22×D6811yescharacteristic
535Q8—342no—
536Q8—342no—
537Q8—681no—
538Q8—681no—
539Q8—681no—
540Q8—681no—
541Q8—681no—
542Q8—681no—
543Q8—1364no—
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—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—342no—
562C2×C4—342no—
563C2×C4—342no—
564C2×C4—342no—
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—681no—
581C2×C4—681no—
582C2×C4—681no—
583C2×C4—681no—
584C2×C4—681no—
585C2×C4—1364no—
586C2×C4C2×Dic6812yes—
587C2×C4C2×Dic6812yes—
588C2×C4#1058769111yescharacteristic
589C2×C4#1058769111yescharacteristic
590C2×C4#41×D1711yescharacteristic
591C2×C4#41×D1711yescharacteristic
592C2×C4#41×D1711yescharacteristic
593C2×C4#41×D1711yescharacteristic
594C8—41no—
595C8—41no—
596C8—41no—
597C8—41no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22#1176332111yescharacteristic
606C22#1176345411yescharacteristic
607C22#1176345411yescharacteristic
608C22C22×Dic6811yescharacteristic
609C22#1176360911yescharacteristic
610C22#1176362111yescharacteristic
611C22#1176362111yescharacteristic
612C4—22no—
613C4—22no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—682no—
618C4—682no—
619C4—682no—
620C4—682no—
621C4—1361no—
622C4—1361no—
623C4—1361no—
624C4—1361no—
625C4#1176334211yescharacteristic
626C4#1176339111yescharacteristic
627C4#1176352111yescharacteristic
628C4#1176354311yescharacteristic
629C2—42no—
630C2#1453271911yescharacteristic
631C2#1453882411yescharacteristic
632C2#1453906311yescharacteristic
633C2#1454066111yescharacteristic
634C2#1454066111yescharacteristic
635C2#1454082211yescharacteristic
636C2#1454100211yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#1923C2
socleC23×C17C22×D4
prime radicalC24×C17C2×D4
hypercenter#1923D17
hypocenterC17#26726
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
3. #14530107C2semidirect
5. #14529926C2semidirect
7. #14529731C2semidirect
8. #14529460C2semidirect
9. #14529426C2semidirect
10. #14529377C2semidirect
11. #14529124C2semidirect
14. C4×#10587487C2semidirect
178. C22⋊C4×C17Q16semidirect
444. C17#26726semidirect
519. C22⋊C4Dic68semidirect

Maximal subgroups

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

subgroupindex
#145331582
#145317872
#145301072
#145299882
#145299262
#145297942
#145297312
#145294602
#145294262
#145293772
#145291242
#145290892
#145288752
C4×#105874872
C17×#19232
#2672617