Finite Group Databasebeta

← #17064360

Subgroups — #17064360

Order 4352.

836 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
1C4×#10587616C211yesmaximal, characteristic
2#14531182C211yesmaximal, characteristic, complemented
3#14530353C211yesmaximal, characteristic, complemented
4#14530304C211yesmaximal, characteristic, complemented
5#14530267C211yesmaximal, characteristic, complemented
6#14530217C211yesmaximal, characteristic, complemented
7#14530212C211yesmaximal, characteristic, complemented
8#14530199C211yesmaximal, characteristic, complemented
9#14529974C211yesmaximal, characteristic
10#14529967C211yesmaximal, characteristic
11C4×#10587489C211yesmaximal, characteristic, complemented
12C4×#10587488C211yesmaximal, characteristic, complemented
13C4×#10587492C211yesmaximal, characteristic, complemented
14C4×#10587492C211yesmaximal, characteristic, complemented
15C4×C17×C22⋊C8C211yesmaximal, characteristic, complemented
16C2×#10587616C2211yescharacteristic
17C2×C4×D68C2211yescharacteristic
18C2×C4×C22⋊D17—21no—
19C2×#10587489C2211yescharacteristic
20C2×#10587489C2211yescharacteristic
21C2×#10587488C2211yescharacteristic
22C2×#10587488C2211yescharacteristic
23C2×#10587492C2211yescharacteristic
24C2×#10587492C2211yescharacteristic
25C2×#10587492C2211yescharacteristic
26C2×#10587492C2211yescharacteristic
27#11762711C2211yescharacteristic
28#11762707C2211yescharacteristic
29#11762700—21no—
30#11762688—21no—
31#11762677—21no—
32#11762675C2211yescharacteristic
33#11762675C2211yescharacteristic
34#11762672—21no—
35#11762669C2211yescharacteristic
36#11762669C2211yescharacteristic
37#11762669C2211yescharacteristic
38C4×C4⋊Dic17C2211yescharacteristic
39C4×C4⋊Dic17C2211yescharacteristic
40C4×C4⋊Dic17C2211yescharacteristic
41C4×#63227—21no—
42C4×C22⋊Dic17—21no—
43#11762655—21no—
44#11762572C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762572C2211yescharacteristic
51#11762572C2211yescharacteristic
52C22×C42×C17C2211yescharacteristic
53C2×C17×C22⋊C8C2211yescharacteristic
54C2×C17×C22⋊C8C2211yescharacteristic
55C2×C4×C8×C17C2211yescharacteristic
56C2×C4×C8×C17C2211yescharacteristic
57C17×#336C2211yescharacteristic
58C17×#336C2211yescharacteristic
59C23×C4×C17D411yescharacteristic
60C23×C4×C17D411yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C22×C22⋊D17—21no—
63C22×D68C2311yescharacteristic
64C22×C4×D17—21no—
65C22×C8×C17C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C22×C8×C17C2311yescharacteristic
69C2×C42×C17—22no—
70C2×C42×C17—22no—
71C2×C42×C17D411yescharacteristic
72C2×C42×C17D411yescharacteristic
73C2×C42×C17C2311yescharacteristic
74C2×C42×C17C2311yescharacteristic
75C2×C22⋊Dic17—21no—
76C2×C22⋊Dic17—21no—
77C2×C22⋊Dic17—21no—
78#10587616—22no—
79#10587616—22no—
80C4×C22⋊D17—44no—
81C2×#63227—21no—
82C2×#63227—21no—
83C2×#63227—21no—
84C2×#63227—21no—
85C2×C4⋊Dic17C2311yescharacteristic
86C2×C4⋊Dic17C2311yescharacteristic
87C2×C4⋊Dic17C2311yescharacteristic
88C2×C4⋊Dic17C2311yescharacteristic
89C2×C4⋊Dic17C2311yescharacteristic
90C2×C4⋊Dic17C2311yescharacteristic
91C2×C4⋊Dic17C2311yescharacteristic
92C2×#63225—21no—
93C2×C4×Dic17—21no—
94C2×C4×Dic17—21no—
95C2×C4×Dic17—21no—
96C4×D68—22no—
97C4×D68—22no—
98C17×C22⋊C8—22no—
99C17×C22⋊C8—22no—
100C4×C8×C17—22no—
101C4×C8×C17—22no—
102#10587502—21no—
103#10587502—21no—
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—22no—
117#10587489—22no—
118#10587489—22no—
119#10587488—22no—
120#10587488—22no—
121C24×C17C2×D411yescharacteristic
122C23×D17—21no—
123C22×C4×C17—22no—
124C22×C4×C17—22no—
125C22×C4×C17—22no—
126C22×C4×C17—22no—
127C22×C4×C17—22no—
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×C17—41no—
135C22×C4×C17C2×D411yescharacteristic
136C22×C4×C17C2×D411yescharacteristic
137C22×C4×C17C2×D411yescharacteristic
138C22×C4×C17C2×D411yescharacteristic
139C22×C4×C17C2×D411yescharacteristic
140C22×C4×C17C2411yescharacteristic
141C2×C22⋊D17—24no—
142C2×C22⋊D17—42no—
143C2×C22⋊D17—42no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17—21no—
147C22×Dic17—21no—
148C22×Dic17—21no—
149C22×Dic17—21no—
150C22×Dic17—21no—
151C2×D68—21no—
152C2×D68—21no—
153C2×D68—21no—
154C2×D68—21no—
155C2×D68—21no—
156C2×D68#4112yes—
157C2×C4×D17—42no—
158C2×C4×D17—42no—
159C2×C4×D17—42no—
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—21no—
169C2×C8×C17—21no—
170C2×C8×C17#4112yes—
171C2×C8×C17#4112yes—
172C42×C17—22no—
173C42×C17—22no—
174C42×C17—21no—
175C42×C17—21no—
176C42×C17#4112yes—
177C42×C17#4112yes—
178C22⋊Dic17—42no—
179C22⋊Dic17—42no—
180C22⋊Dic17—42no—
181#63227—24no—
182#63227—42no—
183#63227—42no—
184#63227—42no—
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—21no—
194C4⋊Dic17—21no—
195C4⋊Dic17—21no—
196C4⋊Dic17—21no—
197C4⋊Dic17—21no—
198C4⋊Dic17#4112yes—
199#63225—42no—
200C4×Dic17—42no—
201C4×Dic17—42no—
202C4×Dic17—42no—
203#23758—171nomaximal, Sylow
204C23×C17—21no—
205C23×C17—21no—
206C23×C17—21no—
207C23×C17—21no—
208C23×C17—21no—
209C23×C17—21no—
210C23×C17#13512yes—
211C23×C17C22×D411yescharacteristic
212C22×D17—22no—
213C22×D17—41no—
214C22×D17—41no—
215C22×D17—41no—
216C22×D17—41no—
217C22×D17—41no—
218C22×D17—41no—
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—44no—
231C2×C4×C17—41no—
232C2×C4×C17—41no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17—44no—
236C2×C4×C17#12312yes—
237C2×C4×C17#12312yes—
238C2×C4×C17#13512yes—
239C2×C4×C17AGL(1,ℤ/8)12yes—
240C2×C4×C17C2×#4111yescharacteristic
241C2×C4×C17C2×#4111yescharacteristic
242C2×C4×C17C2×#4111yescharacteristic
243C2×C4×C17C2×#4111yescharacteristic
244C2×C4×C17C2×#4111yescharacteristic
245C2×C4×C17C2×#4111yescharacteristic
246C22⋊D17—48no—
247C2×Dic17—22no—
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—41no—
267C2×Dic17—41no—
268D68—22no—
269D68—22no—
270D68—41no—
271D68—41no—
272C4×D17—84no—
273C8×C17—22no—
274C8×C17—22no—
275C8×C17—41no—
276C8×C17—41no—
277C4×#121—171no—
278#2283—171no—
279#2101—171no—
280#2092—171no—
281#2085—171no—
282#2077—171no—
283#2076—171no—
284#2073—171no—
285#2034—171no—
286#2033—171no—
287C4×#107—171no—
288C4×#106—171no—
289C4×#102—171no—
290C4×#102—171no—
291C4×C22⋊C8D1711yescharacteristic, complemented
292C22×C17—22no—
293C22×C17—22no—
294C22×C17—22no—
295C22×C17—41no—
296C22×C17—41no—
297C22×C17—41no—
298C22×C17—41no—
299C22×C17C2×#12311yescharacteristic
300C22×C17#52511yescharacteristic
301C22×C17#53211yescharacteristic
302C22×C17C2×#13511yescharacteristic
303C22×C17C2×#13511yescharacteristic
304C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
305C22×C17#57511yescharacteristic
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—41no—
315C4×C17—41no—
316C4×C17—41no—
317C4×C17#48214yes—
318C4×C17#52911yescharacteristic
319C4×C17#52911yescharacteristic
320C4×C17#52911yescharacteristic
321C4×C17#52911yescharacteristic
322Dic17—42no—
323Dic17—81no—
324Dic17—81no—
325Dic17—81no—
326Dic17—81no—
327Dic17—81no—
328Dic17—81no—
329C2×#121—171no—
330C2×C4×D4—171no—
331C2×C4×D4—341no—
332C22×C42C2×D1711yescharacteristic
333C2×#107—171no—
334C2×#107—171no—
335C2×#106—171no—
336C2×#106—171no—
337C2×#102—171no—
338C2×#102—171no—
339C2×#102—171no—
340C2×#102—171no—
341C2×C22⋊C8C2×D1711yescharacteristic
342C2×C22⋊C8C2×D1711yescharacteristic
343C2×C4×C8C2×D1711yescharacteristic
344C2×C4×C8C2×D1711yescharacteristic
345#390—171no—
346#389—171no—
347#388—341no—
348#386—341no—
349#383—341no—
350#382—171no—
351#382—171no—
352#381—341no—
353#380—171no—
354#380—171no—
355#380—171no—
356C4×C4⋊C4—171no—
357C4×C4⋊C4—171no—
358C4×C4⋊C4—171no—
359C4×C22⋊C4—341no—
360C4×C22⋊C4—341no—
361#376—341no—
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#336C2×D1711yescharacteristic
371#336C2×D1711yescharacteristic
372C2×C17—42no—
373C2×C17#239511yescharacteristic
374C2×C17C2×#48211yescharacteristic
375C2×C17#309111yescharacteristic
376C2×C17#310211yescharacteristic
377C2×C17#310511yescharacteristic
378C2×C17#316811yescharacteristic
379C2×C17#317111yescharacteristic
380D17—82no—
381C22×D4—171no—
382C22×D4—341no—
383C23×C4—341no—
384C23×C4D6811yescharacteristic
385C23×C4D6811yescharacteristic
386C23×C4C22×D1711yescharacteristic
387C22×C8C22×D1711yescharacteristic
388C22×C8C22×D1711yescharacteristic
389C22×C8C22×D1711yescharacteristic
390C22×C8C22×D1711yescharacteristic
391#121—342no—
392#121—342no—
393C4×D4—342no—
394C4×D4—342no—
395C4×D4—684no—
396C2×C4⋊C4—171no—
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—341no—
404C2×C22⋊C4—341no—
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×C42—22no—
412C2×C42—22no—
413C2×C42—341no—
414C2×C42—341no—
415C2×C42—341no—
416C2×C42D6811yescharacteristic
417C2×C42D6811yescharacteristic
418C2×C42C22×D1711yescharacteristic
419C2×C42C22×D1711yescharacteristic
420#107—342no—
421#107—342no—
422#106—342no—
423#106—342no—
424#102—342no—
425#102—342no—
426#102—342no—
427#102—342no—
428C22⋊C8—22no—
429C22⋊C8—22no—
430C4×C8—22no—
431C4×C8—22no—
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#95—341no—
443C17#2375811yescharacteristic, complemented, Sylow
444C24—341no—
445C24C2×D6811yescharacteristic
446C2×D4—172no—
447C2×D4—344no—
448C2×D4—341no—
449C2×D4—341no—
450C2×D4—341no—
451C2×D4—341no—
452C2×D4—341no—
453C2×D4—682no—
454C2×D4—682no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—41no—
467C22×C4—341no—
468C22×C4—341no—
469C22×C4—341no—
470C22×C4—341no—
471C22×C4—341no—
472C22×C4—341no—
473C22×C4—341no—
474C22×C4—682no—
475C22×C4—682no—
476C22×C4—682no—
477C22×C4C2×D6811yescharacteristic
478C22×C4C2×D6811yescharacteristic
479C22×C4C2×D6811yescharacteristic
480C22×C4C2×D6811yescharacteristic
481C22×C4C2×D6811yescharacteristic
482C22×C4C23×D1711yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
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#6325212yes—
494C2×C8#6325212yes—
495C4⋊C4—172no—
496C4⋊C4—341no—
497C4⋊C4—341no—
498C4⋊C4—341no—
499C4⋊C4—341no—
500C4⋊C4—341no—
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—682no—
510C22⋊C4—344no—
511C22⋊C4—682no—
512C22⋊C4—682no—
513C22⋊C4—682no—
514C22⋊C4—682no—
515C22⋊C4—682no—
516C22⋊C4—682no—
517C42—21no—
518C42—21no—
519C42—22no—
520C42—22no—
521C42—682no—
522C42—682no—
523C42—682no—
524C42#6325412yes—
525C42#6325412yes—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—342no—
533C23—681no—
534C23—681no—
535C23—681no—
536C23—681no—
537C23—681no—
538C23—681no—
539C23#1058759012yes—
540C23C22×D6811yescharacteristic
541D4—342no—
542D4—342no—
543D4—688no—
544D4—681no—
545D4—681no—
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—44no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—44no—
563C2×C4—342no—
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—681no—
581C2×C4—681no—
582C2×C4—681no—
583C2×C4—681no—
584C2×C4—1364no—
585C2×C4#1058757212yes—
586C2×C4#1058757212yes—
587C2×C4#1058759012yes—
588C2×C4#1058759412yes—
589C2×C4C2×#6325211yescharacteristic
590C2×C4C2×#6325211yescharacteristic
591C2×C4C2×#6325411yescharacteristic
592C2×C4C2×#6325411yescharacteristic
593C2×C4#41×D1711yescharacteristic
594C2×C4#41×D1711yescharacteristic
595C8—22no—
596C8—22no—
597C8—41no—
598C8—41no—
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—
613C22C2×#1058757211yescharacteristic
614C22#1176332111yescharacteristic
615C22#1176335911yescharacteristic
616C22C2×#1058759011yescharacteristic
617C22C2×#1058759011yescharacteristic
618C22C2×#1058759411yescharacteristic
619C22#1176360911yescharacteristic
620C4—22no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—682no—
625C4—1361no—
626C4—1361no—
627C4—1361no—
628C4—1361no—
629C4—1361no—
630C4—1361no—
631C4#1176313414yes—
632C4#1176333911yescharacteristic
633C4#1176333911yescharacteristic
634C4#1176334111yescharacteristic
635C4#1176334111yescharacteristic
636C2—42no—
637C2—1362no—
638C2#1453204411yescharacteristic
639C2C2×#1176313411yescharacteristic
640C2#1453869911yescharacteristic
641C2#1453880411yescharacteristic
642C2#1453883311yescharacteristic
643C2#1453935411yescharacteristic
644C2#1453937911yescharacteristic
subgroupG/H
centerC22×C4C2×D68
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC4×C17×C22⋊C8C2
socleC23×C17C22×D4
prime radicalC2×#10587616C22
hypercenterC4×C22⋊C8D17
hypocenterC17#23758
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #14531182C2semidirect
3. #14530353C2semidirect
4. #14530304C2semidirect
5. #14530267C2semidirect
6. #14530217C2semidirect
7. #14530212C2semidirect
8. #14530199C2semidirect
11. C4×#10587489C2semidirect
12. C4×#10587488C2semidirect
13. C4×#10587492C2semidirect
14. C4×#10587492C2semidirect
15. C4×C17×C22⋊C8C2semidirect
291. C4×C22⋊C8D17semidirect
443. C17#23758semidirect

Maximal subgroups

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

subgroupindex
C4×#105876162
#145311822
#145303532
#145303042
#145302672
#145302172
#145302122
#145301992
#145299742
#145299672
C4×#105874892
C4×#105874882
C4×#105874922
C4×C17×C22⋊C82
#2375817