Finite Group Databasebeta

← #17063409

Subgroups — #17063409

Order 4352.

950 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762850C211yesmaximal, characteristic
2C2×#11762831C211yesmaximal, characteristic
3#14531265C211yesmaximal, characteristic
4D17×#389C211yesmaximal, characteristic
5#14530288C211yesmaximal, characteristic, complemented
6#14530285C211yesmaximal, characteristic, complemented
7#14530284C211yesmaximal, characteristic, complemented
8#14530282C211yesmaximal, characteristic, complemented
9#14530281C211yesmaximal, characteristic, complemented
10#14530278C211yesmaximal, characteristic, complemented
11#14530275C211yesmaximal, characteristic, complemented
12#14528502C211yesmaximal, characteristic
13#14528502C211yesmaximal, characteristic
14#14528502C211yesmaximal, characteristic
15C17×#2086C211yesmaximal, characteristic, complemented
16C22×#63218C2211yescharacteristic
17C22×#63218C2211yescharacteristic
18C2×#10587578C2211yescharacteristic
19C2×#10587578C2211yescharacteristic
20C2×C4⋊C4×D17—21no—
21C2×C4⋊C4×D17C2211yescharacteristic
22C2×C4⋊C4×D17C2211yescharacteristic
23C2×C42×D17C2211yescharacteristic
24#11762850—24no—
25C2×#10587478C2211yescharacteristic
26C2×#10587488C2211yescharacteristic
27C2×#10587479C2211yescharacteristic
28#11762831—24no—
29C2×C4⋊#3622C2211yescharacteristic
30C2×#10587485C2211yescharacteristic
31C2×#10587485C2211yescharacteristic
32#11762708C2211yescharacteristic
33#11762708C2211yescharacteristic
34#11762707C2211yescharacteristic
35#11762707C2211yescharacteristic
36#11762706—21no—
37#11762705C2211yescharacteristic
38#11762705C2211yescharacteristic
39#11762704—21no—
40#11762683—21no—
41#11762680—21no—
42C4⋊C4×Dic17—21no—
43#11762660—21no—
44#95×D17—21no—
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762571C2211yescharacteristic
53#11762571C2211yescharacteristic
54C2×C17×#107C2211yescharacteristic
55C2×C17×C4⋊C8C2211yescharacteristic
56C17×#389C2211yescharacteristic
57C17×#389C2211yescharacteristic
58C17×#340C2211yescharacteristic
59C17×#340C2211yescharacteristic
60C17×#340C2211yescharacteristic
61C22×C4×D17—21no—
62C22×C4×D17—21no—
63C22×C4×D17D411yescharacteristic
64C22×C4×D17D411yescharacteristic
65C22×C4×D17C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C2×C4⋊C4×C17—21no—
69C2×C4⋊C4×C17—21no—
70C2×C4⋊C4×C17C2311yescharacteristic
71C2×C4⋊C4×C17C2311yescharacteristic
72C2×C4⋊C4×C17C2311yescharacteristic
73C2×C4⋊C4×C17C2311yescharacteristic
74C2×C42×C17C2311yescharacteristic
75C2×#63227—21no—
76C2×#63227—21no—
77C2×C4⋊Dic17—21no—
78C2×C4⋊Dic17—21no—
79C2×C4⋊Dic17C2311yescharacteristic
80C2×C4⋊Dic17C2311yescharacteristic
81C2×C4⋊Dic17C2311yescharacteristic
82C2×C4⋊Dic17C2311yescharacteristic
83C2×#63225—21no—
84C2×#63225—21no—
85C2×#63225—21no—
86C2×#63225—21no—
87C2×#63225—21no—
88C2×#63225—21no—
89C2×C4×Dic17—21no—
90C2×C4×Dic17—21no—
91C2×C4×Dic17D411yescharacteristic
92C2×C4×Dic17D411yescharacteristic
93C2×C4×Dic17C2311yescharacteristic
94C22×#3622C2311yescharacteristic
95C22×#3622C2311yescharacteristic
96C2×#63218—22no—
97C2×#63218—22no—
98C2×#63218—22no—
99C2×#63218—22no—
100C2×#63218—22no—
101C2×#63218D414yes—
102#10587578—22no—
103#10587578—22no—
104#10587578—22no—
105#10587578Q814yes—
106C4⋊C4×D17—22no—
107C4⋊C4×D17—22no—
108C4⋊C4×D17—22no—
109C4⋊C4×D17—44no—
110C4⋊C4×D17Q814yes—
111C42×D17—22no—
112C42×D17—22no—
113C17×#107—22no—
114C17×C4⋊C8—22no—
115C17×#95—21no—
116C17×#95—21no—
117#10587502—21no—
118#10587502—21no—
119#10587502—21no—
120#10587502—21no—
121#10587502—21no—
122#10587502—21no—
123#10587488—22no—
124#10587485—22no—
125#10587485—22no—
126#10587479—22no—
127#10587478—22no—
128C4⋊#3622—22no—
129C23×D17C2×D411yescharacteristic
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×C17C2411yescharacteristic
137C22×Dic17—21no—
138C22×Dic17—21no—
139C22×Dic17—21no—
140C22×Dic17—21no—
141C22×Dic17C2×D411yescharacteristic
142C22×Dic17C2×D411yescharacteristic
143C22×Dic17C2×D411yescharacteristic
144C2×C4×D17—22no—
145C2×C4×D17—22no—
146C2×C4×D17—24no—
147C2×C4×D17—22no—
148C2×C4×D17—22no—
149C2×C4×D17—41no—
150C2×C4×D17—41no—
151C2×C4×D17—42no—
152C2×C4×D17—42no—
153C2×C4×D17—42no—
154C2×C4×D17—42no—
155C2×C4×D17—42no—
156C2×C4×D17C2×D412yes—
157C2×C4×D17C2×Q812yes—
158C2×C4×D17C2×Q812yes—
159C2×C4×D17#4112yes—
160C2×C4×D17#4112yes—
161C2×C4×D17#4112yes—
162C2×C8×C17—21no—
163C2×C8×C17—21no—
164C2×C8×C17—21no—
165C2×C8×C17—21no—
166C2×C8×C17—21no—
167C2×C8×C17C2×D412yes—
168C4⋊C4×C17—21no—
169C4⋊C4×C17—21no—
170C4⋊C4×C17—21no—
171C4⋊C4×C17—21no—
172C4⋊C4×C17—21no—
173C4⋊C4×C17—21no—
174C4⋊C4×C17—42no—
175C4⋊C4×C17—42no—
176C4⋊C4×C17C2×Q812yes—
177C4⋊C4×C17C2×Q812yes—
178C42×C17—21no—
179C42×C17—21no—
180#63227—24no—
181#63227—42no—
182C4⋊Dic17—21no—
183C4⋊Dic17—21no—
184C4⋊Dic17—21no—
185C4⋊Dic17—21no—
186C4⋊Dic17—21no—
187C4⋊Dic17—21no—
188C4⋊Dic17—42no—
189C4⋊Dic17—42no—
190C4⋊Dic17C2×Q812yes—
191C4⋊Dic17C2×Q812yes—
192#63225—24no—
193#63225—42no—
194#63225—42no—
195#63225—42no—
196#63225—42no—
197#63225—42no—
198C4×Dic17—21no—
199C4×Dic17—21no—
200C4×Dic17—22no—
201C4×Dic17—22no—
202C4×Dic17—24no—
203C4×Dic17—42no—
204C2×#3622—21no—
205C2×#3622—21no—
206C2×#3622—21no—
207C2×#3622—21no—
208C2×#3622—21no—
209C2×#3622C2×D412yes—
210#63218—28no—
211#63218—44no—
212#23670—171nomaximal, Sylow
213C23×C17C22×D411yescharacteristic
214C22×D17—21no—
215C22×D17—21no—
216C22×D17—21no—
217C22×D17—21no—
218C22×D17#12112yes—
219C22×D17C22⋊Q812yes—
220C22×D17C22⋊Q812yes—
221C2×C4×C17—21no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—22no—
225C2×C4×C17—22no—
226C2×C4×C17—21no—
227C2×C4×C17—21no—
228C2×C4×C17—41no—
229C2×C4×C17—41no—
230C2×C4×C17—41no—
231C2×C4×C17—41no—
232C2×C4×C17—41no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17—41no—
236C2×C4×C17—41no—
237C2×C4×C17—41no—
238C2×C4×C17AGL(1,ℤ/8)12yes—
239C2×C4×C17C22×D411yescharacteristic
240C2×C4×C17C22×Q811yescharacteristic
241C2×C4×C17C22×Q811yescharacteristic
242C2×C4×C17C2×#4111yescharacteristic
243C2×C4×C17C2×#4111yescharacteristic
244C2×C4×C17C2×#4111yescharacteristic
245C2×Dic17—21no—
246C2×Dic17—21no—
247C2×Dic17—21no—
248C2×Dic17—22no—
249C2×Dic17—22no—
250C2×Dic17—21no—
251C2×Dic17—21no—
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#12112yes—
263C2×Dic17C22⋊Q812yes—
264C2×Dic17C22⋊Q812yes—
265C2×Dic17#13712yes—
266C4×D17—44no—
267C4×D17—44no—
268C4×D17—48no—
269C4×D17—84no—
270C4×D17#12314yes—
271C4×D17#12514yes—
272C4×D17#12514yes—
273C4×D17C4⋊Q814yes—
274C8×C17—22no—
275C8×C17—41no—
276#3622—22no—
277#3622—41no—
278C2×#428—171no—
279C2×#423—171no—
280#2296—171no—
281C2×#389—171no—
282#2088—171no—
283#2088—171no—
284#2088—171no—
285#2088—171no—
286#2087—171no—
287#2087—171no—
288#2086—171no—
289#2086D1711yescharacteristic, complemented
290#1736—171no—
291#1736—171no—
292#1736—171no—
293C22×C17C2×#12111yescharacteristic
294C22×C17C2×C22⋊Q811yescharacteristic
295C22×C17C2×C22⋊Q811yescharacteristic
296C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C17C2×#13711yescharacteristic
298C22×C17#57511yescharacteristic
299C22×C17#57511yescharacteristic
300C2×D17—22no—
301C2×D17—22no—
302C2×D17—22no—
303C2×D17—22no—
304C2×D17—22no—
305C2×D17—22no—
306C2×D17#39814yes—
307C4×C17—22no—
308C4×C17—42no—
309C4×C17—42no—
310C4×C17—41no—
311C4×C17—81no—
312C4×C17—81no—
313C4×C17C2×#12311yescharacteristic
314C4×C17C2×#12511yescharacteristic
315C4×C17C2×#12511yescharacteristic
316C4×C17C2×C4⋊Q811yescharacteristic
317Dic17—22no—
318Dic17—42no—
319Dic17—42no—
320Dic17—41no—
321Dic17—81no—
322Dic17—81no—
323Dic17#39814yes—
324C22×M16—171no—
325C22×M16—171no—
326C2×#117—171no—
327C2×#117—171no—
328C22×C4⋊C4—171no—
329C22×C4⋊C4—171no—
330C22×C4⋊C4—341no—
331C22×C42—171no—
332#428—344no—
333C2×#107—171no—
334C2×#107C2×D1711yescharacteristic
335C2×#106—171no—
336C2×#106—171no—
337#423—344no—
338C2×C4⋊C8—171no—
339C2×C4⋊C8—171no—
340C2×C4⋊C8—171no—
341C2×C4⋊C8C2×D1711yescharacteristic
342#389—171no—
343#389—171no—
344#389—171no—
345#389—171no—
346#389—171no—
347#389—171no—
348#389—341no—
349#389—341no—
350#389C2×D1711yescharacteristic
351#389C2×D1711yescharacteristic
352#385—341no—
353#385—341no—
354C4×C4⋊C4—341no—
355C4×C4⋊C4—341no—
356C2×#95—341no—
357#340—171no—
358#340—171no—
359#340—171no—
360#340—171no—
361#340—171no—
362#340—171no—
363#340—171no—
364#340—171no—
365#340—171no—
366#340C2×D1711yescharacteristic
367#340C2×D1711yescharacteristic
368#340C2×D1711yescharacteristic
369C2×C17C2×#39811yescharacteristic
370C2×C17#305511yescharacteristic
371C2×C17#305611yescharacteristic
372C2×C17#307711yescharacteristic
373C2×C17#307811yescharacteristic
374C2×C17#307911yescharacteristic
375C2×C17#308011yescharacteristic
376D17—24no—
377C23×C4—171no—
378C23×C4—171no—
379C23×C4—171no—
380C23×C4—341no—
381C23×C4—341no—
382C2×M16—174no—
383C2×M16—342no—
384C2×M16—342no—
385C2×M16—342no—
386C2×M16—342no—
387C2×M16—342no—
388C22×C8—171no—
389C22×C8—171no—
390C22×C8C22×D1711yescharacteristic
391C22×C8C22×D1711yescharacteristic
392#117—174no—
393#117—342no—
394#117—342no—
395#117—342no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—171no—
399C2×C4⋊C4—171no—
400C2×C4⋊C4—174no—
401C2×C4⋊C4—171no—
402C2×C4⋊C4—171no—
403C2×C4⋊C4—342no—
404C2×C4⋊C4—342no—
405C2×C4⋊C4—342no—
406C2×C4⋊C4—341no—
407C2×C4⋊C4—341no—
408C2×C4⋊C4—341no—
409C2×C4⋊C4—341no—
410C2×C4⋊C4—341no—
411C2×C4⋊C4—341no—
412C2×C4⋊C4—341no—
413C2×C4⋊C4—341no—
414C2×C4⋊C4—684no—
415C2×C4⋊C4C22×D1711yescharacteristic
416C2×C4⋊C4C22×D1711yescharacteristic
417C2×C4⋊C4C22×D1711yescharacteristic
418C2×C4⋊C4C22×D1711yescharacteristic
419C2×C22⋊C4—341no—
420C2×C22⋊C4—341no—
421C2×C42—171no—
422C2×C42—171no—
423C2×C42—171no—
424C2×C42—342no—
425C2×C42—342no—
426C2×C42—341no—
427C2×C42—341no—
428C2×C42C22×D1711yescharacteristic
429#107—22no—
430#107—342no—
431#106—342no—
432#106—342no—
433C4⋊C8—22no—
434C4⋊C8—342no—
435C4⋊C8—342no—
436C4⋊C8—342no—
437#95—21no—
438#95—21no—
439#95—341no—
440#95—341no—
441#95—341no—
442#95—341no—
443#95—341no—
444#95—341no—
445C17#2367011yescharacteristic, complemented, Sylow
446C24—171no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—171no—
452C22×C4—172no—
453C22×C4—172no—
454C22×C4—172no—
455C22×C4—172no—
456C22×C4—172no—
457C22×C4—172no—
458C22×C4—171no—
459C22×C4—171no—
460C22×C4—342no—
461C22×C4—342no—
462C22×C4—342no—
463C22×C4—344no—
464C22×C4—341no—
465C22×C4—341no—
466C22×C4—342no—
467C22×C4—341no—
468C22×C4—341no—
469C22×C4—681no—
470C22×C4—681no—
471C22×C4—682no—
472C22×C4—682no—
473C22×C4—682no—
474C22×C4—682no—
475C22×C4—682no—
476C22×C4D4×D1711yescharacteristic
477C22×C4D4×D1711yescharacteristic
478C22×C4C23×D1711yescharacteristic
479M16—348no—
480M16—684no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—172no—
487C2×C8—341no—
488C2×C8—341no—
489C2×C8—341no—
490C2×C8—341no—
491C2×C8—341no—
492C2×C8D4×D1712yes—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—172no—
502C4⋊C4—172no—
503C4⋊C4—344no—
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—682no—
515C4⋊C4—682no—
516C4⋊C4—682no—
517C4⋊C4Q8×D1712yes—
518C4⋊C4Q8×D1712yes—
519C22⋊C4—344no—
520C22⋊C4—682no—
521C42—21no—
522C42—21no—
523C42—342no—
524C42—342no—
525C42—344no—
526C42—341no—
527C42—341no—
528C42—682no—
529C23—172no—
530C23—172no—
531C23—172no—
532C23—341no—
533C23—341no—
534C23—341no—
535C23—341no—
536C23C2×D4×D1711yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—172no—
555C2×C4—172no—
556C2×C4—172no—
557C2×C4—174no—
558C2×C4—174no—
559C2×C4—174no—
560C2×C4—174no—
561C2×C4—172no—
562C2×C4—341no—
563C2×C4—341no—
564C2×C4—341no—
565C2×C4—342no—
566C2×C4—342no—
567C2×C4—341no—
568C2×C4—341no—
569C2×C4—684no—
570C2×C4—684no—
571C2×C4—688no—
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—1364no—
583C2×C4#1058759712yes—
584C2×C4C2×D4×D1711yescharacteristic
585C2×C4C2×Q8×D1711yescharacteristic
586C2×C4C2×Q8×D1711yescharacteristic
587C2×C4#41×D1711yescharacteristic
588C2×C4#41×D1711yescharacteristic
589C2×C4#41×D1711yescharacteristic
590C8—22no—
591C8—41no—
592C8—342no—
593C8—681no—
594C22—174no—
595C22—342no—
596C22—342no—
597C22—342no—
598C22—342no—
599C22—342no—
600C22—342no—
601C22#121×D1711yescharacteristic
602C22C22⋊Q8×D1711yescharacteristic
603C22C22⋊Q8×D1711yescharacteristic
604C22C2×#1058759711yescharacteristic
605C22#137×D1711yescharacteristic
606C22#1176360611yescharacteristic
607C22#1176360811yescharacteristic
608C4—22no—
609C4—42no—
610C4—42no—
611C4—41no—
612C4—81no—
613C4—81no—
614C4—174no—
615C4—342no—
616C4—682no—
617C4—682no—
618C4—681no—
619C4—1361no—
620C4—1361no—
621C4#123×D1711yescharacteristic
622C4#125×D1711yescharacteristic
623C4#125×D1711yescharacteristic
624C4C4⋊Q8×D1711yescharacteristic
625C2—344no—
626C2D17×#39811yescharacteristic
627C2#1453840011yescharacteristic
628C2#1453841311yescharacteristic
629C2#1453857611yescharacteristic
630C2#1453858711yescharacteristic
631C2#1453859211yescharacteristic
632C2#1453860311yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2086C2
socleC23×C17C22×D4
prime radicalC23×D17C2×D4
hypercenter#2086D17
hypocenterC17#23670
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2086

Complements

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

NH ≅ G/Ntype
5. #14530288C2semidirect
6. #14530285C2semidirect
7. #14530284C2semidirect
8. #14530282C2semidirect
9. #14530281C2semidirect
10. #14530278C2semidirect
11. #14530275C2semidirect
15. C17×#2086C2semidirect
289. #2086D17semidirect
445. C17#23670semidirect

Maximal subgroups

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

subgroupindex
C2×#117628502
C2×#117628312
#145312652
D17×#3892
#145302882
#145302852
#145302842
#145302822
#145302812
#145302782
#145302752
#145285022
C17×#20862
#2367017