Finite Group Databasebeta

← #17056415

Subgroups — #17056415

Order 4352.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538572C211yesmaximal, characteristic
2#14537727C211yesmaximal, characteristic, complemented
3#14529764C211yesmaximal, characteristic, complemented
4#14529557C211yesmaximal, characteristic, complemented
5#14529534C211yesmaximal, characteristic, complemented
6#14529529C211yesmaximal, characteristic, complemented
7#14529380C211yesmaximal, characteristic, complemented
8#14529380C211yesmaximal, characteristic, complemented
9#14529059C211yesmaximal, characteristic
10#14529059C211yesmaximal, characteristic
11#14528643C211yesmaximal, characteristic, complemented
12#14528626C211yesmaximal, characteristic
13#14528619C211yesmaximal, characteristic
14#14528594C211yesmaximal, characteristic
15C17×#2906C211yesmaximal, characteristic
16#11763366C2211yescharacteristic
17#11763116C411yescharacteristic, complemented
18#11763116C411yescharacteristic, complemented
19#11763109C411yescharacteristic, complemented
20#11763109C411yescharacteristic, complemented
21#11763104C411yescharacteristic, complemented
22#11763099C411yescharacteristic, complemented
23#11763094C411yescharacteristic, complemented
24#11763089C411yescharacteristic, complemented
25#11762938—21no—
26#11762938—21no—
27#11762936—21no—
28#11762933—21no—
29C2×#10587493C2211yescharacteristic
30C2×#10587493C2211yescharacteristic
31#11762845C2211yescharacteristic
32#11762845C2211yescharacteristic
33#11762835C2211yescharacteristic
34#11762835C2211yescharacteristic
35C2×C4⋊#3622C2211yescharacteristic
36C2×#10587508C2211yescharacteristic
37C2×#10587508C2211yescharacteristic
38#11762805C2211yescharacteristic
39#11762805C2211yescharacteristic
40#11762764C2211yescharacteristic
41#11762764C2211yescharacteristic
42C4×#63223C2211yescharacteristic
43C2×#10587486C2211yescharacteristic
44C2×C8×Dic17C2211yescharacteristic
45#11762655C2211yescharacteristic
46#11762573C2211yescharacteristic
47#11762573C2211yescharacteristic
48#11762570C2211yescharacteristic
49#11762570C2211yescharacteristic
50#11762570C2211yescharacteristic
51#11762570C2211yescharacteristic
52#11762568C2211yescharacteristic
53#11762568C2211yescharacteristic
54#11762563C2211yescharacteristic
55#11762563C2211yescharacteristic
56C2×C17×#131C2211yescharacteristic
57C2×C17×#131C2211yescharacteristic
58C4×#41×C17C2211yescharacteristic
59C17×#424—21no—
60C17×#424—21no—
61C17×#424C2211yescharacteristic
62C17×#424C2211yescharacteristic
63C17×#423—21no—
64C17×#423C2211yescharacteristic
65C2×C17×C4⋊C8—21no—
66C2×C17×C4⋊C8C2211yescharacteristic
67C2×#41×C17C2311yescharacteristic
68C17×#131—22no—
69C17×#131—22no—
70C17×#131—41no—
71C17×#131—41no—
72C2×M16×C17—21no—
73C2×M16×C17—21no—
74C2×M16×C17C2311yescharacteristic
75C2×M16×C17C2311yescharacteristic
76C22×C8×C17—21no—
77C22×C8×C17—21no—
78C22×C8×C17C2311yescharacteristic
79C22×C8×C17C2311yescharacteristic
80C4×Q8×C17C2×C411yescharacteristic
81C4×Q8×C17C2×C411yescharacteristic
82C4×D4×C17—21no—
83C4×D4×C17—21no—
84C4×D4×C17C2×C411yescharacteristic
85C4×D4×C17C2×C411yescharacteristic
86C17×#117—21no—
87C17×#117C2311yescharacteristic
88C2×C42×C17—21no—
89C2×C42×C17C2311yescharacteristic
90#10587612C2311yescharacteristic
91#10587612C2311yescharacteristic
92#10587610—21no—
93#10587610—21no—
94C2×C4×Dic17C2311yescharacteristic
95C2×C4×Dic17C2311yescharacteristic
96C2×#63223C2311yescharacteristic
97C2×#63223C2311yescharacteristic
98C22×#3622C2311yescharacteristic
99C22×#3622C2311yescharacteristic
100#10587556C2×C411yescharacteristic
101#10587556C2×C411yescharacteristic
102#10587555C2×C411yescharacteristic
103#10587555C2×C411yescharacteristic
104C4×Dic34—21no—
105C4×Dic34—21no—
106C17×C4⋊C8—21no—
107C17×C4⋊C8—21no—
108C17×C4⋊C8—21no—
109C17×C4⋊C8—21no—
110C17×C4⋊C8—21no—
111C17×C4⋊C8—21no—
112C17×C4⋊C8D411yescharacteristic
113C17×C4⋊C8D411yescharacteristic
114C17×C4⋊C8D411yescharacteristic
115C17×C4⋊C8D411yescharacteristic
116#10587508—22no—
117#10587508Q814yescomplemented
118#10587506C2×C411yescharacteristic
119#10587506C2×C411yescharacteristic
120#10587506C2×C411yescharacteristic
121#10587506C2×C411yescharacteristic
122#10587503C2×C411yescharacteristic
123#10587503C2×C411yescharacteristic
124#10587503C2×C411yescharacteristic
125#10587503C2×C411yescharacteristic
126#10587502—21no—
127#10587502—21no—
128#10587493—41no—
129#10587493—41no—
130#10587486—21no—
131#10587486—21no—
132#10587486—41no—
133#10587485—21no—
134#10587485—21no—
135#10587485—21no—
136#10587485—21no—
137C8×Dic17—21no—
138C8×Dic17—21no—
139C8×Dic17—41no—
140#10587479C2×C411yescharacteristic
141#10587479C2×C411yescharacteristic
142#10587479C2×C411yescharacteristic
143#10587479C2×C411yescharacteristic
144#10587478C2×C411yescharacteristic
145#10587478C2×C411yescharacteristic
146#10587478C2×C411yescharacteristic
147#10587478C2×C411yescharacteristic
148C4⋊#3622C2×C411yescharacteristic
149C4⋊#3622C2×C411yescharacteristic
150C4⋊#3622C2×C411yescharacteristic
151C4⋊#3622C2×C411yescharacteristic
152#10587474—21no—
153C4×#3622—21no—
154#41×C17—21no—
155#41×C17—21no—
156#41×C17C2×Q812yes—
157#41×C17#4112yes—
158C2×Q8×C17C22×C411yescharacteristic
159C2×D4×C17—21no—
160C2×D4×C17C22×C411yescharacteristic
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17#4111yescharacteristic
165C22×C4×C17#4111yescharacteristic
166C22×C4×C17C2411yescharacteristic
167C22×Dic17—21no—
168C22×Dic17—21no—
169C2×Dic34—21no—
170C2×Dic34—21no—
171M16×C17—21no—
172M16×C17—21no—
173M16×C17—21no—
174M16×C17—21no—
175M16×C17—42no—
176M16×C17—42no—
177C2×C8×C17—21no—
178C2×C8×C17—21no—
179C2×C8×C17—21no—
180C2×C8×C17—21no—
181C2×C8×C17—21no—
182C2×C8×C17—21no—
183C2×C8×C17—42no—
184C2×C8×C17—42no—
185C2×C8×C17C2×D411yescharacteristic
186C2×C8×C17C2×D411yescharacteristic
187C2×C8×C17C2×D411yescharacteristic
188C2×C8×C17C2×D411yescharacteristic
189C4⋊C4×C17—21no—
190C4⋊C4×C17—21no—
191C4⋊C4×C17C22×C411yescharacteristic
192C4⋊C4×C17C22×C411yescharacteristic
193C22⋊C4×C17—21no—
194C22⋊C4×C17—21no—
195C22⋊C4×C17—21no—
196C42×C17—21no—
197C42×C17—21no—
198C42×C17—21no—
199C42×C17C22×C411yescharacteristic
200C42×C17C22×C411yescharacteristic
201C42×C17C2×D411yescharacteristic
202C42×C17C2×D411yescharacteristic
203C22⋊Dic17—21no—
204C22⋊Dic17—21no—
205C4⋊Dic17—21no—
206C4⋊Dic17—21no—
207C4⋊Dic17C22×C411yescharacteristic
208C4⋊Dic17C22×C411yescharacteristic
209C4⋊Dic17C22×C411yescharacteristic
210C4⋊Dic17C22×C411yescharacteristic
211#63225—21no—
212#63225—21no—
213#63225—21no—
214#63225—21no—
215C4×Dic17—21no—
216C4×Dic17—21no—
217C4×Dic17—21no—
218C4×Dic17—21no—
219C4×Dic17—21no—
220C4×Dic17C2×Q812yes—
221#63223—21no—
222#63223—21no—
223#63223—21no—
224#63223C2×Q812yes—
225C2×#3622—21no—
226C2×#3622—21no—
227C2×#3622—21no—
228C2×#3622—21no—
229C2×#3622—21no—
230C2×#3622—21no—
231C2×#3622C22×C411yescharacteristic
232C2×#3622C22×C411yescharacteristic
233C2×#3622C22×C411yescharacteristic
234C2×#3622C22×C411yescharacteristic
235#22984—171nomaximal, Sylow
236C23×C17—21no—
237C23×C17C2×#4111yescharacteristic
238Q8×C17—21no—
239Q8×C17C4×Q812yes—
240D4×C17—22no—
241D4×C17—22no—
242D4×C17—21no—
243D4×C17C4×Q812yes—
244C2×C4×C17—21no—
245C2×C4×C17—22no—
246C2×C4×C17—22no—
247C2×C4×C17—21no—
248C2×C4×C17—21no—
249C2×C4×C17—41no—
250C2×C4×C17—41no—
251C2×C4×C17—42no—
252C2×C4×C17—81no—
253C2×C4×C17C4×D411yescharacteristic
254C2×C4×C17C4×D411yescharacteristic
255C2×C4×C17C4×D411yescharacteristic
256C2×C4×C17C4×D411yescharacteristic
257C2×C4×C17C23×C411yescharacteristic
258C2×C4×C17C22×D411yescharacteristic
259C2×C4×C17C22×Q811yescharacteristic
260C2×C4×C17C2×#4111yescharacteristic
261C2×C4×C17H(5,𝔽2)11yescharacteristic
262C2×C4×C172−1+411yescharacteristic
263C2×Dic17—21no—
264C2×Dic17—21no—
265C2×Dic17—21no—
266C2×Dic17—21no—
267C2×Dic17—22no—
268C2×Dic17—41no—
269C2×Dic17—41no—
270C2×Dic17—41no—
271C2×Dic17—41no—
272C2×Dic17—41no—
273Dic34—42no—
274Dic34—81no—
275C8×C17—21no—
276C8×C17—21no—
277C8×C17—21no—
278C8×C17—21no—
279C8×C17—41no—
280C8×C17—41no—
281#3622—21no—
282#3622—21no—
283#3622—21no—
284#3622—21no—
285#3622—22no—
286#3622—41no—
287#3076—171no—
288#2962—171no—
289#2906D1711yescharacteristic
290#1995—171no—
291#1950—171no—
292#1946—171no—
293#1945—171no—
294#1922—171no—
295#1922—171no—
296#1866—171no—
297#1866—171no—
298#1768—171no—
299#1765—171no—
300#1764—171no—
301#1759—171no—
302C22×C17—21no—
303C22×C17—21no—
304C22×C17—22no—
305C22×C17—41no—
306C22×C17—41no—
307C22×C17C2×C4×D411yescharacteristic
308C22×C17#55211yescharacteristic
309C22×C17#55411yescharacteristic
310C4×C17—22no—
311C4×C17—21no—
312C4×C17—21no—
313C4×C17—21no—
314C4×C17—21no—
315C4×C17—41no—
316C4×C17—41no—
317C4×C17C2×C4×Q811yescharacteristic
318C4×C17#52011yescharacteristic
319C4×C17#54611yescharacteristic
320C4×C17D4×Q811yescharacteristic
321Dic17—42no—
322Dic17—41no—
323Dic17—41no—
324Dic17—41no—
325Dic17—41no—
326Dic17—81no—
327C2×#131C2×D1711yescharacteristic
328C2×#131C2×D1711yescharacteristic
329#533—171no—
330C4×#41C2×D1711yescharacteristic
331#479—171no—
332#479—171no—
333#478—171no—
334#478—171no—
335#477—171no—
336#476—171no—
337#475—171no—
338#474—171no—
339#446—341no—
340#446—341no—
341#446—341no—
342C8×Q8—341no—
343C2×#108—171no—
344C2×#108—171no—
345#427—171no—
346#427—171no—
347#424—21no—
348#424—21no—
349#424—171no—
350#424—171no—
351#424C2×D1711yescharacteristic
352#424C2×D1711yescharacteristic
353#423—21no—
354#423C2×D1711yescharacteristic
355C2×C4⋊C8—21no—
356C2×C4⋊C8—171no—
357C2×C4⋊C8C2×D1711yescharacteristic
358C2×#104—171no—
359C2×#104—171no—
360#416—171no—
361#416—171no—
362#405—171no—
363#405—171no—
364C4×M16—171no—
365C2×#97—171no—
366C2×C4×C8—171no—
367#376—171no—
368#341—171no—
369#341—171no—
370#339—171no—
371#339—171no—
372#339—171no—
373#339—171no—
374#339—171no—
375#339—171no—
376#336—171no—
377#336—171no—
378C2×C17—21no—
379C2×C17—21no—
380C2×C17—42no—
381C2×C17#236011yescharacteristic
382C2×C17#295511yescharacteristic
383C2×C17#295711yescharacteristic
384C2×#41C22×D1711yescharacteristic
385#131—22no—
386#131—22no—
387#131—41no—
388#131—41no—
389C2×M16—21no—
390C2×M16—21no—
391C2×M16—171no—
392C2×M16—171no—
393C2×M16C22×D1711yescharacteristic
394C2×M16C22×D1711yescharacteristic
395C22×C8—21no—
396C22×C8—21no—
397C22×C8—171no—
398C22×C8—171no—
399C22×C8C22×D1711yescharacteristic
400C22×C8C22×D1711yescharacteristic
401C4⋊Q8—171no—
402C4⋊Q8—171no—
403#125—171no—
404#125—171no—
405C22⋊Q8—341no—
406C22⋊Q8—341no—
407C4×Q8—341no—
408C4×Q8—341no—
409C4×Q8C4×D1711yescharacteristic
410C4×Q8C4×D1711yescharacteristic
411C4×D4—21no—
412C4×D4—21no—
413C4×D4C4×D1711yescharacteristic
414C4×D4C4×D1711yescharacteristic
415#117—21no—
416#117—171no—
417#117—171no—
418#117C22×D1711yescharacteristic
419C2×C42—21no—
420C2×C42—171no—
421C2×C42—171no—
422C2×C42C22×D1711yescharacteristic
423#108—681no—
424#108—681no—
425#107—171no—
426#107—171no—
427#107—171no—
428#107—171no—
429#106—171no—
430#106—171no—
431#106—171no—
432#106—171no—
433C4⋊C8—21no—
434C4⋊C8—21no—
435C4⋊C8—21no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—171no—
440C4⋊C8—171no—
441C4⋊C8—171no—
442C4⋊C8—171no—
443C4⋊C8—341no—
444C4⋊C8—341no—
445C4⋊C8—341no—
446C4⋊C8—341no—
447C4⋊C8C22⋊D1711yescharacteristic
448C4⋊C8C22⋊D1711yescharacteristic
449C4⋊C8C22⋊D1711yescharacteristic
450C4⋊C8C22⋊D1711yescharacteristic
451#104—174no—
452#104—342no—
453#103—171no—
454#103—171no—
455#103—171no—
456#103—171no—
457#102—171no—
458#102—171no—
459#102—171no—
460#102—171no—
461#97—341no—
462#97—341no—
463#97—341no—
464#97—681no—
465C4×C8—341no—
466C4×C8—341no—
467C4×C8—341no—
468C4×C8—681no—
469#95—341no—
470#95—341no—
471C17#2298411yescharacteristic, complemented, Sylow
472#41—21no—
473#41—21no—
474#41#6325412yes—
475#41Q8×D1712yes—
476C2×Q8—341no—
477C2×Q8—341no—
478C2×Q8C2×C4×D1711yescharacteristic
479C2×D4—21no—
480C2×D4C2×C4×D1711yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—341no—
485C22×C4—341no—
486C22×C4#6325211yescharacteristic
487C22×C4#6325211yescharacteristic
488C22×C4C23×D1711yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—42no—
494M16—42no—
495M16—172no—
496M16—341no—
497M16—341no—
498M16—341no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—42no—
506C2×C8—42no—
507C2×C8—171no—
508C2×C8—171no—
509C2×C8—171no—
510C2×C8—171no—
511C2×C8—341no—
512C2×C8—341no—
513C2×C8—341no—
514C2×C8—341no—
515C2×C8—341no—
516C2×C8—341no—
517C2×C8C2×C22⋊D1711yescharacteristic
518C2×C8C2×C22⋊D1711yescharacteristic
519C2×C8C2×C22⋊D1711yescharacteristic
520C2×C8C2×C22⋊D1711yescharacteristic
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—171no—
524C4⋊C4—171no—
525C4⋊C4—171no—
526C4⋊C4—171no—
527C4⋊C4—341no—
528C4⋊C4—341no—
529C4⋊C4—341no—
530C4⋊C4—341no—
531C4⋊C4—341no—
532C4⋊C4—341no—
533C4⋊C4C2×C4×D1711yescharacteristic
534C4⋊C4C2×C4×D1711yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—341no—
539C22⋊C4—341no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—172no—
544C42—341no—
545C42—341no—
546C42—341no—
547C42—341no—
548C42—341no—
549C42C2×C4×D1711yescharacteristic
550C42C2×C4×D1711yescharacteristic
551C42C2×C22⋊D1711yescharacteristic
552C42C2×C22⋊D1711yescharacteristic
553C23—21no—
554C23C2×#6325211yescharacteristic
555Q8—21no—
556Q8—682no—
557Q8—1361no—
558Q8#1058757312yes—
559D4—22no—
560D4—22no—
561D4—21no—
562D4#1058757312yes—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—81no—
572C2×C4—342no—
573C2×C4—341no—
574C2×C4—341no—
575C2×C4—341no—
576C2×C4—341no—
577C2×C4—681no—
578C2×C4—681no—
579C2×C4—681no—
580C2×C4—681no—
581C2×C4—681no—
582C2×C4C4×C22⋊D1711yescharacteristic
583C2×C4C4×C22⋊D1711yescharacteristic
584C2×C4C4×C22⋊D1711yescharacteristic
585C2×C4C4×C22⋊D1711yescharacteristic
586C2×C4C22×C4×D1711yescharacteristic
587C2×C4C2×#6325411yescharacteristic
588C2×C4#1058769111yescharacteristic
589C2×C4C2×Q8×D1711yescharacteristic
590C2×C4#1058769411yescharacteristic
591C2×C4C22×C22⋊D1711yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—342no—
599C8—341no—
600C8—341no—
601C8—341no—
602C8—341no—
603C8—681no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22C2×C4×C22⋊D1711yescharacteristic
610C22#1176349411yescharacteristic
611C22#1176351411yescharacteristic
612C4—22no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—41no—
618C4—41no—
619C4—682no—
620C4—681no—
621C4—681no—
622C4—681no—
623C4—681no—
624C4—1361no—
625C4C2×#1058757311yescharacteristic
626C4#1176329011yescharacteristic
627C4#1176345311yescharacteristic
628C4Q8×C22⋊D1711yescharacteristic
629C2—21no—
630C2—21no—
631C2—42no—
632C2#1453178911yescharacteristic
633C2#1453768511yescharacteristic
634C2#1453769911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2906C2
socleC22×C17C2×C4×D4
prime radicalC2×#41×C17C23
cosocleC22×C4×C17C24
hypercenter#2906D17
hypocenterC17#22984
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #14537727C2semidirect
3. #14529764C2semidirect
4. #14529557C2semidirect
5. #14529534C2semidirect
6. #14529529C2semidirect
7. #14529380C2semidirect
8. #14529380C2semidirect
11. #14528643C2semidirect
17. #11763116C4semidirect
18. #11763116C4semidirect
19. #11763109C4semidirect
20. #11763109C4semidirect
21. #11763104C4semidirect
22. #11763099C4semidirect
23. #11763094C4semidirect
24. #11763089C4semidirect
117. #10587508Q8semidirect
471. C17#22984semidirect

Maximal subgroups

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

subgroupindex
#145385722
#145377272
#145297642
#145295572
#145295342
#145295292
#145293802
#145290592
#145286432
#145286262
#145286192
#145285942
C17×#29062
#2298417