Finite Group Databasebeta

← #17031983

Subgroups — #17031983

Order 4352.

1606 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763288C211yesmaximal, characteristic
2C2×#11762781C212yesmaximal
3#14531139C212yesmaximal, complemented
4#99×Dic17C212yesmaximal, complemented
5C4×#10587477C212yesmaximal, complemented
6C4×#10587505C211yesmaximal, characteristic, complemented
7#14528571C212yesmaximal, complemented
8#14528515C212yesmaximal, complemented
9C4×C17×#99C211yesmaximal, characteristic, complemented
10C22×#63254C2211yescharacteristic
11#11763288—24no—
12#11763288—24no—
13C2×C4×Dic34C411yescharacteristic, complemented
14C2×#10587573C411yescharacteristic, complemented
15C2×D4×Dic17C2211yescharacteristic
16C2×C4×C22⋊D17C411yescharacteristic, complemented
17C2×C4×C22⋊D17C2211yescharacteristic
18C2×#10587567C411yescharacteristic, complemented
19C2×#10587567C2211yescharacteristic
20C2×#10587558C411yescharacteristic, complemented
21C2×#10587563C411yescharacteristic, complemented
22C2×#10587563C2211yescharacteristic
23C2×#10587563C2214yes—
24C22×#63225C411yescharacteristic, complemented
25C22×#63225C2211yescharacteristic
26C2×C4⋊C4×D17C411yescharacteristic, complemented
27#11762781C4116yescomplemented
28C2×#10587505C2212yes—
29C2×#10587477C2214yes—
30C4×#63225—24no—
31#11762660—24no—
32C22⋊C4×Dic17C2214yes—
33C4×C22⋊Dic17C2212yes—
34#11762576C2212yes—
35#11762575C2214yes—
36C2×C4×D4×C17C2211yescharacteristic
37C2×C17×#99C2212yes—
38C4×C22⋊C4×C17C2212yes—
39C17×#342C2212yes—
40C22×D4×C17C2311yescharacteristic
41C23×C4×C17C2×C411yescharacteristic
42C23×C4×C17C2311yescharacteristic
43C22×C22⋊D17C2×C411yescharacteristic
44C22×C22⋊D17C2311yescharacteristic
45C23×Dic17C2×C411yescharacteristic
46C23×Dic17C2×C411yescharacteristic
47C23×Dic17C2311yescharacteristic
48C23×Dic17C2311yescharacteristic
49C2×#63254—24no—
50C2×#63254—24no—
51C2×#63254C2×C418yes—
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17C2×C411yescharacteristic
54C22×C4×D17C2×C411yescharacteristic
55C22×Dic34C2×C411yescharacteristic
56C4×D4×C17—22no—
57C4×D4×C17—22no—
58C2×C4⋊C4×C17C2×C411yescharacteristic
59C2×C22⋊C4×C17C2×C411yescharacteristic
60C2×C22⋊C4×C17C2311yescharacteristic
61C2×C22⋊C4×C17C2314yes—
62C2×C42×C17—22no—
63C2×C42×C17C2×C411yescharacteristic
64C2×C22⋊Dic17C2×C411yescharacteristic
65C2×C22⋊Dic17C2311yescharacteristic
66C2×C22⋊Dic17C2314yes—
67D4×Dic17—24no—
68C4×C22⋊D17—22no—
69C4×C22⋊D17—22no—
70C4×C22⋊D17—22no—
71C4×C22⋊D17—22no—
72C2×#63227C2×C411yescharacteristic
73C2×#63227C2×C411yescharacteristic
74C2×C4⋊Dic17C2×C411yescharacteristic
75C2×#63225—22no—
76C2×#63225—22no—
77C2×#63225—24no—
78C2×#63225C2×C411yescharacteristic
79C2×#63225C2×C411yescharacteristic
80C2×#63225C2×C411yescharacteristic
81C2×#63225C2×C411yescharacteristic
82C2×#63225C2×C411yescharacteristic
83C2×#63225C2×C411yescharacteristic
84C2×#63225C2×C411yescharacteristic
85C2×#63225C2×C411yescharacteristic
86C2×#63225D414yes—
87C2×#63225D414yes—
88C2×C4×Dic17—22no—
89C2×C4×Dic17—24no—
90C2×C4×Dic17—24no—
91C2×C4×Dic17C2×C411yescharacteristic
92C2×C4×Dic17C2×C411yescharacteristic
93C2×C4×Dic17C2×C411yescharacteristic
94C2×C4×Dic17C2×C411yescharacteristic
95C2×C4×Dic17C2×C411yescharacteristic
96C4⋊C4×D17—24no—
97#10587573—24no—
98#10587567—24no—
99#10587567—24no—
100#10587563—24no—
101#10587563—24no—
102#10587563—28no—
103#10587563C2×C4116yescomplemented
104#10587558—22no—
105#10587558—22no—
106C4×Dic34—22no—
107C4×Dic34—22no—
108C17×#99C2×C418yescomplemented
109C17×#95—22no—
110#10587505C2×C418yescomplemented
111#10587502—22no—
112#10587502—24no—
113#10587477C2×C4116yescomplemented
114C24×C17C22×C411yescharacteristic
115C24×C17C2411yescharacteristic
116C23×D17C22×C411yescharacteristic
117C2×D4×C17—22no—
118C2×D4×C17—22no—
119C2×D4×C17C22×C414yes—
120C22×C4×C17—24no—
121C22×C4×C17—21no—
122C22×C4×C17—21no—
123C22×C4×C17—81no—
124C22×C4×C17—81no—
125C22×C4×C17C22×C411yescharacteristic
126C22×C4×C17C22×C411yescharacteristic
127C22×C4×C17C22×C411yescharacteristic
128C22×C4×C17C22×C411yescharacteristic
129C22×C4×C17C22×C411yescharacteristic
130C22×C4×C17C2×D412yes—
131C22×C4×C17C2×D412yes—
132C2×C22⋊D17—22no—
133C2×C22⋊D17—22no—
134C2×C22⋊D17—22no—
135C2×C22⋊D17—22no—
136C2×C22⋊D17C4214yescomplemented
137C2×C22⋊D17C22×C414yes—
138C22×Dic17—22no—
139C22×Dic17—22no—
140C22×Dic17—24no—
141C22×Dic17—22no—
142C22×Dic17—81no—
143C22×Dic17—81no—
144C22×Dic17C4214yescomplemented
145C22×Dic17C22×C411yescharacteristic
146C22×Dic17C22×C411yescharacteristic
147C22×Dic17C22×C411yescharacteristic
148C22×Dic17C22×C411yescharacteristic
149C22×Dic17C22×C411yescharacteristic
150C22×Dic17C22×C411yescharacteristic
151C22×Dic17C22×C411yescharacteristic
152C22×Dic17C22×C414yes—
153C22×Dic17C2×D414yes—
154C22×Dic17C2×D414yes—
155C22×Dic17#4114yes—
156#63254—216no—
157#63254—216no—
158C2×C4×D17—22no—
159C2×C4×D17—22no—
160C2×C4×D17—22no—
161C2×C4×D17—22no—
162C2×C4×D17—81no—
163C2×C4×D17—81no—
164C2×C4×D17C4214yescomplemented
165C2×Dic34—22no—
166C2×Dic34—22no—
167C2×Dic34C4214yescomplemented
168C4⋊C4×C17—22no—
169C22⋊C4×C17—22no—
170C22⋊C4×C17—24no—
171C22⋊C4×C17—22no—
172C22⋊C4×C17C22×C418yes—
173C42×C17—21no—
174C42×C17—21no—
175C42×C17—82no—
176C22⋊Dic17—22no—
177C22⋊Dic17—24no—
178C22⋊Dic17—22no—
179C22⋊Dic17C22×C418yes—
180#63227—21no—
181#63227—21no—
182#63227—22no—
183C4⋊Dic17—22no—
184#63225—21no—
185#63225—21no—
186#63225—22no—
187#63225—22no—
188#63225—22no—
189#63225—216no—
190#63225C22⋊C412yes—
191#63225C22⋊C412yes—
192#63225C22⋊C412yes—
193#63225C22⋊C412yes—
194#63225C22⋊C414yes—
195#63225C22⋊C414yes—
196C4×Dic17—22no—
197C4×Dic17—22no—
198C4×Dic17—22no—
199C4×Dic17—22no—
200C4×Dic17—22no—
201C4×Dic17—216no—
202C4×Dic17—84no—
203C4×Dic17—82no—
204#20393—171nomaximal, Sylow
205C23×C17—21no—
206C23×C17—21no—
207C23×C17—41no—
208C23×C17—41no—
209C23×C17—41no—
210C23×C17—41no—
211C23×C17C2×C4212yes—
212C23×C17C23×C411yescharacteristic
213C23×C17C23×C412yes—
214C23×C17C22×D412yes—
215C23×C17C2×#4112yes—
216C22×D17—21no—
217C22×D17—21no—
218C22×D17—41no—
219C22×D17—41no—
220C22×D17C2×C4212yes—
221D4×C17—28no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17—28no—
227C2×C4×C17—42no—
228C2×C4×C17—41no—
229C2×C4×C17—41no—
230C2×C4×C17—42no—
231C2×C4×C17—44no—
232C2×C4×C17—44no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17—81no—
236C2×C4×C17—81no—
237C2×C4×C17C2×C4212yes—
238C2×C4×C17C2×C22⋊C411yescharacteristic
239C2×C4×C17C2×C22⋊C411yescharacteristic
240C2×C4×C17C2×C22⋊C412yes—
241C22⋊D17—28no—
242C22⋊D17—28no—
243C2×Dic17—21no—
244C2×Dic17—21no—
245C2×Dic17—28no—
246C2×Dic17—21no—
247C2×Dic17—21no—
248C2×Dic17—28no—
249C2×Dic17—41no—
250C2×Dic17—41no—
251C2×Dic17—44no—
252C2×Dic17—44no—
253C2×Dic17—44no—
254C2×Dic17—41no—
255C2×Dic17—41no—
256C2×Dic17—82no—
257C2×Dic17C2×C4212yes—
258C2×Dic17C2×C4212yes—
259C2×Dic17C2×C4212yes—
260C2×Dic17C2×C22⋊C412yes—
261C2×Dic17C2×C22⋊C412yes—
262C2×Dic17C2×C22⋊C412yes—
263C2×Dic17C2×C22⋊C412yes—
264C2×Dic17#11712yes—
265C2×Dic17#11712yes—
266C2×Dic17C4×D418yes—
267C2×Dic17C4×D418yes—
268C4×D17—28no—
269C4×D17—82no—
270C4×D17—82no—
271Dic34—28no—
272C2×#520—171no—
273C2×#410—172no—
274#2274—172no—
275C4×#99—172no—
276C4×#99—172no—
277C4×#99—172no—
278C4×#99—171no—
279C4×#99D1711yescharacteristic, complemented
280#1740—172no—
281C22×C17—22no—
282C22×C17—21no—
283C22×C17—22no—
284C22×C17—21no—
285C22×C17—22no—
286C22×C17—42no—
287C22×C17—42no—
288C22×C17—42no—
289C22×C17—42no—
290C22×C17—41no—
291C22×C17—41no—
292C22×C17C22×C4211yescharacteristic
293C22×C17C22×C22⋊C411yescharacteristic
294C22×C17C2×#11711yescharacteristic
295C22×C17C2×C4×D414yes—
296C2×D17—22no—
297C2×D17—42no—
298C2×D17—41no—
299C2×D17—41no—
300C2×D17—42no—
301C4×C17—22no—
302C4×C17—21no—
303C4×C17—21no—
304C4×C17—22no—
305C4×C17—48no—
306C4×C17—41no—
307C4×C17—41no—
308Dic17—22no—
309Dic17—22no—
310Dic17—22no—
311Dic17—48no—
312Dic17—41no—
313Dic17—41no—
314Dic17C4×C22⋊C414yes—
315Dic17C4×C22⋊C414yes—
316C22×#41—171no—
317#520—344no—
318#520—344no—
319C2×C4×Q8—171no—
320C2×C4×Q8—171no—
321C2×C4×D4—171no—
322C2×C4×D4—171no—
323C2×C4×D4—171no—
324C2×C4×D4—171no—
325C2×C4×D4—171no—
326C2×C4×D4C2×D1711yescharacteristic
327C2×#117—171no—
328C2×#117—171no—
329C2×#117—171no—
330C2×#117—174no—
331C22×C4⋊C4—171no—
332C22×C4⋊C4—171no—
333C22×C4⋊C4—171no—
334#410—1716no—
335C2×#99—172no—
336C2×#99—174no—
337C2×#99C2×D1712yes—
338C4×C4⋊C4—344no—
339C4×C4⋊C4—344no—
340C4×C22⋊C4—172no—
341C4×C22⋊C4—174no—
342C4×C22⋊C4C2×D1712yes—
343#342—174no—
344#342—172no—
345#342C2×D1712yes—
346C2×C17—24no—
347C2×C17—21no—
348C2×C17—21no—
349C2×C17—42no—
350C2×C17C2×C4×C22⋊C411yescharacteristic
351C2×C17#288311yescharacteristic
352C2×C17#288411yescharacteristic
353D17—42no—
354C2×#41—178no—
355C2×#41—344no—
356C2×#41—344no—
357C22×Q8—171no—
358C22×D4—171no—
359C22×D4—171no—
360C22×D4C22×D1711yescharacteristic
361C23×C4—171no—
362C23×C4—171no—
363C23×C4—171no—
364C23×C4—171no—
365C23×C4—171no—
366C23×C4—171no—
367C23×C4—171no—
368C23×C4C4×D1711yescharacteristic
369C23×C4C22×D1711yescharacteristic
370C4×Q8—342no—
371C4×Q8—342no—
372C4×Q8—344no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—344no—
376C4×D4—344no—
377C4×D4—342no—
378C4×D4—342no—
379C4×D4—344no—
380C4×D4—342no—
381C4×D4—342no—
382#117—1716no—
383#117—342no—
384#117—342no—
385#117—344no—
386#117—344no—
387#117—348no—
388C2×C4⋊C4—171no—
389C2×C4⋊C4—171no—
390C2×C4⋊C4—171no—
391C2×C4⋊C4—171no—
392C2×C4⋊C4—174no—
393C2×C4⋊C4—174no—
394C2×C4⋊C4—171no—
395C2×C4⋊C4—171no—
396C2×C4⋊C4—171no—
397C2×C4⋊C4—171no—
398C2×C4⋊C4—171no—
399C2×C4⋊C4—344no—
400C2×C4⋊C4—342no—
401C2×C4⋊C4—342no—
402C2×C4⋊C4—344no—
403C2×C4⋊C4C4×D1711yescharacteristic
404C2×C22⋊C4—174no—
405C2×C22⋊C4—171no—
406C2×C22⋊C4—171no—
407C2×C22⋊C4—171no—
408C2×C22⋊C4—171no—
409C2×C22⋊C4C4×D1711yescharacteristic
410C2×C22⋊C4C22×D1711yescharacteristic
411C2×C22⋊C4C22×D1714yes—
412C2×C42—22no—
413C2×C42—171no—
414C2×C42—171no—
415C2×C42—171no—
416C2×C42—171no—
417C2×C42—171no—
418C2×C42—344no—
419C2×C42—344no—
420C2×C42—342no—
421C2×C42C4×D1711yescharacteristic
422#99—178no—
423#99—1716no—
424#99C4×D1718yescomplemented
425#95—22no—
426#95—344no—
427#95—342no—
428C17#2039311yescharacteristic, complemented, Sylow
429C24—171no—
430C24C2×C4×D1711yescharacteristic
431C24C23×D1711yescharacteristic
432#41—3416no—
433#41—3416no—
434C2×Q8—174no—
435C2×Q8—342no—
436C2×Q8—342no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—174no—
440C2×D4—174no—
441C2×D4—342no—
442C2×D4—342no—
443C2×D4—342no—
444C2×D4—342no—
445C2×D4C2×C4×D1714yes—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—81no—
450C22×C4—81no—
451C22×C4—171no—
452C22×C4—171no—
453C22×C4—174no—
454C22×C4—174no—
455C22×C4—174no—
456C22×C4—171no—
457C22×C4—174no—
458C22×C4—171no—
459C22×C4—171no—
460C22×C4—174no—
461C22×C4—174no—
462C22×C4—171no—
463C22×C4—171no—
464C22×C4—342no—
465C22×C4—342no—
466C22×C4—342no—
467C22×C4—342no—
468C22×C4—342no—
469C22×C4—342no—
470C22×C4—344no—
471C22×C4—342no—
472C22×C4—1361no—
473C22×C4—1361no—
474C22×C4—1361no—
475C22×C4—1361no—
476C22×C4C2×C4×D1711yescharacteristic
477C22×C4C2×C4×D1711yescharacteristic
478C22×C4C2×C4×D1711yescharacteristic
479C22×C4C2×C4×D1711yescharacteristic
480C22×C4C2×C4×D1711yescharacteristic
481C22×C4D4×D1712yes—
482C22×C4D4×D1712yes—
483C4⋊C4—22no—
484C4⋊C4—172no—
485C4⋊C4—172no—
486C4⋊C4—174no—
487C4⋊C4—172no—
488C4⋊C4—172no—
489C4⋊C4—174no—
490C4⋊C4—342no—
491C4⋊C4—342no—
492C4⋊C4—342no—
493C4⋊C4—342no—
494C4⋊C4—3416no—
495C4⋊C4—341no—
496C4⋊C4—341no—
497C22⋊C4—22no—
498C22⋊C4—24no—
499C22⋊C4—22no—
500C22⋊C4—178no—
501C22⋊C4—342no—
502C22⋊C4—342no—
503C22⋊C4—342no—
504C22⋊C4—344no—
505C22⋊C4—341no—
506C22⋊C4—341no—
507C22⋊C4C2×C4×D1718yes—
508C42—21no—
509C42—21no—
510C42—82no—
511C42—342no—
512C42—342no—
513C42—342no—
514C42—342no—
515C42—3416no—
516C42—342no—
517C42—1362no—
518C42—1364no—
519C23—21no—
520C23—21no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—172no—
526C23—341no—
527C23—341no—
528C23—681no—
529C23—681no—
530C23C42×D1712yes—
531C23C22×C4×D1711yescharacteristic
532C23C22×C4×D1712yes—
533C23C2×D4×D1712yes—
534C23#41×D1712yes—
535Q8—348no—
536D4—28no—
537D4—348no—
538D4—348no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—28no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—44no—
549C2×C4—44no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—81no—
553C2×C4—81no—
554C2×C4—172no—
555C2×C4—172no—
556C2×C4—172no—
557C2×C4—172no—
558C2×C4—172no—
559C2×C4—172no—
560C2×C4—178no—
561C2×C4—178no—
562C2×C4—172no—
563C2×C4—172no—
564C2×C4—172no—
565C2×C4—348no—
566C2×C4—348no—
567C2×C4—341no—
568C2×C4—341no—
569C2×C4—341no—
570C2×C4—341no—
571C2×C4—348no—
572C2×C4—684no—
573C2×C4—681no—
574C2×C4—681no—
575C2×C4—684no—
576C2×C4—684no—
577C2×C4—681no—
578C2×C4—681no—
579C2×C4—1362no—
580C2×C4—1362no—
581C2×C4—1362no—
582C2×C4C42×D1712yes—
583C2×C4C22⋊C4×D1711yescharacteristic
584C2×C4C22⋊C4×D1711yescharacteristic
585C2×C4C22⋊C4×D1712yes—
586C22—22no—
587C22—21no—
588C22—22no—
589C22—21no—
590C22—22no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—342no—
598C22—682no—
599C22—682no—
600C22—681no—
601C22—681no—
602C22C2×C42×D1711yescharacteristic
603C22C2×C22⋊C4×D1711yescharacteristic
604C22#117×D1711yescharacteristic
605C22C4×D4×D1714yes—
606C4—21no—
607C4—21no—
608C4—22no—
609C4—22no—
610C4—48no—
611C4—41no—
612C4—41no—
613C4—174no—
614C4—174no—
615C4—342no—
616C4—342no—
617C4—342no—
618C4—688no—
619C4—681no—
620C4—681no—
621C2—24no—
622C2—21no—
623C2—21no—
624C2—42no—
625C2—682no—
626C2C4×C22⋊C4×D1711yescharacteristic
627C2#1453724211yescharacteristic
628C2#1453724611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D17
commutatorC22×C17C22×C42
FrattiniC24C23×D17
FittingC4×C17×#99C2
socleC22×C17C22×C22⋊C4
prime radicalC22×#63254C22
cosocleC24×C17C24
hypercenterC4×#99D17
hypocenterC17#20393
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #14531139C2semidirect
4. #99×Dic17C2semidirect
5. C4×#10587477C2semidirect
6. C4×#10587505C2semidirect
7. #14528571C2semidirect
8. #14528515C2semidirect
9. C4×C17×#99C2semidirect
13. C2×C4×Dic34C4semidirect
14. C2×#10587573C4semidirect
16. C2×C4×C22⋊D17C4semidirect
18. C2×#10587567C4semidirect
20. C2×#10587558C4semidirect
21. C2×#10587563C4semidirect
24. C22×#63225C4semidirect
26. C2×C4⋊C4×D17C4semidirect
27. #11762781C4semidirect
103. #10587563C2×C4semidirect
108. C17×#99C2×C4semidirect
110. #10587505C2×C4semidirect
113. #10587477C2×C4semidirect
136. C2×C22⋊D17C42semidirect
144. C22×Dic17C42semidirect
164. C2×C4×D17C42semidirect
167. C2×Dic34C42semidirect
279. C4×#99D17semidirect
424. #99C4×D17semidirect
428. C17#20393semidirect

Maximal subgroups

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

subgroupindex
C2×#117632882
C2×#117627812
#145311392
#99×Dic172
C4×#105874772
C4×#105875052
#145285712
#145285152
C4×C17×#992
#2039317