Finite Group Databasebeta

← #17050944

Subgroups — #17050944

Order 4352.

1110 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763518C211yesmaximal, characteristic
2C2×#11762938C211yesmaximal, characteristic, complemented
3#14531696C211yesmaximal, characteristic, complemented
4#14529752C211yesmaximal, characteristic, complemented
5#14529751C211yesmaximal, characteristic, complemented
6#14529743C211yesmaximal, characteristic, complemented
7#14529740C211yesmaximal, characteristic, complemented
8#14529739C211yesmaximal, characteristic, complemented
9#14529730C211yesmaximal, characteristic, complemented
10#14528782C211yesmaximal, characteristic
11#14528782C211yesmaximal, characteristic
12#14528611C211yesmaximal, characteristic
13#14528609C211yesmaximal, characteristic
14#102×Dic17C211yesmaximal, characteristic
15C17×#1802C211yesmaximal, characteristic
16#11763518—24no—
17#11763518C418yescomplemented
18C2×#10587574C2211yescharacteristic
19C2×#10587556C2211yescharacteristic
20C2×#10587576C2211yescharacteristic
21C2×#10587610—21no—
22C2×#10587564—21no—
23C2×#10587564—21no—
24C2×C4×Dic34C2211yescharacteristic
25C2×#10587573—21no—
26C2×D4×Dic17C2211yescharacteristic
27C2×D4×Dic17C2211yescharacteristic
28C22×#63225—21no—
29#11762938—24no—
30C2×#10587485C2211yescharacteristic
31C2×#10587485C2211yescharacteristic
32C2×#10587503C2211yescharacteristic
33C2×#10587503C2211yescharacteristic
34C2×#10587474C2211yescharacteristic
35C2×#10587486C2211yescharacteristic
36C2×C8×Dic17C2211yescharacteristic
37#11762705—21no—
38#11762704—21no—
39#11762704—21no—
40#11762678C2211yescharacteristic
41#11762678C2211yescharacteristic
42C4⋊C4×Dic17C2211yescharacteristic
43C4⋊C4×Dic17C2211yescharacteristic
44C4×C4⋊Dic17C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762571C2211yescharacteristic
53#11762571C2211yescharacteristic
54#11762571C2211yescharacteristic
55C2×C4×D4×C17C2211yescharacteristic
56C2×C17×C4⋊C8C2211yescharacteristic
57C2×C17×#102C2211yescharacteristic
58C2×C17×#102C2211yescharacteristic
59C17×#384C2211yescharacteristic
60C17×#340C2211yescharacteristic
61C17×#340C2211yescharacteristic
62C22×D4×C17C2311yescharacteristic
63C23×C4×C17—21no—
64C23×Dic17—21no—
65C23×Dic17—21no—
66C22×Dic34—21no—
67C22×Dic34D411yescharacteristic
68C22×C8×C17C2311yescharacteristic
69C22×C8×C17C2311yescharacteristic
70C4×D4×C17—22no—
71C4×D4×C17C2×C414yes—
72C2×C4⋊C4×C17—21no—
73C2×C4⋊C4×C17—21no—
74C2×C4⋊C4×C17C2311yescharacteristic
75C2×C4⋊C4×C17C2311yescharacteristic
76C2×C4⋊C4×C17C2311yescharacteristic
77C2×C22⋊C4×C17—21no—
78C2×C42×C17C2311yescharacteristic
79C2×C22⋊Dic17—21no—
80C2×C22⋊Dic17—21no—
81D4×Dic17—22no—
82D4×Dic17—22no—
83D4×Dic17C2×C414yes—
84D4×Dic17C2×C414yes—
85C2×C4⋊Dic17—21no—
86C2×C4⋊Dic17D411yescharacteristic
87C2×C4⋊Dic17C2311yescharacteristic
88C2×C4⋊Dic17C2311yescharacteristic
89C2×C4⋊Dic17C2311yescharacteristic
90C2×C4⋊Dic17C2311yescharacteristic
91#10587610—28no—
92C2×#63225—28no—
93C2×#63225—21no—
94C2×#63225—21no—
95C2×#63225—21no—
96C2×#63225—21no—
97C2×#63225—21no—
98C2×#63225—21no—
99C2×#63225—21no—
100C2×#63225—21no—
101C2×#63225D411yescharacteristic
102C2×#63225D411yescharacteristic
103C2×C4×Dic17—21no—
104C2×C4×Dic17—21no—
105C2×C4×Dic17—21no—
106C2×C4×Dic17C2311yescharacteristic
107C2×C4×Dic17C2311yescharacteristic
108C22×#3622C2311yescharacteristic
109C22×#3622C2311yescharacteristic
110#10587576—22no—
111#10587576C2×C414yes—
112#10587574—22no—
113#10587574C2×C414yes—
114#10587573—44no—
115#10587564—28no—
116#10587564—28no—
117#10587556—22no—
118#10587556C2×C414yes—
119C4×Dic34C2×C414yes—
120C4×Dic34D414yes—
121C17×C4⋊C8—22no—
122C17×#102—22no—
123C17×#102—22no—
124#10587503—22no—
125#10587503Q814yescomplemented
126#10587502—21no—
127#10587502—21no—
128#10587502—21no—
129#10587486—22no—
130#10587485—22no—
131#10587485—22no—
132C8×Dic17—22no—
133#10587474—22no—
134C24×C17—21no—
135C2×D4×C17—21no—
136C2×D4×C17—21no—
137C2×D4×C17—21no—
138C2×D4×C17C22×C412yes—
139C2×D4×C17C2×Q812yes—
140C2×D4×C17#4112yes—
141C22×C4×C17—21no—
142C22×C4×C17—24no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—81no—
146C22×C4×C17—81no—
147C22×C4×C17C2×D411yescharacteristic
148C22×C4×C17C2×D411yescharacteristic
149C22×C4×C17C2411yescharacteristic
150C22×Dic17—21no—
151C22×Dic17—21no—
152C22×Dic17—21no—
153C22×Dic17—24no—
154C22×Dic17—24no—
155C22×Dic17—21no—
156C22×Dic17—42no—
157C22×Dic17—42no—
158C22×Dic17—81no—
159C22×Dic17—81no—
160C22×Dic17C2×D411yescharacteristic
161C22×Dic17C2×D411yescharacteristic
162C22×Dic17C2×D411yescharacteristic
163C22×Dic17C2×D411yescharacteristic
164C2×Dic34—22no—
165C2×Dic34—22no—
166C2×Dic34—24no—
167C2×Dic34—81no—
168C2×Dic34—81no—
169C2×Dic34C22⋊C414yes—
170C2×C8×C17—21no—
171C2×C8×C17—21no—
172C2×C8×C17—21no—
173C2×C8×C17—21no—
174C2×C8×C17—21no—
175C2×C8×C17—21no—
176C4⋊C4×C17—21no—
177C4⋊C4×C17—21no—
178C4⋊C4×C17—21no—
179C4⋊C4×C17—21no—
180C4⋊C4×C17—21no—
181C4⋊C4×C17—42no—
182C4⋊C4×C17—81no—
183C4⋊C4×C17C22×C412yes—
184C22⋊C4×C17—24no—
185C42×C17C22×C412yes—
186C42×C17C2×D412yes—
187C22⋊Dic17—24no—
188C22⋊Dic17—24no—
189C4⋊Dic17—21no—
190C4⋊Dic17—21no—
191C4⋊Dic17—21no—
192C4⋊Dic17—24no—
193C4⋊Dic17—21no—
194C4⋊Dic17—21no—
195C4⋊Dic17C22⋊C414yes—
196C4⋊Dic17C22×C412yes—
197C4⋊Dic17C22×C412yes—
198C4⋊Dic17C2×Q812yes—
199#63225—24no—
200#63225—24no—
201#63225—24no—
202#63225—24no—
203#63225—42no—
204#63225—42no—
205#63225—81no—
206#63225—81no—
207#63225C22⋊C414yes—
208#63225C22⋊C414yes—
209C4×Dic17—42no—
210C4×Dic17—42no—
211C4×Dic17—42no—
212C4×Dic17C22×C412yes—
213C4×Dic17C22×C412yes—
214C4×Dic17C2×D412yes—
215C4×Dic17C2×D412yes—
216C2×#3622—21no—
217C2×#3622—21no—
218C2×#3622—21no—
219C2×#3622—21no—
220C2×#3622—21no—
221C2×#3622C2×Q812yes—
222#22522—171nomaximal, Sylow
223C23×C17—22no—
224C23×C17—22no—
225C23×C17—22no—
226C23×C17—41no—
227C23×C17—41no—
228C23×C17—41no—
229C23×C17—41no—
230C23×C17C22×D411yescharacteristic
231D4×C17—22no—
232D4×C17—22no—
233D4×C17—22no—
234D4×C17C4×Q814yescomplemented
235C2×C4×C17—21no—
236C2×C4×C17—21no—
237C2×C4×C17—21no—
238C2×C4×C17—21no—
239C2×C4×C17—22no—
240C2×C4×C17—41no—
241C2×C4×C17—41no—
242C2×C4×C17—41no—
243C2×C4×C17—41no—
244C2×C4×C17—41no—
245C2×C4×C17—41no—
246C2×C4×C17—41no—
247C2×C4×C17—41no—
248C2×C4×C17—84no—
249C2×C4×C17C2×C22⋊C412yes—
250C2×C4×C17C2×C22⋊C412yes—
251C2×C4×C17C23×C411yescharacteristic
252C2×C4×C17C22×D411yescharacteristic
253C2×C4×C17C22×Q811yescharacteristic
254C2×C4×C17C2×#4111yescharacteristic
255C2×C4×C172−1+411yescharacteristic
256C2×C4×C172−1+411yescharacteristic
257C2×Dic17—21no—
258C2×Dic17—21no—
259C2×Dic17—21no—
260C2×Dic17—21no—
261C2×Dic17—21no—
262C2×Dic17—21no—
263C2×Dic17—22no—
264C2×Dic17—22no—
265C2×Dic17—22no—
266C2×Dic17—41no—
267C2×Dic17—41no—
268C2×Dic17—41no—
269C2×Dic17—41no—
270C2×Dic17—41no—
271C2×Dic17—41no—
272C2×Dic17—48no—
273C2×Dic17—41no—
274C2×Dic17—41no—
275C2×Dic17—41no—
276C2×Dic17—84no—
277C2×Dic17C2×C22⋊C412yes—
278C2×Dic17C2×C22⋊C412yes—
279C2×Dic17C2×C22⋊C412yes—
280C2×Dic17C2×C22⋊C412yes—
281C2×Dic17AGL(1,ℤ/8)12yes—
282C2×Dic17#13712yes—
283Dic34—28no—
284Dic34—84no—
285C8×C17—41no—
286C8×C17—41no—
287#3622—22no—
288#3622—41no—
289C2×#554—171no—
290C2×#446—171no—
291Q8×C4⋊C4—171no—
292#1992—171no—
293#1992—171no—
294#1990—171no—
295#1989—171no—
296#1989—171no—
297#1987—171no—
298#1802—171no—
299#1802—171no—
300#1802D1711yescharacteristic
301#1762—171no—
302#1762—171no—
303C4×#102—171no—
304C22×C17—24no—
305C22×C17—42no—
306C22×C17—42no—
307C22×C17—42no—
308C22×C17—42no—
309C22×C17—42no—
310C22×C17—42no—
311C22×C17C22×C22⋊C411yescharacteristic
312C22×C17#54811yescharacteristic
313C22×C17D4×Q811yescharacteristic
314C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C17C2×#13711yescharacteristic
316C22×C17#57611yescharacteristic
317C22×C17#57711yescharacteristic
318C4×C17—22no—
319C4×C17—22no—
320C4×C17—42no—
321C4×C17—81no—
322C4×C17—81no—
323C4×C17C2×C4×Q811yescharacteristic
324C4×C17#51911yescharacteristic
325C4×C17#54811yescharacteristic
326C4×C17D4×Q811yescharacteristic
327Dic17—22no—
328Dic17—22no—
329Dic17—22no—
330Dic17—42no—
331Dic17—42no—
332Dic17—42no—
333Dic17—81no—
334Dic17#41714yes—
335#554—178no—
336#554—344no—
337C2×C4⋊Q8—171no—
338C2×#125—171no—
339C2×#125—171no—
340C2×C22⋊Q8—341no—
341C2×C22⋊Q8—341no—
342C2×C22⋊Q8—341no—
343C2×C4×Q8—171no—
344C2×C4×Q8—341no—
345C2×C4×D4—171no—
346C2×C4×D4—171no—
347C2×C4×D4C2×D1711yescharacteristic
348C22×C4⋊C4—341no—
349#446—344no—
350C2×C4⋊C8—171no—
351C2×C4⋊C8—171no—
352C2×C4⋊C8C2×D1711yescharacteristic
353C2×#102—171no—
354C2×#102—171no—
355C2×#102C2×D1711yescharacteristic
356C2×#102C2×D1711yescharacteristic
357C2×#97—171no—
358C2×#97—171no—
359C2×C4×C8—171no—
360#389—341no—
361#389—341no—
362#389—341no—
363#384—171no—
364#384—171no—
365#384C2×D1711yescharacteristic
366C4×C4⋊C4—171no—
367C4×C4⋊C4—171no—
368C4×C4⋊C4—171no—
369#340—171no—
370#340—171no—
371#340—171no—
372#340—171no—
373#340—171no—
374#340—171no—
375#340—171no—
376#340—171no—
377#340—171no—
378#340—171no—
379#340C2×D1711yescharacteristic
380#340C2×D1711yescharacteristic
381C2×C17—44no—
382C2×C17Q8×C22⋊C411yescharacteristic
383C2×C17C2×#41711yescharacteristic
384C2×C17#289711yescharacteristic
385C2×C17#336611yescharacteristic
386C2×C17#337211yescharacteristic
387C2×C17#338411yescharacteristic
388C2×C17#338511yescharacteristic
389C22×Q8—171no—
390C22×Q8—341no—
391C22×D4C22×D1711yescharacteristic
392C23×C4—21no—
393C23×C4—341no—
394C23×C4—341no—
395C22×C8—171no—
396C22×C8—171no—
397C22×C8C22×D1711yescharacteristic
398C22×C8C22×D1711yescharacteristic
399C4⋊Q8—174no—
400C4⋊Q8—342no—
401#125—174no—
402#125—174no—
403#125—342no—
404#125—342no—
405C22⋊Q8—348no—
406C22⋊Q8—348no—
407C22⋊Q8—348no—
408C4×Q8—174no—
409C4×Q8—174no—
410C4×Q8—684no—
411C4×D4—22no—
412C4×D4—174no—
413C4×D4—174no—
414C4×D4—342no—
415C4×D4—342no—
416C4×D4C4×D1714yes—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—171no—
420C2×C4⋊C4—171no—
421C2×C4⋊C4—171no—
422C2×C4⋊C4—171no—
423C2×C4⋊C4—171no—
424C2×C4⋊C4—171no—
425C2×C4⋊C4—171no—
426C2×C4⋊C4—348no—
427C2×C4⋊C4—341no—
428C2×C4⋊C4—341no—
429C2×C4⋊C4—341no—
430C2×C4⋊C4—341no—
431C2×C4⋊C4—341no—
432C2×C4⋊C4—341no—
433C2×C4⋊C4—341no—
434C2×C4⋊C4—341no—
435C2×C4⋊C4—341no—
436C2×C4⋊C4C22×D1711yescharacteristic
437C2×C4⋊C4C22×D1711yescharacteristic
438C2×C4⋊C4C22×D1711yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—341no—
441C2×C22⋊C4—341no—
442C2×C42—171no—
443C2×C42—171no—
444C2×C42—341no—
445C2×C42—341no—
446C2×C42—341no—
447C2×C42C22×D1711yescharacteristic
448C4⋊C8—22no—
449C4⋊C8—342no—
450C4⋊C8—342no—
451#102—22no—
452#102—22no—
453#102—174no—
454#102—342no—
455#97—342no—
456#97—342no—
457C4×C8—342no—
458#95—341no—
459#95—341no—
460#95—341no—
461C17#2252211yescharacteristic, complemented, Sylow
462C24—21no—
463C2×Q8—174no—
464C2×Q8—342no—
465C2×Q8—342no—
466C2×Q8—344no—
467C2×Q8—1361no—
468C2×Q8—1361no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4C2×C4×D1712yes—
473C2×D4#6325412yes—
474C2×D4Q8×D1712yes—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—81no—
480C22×C4—81no—
481C22×C4—171no—
482C22×C4—171no—
483C22×C4—171no—
484C22×C4—171no—
485C22×C4—344no—
486C22×C4—344no—
487C22×C4—341no—
488C22×C4—341no—
489C22×C4—341no—
490C22×C4—341no—
491C22×C4—682no—
492C22×C4—682no—
493C22×C4—1361no—
494C22×C4—1361no—
495C22×C4D4×D1711yescharacteristic
496C22×C4D4×D1711yescharacteristic
497C22×C4C23×D1711yescharacteristic
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—172no—
505C2×C8—341no—
506C2×C8—341no—
507C2×C8—341no—
508C2×C8—341no—
509C2×C8—341no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—42no—
516C4⋊C4—81no—
517C4⋊C4—174no—
518C4⋊C4—174no—
519C4⋊C4—174no—
520C4⋊C4—172no—
521C4⋊C4—172no—
522C4⋊C4—172no—
523C4⋊C4—344no—
524C4⋊C4—344no—
525C4⋊C4—344no—
526C4⋊C4—341no—
527C4⋊C4—341no—
528C4⋊C4—341no—
529C4⋊C4—344no—
530C4⋊C4—344no—
531C4⋊C4—341no—
532C4⋊C4—341no—
533C4⋊C4—682no—
534C4⋊C4—682no—
535C4⋊C4—1361no—
536C4⋊C4—1361no—
537C4⋊C4C2×C4×D1712yes—
538C22⋊C4—24no—
539C22⋊C4—344no—
540C22⋊C4—344no—
541C42—172no—
542C42—172no—
543C42—172no—
544C42—172no—
545C42—682no—
546C42—682no—
547C42—682no—
548C42C2×C4×D1712yes—
549C42D4×D1712yes—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23C2×D4×D1711yescharacteristic
558Q8—348no—
559Q8—1364no—
560D4—22no—
561D4—22no—
562D4—22no—
563D4#1058757314yescomplemented
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—84no—
578C2×C4—172no—
579C2×C4—172no—
580C2×C4—172no—
581C2×C4—172no—
582C2×C4—172no—
583C2×C4—172no—
584C2×C4—341no—
585C2×C4—341no—
586C2×C4—341no—
587C2×C4—341no—
588C2×C4—341no—
589C2×C4—341no—
590C2×C4—342no—
591C2×C4—342no—
592C2×C4—342no—
593C2×C4—688no—
594C2×C4—681no—
595C2×C4—681no—
596C2×C4—681no—
597C2×C4—681no—
598C2×C4—681no—
599C2×C4—681no—
600C2×C4—681no—
601C2×C4—681no—
602C2×C4—681no—
603C2×C4—1364no—
604C2×C4C22⋊C4×D1712yes—
605C2×C4C22⋊C4×D1712yes—
606C2×C4C22×C4×D1711yescharacteristic
607C2×C4C2×D4×D1711yescharacteristic
608C2×C4C2×#6325411yescharacteristic
609C2×C4C2×Q8×D1711yescharacteristic
610C2×C4#1058769711yescharacteristic
611C2×C4#1058769711yescharacteristic
612C8—41no—
613C8—41no—
614C8—342no—
615C8—681no—
616C22—24no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22C2×C22⋊C4×D1711yescharacteristic
624C22#1176346511yescharacteristic
625C22#1176347211yescharacteristic
626C22AGL(1,ℤ/8)×D1711yescharacteristic
627C22#137×D1711yescharacteristic
628C22#1176361011yescharacteristic
629C22#1176361511yescharacteristic
630C4—22no—
631C4—22no—
632C4—42no—
633C4—81no—
634C4—81no—
635C4—174no—
636C4—342no—
637C4—342no—
638C4—342no—
639C4—682no—
640C4—682no—
641C4—682no—
642C4—1361no—
643C4C2×#1058757311yescharacteristic
644C4#1176328611yescharacteristic
645C4#1176346511yescharacteristic
646C4#1176347211yescharacteristic
647C2—44no—
648C2#1453161611yescharacteristic
649C2D17×#41711yescharacteristic
650C2#1453730511yescharacteristic
651C2#1454148611yescharacteristic
652C2#1454156011yescharacteristic
653C2#1454167811yescharacteristic
654C2#1454168911yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1802C2
socleC23×C17C22×D4
prime radicalC22×D4×C17C23
cosocleC22×C4×C17C24
hypercenter#1802D17
hypocenterC17#22522
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#11762938C2semidirect
3. #14531696C2semidirect
4. #14529752C2semidirect
5. #14529751C2semidirect
6. #14529743C2semidirect
7. #14529740C2semidirect
8. #14529739C2semidirect
9. #14529730C2semidirect
17. #11763518C4semidirect
125. #10587503Q8semidirect
234. D4×C17C4×Q8semidirect
461. C17#22522semidirect
563. D4#10587573semidirect

Maximal subgroups

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

subgroupindex
C2×#117635182
C2×#117629382
#145316962
#145297522
#145297512
#145297432
#145297402
#145297392
#145297302
#145287822
#145286112
#145286092
#102×Dic172
C17×#18022
#2252217