Finite Group Databasebeta

← #17043877

Subgroups — #17043877

Order 4352.

970 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763437C211yesmaximal, characteristic
2#14531393C211yesmaximal, characteristic
3#14529757C211yesmaximal, characteristic, complemented
4#14529753C211yesmaximal, characteristic, complemented
5#14529749C211yesmaximal, characteristic, complemented
6#14529745C211yesmaximal, characteristic, complemented
7#14529739C211yesmaximal, characteristic, complemented
8#14529739C211yesmaximal, characteristic, complemented
9#14529735C211yesmaximal, characteristic, complemented
10#14529731C211yesmaximal, characteristic, complemented
11#14528880C211yesmaximal, characteristic
12#14528880C211yesmaximal, characteristic
13#14528875C211yesmaximal, characteristic
14#14528871C211yesmaximal, characteristic
15C2×C17×#433C211yesmaximal, characteristic
16#11763437—24no—
17#11763437C418yescomplemented
18C2×#10587555C2211yescharacteristic
19C2×#10587555C2211yescharacteristic
20C2×#10587574—21no—
21C2×#10587556C2211yescharacteristic
22C2×#10587556C2211yescharacteristic
23C2×#10587576—21no—
24C2×#10587564—21no—
25C2×#10587564—21no—
26C2×#10587612C2211yescharacteristic
27C22×C4⋊Dic17C2211yescharacteristic
28#11762702—21no—
29#11762702—21no—
30#11762695—21no—
31#11762695—21no—
32#11762679C2211yescharacteristic
33#11762675C2211yescharacteristic
34#11762669C2211yescharacteristic
35#11762669C2211yescharacteristic
36C4×C4⋊Dic17C2211yescharacteristic
37C4×C4⋊Dic17C2211yescharacteristic
38#11762572C2211yescharacteristic
39#11762572C2211yescharacteristic
40#11762572C2211yescharacteristic
41#11762572C2211yescharacteristic
42#11762572C2211yescharacteristic
43#11762572C2211yescharacteristic
44#11762572C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762572C2211yescharacteristic
51#11762572C2211yescharacteristic
52#11762572C2211yescharacteristic
53#11762572C2211yescharacteristic
54C2×C17×#117C2211yescharacteristic
55C17×#433—24no—
56C2×C17×C4⋊C8C2211yescharacteristic
57C2×C17×C4⋊C8C2211yescharacteristic
58C2×C17×C22⋊C8C2211yescharacteristic
59C2×C17×C22⋊C8C2211yescharacteristic
60C2×C17×#97C2211yescharacteristic
61C2×C4×C8×C17C2211yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×Dic17—21no—
64C22×Dic34—21no—
65C22×Dic34—21no—
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C22×C8×C17C2311yescharacteristic
69C22×C8×C17C2311yescharacteristic
70C17×#117C2×C414yes—
71C17×#117D414yes—
72C2×C4⋊C4×C17D411yescharacteristic
73C2×C4⋊C4×C17D411yescharacteristic
74C2×C22⋊C4×C17D411yescharacteristic
75C2×C22⋊C4×C17D411yescharacteristic
76C2×C42×C17C2311yescharacteristic
77C2×C42×C17C2311yescharacteristic
78C2×C22⋊Dic17—21no—
79C2×C22⋊Dic17—21no—
80C2×C22⋊Dic17—21no—
81#10587612—22no—
82#10587612C2×C414yes—
83C2×C4⋊Dic17—21no—
84C2×C4⋊Dic17—22no—
85C2×C4⋊Dic17—21no—
86C2×C4⋊Dic17—21no—
87C2×C4⋊Dic17—21no—
88C2×C4⋊Dic17—21no—
89C2×C4⋊Dic17C2×C414yes—
90C2×C4⋊Dic17C2311yescharacteristic
91C2×C4⋊Dic17C2311yescharacteristic
92C2×C4⋊Dic17C2311yescharacteristic
93C2×C4⋊Dic17C2311yescharacteristic
94C2×C4⋊Dic17C2311yescharacteristic
95C2×C4⋊Dic17C2311yescharacteristic
96C2×C4⋊Dic17C2311yescharacteristic
97C2×C4⋊Dic17C2311yescharacteristic
98C2×#63225—21no—
99C2×#63225—21no—
100C2×#63225—21no—
101C2×#63225—21no—
102C2×C4×Dic17—21no—
103C2×C4×Dic17—21no—
104C2×C4×Dic17—21no—
105#10587576—28no—
106#10587574—28no—
107#10587564—28no—
108#10587564—28no—
109#10587556—22no—
110#10587556—22no—
111#10587556C2×C414yes—
112#10587556C2×C414yes—
113#10587555—22no—
114#10587555—22no—
115#10587555C2×C414yes—
116#10587555C2×C414yes—
117C17×C4⋊C8—22no—
118C17×C4⋊C8—22no—
119C17×C22⋊C8—22no—
120C17×C22⋊C8—22no—
121C17×#97—22no—
122C4×C8×C17—22no—
123#10587502—21no—
124#10587502—21no—
125#10587502—21no—
126#10587502—21no—
127#10587502—21no—
128#10587502—21no—
129C24×C17C2×D411yescharacteristic
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17C22×C412yes—
135C22×C4×C17C2×D411yescharacteristic
136C22×C4×C17C2×D411yescharacteristic
137C22×C4×C17C2×D411yescharacteristic
138C22×C4×C17C2×D411yescharacteristic
139C22×C4×C17C2×D411yescharacteristic
140C22×C4×C17C2×D412yes—
141C22×C4×C17C2411yescharacteristic
142C22×Dic17—21no—
143C22×Dic17—21no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17—24no—
147C22×Dic17—21no—
148C22×Dic17—21no—
149C22×Dic17—21no—
150C22×Dic17—21no—
151C22×Dic17—81no—
152C22×Dic17—81no—
153C2×Dic34—24no—
154C2×Dic34—24no—
155C2×Dic34—81no—
156C2×Dic34—81no—
157C2×Dic34—81no—
158C2×Dic34—81no—
159C2×C8×C17—21no—
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—21no—
171C4⋊C4×C17C22⋊C414yes—
172C4⋊C4×C17C22⋊C414yes—
173C22⋊C4×C17C22⋊C414yes—
174C22⋊C4×C17C22⋊C414yes—
175C42×C17C22×C412yes—
176C42×C17C22×C412yes—
177C42×C17C2×D412yes—
178C42×C17C2×D412yes—
179C22⋊Dic17—24no—
180C22⋊Dic17—81no—
181C22⋊Dic17—81no—
182C4⋊Dic17—24no—
183C4⋊Dic17—24no—
184C4⋊Dic17—24no—
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—81no—
198C4⋊Dic17—81no—
199C4⋊Dic17C22×C412yes—
200C4⋊Dic17C22×C412yes—
201C4⋊Dic17C22×C412yes—
202C4⋊Dic17C22×C412yes—
203#63225—24no—
204#63225—24no—
205#63225—24no—
206#63225—24no—
207C4×Dic17—24no—
208C4×Dic17—81no—
209C4×Dic17—81no—
210#21843—171nomaximal, Sylow
211C23×C17—21no—
212C23×C17—21no—
213C23×C17—21no—
214C23×C17—21no—
215C23×C17—21no—
216C23×C17—21no—
217C23×C17C2×C22⋊C412yes—
218C23×C17C22×D411yescharacteristic
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—22no—
230C2×C4×C17—22no—
231C2×C4×C17—22no—
232C2×C4×C17—22no—
233C2×C4×C17C2×C22⋊C412yes—
234C2×C4×C17C2×C22⋊C412yes—
235C2×C4×C17C2×C22⋊C412yes—
236C2×C4×C17C2×C22⋊C412yes—
237C2×C4×C17C2×C22⋊C412yes—
238C2×C4×C17C23×C411yescharacteristic
239C2×C4×C17C22×D411yescharacteristic
240C2×C4×C172−1+411yescharacteristic
241C2×C4×C172−1+411yescharacteristic
242C2×C4×C172−1+411yescharacteristic
243C2×C4×C172−1+411yescharacteristic
244C2×Dic17—22no—
245C2×Dic17—22no—
246C2×Dic17—22no—
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—
268C2×Dic17—84no—
269Dic34—84no—
270Dic34—84no—
271C8×C17—41no—
272C8×C17—41no—
273C8×C17—41no—
274C8×C17—41no—
275C2×#544—171no—
276C2×#433D1711yescharacteristic
277#2314—171no—
278#1993—171no—
279#1992—171no—
280#1991—171no—
281#1990—171no—
282#1989—171no—
283#1989—171no—
284#1988—171no—
285#1987—171no—
286#1825—171no—
287#1825—171no—
288#1824—171no—
289#1823—171no—
290C22×C17—22no—
291C22×C17—22no—
292C22×C17—22no—
293C22×C17—41no—
294C22×C17—41no—
295C22×C17—41no—
296C22×C17—41no—
297C22×C17C22×C22⋊C411yescharacteristic
298C22×C17#53611yescharacteristic
299C22×C17#53611yescharacteristic
300C22×C17#57611yescharacteristic
301C22×C17#57711yescharacteristic
302C22×C17#57711yescharacteristic
303C22×C17#57811yescharacteristic
304C4×C17—22no—
305C4×C17—22no—
306C4×C17—22no—
307C4×C17—22no—
308C4×C17—22no—
309C4×C17#51911yescharacteristic
310C4×C17#51911yescharacteristic
311C4×C17#53611yescharacteristic
312C4×C17#53611yescharacteristic
313Dic17—42no—
314Dic17—42no—
315Dic17—42no—
316Dic17—42no—
317Dic17—81no—
318Dic17—81no—
319Dic17—81no—
320Dic17—81no—
321#544—178no—
322#544—344no—
323C2×C4⋊Q8—171no—
324C2×C4⋊Q8—171no—
325C2×C4⋊Q8—341no—
326C2×#125—171no—
327C2×#125—171no—
328C2×#125—341no—
329C2×C22⋊Q8—341no—
330C2×C22⋊Q8—341no—
331C2×#117—171no—
332C2×#117C2×D1711yescharacteristic
333C22×C4⋊C4—171no—
334#433—24no—
335C2×C4⋊C8C2×D1711yescharacteristic
336C2×C4⋊C8C2×D1711yescharacteristic
337C2×C22⋊C8C2×D1711yescharacteristic
338C2×C22⋊C8C2×D1711yescharacteristic
339C2×#97C2×D1711yescharacteristic
340C2×C4×C8C2×D1711yescharacteristic
341#388—341no—
342#388—341no—
343#387—341no—
344#387—341no—
345#384—171no—
346#382—171no—
347#380—171no—
348#380—171no—
349C4×C4⋊C4—171no—
350C4×C4⋊C4—171no—
351#340—171no—
352#340—171no—
353#340—171no—
354#340—171no—
355#340—171no—
356#340—171no—
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#340—171no—
367C2×C17—42no—
368C2×C17#231011yescharacteristic
369C2×C17#289711yescharacteristic
370C2×C17#289811yescharacteristic
371C2×C17#324111yescharacteristic
372C2×C17#324211yescharacteristic
373C2×C17#324311yescharacteristic
374C2×C17#324411yescharacteristic
375C22×Q8—341no—
376C22×Q8—341no—
377C23×C4—341no—
378C23×C4C22×D1711yescharacteristic
379C22×C8C22×D1711yescharacteristic
380C22×C8C22×D1711yescharacteristic
381C22×C8C22×D1711yescharacteristic
382C22×C8C22×D1711yescharacteristic
383C4⋊Q8—174no—
384C4⋊Q8—174no—
385C4⋊Q8—348no—
386C4⋊Q8—342no—
387C4⋊Q8—342no—
388#125—174no—
389#125—174no—
390#125—348no—
391#125—342no—
392#125—342no—
393C22⋊Q8—348no—
394C22⋊Q8—348no—
395#117—174no—
396#117—342no—
397#117C4×D1714yes—
398#117C22⋊D1714yes—
399C2×C4⋊C4—174no—
400C2×C4⋊C4—171no—
401C2×C4⋊C4—171no—
402C2×C4⋊C4—171no—
403C2×C4⋊C4—171no—
404C2×C4⋊C4—171no—
405C2×C4⋊C4—171no—
406C2×C4⋊C4—171no—
407C2×C4⋊C4—171no—
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—341no—
415C2×C4⋊C4—342no—
416C2×C4⋊C4—341no—
417C2×C4⋊C4—341no—
418C2×C4⋊C4D6811yescharacteristic
419C2×C4⋊C4D6811yescharacteristic
420C2×C22⋊C4—341no—
421C2×C22⋊C4—341no—
422C2×C22⋊C4—341no—
423C2×C22⋊C4D6811yescharacteristic
424C2×C22⋊C4D6811yescharacteristic
425C2×C42—341no—
426C2×C42—341no—
427C2×C42—341no—
428C2×C42C22×D1711yescharacteristic
429C2×C42C22×D1711yescharacteristic
430C4⋊C8—22no—
431C4⋊C8—22no—
432C22⋊C8—22no—
433C22⋊C8—22no—
434#97—22no—
435C4×C8—22no—
436#95—341no—
437#95—341no—
438#95—341no—
439#95—341no—
440#95—341no—
441#95—341no—
442C17#2184311yescharacteristic, complemented, Sylow
443C24C2×D6811yescharacteristic
444C2×Q8—344no—
445C2×Q8—344no—
446C2×Q8—1361no—
447C2×Q8—1361no—
448C2×Q8—1361no—
449C2×Q8—1361no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—341no—
455C22×C4—341no—
456C22×C4—341no—
457C22×C4—341no—
458C22×C4—344no—
459C22×C4—341no—
460C22×C4—341no—
461C22×C4—341no—
462C22×C4—341no—
463C22×C4—1361no—
464C22×C4—1361no—
465C22×C4C2×C4×D1712yes—
466C22×C4C2×D6811yescharacteristic
467C22×C4C2×D6811yescharacteristic
468C22×C4C2×D6811yescharacteristic
469C22×C4C2×D6811yescharacteristic
470C22×C4C2×D6811yescharacteristic
471C22×C4C2×C22⋊D1712yes—
472C22×C4C23×D1711yescharacteristic
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C4⋊C4—172no—
486C4⋊C4—172no—
487C4⋊C4—172no—
488C4⋊C4—172no—
489C4⋊C4—341no—
490C4⋊C4—341no—
491C4⋊C4—341no—
492C4⋊C4—341no—
493C4⋊C4—344no—
494C4⋊C4—344no—
495C4⋊C4—344no—
496C4⋊C4—344no—
497C4⋊C4—344no—
498C4⋊C4—344no—
499C4⋊C4—344no—
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—1361no—
509C4⋊C4—1361no—
510C4⋊C4#6322714yes—
511C4⋊C4#6322714yes—
512C22⋊C4—344no—
513C22⋊C4—1361no—
514C22⋊C4—1361no—
515C22⋊C4#6322714yes—
516C22⋊C4#6322714yes—
517C42—344no—
518C42—1361no—
519C42—1361no—
520C42C2×C4×D1712yes—
521C42C2×C4×D1712yes—
522C42C2×C22⋊D1712yes—
523C42C2×C22⋊D1712yes—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23C2×#6322712yes—
531C23C22×D6811yescharacteristic
532Q8—1364no—
533Q8—1364no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—342no—
549C2×C4—342no—
550C2×C4—342no—
551C2×C4—342no—
552C2×C4—681no—
553C2×C4—681no—
554C2×C4—681no—
555C2×C4—681no—
556C2×C4—681no—
557C2×C4—681no—
558C2×C4—681no—
559C2×C4—681no—
560C2×C4—681no—
561C2×C4—681no—
562C2×C4—681no—
563C2×C4—681no—
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—1364no—
573C2×C4C2×#6322712yes—
574C2×C4C2×#6322712yes—
575C2×C4C2×#6322712yes—
576C2×C4C2×#6322712yes—
577C2×C4C2×#6322712yes—
578C2×C4C22×C4×D1711yescharacteristic
579C2×C4#1058769711yescharacteristic
580C2×C4#1058769711yescharacteristic
581C2×C4#1058769711yescharacteristic
582C2×C4#1058769711yescharacteristic
583C2×C4C22×C22⋊D1711yescharacteristic
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C22—22no—
589C22—22no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22C22×#6322711yescharacteristic
596C22#1176338511yescharacteristic
597C22#1176338511yescharacteristic
598C22#1176361411yescharacteristic
599C22#1176362111yescharacteristic
600C22#1176362111yescharacteristic
601C22#1176362611yescharacteristic
602C4—22no—
603C4—22no—
604C4—22no—
605C4—22no—
606C4—22no—
607C4—682no—
608C4—682no—
609C4—682no—
610C4—682no—
611C4—1361no—
612C4—1361no—
613C4—1361no—
614C4—1361no—
615C4#1176328611yescharacteristic
616C4#1176328611yescharacteristic
617C4#1176338011yescharacteristic
618C4#1176338011yescharacteristic
619C2—42no—
620C2#1453136811yescharacteristic
621C2#1453731111yescharacteristic
622C2#1453731811yescharacteristic
623C2#1454003911yescharacteristic
624C2#1454005411yescharacteristic
625C2#1454006911yescharacteristic
626C2#1454008411yescharacteristic
subgroupG/H
centerC23C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#433C2
socleC23×C17C22×D4
prime radicalC24×C17C2×D4
cosocleC22×C4×C17C24
hypercenterC2×#433D17
hypocenterC17#21843
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
3. #14529757C2semidirect
4. #14529753C2semidirect
5. #14529749C2semidirect
6. #14529745C2semidirect
7. #14529739C2semidirect
8. #14529739C2semidirect
9. #14529735C2semidirect
10. #14529731C2semidirect
17. #11763437C4semidirect
442. C17#21843semidirect

Maximal subgroups

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

subgroupindex
C2×#117634372
#145313932
#145297572
#145297532
#145297492
#145297452
#145297392
#145297352
#145297312
#145288802
#145288752
#145288712
C2×C17×#4332
#2184317