Finite Group Databasebeta

← #17044683

Subgroups — #17044683

Order 4352.

790 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
1C2×#11762871C211yesmaximal, characteristic
2C2×#11762869C211yesmaximal, characteristic
3#14531264C211yesmaximal, characteristic
4#14529507C211yesmaximal, characteristic, complemented
5#14529506C211yesmaximal, characteristic, complemented
6#14529504C211yesmaximal, characteristic, complemented
7#14529503C211yesmaximal, characteristic, complemented
8#14529501C211yesmaximal, characteristic, complemented
9#14529500C211yesmaximal, characteristic, complemented
10#14529499C211yesmaximal, characteristic, complemented
11#14528767C211yesmaximal, characteristic
12#14528765C211yesmaximal, characteristic
13#14528763C211yesmaximal, characteristic
14#14528761C211yesmaximal, characteristic
15C17×#1940C211yesmaximal, characteristic, complemented
16C2×#10587558C2211yescharacteristic
17C2×#10587558C2211yescharacteristic
18C2×C42×D17C2211yescharacteristic
19#11762871—24no—
20#11762869—24no—
21C2×C4⋊#3622C2211yescharacteristic
22C2×C4⋊#3622C2211yescharacteristic
23C2×C4⋊#3622C2211yescharacteristic
24C2×#10587485C2211yescharacteristic
25C2×#10587485C2211yescharacteristic
26C2×#10587485C2211yescharacteristic
27C2×#10587485C2211yescharacteristic
28C2×#10587485C2211yescharacteristic
29C2×#10587485C2211yescharacteristic
30C2×#10587491C2211yescharacteristic
31C2×#10587491C2211yescharacteristic
32C2×#10587491C2211yescharacteristic
33C2×#10587491C2211yescharacteristic
34C2×#10587486C2211yescharacteristic
35C2×C4×#3622C2211yescharacteristic
36C2×C8×Dic17C2211yescharacteristic
37#11762706C411yescharacteristic
38#11762706C411yescharacteristic
39#11762704C411yescharacteristic
40#11762704C411yescharacteristic
41#11762683C411yescharacteristic
42#11762683C411yescharacteristic
43#11762680C411yescharacteristic
44#11762680C411yescharacteristic
45C4×#63225C2211yescharacteristic
46C4×#63225C2211yescharacteristic
47C4×C4⋊Dic17C2211yescharacteristic
48#11762564C2211yescharacteristic
49#11762564C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52#11762563C2211yescharacteristic
53#11762563C2211yescharacteristic
54C2×C17×C4⋊C8C2211yescharacteristic
55C2×C17×C4⋊C8C2211yescharacteristic
56C2×C17×C4⋊C8C2211yescharacteristic
57C2×C17×#97C2211yescharacteristic
58C4×C4⋊C4×C17C2211yescharacteristic
59C17×#336C2211yescharacteristic
60C17×#336C2211yescharacteristic
61C22×C4×D17C2×C411yescharacteristic
62C22×C4×D17C2×C411yescharacteristic
63C22×C4×D17C2311yescharacteristic
64C22×C8×C17C2311yescharacteristic
65C22×C8×C17C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C2×C4⋊C4×C17C2×C411yescharacteristic
69C2×C4⋊C4×C17C2×C411yescharacteristic
70C2×C42×C17C2311yescharacteristic
71C2×C42×C17C2311yescharacteristic
72C2×C42×C17C2311yescharacteristic
73C2×#63227C2×C411yescharacteristic
74C2×#63227C2×C411yescharacteristic
75C2×#63227C2×C411yescharacteristic
76C2×#63227C2×C411yescharacteristic
77C2×C4⋊Dic17C2×C411yescharacteristic
78C2×C4⋊Dic17C2×C411yescharacteristic
79C2×#63225C2×C411yescharacteristic
80C2×#63225C2×C411yescharacteristic
81C2×#63225C2×C411yescharacteristic
82C2×#63225C2×C411yescharacteristic
83C2×#63225C2×C411yescharacteristic
84C2×#63225C2×C411yescharacteristic
85C2×#63225C2×C411yescharacteristic
86C2×#63225C2×C411yescharacteristic
87C2×C4×Dic17C2×C411yescharacteristic
88C2×C4×Dic17C2×C411yescharacteristic
89C2×C4×Dic17C2311yescharacteristic
90C2×C4×Dic17C2311yescharacteristic
91C2×C4×Dic17C2311yescharacteristic
92C22×#3622C2311yescharacteristic
93C22×#3622C2311yescharacteristic
94C22×#3622C2311yescharacteristic
95C22×#3622C2311yescharacteristic
96#10587558—41no—
97#10587558—41no—
98#10587558D414yes—
99#10587558Q814yes—
100C42×D17—41no—
101C42×D17—41no—
102C17×C4⋊C8—22no—
103C17×C4⋊C8—41no—
104C17×C4⋊C8—41no—
105C17×#97—22no—
106C17×#95C2×C411yescharacteristic
107C17×#95C2×C411yescharacteristic
108#10587502C2×C411yescharacteristic
109#10587502C2×C411yescharacteristic
110#10587502C2×C411yescharacteristic
111#10587502C2×C411yescharacteristic
112#10587502C2×C411yescharacteristic
113#10587502C2×C411yescharacteristic
114#10587491—22no—
115#10587491—22no—
116#10587491—22no—
117#10587491—22no—
118#10587486—22no—
119#10587485—22no—
120#10587485—22no—
121#10587485—41no—
122#10587485—41no—
123#10587485—41no—
124#10587485—41no—
125C8×Dic17—22no—
126C4⋊#3622—22no—
127C4⋊#3622—41no—
128C4⋊#3622—41no—
129C4×#3622—22no—
130C23×D17C22×C411yescharacteristic
131C22×C4×C17C22×C411yescharacteristic
132C22×C4×C17C22×C411yescharacteristic
133C22×C4×C17C22×C411yescharacteristic
134C22×C4×C17C22×C411yescharacteristic
135C22×C4×C17C22×C411yescharacteristic
136C22×C4×C17C22×C411yescharacteristic
137C22×C4×C17C2411yescharacteristic
138C22×Dic17C22×C411yescharacteristic
139C22×Dic17C22×C411yescharacteristic
140C22×Dic17C22×C411yescharacteristic
141C22×Dic17C22×C411yescharacteristic
142C22×Dic17C22×C411yescharacteristic
143C22×Dic17C22×C411yescharacteristic
144C22×Dic17C22×C411yescharacteristic
145C2×C4×D17—21no—
146C2×C4×D17—21no—
147C2×C4×D17—21no—
148C2×C4×D17—21no—
149C2×C4×D17—22no—
150C2×C4×D17—22no—
151C2×C4×D17—41no—
152C2×C4×D17—41no—
153C2×C4×D17—41no—
154C2×C4×D17—41no—
155C2×C4×D17C2×D412yes—
156C2×C4×D17C2×Q812yes—
157C2×C8×C17—21no—
158C2×C8×C17—21no—
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—
169C4⋊C4×C17—22no—
170C4⋊C4×C17—41no—
171C42×C17—21no—
172C42×C17—21no—
173C42×C17—21no—
174C42×C17—21no—
175C42×C17C2×D412yes—
176C42×C17C2×Q812yes—
177#63227—41no—
178#63227—41no—
179#63227C4⋊C414yes—
180#63227C4⋊C414yes—
181C4⋊Dic17—22no—
182C4⋊Dic17—41no—
183#63225—22no—
184#63225—22no—
185#63225—41no—
186#63225—41no—
187#63225—41no—
188#63225—41no—
189#63225C4⋊C414yes—
190#63225C4⋊C414yes—
191C4×Dic17—21no—
192C4×Dic17—21no—
193C4×Dic17—21no—
194C4×Dic17—21no—
195C4×Dic17—41no—
196C4×Dic17—41no—
197C4×Dic17C2×D412yes—
198C4×Dic17C2×Q812yes—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—21no—
202C2×#3622—21no—
203C2×#3622—21no—
204C2×#3622—21no—
205C2×#3622—21no—
206C2×#3622—21no—
207C2×#3622—21no—
208C2×#3622—21no—
209C2×#3622—21no—
210C2×#3622—21no—
211#21957—171nomaximal, Sylow
212C23×C17C23×C411yescharacteristic
213C22×D17—21no—
214C22×D17—21no—
215C22×D17—21no—
216C22×D17—21no—
217C22×D17—21no—
218C22×D17—21no—
219C22×D17C2×C4⋊C412yes—
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—21no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—21no—
233C2×C4×C17—21no—
234C2×C4×C17—21no—
235C2×C4×C17C2×C4⋊C412yes—
236C2×C4×C17C2×C4⋊C412yes—
237C2×C4×C17#13112yes—
238C2×C4×C17C22×D411yescharacteristic
239C2×C4×C17C22×Q811yescharacteristic
240C2×C4×C17H(5,𝔽2)11yescharacteristic
241C2×C4×C17H(5,𝔽2)11yescharacteristic
242C2×C4×C172−1+411yescharacteristic
243C2×C4×C172−1+411yescharacteristic
244C2×Dic17—21no—
245C2×Dic17—21no—
246C2×Dic17—21no—
247C2×Dic17—21no—
248C2×Dic17—21no—
249C2×Dic17—21no—
250C2×Dic17—21no—
251C2×Dic17—21no—
252C2×Dic17—21no—
253C2×Dic17—21no—
254C2×Dic17—21no—
255C2×Dic17—21no—
256C2×Dic17—21no—
257C2×Dic17—21no—
258C2×Dic17—21no—
259C2×Dic17—21no—
260C2×Dic17—21no—
261C2×Dic17C2×C4⋊C412yes—
262C2×Dic17C2×C4⋊C412yes—
263C2×Dic17C2×C4⋊C412yes—
264C2×Dic17#13112yes—
265C4×D17—22no—
266C4×D17—22no—
267C4×D17—22no—
268C4×D17—22no—
269C4×D17—44no—
270C4×D17—44no—
271C8×C17—41no—
272C8×C17—41no—
273C8×C17—41no—
274C8×C17—41no—
275#3622—41no—
276#3622—41no—
277#3622—41no—
278#3622—41no—
279C2×#433—171no—
280C2×#433—171no—
281#2296—171no—
282#1940—171no—
283#1940—171no—
284#1940—171no—
285#1940D1711yescharacteristic, complemented
286#1939—171no—
287#1939—171no—
288#1939—171no—
289#1939—171no—
290#1798—171no—
291#1798—171no—
292#1797—171no—
293#1797—171no—
294C22×C17C22×C4⋊C411yescharacteristic
295C22×C17#51811yescharacteristic
296C22×C17#51911yescharacteristic
297C22×C17C2×#13111yescharacteristic
298C22×C17C2×#13111yescharacteristic
299C22×C17#56811yescharacteristic
300C22×C17#56811yescharacteristic
301C2×D17—22no—
302C2×D17—22no—
303C2×D17—22no—
304C2×D17—41no—
305C2×D17—41no—
306C2×D17—41no—
307C2×D17—41no—
308C4×C17—22no—
309C4×C17—22no—
310C4×C17—22no—
311C4×C17—41no—
312C4×C17—41no—
313C4×C17—41no—
314C4×C17#53711yescharacteristic
315C4×C17#53711yescharacteristic
316C4×C17#54411yescharacteristic
317C4×C17#54411yescharacteristic
318Dic17—22no—
319Dic17—22no—
320Dic17—22no—
321Dic17—22no—
322Dic17—41no—
323Dic17—41no—
324Dic17—41no—
325C2×#117—171no—
326C2×#117—171no—
327C22×C42—171no—
328#433—344no—
329#433—344no—
330C2×C4⋊C8—171no—
331C2×C4⋊C8—171no—
332C2×C4⋊C8—171no—
333C2×C4⋊C8—171no—
334C2×C4⋊C8—171no—
335C2×C4⋊C8—171no—
336C2×C4⋊C8—171no—
337C2×C4⋊C8—171no—
338C2×C4⋊C8—171no—
339C2×C4⋊C8C2×D1711yescharacteristic
340C2×C4⋊C8C2×D1711yescharacteristic
341C2×C4⋊C8C2×D1711yescharacteristic
342C2×C22⋊C8—171no—
343C2×C22⋊C8—171no—
344C2×C22⋊C8—171no—
345C2×C22⋊C8—171no—
346C2×#97—171no—
347C2×#97C2×D1711yescharacteristic
348C2×C4×C8—171no—
349C2×C4×C8—171no—
350#389—171no—
351#389—171no—
352#389—171no—
353#389—171no—
354#385—171no—
355#385—171no—
356#385—171no—
357#385—171no—
358C4×C4⋊C4—171no—
359C4×C4⋊C4—171no—
360C4×C4⋊C4—171no—
361C4×C4⋊C4C2×D1711yescharacteristic
362#336—171no—
363#336—171no—
364#336—171no—
365#336—171no—
366#336—171no—
367#336—171no—
368#336C2×D1711yescharacteristic
369#336C2×D1711yescharacteristic
370C2×C17#231611yescharacteristic
371C2×C17#290611yescharacteristic
372C2×C17#290611yescharacteristic
373C2×C17#297611yescharacteristic
374C2×C17#297611yescharacteristic
375C2×C17#298611yescharacteristic
376C2×C17#298711yescharacteristic
377D17—42no—
378C23×C4—171no—
379C23×C4—171no—
380C23×C4—171no—
381C22×C8—171no—
382C22×C8—171no—
383C22×C8—171no—
384C22×C8—171no—
385C22×C8C22×D1711yescharacteristic
386C22×C8C22×D1711yescharacteristic
387C22×C8C22×D1711yescharacteristic
388C22×C8C22×D1711yescharacteristic
389#117—174no—
390#117—174no—
391#117—681no—
392#117—681no—
393C2×C4⋊C4—171no—
394C2×C4⋊C4—171no—
395C2×C4⋊C4—171no—
396C2×C4⋊C4—171no—
397C2×C4⋊C4—171no—
398C2×C4⋊C4—171no—
399C2×C4⋊C4—171no—
400C2×C4⋊C4—171no—
401C2×C4⋊C4—171no—
402C2×C4⋊C4—171no—
403C2×C4⋊C4C4×D1711yescharacteristic
404C2×C4⋊C4C4×D1711yescharacteristic
405C2×C22⋊C4—171no—
406C2×C22⋊C4—171no—
407C2×C22⋊C4—171no—
408C2×C22⋊C4—171no—
409C2×C42—171no—
410C2×C42—171no—
411C2×C42—171no—
412C2×C42—171no—
413C2×C42—171no—
414C2×C42—681no—
415C2×C42—681no—
416C2×C42C22×D1711yescharacteristic
417C2×C42C22×D1711yescharacteristic
418C2×C42C22×D1711yescharacteristic
419C4⋊C8—22no—
420C4⋊C8—41no—
421C4⋊C8—41no—
422C4⋊C8—342no—
423C4⋊C8—342no—
424C4⋊C8—342no—
425C4⋊C8—681no—
426C4⋊C8—681no—
427C4⋊C8—681no—
428C4⋊C8—681no—
429C4⋊C8—681no—
430C4⋊C8—681no—
431C22⋊C8—342no—
432C22⋊C8—342no—
433C22⋊C8—342no—
434C22⋊C8—342no—
435#97—22no—
436#97—342no—
437C4×C8—342no—
438C4×C8—342no—
439#95—171no—
440#95—171no—
441#95—171no—
442#95—171no—
443#95—171no—
444#95—171no—
445#95C4×D1711yescharacteristic
446#95C4×D1711yescharacteristic
447C17#2195711yescharacteristic, complemented, Sylow
448C24—171no—
449C22×C4—171no—
450C22×C4—171no—
451C22×C4—171no—
452C22×C4—171no—
453C22×C4—172no—
454C22×C4—172no—
455C22×C4—171no—
456C22×C4—171no—
457C22×C4—171no—
458C22×C4—342no—
459C22×C4—341no—
460C22×C4—341no—
461C22×C4—341no—
462C22×C4—341no—
463C22×C4—342no—
464C22×C4—681no—
465C22×C4—681no—
466C22×C4—681no—
467C22×C4—681no—
468C22×C4C2×C4×D1711yescharacteristic
469C22×C4C2×C4×D1711yescharacteristic
470C22×C4C2×C4×D1711yescharacteristic
471C22×C4C2×C4×D1711yescharacteristic
472C22×C4C2×C4×D1711yescharacteristic
473C22×C4C2×C4×D1711yescharacteristic
474C22×C4C23×D1711yescharacteristic
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—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—341no—
488C2×C8—341no—
489C2×C8—341no—
490C2×C8—341no—
491C2×C8—341no—
492C2×C8—341no—
493C2×C8—341no—
494C2×C8—341no—
495C2×C8—341no—
496C2×C8—341no—
497C2×C8—341no—
498C2×C8—341no—
499C4⋊C4—22no—
500C4⋊C4—41no—
501C4⋊C4—174no—
502C4⋊C4—174no—
503C4⋊C4—342no—
504C4⋊C4—342no—
505C4⋊C4—342no—
506C4⋊C4—681no—
507C4⋊C4—681no—
508C4⋊C4—681no—
509C4⋊C4—681no—
510C4⋊C4—681no—
511C22⋊C4—174no—
512C22⋊C4—174no—
513C22⋊C4—681no—
514C22⋊C4—681no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—172no—
520C42—172no—
521C42—341no—
522C42—341no—
523C42—341no—
524C42—341no—
525C42—681no—
526C42—681no—
527C42D4×D1712yes—
528C42Q8×D1712yes—
529C23—172no—
530C23—341no—
531C23—341no—
532C23—341no—
533C23—341no—
534C23—341no—
535C23—341no—
536C23C22×C4×D1711yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—172no—
553C2×C4—172no—
554C2×C4—172no—
555C2×C4—172no—
556C2×C4—341no—
557C2×C4—341no—
558C2×C4—341no—
559C2×C4—341no—
560C2×C4—341no—
561C2×C4—341no—
562C2×C4—341no—
563C2×C4—341no—
564C2×C4—342no—
565C2×C4—342no—
566C2×C4—342no—
567C2×C4—342no—
568C2×C4—341no—
569C2×C4—341no—
570C2×C4—341no—
571C2×C4—341no—
572C2×C4—341no—
573C2×C4—341no—
574C2×C4—341no—
575C2×C4—341no—
576C2×C4—341no—
577C2×C4—684no—
578C2×C4—684no—
579C2×C4C4⋊C4×D1712yes—
580C2×C4C4⋊C4×D1712yes—
581C2×C4#1058759312yes—
582C2×C4C2×D4×D1711yescharacteristic
583C2×C4#1058769111yescharacteristic
584C2×C4C2×Q8×D1711yescharacteristic
585C2×C4#1058769411yescharacteristic
586C2×C4#1058769611yescharacteristic
587C2×C4#1058769711yescharacteristic
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—681no—
593C8—681no—
594C8—681no—
595C8—681no—
596C22—342no—
597C22—342no—
598C22—342no—
599C22—681no—
600C22—681no—
601C22—681no—
602C22—681no—
603C22C2×C4⋊C4×D1711yescharacteristic
604C22#1176328111yescharacteristic
605C22#1176328511yescharacteristic
606C22#131×D1711yescharacteristic
607C22C2×#1058759311yescharacteristic
608C22#1176357411yescharacteristic
609C22#1176357511yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—342no—
617C4—342no—
618C4—342no—
619C4—342no—
620C4—681no—
621C4—681no—
622C4—681no—
623C4#1176338811yescharacteristic
624C4#1176338911yescharacteristic
625C4#1176343611yescharacteristic
626C4#1176343911yescharacteristic
627C2—682no—
628C2#1453139911yescharacteristic
629C2#1453735111yescharacteristic
630C2#1453735311yescharacteristic
631C2#1453783111yescharacteristic
632C2#1453783311yescharacteristic
633C2#1453788211yescharacteristic
634C2#1453788711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1940C2
prime radicalC23×D17C22×C4
cosocleC22×C4×C17C24
hypercenter#1940D17
hypocenterC17#21957
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
4. #14529507C2semidirect
5. #14529506C2semidirect
6. #14529504C2semidirect
7. #14529503C2semidirect
8. #14529501C2semidirect
9. #14529500C2semidirect
10. #14529499C2semidirect
15. C17×#1940C2semidirect
285. #1940D17semidirect
447. C17#21957semidirect

Maximal subgroups

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

subgroupindex
C2×#117628712
C2×#117628692
#145312642
#145295072
#145295062
#145295042
#145295032
#145295012
#145295002
#145294992
#145287672
#145287652
#145287632
#145287612
C17×#19402
#2195717