Finite Group Databasebeta

← #16950284

Subgroups — #16950284

Order 4352.

808 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 808 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10587623C211yesmaximal, characteristic
2C2×#11762595C212yesmaximal
3#14528776C211yesmaximal, characteristic, complemented
4#14526901C212yesmaximal, complemented
5C17×#1799C211yesmaximal, characteristic, complemented
6C23×C4×D17C411yescharacteristic, complemented
7C2×#10587623C2211yescharacteristic
8C2×C4×C22⋊D17—21no—
9#11762833—21no—
10C2×#10587504C2212yes—
11#11762689C2211yescharacteristic
12#11762685—21no—
13#11762681C411yescharacteristic, complemented
14#11762680—21no—
15#11762664C411yescharacteristic, complemented
16C4×#63227—21no—
17C4×C22⋊Dic17C411yescharacteristic, complemented
18#11762595—24no—
19#11762578—21no—
20C2×C4×D4×C17C2211yescharacteristic
21C2×C17×#99C2212yes—
22C17×#380—21no—
23C17×#342—21no—
24C24×D17C2×C411yescharacteristic
25C22×D4×C17C2311yescharacteristic
26C23×C4×C17C2×C411yescharacteristic
27C23×C4×C17D411yescharacteristic
28C22×C22⋊D17—21no—
29C23×Dic17C2×C411yescharacteristic
30C22×C4×D17—21no—
31C22×C4×D17—21no—
32C22×C4×D17—44no—
33C22×C4×D17—41no—
34C22×C4×D17—41no—
35C4×D4×C17—41no—
36C4×D4×C17—41no—
37C2×C4⋊C4×C17—41no—
38C2×C4⋊C4×C17D411yescharacteristic
39C2×C22⋊C4×C17—22no—
40C2×C22⋊C4×C17C2×C411yescharacteristic
41C2×C22⋊C4×C17D411yescharacteristic
42C2×C42×C17D411yescharacteristic
43C2×C22⋊Dic17—21no—
44C2×C22⋊Dic17C2×C411yescharacteristic
45C2×C22⋊Dic17C2×C411yescharacteristic
46#10587623—21no—
47#10587623—21no—
48#10587623D412yes—
49#10587623Q812yes—
50C4×C22⋊D17—44no—
51C2×#63227—21no—
52C2×#63227—21no—
53C2×#63227—21no—
54C2×#63225—21no—
55C2×C4×Dic17—21no—
56C2×#63223—22no—
57C17×#99—22no—
58C17×#99—22no—
59C17×#95—41no—
60#10587504—22no—
61#10587504—22no—
62#10587502—21no—
63#10587502—21no—
64#10587502—21no—
65C4⋊#3622—41no—
66C4⋊#3622—41no—
67C24×C17C22×C411yescharacteristic
68C24×C17C2×D411yescharacteristic
69C23×D17—21no—
70C23×D17—21no—
71C23×D17—42no—
72C23×D17—42no—
73C23×D17—41no—
74C23×D17—41no—
75C23×D17C4⋊C412yescomplemented
76C2×D4×C17—41no—
77C2×D4×C17—41no—
78C2×D4×C17C2×D411yescharacteristic
79C2×D4×C17C2×Q811yescharacteristic
80C2×D4×C17#4111yescharacteristic
81C2×D4×C17#4111yescharacteristic
82C22×C4×C17—21no—
83C22×C4×C17—21no—
84C22×C4×C17—21no—
85C22×C4×C17—21no—
86C22×C4×C17—42no—
87C22×C4×C17—42no—
88C22×C4×C17—42no—
89C22×C4×C17C22⋊C411yescharacteristic
90C22×C4×C17C22⋊C411yescharacteristic
91C22×C4×C17C22⋊C411yescharacteristic
92C22×C4×C17C22⋊C411yescharacteristic
93C22×C4×C17C2×D411yescharacteristic
94C2×C22⋊D17—22no—
95C2×C22⋊D17—22no—
96C2×C22⋊D17—42no—
97C2×C22⋊D17—42no—
98C22×Dic17—21no—
99C22×Dic17—21no—
100C22×Dic17—21no—
101C22×Dic17—42no—
102C22×Dic17—41no—
103C2×C4×D17—24no—
104C2×C4×D17—42no—
105C2×C4×D17—42no—
106C2×C4×D17—42no—
107C2×C4×D17—42no—
108C2×C4×D17—44no—
109C2×C4×D17—44no—
110C2×C4×D17—44no—
111C2×C4×D17—41no—
112C2×C4×D17—41no—
113C2×C4×D17—44no—
114C4⋊C4×C17—41no—
115C4⋊C4×C17—82no—
116C22⋊C4×C17—41no—
117C22⋊C4×C17—41no—
118C22⋊C4×C17—42no—
119C22⋊C4×C17—42no—
120C42×C17—21no—
121C42×C17—21no—
122C22⋊Dic17—21no—
123C22⋊Dic17—42no—
124C22⋊Dic17—41no—
125C22⋊Dic17C4⋊C412yescomplemented
126#63227—22no—
127#63227—22no—
128#63227—42no—
129#63227—42no—
130#63225—42no—
131C4×Dic17—42no—
132#63223—42no—
133#63223—42no—
134C2×#3622—42no—
135#12793—171nomaximal, Sylow
136C23×C17—21no—
137C23×C17—21no—
138C23×C17—21no—
139C23×C17—21no—
140C23×C17—41no—
141C23×C17—41no—
142C23×C17—41no—
143C23×C17—41no—
144C23×C17C2×C22⋊C411yescharacteristic
145C23×C17C2×C4⋊C411yescharacteristic
146C23×C17#11711yescharacteristic
147C23×C17#12111yescharacteristic
148C23×C17C22⋊Q811yescharacteristic
149C22×D17—22no—
150C22×D17—22no—
151C22×D17—22no—
152C22×D17—44no—
153C22×D17—44no—
154C22×D17—41no—
155C22×D17—41no—
156C22×D17—42no—
157C22×D17—42no—
158C22×D17—48no—
159C22×D17—42no—
160C22×D17—41no—
161C22×D17—41no—
162C22×D17—42no—
163C22×D17—42no—
164C22×D17—42no—
165D4×C17—41no—
166D4×C17—41no—
167D4×C17—41no—
168D4×C17—41no—
169C2×C4×C17—21no—
170C2×C4×C17—21no—
171C2×C4×C17—22no—
172C2×C4×C17—21no—
173C2×C4×C17—21no—
174C2×C4×C17—21no—
175C2×C4×C17—42no—
176C2×C4×C17—42no—
177C2×C4×C17—42no—
178C2×C4×C17—41no—
179C2×C4×C17—41no—
180C2×C4×C17—41no—
181C2×C4×C17—81no—
182C2×C4×C17—82no—
183C2×C4×C17—82no—
184C2×C4×C17—82no—
185C2×C4×C17#9911yescharacteristic
186C2×C4×C17#9911yescharacteristic
187C2×C4×C17#12111yescharacteristic
188C2×C4×C17C22⋊Q811yescharacteristic
189C22⋊D17—44no—
190C22⋊D17—44no—
191C2×Dic17—22no—
192C2×Dic17—22no—
193C2×Dic17—41no—
194C2×Dic17—41no—
195C2×Dic17—41no—
196C2×Dic17—42no—
197C2×Dic17—41no—
198C2×Dic17—42no—
199C2×Dic17—41no—
200C2×Dic17—41no—
201C2×Dic17—41no—
202C4×D17—44no—
203C4×D17—48no—
204C4×D17—44no—
205#3622—82no—
206C4×#120—171no—
207C2×AΣL(1,𝔽16)—172no—
208#1800—171no—
209#1799D1711yescharacteristic, complemented
210#1390—172no—
211C22×C17—21no—
212C22×C17—21no—
213C22×C17—21no—
214C22×C17—21no—
215C22×C17—21no—
216C22×C17—21no—
217C22×C17—41no—
218C22×C17—41no—
219C22×C17—41no—
220C22×C17—41no—
221C22×C17—42no—
222C22×C17—41no—
223C22×C17—41no—
224C22×C17—41no—
225C22×C17—41no—
226C22×C17—81no—
227C22×C17#38011yescharacteristic
228C22×C17C2×#9911yescharacteristic
229C22×C17#41011yescharacteristic
230C2×D17—24no—
231C2×D17—42no—
232C2×D17—42no—
233C2×D17—42no—
234C2×D17—44no—
235C2×D17—44no—
236C2×D17—44no—
237C2×D17—42no—
238C2×D17—42no—
239C2×D17—42no—
240C2×D17—44no—
241C4×C17—21no—
242C4×C17—21no—
243C4×C17—21no—
244C4×C17—41no—
245C4×C17—41no—
246C4×C17—41no—
247C4×C17—162no—
248C4×C17AΣL(1,𝔽16)12yescomplemented
249Dic17—42no—
250Dic17—42no—
251Dic17—81no—
252C24×C4—171no—
253C2×#120—171no—
254C2×C4×D4—341no—
255C2×C4×D4C2×D1711yescharacteristic
256#423—341no—
257C2×#100—172no—
258C2×#99C2×D1712yes—
259#386—171no—
260#386—341no—
261#385—171no—
262#385—341no—
263#380—21no—
264#379—171no—
265C4×C22⋊C4—171no—
266C4×C22⋊C4—341no—
267AΣL(1,𝔽16)—344no—
268#343—341no—
269#342—21no—
270C2×C17—21no—
271C2×C17—21no—
272C2×C17—41no—
273C2×C17—41no—
274C2×C17—41no—
275C2×C17—41no—
276C2×C17#179911yescharacteristic
277C2×C17C2×AΣL(1,𝔽16)11yescharacteristic
278C2×C17#212011yescharacteristic
279D17—44no—
280C25—171no—
281C22×D4—341no—
282C22×D4C22×D1711yescharacteristic
283C23×C4—171no—
284C23×C4—341no—
285C23×C4—341no—
286C23×C4—681no—
287C23×C4—681no—
288C23×C4—684no—
289C23×C4C4×D1711yescharacteristic
290C23×C4C22⋊D1711yescharacteristic
291C2×M16—342no—
292#120—172no—
293#120—172no—
294#120—341no—
295#120—341no—
296C4×D4—41no—
297C4×D4—41no—
298C4×D4—684no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—341no—
301C2×C4⋊C4D6811yescharacteristic
302C2×C22⋊C4—22no—
303C2×C22⋊C4—171no—
304C2×C22⋊C4—171no—
305C2×C22⋊C4—341no—
306C2×C22⋊C4—341no—
307C2×C22⋊C4—341no—
308C2×C22⋊C4—341no—
309C2×C22⋊C4C4×D1711yescharacteristic
310C2×C22⋊C4C22⋊D1711yescharacteristic
311C2×C42—341no—
312C2×C42D6811yescharacteristic
313C4⋊C8—681no—
314C4⋊C8—681no—
315#100—342no—
316#100—342no—
317#99—22no—
318#99—22no—
319#95—41no—
320#95—341no—
321#95—341no—
322#95—341no—
323C17#1279311yescharacteristic, complemented, Sylow
324C24—172no—
325C24—341no—
326C24—341no—
327C24—681no—
328C24—681no—
329C24—682no—
330C24—682no—
331C24C2×C4×D1711yescharacteristic
332C24C2×C22⋊D1711yescharacteristic
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—342no—
336C2×D4—342no—
337C2×D4—682no—
338C2×D4—682no—
339C2×D4D4×D1711yescharacteristic
340C2×D4#6325411yescharacteristic
341C2×D4Q8×D1711yescharacteristic
342C2×D4#6325611yescharacteristic
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—344no—
351C22×C4—341no—
352C22×C4—341no—
353C22×C4—341no—
354C22×C4—682no—
355C22×C4—682no—
356C22×C4—682no—
357C22×C4—682no—
358C22×C4—684no—
359C22×C4—684no—
360C22×C4—684no—
361C22×C4—684no—
362C22×C4—682no—
363C22×C4—681no—
364C22×C4—681no—
365C22×C4—681no—
366C22×C4#6322711yescharacteristic
367C22×C4#6322711yescharacteristic
368C22×C4#6322711yescharacteristic
369C22×C4#6322711yescharacteristic
370C22×C4C2×D6811yescharacteristic
371M16—682no—
372M16—682no—
373C2×C8—682no—
374C4⋊C4—41no—
375C4⋊C4—82no—
376C4⋊C4—682no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—42no—
380C22⋊C4—42no—
381C22⋊C4—172no—
382C22⋊C4—341no—
383C22⋊C4—342no—
384C22⋊C4—342no—
385C22⋊C4—682no—
386C22⋊C4—682no—
387C22⋊C4—682no—
388C22⋊C4—681no—
389C42—21no—
390C42—21no—
391C42—682no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—342no—
401C23—342no—
402C23—342no—
403C23—682no—
404C23—681no—
405C23—681no—
406C23—682no—
407C23—684no—
408C23—684no—
409C23—682no—
410C23—682no—
411C23—682no—
412C23—688no—
413C23—682no—
414C23—681no—
415C23—681no—
416C23C4⋊C4×D1711yescharacteristic
417C23#1058757811yescharacteristic
418C23C2×#6322711yescharacteristic
419C23#1058762411yescharacteristic
420C23#1058763211yescharacteristic
421D4—41no—
422D4—41no—
423D4—41no—
424D4—41no—
425D4—684no—
426D4—684no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—81no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4—342no—
444C2×C4—342no—
445C2×C4—684no—
446C2×C4—688no—
447C2×C4—681no—
448C2×C4—681no—
449C2×C4—681no—
450C2×C4—682no—
451C2×C4—681no—
452C2×C4—684no—
453C2×C4—682no—
454C2×C4—681no—
455C2×C4—681no—
456C2×C4—681no—
457C2×C4#1058747711yescharacteristic
458C2×C4#1058747711yescharacteristic
459C2×C4#1058758111yescharacteristic
460C2×C4#1058758311yescharacteristic
461C8—1362no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—42no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—81no—
478C22—344no—
479C22—682no—
480C22—682no—
481C22—682no—
482C22—684no—
483C22—684no—
484C22—684no—
485C22—684no—
486C22—682no—
487C22—682no—
488C22—682no—
489C22#1176266611yescharacteristic
490C22C2×#1058747711yescharacteristic
491C22#1176278211yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—41no—
496C4—41no—
497C4—41no—
498C4—162no—
499C4—682no—
500C4—682no—
501C4—1361no—
502C4#1176259512yescomplemented
503C2—21no—
504C2—21no—
505C2—41no—
506C2—41no—
507C2—41no—
508C2—41no—
509C2—684no—
510C2#1452876911yescharacteristic
511C2C2×#1176259511yescharacteristic
512C2#1453042311yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC24×C17C22×C4
FrattiniC22×D4C22×D17
FittingC17×#1799C2
socleC22×C17C2×#99
prime radicalC2×#10587623C22
cosocleC22×D4×C17C23
hypercenter#1799D17
hypocenterC17#12793
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #14528776C2semidirect
4. #14526901C2semidirect
5. C17×#1799C2semidirect
6. C23×C4×D17C4semidirect
13. #11762681C4semidirect
15. #11762664C4semidirect
17. C4×C22⋊Dic17C4semidirect
75. C23×D17C4⋊C4semidirect
125. C22⋊Dic17C4⋊C4semidirect
209. #1799D17semidirect
248. C4×C17AΣL(1,𝔽16)semidirect
323. C17#12793semidirect
502. C4#11762595semidirect

Maximal subgroups

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

subgroupindex
C4×#105876232
C2×#117625952
#145287762
#145269012
C17×#17992
#1279317