Finite Group Databasebeta

← #16937352

Subgroups — #16937352

Order 4352.

500 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534023C211yesmaximal, characteristic, complemented
2#14529711C211yesmaximal, characteristic
3#14529710C211yesmaximal, characteristic
4#14529590C211yesmaximal, characteristic
5#14526668C211yesmaximal, characteristic, complemented
6#14526624C211yesmaximal, characteristic, complemented
7C17×#1279C211yesmaximal, characteristic, complemented
8C2×#10587560C2211yescharacteristic
9C2×C4⋊#3622C2211yescharacteristic
10C2×#10587492—22no—
11C2×#10587492—21no—
12C2×#10587492—21no—
13C2×#10587480—21no—
14C2×#10587480—21no—
15#11762751—22no—
16#11762707—21no—
17#11762705—21no—
18#11762679C2211yescharacteristic
19#11762675—21no—
20#11762674—21no—
21C4×C4⋊Dic17C2211yescharacteristic
22C2×C17×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C17C2211yescharacteristic
24C4×C4⋊C4×C17C2211yescharacteristic
25C22×D68—21no—
26C22×D68—21no—
27C22×D68—21no—
28C22×C8×C17—21no—
29C22×C8×C17—21no—
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C4⋊C4×C17D411yescharacteristic
32C2×C42×C17—21no—
33C2×C42×C17C2311yescharacteristic
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17D411yescharacteristic
37C2×C4⋊Dic17D411yescharacteristic
38C2×C4⋊Dic17D412yes—
39C2×#63225—22no—
40C2×C4×Dic17—21no—
41C22×#3622—21no—
42#10587560—21no—
43#10587560—21no—
44#10587560—21no—
45#10587560Q812yes—
46C17×C4⋊C8—21no—
47C17×C4⋊C8—21no—
48C4×C8×C17—21no—
49C4×C8×C17—21no—
50C17×#95—21no—
51#10587502—22no—
52#10587502—22no—
53#10587502—22no—
54#10587502—21no—
55#10587492—44no—
56#10587492—42no—
57#10587492—42no—
58#10587480—42no—
59#10587480—42no—
60C4⋊#3622—21no—
61C4⋊#3622—21no—
62C23×D17—41no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17C2×D411yescharacteristic
66C22×C4×C17C2×D411yescharacteristic
67C22×C4×C17C2×D411yescharacteristic
68C22×Dic17—21no—
69C22×Dic17—21no—
70C22×Dic17—22no—
71C2×D68—22no—
72C2×D68—22no—
73C2×D68—22no—
74C2×D68—42no—
75C2×D68—42no—
76C2×D68—41no—
77C2×D68—41no—
78C2×D68—41no—
79C2×D68—41no—
80C2×D68—41no—
81C2×D68—41no—
82C2×D68—41no—
83C2×D68—41no—
84C2×D68—41no—
85C2×D68—41no—
86C2×D68—41no—
87C2×C8×C17—22no—
88C2×C8×C17—41no—
89C2×C8×C17—41no—
90C2×C8×C17—41no—
91C2×C8×C17—41no—
92C2×C8×C17—41no—
93C4⋊C4×C17—21no—
94C4⋊C4×C17—21no—
95C4⋊C4×C17—21no—
96C4⋊C4×C17—21no—
97C42×C17—41no—
98C42×C17—41no—
99C42×C17C2×Q811yescharacteristic
100C42×C17#4111yescharacteristic
101C42×C17#4111yescharacteristic
102C42×C17#4111yescharacteristic
103C4⋊Dic17—21no—
104C4⋊Dic17—21no—
105C4⋊Dic17—21no—
106C4⋊Dic17—21no—
107C4⋊Dic17—41no—
108C4⋊Dic17—41no—
109C4⋊Dic17—41no—
110C4⋊Dic17—41no—
111C4⋊Dic17—42no—
112#63225—82no—
113C4×Dic17—41no—
114C4×Dic17—41no—
115C2×#3622—41no—
116C2×#3622—41no—
117C2×#3622—41no—
118#10351—171nomaximal, Sylow
119C23×C17#12011yescharacteristic
120C22×D17—42no—
121C22×D17—81no—
122C22×D17—81no—
123C22×D17—81no—
124C22×D17—81no—
125C22×D17—81no—
126C22×D17—81no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17C22⋊Q811yescharacteristic
136C2×C4×C17C22⋊Q811yescharacteristic
137C2×C4×C17C22⋊Q811yescharacteristic
138C2×C4×C17#12411yescharacteristic
139C2×C4×C17#12411yescharacteristic
140C2×C4×C17#12411yescharacteristic
141C2×C4×C17#13511yescharacteristic
142C2×C4×C17#13511yescharacteristic
143C2×C4×C17#13511yescharacteristic
144C2×C4×C17#13511yescharacteristic
145C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—42no—
154C2×Dic17—42no—
155C2×Dic17—41no—
156C2×Dic17—42no—
157C2×Dic17—41no—
158D68—44no—
159D68—42no—
160D68—42no—
161D68—42no—
162D68—42no—
163D68—82no—
164D68—81no—
165D68—81no—
166D68—81no—
167D68—81no—
168C8×C17—42no—
169C8×C17—81no—
170#3622—81no—
171#2571—171no—
172#1982—171no—
173#1982—171no—
174#1957—171no—
175#1296—171no—
176#1279—171no—
177#1279D1711yescharacteristic, complemented
178C22×C17#39311yescharacteristic
179C22×C17#44911yescharacteristic
180C22×C17#44911yescharacteristic
181C22×C17#44911yescharacteristic
182C22×C17#44911yescharacteristic
183C22×C17#45311yescharacteristic
184C22×C17#45411yescharacteristic
185C2×D17—82no—
186C2×D17—82no—
187C2×D17—82no—
188C2×D17—161no—
189C2×D17—161no—
190C2×D17—161no—
191C2×D17—161no—
192C4×C17—21no—
193C4×C17—21no—
194C4×C17—81no—
195C4×C17—81no—
196C4×C17#47811yescharacteristic
197C4×C17#47811yescharacteristic
198C4×C17#47811yescharacteristic
199C4×C17#47811yescharacteristic
200C4×C17#48811yescharacteristic
201C4×C17#48811yescharacteristic
202C4×C17#49011yescharacteristic
203C4×C17#49011yescharacteristic
204Dic17—82no—
205Dic17—81no—
206Dic17—81no—
207C2×#127—171no—
208C2×C4⋊C8—171no—
209C2×C4⋊C8C2×D1711yescharacteristic
210C2×#102—342no—
211C2×#102—341no—
212C2×#102—341no—
213C2×#102—341no—
214C2×#102—341no—
215C2×C4×C8C2×D1711yescharacteristic
216#400—342no—
217#389—341no—
218#389—341no—
219#384—171no—
220#382—341no—
221#382—341no—
222C4×C4⋊C4—171no—
223C4×C4⋊C4C2×D1711yescharacteristic
224C2×C17#162011yescharacteristic
225C2×C17#162411yescharacteristic
226C2×C17#162811yescharacteristic
227C2×C17#162811yescharacteristic
228C2×C17#202511yescharacteristic
229C2×C17#202511yescharacteristic
230C2×C17#202711yescharacteristic
231D17—162no—
232C22×D4—341no—
233C22×D4—341no—
234C22×D4—341no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—341no—
238#127—172no—
239#127—341no—
240#127—341no—
241#127—341no—
242C2×C4⋊C4—171no—
243C2×C4⋊C4—171no—
244C2×C4⋊C4—172no—
245C2×C4⋊C4—341no—
246C2×C4⋊C4—341no—
247C2×C4⋊C4—342no—
248C2×C4⋊C4D6811yescharacteristic
249C2×C4⋊C4D6811yescharacteristic
250C2×C42—21no—
251C2×C42—341no—
252C2×C42C22×D1711yescharacteristic
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—341no—
256C4⋊C8—341no—
257#102—682no—
258#102—682no—
259#102—682no—
260#102—682no—
261#102—684no—
262C4×C8—21no—
263C4×C8—21no—
264#95—21no—
265#95—342no—
266#95—342no—
267#95—342no—
268#95—341no—
269C17#1035111yescharacteristic, complemented, Sylow
270C24—681no—
271C2×D4—342no—
272C2×D4—342no—
273C2×D4—342no—
274C2×D4—682no—
275C2×D4—682no—
276C2×D4—681no—
277C2×D4—681no—
278C2×D4—681no—
279C2×D4—681no—
280C2×D4—681no—
281C2×D4—681no—
282C2×D4—681no—
283C2×D4—681no—
284C2×D4—681no—
285C2×D4—681no—
286C2×D4—681no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—341no—
290C22×C4—341no—
291C22×C4—342no—
292C22×C4C2×D6811yescharacteristic
293C22×C4D4×D1711yescharacteristic
294C22×C4D4×D1711yescharacteristic
295C2×C8—22no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—681no—
302C2×C8—681no—
303C2×C8—681no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—341no—
309C4⋊C4—341no—
310C4⋊C4—341no—
311C4⋊C4—341no—
312C4⋊C4—682no—
313C4⋊C4—681no—
314C4⋊C4—681no—
315C4⋊C4—681no—
316C4⋊C4—681no—
317C4⋊C4—1362no—
318C42—41no—
319C42—41no—
320C42—681no—
321C42—681no—
322C42#6325211yescharacteristic
323C42#6325211yescharacteristic
324C42#6325411yescharacteristic
325C42Q8×D1711yescharacteristic
326C23—682no—
327C23—1361no—
328C23—1361no—
329C23—1361no—
330C23—1361no—
331C23—1361no—
332C23—1361no—
333C23#1058756811yescharacteristic
334D4—684no—
335D4—682no—
336D4—682no—
337D4—682no—
338D4—682no—
339D4—1362no—
340D4—1361no—
341D4—1361no—
342D4—1361no—
343D4—1361no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—681no—
353C2×C4—681no—
354C2×C4—681no—
355C2×C4—682no—
356C2×C4—681no—
357C2×C4—682no—
358C2×C4—682no—
359C2×C4—681no—
360C2×C4—681no—
361C2×C4#1058756111yescharacteristic
362C2×C4#1058757111yescharacteristic
363C2×C4#1058757111yescharacteristic
364C2×C4#1058758211yescharacteristic
365C2×C4#1058758211yescharacteristic
366C2×C4#1058758311yescharacteristic
367C2×C4#1058759011yescharacteristic
368C2×C4#1058759011yescharacteristic
369C2×C4#1058759411yescharacteristic
370C2×C4#1058759411yescharacteristic
371C2×C4#1058759711yescharacteristic
372C2×C4#1058760011yescharacteristic
373C2×C4#1058760211yescharacteristic
374C2×C4#1058760511yescharacteristic
375C8—42no—
376C8—81no—
377C8—1361no—
378C22—2721no—
379C22—2721no—
380C22—2721no—
381C22—2721no—
382C22—1362no—
383C22—1362no—
384C22—1362no—
385C22#1176272211yescharacteristic
386C22#1176295511yescharacteristic
387C22#1176295611yescharacteristic
388C22#1176295611yescharacteristic
389C22#1176295711yescharacteristic
390C22#1176297811yescharacteristic
391C22#1176298311yescharacteristic
392C4—21no—
393C4—21no—
394C4—81no—
395C4—81no—
396C4—1362no—
397C4—1361no—
398C4—1361no—
399C4#1176310811yescharacteristic
400C4#1176311011yescharacteristic
401C4#1176311011yescharacteristic
402C4#1176311211yescharacteristic
403C4#1176316411yescharacteristic
404C4#1176316511yescharacteristic
405C4#1176317211yescharacteristic
406C4#1176317411yescharacteristic
407C2—2722no—
408C2#1452784511yescharacteristic
409C2#1452786911yescharacteristic
410C2#1452789611yescharacteristic
411C2#1452789711yescharacteristic
412C2#1452992911yescharacteristic
413C2#1452993111yescharacteristic
414C2#1452993911yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1279C2
socleC23×C17#120
prime radicalC2×#10587560C22
hypercenter#1279D17
hypocenterC17#10351
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
1. #14534023C2semidirect
5. #14526668C2semidirect
6. #14526624C2semidirect
7. C17×#1279C2semidirect
177. #1279D17semidirect
269. C17#10351semidirect

Maximal subgroups

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

subgroupindex
#145340232
#145297112
#145297102
#145295902
#145266682
#145266242
C17×#12792
#1035117