Finite Group Databasebeta

← #16938779

Subgroups — #16938779

Order 4352.

406 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534023C211yesmaximal, characteristic
2#14529548C211yesmaximal, characteristic
3#14529547C211yesmaximal, characteristic
4#14528944C211yesmaximal, characteristic
5#14526668C211yesmaximal, characteristic
6#14526624C211yesmaximal, characteristic
7C17×#1279C211yesmaximal, characteristic
8C2×#10587489—22no—
9C2×#10587488—21no—
10C2×#10587479—21no—
11C2×C4⋊#3622C2211yescharacteristic
12#11762751—22no—
13#11762707—21no—
14#11762705—21no—
15#11762679C2211yescharacteristic
16#11762679C2211yescharacteristic
17#11762675—21no—
18#11762674—21no—
19C4×C4⋊Dic17C2211yescharacteristic
20#11762572—21no—
21#11762571—21no—
22C2×C17×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C17C2211yescharacteristic
24C4×C4⋊C4×C17C2211yescharacteristic
25C22×C8×C17—21no—
26C22×C8×C17—21no—
27C2×C4⋊C4×C17D411yescharacteristic
28C2×C4⋊C4×C17D411yescharacteristic
29C2×C42×C17—21no—
30C2×C42×C17C2311yescharacteristic
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
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—
42C17×C4⋊C8—21no—
43C17×C4⋊C8Q812yes—
44C4×C8×C17—21no—
45C4×C8×C17Q812yes—
46C17×#95—21no—
47#10587502—22no—
48#10587502—22no—
49#10587502—22no—
50#10587502—21no—
51#10587489—44no—
52#10587488—42no—
53#10587479—42no—
54C4⋊#3622—21no—
55C4⋊#3622Q812yes—
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17C2×D411yescharacteristic
59C22×C4×C17C2×D411yescharacteristic
60C22×C4×C17C2×D411yescharacteristic
61C22×Dic17—21no—
62C22×Dic17—21no—
63C22×Dic17—22no—
64C22×Dic17—41no—
65C2×C8×C17—22no—
66C2×C8×C17—22no—
67C2×C8×C17—22no—
68C2×C8×C17—22no—
69C2×C8×C17—41no—
70C2×C8×C17—41no—
71C4⋊C4×C17—21no—
72C4⋊C4×C17—21no—
73C4⋊C4×C17—21no—
74C4⋊C4×C17—21no—
75C42×C17—41no—
76C42×C17—41no—
77C42×C17C2×Q811yescharacteristic
78C42×C17C2×Q811yescharacteristic
79C42×C17C2×Q811yescharacteristic
80C42×C17#4111yescharacteristic
81C4⋊Dic17—21no—
82C4⋊Dic17—21no—
83C4⋊Dic17—21no—
84C4⋊Dic17—21no—
85C4⋊Dic17—41no—
86C4⋊Dic17—41no—
87C4⋊Dic17—41no—
88C4⋊Dic17—41no—
89C4⋊Dic17—42no—
90C4⋊Dic17—42no—
91C4⋊Dic17—41no—
92C4⋊Dic17—41no—
93C4⋊Dic17—41no—
94C4⋊Dic17—41no—
95#63225—82no—
96C4×Dic17—41no—
97C4×Dic17—41no—
98C2×#3622—22no—
99C2×#3622—41no—
100C2×#3622—41no—
101#10576—171nomaximal, Sylow
102C23×C17#12011yescharacteristic
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17C22⋊Q811yescharacteristic
112C2×C4×C17C22⋊Q811yescharacteristic
113C2×C4×C17C22⋊Q811yescharacteristic
114C2×C4×C17C4⋊Q811yescharacteristic
115C2×C4×C17C4⋊Q811yescharacteristic
116C2×C4×C17C4⋊Q811yescharacteristic
117C2×C4×C17#13511yescharacteristic
118C2×C4×C17#13511yescharacteristic
119C2×C4×C17#13511yescharacteristic
120C2×C4×C17#13511yescharacteristic
121C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C17#13711yescharacteristic
124C2×C4×C17#13711yescharacteristic
125C2×Dic17—41no—
126C2×Dic17—42no—
127C2×Dic17—42no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—42no—
133C2×Dic17—41no—
134C2×Dic17—81no—
135C2×Dic17—81no—
136C2×Dic17—81no—
137C8×C17—24no—
138C8×C17—42no—
139#3622—42no—
140#2571—171no—
141#1948—171no—
142#1948—171no—
143#1845—171no—
144#1296—171no—
145#1279—171no—
146#1279D1711yescharacteristic
147C22×C17#39511yescharacteristic
148C22×C17#44911yescharacteristic
149C22×C17#44911yescharacteristic
150C22×C17#45211yescharacteristic
151C22×C17#45211yescharacteristic
152C22×C17#45311yescharacteristic
153C22×C17#45611yescharacteristic
154C4×C17—21no—
155C4×C17—21no—
156C4×C17—81no—
157C4×C17—81no—
158C4×C17#47811yescharacteristic
159C4×C17#47811yescharacteristic
160C4×C17#47911yescharacteristic
161C4×C17#47911yescharacteristic
162C4×C17#49911yescharacteristic
163C4×C17#49911yescharacteristic
164C4×C17#50111yescharacteristic
165C4×C17#50111yescharacteristic
166Dic17—82no—
167Dic17—81no—
168Dic17—81no—
169Dic17—161no—
170C2×#107—342no—
171C2×#106—341no—
172C2×#106—341no—
173C2×C4⋊C8—171no—
174C2×C4⋊C8C2×D1711yescharacteristic
175C2×C4×C8C2×D1711yescharacteristic
176#400—342no—
177#389—341no—
178#389—341no—
179#384—171no—
180#384—171no—
181#382—341no—
182#382—341no—
183C4×C4⋊C4—171no—
184C4×C4⋊C4C2×D1711yescharacteristic
185#340—341no—
186#340—341no—
187C2×C17#162011yescharacteristic
188C2×C17#163411yescharacteristic
189C2×C17#165011yescharacteristic
190C2×C17#165011yescharacteristic
191C2×C17#205911yescharacteristic
192C2×C17#205911yescharacteristic
193C2×C17#206011yescharacteristic
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—341no—
197C2×C4⋊C4—171no—
198C2×C4⋊C4—171no—
199C2×C4⋊C4—172no—
200C2×C4⋊C4—341no—
201C2×C4⋊C4—341no—
202C2×C4⋊C4—341no—
203C2×C4⋊C4—341no—
204C2×C4⋊C4—341no—
205C2×C4⋊C4—342no—
206C2×C4⋊C4D6811yescharacteristic
207C2×C4⋊C4D6811yescharacteristic
208C2×C42—21no—
209C2×C42—341no—
210C2×C42C22×D1711yescharacteristic
211#107—684no—
212#106—682no—
213#106—682no—
214C4⋊C8—21no—
215C4⋊C8—172no—
216C4⋊C8—341no—
217C4⋊C8Dic3412yes—
218C4×C8—21no—
219C4×C8Dic3412yes—
220#95—21no—
221#95—342no—
222#95—342no—
223#95—342no—
224#95—341no—
225C17#1057611yescharacteristic, complemented, Sylow
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—341no—
229C22×C4—341no—
230C22×C4—342no—
231C22×C4—681no—
232C22×C4C2×D6811yescharacteristic
233C22×C4D4×D1711yescharacteristic
234C22×C4D4×D1711yescharacteristic
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—22no—
238C2×C8—22no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—342no—
242C2×C8—681no—
243C2×C8—681no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—341no—
249C4⋊C4—341no—
250C4⋊C4—341no—
251C4⋊C4—341no—
252C4⋊C4—682no—
253C4⋊C4—682no—
254C4⋊C4—681no—
255C4⋊C4—681no—
256C4⋊C4—681no—
257C4⋊C4—681no—
258C4⋊C4—681no—
259C4⋊C4—681no—
260C4⋊C4—681no—
261C4⋊C4—681no—
262C4⋊C4—1362no—
263C42—41no—
264C42—41no—
265C42—681no—
266C42—681no—
267C42C2×Dic3411yescharacteristic
268C42C2×Dic3411yescharacteristic
269C42#6325411yescharacteristic
270C42Q8×D1711yescharacteristic
271C23#1058756811yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—682no—
281C2×C4—681no—
282C2×C4—682no—
283C2×C4—681no—
284C2×C4—681no—
285C2×C4—681no—
286C2×C4—682no—
287C2×C4—681no—
288C2×C4—681no—
289C2×C4—1361no—
290C2×C4—1361no—
291C2×C4—1361no—
292C2×C4#1058755511yescharacteristic
293C2×C4#1058756411yescharacteristic
294C2×C4#1058756411yescharacteristic
295C2×C4#1058757411yescharacteristic
296C2×C4#1058757411yescharacteristic
297C2×C4#1058758311yescharacteristic
298C2×C4#1058759011yescharacteristic
299C2×C4#1058759011yescharacteristic
300C2×C4#1058759411yescharacteristic
301C2×C4#1058759511yescharacteristic
302C2×C4#1058759811yescharacteristic
303C2×C4#1058760011yescharacteristic
304C2×C4#1058760111yescharacteristic
305C2×C4#1058760511yescharacteristic
306C8—24no—
307C8—42no—
308C8—682no—
309C22#1176273011yescharacteristic
310C22#1176295611yescharacteristic
311C22#1176295711yescharacteristic
312C22#1176297211yescharacteristic
313C22#1176297311yescharacteristic
314C22#1176297811yescharacteristic
315C22#1176299311yescharacteristic
316C4—21no—
317C4—21no—
318C4—81no—
319C4—81no—
320C4—2721no—
321C4—1361no—
322C4—1362no—
323C4—1361no—
324C4#1176310711yescharacteristic
325C4#1176311011yescharacteristic
326C4#1176311711yescharacteristic
327C4#1176311811yescharacteristic
328C4#1176321011yescharacteristic
329C4#1176321111yescharacteristic
330C4#1176321611yescharacteristic
331C4#1176321811yescharacteristic
332C2#1452784511yescharacteristic
333C2#1452793111yescharacteristic
334C2#1452804211yescharacteristic
335C2#1452804311yescharacteristic
336C2#1453012311yescharacteristic
337C2#1453012511yescharacteristic
338C2#1453012811yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1279C2
socle, prime radicalC23×C17#120
hypercenter#1279D17
hypocenterC17#10576
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
225. C17#10576semidirect

Maximal subgroups

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

subgroupindex
#145340232
#145295482
#145295472
#145289442
#145266682
#145266242
C17×#12792
#1057617