Finite Group Databasebeta

← #16938787

Subgroups — #16938787

Order 4352.

390 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534026C211yesmaximal, characteristic
2#14529548C211yesmaximal, characteristic
3#14529543C211yesmaximal, characteristic
4#14528911C211yesmaximal, characteristic
5#14526623C211yesmaximal, characteristic
6#14526623C211yesmaximal, characteristic
7C17×#1296C211yesmaximal, characteristic
8C2×#10587489—21no—
9C2×#10587488—21no—
10C2×C4×#3622C2211yescharacteristic
11#11762748—22no—
12#11762708—21no—
13#11762708—21no—
14#11762679C2211yescharacteristic
15#11762674—21no—
16#11762674—21no—
17C4×C4⋊Dic17C2211yescharacteristic
18C4×C4⋊Dic17C2211yescharacteristic
19#11762572—21no—
20#11762572—21no—
21#11762571—22no—
22C2×C17×C4⋊C8C2211yescharacteristic
23C2×C17×C4⋊C8C2211yescharacteristic
24C17×#384C2211yescharacteristic
25C22×C8×C17—21no—
26C22×C8×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17D412yes—
30C2×C42×C17C2311yescharacteristic
31C2×C4⋊Dic17—22no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17D411yescharacteristic
36C2×C4⋊Dic17D411yescharacteristic
37C2×C4⋊Dic17D411yescharacteristic
38C2×C4⋊Dic17D411yescharacteristic
39C2×C4×Dic17—21no—
40C2×C4×Dic17—21no—
41C22×#3622—21no—
42C17×C4⋊C8—21no—
43C17×C4⋊C8—21no—
44C17×C4⋊C8Q812yes—
45C17×C4⋊C8Q812yes—
46#10587502—22no—
47#10587502—22no—
48#10587502—22no—
49#10587502—21no—
50#10587502—21no—
51#10587489—42no—
52#10587488—42no—
53C4×#3622—21no—
54C4×#3622Q812yes—
55C22×C4×C17—22no—
56C22×C4×C17C2×D411yescharacteristic
57C22×C4×C17C2×D411yescharacteristic
58C22×C4×C17C2×D411yescharacteristic
59C22×Dic17—21no—
60C22×Dic17—21no—
61C22×Dic17—21no—
62C22×Dic17—21no—
63C22×Dic17—41no—
64C2×C8×C17—22no—
65C2×C8×C17—22no—
66C2×C8×C17—41no—
67C2×C8×C17—41no—
68C2×C8×C17—41no—
69C2×C8×C17—41no—
70C4⋊C4×C17—42no—
71C4⋊C4×C17—41no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C42×C17C2×Q811yescharacteristic
76C42×C17C2×Q811yescharacteristic
77C42×C17C2×Q811yescharacteristic
78C42×C17#4111yescharacteristic
79C4⋊Dic17—21no—
80C4⋊Dic17—21no—
81C4⋊Dic17—21no—
82C4⋊Dic17—21no—
83C4⋊Dic17—21no—
84C4⋊Dic17—21no—
85C4⋊Dic17—21no—
86C4⋊Dic17—21no—
87C4⋊Dic17—42no—
88C4⋊Dic17—41no—
89C4⋊Dic17—41no—
90C4⋊Dic17—41no—
91C4⋊Dic17—41no—
92C4⋊Dic17—82no—
93C4×Dic17—41no—
94C4×Dic17—41no—
95C4×Dic17—41no—
96C4×Dic17—41no—
97C2×#3622—22no—
98C2×#3622—41no—
99C2×#3622—41no—
100#10578—171nomaximal, Sylow
101C23×C17#12011yescharacteristic
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—42no—
105C2×C4×C17—42no—
106C2×C4×C17—42no—
107C2×C4×C17C22⋊Q811yescharacteristic
108C2×C4×C17C22⋊Q811yescharacteristic
109C2×C4×C17C22⋊Q811yescharacteristic
110C2×C4×C17C4⋊Q811yescharacteristic
111C2×C4×C17C4⋊Q811yescharacteristic
112C2×C4×C17C4⋊Q811yescharacteristic
113C2×C4×C17#13511yescharacteristic
114C2×C4×C17#13511yescharacteristic
115C2×C4×C17#13511yescharacteristic
116C2×C4×C17#13511yescharacteristic
117C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C17#13711yescharacteristic
120C2×C4×C17#13711yescharacteristic
121C2×Dic17—41no—
122C2×Dic17—41no—
123C2×Dic17—41no—
124C2×Dic17—41no—
125C2×Dic17—41no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—81no—
134C2×Dic17—81no—
135C2×Dic17—81no—
136C8×C17—42no—
137C8×C17—42no—
138#3622—42no—
139#2571—171no—
140#1948—171no—
141#1947—171no—
142#1834—171no—
143#1296D1711yescharacteristic
144#1279—171no—
145#1279—171no—
146C22×C17#39511yescharacteristic
147C22×C17#44911yescharacteristic
148C22×C17#44911yescharacteristic
149C22×C17#45211yescharacteristic
150C22×C17#45211yescharacteristic
151C22×C17#45411yescharacteristic
152C22×C17#45511yescharacteristic
153C4×C17—21no—
154C4×C17—21no—
155C4×C17—82no—
156C4×C17#47811yescharacteristic
157C4×C17#47811yescharacteristic
158C4×C17#47911yescharacteristic
159C4×C17#47911yescharacteristic
160C4×C17#49911yescharacteristic
161C4×C17#49911yescharacteristic
162C4×C17#50111yescharacteristic
163C4×C17#50111yescharacteristic
164Dic17—81no—
165Dic17—81no—
166Dic17—81no—
167Dic17—81no—
168Dic17—161no—
169C2×#107—341no—
170C2×#106—341no—
171C2×C4⋊C8C2×D1711yescharacteristic
172C2×C4⋊C8C2×D1711yescharacteristic
173C2×C4×C8—171no—
174#400—342no—
175#389—341no—
176#389—341no—
177#384—171no—
178#384C2×D1711yescharacteristic
179#382—341no—
180#382—341no—
181C4×C4⋊C4—171no—
182C4×C4⋊C4—171no—
183#340—341no—
184#340—341no—
185#340—342no—
186C2×C17#162811yescharacteristic
187C2×C17#163811yescharacteristic
188C2×C17#164011yescharacteristic
189C2×C17#164611yescharacteristic
190C2×C17#205911yescharacteristic
191C2×C17#205911yescharacteristic
192C2×C17#206111yescharacteristic
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—341no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—171no—
199C2×C4⋊C4—171no—
200C2×C4⋊C4—171no—
201C2×C4⋊C4—171no—
202C2×C4⋊C4—341no—
203C2×C4⋊C4—341no—
204C2×C4⋊C4—341no—
205C2×C4⋊C4—342no—
206C2×C4⋊C4D6812yes—
207C2×C42—341no—
208C2×C42—341no—
209C2×C42C22×D1711yescharacteristic
210#107—682no—
211#106—682no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8Dic3412yes—
215C4⋊C8Dic3412yes—
216C4×C8—172no—
217C4×C8—341no—
218#95—342no—
219#95—342no—
220#95—342no—
221#95—341no—
222#95—341no—
223C17#1057811yescharacteristic, complemented, Sylow
224C22×C4—22no—
225C22×C4—341no—
226C22×C4—341no—
227C22×C4—341no—
228C22×C4—341no—
229C22×C4—681no—
230C22×C4C2×D6811yescharacteristic
231C22×C4D4×D1711yescharacteristic
232C22×C4D4×D1711yescharacteristic
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—342no—
240C2×C8—681no—
241C2×C8—681no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—341no—
248C4⋊C4—341no—
249C4⋊C4—341no—
250C4⋊C4—341no—
251C4⋊C4—341no—
252C4⋊C4—341no—
253C4⋊C4—341no—
254C4⋊C4—341no—
255C4⋊C4—682no—
256C4⋊C4—681no—
257C4⋊C4—681no—
258C4⋊C4—681no—
259C4⋊C4—681no—
260C4⋊C4—1362no—
261C42—681no—
262C42—681no—
263C42—681no—
264C42—681no—
265C42C2×Dic3411yescharacteristic
266C42C2×Dic3411yescharacteristic
267C42#6325411yescharacteristic
268C42Q8×D1711yescharacteristic
269C23#1058756811yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—681no—
276C2×C4—681no—
277C2×C4—681no—
278C2×C4—681no—
279C2×C4—681no—
280C2×C4—681no—
281C2×C4—681no—
282C2×C4—681no—
283C2×C4—681no—
284C2×C4—681no—
285C2×C4—681no—
286C2×C4—681no—
287C2×C4—1361no—
288C2×C4—1361no—
289C2×C4—1361no—
290C2×C4#1058755511yescharacteristic
291C2×C4#1058756411yescharacteristic
292C2×C4#1058756411yescharacteristic
293C2×C4#1058757411yescharacteristic
294C2×C4#1058757411yescharacteristic
295C2×C4#1058758311yescharacteristic
296C2×C4#1058759711yescharacteristic
297C2×C4#1058759811yescharacteristic
298C2×C4#1058760011yescharacteristic
299C2×C4#1058760111yescharacteristic
300C2×C4#1058760211yescharacteristic
301C2×C4#1058760211yescharacteristic
302C2×C4#1058760411yescharacteristic
303C2×C4#1058760511yescharacteristic
304C8—42no—
305C8—42no—
306C8—682no—
307C22#1176273011yescharacteristic
308C22#1176295511yescharacteristic
309C22#1176295711yescharacteristic
310C22#1176297211yescharacteristic
311C22#1176297411yescharacteristic
312C22#1176298411yescharacteristic
313C22#1176298911yescharacteristic
314C4—21no—
315C4—21no—
316C4—82no—
317C4—2721no—
318C4—1361no—
319C4—1361no—
320C4—1361no—
321C4—1361no—
322C4#1176310711yescharacteristic
323C4#1176311111yescharacteristic
324C4#1176311411yescharacteristic
325C4#1176311811yescharacteristic
326C4#1176320911yescharacteristic
327C4#1176321011yescharacteristic
328C4#1176321611yescharacteristic
329C4#1176321711yescharacteristic
330C2#1452789511yescharacteristic
331C2#1452795711yescharacteristic
332C2#1452797111yescharacteristic
333C2#1452801311yescharacteristic
334C2#1453012111yescharacteristic
335C2#1453012511yescharacteristic
336C2#1453013511yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1296C2
socle, prime radicalC23×C17#120
hypercenter#1296D17
hypocenterC17#10578
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
223. C17#10578semidirect

Maximal subgroups

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

subgroupindex
#145340262
#145295482
#145295432
#145289112
#145266232
C17×#12962
#1057817