Finite Group Databasebeta

← #16934460

Subgroups — #16934460

Order 4352.

430 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537145C211yesmaximal, characteristic
2#14528900C211yesmaximal, characteristic
3C4⋊C8×Dic17C211yesmaximal, characteristic
4#14526668C211yesmaximal, characteristic
5#14526668C211yesmaximal, characteristic
6#14526667C211yesmaximal, characteristic
7C17×#1296C211yesmaximal, characteristic
8C2×#10587576C412yes—
9C2×C4⋊#3622C2211yescharacteristic
10C2×C4⋊#3622C2211yescharacteristic
11C2×C8×Dic17—21no—
12#11762708—21no—
13#11762708—21no—
14#11762705—21no—
15#11762705—21no—
16#11762679C2211yescharacteristic
17#11762674C412yes—
18C42×Dic17C2211yescharacteristic
19#11762563—21no—
20#11762563—21no—
21#11762563—21no—
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×C17C2×C412yes—
30C2×C42×C17C2311yescharacteristic
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—22no—
34C2×C4⋊Dic17C2×C412yes—
35C2×#63225—22no—
36C2×C4×Dic17C2×C411yescharacteristic
37C2×C4×Dic17C2×C411yescharacteristic
38C2×C4×Dic17D411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C22×#3622—21no—
43C22×#3622—21no—
44#10587576—44no—
45C17×C4⋊C8—21no—
46C17×C4⋊C8—21no—
47C17×C4⋊C8—21no—
48C17×C4⋊C8Q812yes—
49#10587502—22no—
50#10587502—22no—
51C8×Dic17—42no—
52C4⋊#3622—21no—
53C4⋊#3622—21no—
54C4⋊#3622—21no—
55C4⋊#3622Q812yes—
56C22×C4×C17—22no—
57C22×C4×C17C22×C411yescharacteristic
58C22×C4×C17C2×D411yescharacteristic
59C22×C4×C17C2×D411yescharacteristic
60C22×Dic17—22no—
61C22×Dic17C22⋊C411yescharacteristic
62C22×Dic17C22⋊C411yescharacteristic
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C22⋊C411yescharacteristic
65C2×C8×C17—22no—
66C2×C8×C17—41no—
67C2×C8×C17—41no—
68C2×C8×C17—41no—
69C2×C8×C17—41no—
70C2×C8×C17—41no—
71C4⋊C4×C17—42no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C42×C17C2×Q811yescharacteristic
77C42×C17C2×Q811yescharacteristic
78C42×C17#4111yescharacteristic
79C42×C17#4111yescharacteristic
80C4⋊Dic17—44no—
81C4⋊Dic17—41no—
82C4⋊Dic17—41no—
83C4⋊Dic17—41no—
84C4⋊Dic17—41no—
85C4⋊Dic17—42no—
86#63225—44no—
87C4×Dic17—21no—
88C4×Dic17—21no—
89C4×Dic17—21no—
90C4×Dic17—21no—
91C4×Dic17—21no—
92C4×Dic17—21no—
93C4×Dic17—21no—
94C4×Dic17—21no—
95C4×Dic17—22no—
96C4×Dic17—22no—
97C2×#3622—22no—
98C2×#3622—41no—
99C2×#3622—41no—
100C2×#3622—41no—
101C2×#3622—41no—
102C2×#3622—41no—
103#9901—171nomaximal, Sylow
104C23×C17C2×C22⋊C411yescharacteristic
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—42no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17C4×Q811yescharacteristic
111C2×C4×C17C4×Q811yescharacteristic
112C2×C4×C17C22⋊Q811yescharacteristic
113C2×C4×C17C22⋊Q811yescharacteristic
114C2×C4×C17#12411yescharacteristic
115C2×C4×C17C4⋊Q811yescharacteristic
116C2×C4×C17#13511yescharacteristic
117C2×C4×C17#13511yescharacteristic
118C2×C4×C17#13511yescharacteristic
119C2×C4×C17#13511yescharacteristic
120C2×C4×C17#13511yescharacteristic
121C2×C4×C17#13511yescharacteristic
122C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C17#13711yescharacteristic
124C2×Dic17—21no—
125C2×Dic17—21no—
126C2×Dic17—21no—
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—21no—
131C2×Dic17—21no—
132C2×Dic17—21no—
133C2×Dic17—21no—
134C2×Dic17—42no—
135C2×Dic17—42no—
136C2×Dic17—42no—
137C2×Dic17#10012yes—
138C2×Dic17#10112yes—
139C8×C17—42no—
140C8×C17—81no—
141#3622—42no—
142#3622—81no—
143#2859—171no—
144#1831—171no—
145C4×C4⋊C8—171no—
146#1296—171no—
147#1296—171no—
148#1296—171no—
149#1296D1711yescharacteristic
150C22×C17#39111yescharacteristic
151C22×C17C2×#10011yescharacteristic
152C22×C17C2×#10111yescharacteristic
153C22×C17#41611yescharacteristic
154C22×C17#41611yescharacteristic
155C22×C17#41611yescharacteristic
156C22×C17#41711yescharacteristic
157C4×C17—21no—
158C4×C17—21no—
159C4×C17—82no—
160C4×C17#47811yescharacteristic
161C4×C17#47811yescharacteristic
162C4×C17#47911yescharacteristic
163C4×C17#47911yescharacteristic
164C4×C17#48811yescharacteristic
165C4×C17#48811yescharacteristic
166C4×C17#49911yescharacteristic
167C4×C17#49911yescharacteristic
168Dic17—22no—
169Dic17—22no—
170Dic17—41no—
171Dic17—41no—
172Dic17—82no—
173C2×#125—172no—
174C2×C4⋊C8—171no—
175C2×C4⋊C8—171no—
176C2×C4⋊C8C2×D1711yescharacteristic
177C2×C4⋊C8C2×D1711yescharacteristic
178C2×C4×C8—341no—
179#389—341no—
180#389—341no—
181#389—341no—
182#389—341no—
183#384—171no—
184#384C2×D1711yescharacteristic
185#382—172no—
186C43—171no—
187#336—341no—
188#336—341no—
189#336—341no—
190C2×C17#154311yescharacteristic
191C2×C17#154411yescharacteristic
192C2×C17#155111yescharacteristic
193C2×C17#155211yescharacteristic
194C2×C17#198911yescharacteristic
195C2×C17#199111yescharacteristic
196C2×C17#199711yescharacteristic
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—341no—
200C22×C8—341no—
201#125—684no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—172no—
205C2×C4⋊C4—342no—
206C2×C4⋊C4—342no—
207C2×C4⋊C4—341no—
208C2×C4⋊C4—341no—
209C2×C4⋊C4C4×D1712yes—
210C2×C42—171no—
211C2×C42—171no—
212C2×C42—171no—
213C2×C42—171no—
214C2×C42—171no—
215C2×C42—171no—
216C2×C42C22×D1711yescharacteristic
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—172no—
221C4⋊C8—341no—
222C4⋊C8—341no—
223C4⋊C8—341no—
224C4⋊C8Dic3412yes—
225C4×C8—682no—
226#95—342no—
227#95—342no—
228C17#990111yescharacteristic, complemented, Sylow
229C22×C4—22no—
230C22×C4—171no—
231C22×C4—171no—
232C22×C4—171no—
233C22×C4—171no—
234C22×C4—342no—
235C22×C4C2×C4×D1711yescharacteristic
236C22×C4D4×D1711yescharacteristic
237C22×C4D4×D1711yescharacteristic
238C2×C8—22no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—342no—
245C2×C8—681no—
246C2×C8—681no—
247C2×C8—681no—
248C2×C8—681no—
249C2×C8—681no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—682no—
256C4⋊C4—684no—
257C4⋊C4—684no—
258C4⋊C4—681no—
259C4⋊C4—681no—
260C4⋊C4—681no—
261C4⋊C4—681no—
262C42—342no—
263C42—342no—
264C42—341no—
265C42—341no—
266C42—341no—
267C42—341no—
268C42—341no—
269C42—341no—
270C42—341no—
271C42—341no—
272C42C2×Dic3411yescharacteristic
273C42#6325211yescharacteristic
274C42#6325411yescharacteristic
275C42Q8×D1711yescharacteristic
276C23C22⋊C4×D1711yescharacteristic
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—172no—
283C2×C4—172no—
284C2×C4—341no—
285C2×C4—341no—
286C2×C4—341no—
287C2×C4—341no—
288C2×C4—341no—
289C2×C4—341no—
290C2×C4—341no—
291C2×C4—341no—
292C2×C4—341no—
293C2×C4—341no—
294C2×C4—682no—
295C2×C4—682no—
296C2×C4—682no—
297C2×C4C4×Dic3411yescharacteristic
298C2×C4#1058756411yescharacteristic
299C2×C4#1058757111yescharacteristic
300C2×C4#1058757311yescharacteristic
301C2×C4#1058757411yescharacteristic
302C2×C4#1058758211yescharacteristic
303C2×C4#1058759711yescharacteristic
304C2×C4#1058759811yescharacteristic
305C2×C4#1058760111yescharacteristic
306C2×C4#1058760211yescharacteristic
307C2×C4#1058760211yescharacteristic
308C2×C4#1058760211yescharacteristic
309C2×C4#1058760511yescharacteristic
310C2×C4#1058760511yescharacteristic
311C8—42no—
312C8—81no—
313C8—682no—
314C8—1361no—
315C22#1176271311yescharacteristic
316C22#100×D1711yescharacteristic
317C22#101×D1711yescharacteristic
318C22#1176280211yescharacteristic
319C22#1176280411yescharacteristic
320C22#1176280411yescharacteristic
321C22#1176280711yescharacteristic
322C4—21no—
323C4—21no—
324C4—82no—
325C4—342no—
326C4—342no—
327C4—681no—
328C4—681no—
329C4—1362no—
330C4#1176311111yescharacteristic
331C4#1176311211yescharacteristic
332C4#1176311811yescharacteristic
333C4#1176311911yescharacteristic
334C4#1176316211yescharacteristic
335C4#1176316511yescharacteristic
336C4#1176320911yescharacteristic
337C4#1176321011yescharacteristic
338C2#1452744511yescharacteristic
339C2#1452744711yescharacteristic
340C2#1452747611yescharacteristic
341C2#1452748311yescharacteristic
342C2#1452973811yescharacteristic
343C2#1452974711yescharacteristic
344C2#1452977111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D17
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1296C2
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C42×C17C23
hypercenter#1296D17
hypocenterC17#9901
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
228. C17#9901semidirect

Maximal subgroups

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

subgroupindex
#145371452
#145289002
C4⋊C8×Dic172
#145266682
#145266672
C17×#12962
#990117