Finite Group Databasebeta

← #16932608

Subgroups — #16932608

Order 4352.

394 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14529720C211yesmaximal, characteristic
2C4×#10587481C211yesmaximal, characteristic
3C2×#11762539C211yesmaximal, characteristic
4C2×#11762530C211yesmaximal, characteristic
5#14526625C211yesmaximal, characteristic
6#14526618C211yesmaximal, characteristic
7C17×#1939C211yesmaximal, characteristic
8C2×C4×Dic34C2211yescharacteristic
9C2×C4⋊#3622C2211yescharacteristic
10C2×#10587481C411yescharacteristic
11C2×#10587481C411yescharacteristic
12C2×C4×#3622C2211yescharacteristic
13C2×C4×#3622C2211yescharacteristic
14#11762571C411yescharacteristic
15#11762571C411yescharacteristic
16#11762563—21no—
17#11762563—21no—
18#11762539—22no—
19#11762530—22no—
20C2×C17×C4⋊C8—21no—
21C2×C17×C4⋊C8C2211yescharacteristic
22C2×C4×C8×C17C2211yescharacteristic
23C4×C4⋊C4×C17C2211yescharacteristic
24C17×#336—21no—
25C22×Dic34C2×C411yescharacteristic
26C22×C8×C17—21no—
27C22×C8×C17D411yescharacteristic
28C22×C8×C17D411yescharacteristic
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C42×C17—21no—
32C2×C42×C17C2311yescharacteristic
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×#63225—21no—
35C2×C4×Dic17—21no—
36C22×#3622—21no—
37C22×#3622—21no—
38C22×#3622C2×C411yescharacteristic
39C22×#3622C2×C411yescharacteristic
40C4×Dic34—21no—
41C4×Dic34—21no—
42C4×Dic34—21no—
43C4×Dic34—21no—
44C17×C4⋊C8—21no—
45C17×C4⋊C8—21no—
46C17×C4⋊C8—42no—
47C4×C8×C17—21no—
48C4×C8×C17—21no—
49C17×#95—21no—
50#10587481—22no—
51#10587481—22no—
52C4⋊#3622—21no—
53C4⋊#3622—21no—
54C4×#3622—21no—
55C4×#3622—21no—
56C4×#3622—21no—
57C4×#3622D412yes—
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17C22×C411yescharacteristic
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17#4111yescharacteristic
63C22×Dic17—21no—
64C22×Dic17—21no—
65C2×Dic34—21no—
66C2×Dic34—21no—
67C2×Dic34—21no—
68C2×Dic34—21no—
69C2×Dic34—21no—
70C2×Dic34M1612yes—
71C2×C8×C17—21no—
72C2×C8×C17—21no—
73C2×C8×C17—21no—
74C2×C8×C17—21no—
75C2×C8×C17—41no—
76C2×C8×C17—41no—
77C2×C8×C17—41no—
78C2×C8×C17SD1612yes—
79C2×C8×C17Q1612yes—
80C4⋊C4×C17—21no—
81C4⋊C4×C17—21no—
82C4⋊C4×C17—21no—
83C4⋊C4×C17M1612yes—
84C42×C17—41no—
85C42×C17—41no—
86C42×C17C2×D411yescharacteristic
87C42×C17#4111yescharacteristic
88C42×C17#4111yescharacteristic
89C42×C17#4111yescharacteristic
90C4⋊Dic17—21no—
91C4⋊Dic17—21no—
92#63225—41no—
93#63225—41no—
94C4×Dic17—41no—
95C4×Dic17—41no—
96C2×#3622—21no—
97C2×#3622—21no—
98C2×#3622—22no—
99C2×#3622—21no—
100C2×#3622—21no—
101C2×#3622—21no—
102C2×#3622—21no—
103C2×#3622—41no—
104C2×#3622—41no—
105C2×#3622—41no—
106C2×#3622—41no—
107C2×#3622—41no—
108#9557—171nomaximal, Sylow
109C23×C17C4×D411yescharacteristic
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—22no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17#11711yescharacteristic
119C2×C4×C17C4×D411yescharacteristic
120C2×C4×C17#12111yescharacteristic
121C2×C4×C17#12311yescharacteristic
122C2×C4×C17#12411yescharacteristic
123C2×C4×C17#12611yescharacteristic
124C2×C4×C17C2×M1611yescharacteristic
125C2×C4×C17C2×M1611yescharacteristic
126C2×C4×C17#13111yescharacteristic
127C2×C4×C17#13111yescharacteristic
128C2×C4×C17C2×SD1611yescharacteristic
129C2×C4×C17C2×Q1611yescharacteristic
130C2×C4×C17#13511yescharacteristic
131C2×C4×C17#13511yescharacteristic
132C2×Dic17—22no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138Dic34—22no—
139Dic34—22no—
140Dic34—41no—
141Dic34—41no—
142C8×C17—22no—
143C8×C17—22no—
144C8×C17—81no—
145#3622—42no—
146#3622—41no—
147#3622—41no—
148#3622—81no—
149#1984—171no—
150#1939D1711yescharacteristic
151C4×#103—171no—
152C2×Q8⋊C8—171no—
153C2×#322—171no—
154#1279—171no—
155#1277—171no—
156C22×C17#38811yescharacteristic
157C22×C17#43511yescharacteristic
158C22×C17#43511yescharacteristic
159C22×C17C4×SD1611yescharacteristic
160C22×C17C4×Q1611yescharacteristic
161C22×C17#44411yescharacteristic
162C22×C17#44411yescharacteristic
163C4×C17—21no—
164C4×C17—21no—
165C4×C17—42no—
166C4×C17—81no—
167C4×C17#43211yescharacteristic
168C4×C17#43311yescharacteristic
169C4×C17#43511yescharacteristic
170C4×C17#43611yescharacteristic
171C4×C17#46511yescharacteristic
172C4×C17#46711yescharacteristic
173C4×C17#48711yescharacteristic
174C4×C17#48811yescharacteristic
175Dic17—42no—
176Dic17—81no—
177C2×C4×Q8—171no—
178C2×C4⋊C8—21no—
179C2×C4⋊C8—171no—
180C2×C4⋊C8C2×D1711yescharacteristic
181C2×#103—171no—
182C2×#103—171no—
183C2×C4×C8—171no—
184C2×C4×C8—171no—
185C2×C4×C8C2×D1711yescharacteristic
186C4×C4⋊C4C2×D1711yescharacteristic
187#340—171no—
188#340—171no—
189#336—21no—
190#336—341no—
191#336—341no—
192Q8⋊C8—342no—
193#322—342no—
194C2×C17#158211yescharacteristic
195C2×C17#158311yescharacteristic
196C2×C17#158411yescharacteristic
197C2×C17#158411yescharacteristic
198C2×C17#192411yescharacteristic
199C2×C17#193311yescharacteristic
200C2×C17#193811yescharacteristic
201C22×Q8—171no—
202C22×C8—21no—
203C22×C8—171no—
204C22×C8—171no—
205C22×C8—341no—
206C22×C8—341no—
207C22×C8C22⋊D1711yescharacteristic
208C22×C8C22⋊D1711yescharacteristic
209C4×Q8—341no—
210C4×Q8—341no—
211C4×Q8—341no—
212C4×Q8—341no—
213C2×C4⋊C4—171no—
214C2×C4⋊C4—341no—
215C2×C4⋊C4C4×D1711yescharacteristic
216C2×C4⋊C4C4×D1711yescharacteristic
217C2×C42—21no—
218C2×C42—341no—
219C2×C42C22×D1711yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—42no—
223C4⋊C8—341no—
224C4⋊C8—341no—
225#103—342no—
226#103—342no—
227C4×C8—21no—
228C4×C8—21no—
229C4×C8—172no—
230C4×C8—341no—
231C4×C8—341no—
232C4×C8—341no—
233#95—21no—
234C17#955711yescharacteristic, complemented, Sylow
235C2×Q8—172no—
236C2×Q8—341no—
237C2×Q8—341no—
238C2×Q8—341no—
239C2×Q8—341no—
240C2×Q8—341no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—341no—
244C22×C4—341no—
245C22×C4C2×C4×D1711yescharacteristic
246C22×C4#6325211yescharacteristic
247C22×C4C2×C22⋊D1711yescharacteristic
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—341no—
256C2×C8—341no—
257C2×C8—342no—
258C2×C8—341no—
259C2×C8—341no—
260C2×C8—341no—
261C2×C8—341no—
262C2×C8—681no—
263C2×C8—681no—
264C2×C8—681no—
265C2×C8—681no—
266C2×C8—681no—
267C2×C8#6322912yes—
268C2×C8#6323112yes—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—341no—
273C4⋊C4—341no—
274C4⋊C4—681no—
275C4⋊C4—681no—
276C4⋊C4#6321812yes—
277C42—41no—
278C42—41no—
279C42—681no—
280C42—681no—
281C42D4×D1711yescharacteristic
282C42#6325411yescharacteristic
283C42#6325611yescharacteristic
284C42#6325611yescharacteristic
285C23C4×C22⋊D1711yescharacteristic
286Q8—342no—
287Q8—342no—
288Q8—681no—
289Q8—681no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—342no—
299C2×C4—681no—
300C2×C4—681no—
301C2×C4—681no—
302C2×C4—681no—
303C2×C4—681no—
304C2×C4#1058757811yescharacteristic
305C2×C4#1058757911yescharacteristic
306C2×C4#1058758011yescharacteristic
307C2×C4#1058758411yescharacteristic
308C2×C4C2×#6321811yescharacteristic
309C2×C4#1058758711yescharacteristic
310C2×C4M16×D1711yescharacteristic
311C2×C4#1058759311yescharacteristic
312C2×C4C2×#6322911yescharacteristic
313C2×C4#1058762511yescharacteristic
314C2×C4C2×#6323111yescharacteristic
315C2×C4#1058763311yescharacteristic
316C2×C4#1058763611yescharacteristic
317C2×C4#1058763611yescharacteristic
318C8—22no—
319C8—22no—
320C8—81no—
321C8—682no—
322C8—681no—
323C8—681no—
324C8—1361no—
325C22#1176269911yescharacteristic
326C22#1176287811yescharacteristic
327C22#1176288011yescharacteristic
328C22C4×#6322911yescharacteristic
329C22C4×#6323111yescharacteristic
330C22#1176292911yescharacteristic
331C22#1176292911yescharacteristic
332C4—21no—
333C4—21no—
334C4—42no—
335C4—81no—
336C4—682no—
337C4—1361no—
338C4#1176286511yescharacteristic
339C4#1176286911yescharacteristic
340C4#1176287911yescharacteristic
341C4#1176288611yescharacteristic
342C4#1176303611yescharacteristic
343C4#1176304811yescharacteristic
344C4#1176316111yescharacteristic
345C4#1176316611yescharacteristic
346C2#1452762011yescharacteristic
347C2#1452762511yescharacteristic
348C2#1452763211yescharacteristic
349C2#1452763411yescharacteristic
350C2#1452939611yescharacteristic
351C2#1452945911yescharacteristic
352C2#1452949411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D17
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1939C2
socle, prime radicalC23×C17C4×D4
cosocleC2×C42×C17C23
hypercenter#1939D17
hypocenterC17#9557
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1939

Complements

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

NH ≅ G/Ntype
234. C17#9557semidirect

Maximal subgroups

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

subgroupindex
#145297202
C4×#105874812
C2×#117625392
C2×#117625302
#145266252
#145266182
C17×#19392
#955717