Finite Group Databasebeta

← #16922944

Subgroups — #16922944

Order 4352.

352 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537170C211yesmaximal, characteristic
2#14528926C211yesmaximal, characteristic
3#14528899C211yesmaximal, characteristic
4#14526608C211yesmaximal, characteristic
5#14526607C211yesmaximal, characteristic
6#14526606C211yesmaximal, characteristic
7C17×#1271C211yesmaximal, characteristic
8C2×#10587485—21no—
9#11762708C411yescharacteristic
10#11762707C2211yescharacteristic
11#11762705C411yescharacteristic
12#11762695—21no—
13#11762694—21no—
14#11762691—21no—
15#11762690—21no—
16#11762674C411yescharacteristic
17#11762674C411yescharacteristic
18C42×Dic17C2211yescharacteristic
19#11762564C2211yescharacteristic
20#11762564C2211yescharacteristic
21#11762563—21no—
22#11762563—21no—
23#11762563—21no—
24C17×#389C2211yescharacteristic
25C17×#336C2211yescharacteristic
26C17×#336C2211yescharacteristic
27C22×C8×C17—21no—
28C22×C8×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C42×C17C2311yescharacteristic
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17C2×C411yescharacteristic
35C2×C4⋊Dic17C2×C411yescharacteristic
36C2×#63225—21no—
37C2×#63225—21no—
38C2×C4×Dic17C2×C411yescharacteristic
39C2×C4×Dic17C2×C411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17D411yescharacteristic
44C22×#3622—21no—
45C22×#3622—21no—
46C17×#95—21no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587485—42no—
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17C22×C411yescharacteristic
58C22×C4×C17C2×D411yescharacteristic
59C22×C4×C17C2×D411yescharacteristic
60C22×Dic17—21no—
61C22×Dic17—21no—
62C22×Dic17C22⋊C411yescharacteristic
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C22⋊C411yescharacteristic
65C22×Dic17C22⋊C411yescharacteristic
66C2×C8×C17—41no—
67C2×C8×C17—41no—
68C2×C8×C17—41no—
69C2×C8×C17—41no—
70C2×C8×C17—41no—
71C2×C8×C17—41no—
72C4⋊C4×C17—21no—
73C4⋊C4×C17—21no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C42×C17—41no—
78C4⋊Dic17—21no—
79C4⋊Dic17—21no—
80C4⋊Dic17—42no—
81C4⋊Dic17—41no—
82#63225—42no—
83#63225—41no—
84#63225—41no—
85C4×Dic17—21no—
86C4×Dic17—21no—
87C4×Dic17—21no—
88C4×Dic17—21no—
89C4×Dic17—21no—
90C4×Dic17—21no—
91C4×Dic17—22no—
92C4×Dic17—41no—
93C4×Dic17—41no—
94C2×#3622—41no—
95C2×#3622—41no—
96C2×#3622—41no—
97C2×#3622—41no—
98C2×#3622—41no—
99C2×#3622—41no—
100#7717—171nomaximal, Sylow
101C23×C17C2×C22⋊C411yescharacteristic
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—41no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17#13111yescharacteristic
115C2×C4×C17#13111yescharacteristic
116C2×C4×C17#13511yescharacteristic
117C2×C4×C17#13511yescharacteristic
118C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C17#13711yescharacteristic
120C2×Dic17—21no—
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17—21no—
125C2×Dic17—21no—
126C2×Dic17—21no—
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—21no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17#10112yes—
138C8×C17—81no—
139C8×C17—81no—
140#3622—81no—
141#3622—81no—
142#2864—171no—
143#1839—171no—
144#1831—171no—
145#1271—171no—
146#1271—171no—
147#1271—171no—
148#1271D1711yescharacteristic
149C22×C17#40811yescharacteristic
150C22×C17#41011yescharacteristic
151C22×C17C2×#10111yescharacteristic
152C22×C17#41611yescharacteristic
153C22×C17#41711yescharacteristic
154C22×C17#42111yescharacteristic
155C22×C17#42111yescharacteristic
156C4×C17—21no—
157C4×C17—21no—
158C4×C17—21no—
159C4×C17—21no—
160C4×C17—21no—
161C4×C17—21no—
162C4×C17—81no—
163C4×C17—81no—
164Dic17—22no—
165Dic17—41no—
166Dic17—41no—
167Dic17—41no—
168Dic17—81no—
169Dic17—81no—
170C2×C4⋊C8—341no—
171#389—171no—
172#389—171no—
173#389—171no—
174#389C2×D1711yescharacteristic
175#387—341no—
176#387—341no—
177#387—341no—
178#387—341no—
179#382—171no—
180#382—171no—
181C43—171no—
182#336—171no—
183#336—171no—
184#336—341no—
185#336—341no—
186#336—341no—
187#336C2×D1711yescharacteristic
188#336C2×D1711yescharacteristic
189C2×C17#147011yescharacteristic
190C2×C17#148211yescharacteristic
191C2×C17#149511yescharacteristic
192C2×C17#151211yescharacteristic
193C2×C17#152111yescharacteristic
194C2×C17#153711yescharacteristic
195C2×C17#155211yescharacteristic
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—341no—
199C22×C8—341no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—171no—
202C2×C4⋊C4—171no—
203C2×C4⋊C4—341no—
204C2×C4⋊C4—341no—
205C2×C4⋊C4—341no—
206C2×C4⋊C4C4×D1711yescharacteristic
207C2×C4⋊C4C4×D1711yescharacteristic
208C2×C42—171no—
209C2×C42—171no—
210C2×C42—171no—
211C2×C42—171no—
212C2×C42—171no—
213C2×C42—171no—
214C2×C42C22×D1711yescharacteristic
215C4⋊C8—682no—
216#95—21no—
217#95—341no—
218#95—341no—
219#95—341no—
220#95—341no—
221#95—341no—
222#95—341no—
223#95—341no—
224C17#771711yescharacteristic, complemented, Sylow
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—171no—
228C22×C4—171no—
229C22×C4—171no—
230C22×C4—171no—
231C22×C4—341no—
232C22×C4—341no—
233C22×C4C2×C4×D1711yescharacteristic
234C22×C4D4×D1711yescharacteristic
235C22×C4D4×D1711yescharacteristic
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—681no—
243C2×C8—681no—
244C2×C8—681no—
245C2×C8—681no—
246C2×C8—681no—
247C2×C8—681no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—341no—
254C4⋊C4—341no—
255C4⋊C4—681no—
256C4⋊C4—682no—
257C4⋊C4—682no—
258C4⋊C4—681no—
259C4⋊C4—681no—
260C42—41no—
261C42—342no—
262C42—341no—
263C42—341no—
264C42—341no—
265C42—341no—
266C42—341no—
267C42—341no—
268C42—681no—
269C42—681no—
270C23C22⋊C4×D1711yescharacteristic
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
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—341no—
295C2×C4—681no—
296C2×C4—681no—
297C2×C4—681no—
298C2×C4—681no—
299C2×C4—681no—
300C2×C4—681no—
301C2×C4#1058758711yescharacteristic
302C2×C4#1058759311yescharacteristic
303C2×C4#1058759711yescharacteristic
304C2×C4#1058760111yescharacteristic
305C2×C4#1058760211yescharacteristic
306C2×C4#1058760511yescharacteristic
307C8—81no—
308C8—81no—
309C8—1361no—
310C8—1361no—
311C22#1176277411yescharacteristic
312C22#1176278111yescharacteristic
313C22#101×D1711yescharacteristic
314C22#1176280411yescharacteristic
315C22#1176280711yescharacteristic
316C22#1176282411yescharacteristic
317C22#1176282411yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—81no—
325C4—81no—
326C4—342no—
327C4—681no—
328C4—681no—
329C4—681no—
330C4—1361no—
331C4—1361no—
332C2#1452713811yescharacteristic
333C2#1452719111yescharacteristic
334C2#1452724611yescharacteristic
335C2#1452731911yescharacteristic
336C2#1452736011yescharacteristic
337C2#1452742011yescharacteristic
338C2#1452748311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D17
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1271C2
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C42×C17C23
hypercenter#1271D17
hypocenterC17#7717
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
224. C17#7717semidirect

Maximal subgroups

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

subgroupindex
#145371702
#145289262
#145288992
#145266082
#145266072
#145266062
C17×#12712
#771717