Finite Group Databasebeta

← #16923453

Subgroups — #16923453

Order 4352.

366 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 81 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#14536769C211yesmaximal, characteristic
2#14530328C211yesmaximal, characteristic
3#14530256C211yesmaximal, characteristic
4#14526609C211yesmaximal, characteristic
5#14526608C211yesmaximal, characteristic
6#14526607C211yesmaximal, characteristic
7C17×#2083C211yesmaximal, characteristic
8C2×#10587478—21no—
9C2×#10587479—21no—
10C2×#10587481—21no—
11#11762751—21no—
12#11762740—21no—
13#11762739—21no—
14#11762715C2211yescharacteristic
15#11762713—21no—
16#11762707C2211yescharacteristic
17#11762695—21no—
18#11762690—21no—
19#11762571—21no—
20#11762564C2211yescharacteristic
21#11762564C2211yescharacteristic
22C2×C17×#107—21no—
23C17×#389C2211yescharacteristic
24C17×#384C2211yescharacteristic
25C17×#340—21no—
26C17×#336C2211yescharacteristic
27C22×Dic34D411yescharacteristic
28C22×C8×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C4⋊C4×C17D411yescharacteristic
35C2×C42×C17C2311yescharacteristic
36C2×C4⋊Dic17D411yescharacteristic
37C2×C4⋊Dic17D411yescharacteristic
38C2×C4⋊Dic17D411yescharacteristic
39C2×#63225—21no—
40C2×#63225—21no—
41C2×#63225—21no—
42C2×C4×Dic17—21no—
43C22×#3622—21no—
44C22×#3622—21no—
45C17×#107—42no—
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#10587502—21no—
55#10587481—42no—
56#10587479—42no—
57#10587478—42no—
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—41no—
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C22×C4×C17C2×D411yescharacteristic
64C22×Dic17—21no—
65C22×Dic17—21no—
66C22×Dic17—21no—
67C22×Dic17—21no—
68C2×Dic34—21no—
69C2×Dic34—41no—
70C2×Dic34—41no—
71C2×Dic34Q1612yes—
72C2×C8×C17—22no—
73C2×C8×C17—41no—
74C2×C8×C17—41no—
75C4⋊C4×C17—21no—
76C4⋊C4×C17—21no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—41no—
83C4⋊C4×C17—41no—
84C4⋊C4×C17—41no—
85C4⋊C4×C17—41no—
86C42×C17—41no—
87C4⋊Dic17—21no—
88C4⋊Dic17—21no—
89C4⋊Dic17—41no—
90C4⋊Dic17—41no—
91#63225—41no—
92#63225—41no—
93#63225—81no—
94#63225—81no—
95C4×Dic17—81no—
96C2×#3622—22no—
97C2×#3622—22no—
98C2×#3622—41no—
99C2×#3622—41no—
100C2×#3622—41no—
101C2×#3622—41no—
102#7802—171nomaximal, Sylow
103C23×C17#12011yescharacteristic
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—81no—
117C2×C4×C17—81no—
118C2×C4×C17—81no—
119C2×C4×C17C2×Q1611yescharacteristic
120C2×C4×C17#13511yescharacteristic
121C2×C4×C17#13511yescharacteristic
122C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C17#13711yescharacteristic
125C2×Dic17—22no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137Dic34—42no—
138Dic34—81no—
139C8×C17—42no—
140#3622—42no—
141#3622—42no—
142#2809—171no—
143#2096—171no—
144#2083—171no—
145#2083D1711yescharacteristic
146#1272—171no—
147#1271—171no—
148#1271—171no—
149C22×C17#44911yescharacteristic
150C22×C17#44911yescharacteristic
151C22×C17#45111yescharacteristic
152C22×C17#45311yescharacteristic
153C22×C17#45611yescharacteristic
154C22×C17#45611yescharacteristic
155C22×C17#45811yescharacteristic
156C4×C17—21no—
157C4×C17—21no—
158C4×C17—21no—
159C4×C17—21no—
160C4×C17—21no—
161C4×C17—21no—
162C4×C17—81no—
163C4×C17—81no—
164C4×C17—161no—
165Dic17—42no—
166Dic17—81no—
167Dic17—81no—
168Dic17—81no—
169C2×#107—21no—
170C2×#107—341no—
171C2×#106—341no—
172C2×#103—341no—
173#400—341no—
174#398—341no—
175#398—341no—
176#391—171no—
177#391—341no—
178#389—171no—
179#389C2×D1711yescharacteristic
180#387—341no—
181#387—341no—
182#384C2×D1711yescharacteristic
183#340—21no—
184#340—341no—
185#336—171no—
186#336—171no—
187#336C2×D1711yescharacteristic
188C2×C17#160911yescharacteristic
189C2×C17#160911yescharacteristic
190C2×C17#161411yescharacteristic
191C2×C17#162411yescharacteristic
192C2×C17#164811yescharacteristic
193C2×C17#164811yescharacteristic
194C2×C17#166011yescharacteristic
195C22×Q8—171no—
196C22×C8—21no—
197C22×C8—341no—
198C22×C8—341no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—171no—
204C2×C4⋊C4—171no—
205C2×C4⋊C4—171no—
206C2×C4⋊C4—341no—
207C2×C4⋊C4—341no—
208C2×C4⋊C4—341no—
209C2×C4⋊C4C22⋊D1711yescharacteristic
210C2×C4⋊C4C22⋊D1711yescharacteristic
211C2×C42—341no—
212C2×C42C22×D1711yescharacteristic
213#107—42no—
214#107—682no—
215#106—682no—
216#103—682no—
217#95—21no—
218#95—341no—
219#95—341no—
220#95—341no—
221#95—341no—
222#95—341no—
223#95—341no—
224#95—341no—
225#95—341no—
226C17#780211yescharacteristic, complemented, Sylow
227C2×Q8—172no—
228C2×Q8—341no—
229C2×Q8—681no—
230C2×Q8—681no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—341no—
235C22×C4—341no—
236C22×C4—341no—
237C22×C4—341no—
238C22×C4D4×D1711yescharacteristic
239C22×C4D4×D1711yescharacteristic
240C22×C4C2×C22⋊D1711yescharacteristic
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—342no—
245C2×C8—342no—
246C2×C8—681no—
247C2×C8—681no—
248C2×C8—681no—
249C2×C8—681no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—341no—
262C4⋊C4—341no—
263C4⋊C4—681no—
264C4⋊C4—681no—
265C4⋊C4—681no—
266C4⋊C4—681no—
267C4⋊C4—1361no—
268C4⋊C4—1361no—
269C42—41no—
270C42—1361no—
271C23#1058762311yescharacteristic
272Q8—682no—
273Q8—1361no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—342no—
290C2×C4—681no—
291C2×C4—681no—
292C2×C4—681no—
293C2×C4—681no—
294C2×C4—681no—
295C2×C4—681no—
296C2×C4—681no—
297C2×C4—681no—
298C2×C4—681no—
299C2×C4—681no—
300C2×C4—681no—
301C2×C4#1058759711yescharacteristic
302C2×C4#1058759811yescharacteristic
303C2×C4Q16×D1711yescharacteristic
304C2×C4#1058760411yescharacteristic
305C2×C4#1058761811yescharacteristic
306C2×C4#1058763611yescharacteristic
307C8—42no—
308C8—682no—
309C8—682no—
310C22#1176295111yescharacteristic
311C22#1176295211yescharacteristic
312C22#1176296311yescharacteristic
313C22#1176297511yescharacteristic
314C22#1176299011yescharacteristic
315C22#1176299111yescharacteristic
316C22#1176299811yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—81no—
325C4—161no—
326C4—682no—
327C4—1361no—
328C4—1361no—
329C4—1361no—
330C2#1452777811yescharacteristic
331C2#1452777911yescharacteristic
332C2#1452780711yescharacteristic
333C2#1452786611yescharacteristic
334C2#1452802311yescharacteristic
335C2#1452802411yescharacteristic
336C2#1452809411yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2083C2
socle, prime radicalC23×C17#120
hypercenter#2083D17
hypocenterC17#7802
LCSG ▷ C2×C42×C17 ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

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

NH ≅ G/Ntype
226. C17#7802semidirect

Maximal subgroups

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

subgroupindex
#145367692
#145303282
#145302562
#145266092
#145266082
#145266072
C17×#20832
#780217