Finite Group Databasebeta

← #16923652

Subgroups — #16923652

Order 4352.

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

normal subgroups only

This group has 350 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#14536739C211yesmaximal, characteristic
2#14530346C211yesmaximal, characteristic
3#14530346C211yesmaximal, characteristic
4#14526610C211yesmaximal, characteristic
5#14526608C211yesmaximal, characteristic
6#14526606C211yesmaximal, characteristic
7C17×#2095C211yesmaximal, characteristic
8#11762751—21no—
9#11762749—21no—
10#11762728—21no—
11#11762707C2211yescharacteristic
12#11762707C2211yescharacteristic
13#11762706—21no—
14#11762692—21no—
15#11762690—21no—
16#11762571—21no—
17#11762571—21no—
18#11762571—21no—
19#11762571—21no—
20#11762564C2211yescharacteristic
21#11762564C2211yescharacteristic
22C2×C17×#107—21no—
23C2×C17×#103—21no—
24C17×#391C2211yescharacteristic
25C17×#384C2211yescharacteristic
26C17×#336C2211yescharacteristic
27C22×Q8×C17D411yescharacteristic
28C22×C8×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C42×C17C2311yescharacteristic
34C2×C4⋊Dic17D411yescharacteristic
35C2×C4⋊Dic17D411yescharacteristic
36C2×C4⋊Dic17D411yescharacteristic
37C2×C4⋊Dic17D411yescharacteristic
38C2×#63225—21no—
39C2×#63225—21no—
40C2×#63225—21no—
41C2×#63225—21no—
42C2×C4×Dic17—21no—
43C22×#3622—21no—
44C22×#3622—21no—
45C17×#107—42no—
46C17×#103—42no—
47C17×#95—21no—
48C17×#95—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56C2×Q8×C17—21no—
57C2×Q8×C17—21no—
58C2×Q8×C17—41no—
59C2×Q8×C17—41no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—41no—
63C22×C4×C17C2×D411yescharacteristic
64C22×C4×C17C2×D411yescharacteristic
65C22×C4×C17C2×D411yescharacteristic
66C22×Dic17—21no—
67C22×Dic17—21no—
68C22×Dic17—21no—
69C22×Dic17—21no—
70C2×C8×C17—22no—
71C2×C8×C17—41no—
72C2×C8×C17—41no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—42no—
77C4⋊C4×C17—42no—
78C42×C17—41no—
79C4⋊Dic17—21no—
80C4⋊Dic17—21no—
81C4⋊Dic17—21no—
82C4⋊Dic17—41no—
83C4⋊Dic17—41no—
84C4⋊Dic17Q1612yes—
85#63225—41no—
86#63225—41no—
87#63225—41no—
88#63225—41no—
89#63225—81no—
90#63225—81no—
91C4×Dic17—81no—
92C2×#3622—41no—
93C2×#3622—41no—
94C2×#3622—41no—
95C2×#3622—41no—
96C2×#3622—41no—
97C2×#3622—41no—
98#7835—171nomaximal, Sylow
99C23×C17#12011yescharacteristic
100Q8×C17—42no—
101Q8×C17—81no—
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—81no—
115C2×C4×C17—81no—
116C2×C4×C17—81no—
117C2×C4×C17C2×Q1611yescharacteristic
118C2×C4×C17#13511yescharacteristic
119C2×C4×C17#13511yescharacteristic
120C2×C4×C17#13711yescharacteristic
121C2×C4×C17#13711yescharacteristic
122C2×C4×C17#13711yescharacteristic
123C2×Dic17—22no—
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—41no—
134C2×Dic17—41no—
135C8×C17—42no—
136#3622—81no—
137#3622—81no—
138#2805—171no—
139#2100—171no—
140#2100—171no—
141#2095D1711yescharacteristic
142#1272—171no—
143#1271—171no—
144#1271—171no—
145C22×C17#45111yescharacteristic
146C22×C17#45211yescharacteristic
147C22×C17#45211yescharacteristic
148C22×C17#45311yescharacteristic
149C22×C17#45411yescharacteristic
150C22×C17#45411yescharacteristic
151C22×C17#45811yescharacteristic
152C4×C17—21no—
153C4×C17—21no—
154C4×C17—21no—
155C4×C17—21no—
156C4×C17—21no—
157C4×C17—21no—
158C4×C17—81no—
159C4×C17—81no—
160C4×C17—161no—
161Dic17—42no—
162Dic17—81no—
163Dic17—81no—
164Dic17—81no—
165C2×#107—21no—
166C2×#103—21no—
167#400—341no—
168#400—341no—
169#395—341no—
170#391C2×D1711yescharacteristic
171#389—171no—
172#389—171no—
173#389—341no—
174#387—341no—
175#387—341no—
176#384C2×D1711yescharacteristic
177#340—341no—
178#340—341no—
179#340—341no—
180#340—341no—
181#336—171no—
182#336—171no—
183#336C2×D1711yescharacteristic
184C2×C17#161511yescharacteristic
185C2×C17#161711yescharacteristic
186C2×C17#161811yescharacteristic
187C2×C17#163211yescharacteristic
188C2×C17#163611yescharacteristic
189C2×C17#163811yescharacteristic
190C2×C17#165711yescharacteristic
191C22×Q8C22⋊D1711yescharacteristic
192C22×C8—21no—
193C22×C8—341no—
194C22×C8—341no—
195C2×C4⋊C4—21no—
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—341no—
206C2×C4⋊C4C22⋊D1711yescharacteristic
207C2×C42—341no—
208C2×C42C22×D1711yescharacteristic
209#107—42no—
210#103—42no—
211#95—21no—
212#95—21no—
213#95—341no—
214#95—341no—
215#95—341no—
216#95—341no—
217#95—341no—
218#95—341no—
219#95—341no—
220C17#783511yescharacteristic, complemented, Sylow
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—41no—
224C2×Q8—41no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—41no—
228C22×C4—341no—
229C22×C4—341no—
230C22×C4—341no—
231C22×C4—341no—
232C22×C4D4×D1711yescharacteristic
233C22×C4D4×D1711yescharacteristic
234C22×C4C2×C22⋊D1711yescharacteristic
235C2×C8—22no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—681no—
239C2×C8—681no—
240C2×C8—681no—
241C2×C8—681no—
242C2×C8—681no—
243C2×C8—681no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—172no—
250C4⋊C4—341no—
251C4⋊C4—341no—
252C4⋊C4—341no—
253C4⋊C4—681no—
254C4⋊C4—681no—
255C4⋊C4—681no—
256C4⋊C4—681no—
257C4⋊C4—681no—
258C4⋊C4—681no—
259C4⋊C4—1361no—
260C4⋊C4—1361no—
261C42—41no—
262C42—1361no—
263C23#1058762311yescharacteristic
264Q8—42no—
265Q8—81no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—342no—
282C2×C4—681no—
283C2×C4—681no—
284C2×C4—681no—
285C2×C4—681no—
286C2×C4—681no—
287C2×C4—681no—
288C2×C4—681no—
289C2×C4—681no—
290C2×C4—681no—
291C2×C4—681no—
292C2×C4—681no—
293C2×C4Q16×D1711yescharacteristic
294C2×C4#1058760411yescharacteristic
295C2×C4#1058760411yescharacteristic
296C2×C4#1058760511yescharacteristic
297C2×C4#1058762811yescharacteristic
298C2×C4#1058763611yescharacteristic
299C8—42no—
300C8—1361no—
301C8—1361no—
302C22#1176296311yescharacteristic
303C22#1176296911yescharacteristic
304C22#1176297011yescharacteristic
305C22#1176297611yescharacteristic
306C22#1176298011yescharacteristic
307C22#1176298011yescharacteristic
308C22#1176299811yescharacteristic
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—81no—
316C4—81no—
317C4—161no—
318C4—682no—
319C4—1361no—
320C4—1361no—
321C4—1361no—
322C2#1452781411yescharacteristic
323C2#1452782411yescharacteristic
324C2#1452783011yescharacteristic
325C2#1452791511yescharacteristic
326C2#1452794011yescharacteristic
327C2#1452795511yescharacteristic
328C2#1452808011yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2095C2
socle, prime radicalC23×C17#120
hypercenter#2095D17
hypocenterC17#7835
LCSG ▷ C2×C42×C17 ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2095

Complements

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

NH ≅ G/Ntype
220. C17#7835semidirect

Maximal subgroups

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

subgroupindex
#145367392
#145303462
#145266102
#145266082
#145266062
C17×#20952
#783517