Finite Group Databasebeta

← #16923428

Subgroups — #16923428

Order 4352.

374 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 91 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#14530342C211yesmaximal, characteristic
2#14530260C211yesmaximal, characteristic
3#14530255C211yesmaximal, characteristic
4#14526607C211yesmaximal, characteristic
5#14526607C211yesmaximal, characteristic
6#14526607C211yesmaximal, characteristic
7C17×#2726C211yesmaximal, characteristic
8C2×#10587478—21no—
9C2×#10587479—21no—
10#11762679C2211yescharacteristic
11#11762571—21no—
12#11762571—21no—
13#11762571—21no—
14#11762571—21no—
15#11762564C2211yescharacteristic
16#11762564C2211yescharacteristic
17#11762564C2211yescharacteristic
18C2×C17×#125—21no—
19C17×#398—21no—
20C17×#398—21no—
21C17×#398—21no—
22C17×#389—21no—
23C17×#389C2211yescharacteristic
24C17×#389C2211yescharacteristic
25C17×#389C2211yescharacteristic
26C17×#387—21no—
27C17×#125—42no—
28C17×#125—42no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17D411yescharacteristic
37C2×C4⋊C4×C17D411yescharacteristic
38C2×C4⋊C4×C17D411yescharacteristic
39C2×C4⋊C4×C17D411yescharacteristic
40C2×C4⋊C4×C17D411yescharacteristic
41C2×C4⋊C4×C17D411yescharacteristic
42C2×C42×C17—21no—
43C2×C42×C17C2311yescharacteristic
44C2×C4⋊Dic17—21no—
45C2×C4⋊Dic17—21no—
46C2×C4⋊Dic17—21no—
47C22×#3622—21no—
48C22×#3622—21no—
49C22×#3622—21no—
50C17×#95—21no—
51C17×#95—21no—
52C17×#95—21no—
53C17×#95—21no—
54C17×#95—21no—
55C17×#95—21no—
56#10587479—42no—
57#10587478—42no—
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17C2×D411yescharacteristic
65C22×C4×C17C2×D411yescharacteristic
66C22×C4×C17C2×D411yescharacteristic
67C22×Dic17—41no—
68C4⋊C4×C17—21no—
69C4⋊C4×C17—21no—
70C4⋊C4×C17—21no—
71C4⋊C4×C17—21no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—42no—
76C4⋊C4×C17—42no—
77C4⋊C4×C17—42no—
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—81no—
85C4⋊C4×C17D812yes—
86C4⋊C4×C17SD1612yes—
87C42×C17—41no—
88C42×C17—42no—
89C4⋊Dic17—42no—
90C4⋊Dic17—41no—
91C4⋊Dic17—41no—
92C4⋊Dic17—41no—
93C4⋊Dic17—41no—
94C2×#3622—22no—
95C2×#3622—22no—
96C2×#3622—41no—
97C2×#3622—41no—
98C2×#3622—41no—
99C2×#3622—41no—
100C2×#3622—41no—
101C2×#3622—41no—
102C2×#3622—41no—
103#7798—171nomaximal, Sylow
104C23×C17#12011yescharacteristic
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—22no—
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—41no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17C2×D811yescharacteristic
130C2×C4×C17C2×SD1611yescharacteristic
131C2×C4×C17#13511yescharacteristic
132C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C17#13711yescharacteristic
134C2×C4×C17#13711yescharacteristic
135C2×Dic17—81no—
136C2×Dic17—81no—
137C2×Dic17—81no—
138#3622—42no—
139#3622—42no—
140#3622—81no—
141#2726D1711yescharacteristic
142#2099—171no—
143#2084—171no—
144#2083—171no—
145#1271—171no—
146#1271—171no—
147#1271—171no—
148C22×C17#44711yescharacteristic
149C22×C17#44811yescharacteristic
150C22×C17#45211yescharacteristic
151C22×C17#45411yescharacteristic
152C22×C17#45611yescharacteristic
153C22×C17#45611yescharacteristic
154C22×C17#45811yescharacteristic
155C4×C17—21no—
156C4×C17—21no—
157C4×C17—21no—
158C4×C17—21no—
159C4×C17—21no—
160C4×C17—21no—
161C4×C17—42no—
162C4×C17—42no—
163C4×C17—81no—
164C4×C17—81no—
165C4×C17—81no—
166C4×C17—81no—
167Dic17—161no—
168C2×#125—21no—
169C2×#107—341no—
170C2×#106—341no—
171#398—21no—
172#398—21no—
173#398—21no—
174#389—21no—
175#389C2×D1711yescharacteristic
176#389C2×D1711yescharacteristic
177#389C2×D1711yescharacteristic
178#387—21no—
179#384—171no—
180#340—341no—
181#340—341no—
182#340—341no—
183#340—341no—
184#336—171no—
185#336—171no—
186#336—171no—
187C2×C17#161011yescharacteristic
188C2×C17#161111yescharacteristic
189C2×C17#161511yescharacteristic
190C2×C17#162711yescharacteristic
191C2×C17#164711yescharacteristic
192C2×C17#165311yescharacteristic
193C2×C17#166311yescharacteristic
194C22×C8—341no—
195C22×C8—341no—
196C22×C8—341no—
197#125—42no—
198#125—42no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—341no—
207C2×C4⋊C4—341no—
208C2×C4⋊C4—341no—
209C2×C4⋊C4C22⋊D1711yescharacteristic
210C2×C4⋊C4C22⋊D1711yescharacteristic
211C2×C4⋊C4C22⋊D1711yescharacteristic
212C2×C4⋊C4C22⋊D1711yescharacteristic
213C2×C4⋊C4C22⋊D1711yescharacteristic
214C2×C4⋊C4C22⋊D1711yescharacteristic
215C2×C42—21no—
216C2×C42C22×D1711yescharacteristic
217#107—682no—
218#106—682no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225C17#779811yescharacteristic, complemented, Sylow
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—681no—
233C22×C4C2×C22⋊D1711yescharacteristic
234C22×C4C2×C22⋊D1711yescharacteristic
235C22×C4C2×C22⋊D1711yescharacteristic
236C2×C8—342no—
237C2×C8—342no—
238C2×C8—681no—
239C2×C8—681no—
240C2×C8—681no—
241C2×C8—681no—
242C2×C8—681no—
243C2×C8—681no—
244C2×C8—681no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—682no—
263C4⋊C4—681no—
264C4⋊C4—681no—
265C4⋊C4—681no—
266C4⋊C4—681no—
267C4⋊C4#6322812yes—
268C4⋊C4#6323012yes—
269C42—41no—
270C42—42no—
271C23#1058763911yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—1361no—
297C2×C4—1361no—
298C2×C4—1361no—
299C2×C4C2×#6322811yescharacteristic
300C2×C4#1058761811yescharacteristic
301C2×C4C2×#6323011yescharacteristic
302C2×C4#1058762811yescharacteristic
303C2×C4#1058763611yescharacteristic
304C2×C4#1058763711yescharacteristic
305C8—682no—
306C8—682no—
307C8—1361no—
308C22#1176294311yescharacteristic
309C22#1176294811yescharacteristic
310C22#1176297111yescharacteristic
311C22#1176298211yescharacteristic
312C22#1176299211yescharacteristic
313C22#1176299211yescharacteristic
314C22#1176299911yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—42no—
323C4—81no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—2721no—
328C2#1452778711yescharacteristic
329C2#1452779211yescharacteristic
330C2#1452781511yescharacteristic
331C2#1452788711yescharacteristic
332C2#1452801911yescharacteristic
333C2#1452806111yescharacteristic
334C2#1452811211yescharacteristic
subgroupG/H
centerC23#10587639
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2726C2
socle, prime radicalC23×C17#120
hypercenter#2726D17
hypocenterC17#7798
LCSG ▷ C2×C42×C17 ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2726

Complements

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

NH ≅ G/Ntype
225. C17#7798semidirect

Maximal subgroups

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

subgroupindex
#145303422
#145302602
#145302552
#145266072
C17×#27262
#779817