Finite Group Databasebeta

← #16946415

Subgroups — #16946415

Order 4352.

442 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 59 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#14535816C211yesmaximal, characteristic, complemented
2#14527787C212yesmaximal
3#14526789C212yesmaximal, complemented
4#14526718C211yesmaximal, characteristic, complemented
5C17×#2007C211yesmaximal, characteristic
6C2×#10587630—21no—
7#11763120—22no—
8#11762739C2212yes—
9#11762730—22no—
10#11762707—21no—
11#11762694—22no—
12#11762543—22no—
13#11762535C2212yes—
14C2×C17×#137—21no—
15C17×#537C2211yescharacteristic
16C2×C17×#104—21no—
17C17×#391C2211yescharacteristic
18C17×#343C2211yescharacteristic
19C2×#41×C17—21no—
20C22×Q8×C17D411yescharacteristic
21C22×Dic34—21no—
22C17×#137—42no—
23C17×#137—42no—
24C2×Q16×C17—41no—
25C2×SD16×C17—41no—
26C2×M16×C17—21no—
27C17×C22⋊Q8—41no—
28C17×#121—22no—
29C17×#121—41no—
30C2×C4⋊C4×C17C2311yescharacteristic
31C2×C42×C17D411yescharacteristic
32#10587630—42no—
33#10587630—42no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17D412yes—
37C2×#63225—22no—
38C2×#63225—22no—
39C2×C4×Dic17—21no—
40C17×#104—42no—
41C17×#95—22no—
42#10587503—42no—
43#10587502—22no—
44#10587502—22no—
45#10587502D412yes—
46C22⋊#3622—22no—
47#10587478—42no—
48#41×C17—41no—
49#41×C17—41no—
50#41×C17—41no—
51#41×C17—41no—
52C2×Q8×C17—21no—
53C2×Q8×C17—21no—
54C2×Q8×C17—41no—
55C2×Q8×C17—41no—
56C2×Q8×C17D812yes—
57C2×D4×C17—21no—
58C2×D4×C17—22no—
59C2×D4×C17—41no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—41no—
63C22×C4×C17C2×D412yes—
64C22×C4×C17C2×D411yescharacteristic
65C22×Dic17—22no—
66C22×Dic17—22no—
67C2×Dic34—42no—
68C2×Dic34—81no—
69C2×Dic34—81no—
70Q16×C17—44no—
71SD16×C17—44no—
72M16×C17—22no—
73M16×C17—41no—
74C2×C8×C17—41no—
75C4⋊C4×C17—22no—
76C4⋊C4×C17—41no—
77C22⋊C4×C17—42no—
78C42×C17—41no—
79C4⋊Dic17—24no—
80C4⋊Dic17—42no—
81C4⋊Dic17—81no—
82#63225—44no—
83#63225—42no—
84#63225—42no—
85C4×Dic17—42no—
86C2×#3622—42no—
87#12101—171nomaximal, Sylow
88C23×C17—41no—
89C23×C17#12011yescharacteristic
90Q8×C17—42no—
91Q8×C17—41no—
92Q8×C17—41no—
93Q8×C17—81no—
94D4×C17—41no—
95D4×C17—41no—
96D4×C17—82no—
97D4×C17—81no—
98D4×C17—81no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—22no—
102C2×C4×C17—22no—
103C2×C4×C17—22no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—42no—
109C2×C4×C17—41no—
110C2×C4×C17—81no—
111C2×C4×C17—81no—
112C2×C4×C17C2×D811yescharacteristic
113C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
114C2×Dic17—24no—
115C2×Dic17—42no—
116C2×Dic17—42no—
117C2×Dic17—42no—
118C2×Dic17—42no—
119C2×Dic17—42no—
120Dic34—84no—
121C8×C17—42no—
122#3622—82no—
123#2734—171no—
124#2007D1711yescharacteristic
125#1610—172no—
126#1346—172no—
127#1319—171no—
128C22×C17—21no—
129C22×C17—21no—
130C22×C17—81no—
131C22×C17—81no—
132C22×C17—81no—
133C22×C17#44711yescharacteristic
134C22×C17#45311yescharacteristic
135C22×C17B(4,𝔽2)11yescharacteristic
136C4×C17—21no—
137C4×C17—21no—
138C4×C17—42no—
139C4×C17—42no—
140C4×C17—42no—
141C4×C17—81no—
142Dic17—44no—
143Dic17—82no—
144C2×#137—21no—
145#537C2×D1711yescharacteristic
146C2×C4⋊Q8—341no—
147#480—342no—
148C2×#104—21no—
149#398—172no—
150#395—342no—
151#391C2×D1711yescharacteristic
152#389—341no—
153#387—342no—
154#343C2×D1711yescharacteristic
155#327—342no—
156#324—172no—
157C2×C17—21no—
158C2×C17—21no—
159C2×C17—161no—
160C2×C17#159511yescharacteristic
161C2×C17#220111yescharacteristic
162C2×C17#220511yescharacteristic
163C2×#41—21no—
164C22×Q8—341no—
165C22×Q8C22⋊D1711yescharacteristic
166#137—42no—
167#137—42no—
168C2×Q16—41no—
169C2×SD16—41no—
170C2×M16—21no—
171C4⋊Q8—682no—
172C4⋊Q8—682no—
173C22⋊Q8—41no—
174#121—22no—
175#121—41no—
176C2×C4⋊C4—172no—
177C2×C4⋊C4—341no—
178C2×C4⋊C4—342no—
179C2×C4⋊C4—342no—
180C2×C4⋊C4—341no—
181C2×C4⋊C4C22×D1711yescharacteristic
182C2×C42—341no—
183C2×C42C22⋊D1711yescharacteristic
184#107—682no—
185#104—42no—
186#102—682no—
187C22⋊C8—342no—
188#95—22no—
189#95—172no—
190#95—342no—
191#95—342no—
192C17#1210111yescharacteristic, complemented, Sylow
193#41—41no—
194#41—41no—
195#41—41no—
196#41—41no—
197C2×Q8—21no—
198C2×Q8—21no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8—682no—
202C2×Q8—1361no—
203C2×Q8—1361no—
204C2×Q8#6322812yes—
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—41no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—41no—
211C22×C4—342no—
212C22×C4—342no—
213C22×C4D4×D1712yes—
214C22×C4C2×C22⋊D1711yescharacteristic
215Q16—44no—
216SD16—44no—
217M16—22no—
218M16—41no—
219C2×C8—41no—
220C2×C8—682no—
221C4⋊C4—22no—
222C4⋊C4—41no—
223C4⋊C4—344no—
224C4⋊C4—682no—
225C4⋊C4—684no—
226C4⋊C4—682no—
227C4⋊C4—682no—
228C4⋊C4—1361no—
229C22⋊C4—42no—
230C42—41no—
231C42—682no—
232C23—41no—
233C23#1058762311yescharacteristic
234Q8—42no—
235Q8—41no—
236Q8—41no—
237Q8—81no—
238Q8—1364no—
239D4—41no—
240D4—41no—
241D4—82no—
242D4—81no—
243D4—81no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—344no—
258C2×C4—682no—
259C2×C4—682no—
260C2×C4—682no—
261C2×C4—682no—
262C2×C4—682no—
263C2×C4C2×#6322811yescharacteristic
264C2×C4#1058763511yescharacteristic
265C8—42no—
266C8—1362no—
267C22—21no—
268C22—21no—
269C22—81no—
270C22—81no—
271C22—81no—
272C22#1176294211yescharacteristic
273C22#1176297611yescharacteristic
274C22#1176299511yescharacteristic
275C4—21no—
276C4—21no—
277C4—42no—
278C4—42no—
279C4—42no—
280C4—81no—
281C4—684no—
282C4—1362no—
283C2—21no—
284C2—21no—
285C2—161no—
286C2#1452770111yescharacteristic
287C2#1453079611yescharacteristic
288C2#1453081311yescharacteristic
subgroupG/H
centerC22#11762995
commutator, cosocleC2×C4⋊C4×C17C23
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2007C2
socleC22×C17B(4,𝔽2)
prime radicalC17×#537C22
hypercenter#2007D17
hypocenterC17#12101
LCSG ▷ C2×C4⋊C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2007

Complements

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

NH ≅ G/Ntype
1. #14535816C2semidirect
3. #14526789C2semidirect
4. #14526718C2semidirect
192. C17#12101semidirect

Maximal subgroups

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

subgroupindex
#145358162
#145277872
#145267892
#145267182
C17×#20072
#1210117