Finite Group Databasebeta

← #16935288

Subgroups — #16935288

Order 4352.

636 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 105 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#14538780C212yesmaximal, complemented
2#14529582C211yesmaximal, characteristic, complemented
3#14527183C212yesmaximal, complemented
4#14526615C211yesmaximal, characteristic, complemented
5C17×#3150C211yesmaximal, characteristic, complemented
6C2×C4×D68C2211yescharacteristic
7#11763120—22no—
8#11763086—22no—
9#11763001—22no—
10#11762942—22no—
11C4×#63228—24no—
12#11762862C2212yes—
13C2×C4⋊#3622C2211yescharacteristic
14C2×#10587491—22no—
15D4⋊#3622—24no—
16C2×C17×#135—22no—
17C17×#532C2212yes—
18C17×#497—22no—
19C17×#496—22no—
20C2×C17×#97C2211yescharacteristic
21C2×#41×C17—22no—
22C22×D68D411yescharacteristic
23C22×C4×D17—21no—
24C17×#135—44no—
25C17×#135—44no—
26C2×Q16×C17—22no—
27C2×SD16×C17—24no—
28C2×D8×C17—22no—
29C22×C8×C17D412yes—
30C17×C4⋊Q8D412yes—
31C17×#127D412yes—
32C17×#124—22no—
33C17×#121—22no—
34C17×#121—22no—
35C4×D4×C17—22no—
36C4×D4×C17—22no—
37C2×C42×C17C2311yescharacteristic
38C2×#63228—24no—
39C2×#63227—21no—
40C2×C4⋊Dic17D411yescharacteristic
41C22×#3622—21no—
42C4×D68—22no—
43C4×D68—22no—
44C17×#97—22no—
45#10587503—24no—
46C22⋊#3622—22no—
47#10587491—44no—
48#10587480—24no—
49#10587478—24no—
50C4⋊#3622—22no—
51C4⋊#3622—22no—
52C4×#3622D414yes—
53C23×D17—21no—
54#41×C17—44no—
55#41×C17—44no—
56C2×Q8×C17—22no—
57C2×D4×C17—22no—
58C2×D4×C17—22no—
59C2×D4×C17—22no—
60C2×D4×C17—42no—
61C22×C4×C17—42no—
62C22×C4×C17C2×D411yescharacteristic
63C22×C4×C17C2×D411yescharacteristic
64C22×C4×C17#4111yescharacteristic
65C22×Dic17—21no—
66C2×D68—22no—
67C2×D68—42no—
68C2×C4×D17—41no—
69C2×C4×D17—41no—
70C2×C4×D17—42no—
71C2×C4×D17—42no—
72Q16×C17—44no—
73SD16×C17—48no—
74D8×C17—44no—
75C2×C8×C17—22no—
76C2×C8×C17—22no—
77C2×C8×C17D814yescomplemented
78C4⋊C4×C17—22no—
79C4⋊C4×C17—22no—
80C22⋊C4×C17—42no—
81C22⋊C4×C17—42no—
82C42×C17C2×D412yes—
83C42×C17C2×D412yes—
84#63228—48no—
85#63227—42no—
86C4⋊Dic17—22no—
87C2×#3622—24no—
88C2×#3622—41no—
89C2×#3622—42no—
90#10032—171nomaximal, Sylow
91C23×C17—42no—
92C23×C17#12111yescharacteristic
93C22×D17—22no—
94C22×D17—41no—
95C22×D17—42no—
96C22×D17—41no—
97C22×D17—42no—
98Q8×C17—44no—
99D4×C17—44no—
100D4×C17—44no—
101D4×C17—44no—
102D4×C17—84no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—42no—
106C2×C4×C17—82no—
107C2×C4×C17—82no—
108C2×C4×C17#12012yes—
109C2×C4×C17#12011yescharacteristic
110C2×C4×C17#12112yes—
111C2×C4×C17#12711yescharacteristic
112C2×C4×C17C2×D812yes—
113C2×C4×C17AGL(1,ℤ/8)12yes—
114C2×Dic17—41no—
115C2×Dic17—42no—
116D68—24no—
117D68—42no—
118C4×D17—82no—
119C4×D17—81no—
120C4×D17—81no—
121C8×C17—24no—
122#3622—44no—
123#3622—81no—
124#3150D1711yescharacteristic, complemented
125#3100—172no—
126#1955—171no—
127#1480—172no—
128#1275—171no—
129C22×C17—21no—
130C22×C17—21no—
131C22×C17—82no—
132C22×C17—82no—
133C22×C17—82no—
134C22×C17#39211yescharacteristic
135C22×C17#45912yes—
136C2×D17—44no—
137C2×D17—42no—
138C2×D17—82no—
139C2×D17—81no—
140C2×D17—81no—
141C4×C17—22no—
142C4×C17—22no—
143C4×C17—82no—
144C4×C17#44712yes—
145C4×C17#49311yescharacteristic
146C4×C17#49611yescharacteristic
147Dic17—81no—
148C2×#135—22no—
149#532C2×D1712yes—
150C2×C4×D4—171no—
151#497—22no—
152#496—22no—
153#480—342no—
154#474—342no—
155#459—342no—
156#447—342no—
157C4×D8—344no—
158#431—172no—
159C2×C4⋊C8—171no—
160C2×C22⋊C8—342no—
161C2×#97C2×D1711yescharacteristic
162D4⋊C8—344no—
163C2×C17—22no—
164C2×C17—162no—
165C2×C17#201011yescharacteristic
166C2×C17#201111yescharacteristic
167C2×C17#201711yescharacteristic
168D17—82no—
169C2×#41—22no—
170C22×D4—171no—
171C23×C4—341no—
172#135—44no—
173#135—44no—
174C2×Q16—22no—
175C2×SD16—24no—
176C2×D8—22no—
177C2×D8—344no—
178C22×C8—341no—
179C22×C8C22⋊D1712yes—
180C4⋊Q8C22⋊D1712yes—
181#127C22⋊D1712yes—
182#124—22no—
183#121—22no—
184#121—22no—
185C4×D4—22no—
186C4×D4—22no—
187C4×D4—342no—
188C4×D4—342no—
189C2×C4⋊C4—171no—
190C2×C22⋊C4—341no—
191C2×C42C22×D1711yescharacteristic
192#107—344no—
193C4⋊C8—342no—
194C4⋊C8—342no—
195#102—344no—
196#102—344no—
197C22⋊C8—342no—
198C22⋊C8—684no—
199#97—22no—
200C4×C8—174no—
201C17#1003211yescharacteristic, complemented, Sylow
202C24—341no—
203#41—44no—
204#41—44no—
205C2×Q8—22no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—42no—
210C2×D4—342no—
211C2×D4—682no—
212C22×C4—42no—
213C22×C4—341no—
214C22×C4—682no—
215C22×C4—682no—
216C22×C4—681no—
217C22×C4—681no—
218C22×C4D4×D1711yescharacteristic
219C22×C4#6325411yescharacteristic
220C22×C4C2×C22⋊D1711yescharacteristic
221Q16—44no—
222SD16—48no—
223D8—44no—
224D8—688no—
225C2×C8—22no—
226C2×C8—22no—
227C2×C8—344no—
228C2×C8—682no—
229C2×C8—681no—
230C2×C8#6322814yescomplemented
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—342no—
234C22⋊C4—42no—
235C22⋊C4—42no—
236C22⋊C4—682no—
237C42D4×D1712yes—
238C42C2×C22⋊D1712yes—
239C23—42no—
240C23—342no—
241C23—681no—
242C23—682no—
243C23—681no—
244C23—682no—
245C23#1058762411yescharacteristic
246Q8—44no—
247D4—44no—
248D4—44no—
249D4—44no—
250D4—84no—
251D4—344no—
252D4—682no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—681no—
259C2×C4—682no—
260C2×C4—1361no—
261C2×C4—1361no—
262C2×C4—1362no—
263C2×C4C2×#6322812yes—
264C2×C4#1058761812yes—
265C2×C4#1058762312yes—
266C2×C4#1058762512yes—
267C2×C4#1058762611yescharacteristic
268C2×C4#1058763911yescharacteristic
269C8—24no—
270C8—684no—
271C8—1361no—
272C22—21no—
273C22—21no—
274C22—82no—
275C22—82no—
276C22—82no—
277C22—684no—
278C22—682no—
279C22—1362no—
280C22—1361no—
281C22—1361no—
282C22#1176271711yescharacteristic
283C22#1176300112yes—
284C4—22no—
285C4—22no—
286C4—82no—
287C4—1361no—
288C4#1176294312yes—
289C4#1176318511yescharacteristic
290C4#1176319611yescharacteristic
291C2—22no—
292C2—162no—
293C2—1362no—
294C2#1452984811yescharacteristic
295C2#1452985511yescharacteristic
296C2#1452988711yescharacteristic
subgroupG/H
centerC2×C4#10587626
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#3150C2
socleC22×C17#392
hypercenter#3150D17
hypocenterC17#10032
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3150

Complements

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

NH ≅ G/Ntype
1. #14538780C2semidirect
2. #14529582C2semidirect
3. #14527183C2semidirect
4. #14526615C2semidirect
5. C17×#3150C2semidirect
77. C2×C8×C17D8semidirect
124. #3150D17semidirect
201. C17#10032semidirect
230. C2×C8#63228semidirect

Maximal subgroups

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

subgroupindex
#145387802
#145295822
#145271832
#145266152
C17×#31502
#1003217