Finite Group Databasebeta

← #17958258

Subgroups — #17958258

Order 4352.

310 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 84 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#14545146C211yesmaximal, characteristic, complemented
2#14545142C211yesmaximal, characteristic, complemented
3#14543722C212yesmaximal, complemented
4#14543707C212yesmaximal
5#14537427C211yesmaximal, characteristic
6#11763730—21no—
7#11763730—21no—
8C22⋊#63216C2212yes—
9C22⋊#63216C2212yes—
10#11763698—21no—
11#11763695—21no—
12#11763277C411yescharacteristic
13#11762869—21no—
14#11762869—21no—
15#11762861—21no—
16#11762861—21no—
17#11762836C2211yescharacteristic
18#11762777C2211yescharacteristic
19#11762775C411yescharacteristic
20M16×Dic17C411yescharacteristic
21C2×C8×Dic17C2211yescharacteristic
22C17×#424C411yescharacteristic
23C2×#63252C2×C411yescharacteristic
24C2×M16×C17C2×C411yescharacteristic
25C22×C8×C17C2×C411yescharacteristic
26C17×#117C2×C411yescharacteristic
27C2×C4×Dic17C2×C411yescharacteristic
28C2×#63223C2×C411yescharacteristic
29C22×#3622C2311yescharacteristic
30#10587579C811yescharacteristic
31#10587579C811yescharacteristic
32#10587573C811yescharacteristic
33#10587573C811yescharacteristic
34#10587567—21no—
35#10587567—21no—
36#10587558—21no—
37C42×D17—21no—
38C2×#63216—22no—
39C2×#63216—22no—
40C17×C4⋊C8—21no—
41C17×C4⋊C8—21no—
42#10587491—21no—
43#10587491—21no—
44#10587491—21no—
45#10587491—21no—
46#10587486—21no—
47C8×Dic17—21no—
48C8×Dic17D411yescharacteristic
49C8×Dic17D411yescharacteristic
50C8×Dic17D411yescharacteristic
51C8×Dic17D411yescharacteristic
52C4⋊#3622—21no—
53C4⋊#3622—21no—
54C22×C4×C17C22×C411yescharacteristic
55C2×C22⋊D17—21no—
56C22×Dic17M1611yescharacteristic
57C22×Dic17M1611yescharacteristic
58#63252—41no—
59#63252—41no—
60C2×D68C2×C811yescharacteristic
61C2×C4×D17—21no—
62C2×C4×D17—21no—
63C2×C4×D17—21no—
64C2×Dic34C2×C811yescharacteristic
65M16×C17—41no—
66C2×C8×C17—21no—
67C2×C8×C17—41no—
68C2×C8×C17C22⋊C411yescharacteristic
69C2×C8×C17C22⋊C411yescharacteristic
70C4⋊C4×C17C2×C811yescharacteristic
71C4⋊C4×C17C2×C811yescharacteristic
72C22⋊C4×C17—21no—
73C42×C17—21no—
74#63227—21no—
75#63227—21no—
76#63225—21no—
77#63225—21no—
78C4×Dic17—21no—
79C4×Dic17—21no—
80C4×Dic17C22⋊C411yescharacteristic
81C4×Dic17C22⋊C411yescharacteristic
82C4×Dic17C2×C811yescharacteristic
83C4×Dic17C2×C811yescharacteristic
84#63223—41no—
85C2×#3622—21no—
86C2×#3622—41no—
87C2×#3622C2×D411yescharacteristic
88C2×#3622C2×D411yescharacteristic
89#63216—42no—
90#63216—42no—
91#11464—171nomaximal, Sylow
92C23×C17C2×M1611yescharacteristic
93C22×D17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17C2×C22⋊C411yescharacteristic
99C2×C4×C17C22×C811yescharacteristic
100C22⋊D17—42no—
101C2×Dic17—22no—
102C2×Dic17—21no—
103C2×Dic17—41no—
104C2×Dic17C22⋊C811yescharacteristic
105C2×Dic17C22⋊C811yescharacteristic
106C2×Dic17C22⋊C811yescharacteristic
107C2×Dic17C22⋊C811yescharacteristic
108D68—41no—
109C4×D17—42no—
110C4×D17—41no—
111C4×D17—41no—
112C4×D17—42no—
113Dic34—41no—
114C8×C17—21no—
115C8×C17—21no—
116C8×C17—41no—
117#3622—21no—
118#3622—21no—
119#3622—41no—
120#2922—171no—
121#2163—171no—
122#2162—171no—
123#1323—172no—
124#1315—172no—
125C22×C17—21no—
126C22×C17—21no—
127C22×C17—21no—
128C22×C17C2×C22⋊C811yescharacteristic
129C2×D17—41no—
130C2×D17—41no—
131C2×D17—41no—
132C4×C17—21no—
133C4×C17—41no—
134C4×C17—41no—
135C4×C17#41011yescharacteristic
136C4×C17#41311yescharacteristic
137Dic17—21no—
138Dic17—21no—
139Dic17—21no—
140Dic17—41no—
141Dic17#35012yes—
142C4×#41—171no—
143#433—341no—
144#433—341no—
145#431—341no—
146#431—341no—
147#424—171no—
148#424#59511yescharacteristic
149#408—171no—
150#408—171no—
151C4×M16—171no—
152C2×C4×C8—171no—
153C4⋊C16—341no—
154C4⋊C16—341no—
155C22⋊C16—172no—
156C22⋊C16—172no—
157#346—341no—
158C4×C16—341no—
159C2×C17—41no—
160C2×C17#145811yescharacteristic
161C2×C17C2×#35011yescharacteristic
162C2×C17#211711yescharacteristic
163D17—81no—
164C2×#41—171no—
165C2×M16—171no—
166C2×M16C2×#59511yescharacteristic
167C22×C8—171no—
168C22×C8C2×#59511yescharacteristic
169C4×Q8—171no—
170C4×Q8—171no—
171C4×D4—171no—
172C4×D4—171no—
173C4×D4—341no—
174C4×D4—341no—
175#117—341no—
176#117C2×#59511yescharacteristic
177C2×C42—171no—
178C2×C42—341no—
179C2×C16—342no—
180C2×C16—342no—
181C4⋊C8—21no—
182C4⋊C8—21no—
183C4⋊C8—341no—
184C4⋊C8—341no—
185C22⋊C8—341no—
186C22⋊C8—341no—
187C22⋊C8—341no—
188C22⋊C8—341no—
189#97—341no—
190C4×C8—171no—
191C4×C8—171no—
192C4×C8—171no—
193C4×C8—171no—
194C4×C8—341no—
195C17#1146411yescharacteristic, complemented, Sylow
196#41—681no—
197#41—681no—
198C2×Q8—171no—
199C2×D4—171no—
200C2×D4—341no—
201C22×C4—171no—
202C22×C4—171no—
203C22×C4—341no—
204C22×C4—341no—
205C22×C4—341no—
206C22×C4C22×#59511yescharacteristic
207M16—41no—
208M16—681no—
209C2×C8—21no—
210C2×C8—41no—
211C2×C8—171no—
212C2×C8—171no—
213C2×C8—341no—
214C2×C8—681no—
215C2×C8C22⋊#59511yescharacteristic
216C2×C8C22⋊#59511yescharacteristic
217C4⋊C4—341no—
218C4⋊C4—341no—
219C4⋊C4#6324211yescharacteristic
220C4⋊C4#6324211yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—341no—
223C22⋊C4—341no—
224C42—21no—
225C42—171no—
226C42—171no—
227C42—171no—
228C42—171no—
229C42—341no—
230C42—341no—
231C16—682no—
232C16—682no—
233C23—341no—
234C23D17⋊M1611yescharacteristic
235Q8—681no—
236D4—681no—
237D4—682no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—171no—
243C2×C4—171no—
244C2×C4—171no—
245C2×C4—171no—
246C2×C4—342no—
247C2×C4—341no—
248C2×C4—682no—
249C2×C4—682no—
250C2×C4—681no—
251C2×C4—681no—
252C2×C4—681no—
253C2×C4C2×#6324211yescharacteristic
254C2×C4C2×C22⋊#59511yescharacteristic
255C8—21no—
256C8—21no—
257C8—41no—
258C8—341no—
259C8—341no—
260C8—681no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—681no—
265C22—681no—
266C22—681no—
267C22#1176377711yescharacteristic
268C4—21no—
269C4—41no—
270C4—41no—
271C4—172no—
272C4—341no—
273C4—341no—
274C4—341no—
275C4—681no—
276C4#1176379011yescharacteristic
277C4#1176379611yescharacteristic
278C2—41no—
279C2—1361no—
280C2#1454401811yescharacteristic
281C2#1454502411yescharacteristic
282C2#1454502711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#424C4
socleC22×C17C2×C22⋊C8
prime radicalC2×#63252C2×C4
cosocleC22×#3622C23
hypercenter#424#595
hypocenterC17#11464
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #14545146C2semidirect
2. #14545142C2semidirect
3. #14543722C2semidirect
195. C17#11464semidirect

Maximal subgroups

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

subgroupindex
#145451462
#145451422
#145437222
#145437072
#145374272
#1146417