Finite Group Databasebeta

← #17958256

Subgroups — #17958256

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#14543723C212yesmaximal, complemented
4#14543706C212yesmaximal
5#14537424C211yesmaximal, characteristic
6#11763730—21no—
7#11763730—21no—
8C22⋊#63216C2212yes—
9C22⋊#63216C2212yes—
10#11763698—21no—
11#11763695—21no—
12#41×Dic17C411yescharacteristic
13#11762867—21no—
14#11762867—21no—
15#11762859—21no—
16#11762859—21no—
17#11762837C2211yescharacteristic
18#11762835C411yescharacteristic
19#11762776C2211yescharacteristic
20M16×Dic17C411yescharacteristic
21C2×C8×Dic17C2211yescharacteristic
22C17×#408C411yescharacteristic
23C2×#41×C17C2×C411yescharacteristic
24C2×M16×C17C2×C411yescharacteristic
25C22×C8×C17C2×C411yescharacteristic
26Q8×Dic17C811yescharacteristic
27Q8×Dic17C811yescharacteristic
28D4×Dic17—21no—
29D4×Dic17—21no—
30D4×Dic17C811yescharacteristic
31D4×Dic17C811yescharacteristic
32#10587612—21no—
33#10587612C2×C411yescharacteristic
34C2×C4×Dic17—21no—
35C2×C4×Dic17C2×C411yescharacteristic
36C2×#63223C2×C411yescharacteristic
37C22×#3622C2311yescharacteristic
38C2×#63216—22no—
39C2×#63216—22no—
40C17×C22⋊C8—21no—
41C17×C22⋊C8—21no—
42C22⋊#3622—21no—
43C22⋊#3622—21no—
44#10587486—21no—
45#10587485—21no—
46#10587485—21no—
47#10587485—21no—
48#10587485—21no—
49C8×Dic17—21no—
50C8×Dic17D411yescharacteristic
51C8×Dic17D411yescharacteristic
52C8×Dic17D411yescharacteristic
53C8×Dic17D411yescharacteristic
54#41×C17—41no—
55#41×C17—41no—
56C2×Q8×C17C2×C811yescharacteristic
57C2×D4×C17—21no—
58C2×D4×C17C2×C811yescharacteristic
59C22×C4×C17—21no—
60C22×C4×C17C22×C411yescharacteristic
61C22×Dic17—21no—
62C22×Dic17—21no—
63C22×Dic17M1611yescharacteristic
64C22×Dic17M1611yescharacteristic
65M16×C17—41no—
66C2×C8×C17—21no—
67C2×C8×C17—41no—
68C2×C8×C17C22⋊C411yescharacteristic
69C2×C8×C17C22⋊C411yescharacteristic
70C22⋊Dic17—21no—
71C22⋊Dic17—21no—
72C22⋊Dic17—21no—
73C4⋊Dic17—21no—
74C4⋊Dic17—21no—
75C4⋊Dic17C2×C811yescharacteristic
76C4⋊Dic17C2×C811yescharacteristic
77C4×Dic17—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×C17—21no—
93C23×C17C2×M1611yescharacteristic
94Q8×C17—41no—
95D4×C17—41no—
96D4×C17—42no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17C2×C22⋊C411yescharacteristic
103C2×C4×C17C22×C811yescharacteristic
104C2×Dic17—22no—
105C2×Dic17—21no—
106C2×Dic17—21no—
107C2×Dic17—41no—
108C2×Dic17—42no—
109C2×Dic17—42no—
110C2×Dic17C22⋊C811yescharacteristic
111C2×Dic17C22⋊C811yescharacteristic
112C2×Dic17C22⋊C811yescharacteristic
113C2×Dic17C22⋊C811yescharacteristic
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×C17—41no—
129C22×C17—41no—
130C22×C17—41no—
131C22×C17C2×C22⋊C811yescharacteristic
132C4×C17—21no—
133C4×C17—41no—
134C4×C17#41011yescharacteristic
135C4×C17#41311yescharacteristic
136Dic17—21no—
137Dic17—21no—
138Dic17—21no—
139Dic17—41no—
140Dic17—41no—
141Dic17#35012yes—
142C4×#41—171no—
143#433—341no—
144#433—341no—
145#431—341no—
146#431—341no—
147#424—171no—
148#424—171no—
149#408—171no—
150#408#59511yescharacteristic
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—81no—
161C2×C17#145811yescharacteristic
162C2×C17C2×#35011yescharacteristic
163C2×C17#211711yescharacteristic
164C2×#41C2×#59511yescharacteristic
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—171no—
176#117—341no—
177C2×C42—171no—
178C2×C42—341no—
179C2×C16—342no—
180C2×C16—342no—
181C4⋊C8—341no—
182C4⋊C8—341no—
183C4⋊C8—341no—
184C4⋊C8—341no—
185C22⋊C8—21no—
186C22⋊C8—21no—
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—41no—
197#41—41no—
198C2×Q8#6324211yescharacteristic
199C2×D4—21no—
200C2×D4#6324211yescharacteristic
201C22×C4—21no—
202C22×C4—171no—
203C22×C4—171no—
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—171no—
218C4⋊C4—171no—
219C4⋊C4—341no—
220C4⋊C4—341no—
221C22⋊C4—341no—
222C22⋊C4—341no—
223C22⋊C4—341no—
224C42—171no—
225C42—171no—
226C42—171no—
227C42—171no—
228C42—341no—
229C42—341no—
230C42—341no—
231C16—682no—
232C16—682no—
233C23—21no—
234C23D17⋊M1611yescharacteristic
235Q8—41no—
236D4—41no—
237D4—42no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—171no—
244C2×C4—171no—
245C2×C4—171no—
246C2×C4—171no—
247C2×C4—342no—
248C2×C4—341no—
249C2×C4—341no—
250C2×C4—682no—
251C2×C4—681no—
252C2×C4—682no—
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—41no—
265C22—41no—
266C22—41no—
267C22#1176377711yescharacteristic
268C4—21no—
269C4—41no—
270C4—172no—
271C4—341no—
272C4—341no—
273C4—341no—
274C4—681no—
275C4—681no—
276C4#1176378911yescharacteristic
277C4#1176379611yescharacteristic
278C2—41no—
279C2—81no—
280C2#1454401611yescharacteristic
281C2#1454502411yescharacteristic
282C2#1454502711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#408C4
socleC22×C17C2×C22⋊C8
prime radicalC2×#41×C17C2×C4
cosocleC22×#3622C23
hypercenter#408#595
hypocenterC17#11464
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #14545146C2semidirect
2. #14545142C2semidirect
3. #14543723C2semidirect
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
#145437232
#145437062
#145374242
#1146417