Finite Group Databasebeta

← #17950089

Subgroups — #17950089

Order 4352.

464 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 100 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#14544569C211yesmaximal, characteristic, complemented
2C4×C4⋊#3624C211yesmaximal, characteristic, complemented
3#14543602C212yesmaximal, complemented
4#14543601C212yesmaximal
5#14537152C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×C4⋊#3624—21no—
8C2×#10587542—21no—
9C2×C4×#3624—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587584—21no—
13#11762711C411yescharacteristic
14#11762710C411yescharacteristic
15#11762710C2211yescharacteristic
16#11762708C2211yescharacteristic
17#11762705C411yescharacteristic
18#11762701—21no—
19#11762699—21no—
20#11762698—21no—
21C42×Dic17C2211yescharacteristic
22C17×#389C411yescharacteristic
23C22×D68C2×C411yescharacteristic
24C22×#3624—22no—
25C22×#3624—22no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C42×C17C2×C411yescharacteristic
30C2×#63227—21no—
31C2×#63227—21no—
32C2×#63227—21no—
33C2×#63227—21no—
34C2×#63227—21no—
35C2×#63227—21no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17C2×C411yescharacteristic
38C2×#63225—21no—
39C2×C4×Dic17C2×C411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17D411yescharacteristic
44C2×C4×Dic17C2311yescharacteristic
45#10587584—42no—
46#10587584—42no—
47#10587544—24no—
48#10587542—42no—
49C4⋊#3624—24no—
50C4×#3624—42no—
51C17×#95—21no—
52#10587502—21no—
53#10587502—21no—
54C23×D17—21no—
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22×C411yescharacteristic
60C22×Dic17—21no—
61C22×Dic17C22⋊C411yescharacteristic
62C22×Dic17C22⋊C411yescharacteristic
63C22×Dic17C2×D411yescharacteristic
64C22×Dic17C2×D411yescharacteristic
65C2×D68—22no—
66C2×D68—41no—
67C2×D68—41no—
68C2×#3624—24no—
69C2×#3624—24no—
70C2×#3624—42no—
71C2×#3624—42no—
72C2×#3624—42no—
73C2×#3624—42no—
74C4⋊C4×C17—22no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—42no—
77C42×C17—22no—
78#63227—42no—
79#63227—42no—
80#63227—42no—
81#63227—42no—
82#63227—41no—
83#63227—41no—
84#63227—41no—
85#63227—41no—
86C4⋊Dic17—41no—
87C4⋊Dic17—41no—
88C4⋊Dic17—41no—
89#63225—42no—
90C4×Dic17—22no—
91C4×Dic17—22no—
92C4×Dic17—21no—
93C4×Dic17—21no—
94C4×Dic17—41no—
95C4×Dic17—41no—
96C4×Dic17D812yes—
97C4×Dic17SD1612yes—
98#7686—171nomaximal, Sylow
99C23×C17C2×C22⋊C411yescharacteristic
100C22×D17—41no—
101C22×D17—41no—
102C22×D17—41no—
103C22×D17—41no—
104C22×D17—41no—
105C22×D17—41no—
106C22×D17—41no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
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#10212yes—
120C2×C4×C17#10412yes—
121C2×C4×C17#13112yes—
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17—21no—
125C2×Dic17—21no—
126C2×Dic17—21no—
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17#10212yes—
134C2×Dic17#10412yes—
135C2×Dic17C2×D811yescharacteristic
136C2×Dic17C2×SD1611yescharacteristic
137C2×Dic17AGL(1,ℤ/8)11yescharacteristic
138C2×Dic17#13711yescharacteristic
139D68—82no—
140#3624—44no—
141#3624—44no—
142#2860—171no—
143#1767—171no—
144C4×C4⋊C8—171no—
145#1271—172no—
146#1270—172no—
147C22×C17#40811yescharacteristic
148C22×C17#41011yescharacteristic
149C22×C17#41311yescharacteristic
150C22×C17C2×#10211yescharacteristic
151C22×C17#41711yescharacteristic
152C22×C17C2×#10411yescharacteristic
153C22×C17C2×#10411yescharacteristic
154C2×D17—81no—
155C2×D17—81no—
156C2×D17—81no—
157C2×D17—81no—
158C2×D17—81no—
159C2×D17—81no—
160C2×D17—81no—
161C4×C17—22no—
162C4×C17—22no—
163C4×C17—22no—
164C4×C17—81no—
165C4×C17—81no—
166Dic17—22no—
167Dic17—21no—
168Dic17—21no—
169Dic17—21no—
170Dic17—21no—
171Dic17—22no—
172Dic17—81no—
173C2×#126—341no—
174C2×C4⋊C8—341no—
175C2×C4⋊C8—341no—
176C2×#97—341no—
177C2×C4×C8—341no—
178#390—171no—
179#390—171no—
180#390—171no—
181#389—171no—
182#389—171no—
183#389#59511yescharacteristic
184#388—341no—
185#388—341no—
186#388—341no—
187C43—171no—
188#336—172no—
189#336—172no—
190C2×C17#147311yescharacteristic
191C2×C17#148311yescharacteristic
192C2×C17#149211yescharacteristic
193C2×C17#150211yescharacteristic
194C2×C17#150911yescharacteristic
195C2×C17#152411yescharacteristic
196C2×C17#154711yescharacteristic
197D17—161no—
198C22×D4—171no—
199C22×C8—342no—
200C22×C8—342no—
201#126—682no—
202#126—682no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—171no—
205C2×C4⋊C4—341no—
206C2×C4⋊C4—341no—
207C2×C4⋊C4C2×#59511yescharacteristic
208C2×C4⋊C4C2×#59511yescharacteristic
209C2×C22⋊C4—341no—
210C2×C22⋊C4—341no—
211C2×C22⋊C4—341no—
212C2×C22⋊C4—341no—
213C2×C22⋊C4—341no—
214C2×C22⋊C4—341no—
215C2×C42—171no—
216C2×C42—171no—
217C2×C42—171no—
218C2×C42—171no—
219C2×C42—171no—
220C2×C42—171no—
221C2×C42C2×#59511yescharacteristic
222C4⋊C8—344no—
223C4⋊C8—344no—
224#97—682no—
225C4×C8—682no—
226#95—21no—
227#95—341no—
228#95—341no—
229C17#768611yescharacteristic, complemented, Sylow
230C24—341no—
231C2×D4—342no—
232C2×D4—681no—
233C2×D4—681no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—171no—
237C22×C4—171no—
238C22×C4—171no—
239C22×C4—171no—
240C22×C4—341no—
241C22×C4C22⋊#59511yescharacteristic
242C22×C4C22⋊#59511yescharacteristic
243C22×C4C22×#59511yescharacteristic
244C2×C8—344no—
245C2×C8—344no—
246C2×C8—682no—
247C2×C8—682no—
248C2×C8—682no—
249C2×C8—682no—
250C4⋊C4—22no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—681no—
254C4⋊C4—682no—
255C4⋊C4—681no—
256C4⋊C4—681no—
257C22⋊C4—681no—
258C22⋊C4—682no—
259C22⋊C4—681no—
260C22⋊C4—681no—
261C22⋊C4—681no—
262C22⋊C4—682no—
263C22⋊C4—682no—
264C22⋊C4—682no—
265C42—22no—
266C42—172no—
267C42—172no—
268C42—341no—
269C42—342no—
270C42—341no—
271C42—342no—
272C42—681no—
273C42—681no—
274C23—681no—
275C23—681no—
276C23—681no—
277C23—681no—
278C23—681no—
279C23—681no—
280C23—681no—
281C23C2×C22⋊#59511yescharacteristic
282D4—1362no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—171no—
296C2×C4—172no—
297C2×C4—171no—
298C2×C4—171no—
299C2×C4—171no—
300C2×C4—172no—
301C2×C4—341no—
302C2×C4—341no—
303C2×C4—341no—
304C2×C4—341no—
305C2×C4—341no—
306C2×C4—341no—
307C2×C4—341no—
308C2×C4—341no—
309C2×C4—681no—
310C2×C4—681no—
311C2×C4—681no—
312C2×C4#1058754712yes—
313C2×C4#1058755012yes—
314C2×C4#1058767812yes—
315C8—684no—
316C8—684no—
317C22—1361no—
318C22—1361no—
319C22—1361no—
320C22—1361no—
321C22—1361no—
322C22—1361no—
323C22—1361no—
324C22#1176378211yescharacteristic
325C22#1176379011yescharacteristic
326C22#1176379511yescharacteristic
327C22C2×#1058754711yescharacteristic
328C22#1176380011yescharacteristic
329C22D17⋊#10411yescharacteristic
330C22C2×#1058755011yescharacteristic
331C4—22no—
332C4—22no—
333C4—22no—
334C4—81no—
335C4—81no—
336C4—341no—
337C4—341no—
338C4—341no—
339C4—341no—
340C4—342no—
341C4—342no—
342C4—1361no—
343C2—2721no—
344C2#1454406811yescharacteristic
345C2#1454410111yescharacteristic
346C2#1454412911yescharacteristic
347C2#1454416511yescharacteristic
348C2#1454418711yescharacteristic
349C2#1454423611yescharacteristic
350C2#1454429511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#389C4
socleC23×C17C2×C22⋊C4
prime radicalC22×D68C2×C4
cosocleC2×C4×Dic17C23
hypercenter#389#595
hypocenterC17#7686
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
1. #14544569C2semidirect
2. C4×C4⋊#3624C2semidirect
3. #14543602C2semidirect
229. C17#7686semidirect

Maximal subgroups

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

subgroupindex
#145445692
C4×C4⋊#36242
#145436022
#145436012
#145371522
#768617