Finite Group Databasebeta

← #16938947

Subgroups — #16938947

Order 4352.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14529744C211yesmaximal, characteristic
2#14529706C211yesmaximal, characteristic
3#14529545C211yesmaximal, characteristic
4#14529500C211yesmaximal, characteristic
5C2×#11762561C211yesmaximal, characteristic
6C2×#11762554C211yesmaximal, characteristic
7C17×#1296C211yesmaximal, characteristic
8C2×#10587555C2211yescharacteristic
9C2×#10587479—21no—
10C2×C4⋊#3622C2211yescharacteristic
11C2×#10587485—21no—
12C2×#10587487—21no—
13C2×#10587487—21no—
14C2×C4×#3622C2211yescharacteristic
15C4×C4⋊Dic17C2211yescharacteristic
16#11762571—21no—
17#11762571—21no—
18#11762571—21no—
19#11762563—21no—
20#11762561—22no—
21#11762554—22no—
22C2×C17×C4⋊C8C2211yescharacteristic
23C2×C17×C4⋊C8C2211yescharacteristic
24C17×#384C2211yescharacteristic
25C22×Dic34—21no—
26C22×C8×C17—21no—
27C22×C8×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C42×C17C2311yescharacteristic
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17D411yescharacteristic
35C2×C4⋊Dic17D411yescharacteristic
36C2×C4×Dic17—21no—
37C22×#3622—21no—
38C22×#3622D411yescharacteristic
39C22×#3622D411yescharacteristic
40#10587555—21no—
41#10587555—21no—
42#10587555—21no—
43#10587555Q812yes—
44C17×C4⋊C8—21no—
45C17×C4⋊C8—21no—
46C17×C4⋊C8—21no—
47C17×C4⋊C8—21no—
48#10587502—21no—
49#10587487—42no—
50#10587487—42no—
51#10587485—42no—
52#10587479—42no—
53C4⋊#3622—21no—
54C4⋊#3622D412yes—
55C4×#3622—21no—
56C4×#3622—21no—
57C22×C4×C17—41no—
58C22×C4×C17C2×D411yescharacteristic
59C22×C4×C17C2×D411yescharacteristic
60C22×C4×C17#4111yescharacteristic
61C22×Dic17—21no—
62C22×Dic17—21no—
63C22×Dic17—41no—
64C2×Dic34—22no—
65C2×Dic34—41no—
66C2×Dic34—41no—
67C2×Dic34—41no—
68C2×Dic34—41no—
69C2×Dic34—41no—
70C2×C8×C17—41no—
71C2×C8×C17—41no—
72C2×C8×C17—41no—
73C2×C8×C17—41no—
74C2×C8×C17—41no—
75C2×C8×C17—41no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—81no—
81C42×C17C2×D411yescharacteristic
82C42×C17C2×Q811yescharacteristic
83C42×C17#4111yescharacteristic
84C42×C17#4111yescharacteristic
85C4⋊Dic17—21no—
86C4⋊Dic17—22no—
87C4⋊Dic17—22no—
88C4⋊Dic17—21no—
89C4⋊Dic17—21no—
90C4⋊Dic17—41no—
91C4⋊Dic17—41no—
92C4⋊Dic17D812yes—
93C4×Dic17—41no—
94C4×Dic17—41no—
95C2×#3622—21no—
96C2×#3622—21no—
97C2×#3622—21no—
98C2×#3622—22no—
99C2×#3622—21no—
100C2×#3622—21no—
101C2×#3622—41no—
102C2×#3622—41no—
103C2×#3622SD1612yes—
104#10602—171nomaximal, Sylow
105C23×C17#12111yescharacteristic
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—81no—
109C2×C4×C17—81no—
110C2×C4×C17—81no—
111C2×C4×C17#12111yescharacteristic
112C2×C4×C17#12111yescharacteristic
113C2×C4×C17C22⋊Q811yescharacteristic
114C2×C4×C17C22⋊Q811yescharacteristic
115C2×C4×C17C22⋊Q811yescharacteristic
116C2×C4×C17#12611yescharacteristic
117C2×C4×C17C2×D811yescharacteristic
118C2×C4×C17C2×SD1611yescharacteristic
119C2×C4×C17#13511yescharacteristic
120C2×C4×C17#13511yescharacteristic
121C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C17#13711yescharacteristic
123C2×C4×C17#13711yescharacteristic
124C2×C4×C17#13711yescharacteristic
125C2×Dic17—22no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—42no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—81no—
133C2×Dic17—81no—
134Dic34—42no—
135Dic34—42no—
136Dic34—81no—
137Dic34—81no—
138C8×C17—81no—
139C8×C17—81no—
140#3622—22no—
141#3622—42no—
142#3622—41no—
143#1990—171no—
144#1981—171no—
145#1948—171no—
146#1939—171no—
147C2×#335—171no—
148C2×#332—171no—
149#1296D1711yescharacteristic
150C22×C17#39611yescharacteristic
151C22×C17#46111yescharacteristic
152C22×C17#46411yescharacteristic
153C22×C17#46611yescharacteristic
154C22×C17#46811yescharacteristic
155C22×C17#47111yescharacteristic
156C22×C17#47311yescharacteristic
157C4×C17—21no—
158C4×C17—21no—
159C4×C17—161no—
160C4×C17#45911yescharacteristic
161C4×C17#46411yescharacteristic
162C4×C17#46511yescharacteristic
163C4×C17#47011yescharacteristic
164C4×C17#47411yescharacteristic
165C4×C17#47511yescharacteristic
166C4×C17#47811yescharacteristic
167C4×C17#47911yescharacteristic
168Dic17—42no—
169Dic17—82no—
170Dic17—81no—
171C2×C4⋊Q8—171no—
172C2×#106—341no—
173C2×C4⋊C8—171no—
174C2×C4⋊C8—341no—
175C2×C4⋊C8C2×D1711yescharacteristic
176C2×C4⋊C8C2×D1711yescharacteristic
177C2×#103—341no—
178C2×#103—341no—
179C2×C4×C8—171no—
180#384C2×D1711yescharacteristic
181C4×C4⋊C4—171no—
182#340—341no—
183#340—341no—
184#340—341no—
185#336—341no—
186#335—342no—
187#332—342no—
188C2×C17#167311yescharacteristic
189C2×C17#168211yescharacteristic
190C2×C17#169111yescharacteristic
191C2×C17#170011yescharacteristic
192C2×C17#206411yescharacteristic
193C2×C17#206611yescharacteristic
194C2×C17#206711yescharacteristic
195C22×Q8—341no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—171no—
199C22×C8—171no—
200C22×C8—341no—
201C4⋊Q8—172no—
202C4⋊Q8—341no—
203C4⋊Q8—341no—
204C4⋊Q8—341no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—171no—
209C2×C4⋊C4—171no—
210C2×C4⋊C4—341no—
211C2×C4⋊C4—341no—
212C2×C42—341no—
213C2×C42C22×D1711yescharacteristic
214#106—682no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—172no—
220C4⋊C8—341no—
221C4⋊C8—682no—
222#103—682no—
223#103—682no—
224C4×C8—341no—
225C4×C8—341no—
226#95—341no—
227C17#1060211yescharacteristic, complemented, Sylow
228C2×Q8—342no—
229C2×Q8—681no—
230C2×Q8—681no—
231C2×Q8—681no—
232C2×Q8—681no—
233C2×Q8—681no—
234C22×C4—41no—
235C22×C4—341no—
236C22×C4—341no—
237C22×C4—681no—
238C22×C4#6325211yescharacteristic
239C22×C4D4×D1711yescharacteristic
240C22×C4D4×D1711yescharacteristic
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—172no—
248C2×C8—341no—
249C2×C8—341no—
250C2×C8—341no—
251C2×C8—342no—
252C2×C8—341no—
253C2×C8—341no—
254C2×C8—681no—
255C2×C8—681no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—81no—
261C4⋊C4—172no—
262C4⋊C4—341no—
263C4⋊C4—342no—
264C4⋊C4—342no—
265C4⋊C4—341no—
266C4⋊C4—341no—
267C4⋊C4—681no—
268C4⋊C4—681no—
269C42—681no—
270C42—681no—
271C42#6325211yescharacteristic
272C42#6325211yescharacteristic
273C42D4×D1711yescharacteristic
274C42Q8×D1711yescharacteristic
275C23#1058757011yescharacteristic
276Q8—682no—
277Q8—682no—
278Q8—1361no—
279Q8—1361no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—342no—
286C2×C4—681no—
287C2×C4—681no—
288C2×C4—682no—
289C2×C4—681no—
290C2×C4—681no—
291C2×C4—681no—
292C2×C4—1361no—
293C2×C4—1361no—
294C2×C4#1058756211yescharacteristic
295C2×C4#1058757011yescharacteristic
296C2×C4#1058757011yescharacteristic
297C2×C4#1058758211yescharacteristic
298C2×C4#1058758211yescharacteristic
299C2×C4#1058758211yescharacteristic
300C2×C4D8×D1711yescharacteristic
301C2×C4#1058759811yescharacteristic
302C2×C4SD16×D1711yescharacteristic
303C2×C4#1058760011yescharacteristic
304C2×C4#1058760111yescharacteristic
305C2×C4#1058760211yescharacteristic
306C2×C4#1058760411yescharacteristic
307C2×C4#1058760411yescharacteristic
308C8—81no—
309C8—81no—
310C8—342no—
311C8—682no—
312C8—681no—
313C22#1176273311yescharacteristic
314C22#1176301311yescharacteristic
315C22#1176303011yescharacteristic
316C22#1176304411yescharacteristic
317C22#1176305811yescharacteristic
318C22#1176307111yescharacteristic
319C22#1176308311yescharacteristic
320C4—21no—
321C4—21no—
322C4—161no—
323C4—682no—
324C4—1361no—
325C4—1362no—
326C4#1176300311yescharacteristic
327C4#1176303411yescharacteristic
328C4#1176303711yescharacteristic
329C4#1176306611yescharacteristic
330C4#1176308811yescharacteristic
331C4#1176309311yescharacteristic
332C4#1176310811yescharacteristic
333C4#1176311511yescharacteristic
334C2#1452817211yescharacteristic
335C2#1452822711yescharacteristic
336C2#1452828611yescharacteristic
337C2#1452833711yescharacteristic
338C2#1453015211yescharacteristic
339C2#1453016611yescharacteristic
340C2#1453017311yescharacteristic
subgroupG/H
centerC23#10587570
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1296C2
socle, prime radicalC23×C17#121
hypercenter#1296D17
hypocenterC17#10602
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
227. C17#10602semidirect

Maximal subgroups

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

subgroupindex
#145297442
#145297062
#145295452
#145295002
C2×#117625612
C2×#117625542
C17×#12962
#1060217