Finite Group Databasebeta

← #16938900

Subgroups — #16938900

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#14529737C211yesmaximal, characteristic
2#14529587C211yesmaximal, characteristic
3#14529548C211yesmaximal, characteristic
4#14529500C211yesmaximal, characteristic
5C2×#11762559C211yesmaximal, characteristic
6#14526668C211yesmaximal, characteristic
7C2×C17×#332C211yesmaximal, characteristic
8C2×#10587488—21no—
9C2×C4⋊#3622C2211yescharacteristic
10C2×#10587485—21no—
11C2×#10587506—21no—
12C2×#10587506—21no—
13C2×C4×#3622C2211yescharacteristic
14#11762679C2211yescharacteristic
15C4×C4⋊Dic17C2211yescharacteristic
16#11762572—21no—
17#11762571—21no—
18#11762571—21no—
19#11762563—21no—
20#11762559—22no—
21C2×C17×C4⋊Q8C2211yescharacteristic
22C2×C17×C4⋊C8C2211yescharacteristic
23C2×C17×C4⋊C8C2211yescharacteristic
24C17×#332—22no—
25C22×Q8×C17—21no—
26C22×C8×C17—21no—
27C22×C8×C17—21no—
28C17×C4⋊Q8—21no—
29C17×C4⋊Q8—21no—
30C17×C4⋊Q8—21no—
31C17×C4⋊Q8Q812yes—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C42×C17C2311yescharacteristic
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17D411yescharacteristic
39C2×C4⋊Dic17D411yescharacteristic
40C2×C4×Dic17—21no—
41C22×#3622—21no—
42C22×#3622D411yescharacteristic
43C22×#3622D411yescharacteristic
44C17×C4⋊C8—21no—
45C17×C4⋊C8—21no—
46C17×C4⋊C8—21no—
47C17×C4⋊C8D412yes—
48#10587506—42no—
49#10587506—42no—
50#10587502—21no—
51#10587488—42no—
52#10587485—42no—
53C4⋊#3622—21no—
54C4⋊#3622—21no—
55C4×#3622—21no—
56C4×#3622—21no—
57C2×Q8×C17—22no—
58C2×Q8×C17—41no—
59C2×Q8×C17—41no—
60C2×Q8×C17—41no—
61C2×Q8×C17—41no—
62C2×Q8×C17—41no—
63C22×C4×C17—41no—
64C22×C4×C17C2×D411yescharacteristic
65C22×C4×C17C2×D411yescharacteristic
66C22×C4×C17#4111yescharacteristic
67C22×Dic17—21no—
68C22×Dic17—21no—
69C22×Dic17—41no—
70C2×C8×C17—22no—
71C2×C8×C17—41no—
72C2×C8×C17—41no—
73C2×C8×C17—41no—
74C2×C8×C17—41no—
75C2×C8×C17—41no—
76C4⋊C4×C17—22no—
77C4⋊C4×C17—22no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C42×C17C2×D411yescharacteristic
81C42×C17C2×Q811yescharacteristic
82C42×C17#4111yescharacteristic
83C42×C17#4111yescharacteristic
84C4⋊Dic17—21no—
85C4⋊Dic17—21no—
86C4⋊Dic17—21no—
87C4⋊Dic17—41no—
88C4⋊Dic17—41no—
89C4⋊Dic17—41no—
90C4⋊Dic17—41no—
91C4⋊Dic17—81no—
92C4⋊Dic17SD1612yes—
93C4×Dic17—41no—
94C4×Dic17—41no—
95C2×#3622—21no—
96C2×#3622—21no—
97C2×#3622—21no—
98C2×#3622—21no—
99C2×#3622—21no—
100C2×#3622—41no—
101C2×#3622—41no—
102C2×#3622—41no—
103C2×#3622SD1612yes—
104#10596—171nomaximal, Sylow
105C23×C17#12111yescharacteristic
106Q8×C17—42no—
107Q8×C17—42no—
108Q8×C17—81no—
109Q8×C17—81no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—42no—
113C2×C4×C17—81no—
114C2×C4×C17—81no—
115C2×C4×C17#12111yescharacteristic
116C2×C4×C17#12111yescharacteristic
117C2×C4×C17C22⋊Q811yescharacteristic
118C2×C4×C17C22⋊Q811yescharacteristic
119C2×C4×C17C22⋊Q811yescharacteristic
120C2×C4×C17#12611yescharacteristic
121C2×C4×C17C2×SD1611yescharacteristic
122C2×C4×C17C2×SD1611yescharacteristic
123C2×C4×C17#13511yescharacteristic
124C2×C4×C17#13511yescharacteristic
125C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C17#13711yescharacteristic
128C2×C4×C17#13711yescharacteristic
129C2×Dic17—22no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—81no—
136C2×Dic17—81no—
137C2×Dic17—81no—
138C8×C17—42no—
139C8×C17—81no—
140#3622—22no—
141#3622—41no—
142#3622—81no—
143#1988—171no—
144#1956—171no—
145#1948—171no—
146#1939—171no—
147C2×#334—171no—
148C2×#332D1711yescharacteristic
149#1296—171no—
150C22×C17#39611yescharacteristic
151C22×C17#46011yescharacteristic
152C22×C17#46311yescharacteristic
153C22×C17#46511yescharacteristic
154C22×C17#47011yescharacteristic
155C22×C17#47111yescharacteristic
156C22×C17#47311yescharacteristic
157C4×C17—21no—
158C4×C17—21no—
159C4×C17—82no—
160C4×C17#46111yescharacteristic
161C4×C17#46411yescharacteristic
162C4×C17#46511yescharacteristic
163C4×C17#46911yescharacteristic
164C4×C17#47511yescharacteristic
165C4×C17#47611yescharacteristic
166C4×C17#47811yescharacteristic
167C4×C17#47911yescharacteristic
168Dic17—42no—
169Dic17—81no—
170Dic17—161no—
171C2×C4⋊Q8C2×D1711yescharacteristic
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#384—171no—
181C4×C4⋊C4—171no—
182#340—341no—
183#340—341no—
184#340—341no—
185#336—341no—
186#334—342no—
187#332—22no—
188C2×C17#166611yescharacteristic
189C2×C17#167911yescharacteristic
190C2×C17#169011yescharacteristic
191C2×C17#170311yescharacteristic
192C2×C17#206411yescharacteristic
193C2×C17#206511yescharacteristic
194C2×C17#206611yescharacteristic
195C22×Q8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—171no—
199C22×C8—171no—
200C22×C8—341no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8Dic3412yes—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—171no—
208C2×C4⋊C4—171no—
209C2×C4⋊C4—341no—
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—341no—
219C4⋊C8—341no—
220C4⋊C8—682no—
221C4⋊C8C22⋊D1712yes—
222#103—682no—
223#103—682no—
224C4×C8—341no—
225C4×C8—341no—
226#95—341no—
227C17#1059611yescharacteristic, complemented, Sylow
228C2×Q8—22no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C22×C4—41no—
235C22×C4—341no—
236C22×C4—341no—
237C22×C4—681no—
238C22×C4#6325211yescharacteristic
239C22×C4D4×D1711yescharacteristic
240C22×C4D4×D1711yescharacteristic
241C2×C8—22no—
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—341no—
252C2×C8—341no—
253C2×C8—681no—
254C2×C8—681no—
255C2×C8—681no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—172no—
261C4⋊C4—341no—
262C4⋊C4—341no—
263C4⋊C4—341no—
264C4⋊C4—681no—
265C4⋊C4—681no—
266C4⋊C4—681no—
267C4⋊C4—681no—
268C4⋊C4—1361no—
269C42—681no—
270C42—681no—
271C42C2×Dic3411yescharacteristic
272C42#6325411yescharacteristic
273C42#6325411yescharacteristic
274C42C2×C22⋊D1711yescharacteristic
275C23#1058757011yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—81no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—342no—
286C2×C4—681no—
287C2×C4—681no—
288C2×C4—681no—
289C2×C4—681no—
290C2×C4—681no—
291C2×C4—1361no—
292C2×C4—1361no—
293C2×C4—1361no—
294C2×C4#1058756411yescharacteristic
295C2×C4#1058756411yescharacteristic
296C2×C4#1058756511yescharacteristic
297C2×C4#1058759711yescharacteristic
298C2×C4#1058759711yescharacteristic
299C2×C4SD16×D1711yescharacteristic
300C2×C4SD16×D1711yescharacteristic
301C2×C4#1058760111yescharacteristic
302C2×C4#1058760211yescharacteristic
303C2×C4#1058760411yescharacteristic
304C2×C4#1058760511yescharacteristic
305C2×C4#1058761011yescharacteristic
306C2×C4#1058762411yescharacteristic
307C2×C4#1058762511yescharacteristic
308C8—42no—
309C8—81no—
310C8—342no—
311C8—681no—
312C8—1361no—
313C22#1176273211yescharacteristic
314C22#1176300811yescharacteristic
315C22#1176302311yescharacteristic
316C22#1176304111yescharacteristic
317C22#1176306611yescharacteristic
318C22#1176307511yescharacteristic
319C22#1176308311yescharacteristic
320C4—21no—
321C4—21no—
322C4—82no—
323C4—2721no—
324C4—682no—
325C4—1361no—
326C4#1176301211yescharacteristic
327C4#1176303311yescharacteristic
328C4#1176303511yescharacteristic
329C4#1176305911yescharacteristic
330C4#1176309211yescharacteristic
331C4#1176309711yescharacteristic
332C4#1176311111yescharacteristic
333C4#1176311811yescharacteristic
334C2#1452813511yescharacteristic
335C2#1452820611yescharacteristic
336C2#1452827711yescharacteristic
337C2#1452835811yescharacteristic
338C2#1453014711yescharacteristic
339C2#1453015611yescharacteristic
340C2#1453016111yescharacteristic
subgroupG/H
centerC23#10587570
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC2×C17×#332C2
socle, prime radicalC23×C17#121
hypercenterC2×#332D17
hypocenterC17#10596
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
227. C17#10596semidirect

Maximal subgroups

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

subgroupindex
#145297372
#145295872
#145295482
#145295002
C2×#117625592
#145266682
C2×C17×#3322
#1059617