Finite Group Databasebeta

← #16938660

Subgroups — #16938660

Order 4352.

364 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 103 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#14539330C211yesmaximal, characteristic
2#14527475C211yesmaximal, characteristic
3#14527466C211yesmaximal, characteristic
4C2×#11762554C211yesmaximal, characteristic
5#14527186C211yesmaximal, characteristic
6#14526635C211yesmaximal, characteristic
7C17×#1950C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9C2×#10587555C2211yescharacteristic
10#11763218—22no—
11#11763214—21no—
12#11763207—21no—
13#11762862C2211yescharacteristic
14#11762851—21no—
15#11762851—21no—
16C2×C4⋊#3622C2211yescharacteristic
17#11762557—22no—
18#11762557—21no—
19#11762554—21no—
20#11762554—22no—
21#11762539—22no—
22C2×C17×#108—21no—
23C17×#423C2211yescharacteristic
24C2×C17×C4⋊C8C2211yescharacteristic
25C4×M16×C17C2211yescharacteristic
26C17×#341—21no—
27C22×Dic34—21no—
28C2×M16×C17—21no—
29C2×M16×C17D411yescharacteristic
30C2×M16×C17D411yescharacteristic
31C22×C8×C17—21no—
32C2×C42×C17C2311yescharacteristic
33#10587612—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17—21no—
36#10587610—21no—
37#10587610—21no—
38C22×#3622—21no—
39#10587556—21no—
40#10587555—21no—
41#10587555—21no—
42#10587555—21no—
43#10587555D411yescharacteristic
44#10587555D411yescharacteristic
45#10587555D412yes—
46C4×Dic34—21no—
47C4×Dic34—21no—
48C17×#108—42no—
49C17×C4⋊C8—21no—
50C17×C4⋊C8—21no—
51C17×C4⋊C8—21no—
52C17×C4⋊C8D412yes—
53C17×#97—21no—
54C4×C8×C17—21no—
55C22⋊#3622—21no—
56#10587489—22no—
57#10587489—22no—
58#10587488—22no—
59#10587488—22no—
60C4⋊#3622—21no—
61C4⋊#3622—21no—
62C4⋊#3622—21no—
63C4×#3622—21no—
64C22×C4×C17C2×D411yescharacteristic
65C22×C4×C17#4111yescharacteristic
66C22×C4×C17#4111yescharacteristic
67C22×Dic17—41no—
68C2×Dic34—21no—
69C2×Dic34—22no—
70C2×Dic34—21no—
71C2×Dic34—41no—
72C2×Dic34—81no—
73C2×Dic34—81no—
74M16×C17—21no—
75M16×C17—21no—
76M16×C17—41no—
77M16×C17—41no—
78M16×C17SD1612yes—
79M16×C17Q1612yes—
80C2×C8×C17—21no—
81C2×C8×C17—21no—
82C2×C8×C17—22no—
83C2×C8×C17—41no—
84C2×C8×C17—41no—
85C2×C8×C17—41no—
86C42×C17C2×D411yescharacteristic
87C42×C17C2×D411yescharacteristic
88C42×C17C2×D411yescharacteristic
89C42×C17#4111yescharacteristic
90C22⋊Dic17—41no—
91C4⋊Dic17—21no—
92C4⋊Dic17—22no—
93C4⋊Dic17—21no—
94C4⋊Dic17—21no—
95C4⋊Dic17—22no—
96C4⋊Dic17—21no—
97C4⋊Dic17—41no—
98C4⋊Dic17—41no—
99#63225—41no—
100#63225—41no—
101C4×Dic17—41no—
102C2×#3622—41no—
103C2×#3622—41no—
104C2×#3622—81no—
105#10556—171nomaximal, Sylow
106C23×C17#12411yescharacteristic
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—41no—
110C2×C4×C17#12011yescharacteristic
111C2×C4×C17#12111yescharacteristic
112C2×C4×C17#12111yescharacteristic
113C2×C4×C17#12111yescharacteristic
114C2×C4×C17#12311yescharacteristic
115C2×C4×C17#12311yescharacteristic
116C2×C4×C17C2×SD1611yescharacteristic
117C2×C4×C17C2×Q1611yescharacteristic
118C2×C4×C17#13711yescharacteristic
119C2×C4×C17#13711yescharacteristic
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17—42no—
123C2×Dic17—82no—
124Dic34—41no—
125Dic34—41no—
126Dic34—81no—
127Dic34—81no—
128Dic34—81no—
129Dic34—82no—
130C8×C17—22no—
131C8×C17—22no—
132C8×C17—42no—
133C8×C17—81no—
134#3622—81no—
135#3622—81no—
136#3165—171no—
137#1950D1711yescharacteristic
138#1550—171no—
139#1548—171no—
140C2×#332—171no—
141#1481—171no—
142#1283—171no—
143C22×C17—21no—
144C22×C17—21no—
145C22×C17#39411yescharacteristic
146C22×C17#48711yescharacteristic
147C22×C17#49111yescharacteristic
148C4×C17—21no—
149C4×C17—21no—
150C4×C17—21no—
151C4×C17#44811yescharacteristic
152C4×C17#45111yescharacteristic
153C4×C17#46111yescharacteristic
154C4×C17#46211yescharacteristic
155C4×C17#47111yescharacteristic
156C4×C17#47211yescharacteristic
157Dic17—81no—
158Dic17—81no—
159Dic17—82no—
160#533—171no—
161C2×C4⋊Q8—171no—
162#501—342no—
163#500—341no—
164#498—341no—
165#431—171no—
166C2×#108—21no—
167#428—341no—
168#428—341no—
169#423C2×D1711yescharacteristic
170C2×C4⋊C8—171no—
171C2×C4⋊C8C2×D1711yescharacteristic
172C4×M16C2×D1711yescharacteristic
173#341—21no—
174#333—342no—
175#333—341no—
176#332—341no—
177#332—342no—
178Q8⋊C8—342no—
179C2×C17—21no—
180C2×C17—21no—
181C2×C17#204311yescharacteristic
182C2×C17#204911yescharacteristic
183C2×C17#205111yescharacteristic
184C22×Q8—341no—
185C2×M16—21no—
186C2×M16C22⋊D1711yescharacteristic
187C2×M16C22⋊D1711yescharacteristic
188C22×C8—21no—
189C22×C8—341no—
190C4⋊Q8—172no—
191C4⋊Q8—171no—
192C4⋊Q8—171no—
193C4⋊Q8—341no—
194C4⋊Q8—341no—
195C4⋊Q8—341no—
196#125—341no—
197C22⋊Q8—341no—
198C22⋊Q8—341no—
199C4×Q8—341no—
200C4×Q8—341no—
201#117—341no—
202C2×C4⋊C4—341no—
203C2×C4⋊C4—341no—
204C2×C42C22×D1711yescharacteristic
205#108—42no—
206#107—342no—
207#107—342no—
208#106—342no—
209#106—342no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—341no—
214C4⋊C8—341no—
215C4⋊C8—341no—
216C4⋊C8D6812yes—
217C22⋊C8—341no—
218#97—21no—
219C4×C8—21no—
220C4×C8—341no—
221C17#1055611yescharacteristic, complemented, Sylow
222C2×Q8—341no—
223C2×Q8—342no—
224C2×Q8—341no—
225C2×Q8—681no—
226C2×Q8—1361no—
227C2×Q8—1361no—
228C22×C4—681no—
229C22×C4#6325611yescharacteristic
230C22×C4#6325611yescharacteristic
231C22×C4C2×C22⋊D1711yescharacteristic
232M16—21no—
233M16—21no—
234M16—41no—
235M16—41no—
236M16#6322912yes—
237M16#6323112yes—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—681no—
245C2×C8—681no—
246C2×C8—1361no—
247C4⋊C4—341no—
248C4⋊C4—342no—
249C4⋊C4—341no—
250C4⋊C4—341no—
251C4⋊C4—342no—
252C4⋊C4—341no—
253C4⋊C4—681no—
254C4⋊C4—681no—
255C4⋊C4—681no—
256C4⋊C4—681no—
257C22⋊C4—681no—
258C42—681no—
259C42C2×D6811yescharacteristic
260C42#6325211yescharacteristic
261C42D4×D1711yescharacteristic
262C42D4×D1711yescharacteristic
263C23#1058763311yescharacteristic
264Q8—681no—
265Q8—681no—
266Q8—1362no—
267Q8—1361no—
268Q8—1361no—
269Q8—1361no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—681no—
274C2×C4—681no—
275C2×C4—682no—
276C2×C4—1362no—
277C2×C4#1058758011yescharacteristic
278C2×C4#1058758011yescharacteristic
279C2×C4#1058758111yescharacteristic
280C2×C4#1058758111yescharacteristic
281C2×C4#1058761611yescharacteristic
282C2×C4C2×#6322911yescharacteristic
283C2×C4#1058762311yescharacteristic
284C2×C4C2×#6323111yescharacteristic
285C2×C4#1058763711yescharacteristic
286C2×C4#1058763711yescharacteristic
287C8—22no—
288C8—22no—
289C8—42no—
290C8—81no—
291C8—1361no—
292C8—1361no—
293C22—21no—
294C22—21no—
295C22#1176272611yescharacteristic
296C22#1176316111yescharacteristic
297C22#1176317911yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—1361no—
302C4—1362no—
303C4—1361no—
304C4#1176294711yescharacteristic
305C4#1176296411yescharacteristic
306C4#1176301411yescharacteristic
307C4#1176301911yescharacteristic
308C4#1176307311yescharacteristic
309C4#1176308011yescharacteristic
310C2—21no—
311C2—21no—
312C2#1453003011yescharacteristic
313C2#1453006611yescharacteristic
314C2#1453007811yescharacteristic
subgroupG/H
centerC22#11762726
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1950C2
socleC22×C17#394
prime radicalC23×C17#124
hypercenter#1950D17
hypocenterC17#10556
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
221. C17#10556semidirect

Maximal subgroups

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

subgroupindex
#145393302
#145274752
#145274662
C2×#117625542
#145271862
#145266352
C17×#19502
#1055617