Finite Group Databasebeta

← #16937994

Subgroups — #16937994

Order 4352.

376 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#11763101C211yesmaximal, characteristic
2#14528777C211yesmaximal, characteristic
3#14527559C211yesmaximal, characteristic
4#14527469C211yesmaximal, characteristic
5#14527178C211yesmaximal, characteristic
6#14526679C211yesmaximal, characteristic
7C17×#1548C211yesmaximal, characteristic
8C2×C4×Dic34C2211yescharacteristic
9#11763101—22no—
10#11763101—22no—
11#11762862C2211yescharacteristic
12C2×#10587478—21no—
13#11762833C2211yescharacteristic
14C2×C4⋊#3622C2211yescharacteristic
15C2×#10587481—21no—
16C2×#10587495—21no—
17#11762577—21no—
18#11762562—22no—
19#11762555—22no—
20#11762539—22no—
21C2×C17×C4⋊Q8C2211yescharacteristic
22C17×#431C2211yescharacteristic
23C17×#423C2211yescharacteristic
24C17×#333—22no—
25C22×Q8×C17—21no—
26C22×Dic34D411yescharacteristic
27C2×M16×C17—21no—
28C17×C4⋊Q8—21no—
29C17×C4⋊Q8—21no—
30C17×C4⋊Q8—21no—
31C17×C4⋊Q8D412yes—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C42×C17C2311yescharacteristic
35C2×C4⋊Dic17D411yescharacteristic
36C2×#63225—21no—
37C2×C4×Dic17—21no—
38C2×#63223—21no—
39C22×#3622—21no—
40C4×Dic34—21no—
41C4×Dic34—21no—
42C4×Dic34—21no—
43C4×Dic34—21no—
44C17×C4⋊C8—21no—
45C17×C4⋊C8—21no—
46C17×C4⋊C8D412yes—
47C17×C22⋊C8—21no—
48C4×C8×C17—21no—
49C22⋊#3622—21no—
50#10587495—42no—
51#10587481—24no—
52#10587478—24no—
53C4⋊#3622—21no—
54C4⋊#3622—21no—
55C4⋊#3622—21no—
56C4⋊#3622—21no—
57C4⋊#3622D412yes—
58C4×#3622—21no—
59C2×Q8×C17—22no—
60C2×Q8×C17—41no—
61C2×Q8×C17—82no—
62C22×C4×C17—41no—
63C22×C4×C17C2×D411yescharacteristic
64C22×C4×C17#4111yescharacteristic
65C22×C4×C17#4111yescharacteristic
66C22×Dic17—21no—
67C22×Dic17—21no—
68C2×Dic34—21no—
69C2×Dic34—21no—
70C2×Dic34—21no—
71C2×Dic34—21no—
72C2×Dic34—21no—
73C2×Dic34Q1612yes—
74M16×C17—41no—
75M16×C17—41no—
76C2×C8×C17—22no—
77C2×C8×C17—41no—
78C4⋊C4×C17—22no—
79C4⋊C4×C17—22no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C42×C17C2×D411yescharacteristic
83C42×C17C2×D411yescharacteristic
84C42×C17C2×D411yescharacteristic
85C42×C17#4111yescharacteristic
86C4⋊Dic17—21no—
87C4⋊Dic17—21no—
88#63225—41no—
89#63225—41no—
90C4×Dic17—41no—
91C4×Dic17—41no—
92#63223—41no—
93#63223—41no—
94C2×#3622—22no—
95C2×#3622—41no—
96C2×#3622—41no—
97C2×#3622—41no—
98C2×#3622—41no—
99#10455—171nomaximal, Sylow
100C23×C17#12311yescharacteristic
101Q8×C17—82no—
102Q8×C17—82no—
103C2×C4×C17—22no—
104C2×C4×C17—41no—
105C2×C4×C17—42no—
106C2×C4×C17—82no—
107C2×C4×C17#12011yescharacteristic
108C2×C4×C17#12111yescharacteristic
109C2×C4×C17#12111yescharacteristic
110C2×C4×C17#12111yescharacteristic
111C2×C4×C17#12311yescharacteristic
112C2×C4×C17#12411yescharacteristic
113C2×C4×C17C2×Q1611yescharacteristic
114C2×C4×C17#13511yescharacteristic
115C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C17#13711yescharacteristic
117C2×Dic17—22no—
118C2×Dic17—41no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17—81no—
122Dic34—22no—
123Dic34—22no—
124Dic34—41no—
125Dic34—41no—
126C8×C17—42no—
127C8×C17—81no—
128#3622—42no—
129#3622—81no—
130#3622—81no—
131C2×#477—171no—
132#1801—171no—
133#1571—171no—
134#1549—171no—
135#1548D1711yescharacteristic
136#1479—171no—
137#1301—171no—
138C22×C17—21no—
139C22×C17—21no—
140C22×C17#39411yescharacteristic
141C22×C17#48411yescharacteristic
142C22×C17#48511yescharacteristic
143C4×C17—21no—
144C4×C17—21no—
145C4×C17—21no—
146C4×C17—82no—
147C4×C17#44911yescharacteristic
148C4×C17#45111yescharacteristic
149C4×C17#46711yescharacteristic
150C4×C17#46811yescharacteristic
151C4×C17#47312yes—
152Dic17—42no—
153Dic17—81no—
154C2×C4⋊Q8C2×D1711yescharacteristic
155C2×C4×Q8—171no—
156#477—342no—
157#477—342no—
158#431—171no—
159#431C2×D1711yescharacteristic
160C2×#107—341no—
161#423—171no—
162#423C2×D1711yescharacteristic
163C2×C4⋊C8—171no—
164C2×#103—341no—
165C2×#101—341no—
166#343—341no—
167#335—342no—
168#333—22no—
169#332—342no—
170Q8⋊C8—342no—
171C2×C17—21no—
172C2×C17—21no—
173C2×C17#203611yescharacteristic
174C2×C17#204711yescharacteristic
175C2×C17#204811yescharacteristic
176C22×Q8—21no—
177C22×Q8—171no—
178C2×M16—21no—
179C2×M16—341no—
180C22×C8—341no—
181C4⋊Q8—21no—
182C4⋊Q8—21no—
183C4⋊Q8—21no—
184C4⋊Q8D6812yes—
185C4×Q8—341no—
186C4×Q8—341no—
187C4×Q8—341no—
188C4×Q8—341no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—171no—
192C2×C4⋊C4—341no—
193C2×C42—341no—
194C2×C42C22×D1711yescharacteristic
195#107—344no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—172no—
199C4⋊C8—341no—
200C4⋊C8—341no—
201C4⋊C8—341no—
202C4⋊C8—341no—
203C4⋊C8C22⋊D1712yes—
204#103—344no—
205#101—682no—
206C22⋊C8—21no—
207C22⋊C8—341no—
208C4×C8—21no—
209C4×C8—341no—
210C17#1045511yescharacteristic, complemented, Sylow
211C2×Q8—22no—
212C2×Q8—41no—
213C2×Q8—82no—
214C2×Q8—172no—
215C2×Q8—341no—
216C2×Q8—341no—
217C2×Q8—341no—
218C2×Q8—341no—
219C2×Q8—341no—
220C22×C4—41no—
221C22×C4—341no—
222C22×C4—341no—
223C22×C4#6325211yescharacteristic
224C22×C4D4×D1711yescharacteristic
225C22×C4#6325411yescharacteristic
226M16—41no—
227M16—41no—
228M16—681no—
229M16—681no—
230C2×C8—22no—
231C2×C8—41no—
232C2×C8—342no—
233C2×C8—681no—
234C2×C8—681no—
235C2×C8—681no—
236C2×C8—681no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—341no—
242C4⋊C4—341no—
243C4⋊C4—681no—
244C4⋊C4—681no—
245C42—681no—
246C42—681no—
247C42C2×D6811yescharacteristic
248C42D4×D1711yescharacteristic
249C42#6325411yescharacteristic
250C42C2×C22⋊D1711yescharacteristic
251C23#1058756911yescharacteristic
252Q8—82no—
253Q8—82no—
254Q8—342no—
255Q8—342no—
256Q8—681no—
257Q8—681no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4—342no—
263C2×C4—681no—
264C2×C4—681no—
265C2×C4—681no—
266C2×C4—1361no—
267C2×C4#1058756811yescharacteristic
268C2×C4#1058757111yescharacteristic
269C2×C4#1058757211yescharacteristic
270C2×C4#1058760011yescharacteristic
271C2×C4#1058760111yescharacteristic
272C2×C4Q16×D1711yescharacteristic
273C2×C4#1058760511yescharacteristic
274C2×C4#1058761611yescharacteristic
275C2×C4#1058762411yescharacteristic
276C2×C4#1058762511yescharacteristic
277C8—42no—
278C8—81no—
279C8—682no—
280C8—1361no—
281C8—1361no—
282C22—21no—
283C22—21no—
284C22#1176272511yescharacteristic
285C22#1176314311yescharacteristic
286C22#1176314911yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—82no—
291C4—682no—
292C4—1361no—
293C4#1176295711yescharacteristic
294C4#1176296611yescharacteristic
295C4#1176304711yescharacteristic
296C4#1176305211yescharacteristic
297C4#1176308212yes—
298C2—21no—
299C2—21no—
300C2#1452998611yescharacteristic
301C2#1453005111yescharacteristic
302C2#1453005611yescharacteristic
subgroupG/H
centerC22#11762725
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1548C2
socleC22×C17#394
prime radicalC23×C17#123
hypercenter#1548D17
hypocenterC17#10455
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
210. C17#10455semidirect

Maximal subgroups

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

subgroupindex
C2×#117631012
#145287772
#145275592
#145274692
#145271782
#145266792
C17×#15482
#1045517