Finite Group Databasebeta

← #16938100

Subgroups — #16938100

Order 4352.

366 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 93 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#14538589C211yesmaximal, characteristic
2#14527554C211yesmaximal, characteristic
3#14527442C211yesmaximal, characteristic
4#14527347C211yesmaximal, characteristic
5#14527108C211yesmaximal, characteristic
6#14526642C211yesmaximal, characteristic
7C17×#1805C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9#11763116—22no—
10#11763104—21no—
11#11763094—21no—
12#11762862C2211yescharacteristic
13#11762862C2211yescharacteristic
14#11762849—21no—
15#11762833C2211yescharacteristic
16#11762818—21no—
17#11762559—22no—
18#11762557—21no—
19#11762554—21no—
20#11762545—22no—
21#11762535—22no—
22C2×C4×Q8×C17C2211yescharacteristic
23C2×C17×C4⋊C8C2211yescharacteristic
24C2×C17×#103—21no—
25C17×#382C2211yescharacteristic
26C17×#340—21no—
27C22×Q8×C17D411yescharacteristic
28C22×C8×C17—21no—
29C4×Q8×C17—21no—
30C4×Q8×C17—21no—
31C4×Q8×C17—21no—
32C4×Q8×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17D411yescharacteristic
36C2×C42×C17—21no—
37C2×C42×C17C2311yescharacteristic
38#10587612—21no—
39#10587610—21no—
40#10587610—21no—
41C2×#63223—21no—
42#10587556—21no—
43#10587555D411yescharacteristic
44#10587555D411yescharacteristic
45C4×Dic34—21no—
46C4×Dic34—21no—
47C17×C4⋊C8—21no—
48C17×C4⋊C8—21no—
49C17×#103—42no—
50C17×#95—21no—
51C17×#95—21no—
52#10587506—22no—
53#10587506—22no—
54C22⋊#3622—21no—
55C22⋊#3622D412yes—
56#10587479—22no—
57#10587478—22no—
58C4⋊#3622—21no—
59C4⋊#3622—21no—
60C4⋊#3622—21no—
61C4⋊#3622D412yes—
62C4×#3622—21no—
63C4×#3622—21no—
64C2×Q8×C17—21no—
65C2×Q8×C17—21no—
66C2×Q8×C17—21no—
67C2×Q8×C17—21no—
68C2×Q8×C17—21no—
69C2×Q8×C17SD1612yes—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—41no—
73C22×C4×C17C2×D411yescharacteristic
74C22×C4×C17C2×D411yescharacteristic
75C22×C4×C17#4111yescharacteristic
76C2×Dic34—21no—
77C2×Dic34—21no—
78C2×C8×C17—41no—
79C2×C8×C17—41no—
80C2×C8×C17—41no—
81C4⋊C4×C17—21no—
82C4⋊C4×C17—21no—
83C4⋊C4×C17—41no—
84C4⋊C4×C17—41no—
85C4⋊C4×C17—41no—
86C4⋊C4×C17—41no—
87C42×C17—41no—
88C42×C17—41no—
89C42×C17C2×D411yescharacteristic
90C42×C17C2×D411yescharacteristic
91C42×C17#4111yescharacteristic
92C42×C17#4111yescharacteristic
93C22⋊Dic17—41no—
94C4⋊Dic17—21no—
95C4⋊Dic17—21no—
96C4⋊Dic17—21no—
97C4⋊Dic17—21no—
98#63225—41no—
99#63225—41no—
100C4×Dic17—41no—
101#63223—41no—
102#63223—41no—
103C2×#3622—22no—
104C2×#3622—22no—
105C2×#3622—41no—
106#10470—171nomaximal, Sylow
107C23×C17#12111yescharacteristic
108Q8×C17—22no—
109Q8×C17—22no—
110Q8×C17—41no—
111Q8×C17—41no—
112C2×C4×C17—22no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17—81no—
119C2×C4×C17—81no—
120C2×C4×C17—81no—
121C2×C4×C17—81no—
122C2×C4×C17#12011yescharacteristic
123C2×C4×C17#12111yescharacteristic
124C2×C4×C17#12111yescharacteristic
125C2×C4×C17#12311yescharacteristic
126C2×C4×C17#12311yescharacteristic
127C2×C4×C17#12411yescharacteristic
128C2×C4×C17C2×SD1611yescharacteristic
129C2×C4×C17#13511yescharacteristic
130C2×C4×C17#13711yescharacteristic
131C2×C4×C17#13711yescharacteristic
132C2×Dic17—41no—
133C2×Dic17—41no—
134Dic34—81no—
135Dic34—81no—
136C8×C17—81no—
137#3622—42no—
138#3622—42no—
139#3622—81no—
140#3078—171no—
141#1805D1711yescharacteristic
142#1570—171no—
143#1542—171no—
144#1518—171no—
145#1461—171no—
146#1286—171no—
147C22×C17—21no—
148C22×C17—21no—
149C22×C17#39411yescharacteristic
150C22×C17#46511yescharacteristic
151C22×C17#47011yescharacteristic
152C4×C17—21no—
153C4×C17—21no—
154C4×C17—21no—
155C4×C17—21no—
156C4×C17—42no—
157C4×C17—81no—
158C4×C17—161no—
159C4×C17#44811yescharacteristic
160C4×C17#45211yescharacteristic
161C4×C17#48311yescharacteristic
162C4×C17#48511yescharacteristic
163Dic17—81no—
164Dic17—81no—
165#533—171no—
166C2×C4×Q8C2×D1711yescharacteristic
167#479—342no—
168#477—341no—
169#475—341no—
170#431—171no—
171#431—171no—
172#428—341no—
173#423—171no—
174C2×C4⋊C8C2×D1711yescharacteristic
175#419—341no—
176C2×#103—21no—
177#382C2×D1711yescharacteristic
178#340—21no—
179#334—342no—
180#333—341no—
181#332—341no—
182#328—342no—
183#324—342no—
184C2×C17—21no—
185C2×C17—21no—
186C2×C17#203511yescharacteristic
187C2×C17#204911yescharacteristic
188C2×C17#205311yescharacteristic
189C22×Q8C22⋊D1711yescharacteristic
190C2×M16—341no—
191C22×C8—21no—
192C4⋊Q8—171no—
193C4⋊Q8—171no—
194#125—341no—
195C22⋊Q8—341no—
196C22⋊Q8—341no—
197C4×Q8—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8—341no—
202C4×Q8—341no—
203#117—341no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4C22⋊D1711yescharacteristic
207C2×C42—21no—
208C2×C42C22×D1711yescharacteristic
209#107—342no—
210#106—342no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—172no—
214C4⋊C8—341no—
215C4⋊C8—341no—
216C4⋊C8—341no—
217#103—42no—
218#103—342no—
219#103—342no—
220C22⋊C8—172no—
221C22⋊C8—341no—
222C4×C8—341no—
223C4×C8—341no—
224#95—21no—
225#95—21no—
226C17#1047011yescharacteristic, complemented, Sylow
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—341no—
233C2×Q8—341no—
234C2×Q8#6322912yes—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—41no—
238C22×C4D4×D1711yescharacteristic
239C22×C4#6325411yescharacteristic
240C22×C4C2×C22⋊D1711yescharacteristic
241M16—681no—
242M16—681no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—342no—
247C2×C8—342no—
248C2×C8—681no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—341no—
256C4⋊C4—341no—
257C4⋊C4—341no—
258C4⋊C4—341no—
259C4⋊C4—681no—
260C4⋊C4—681no—
261C22⋊C4—681no—
262C42—41no—
263C42—41no—
264C42—681no—
265C42#6325211yescharacteristic
266C42#6325211yescharacteristic
267C42D4×D1711yescharacteristic
268C42D4×D1711yescharacteristic
269C23#1058762511yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274Q8—1361no—
275Q8—1361no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—681no—
287C2×C4—681no—
288C2×C4#1058756911yescharacteristic
289C2×C4#1058757011yescharacteristic
290C2×C4#1058757011yescharacteristic
291C2×C4#1058757111yescharacteristic
292C2×C4#1058761511yescharacteristic
293C2×C4C2×#6322911yescharacteristic
294C2×C4#1058762311yescharacteristic
295C2×C4#1058762811yescharacteristic
296C2×C4#1058763611yescharacteristic
297C2×C4#1058763711yescharacteristic
298C8—81no—
299C8—682no—
300C8—682no—
301C8—1361no—
302C22—21no—
303C22—21no—
304C22#1176272411yescharacteristic
305C22#1176303611yescharacteristic
306C22#1176306511yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—42no—
312C4—81no—
313C4—161no—
314C4—1361no—
315C4—1361no—
316C4#1176294711yescharacteristic
317C4#1176296911yescharacteristic
318C4#1176313911yescharacteristic
319C4#1176315011yescharacteristic
320C2—21no—
321C2—21no—
322C2#1452998011yescharacteristic
323C2#1453006211yescharacteristic
324C2#1453008811yescharacteristic
subgroupG/H
centerC22#11762724
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1805C2
socleC22×C17#394
prime radicalC23×C17#121
hypercenter#1805D17
hypocenterC17#10470
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
226. C17#10470semidirect

Maximal subgroups

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

subgroupindex
#145385892
#145275542
#145274422
#145273472
#145271082
#145266422
C17×#18052
#1047017