Finite Group Databasebeta

← #16927936

Subgroups — #16927936

Order 4352.

446 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 95 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#14531724C211yesmaximal, characteristic
2#14527125C211yesmaximal, characteristic
3#14526678C212yesmaximal, complemented
4#14526649C212yesmaximal, complemented
5C4×C17×#100C211yesmaximal, characteristic
6#11762866C2212yes—
7#11762702—21no—
8#11762695—21no—
9#11762689—21no—
10#11762677C2211yescharacteristic
11#11762672C411yescharacteristic
12#11762669C411yescharacteristic
13C22⋊C4×Dic17—21no—
14C4×C22⋊Dic17C411yescharacteristic
15#11762655C2211yescharacteristic
16C2×#10587502C411yescharacteristic
17#11762533—21no—
18#11762533—21no—
19C2×C4×D4×C17C2211yescharacteristic
20C2×C17×#100—21no—
21C4×M16×C17C2212yes—
22C17×#343—21no—
23C22×D4×C17D411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×Dic17—21no—
27C2×M16×C17—22no—
28C4×D4×C17—22no—
29C4×D4×C17—22no—
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C22⋊C4×C17D411yescharacteristic
32C2×C22⋊C4×C17D411yescharacteristic
33C2×C42×C17C2311yescharacteristic
34C2×C22⋊Dic17—21no—
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37C2×C4⋊Dic17—21no—
38C2×C4×Dic17—21no—
39C2×C4×Dic17—21no—
40C17×#100—24no—
41C17×#97—22no—
42C4×C8×C17—22no—
43#10587502—21no—
44#10587502—21no—
45#10587502—21no—
46#10587502—21no—
47#10587502—21no—
48#10587502C2×C411yescharacteristic
49#10587502C2×C411yescharacteristic
50#10587502C2×C411yescharacteristic
51#10587502C2×C411yescharacteristic
52C22⋊#3622—22no—
53C4⋊#3622—22no—
54#10587474—22no—
55C24×C17C22⋊C411yescharacteristic
56C24×C17C22⋊C411yescharacteristic
57C2×D4×C17—22no—
58C2×D4×C17—22no—
59C2×D4×C17—41no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—81no—
65C22×C4×C17—81no—
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C22×C411yescharacteristic
69C22×C4×C17C2×D411yescharacteristic
70C22×C4×C17C2×D411yescharacteristic
71C22×Dic17—21no—
72C22×Dic17—21no—
73C22×Dic17—21no—
74C22×Dic17—21no—
75C22×Dic17—42no—
76C22×Dic17—42no—
77C22×Dic17—81no—
78M16×C17—24no—
79M16×C17—42no—
80C2×C8×C17—42no—
81C4⋊C4×C17—22no—
82C22⋊C4×C17—22no—
83C22⋊C4×C17—22no—
84C42×C17#4112yes—
85C42×C17#4112yes—
86C22⋊Dic17—42no—
87C22⋊Dic17—42no—
88C22⋊Dic17—81no—
89C4⋊Dic17—81no—
90C4×Dic17—42no—
91C4×Dic17—81no—
92C2×#3622—42no—
93#8773—171nomaximal, Sylow
94C23×C17—21no—
95C23×C17—21no—
96C23×C17—21no—
97C23×C17—21no—
98C23×C17—21no—
99C23×C17—41no—
100C23×C17—41no—
101C23×C17—41no—
102C23×C17—41no—
103C23×C17#10412yes—
104C23×C17C2×C22⋊C411yescharacteristic
105D4×C17—44no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—81no—
115C2×C4×C17—81no—
116C2×C4×C17—81no—
117C2×C4×C17—81no—
118C2×C4×C17#11711yescharacteristic
119C2×C4×C17#11711yescharacteristic
120C2×C4×C17#12312yes—
121C2×C4×C17#12312yes—
122C2×Dic17—22no—
123C2×Dic17—41no—
124C2×Dic17—41no—
125C2×Dic17—41no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—84no—
135C8×C17—44no—
136#3622—82no—
137#2353—171no—
138C4×#100D1711yescharacteristic
139#1466—171no—
140#1300—172no—
141#1288—172no—
142C22×C17—21no—
143C22×C17—21no—
144C22×C17—22no—
145C22×C17—42no—
146C22×C17—42no—
147C22×C17—41no—
148C22×C17—41no—
149C22×C17—41no—
150C22×C17—41no—
151C22×C17—41no—
152C22×C17—81no—
153C22×C17—81no—
154C22×C17#38111yescharacteristic
155C22×C17C2×#10411yescharacteristic
156C22×C17#42111yescharacteristic
157C4×C17—22no—
158C4×C17—22no—
159C4×C17—21no—
160C4×C17—21no—
161C4×C17—41no—
162C4×C17—41no—
163Dic17—42no—
164Dic17—81no—
165Dic17—81no—
166Dic17—81no—
167C2×C4×D4C2×D1711yescharacteristic
168#432—172no—
169C2×#100—21no—
170C4×M16C2×D1712yes—
171#388—341no—
172#387—341no—
173#386—341no—
174#383—171no—
175#381—171no—
176#380—171no—
177C4×C22⋊C4—171no—
178C4×C22⋊C4—341no—
179#376—171no—
180C2×#95—171no—
181#343—21no—
182#323—341no—
183#323—341no—
184C2×C17—21no—
185C2×C17—21no—
186C2×C17—42no—
187C2×C17—81no—
188C2×C17#182611yescharacteristic
189C2×C17#182711yescharacteristic
190C2×C17#182911yescharacteristic
191C22×D4C22⋊D1711yescharacteristic
192C23×C4—341no—
193C23×C4C4×D1711yescharacteristic
194C23×C4C4×D1711yescharacteristic
195C2×M16—22no—
196C4×D4—22no—
197C4×D4—22no—
198C2×C4⋊C4—341no—
199C2×C4⋊C4C22⋊D1711yescharacteristic
200C2×C22⋊C4—341no—
201C2×C22⋊C4—341no—
202C2×C22⋊C4—341no—
203C2×C22⋊C4D6811yescharacteristic
204C2×C22⋊C4D6811yescharacteristic
205C2×C42—341no—
206C2×C42—341no—
207C2×C42C22×D1711yescharacteristic
208C4⋊C8—342no—
209#100—24no—
210C22⋊C8—342no—
211#97—22no—
212#97—342no—
213C4×C8—22no—
214#95—171no—
215#95—171no—
216#95—171no—
217#95—171no—
218#95—341no—
219#95—341no—
220#95—341no—
221#95—341no—
222#95—341no—
223C17#877311yescharacteristic, complemented, Sylow
224C24#6322711yescharacteristic
225C24#6322711yescharacteristic
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—41no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—81no—
234C22×C4—81no—
235C22×C4—341no—
236C22×C4—341no—
237C22×C4—341no—
238C22×C4—341no—
239C22×C4—682no—
240C22×C4—682no—
241C22×C4—1361no—
242C22×C4#6322711yescharacteristic
243C22×C4#6322711yescharacteristic
244C22×C4C2×C4×D1711yescharacteristic
245C22×C4C2×D6811yescharacteristic
246C22×C4C2×C22⋊D1711yescharacteristic
247M16—24no—
248M16—42no—
249C2×C8—42no—
250C2×C8—682no—
251C4⋊C4—22no—
252C4⋊C4—1361no—
253C22⋊C4—22no—
254C22⋊C4—22no—
255C22⋊C4—682no—
256C22⋊C4—682no—
257C22⋊C4—1361no—
258C42—682no—
259C42—1361no—
260C42#6325412yes—
261C42#6325412yes—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23#1058747612yes—
272C23C2×#6322711yescharacteristic
273D4—44no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
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—342no—
287C2×C4—681no—
288C2×C4—681no—
289C2×C4—681no—
290C2×C4—681no—
291C2×C4—681no—
292C2×C4—681no—
293C2×C4—681no—
294C2×C4—681no—
295C2×C4—681no—
296C2×C4—681no—
297C2×C4—681no—
298C2×C4—1364no—
299C2×C4#1058756311yescharacteristic
300C2×C4#1058756311yescharacteristic
301C2×C4#1058757212yes—
302C2×C4#1058762112yes—
303C8—44no—
304C8—1362no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—42no—
309C22—42no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—81no—
316C22—81no—
317C22#1176267011yescharacteristic
318C22C2×#1058747611yescharacteristic
319C22#1176282711yescharacteristic
320C4—22no—
321C4—22no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—682no—
327C4—1361no—
328C4—1361no—
329C4—1361no—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—81no—
334C2#1452888411yescharacteristic
335C2#1452888911yescharacteristic
336C2#1452889311yescharacteristic
subgroupG/H
centerC22#11762670
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC4×C17×#100C2
socleC22×C17#381
prime radicalC22×D4×C17D4
cosocleC2×C42×C17C23
hypercenterC4×#100D17
hypocenterC17#8773
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
3. #14526678C2semidirect
4. #14526649C2semidirect
223. C17#8773semidirect

Maximal subgroups

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

subgroupindex
#145317242
#145271252
#145266782
#145266492
C4×C17×#1002
#877317