Finite Group Databasebeta

← #16938785

Subgroups — #16938785

Order 4352.

390 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14529547C211yesmaximal, characteristic
2#14529542C211yesmaximal, characteristic
3#14528911C211yesmaximal, characteristic
4#14526667C211yesmaximal, characteristic
5#14526625C211yesmaximal, characteristic
6#14526625C211yesmaximal, characteristic
7C17×#2571C211yesmaximal, characteristic
8C2×#10587478—21no—
9C2×#10587479—21no—
10C2×C4⋊#3622C2211yescharacteristic
11C2×C4⋊#3622C2211yescharacteristic
12C2×C4×#3622C2211yescharacteristic
13#11762679C2211yescharacteristic
14#11762571—21no—
15#11762571—21no—
16#11762571—22no—
17C17×#400—22no—
18C17×#389—21no—
19C17×#389—21no—
20C17×#384C2211yescharacteristic
21C17×#382—21no—
22C17×#382—21no—
23C4×C4⋊C4×C17C2211yescharacteristic
24C4×C4⋊C4×C17C2211yescharacteristic
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—22no—
28C2×C4⋊C4×C17D411yescharacteristic
29C2×C4⋊C4×C17D411yescharacteristic
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C4⋊C4×C17D411yescharacteristic
32C2×C4⋊C4×C17D412yes—
33C2×C42×C17—21no—
34C2×C42×C17—21no—
35C2×C42×C17C2311yescharacteristic
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17—21no—
39C22×#3622—21no—
40C22×#3622—21no—
41C22×#3622—21no—
42C17×#95—22no—
43C17×#95—22no—
44C17×#95—22no—
45C17×#95—21no—
46C17×#95—21no—
47#10587479—42no—
48#10587478—42no—
49C4⋊#3622—21no—
50C4⋊#3622—21no—
51C4⋊#3622Q812yes—
52C4⋊#3622Q812yes—
53C4×#3622—21no—
54C4×#3622Q812yes—
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—22no—
60C22×C4×C17C2×D411yescharacteristic
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C22×Dic17—41no—
64C4⋊C4×C17—21no—
65C4⋊C4×C17—21no—
66C4⋊C4×C17—21no—
67C4⋊C4×C17—21no—
68C4⋊C4×C17—21no—
69C4⋊C4×C17—21no—
70C4⋊C4×C17—21no—
71C4⋊C4×C17—21no—
72C4⋊C4×C17—42no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—82no—
78C42×C17—41no—
79C42×C17—41no—
80C42×C17—41no—
81C42×C17—41no—
82C42×C17C2×Q811yescharacteristic
83C42×C17C2×Q811yescharacteristic
84C42×C17C2×Q811yescharacteristic
85C42×C17#4111yescharacteristic
86C4⋊Dic17—42no—
87C4⋊Dic17—41no—
88C4⋊Dic17—41no—
89C4⋊Dic17—41no—
90C4⋊Dic17—41no—
91C2×#3622—22no—
92C2×#3622—22no—
93C2×#3622—22no—
94C2×#3622—41no—
95C2×#3622—41no—
96C2×#3622—41no—
97C2×#3622—41no—
98C2×#3622—41no—
99C2×#3622—41no—
100#10578—171nomaximal, Sylow
101C23×C17#12011yescharacteristic
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—42no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—42no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—42no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17C22⋊Q811yescharacteristic
120C2×C4×C17C22⋊Q811yescharacteristic
121C2×C4×C17C22⋊Q811yescharacteristic
122C2×C4×C17C4⋊Q811yescharacteristic
123C2×C4×C17C4⋊Q811yescharacteristic
124C2×C4×C17C4⋊Q811yescharacteristic
125C2×C4×C17#13511yescharacteristic
126C2×C4×C17#13511yescharacteristic
127C2×C4×C17#13511yescharacteristic
128C2×C4×C17#13511yescharacteristic
129C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C17#13711yescharacteristic
132C2×C4×C17#13711yescharacteristic
133C2×Dic17—81no—
134C2×Dic17—81no—
135C2×Dic17—81no—
136#3622—42no—
137#3622—42no—
138#3622—42no—
139#2571D1711yescharacteristic
140#1948—171no—
141#1947—171no—
142#1834—171no—
143#1296—171no—
144#1279—171no—
145#1279—171no—
146C22×C17#39511yescharacteristic
147C22×C17#44911yescharacteristic
148C22×C17#44911yescharacteristic
149C22×C17#45211yescharacteristic
150C22×C17#45211yescharacteristic
151C22×C17#45411yescharacteristic
152C22×C17#45511yescharacteristic
153C4×C17—21no—
154C4×C17—21no—
155C4×C17—81no—
156C4×C17—81no—
157C4×C17—82no—
158C4×C17—81no—
159C4×C17—81no—
160C4×C17#47811yescharacteristic
161C4×C17#47811yescharacteristic
162C4×C17#47911yescharacteristic
163C4×C17#47911yescharacteristic
164C4×C17#49911yescharacteristic
165C4×C17#49911yescharacteristic
166C4×C17#50111yescharacteristic
167C4×C17#50111yescharacteristic
168Dic17—161no—
169C2×#107—341no—
170C2×#106—341no—
171C2×C4⋊C8—171no—
172C2×C4⋊C8—171no—
173C2×C4×C8—171no—
174#400—22no—
175#389—21no—
176#389—21no—
177#384—171no—
178#384C2×D1711yescharacteristic
179#382—21no—
180#382—21no—
181C4×C4⋊C4C2×D1711yescharacteristic
182C4×C4⋊C4C2×D1711yescharacteristic
183#340—342no—
184#340—341no—
185#340—341no—
186C2×C17#162811yescharacteristic
187C2×C17#163811yescharacteristic
188C2×C17#164011yescharacteristic
189C2×C17#164611yescharacteristic
190C2×C17#205911yescharacteristic
191C2×C17#205911yescharacteristic
192C2×C17#206111yescharacteristic
193C22×C8—341no—
194C22×C8—341no—
195C22×C8—341no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—341no—
200C2×C4⋊C4—341no—
201C2×C4⋊C4—341no—
202C2×C4⋊C4C22⋊D1711yescharacteristic
203C2×C4⋊C4C22⋊D1711yescharacteristic
204C2×C4⋊C4C22⋊D1711yescharacteristic
205C2×C4⋊C4C22⋊D1711yescharacteristic
206C2×C4⋊C4C22⋊D1712yes—
207C2×C42—21no—
208C2×C42—21no—
209C2×C42C22×D1711yescharacteristic
210#107—682no—
211#106—682no—
212C4⋊C8—172no—
213C4⋊C8—172no—
214C4⋊C8—341no—
215C4⋊C8—341no—
216C4×C8—172no—
217C4×C8—341no—
218#95—22no—
219#95—22no—
220#95—22no—
221#95—21no—
222#95—21no—
223C17#1057811yescharacteristic, complemented, Sylow
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—681no—
230C22×C4C2×C22⋊D1711yescharacteristic
231C22×C4C2×C22⋊D1711yescharacteristic
232C22×C4C2×C22⋊D1711yescharacteristic
233C2×C8—342no—
234C2×C8—342no—
235C2×C8—342no—
236C2×C8—681no—
237C2×C8—681no—
238C2×C8—681no—
239C2×C8—681no—
240C2×C8—681no—
241C2×C8—681no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—82no—
256C4⋊C4—682no—
257C4⋊C4—681no—
258C4⋊C4—681no—
259C4⋊C4—681no—
260C4⋊C4—681no—
261C42—41no—
262C42—41no—
263C42—41no—
264C42—41no—
265C42Q8×D1711yescharacteristic
266C42Q8×D1711yescharacteristic
267C42Q8×D1711yescharacteristic
268C42#6325611yescharacteristic
269C23#1058763911yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—1361no—
288C2×C4—1361no—
289C2×C4—1361no—
290C2×C4#1058763011yescharacteristic
291C2×C4#1058763011yescharacteristic
292C2×C4#1058763011yescharacteristic
293C2×C4#1058763211yescharacteristic
294C2×C4#1058763211yescharacteristic
295C2×C4#1058763211yescharacteristic
296C2×C4#1058763511yescharacteristic
297C2×C4#1058763511yescharacteristic
298C2×C4#1058763611yescharacteristic
299C2×C4#1058763611yescharacteristic
300C2×C4#1058763611yescharacteristic
301C2×C4#1058763611yescharacteristic
302C2×C4#1058763711yescharacteristic
303C2×C4#1058763711yescharacteristic
304C8—682no—
305C8—682no—
306C8—682no—
307C22#1176272811yescharacteristic
308C22#1176295411yescharacteristic
309C22#1176295411yescharacteristic
310C22#1176297111yescharacteristic
311C22#1176297111yescharacteristic
312C22#1176298211yescharacteristic
313C22#1176298711yescharacteristic
314C4—21no—
315C4—21no—
316C4—81no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—82no—
321C4—2721no—
322C4#1176310611yescharacteristic
323C4#1176310611yescharacteristic
324C4#1176311311yescharacteristic
325C4#1176311311yescharacteristic
326C4#1176320811yescharacteristic
327C4#1176320811yescharacteristic
328C4#1176321911yescharacteristic
329C4#1176321911yescharacteristic
330C2#1452789411yescharacteristic
331C2#1452795611yescharacteristic
332C2#1452797011yescharacteristic
333C2#1452801211yescharacteristic
334C2#1453011911yescharacteristic
335C2#1453011911yescharacteristic
336C2#1453013111yescharacteristic
subgroupG/H
centerC23#10587639
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2571C2
socle, prime radicalC23×C17#120
hypercenter#2571D17
hypocenterC17#10578
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

Complements

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

NH ≅ G/Ntype
223. C17#10578semidirect

Maximal subgroups

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

subgroupindex
#145295472
#145295422
#145289112
#145266672
#145266252
C17×#25712
#1057817