Finite Group Databasebeta

← #16938783

Subgroups — #16938783

Order 4352.

406 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534023C211yesmaximal, characteristic
2#14529540C211yesmaximal, characteristic
3#14528940C211yesmaximal, characteristic
4#14526668C211yesmaximal, characteristic
5#14526625C211yesmaximal, characteristic
6#14526623C211yesmaximal, characteristic
7C17×#1947C211yesmaximal, characteristic
8C2×#10587478—21no—
9C2×#10587479—22no—
10C2×C4⋊#3622C2211yescharacteristic
11C2×C4×#3622C2211yescharacteristic
12#11762751—22no—
13#11762707—21no—
14#11762705—21no—
15#11762679C2211yescharacteristic
16#11762675—21no—
17#11762674—21no—
18C4×C4⋊Dic17C2211yescharacteristic
19#11762571—21no—
20C2×C17×#107—21no—
21C2×C17×C4⋊C8C2211yescharacteristic
22C17×#384C2211yescharacteristic
23C4×C4⋊C4×C17C2211yescharacteristic
24C17×#340—21no—
25C22×C8×C17—21no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17D411yescharacteristic
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C42×C17—21no—
32C2×C42×C17C2311yescharacteristic
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17D411yescharacteristic
36C2×C4⋊Dic17D411yescharacteristic
37C2×C4⋊Dic17D412yes—
38C2×#63225—22no—
39C2×C4×Dic17—21no—
40C22×#3622—21no—
41C22×#3622—21no—
42C17×#107—42no—
43C17×C4⋊C8—21no—
44C17×C4⋊C8Q812yes—
45C17×#95—21no—
46#10587502—22no—
47#10587502—22no—
48#10587502—22no—
49#10587502—21no—
50#10587479—44no—
51#10587478—42no—
52C4⋊#3622—21no—
53C4⋊#3622Q812yes—
54C4×#3622—21no—
55C4×#3622Q812yes—
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—41no—
59C22×C4×C17C2×D411yescharacteristic
60C22×C4×C17C2×D411yescharacteristic
61C22×C4×C17C2×D411yescharacteristic
62C22×Dic17—21no—
63C22×Dic17—21no—
64C22×Dic17—22no—
65C2×C8×C17—22no—
66C2×C8×C17—41no—
67C2×C8×C17—41no—
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—
77C42×C17—41no—
78C42×C17—41no—
79C42×C17C2×Q811yescharacteristic
80C42×C17C2×Q811yescharacteristic
81C42×C17C2×Q811yescharacteristic
82C42×C17#4111yescharacteristic
83C4⋊Dic17—21no—
84C4⋊Dic17—21no—
85C4⋊Dic17—21no—
86C4⋊Dic17—21no—
87C4⋊Dic17—41no—
88C4⋊Dic17—41no—
89C4⋊Dic17—41no—
90C4⋊Dic17—41no—
91C4⋊Dic17—42no—
92#63225—82no—
93C4×Dic17—41no—
94C4×Dic17—41no—
95C2×#3622—22no—
96C2×#3622—22no—
97C2×#3622—22no—
98C2×#3622—22no—
99C2×#3622—41no—
100C2×#3622—41no—
101#10577—171nomaximal, Sylow
102C23×C17#12011yescharacteristic
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—81no—
112C2×C4×C17—81no—
113C2×C4×C17—81no—
114C2×C4×C17C22⋊Q811yescharacteristic
115C2×C4×C17C22⋊Q811yescharacteristic
116C2×C4×C17C22⋊Q811yescharacteristic
117C2×C4×C17C4⋊Q811yescharacteristic
118C2×C4×C17C4⋊Q811yescharacteristic
119C2×C4×C17C4⋊Q811yescharacteristic
120C2×C4×C17#13511yescharacteristic
121C2×C4×C17#13511yescharacteristic
122C2×C4×C17#13511yescharacteristic
123C2×C4×C17#13511yescharacteristic
124C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C17#13711yescharacteristic
127C2×C4×C17#13711yescharacteristic
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—42no—
133C2×Dic17—42no—
134C2×Dic17—41no—
135C2×Dic17—42no—
136C2×Dic17—41no—
137C8×C17—42no—
138#3622—24no—
139#3622—42no—
140#2571—171no—
141#1947—171no—
142#1947D1711yescharacteristic
143#1844—171no—
144#1296—171no—
145#1279—171no—
146#1279—171no—
147C22×C17#39511yescharacteristic
148C22×C17#44911yescharacteristic
149C22×C17#44911yescharacteristic
150C22×C17#45211yescharacteristic
151C22×C17#45211yescharacteristic
152C22×C17#45311yescharacteristic
153C22×C17#45611yescharacteristic
154C4×C17—21no—
155C4×C17—21no—
156C4×C17—81no—
157C4×C17—81no—
158C4×C17—161no—
159C4×C17#47811yescharacteristic
160C4×C17#47811yescharacteristic
161C4×C17#47911yescharacteristic
162C4×C17#47911yescharacteristic
163C4×C17#49911yescharacteristic
164C4×C17#49911yescharacteristic
165C4×C17#50111yescharacteristic
166C4×C17#50111yescharacteristic
167Dic17—81no—
168Dic17—82no—
169Dic17—81no—
170C2×#107—21no—
171C2×#107—341no—
172C2×#106—342no—
173C2×C4⋊C8—171no—
174C2×C4⋊C8C2×D1711yescharacteristic
175C2×C4×C8—171no—
176#400—342no—
177#389—341no—
178#389—341no—
179#384—171no—
180#384C2×D1711yescharacteristic
181#382—341no—
182#382—341no—
183C4×C4⋊C4—171no—
184C4×C4⋊C4C2×D1711yescharacteristic
185#340—21no—
186#340—341no—
187C2×C17#162411yescharacteristic
188C2×C17#163011yescharacteristic
189C2×C17#165211yescharacteristic
190C2×C17#165211yescharacteristic
191C2×C17#205911yescharacteristic
192C2×C17#205911yescharacteristic
193C2×C17#206011yescharacteristic
194C22×C8—21no—
195C22×C8—341no—
196C22×C8—341no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—171no—
201C2×C4⋊C4—171no—
202C2×C4⋊C4—172no—
203C2×C4⋊C4—341no—
204C2×C4⋊C4—341no—
205C2×C4⋊C4—342no—
206C2×C4⋊C4C22⋊D1711yescharacteristic
207C2×C4⋊C4C22⋊D1711yescharacteristic
208C2×C42—21no—
209C2×C42—341no—
210C2×C42C22×D1711yescharacteristic
211#107—42no—
212#107—682no—
213#106—684no—
214C4⋊C8—21no—
215C4⋊C8—172no—
216C4⋊C8—341no—
217C4⋊C8Dic3412yes—
218C4×C8—172no—
219C4×C8—341no—
220#95—21no—
221#95—342no—
222#95—342no—
223#95—342no—
224#95—341no—
225C17#1057711yescharacteristic, complemented, Sylow
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—341no—
230C22×C4—341no—
231C22×C4—342no—
232C22×C4D4×D1711yescharacteristic
233C22×C4D4×D1711yescharacteristic
234C22×C4C2×C22⋊D1711yescharacteristic
235C2×C8—22no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—342no—
239C2×C8—342no—
240C2×C8—342no—
241C2×C8—342no—
242C2×C8—681no—
243C2×C8—681no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—341no—
254C4⋊C4—341no—
255C4⋊C4—341no—
256C4⋊C4—341no—
257C4⋊C4—682no—
258C4⋊C4—681no—
259C4⋊C4—681no—
260C4⋊C4—681no—
261C4⋊C4—681no—
262C4⋊C4—1362no—
263C42—41no—
264C42—41no—
265C42—681no—
266C42—681no—
267C42C2×Dic3411yescharacteristic
268C42#6325211yescharacteristic
269C42Q8×D1711yescharacteristic
270C42Q8×D1711yescharacteristic
271C23#1058762311yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—681no—
284C2×C4—681no—
285C2×C4—681no—
286C2×C4—682no—
287C2×C4—681no—
288C2×C4—682no—
289C2×C4—682no—
290C2×C4—681no—
291C2×C4—681no—
292C2×C4#1058757411yescharacteristic
293C2×C4#1058757411yescharacteristic
294C2×C4#1058758211yescharacteristic
295C2×C4#1058758211yescharacteristic
296C2×C4#1058759711yescharacteristic
297C2×C4#1058759811yescharacteristic
298C2×C4#1058760411yescharacteristic
299C2×C4#1058760511yescharacteristic
300C2×C4#1058761011yescharacteristic
301C2×C4#1058761811yescharacteristic
302C2×C4#1058762811yescharacteristic
303C2×C4#1058763011yescharacteristic
304C2×C4#1058763611yescharacteristic
305C2×C4#1058763611yescharacteristic
306C8—42no—
307C8—344no—
308C8—682no—
309C22#1176272911yescharacteristic
310C22#1176295111yescharacteristic
311C22#1176295211yescharacteristic
312C22#1176296911yescharacteristic
313C22#1176297011yescharacteristic
314C22#1176297511yescharacteristic
315C22#1176299011yescharacteristic
316C4—21no—
317C4—21no—
318C4—81no—
319C4—81no—
320C4—161no—
321C4—1361no—
322C4—1361no—
323C4—1362no—
324C4#1176310911yescharacteristic
325C4#1176311211yescharacteristic
326C4#1176311511yescharacteristic
327C4#1176311611yescharacteristic
328C4#1176320811yescharacteristic
329C4#1176321011yescharacteristic
330C4#1176321511yescharacteristic
331C4#1176321711yescharacteristic
332C2#1452786611yescharacteristic
333C2#1452790411yescharacteristic
334C2#1452805211yescharacteristic
335C2#1452805311yescharacteristic
336C2#1453012011yescharacteristic
337C2#1453012211yescharacteristic
338C2#1453012711yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1947C2
socle, prime radicalC23×C17#120
hypercenter#1947D17
hypocenterC17#10577
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
225. C17#10577semidirect

Maximal subgroups

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

subgroupindex
#145340232
#145295402
#145289402
#145266682
#145266252
#145266232
C17×#19472
#1057717