Finite Group Databasebeta

← #16938880

Subgroups — #16938880

Order 4352.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14529744C211yesmaximal, characteristic
2#14529732C211yesmaximal, characteristic
3#14529503C211yesmaximal, characteristic
4C2×#11762561C211yesmaximal, characteristic
5C2×#11762557C211yesmaximal, characteristic
6#14526667C211yesmaximal, characteristic
7C17×#1947C211yesmaximal, characteristic
8C2×#10587555C2211yescharacteristic
9C2×C4⋊#3622—21no—
10C2×C4⋊#3622C2211yescharacteristic
11C2×C4⋊#3622C2211yescharacteristic
12C2×C4×#3622C2211yescharacteristic
13#11762571—21no—
14#11762571—21no—
15#11762571—21no—
16#11762571—21no—
17#11762564—21no—
18#11762561—22no—
19#11762557—22no—
20C2×C17×#107—21no—
21C2×C17×C4⋊C8C2211yescharacteristic
22C17×#384C2211yescharacteristic
23C4×C4⋊C4×C17C2211yescharacteristic
24C17×#340—21no—
25C22×Dic34—21no—
26C22×C8×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C4⋊C4×C17D411yescharacteristic
32C2×C42×C17—21no—
33C2×C42×C17C2311yescharacteristic
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17—21no—
36C22×#3622—21no—
37C22×#3622—21no—
38C22×#3622D411yescharacteristic
39C22×#3622D411yescharacteristic
40#10587555—21no—
41#10587555—21no—
42#10587555—21no—
43#10587555Q812yes—
44C17×#107—42no—
45C17×C4⋊C8—21no—
46C17×C4⋊C8D412yes—
47C17×#95—21no—
48C4⋊#3622—21no—
49C4⋊#3622—21no—
50C4⋊#3622—21no—
51C4⋊#3622—21no—
52C4⋊#3622—42no—
53C4×#3622—21no—
54C4×#3622—21no—
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17—41no—
58C22×C4×C17C2×D411yescharacteristic
59C22×C4×C17C2×D411yescharacteristic
60C22×C4×C17#4111yescharacteristic
61C22×Dic17—41no—
62C2×Dic34—22no—
63C2×Dic34—41no—
64C2×Dic34—81no—
65C2×Dic34—81no—
66C2×C8×C17—22no—
67C2×C8×C17—41no—
68C2×C8×C17—41no—
69C4⋊C4×C17—21no—
70C4⋊C4×C17—21no—
71C4⋊C4×C17—21no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—81no—
77C4⋊C4×C17Q1612yes—
78C42×C17—41no—
79C42×C17—41no—
80C42×C17C2×D411yescharacteristic
81C42×C17C2×Q811yescharacteristic
82C42×C17#4111yescharacteristic
83C42×C17#4111yescharacteristic
84C4⋊Dic17—22no—
85C4⋊Dic17—22no—
86C4⋊Dic17—41no—
87C4⋊Dic17—41no—
88C2×#3622—21no—
89C2×#3622—21no—
90C2×#3622—21no—
91C2×#3622—21no—
92C2×#3622—21no—
93C2×#3622—41no—
94C2×#3622—41no—
95C2×#3622—41no—
96C2×#3622—41no—
97C2×#3622—41no—
98C2×#3622—41no—
99C2×#3622Q1612yes—
100#10593—171nomaximal, Sylow
101C23×C17#12111yescharacteristic
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—22no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—41no—
110C2×C4×C17—81no—
111C2×C4×C17—81no—
112C2×C4×C17—81no—
113C2×C4×C17#12111yescharacteristic
114C2×C4×C17#12111yescharacteristic
115C2×C4×C17C22⋊Q811yescharacteristic
116C2×C4×C17C22⋊Q811yescharacteristic
117C2×C4×C17C22⋊Q811yescharacteristic
118C2×C4×C17#12611yescharacteristic
119C2×C4×C17C2×Q1611yescharacteristic
120C2×C4×C17C2×Q1611yescharacteristic
121C2×C4×C17#13511yescharacteristic
122C2×C4×C17#13511yescharacteristic
123C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C17#13711yescharacteristic
126C2×C4×C17#13711yescharacteristic
127C2×Dic17—42no—
128C2×Dic17—81no—
129C2×Dic17—81no—
130Dic34—82no—
131Dic34—82no—
132C8×C17—42no—
133#3622—22no—
134#3622—41no—
135#3622—81no—
136#3622—81no—
137#1990—171no—
138#1987—171no—
139#1947D1711yescharacteristic
140#1939—171no—
141C2×#335—171no—
142C2×#333—171no—
143#1296—171no—
144C22×C17#39611yescharacteristic
145C22×C17#46211yescharacteristic
146C22×C17#46311yescharacteristic
147C22×C17#46711yescharacteristic
148C22×C17#46811yescharacteristic
149C22×C17#47111yescharacteristic
150C22×C17#47211yescharacteristic
151C4×C17—21no—
152C4×C17—21no—
153C4×C17—42no—
154C4×C17—81no—
155C4×C17—161no—
156C4×C17#46211yescharacteristic
157C4×C17#46311yescharacteristic
158C4×C17#46711yescharacteristic
159C4×C17#46811yescharacteristic
160C4×C17#47711yescharacteristic
161C4×C17#47711yescharacteristic
162C4×C17#47911yescharacteristic
163C4×C17#47911yescharacteristic
164Dic17—82no—
165C2×C4⋊Q8—171no—
166C2×#107—21no—
167C2×C4⋊C8—171no—
168C2×C4⋊C8—171no—
169C2×C4⋊C8—341no—
170C2×C4⋊C8C2×D1711yescharacteristic
171C2×C4×C8—171no—
172#384C2×D1711yescharacteristic
173C4×C4⋊C4C2×D1711yescharacteristic
174#340—21no—
175#340—341no—
176#340—341no—
177#340—341no—
178#340—341no—
179#336—341no—
180#335—342no—
181#333—342no—
182C2×C17#167611yescharacteristic
183C2×C17#168311yescharacteristic
184C2×C17#169211yescharacteristic
185C2×C17#169711yescharacteristic
186C2×C17#206311yescharacteristic
187C2×C17#206811yescharacteristic
188C2×C17#206811yescharacteristic
189C22×Q8—341no—
190C22×C8—21no—
191C22×C8—171no—
192C22×C8—171no—
193C22×C8—341no—
194C22×C8—341no—
195C4⋊Q8—172no—
196C4⋊Q8—341no—
197C4⋊Q8—341no—
198C4⋊Q8—341no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—341no—
203C2×C4⋊C4—341no—
204C2×C4⋊C4C22⋊D1711yescharacteristic
205C2×C4⋊C4C22⋊D1711yescharacteristic
206C2×C42—21no—
207C2×C42C22×D1711yescharacteristic
208#107—42no—
209C4⋊C8—21no—
210C4⋊C8—341no—
211C4⋊C8—341no—
212C4⋊C8—341no—
213C4⋊C8—341no—
214C4⋊C8—682no—
215C4⋊C8D6812yes—
216C4×C8—341no—
217C4×C8—341no—
218#95—21no—
219C17#1059311yescharacteristic, complemented, Sylow
220C2×Q8—342no—
221C2×Q8—681no—
222C2×Q8—1361no—
223C2×Q8—1361no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4—681no—
228C22×C4D4×D1711yescharacteristic
229C22×C4#6325411yescharacteristic
230C22×C4C2×C22⋊D1711yescharacteristic
231C2×C8—22no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—172no—
235C2×C8—341no—
236C2×C8—341no—
237C2×C8—341no—
238C2×C8—341no—
239C2×C8—341no—
240C2×C8—681no—
241C2×C8—681no—
242C2×C8—681no—
243C2×C8—681no—
244C2×C8—681no—
245C2×C8—681no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—81no—
254C4⋊C4—342no—
255C4⋊C4—342no—
256C4⋊C4—681no—
257C4⋊C4—681no—
258C4⋊C4#6323112yes—
259C42—41no—
260C42—41no—
261C42C2×D6811yescharacteristic
262C42#6325211yescharacteristic
263C42Q8×D1711yescharacteristic
264C42#6325611yescharacteristic
265C23#1058762511yescharacteristic
266Q8—1362no—
267Q8—1362no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—682no—
280C2×C4—1361no—
281C2×C4—1361no—
282C2×C4#1058758111yescharacteristic
283C2×C4#1058758211yescharacteristic
284C2×C4#1058758311yescharacteristic
285C2×C4#1058758411yescharacteristic
286C2×C4#1058759711yescharacteristic
287C2×C4#1058759811yescharacteristic
288C2×C4Q16×D1711yescharacteristic
289C2×C4#1058760411yescharacteristic
290C2×C4#1058761611yescharacteristic
291C2×C4#1058761811yescharacteristic
292C2×C4C2×#6323111yescharacteristic
293C2×C4#1058763211yescharacteristic
294C2×C4#1058763611yescharacteristic
295C2×C4#1058763711yescharacteristic
296C8—42no—
297C8—342no—
298C8—681no—
299C8—1361no—
300C8—1361no—
301C22#1176273111yescharacteristic
302C22#1176301711yescharacteristic
303C22#1176302211yescharacteristic
304C22#1176304811yescharacteristic
305C22#1176305311yescharacteristic
306C22#1176307411yescharacteristic
307C22#1176307711yescharacteristic
308C4—21no—
309C4—21no—
310C4—42no—
311C4—81no—
312C4—161no—
313C4—1362no—
314C4#1176301911yescharacteristic
315C4#1176302411yescharacteristic
316C4#1176305111yescharacteristic
317C4#1176305611yescharacteristic
318C4#1176310111yescharacteristic
319C4#1176310311yescharacteristic
320C4#1176311311yescharacteristic
321C4#1176311511yescharacteristic
322C2#1452818611yescharacteristic
323C2#1452823311yescharacteristic
324C2#1452828811yescharacteristic
325C2#1452831511yescharacteristic
326C2#1453014111yescharacteristic
327C2#1453017411yescharacteristic
328C2#1453017611yescharacteristic
subgroupG/H
centerC23#10587625
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1947C2
socle, prime radicalC23×C17#121
hypercenter#1947D17
hypocenterC17#10593
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
219. C17#10593semidirect

Maximal subgroups

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

subgroupindex
#145297442
#145297322
#145295032
C2×#117625612
C2×#117625572
#145266672
C17×#19472
#1059317