Finite Group Databasebeta

← #16938876

Subgroups — #16938876

Order 4352.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14529587C211yesmaximal, characteristic
2#14529542C211yesmaximal, characteristic
3#14529503C211yesmaximal, characteristic
4C2×#11762561C211yesmaximal, characteristic
5C2×#11762555C211yesmaximal, characteristic
6#14526668C211yesmaximal, characteristic
7C17×#1988C211yesmaximal, characteristic
8C2×#10587478—21no—
9C2×C4⋊#3622—21no—
10C2×C4⋊#3622C2211yescharacteristic
11C2×C4⋊#3622C2211yescharacteristic
12C2×#10587506—21no—
13C2×#10587506—21no—
14C2×C4×#3622C2211yescharacteristic
15#11762679C2211yescharacteristic
16#11762571—21no—
17#11762564—21no—
18#11762561—22no—
19#11762555—22no—
20C2×C17×C4⋊Q8C2211yescharacteristic
21C2×C17×C4⋊C8C2211yescharacteristic
22C4×C4⋊C4×C17C2211yescharacteristic
23C17×#340—21no—
24C17×#340—21no—
25C22×Q8×C17—21no—
26C22×C8×C17—21no—
27C17×C4⋊Q8—21no—
28C17×C4⋊Q8—21no—
29C17×C4⋊Q8—21no—
30C17×C4⋊Q8Q812yes—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C4⋊C4×C17D411yescharacteristic
35C2×C42×C17—21no—
36C2×C42×C17C2311yescharacteristic
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17—21no—
39C2×C4⋊Dic17—21no—
40C22×#3622—21no—
41C22×#3622—21no—
42C22×#3622D411yescharacteristic
43C22×#3622D411yescharacteristic
44C17×C4⋊C8—21no—
45C17×C4⋊C8—21no—
46C17×#95—21no—
47#10587506—42no—
48#10587506—42no—
49#10587478—42no—
50C4⋊#3622—21no—
51C4⋊#3622—21no—
52C4⋊#3622—21no—
53C4⋊#3622—42no—
54C4⋊#3622D412yes—
55C4×#3622—21no—
56C4×#3622—21no—
57C2×Q8×C17—22no—
58C2×Q8×C17—41no—
59C2×Q8×C17—41no—
60C2×Q8×C17—41no—
61C2×Q8×C17—41no—
62C2×Q8×C17—41no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—41no—
66C22×C4×C17C2×D411yescharacteristic
67C22×C4×C17C2×D411yescharacteristic
68C22×C4×C17#4111yescharacteristic
69C22×Dic17—41no—
70C2×C8×C17—41no—
71C2×C8×C17—41no—
72C2×C8×C17—41no—
73C4⋊C4×C17—21no—
74C4⋊C4×C17—22no—
75C4⋊C4×C17—22no—
76C4⋊C4×C17—21no—
77C4⋊C4×C17—21no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17Q1612yes—
81C42×C17—41no—
82C42×C17—41no—
83C42×C17C2×D411yescharacteristic
84C42×C17C2×Q811yescharacteristic
85C42×C17#4111yescharacteristic
86C42×C17#4111yescharacteristic
87C4⋊Dic17—41no—
88C4⋊Dic17—41no—
89C4⋊Dic17—41no—
90C4⋊Dic17—41no—
91C4⋊Dic17—81no—
92C2×#3622—21no—
93C2×#3622—21no—
94C2×#3622—21no—
95C2×#3622—22no—
96C2×#3622—21no—
97C2×#3622—21no—
98C2×#3622—41no—
99C2×#3622—41no—
100C2×#3622—41no—
101C2×#3622—41no—
102C2×#3622—41no—
103C2×#3622D812yes—
104#10592—171nomaximal, Sylow
105C23×C17#12111yescharacteristic
106Q8×C17—42no—
107Q8×C17—42no—
108Q8×C17—81no—
109Q8×C17—81no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—22no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—42no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17—81no—
120C2×C4×C17—81no—
121C2×C4×C17#12111yescharacteristic
122C2×C4×C17#12111yescharacteristic
123C2×C4×C17C22⋊Q811yescharacteristic
124C2×C4×C17C22⋊Q811yescharacteristic
125C2×C4×C17C22⋊Q811yescharacteristic
126C2×C4×C17#12611yescharacteristic
127C2×C4×C17C2×D811yescharacteristic
128C2×C4×C17C2×Q1611yescharacteristic
129C2×C4×C17#13511yescharacteristic
130C2×C4×C17#13511yescharacteristic
131C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C17#13711yescharacteristic
134C2×C4×C17#13711yescharacteristic
135C2×Dic17—81no—
136C2×Dic17—81no—
137C2×Dic17—81no—
138C8×C17—81no—
139#3622—22no—
140#3622—42no—
141#3622—41no—
142#3622—81no—
143#1988D1711yescharacteristic
144#1956—171no—
145#1947—171no—
146#1939—171no—
147C2×#335—171no—
148C2×#332—171no—
149#1296—171no—
150C22×C17#39611yescharacteristic
151C22×C17#45911yescharacteristic
152C22×C17#46411yescharacteristic
153C22×C17#46711yescharacteristic
154C22×C17#46811yescharacteristic
155C22×C17#47111yescharacteristic
156C22×C17#47311yescharacteristic
157C4×C17—21no—
158C4×C17—21no—
159C4×C17—42no—
160C4×C17—82no—
161C4×C17—81no—
162C4×C17#46211yescharacteristic
163C4×C17#46311yescharacteristic
164C4×C17#46611yescharacteristic
165C4×C17#46811yescharacteristic
166C4×C17#47411yescharacteristic
167C4×C17#47711yescharacteristic
168C4×C17#47811yescharacteristic
169C4×C17#47911yescharacteristic
170Dic17—161no—
171C2×C4⋊Q8C2×D1711yescharacteristic
172C2×#107—341no—
173C2×C4⋊C8—171no—
174C2×C4⋊C8—171no—
175C2×C4⋊C8—341no—
176C2×C4⋊C8C2×D1711yescharacteristic
177C2×#103—341no—
178C2×#103—341no—
179C2×C4×C8—171no—
180#384—171no—
181C4×C4⋊C4C2×D1711yescharacteristic
182#340—21no—
183#340—21no—
184#340—341no—
185#336—341no—
186#335—342no—
187#332—342no—
188C2×C17#166911yescharacteristic
189C2×C17#168411yescharacteristic
190C2×C17#168511yescharacteristic
191C2×C17#170011yescharacteristic
192C2×C17#206411yescharacteristic
193C2×C17#206711yescharacteristic
194C2×C17#206811yescharacteristic
195C22×Q8—21no—
196C22×C8—21no—
197C22×C8—171no—
198C22×C8—171no—
199C22×C8—341no—
200C22×C8—341no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8Dic3412yes—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—341no—
208C2×C4⋊C4—341no—
209C2×C4⋊C4—341no—
210C2×C4⋊C4C22⋊D1711yescharacteristic
211C2×C4⋊C4C22⋊D1711yescharacteristic
212C2×C42—21no—
213C2×C42C22×D1711yescharacteristic
214#107—682no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—172no—
218C4⋊C8—341no—
219C4⋊C8—341no—
220C4⋊C8—341no—
221C4⋊C8—682no—
222#103—682no—
223#103—682no—
224C4×C8—341no—
225C4×C8—341no—
226#95—21no—
227C17#1059211yescharacteristic, complemented, Sylow
228C2×Q8—22no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4—681no—
238C22×C4D4×D1711yescharacteristic
239C22×C4#6325411yescharacteristic
240C22×C4C2×C22⋊D1711yescharacteristic
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—172no—
245C2×C8—341no—
246C2×C8—341no—
247C2×C8—341no—
248C2×C8—341no—
249C2×C8—341no—
250C2×C8—342no—
251C2×C8—681no—
252C2×C8—681no—
253C2×C8—681no—
254C2×C8—681no—
255C2×C8—681no—
256C4⋊C4—21no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—681no—
264C4⋊C4—681no—
265C4⋊C4—681no—
266C4⋊C4—681no—
267C4⋊C4—1361no—
268C4⋊C4#6323112yes—
269C42—41no—
270C42—41no—
271C42C2×Dic3411yescharacteristic
272C42#6325211yescharacteristic
273C42D4×D1711yescharacteristic
274C42#6325411yescharacteristic
275C23#1058762511yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—81no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—1361no—
292C2×C4—1361no—
293C2×C4—1361no—
294C2×C4#1058756411yescharacteristic
295C2×C4#1058756411yescharacteristic
296C2×C4#1058756511yescharacteristic
297C2×C4#1058757011yescharacteristic
298C2×C4D8×D1711yescharacteristic
299C2×C4#1058759711yescharacteristic
300C2×C4#1058760111yescharacteristic
301C2×C4#1058760211yescharacteristic
302C2×C4#1058761011yescharacteristic
303C2×C4#1058762411yescharacteristic
304C2×C4#1058762811yescharacteristic
305C2×C4C2×#6323111yescharacteristic
306C2×C4#1058763511yescharacteristic
307C2×C4#1058763611yescharacteristic
308C8—81no—
309C8—342no—
310C8—682no—
311C8—681no—
312C8—1361no—
313C22#1176273211yescharacteristic
314C22#1176300211yescharacteristic
315C22#1176302911yescharacteristic
316C22#1176304811yescharacteristic
317C22#1176305711yescharacteristic
318C22#1176307411yescharacteristic
319C22#1176308211yescharacteristic
320C4—21no—
321C4—21no—
322C4—42no—
323C4—82no—
324C4—81no—
325C4—2721no—
326C4#1176301611yescharacteristic
327C4#1176302111yescharacteristic
328C4#1176304411yescharacteristic
329C4#1176305411yescharacteristic
330C4#1176308711yescharacteristic
331C4#1176310411yescharacteristic
332C4#1176311111yescharacteristic
333C4#1176311611yescharacteristic
334C2#1452814711yescharacteristic
335C2#1452824011yescharacteristic
336C2#1452825111yescharacteristic
337C2#1452833611yescharacteristic
338C2#1453015111yescharacteristic
339C2#1453016811yescharacteristic
340C2#1453017911yescharacteristic
subgroupG/H
centerC23#10587625
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1988C2
socle, prime radicalC23×C17#121
hypercenter#1988D17
hypocenterC17#10592
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
227. C17#10592semidirect

Maximal subgroups

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

subgroupindex
#145295872
#145295422
#145295032
C2×#117625612
C2×#117625552
#145266682
C17×#19882
#1059217