Finite Group Databasebeta

← #16933429

Subgroups — #16933429

Order 4352.

486 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537161C211yesmaximal, characteristic
2#14528935C211yesmaximal, characteristic
3#14528639C211yesmaximal, characteristic
4C2×#11762556C211yesmaximal, characteristic
5C2×#11762555C211yesmaximal, characteristic
6C2×#11762554C211yesmaximal, characteristic
7C2×C17×#332C211yesmaximal, characteristic
8C2×#10587555C2211yescharacteristic
9C2×C4⋊#3622C2211yescharacteristic
10C2×C4⋊#3622C2211yescharacteristic
11C2×#10587485—22no—
12C2×#10587486—21no—
13#11762716—22no—
14#11762714—21no—
15#11762714—21no—
16#11762674C414yes—
17C42×Dic17C2211yescharacteristic
18#11762563—21no—
19#11762556—22no—
20#11762555—22no—
21#11762554—22no—
22C2×C17×C4⋊Q8C2211yescharacteristic
23C2×C17×C4⋊C8C2211yescharacteristic
24C2×C17×C4⋊C8C2211yescharacteristic
25C17×#332—22no—
26C22×Q8×C17—21no—
27C22×Dic34—21no—
28C22×C8×C17—21no—
29C22×C8×C17—21no—
30C17×C4⋊Q8—21no—
31C17×C4⋊Q8—21no—
32C17×C4⋊Q8—21no—
33C17×C4⋊Q8—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17C2×C412yes—
36C2×C42×C17C2311yescharacteristic
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17C2×C412yes—
39C2×C4×Dic17C2×C412yes—
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D412yes—
43C22×#3622—21no—
44C22×#3622—21no—
45#10587555—21no—
46#10587555—21no—
47#10587555—21no—
48#10587555—21no—
49C17×C4⋊C8—21no—
50C17×C4⋊C8—21no—
51C17×C4⋊C8—21no—
52C17×C4⋊C8D412yes—
53#10587502—24no—
54#10587502—24no—
55#10587486—42no—
56#10587485—44no—
57C4⋊#3622—21no—
58C4⋊#3622—21no—
59C4⋊#3622—21no—
60C4⋊#3622D412yes—
61C2×Q8×C17—41no—
62C2×Q8×C17—41no—
63C2×Q8×C17—42no—
64C2×Q8×C17—42no—
65C22×C4×C17—22no—
66C22×C4×C17C22×C411yescharacteristic
67C22×C4×C17C2×D411yescharacteristic
68C22×C4×C17C2×D411yescharacteristic
69C22×Dic17—22no—
70C22×Dic17C22⋊C412yes—
71C22×Dic17C22⋊C412yes—
72C2×Dic34—41no—
73C2×Dic34—41no—
74C2×Dic34—41no—
75C2×Dic34—41no—
76C2×Dic34—41no—
77C2×Dic34—41no—
78C2×C8×C17—22no—
79C2×C8×C17—41no—
80C2×C8×C17—41no—
81C2×C8×C17—41no—
82C2×C8×C17—42no—
83C4⋊C4×C17—22no—
84C4⋊C4×C17—22no—
85C4⋊C4×C17—41no—
86C4⋊C4×C17—41no—
87C42×C17C2×D411yescharacteristic
88C42×C17C2×D411yescharacteristic
89C42×C17#4111yescharacteristic
90C42×C17#4111yescharacteristic
91C4⋊Dic17—22no—
92C4⋊Dic17—22no—
93C4⋊Dic17—41no—
94C4⋊Dic17—41no—
95C4×Dic17—21no—
96C4×Dic17—21no—
97C4×Dic17—22no—
98C4×Dic17—21no—
99C4×Dic17—22no—
100C4×Dic17—21no—
101C4×Dic17—24no—
102C2×#3622—22no—
103C2×#3622—41no—
104C2×#3622—41no—
105C2×#3622—41no—
106C2×#3622—42no—
107#9708—171nomaximal, Sylow
108C23×C17C2×C22⋊C411yescharacteristic
109Q8×C17—82no—
110Q8×C17—81no—
111Q8×C17—81no—
112C2×C4×C17—22no—
113C2×C4×C17—42no—
114C2×C4×C17—44no—
115C2×C4×C17C4×D411yescharacteristic
116C2×C4×C17C4×D411yescharacteristic
117C2×C4×C17#12111yescharacteristic
118C2×C4×C17#12111yescharacteristic
119C2×C4×C17#12411yescharacteristic
120C2×C4×C17#12711yescharacteristic
121C2×C4×C17#13511yescharacteristic
122C2×C4×C17#13511yescharacteristic
123C2×C4×C17AGL(1,ℤ/8)12yes—
124C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C17#13712yes—
126C2×C4×C17#13711yescharacteristic
127C2×Dic17—22no—
128C2×Dic17—22no—
129C2×Dic17—22no—
130C2×Dic17—22no—
131C2×Dic17—22no—
132C2×Dic17—42no—
133C2×Dic17—42no—
134C2×Dic17—42no—
135C2×Dic17#10114yes—
136Dic34—81no—
137Dic34—81no—
138Dic34—81no—
139Dic34—81no—
140C8×C17—42no—
141C8×C17—81no—
142#3622—42no—
143#3622—81no—
144#2862—171no—
145#1842—171no—
146#1767—171no—
147C2×#332—171no—
148C2×#332—171no—
149C2×#332—171no—
150C2×#332D1711yescharacteristic
151C22×C17#39011yescharacteristic
152C22×C17C2×#10112yes—
153C22×C17#41611yescharacteristic
154C22×C17#41712yes—
155C22×C17#41711yescharacteristic
156C4×C17—21no—
157C4×C17—21no—
158C4×C17—82no—
159C4×C17#46311yescharacteristic
160C4×C17#46311yescharacteristic
161C4×C17#46411yescharacteristic
162C4×C17#46411yescharacteristic
163C4×C17#48912yes—
164C4×C17#49611yescharacteristic
165C4×C17#49711yescharacteristic
166Dic17—24no—
167Dic17—42no—
168Dic17—82no—
169C2×C4⋊Q8—171no—
170C2×C4⋊Q8C2×D1711yescharacteristic
171C2×C4⋊C8—171no—
172C2×C4⋊C8—171no—
173C2×C4⋊C8—342no—
174C2×C4⋊C8C2×D1711yescharacteristic
175C2×C4⋊C8C2×D1711yescharacteristic
176C2×#97—341no—
177#391—341no—
178#391—341no—
179#391—342no—
180#382—174no—
181C43—171no—
182#336—341no—
183#332—22no—
184#332—342no—
185#332—342no—
186#332—342no—
187C2×C17#155212yes—
188C2×C17#156112yes—
189C2×C17#195911yescharacteristic
190C2×C17#196611yescharacteristic
191C2×C17#198311yescharacteristic
192C22×Q8—21no—
193C22×Q8—341no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—341no—
197C22×C8—341no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—341no—
203C4⋊Q8—341no—
204C4⋊Q8—341no—
205C4⋊Q8—341no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—172no—
208C2×C4⋊C4—341no—
209C2×C4⋊C4C4×D1712yes—
210C2×C42—172no—
211C2×C42—171no—
212C2×C42—171no—
213C2×C42—172no—
214C2×C42C22×D1711yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—172no—
219C4⋊C8—341no—
220C4⋊C8—341no—
221C4⋊C8—341no—
222C4⋊C8—684no—
223C4⋊C8C22⋊D1712yes—
224#97—682no—
225#95—344no—
226#95—344no—
227C17#970811yescharacteristic, complemented, Sylow
228C2×Q8—41no—
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—41no—
232C2×Q8—681no—
233C2×Q8—681no—
234C2×Q8—681no—
235C2×Q8—681no—
236C2×Q8—681no—
237C2×Q8—681no—
238C22×C4—22no—
239C22×C4—172no—
240C22×C4—172no—
241C22×C4—342no—
242C22×C4C2×C4×D1711yescharacteristic
243C22×C4D4×D1711yescharacteristic
244C22×C4D4×D1711yescharacteristic
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—42no—
249C2×C8—41no—
250C2×C8—342no—
251C2×C8—681no—
252C2×C8—681no—
253C2×C8—682no—
254C2×C8—681no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—342no—
260C4⋊C4—342no—
261C4⋊C4—681no—
262C4⋊C4—681no—
263C42—344no—
264C42—342no—
265C42—341no—
266C42—342no—
267C42—341no—
268C42—341no—
269C42—341no—
270C42#6325211yescharacteristic
271C42D4×D1711yescharacteristic
272C42#6325411yescharacteristic
273C42C2×C22⋊D1711yescharacteristic
274C23C22⋊C4×D1711yescharacteristic
275Q8—81no—
276Q8—82no—
277Q8—81no—
278Q8—1361no—
279Q8—1361no—
280Q8—1361no—
281Q8—1361no—
282C2×C4—22no—
283C2×C4—42no—
284C2×C4—44no—
285C2×C4—174no—
286C2×C4—342no—
287C2×C4—342no—
288C2×C4—342no—
289C2×C4—342no—
290C2×C4—342no—
291C2×C4—682no—
292C2×C4—682no—
293C2×C4—682no—
294C2×C4#1058756711yescharacteristic
295C2×C4#1058757011yescharacteristic
296C2×C4#1058757111yescharacteristic
297C2×C4#1058759712yes—
298C2×C4#1058760011yescharacteristic
299C2×C4#1058760112yes—
300C2×C4#1058760211yescharacteristic
301C2×C4#1058760411yescharacteristic
302C2×C4#1058760511yescharacteristic
303C2×C4C4×C22⋊D1711yescharacteristic
304C2×C4#1058762511yescharacteristic
305C2×C4#1058762611yescharacteristic
306C8—42no—
307C8—81no—
308C8—682no—
309C8—1361no—
310C22#1176270911yescharacteristic
311C22#101×D1712yes—
312C22#1176280411yescharacteristic
313C22#1176280712yes—
314C22#1176280911yescharacteristic
315C4—21no—
316C4—21no—
317C4—82no—
318C4—344no—
319C4—682no—
320C4—1362no—
321C4#1176302611yescharacteristic
322C4#1176302711yescharacteristic
323C4#1176303311yescharacteristic
324C4#1176303411yescharacteristic
325C4#1176316712yes—
326C4#1176319711yescharacteristic
327C4#1176320011yescharacteristic
328C2#1452748312yes—
329C2#1452752012yes—
330C2#1452959911yescharacteristic
331C2#1452962611yescharacteristic
332C2#1452971311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D17
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC2×C17×#332C2
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C42×C17C23
hypercenterC2×#332D17
hypocenterC17#9708
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
227. C17#9708semidirect

Maximal subgroups

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

subgroupindex
#145371612
#145289352
#145286392
C2×#117625562
C2×#117625552
C2×#117625542
C2×C17×#3322
#970817