Finite Group Databasebeta

← #16933407

Subgroups — #16933407

Order 4352.

538 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537180C211yesmaximal, characteristic
2#14528900C211yesmaximal, characteristic
3#14528639C211yesmaximal, characteristic
4C2×#11762556C211yesmaximal, characteristic
5C2×#11762555C211yesmaximal, characteristic
6C2×#11762554C211yesmaximal, characteristic
7C2×C17×#332C211yesmaximal, characteristic
8C2×#10587555C2211yescharacteristic
9C2×#10587630—22no—
10C2×C4⋊#3622C2211yescharacteristic
11C2×C4⋊#3622C2211yescharacteristic
12C2×#10587486—21no—
13#11762678—21no—
14#11762678—21no—
15#11762678C414yes—
16C42×Dic17C2211yescharacteristic
17#11762563—21no—
18#11762563—22no—
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
37#10587630—44no—
38#10587630—44no—
39C2×C4⋊Dic17—21no—
40C2×C4⋊Dic17C2×C412yes—
41C2×#63225—24no—
42C2×#63225—24no—
43C2×C4×Dic17C2×C412yes—
44C2×C4×Dic17D412yes—
45C2×C4×Dic17D411yescharacteristic
46C2×C4×Dic17D411yescharacteristic
47C22×#3622—21no—
48C22×#3622—21no—
49#10587555—21no—
50#10587555—21no—
51#10587555—21no—
52#10587555—21no—
53C17×C4⋊C8—21no—
54C17×C4⋊C8—21no—
55C17×C4⋊C8—21no—
56C17×C4⋊C8D412yes—
57#10587486—42no—
58C4⋊#3622—21no—
59C4⋊#3622—21no—
60C4⋊#3622—21no—
61C4⋊#3622D412yes—
62C2×Q8×C17—41no—
63C2×Q8×C17—41no—
64C2×Q8×C17—42no—
65C2×Q8×C17—42no—
66C22×C4×C17—22no—
67C22×C4×C17C22×C411yescharacteristic
68C22×C4×C17C2×D411yescharacteristic
69C22×C4×C17C2×D411yescharacteristic
70C22×Dic17—22no—
71C22×Dic17C22⋊C412yes—
72C22×Dic17C22⋊C412yes—
73C2×Dic34—41no—
74C2×Dic34—41no—
75C2×Dic34—42no—
76C2×Dic34—42no—
77C2×C8×C17—22no—
78C2×C8×C17—41no—
79C2×C8×C17—41no—
80C2×C8×C17—41no—
81C2×C8×C17—42no—
82C4⋊C4×C17—22no—
83C4⋊C4×C17—22no—
84C4⋊C4×C17—41no—
85C4⋊C4×C17—41no—
86C42×C17C2×D411yescharacteristic
87C42×C17C2×D411yescharacteristic
88C42×C17#4111yescharacteristic
89C42×C17#4111yescharacteristic
90C4⋊Dic17—22no—
91C4⋊Dic17—22no—
92C4⋊Dic17—41no—
93C4⋊Dic17—41no—
94#63225—48no—
95#63225—48no—
96C4×Dic17—22no—
97C4×Dic17—22no—
98C4×Dic17—21no—
99C4×Dic17—21no—
100C4×Dic17—24no—
101C4×Dic17SD1612yes—
102C4×Dic17Q1612yes—
103C2×#3622—22no—
104C2×#3622—41no—
105C2×#3622—41no—
106C2×#3622—41no—
107C2×#3622—42no—
108#9703—171nomaximal, Sylow
109C23×C17C2×C22⋊C411yescharacteristic
110Q8×C17—82no—
111Q8×C17—81no—
112Q8×C17—81no—
113C2×C4×C17—22no—
114C2×C4×C17—42no—
115C2×C4×C17—44no—
116C2×C4×C17C4×D411yescharacteristic
117C2×C4×C17C4×D411yescharacteristic
118C2×C4×C17#12111yescharacteristic
119C2×C4×C17#12111yescharacteristic
120C2×C4×C17#12411yescharacteristic
121C2×C4×C17#12711yescharacteristic
122C2×C4×C17C2×SD1611yescharacteristic
123C2×C4×C17C2×Q1611yescharacteristic
124C2×C4×C17AGL(1,ℤ/8)12yes—
125C2×C4×C17AGL(1,ℤ/8)12yes—
126C2×C4×C17#13711yescharacteristic
127C2×C4×C17#13711yescharacteristic
128C2×Dic17—22no—
129C2×Dic17—22no—
130C2×Dic17—22no—
131C2×Dic17—22no—
132C2×Dic17—42no—
133C2×Dic17—44no—
134C2×Dic17#10114yes—
135C2×Dic17#10314yes—
136Dic34—82no—
137Dic34—81no—
138Dic34—81no—
139C8×C17—42no—
140C8×C17—81no—
141#3622—42no—
142#3622—81no—
143#2868—171no—
144#1831—171no—
145#1767—171no—
146C2×#332—171no—
147C2×#332—171no—
148C2×#332—171no—
149C2×#332D1711yescharacteristic
150C22×C17#39011yescharacteristic
151C22×C17C2×#10112yes—
152C22×C17C2×#10311yescharacteristic
153C22×C17#41812yes—
154C22×C17#41911yescharacteristic
155C4×C17—21no—
156C4×C17—21no—
157C4×C17—82no—
158C4×C17#46111yescharacteristic
159C4×C17#46111yescharacteristic
160C4×C17#46211yescharacteristic
161C4×C17#46211yescharacteristic
162C4×C17#49012yes—
163C4×C17#49611yescharacteristic
164C4×C17#49611yescharacteristic
165Dic17—24no—
166Dic17—24no—
167Dic17—82no—
168C2×C4⋊Q8—171no—
169C2×C4⋊Q8—342no—
170C2×C4⋊Q8C2×D1711yescharacteristic
171C2×C4⋊C8—171no—
172C2×C4⋊C8—171no—
173C2×C4⋊C8C2×D1711yescharacteristic
174C2×C4⋊C8C2×D1711yescharacteristic
175C2×#97—341no—
176#384—174no—
177#384—341no—
178#384—341no—
179C43—171no—
180#336—342no—
181#336—341no—
182#332—22no—
183#332—342no—
184#332—342no—
185#332—342no—
186C2×C17#154912yes—
187C2×C17#155612yes—
188C2×C17#196111yescharacteristic
189C2×C17#196611yescharacteristic
190C2×C17#198111yescharacteristic
191C22×Q8—21no—
192C22×Q8—341no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—341no—
196C22×C8—341no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—341no—
202C4⋊Q8—341no—
203C4⋊Q8—341no—
204C4⋊Q8—341no—
205C4⋊Q8—684no—
206C4⋊Q8—684no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—172no—
209C2×C4⋊C4—344no—
210C2×C4⋊C4—344no—
211C2×C4⋊C4—341no—
212C2×C4⋊C4C4×D1712yes—
213C2×C42—171no—
214C2×C42—172no—
215C2×C42—172no—
216C2×C42—171no—
217C2×C42C22×D1711yescharacteristic
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—172no—
222C4⋊C8—341no—
223C4⋊C8—341no—
224C4⋊C8—341no—
225C4⋊C8C22⋊D1712yes—
226#97—682no—
227C17#970311yescharacteristic, complemented, Sylow
228C2×Q8—41no—
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—41no—
232C2×Q8—681no—
233C2×Q8—682no—
234C2×Q8—682no—
235C2×Q8—681no—
236C22×C4—22no—
237C22×C4—172no—
238C22×C4—172no—
239C22×C4—342no—
240C22×C4C2×C4×D1711yescharacteristic
241C22×C4D4×D1711yescharacteristic
242C22×C4D4×D1711yescharacteristic
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—42no—
247C2×C8—41no—
248C2×C8—342no—
249C2×C8—681no—
250C2×C8—681no—
251C2×C8—682no—
252C2×C8—681no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—342no—
258C4⋊C4—342no—
259C4⋊C4—688no—
260C4⋊C4—688no—
261C4⋊C4—681no—
262C4⋊C4—681no—
263C42—172no—
264C42—172no—
265C42—344no—
266C42—342no—
267C42—342no—
268C42—341no—
269C42—341no—
270C42#6325211yescharacteristic
271C42D4×D1711yescharacteristic
272C42#6325411yescharacteristic
273C42C2×C22⋊D1711yescharacteristic
274C23C22⋊C4×D1711yescharacteristic
275Q8—82no—
276Q8—81no—
277Q8—81no—
278Q8—1362no—
279Q8—1361no—
280Q8—1361no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—174no—
285C2×C4—174no—
286C2×C4—342no—
287C2×C4—342no—
288C2×C4—342no—
289C2×C4—342no—
290C2×C4—682no—
291C2×C4—684no—
292C2×C4#1058756711yescharacteristic
293C2×C4#1058757011yescharacteristic
294C2×C4#1058757111yescharacteristic
295C2×C4#1058759712yes—
296C2×C4SD16×D1711yescharacteristic
297C2×C4#1058760012yes—
298C2×C4#1058760111yescharacteristic
299C2×C4Q16×D1711yescharacteristic
300C2×C4#1058760411yescharacteristic
301C2×C4C4×C22⋊D1711yescharacteristic
302C2×C4#1058762511yescharacteristic
303C2×C4#1058762611yescharacteristic
304C8—42no—
305C8—81no—
306C8—682no—
307C8—1361no—
308C22#1176270911yescharacteristic
309C22#101×D1712yes—
310C22#103×D1711yescharacteristic
311C22#1176281212yes—
312C22#1176281611yescharacteristic
313C4—21no—
314C4—21no—
315C4—82no—
316C4—344no—
317C4—344no—
318C4—1362no—
319C4#1176301211yescharacteristic
320C4#1176301311yescharacteristic
321C4#1176301711yescharacteristic
322C4#1176301811yescharacteristic
323C4#1176317212yes—
324C4#1176319511yescharacteristic
325C4#1176319711yescharacteristic
326C2#1452746712yes—
327C2#1452749912yes—
328C2#1452960611yescharacteristic
329C2#1452962611yescharacteristic
330C2#1452970511yescharacteristic
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#9703
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#9703semidirect

Maximal subgroups

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

subgroupindex
#145371802
#145289002
#145286392
C2×#117625562
C2×#117625552
C2×#117625542
C2×C17×#3322
#970317