Finite Group Databasebeta

← #16937357

Subgroups — #16937357

Order 4352.

416 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534023C211yesmaximal, characteristic
2#14529732C211yesmaximal, characteristic
3#14529731C211yesmaximal, characteristic
4#14529586C211yesmaximal, characteristic
5#14526668C211yesmaximal, characteristic
6#14526624C211yesmaximal, characteristic
7C17×#1279C211yesmaximal, characteristic
8C2×#10587555C2211yescharacteristic
9C2×C4⋊#3622C2211yescharacteristic
10C2×#10587487—22no—
11#11762751—22no—
12#11762707—21no—
13#11762705—21no—
14#11762679C2211yescharacteristic
15#11762675—21no—
16#11762674—21no—
17C4×C4⋊Dic17C2211yescharacteristic
18#11762572—21no—
19#11762572—21no—
20#11762571—21no—
21#11762571—21no—
22C2×C17×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C17C2211yescharacteristic
24C4×C4⋊C4×C17C2211yescharacteristic
25C22×Dic34—21no—
26C22×C8×C17—21no—
27C22×C8×C17—21no—
28C2×C4⋊C4×C17D411yescharacteristic
29C2×C4⋊C4×C17D411yescharacteristic
30C2×C42×C17—21no—
31C2×C42×C17C2311yescharacteristic
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17D411yescharacteristic
37C2×C4⋊Dic17D411yescharacteristic
38C2×C4⋊Dic17D412yes—
39C2×#63225—22no—
40C2×C4×Dic17—21no—
41C22×#3622—21no—
42#10587555—21no—
43#10587555—21no—
44#10587555—21no—
45#10587555Q812yes—
46C17×C4⋊C8—21no—
47C17×C4⋊C8—21no—
48C4×C8×C17—21no—
49C4×C8×C17—21no—
50C17×#95—21no—
51#10587502—22no—
52#10587502—22no—
53#10587502—22no—
54#10587502—21no—
55#10587487—44no—
56C4⋊#3622—21no—
57C4⋊#3622—21no—
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17C2×D411yescharacteristic
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C22×Dic17—21no—
64C22×Dic17—21no—
65C22×Dic17—22no—
66C22×Dic17—41no—
67C2×Dic34—22no—
68C2×Dic34—42no—
69C2×Dic34—42no—
70C2×Dic34—41no—
71C2×C8×C17—22no—
72C2×C8×C17—41no—
73C2×C8×C17—41no—
74C2×C8×C17—41no—
75C2×C8×C17—41no—
76C2×C8×C17—41no—
77C4⋊C4×C17—21no—
78C4⋊C4×C17—21no—
79C4⋊C4×C17—21no—
80C4⋊C4×C17—21no—
81C42×C17—41no—
82C42×C17—41no—
83C42×C17C2×Q811yescharacteristic
84C42×C17#4111yescharacteristic
85C42×C17#4111yescharacteristic
86C42×C17#4111yescharacteristic
87C4⋊Dic17—22no—
88C4⋊Dic17—22no—
89C4⋊Dic17—21no—
90C4⋊Dic17—21no—
91C4⋊Dic17—21no—
92C4⋊Dic17—21no—
93C4⋊Dic17—41no—
94C4⋊Dic17—41no—
95C4⋊Dic17—41no—
96C4⋊Dic17—41no—
97C4⋊Dic17—41no—
98C4⋊Dic17—41no—
99C4⋊Dic17—42no—
100#63225—82no—
101C4×Dic17—41no—
102C4×Dic17—41no—
103C2×#3622—41no—
104C2×#3622—41no—
105C2×#3622—41no—
106#10352—171nomaximal, Sylow
107C23×C17#12011yescharacteristic
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17C22⋊Q811yescharacteristic
117C2×C4×C17C22⋊Q811yescharacteristic
118C2×C4×C17C22⋊Q811yescharacteristic
119C2×C4×C17#12411yescharacteristic
120C2×C4×C17#12411yescharacteristic
121C2×C4×C17#12411yescharacteristic
122C2×C4×C17#13511yescharacteristic
123C2×C4×C17#13511yescharacteristic
124C2×C4×C17#13511yescharacteristic
125C2×C4×C17#13511yescharacteristic
126C2×C4×C17#13711yescharacteristic
127C2×C4×C17#13711yescharacteristic
128C2×C4×C17#13711yescharacteristic
129C2×C4×C17#13711yescharacteristic
130C2×Dic17—42no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—42no—
136C2×Dic17—42no—
137C2×Dic17—41no—
138C2×Dic17—42no—
139C2×Dic17—41no—
140C2×Dic17—81no—
141C2×Dic17—81no—
142Dic34—44no—
143Dic34—82no—
144C8×C17—42no—
145C8×C17—81no—
146#3622—81no—
147#2571—171no—
148#1987—171no—
149#1987—171no—
150#1956—171no—
151#1296—171no—
152#1279—171no—
153#1279D1711yescharacteristic
154C22×C17#39311yescharacteristic
155C22×C17#45211yescharacteristic
156C22×C17#45211yescharacteristic
157C22×C17#45211yescharacteristic
158C22×C17#45211yescharacteristic
159C22×C17#45311yescharacteristic
160C22×C17#45411yescharacteristic
161C4×C17—21no—
162C4×C17—21no—
163C4×C17—81no—
164C4×C17—81no—
165C4×C17#47911yescharacteristic
166C4×C17#47911yescharacteristic
167C4×C17#47911yescharacteristic
168C4×C17#47911yescharacteristic
169C4×C17#48811yescharacteristic
170C4×C17#48811yescharacteristic
171C4×C17#49111yescharacteristic
172C4×C17#49111yescharacteristic
173Dic17—82no—
174Dic17—81no—
175Dic17—81no—
176Dic17—82no—
177C2×C4⋊Q8—171no—
178C2×C4⋊C8—171no—
179C2×C4⋊C8C2×D1711yescharacteristic
180C2×#103—342no—
181C2×C4×C8C2×D1711yescharacteristic
182#400—342no—
183#389—341no—
184#389—341no—
185#384—171no—
186#382—341no—
187#382—341no—
188C4×C4⋊C4—171no—
189C4×C4⋊C4C2×D1711yescharacteristic
190#340—341no—
191#340—341no—
192#340—341no—
193#340—341no—
194C2×C17#163011yescharacteristic
195C2×C17#163411yescharacteristic
196C2×C17#163811yescharacteristic
197C2×C17#163811yescharacteristic
198C2×C17#202611yescharacteristic
199C2×C17#202611yescharacteristic
200C2×C17#202711yescharacteristic
201C22×Q8—341no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—341no—
205C4⋊Q8—172no—
206C4⋊Q8—341no—
207C4⋊Q8—341no—
208C4⋊Q8—341no—
209C2×C4⋊C4—171no—
210C2×C4⋊C4—171no—
211C2×C4⋊C4—172no—
212C2×C4⋊C4—341no—
213C2×C4⋊C4—341no—
214C2×C4⋊C4—341no—
215C2×C4⋊C4—341no—
216C2×C4⋊C4—342no—
217C2×C4⋊C4D6811yescharacteristic
218C2×C4⋊C4D6811yescharacteristic
219C2×C42—21no—
220C2×C42—341no—
221C2×C42C22×D1711yescharacteristic
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—341no—
225C4⋊C8—341no—
226#103—684no—
227C4×C8—21no—
228C4×C8—21no—
229#95—21no—
230#95—342no—
231#95—342no—
232#95—342no—
233#95—341no—
234C17#1035211yescharacteristic, complemented, Sylow
235C2×Q8—342no—
236C2×Q8—682no—
237C2×Q8—682no—
238C2×Q8—681no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—341no—
242C22×C4—341no—
243C22×C4—342no—
244C22×C4—681no—
245C22×C4C2×D6811yescharacteristic
246C22×C4D4×D1711yescharacteristic
247C22×C4D4×D1711yescharacteristic
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—681no—
255C2×C8—681no—
256C2×C8—681no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—342no—
262C4⋊C4—342no—
263C4⋊C4—341no—
264C4⋊C4—341no—
265C4⋊C4—341no—
266C4⋊C4—341no—
267C4⋊C4—682no—
268C4⋊C4—681no—
269C4⋊C4—681no—
270C4⋊C4—681no—
271C4⋊C4—681no—
272C4⋊C4—681no—
273C4⋊C4—681no—
274C4⋊C4—1362no—
275C42—41no—
276C42—41no—
277C42—681no—
278C42—681no—
279C42#6325211yescharacteristic
280C42#6325211yescharacteristic
281C42#6325411yescharacteristic
282C42Q8×D1711yescharacteristic
283C23#1058756811yescharacteristic
284Q8—684no—
285Q8—1362no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—681no—
295C2×C4—681no—
296C2×C4—681no—
297C2×C4—682no—
298C2×C4—681no—
299C2×C4—682no—
300C2×C4—682no—
301C2×C4—682no—
302C2×C4—681no—
303C2×C4—681no—
304C2×C4—1361no—
305C2×C4—1361no—
306C2×C4#1058756111yescharacteristic
307C2×C4#1058757111yescharacteristic
308C2×C4#1058757111yescharacteristic
309C2×C4#1058758211yescharacteristic
310C2×C4#1058758211yescharacteristic
311C2×C4#1058758311yescharacteristic
312C2×C4#1058759011yescharacteristic
313C2×C4#1058759011yescharacteristic
314C2×C4#1058759511yescharacteristic
315C2×C4#1058759511yescharacteristic
316C2×C4#1058759811yescharacteristic
317C2×C4#1058760111yescharacteristic
318C2×C4#1058760211yescharacteristic
319C2×C4#1058760411yescharacteristic
320C8—42no—
321C8—81no—
322C8—1361no—
323C22#1176272211yescharacteristic
324C22#1176297211yescharacteristic
325C22#1176297311yescharacteristic
326C22#1176297311yescharacteristic
327C22#1176297411yescharacteristic
328C22#1176297811yescharacteristic
329C22#1176298311yescharacteristic
330C4—21no—
331C4—21no—
332C4—81no—
333C4—81no—
334C4—1362no—
335C4—1362no—
336C4—1361no—
337C4—1361no—
338C4#1176311511yescharacteristic
339C4#1176311711yescharacteristic
340C4#1176311711yescharacteristic
341C4#1176311911yescharacteristic
342C4#1176316211yescharacteristic
343C4#1176316411yescharacteristic
344C4#1176317611yescharacteristic
345C4#1176317811yescharacteristic
346C2#1452790711yescharacteristic
347C2#1452793111yescharacteristic
348C2#1452795811yescharacteristic
349C2#1452795911yescharacteristic
350C2#1452993411yescharacteristic
351C2#1452993611yescharacteristic
352C2#1452993911yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1279C2
socle, prime radicalC23×C17#120
hypercenter#1279D17
hypocenterC17#10352
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
234. C17#10352semidirect

Maximal subgroups

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

subgroupindex
#145340232
#145297322
#145297312
#145295862
#145266682
#145266242
C17×#12792
#1035217