Finite Group Databasebeta

← #16938804

Subgroups — #16938804

Order 4352.

442 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533819C211yesmaximal, characteristic
2#14529540C211yesmaximal, characteristic
3#14528940C211yesmaximal, characteristic
4#14526668C211yesmaximal, characteristic
5#14526625C211yesmaximal, characteristic
6#14526623C211yesmaximal, characteristic
7C17×#1948C211yesmaximal, characteristic
8C2×#10587556—21no—
9C2×#10587478—21no—
10C2×#10587479—22no—
11C2×C4⋊#3622C2211yescharacteristic
12C2×C4×#3622C2211yescharacteristic
13#11762743—22no—
14#11762707—21no—
15#11762705—21no—
16#11762679C2211yescharacteristic
17#11762678—21no—
18C4×C4⋊Dic17C2211yescharacteristic
19#11762571—21no—
20C2×C17×#106—21no—
21C2×C17×C4⋊C8C2211yescharacteristic
22C17×#384C2211yescharacteristic
23C4×C4⋊C4×C17C2211yescharacteristic
24C17×#340—21no—
25C22×C8×C17—21no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17D411yescharacteristic
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C42×C17—21no—
32C2×C42×C17C2311yescharacteristic
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17D411yescharacteristic
36C2×C4⋊Dic17D411yescharacteristic
37C2×C4⋊Dic17D412yes—
38C2×#63225—22no—
39C2×#63225—22no—
40C2×#63225—22no—
41C2×C4×Dic17—21no—
42C22×#3622—21no—
43C22×#3622—21no—
44#10587556—42no—
45#10587556—42no—
46C17×#106—42no—
47C17×C4⋊C8—21no—
48C17×C4⋊C8Q812yes—
49C17×#95—21no—
50#10587502—22no—
51#10587502—21no—
52#10587479—44no—
53#10587478—42no—
54C4⋊#3622—21no—
55C4⋊#3622Q812yes—
56C4×#3622—21no—
57C4×#3622Q812yes—
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—41no—
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C22×C4×C17C2×D411yescharacteristic
64C22×Dic17—21no—
65C22×Dic17—21no—
66C22×Dic17—22no—
67C2×C8×C17—22no—
68C2×C8×C17—41no—
69C2×C8×C17—41no—
70C4⋊C4×C17—21no—
71C4⋊C4×C17—21no—
72C4⋊C4×C17—21no—
73C4⋊C4×C17—21no—
74C4⋊C4×C17—42no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C42×C17—41no—
80C42×C17—41no—
81C42×C17C2×Q811yescharacteristic
82C42×C17C2×Q811yescharacteristic
83C42×C17C2×Q811yescharacteristic
84C42×C17#4111yescharacteristic
85C4⋊Dic17—21no—
86C4⋊Dic17—21no—
87C4⋊Dic17—41no—
88C4⋊Dic17—41no—
89C4⋊Dic17—41no—
90C4⋊Dic17—41no—
91C4⋊Dic17—42no—
92C4⋊Dic17SD1612yes—
93C4⋊Dic17SD1612yes—
94#63225—44no—
95#63225—44no—
96#63225—82no—
97C4×Dic17—41no—
98C4×Dic17—41no—
99C2×#3622—22no—
100C2×#3622—22no—
101C2×#3622—22no—
102C2×#3622—22no—
103C2×#3622—41no—
104C2×#3622—41no—
105#10580—171nomaximal, Sylow
106C23×C17#12011yescharacteristic
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—81no—
116C2×C4×C17—81no—
117C2×C4×C17—81no—
118C2×C4×C17C22⋊Q811yescharacteristic
119C2×C4×C17C22⋊Q811yescharacteristic
120C2×C4×C17C22⋊Q811yescharacteristic
121C2×C4×C17C4⋊Q811yescharacteristic
122C2×C4×C17C4⋊Q811yescharacteristic
123C2×C4×C17C4⋊Q811yescharacteristic
124C2×C4×C17C2×SD1611yescharacteristic
125C2×C4×C17C2×SD1611yescharacteristic
126C2×C4×C17#13511yescharacteristic
127C2×C4×C17#13511yescharacteristic
128C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C17#13711yescharacteristic
131C2×C4×C17#13711yescharacteristic
132C2×Dic17—22no—
133C2×Dic17—22no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—42no—
139C2×Dic17—42no—
140C2×Dic17—42no—
141C8×C17—42no—
142#3622—24no—
143#3622—42no—
144#2552—171no—
145#1948D1711yescharacteristic
146#1947—171no—
147#1844—171no—
148#1296—171no—
149#1279—171no—
150#1279—171no—
151C22×C17#39511yescharacteristic
152C22×C17#44811yescharacteristic
153C22×C17#44911yescharacteristic
154C22×C17#45011yescharacteristic
155C22×C17#45211yescharacteristic
156C22×C17#45311yescharacteristic
157C22×C17#45611yescharacteristic
158C4×C17—21no—
159C4×C17—21no—
160C4×C17—81no—
161C4×C17—81no—
162C4×C17—161no—
163C4×C17#47511yescharacteristic
164C4×C17#47611yescharacteristic
165C4×C17#47811yescharacteristic
166C4×C17#47911yescharacteristic
167C4×C17#49811yescharacteristic
168C4×C17#49911yescharacteristic
169C4×C17#50111yescharacteristic
170C4×C17#50111yescharacteristic
171Dic17—42no—
172Dic17—42no—
173Dic17—82no—
174C2×#125—341no—
175C2×#107—341no—
176C2×#106—21no—
177C2×#106—342no—
178C2×C4⋊C8—171no—
179C2×C4⋊C8C2×D1711yescharacteristic
180C2×C4×C8—171no—
181#398—342no—
182#389—341no—
183#389—341no—
184#384—171no—
185#384—341no—
186#384C2×D1711yescharacteristic
187C4×C4⋊C4—171no—
188C4×C4⋊C4C2×D1711yescharacteristic
189#340—21no—
190#340—341no—
191C2×C17#162211yescharacteristic
192C2×C17#163111yescharacteristic
193C2×C17#165311yescharacteristic
194C2×C17#165411yescharacteristic
195C2×C17#205811yescharacteristic
196C2×C17#205911yescharacteristic
197C2×C17#206011yescharacteristic
198C22×C8—21no—
199C22×C8—341no—
200C22×C8—341no—
201#125—682no—
202#125—682no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—171no—
207C2×C4⋊C4—171no—
208C2×C4⋊C4—172no—
209C2×C4⋊C4—342no—
210C2×C4⋊C4—342no—
211C2×C4⋊C4—341no—
212C2×C4⋊C4—341no—
213C2×C4⋊C4—342no—
214C2×C4⋊C4C22⋊D1711yescharacteristic
215C2×C4⋊C4C22⋊D1711yescharacteristic
216C2×C42—21no—
217C2×C42—341no—
218C2×C42C22×D1711yescharacteristic
219#107—682no—
220#106—42no—
221#106—684no—
222C4⋊C8—21no—
223C4⋊C8—172no—
224C4⋊C8—341no—
225C4⋊C8Dic3412yes—
226C4×C8—172no—
227C4×C8—341no—
228#95—21no—
229#95—342no—
230#95—341no—
231C17#1058011yescharacteristic, complemented, Sylow
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—41no—
235C22×C4—341no—
236C22×C4—341no—
237C22×C4—342no—
238C22×C4D4×D1711yescharacteristic
239C22×C4D4×D1711yescharacteristic
240C22×C4C2×C22⋊D1711yescharacteristic
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—342no—
245C2×C8—342no—
246C2×C8—342no—
247C2×C8—342no—
248C2×C8—681no—
249C2×C8—681no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—42no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—172no—
260C4⋊C4—172no—
261C4⋊C4—341no—
262C4⋊C4—341no—
263C4⋊C4—682no—
264C4⋊C4—684no—
265C4⋊C4—684no—
266C4⋊C4—681no—
267C4⋊C4—681no—
268C4⋊C4—681no—
269C4⋊C4—681no—
270C4⋊C4—1362no—
271C42—41no—
272C42—41no—
273C42—681no—
274C42—681no—
275C42C2×Dic3411yescharacteristic
276C42#6325211yescharacteristic
277C42Q8×D1711yescharacteristic
278C42Q8×D1711yescharacteristic
279C23#1058762311yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—342no—
292C2×C4—342no—
293C2×C4—681no—
294C2×C4—681no—
295C2×C4—681no—
296C2×C4—681no—
297C2×C4—682no—
298C2×C4—682no—
299C2×C4—682no—
300C2×C4#1058757411yescharacteristic
301C2×C4#1058757411yescharacteristic
302C2×C4#1058758211yescharacteristic
303C2×C4#1058758211yescharacteristic
304C2×C4SD16×D1711yescharacteristic
305C2×C4SD16×D1711yescharacteristic
306C2×C4#1058760011yescharacteristic
307C2×C4#1058760111yescharacteristic
308C2×C4#1058761011yescharacteristic
309C2×C4#1058761811yescharacteristic
310C2×C4#1058762811yescharacteristic
311C2×C4#1058763011yescharacteristic
312C2×C4#1058763611yescharacteristic
313C2×C4#1058763611yescharacteristic
314C8—42no—
315C8—344no—
316C8—682no—
317C22#1176272911yescharacteristic
318C22#1176294611yescharacteristic
319C22#1176295211yescharacteristic
320C22#1176295811yescharacteristic
321C22#1176296911yescharacteristic
322C22#1176297511yescharacteristic
323C22#1176299011yescharacteristic
324C4—21no—
325C4—21no—
326C4—81no—
327C4—81no—
328C4—161no—
329C4—682no—
330C4—682no—
331C4—1362no—
332C4#1176309311yescharacteristic
333C4#1176309811yescharacteristic
334C4#1176310911yescharacteristic
335C4#1176311611yescharacteristic
336C4#1176320611yescharacteristic
337C4#1176320811yescharacteristic
338C4#1176321511yescharacteristic
339C4#1176321611yescharacteristic
340C2#1452785511yescharacteristic
341C2#1452791011yescharacteristic
342C2#1452806011yescharacteristic
343C2#1452806611yescharacteristic
344C2#1453011511yescharacteristic
345C2#1453012211yescharacteristic
346C2#1453012711yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1948C2
socle, prime radicalC23×C17#120
hypercenter#1948D17
hypocenterC17#10580
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
231. C17#10580semidirect

Maximal subgroups

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

subgroupindex
#145338192
#145295402
#145289402
#145266682
#145266252
#145266232
C17×#19482
#1058017