Finite Group Databasebeta

← #16931065

Subgroups — #16931065

Order 4352.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539709C211yesmaximal, characteristic
2#14529616C211yesmaximal, characteristic
3#14527465C211yesmaximal, characteristic, complemented
4#14527343C211yesmaximal, characteristic
5#14526642C211yesmaximal, characteristic, complemented
6#14526613C211yesmaximal, characteristic, complemented
7C17×#2331C211yesmaximal, characteristic, complemented
8#11763359C2211yescharacteristic
9#11763183C412yescomplemented
10#11763159C412yescomplemented
11#11763011—22no—
12#11762948—22no—
13#11762862C2211yescharacteristic
14#11762862C2211yescharacteristic
15#11762833C2211yescharacteristic
16C2×#10587476—21no—
17C2×#10587476—21no—
18#11762558—22no—
19#11762542—22no—
20C2×C17×C4⋊Q8C2211yescharacteristic
21C17×#391—22no—
22C17×#389—21no—
23C17×#387—22no—
24C17×#382C2211yescharacteristic
25C4×C4⋊C4×C17—21no—
26C17×#376C2211yescharacteristic
27C22×Q8×C17D412yes—
28C2×#63252—21no—
29C17×C4⋊Q8—21no—
30C17×C4⋊Q8—21no—
31C17×C4⋊Q8C2×C412yes—
32C17×C4⋊Q8D412yes—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17—22no—
37C2×C42×C17—22no—
38C2×C42×C17D411yescharacteristic
39C2×C42×C17D411yescharacteristic
40C2×C42×C17C2311yescharacteristic
41C2×#63230—24no—
42#10587616—21no—
43#10587616—21no—
44C2×#63223—21no—
45#10587561—21no—
46#10587560C2×C411yescharacteristic
47C4×D68—21no—
48C4×D68—21no—
49#10587555C2×C411yescharacteristic
50C17×#95—22no—
51C17×#95—22no—
52C17×#95—21no—
53C17×#95—21no—
54C17×#95—21no—
55C17×#95D412yes—
56#10587506—24no—
57C22⋊#3622—21no—
58C22⋊#3622—21no—
59#10587476—42no—
60#10587476—42no—
61C4⋊#3622—21no—
62C4⋊#3622—21no—
63C4⋊#3622—21no—
64C4⋊#3622—21no—
65C4×#3622—21no—
66C4×#3622C2×C412yes—
67C2×Q8×C17—22no—
68C2×Q8×C17—82no—
69C2×Q8×C17C22⋊C414yes—
70C22×C4×C17—22no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17—22no—
74C22×C4×C17C2×D411yescharacteristic
75C22×C4×C17C2×D411yescharacteristic
76C22×C4×C17C2×D411yescharacteristic
77C2×C22⋊D17—41no—
78#63252—41no—
79#63252—41no—
80#63252—41no—
81#63252—41no—
82C2×D68—21no—
83C2×D68—21no—
84C2×D68—21no—
85C2×C4×D17—41no—
86C2×Dic34—21no—
87C4⋊C4×C17—22no—
88C4⋊C4×C17—22no—
89C4⋊C4×C17—22no—
90C4⋊C4×C17—22no—
91C4⋊C4×C17—41no—
92C4⋊C4×C17—41no—
93C4⋊C4×C17—82no—
94C42×C17—21no—
95C42×C17—21no—
96C42×C17—21no—
97C42×C17—82no—
98C42×C17SD1612yescomplemented
99C42×C17C22×C411yescharacteristic
100C42×C17C2×D411yescharacteristic
101C42×C17#4111yescharacteristic
102C42×C17#4111yescharacteristic
103#63230—84no—
104#63227—41no—
105#63227—41no—
106C4⋊Dic17—21no—
107C4⋊Dic17—21no—
108#63223—41no—
109#63223—41no—
110C2×#3622—22no—
111C2×#3622—41no—
112C2×#3622—41no—
113#9301—171nomaximal, Sylow
114C23×C17#12011yescharacteristic
115C22×D17—41no—
116Q8×C17—44no—
117Q8×C17—82no—
118C2×C4×C17—24no—
119C2×C4×C17—22no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—42no—
124C2×C4×C17—42no—
125C2×C4×C17—41no—
126C2×C4×C17—42no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—42no—
130C2×C4×C17—41no—
131C2×C4×C17—42no—
132C2×C4×C17C2×C22⋊C411yescharacteristic
133C2×C4×C17C4×D411yescharacteristic
134C2×C4×C17C4×D411yescharacteristic
135C2×C4×C17#12111yescharacteristic
136C2×C4×C17#12111yescharacteristic
137C2×C4×C17#12311yescharacteristic
138C2×C4×C17C2×SD1611yescharacteristic
139C2×C4×C17#13511yescharacteristic
140C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C17#13711yescharacteristic
142C22⋊D17—81no—
143C22⋊D17—81no—
144C2×Dic17—41no—
145D68—42no—
146D68—41no—
147D68—41no—
148D68—81no—
149C4×D17—81no—
150C4×D17—81no—
151Dic34—41no—
152Dic34—41no—
153#3622—42no—
154#3622—81no—
155#3622—81no—
156#3206—171no—
157#2331D1711yescharacteristic, complemented
158#1963—171no—
159#1548—171no—
160#1517—171no—
161#1286—171no—
162#1274—171no—
163C22×C17—21no—
164C22×C17—21no—
165C22×C17#38611yescharacteristic
166C22×C17#44811yescharacteristic
167C22×C17#44911yescharacteristic
168C2×D17—81no—
169C2×D17—81no—
170C2×D17—81no—
171C4×C17—21no—
172C4×C17—21no—
173C4×C17—21no—
174C4×C17—21no—
175C4×C17—42no—
176C4×C17—44no—
177C4×C17—82no—
178C4×C17—81no—
179C4×C17C4×SD1611yescharacteristic
180C4×C17#44011yescharacteristic
181C4×C17#46011yescharacteristic
182C4×C17#46411yescharacteristic
183Dic17—81no—
184#532—171no—
185C2×C4⋊Q8C2×D1711yescharacteristic
186#492—172no—
187#487—172no—
188#461—342no—
189#448—342no—
190#431—171no—
191#431—171no—
192#423—171no—
193C2×#104—341no—
194C2×#104—341no—
195#391—22no—
196#389—21no—
197#387—22no—
198#382C2×D1711yescharacteristic
199C4×C4⋊C4—21no—
200#376C2×D1711yescharacteristic
201#333—342no—
202#327—342no—
203C2×C17—21no—
204C2×C17—21no—
205C2×C17#188011yescharacteristic
206C2×C17#190511yescharacteristic
207C2×C17#191111yescharacteristic
208D17—161no—
209C2×#41—341no—
210C22×Q8C22⋊D1712yes—
211C2×SD16—344no—
212C2×M16—341no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—171no—
216C4⋊Q8C4×D1712yes—
217C4⋊Q8D6812yes—
218#127—171no—
219#124—341no—
220#121—341no—
221#121—341no—
222C4×D4—341no—
223C4×D4—341no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—22no—
228C2×C42—22no—
229C2×C42C22⋊D1711yescharacteristic
230C2×C42C22⋊D1711yescharacteristic
231C2×C42C22×D1711yescharacteristic
232C4⋊C8—341no—
233C4⋊C8—341no—
234C4⋊C8—341no—
235C4⋊C8—341no—
236#104—682no—
237#104—682no—
238#103—344no—
239C22⋊C8—341no—
240C22⋊C8—341no—
241C4×C8—172no—
242C4×C8—341no—
243#95—22no—
244#95—22no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95C22⋊D1712yes—
249C17#930111yescharacteristic, complemented, Sylow
250#41—681no—
251#41—681no—
252#41—681no—
253#41—681no—
254C2×Q8—22no—
255C2×Q8—82no—
256C2×Q8—341no—
257C2×Q8#6322714yes—
258C2×D4—341no—
259C2×D4—341no—
260C2×D4—341no—
261C2×D4—681no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—681no—
267C22×C4C2×C22⋊D1711yescharacteristic
268C22×C4C2×C22⋊D1711yescharacteristic
269C22×C4C2×C22⋊D1711yescharacteristic
270SD16—1364no—
271M16—681no—
272M16—681no—
273C2×C8—342no—
274C2×C8—681no—
275C2×C8—681no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—82no—
283C4⋊C4—341no—
284C4⋊C4—341no—
285C22⋊C4—681no—
286C22⋊C4—681no—
287C42—21no—
288C42—21no—
289C42—21no—
290C42—82no—
291C42#6323012yescomplemented
292C42C2×C4×D1711yescharacteristic
293C42C2×D6811yescharacteristic
294C42#6325211yescharacteristic
295C42#6325211yescharacteristic
296C23—681no—
297C23#1058763911yescharacteristic
298Q8—44no—
299Q8—82no—
300Q8—681no—
301Q8—681no—
302D4—682no—
303D4—681no—
304D4—681no—
305D4—1361no—
306D4—1361no—
307D4—1361no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—681no—
323C2×C4—1361no—
324C2×C4—1361no—
325C2×C4C2×#6322711yescharacteristic
326C2×C4C4×C22⋊D1711yescharacteristic
327C2×C4C4×C22⋊D1711yescharacteristic
328C2×C4#1058761511yescharacteristic
329C2×C4#1058761611yescharacteristic
330C2×C4#1058761611yescharacteristic
331C2×C4C2×#6323011yescharacteristic
332C2×C4#1058762811yescharacteristic
333C2×C4#1058763511yescharacteristic
334C2×C4#1058763611yescharacteristic
335C8—682no—
336C8—1361no—
337C8—1361no—
338C22—21no—
339C22—21no—
340C22—1361no—
341C22—1361no—
342C22—1361no—
343C22#1176268811yescharacteristic
344C22#1176294811yescharacteristic
345C22#1176295411yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—44no—
352C4—82no—
353C4—81no—
354C4—1361no—
355C4C4×#6323011yescharacteristic
356C4#1176290711yescharacteristic
357C4#1176300911yescharacteristic
358C4#1176303111yescharacteristic
359C2—21no—
360C2—21no—
361C2—2721no—
362C2#1452913911yescharacteristic
363C2#1452927811yescharacteristic
364C2#1452931611yescharacteristic
subgroupG/H
centerC22#11762688
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2331C2
socleC22×C17#386
prime radical#11763359C22
cosocleC2×C42×C17C23
hypercenter#2331D17
hypocenterC17#9301
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2331

Complements

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

NH ≅ G/Ntype
3. #14527465C2semidirect
5. #14526642C2semidirect
6. #14526613C2semidirect
7. C17×#2331C2semidirect
9. #11763183C4semidirect
10. #11763159C4semidirect
98. C42×C17SD16semidirect
157. #2331D17semidirect
249. C17#9301semidirect
291. C42#63230semidirect

Maximal subgroups

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

subgroupindex
#145397092
#145296162
#145274652
#145273432
#145266422
#145266132
C17×#23312
#930117