Finite Group Databasebeta

← #16929524

Subgroups — #16929524

Order 4352.

476 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538788C211yesmaximal, characteristic
2#14529582C211yesmaximal, characteristic
3#14527441C211yesmaximal, characteristic, complemented
4#14527208C211yesmaximal, characteristic
5#14526679C211yesmaximal, characteristic, complemented
6#14526629C211yesmaximal, characteristic, complemented
7C17×#2961C211yesmaximal, characteristic, complemented
8C2×C4×D68C2211yescharacteristic
9#11763137C412yes—
10#11763096—21no—
11#11763011—21no—
12#11762959C412yes—
13C4×#63230—22no—
14#11762862C2211yescharacteristic
15#11762862C2211yescharacteristic
16C2×C4⋊#3622C2211yescharacteristic
17C2×#10587491—21no—
18C2×#10587491—21no—
19#11762558—21no—
20#11762555—21no—
21#11762536—22no—
22C17×#533C2211yescharacteristic
23C17×#446—22no—
24C17×#446—22no—
25C17×#424—21no—
26C17×#423C2211yescharacteristic
27C17×#405—21no—
28C2×C17×#97C2211yescharacteristic
29C22×D68C2×C411yescharacteristic
30C22×C4×D17—21no—
31C2×M16×C17—21no—
32C22×C8×C17D411yescharacteristic
33C22×C8×C17D411yescharacteristic
34C17×C4⋊Q8D411yescharacteristic
35C17×C4⋊Q8D411yescharacteristic
36C17×#125—21no—
37C17×C22⋊Q8—21no—
38C17×C22⋊Q8C2×C412yes—
39C4×Q8×C17—21no—
40C4×Q8×C17D412yes—
41C17×#117—21no—
42C2×C42×C17C2311yescharacteristic
43C2×#63230—22no—
44C2×#63227—21no—
45C2×C4⋊Dic17C2×C411yescharacteristic
46C22×#3622—21no—
47C4×D68—21no—
48C4×D68—21no—
49C4×D68—21no—
50C4×D68—21no—
51C17×C4⋊C8—24no—
52C17×C4⋊C8—21no—
53C17×C4⋊C8D412yes—
54C17×#97—22no—
55C17×#97—21no—
56C17×#97—21no—
57C4×C8×C17—22no—
58#10587506—22no—
59C22⋊#3622—21no—
60C22⋊#3622C2×C412yes—
61#10587491—42no—
62#10587491—42no—
63#10587480—22no—
64#10587479—22no—
65C4⋊#3622—21no—
66C4⋊#3622—21no—
67C4⋊#3622—21no—
68C4⋊#3622—21no—
69C4×#3622—21no—
70C4×#3622—21no—
71C23×D17—21no—
72C2×Q8×C17—21no—
73C2×Q8×C17C22⋊C412yes—
74C22×C4×C17C22×C411yescharacteristic
75C22×C4×C17C2×D411yescharacteristic
76C22×C4×C17#4111yescharacteristic
77C22×Dic17—21no—
78C2×D68—21no—
79C2×D68—21no—
80C2×D68—42no—
81C2×C4×D17—41no—
82C2×C4×D17—41no—
83C2×C4×D17—41no—
84C2×C4×D17—41no—
85C2×C4×D17—41no—
86C2×C4×D17—41no—
87M16×C17—41no—
88M16×C17—41no—
89C2×C8×C17—21no—
90C2×C8×C17—21no—
91C2×C8×C17—21no—
92C2×C8×C17—22no—
93C2×C8×C17—21no—
94C2×C8×C17—21no—
95C2×C8×C17SD1612yescomplemented
96C4⋊C4×C17—22no—
97C4⋊C4×C17—21no—
98C4⋊C4×C17—21no—
99C4⋊C4×C17—21no—
100C4⋊C4×C17—22no—
101C4⋊C4×C17C22⋊C412yes—
102C22⋊C4×C17—22no—
103C42×C17—22no—
104C42×C17C2×D411yescharacteristic
105C42×C17C2×D411yescharacteristic
106C42×C17C2×D411yescharacteristic
107C42×C17#4111yescharacteristic
108#63230—44no—
109#63227—41no—
110#63227—41no—
111C4⋊Dic17—21no—
112C4⋊Dic17—21no—
113C2×#3622—22no—
114C2×#3622—41no—
115C2×#3622—41no—
116C2×#3622—41no—
117C2×#3622—41no—
118#9050—171nomaximal, Sylow
119C23×C17C4×D411yescharacteristic
120C22×D17—22no—
121C22×D17—41no—
122C22×D17—41no—
123C22×D17—41no—
124C22×D17—41no—
125C22×D17—41no—
126C22×D17—41no—
127Q8×C17—42no—
128Q8×C17—81no—
129C2×C4×C17—22no—
130C2×C4×C17—22no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17C2×C22⋊C411yescharacteristic
134C2×C4×C17C4×D411yescharacteristic
135C2×C4×C17#12011yescharacteristic
136C2×C4×C17#12111yescharacteristic
137C2×C4×C17#12111yescharacteristic
138C2×C4×C17#12311yescharacteristic
139C2×C4×C17C2×SD1611yescharacteristic
140C2×C4×C17#13511yescharacteristic
141C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C17#13711yescharacteristic
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146D68—22no—
147D68—22no—
148D68—41no—
149D68—41no—
150C4×D17—81no—
151C4×D17—81no—
152C4×D17—81no—
153C4×D17—81no—
154C8×C17—22no—
155C8×C17—41no—
156C8×C17—42no—
157#3622—42no—
158#3622—81no—
159#3622—81no—
160#3101—171no—
161#2961D1711yescharacteristic, complemented
162#1955—171no—
163#1542—171no—
164#1486—171no—
165#1301—171no—
166#1281—171no—
167C22×C17—21no—
168C22×C17—21no—
169C22×C17#38611yescharacteristic
170C22×C17C4×SD1611yescharacteristic
171C22×C17#44011yescharacteristic
172C2×D17—42no—
173C2×D17—42no—
174C2×D17—42no—
175C2×D17—81no—
176C2×D17—81no—
177C2×D17—81no—
178C2×D17—81no—
179C4×C17—21no—
180C4×C17—21no—
181C4×C17—21no—
182C4×C17—21no—
183C4×C17—42no—
184C4×C17—42no—
185C4×C17#44811yescharacteristic
186C4×C17#44911yescharacteristic
187C4×C17#46011yescharacteristic
188C4×C17#46411yescharacteristic
189Dic17—81no—
190#533C2×D1711yescharacteristic
191C2×C4×D4—171no—
192#483—172no—
193#476—341no—
194#461—341no—
195#450—172no—
196#446—22no—
197#446—22no—
198C4×SD16—342no—
199#431—171no—
200#431—171no—
201#424—21no—
202#423C2×D1711yescharacteristic
203C2×C4⋊C8—171no—
204C2×C22⋊C8—341no—
205C2×C22⋊C8—341no—
206#405—21no—
207C2×#97C2×D1711yescharacteristic
208#333—341no—
209#332—341no—
210D4⋊C8—342no—
211C2×C17—21no—
212C2×C17—21no—
213C2×C17#188011yescharacteristic
214C2×C17#188111yescharacteristic
215C2×C17#189111yescharacteristic
216D17—82no—
217C22×D4—171no—
218C23×C4—341no—
219C2×SD16—342no—
220C2×M16—21no—
221C22×C8—341no—
222C22×C8C22⋊D1711yescharacteristic
223C22×C8C22⋊D1711yescharacteristic
224C4⋊Q8D6811yescharacteristic
225C4⋊Q8D6811yescharacteristic
226#125—21no—
227C22⋊Q8—21no—
228C22⋊Q8C4×D1712yes—
229C4×Q8—21no—
230C4×Q8C22⋊D1712yes—
231C4×D4—341no—
232C4×D4—341no—
233C4×D4—341no—
234C4×D4—341no—
235#117—21no—
236C2×C4⋊C4—171no—
237C2×C22⋊C4—341no—
238C2×C42C22×D1711yescharacteristic
239#106—342no—
240C4⋊C8—24no—
241C4⋊C8—21no—
242C4⋊C8—341no—
243C4⋊C8—341no—
244C4⋊C8—341no—
245C4⋊C8—341no—
246C4⋊C8C22⋊D1712yes—
247#103—342no—
248#102—342no—
249C22⋊C8—172no—
250C22⋊C8—341no—
251C22⋊C8—682no—
252C22⋊C8—682no—
253#97—22no—
254#97—21no—
255#97—21no—
256C4×C8—22no—
257C4×C8—341no—
258C4×C8—341no—
259C17#905011yescharacteristic, complemented, Sylow
260C24—341no—
261C2×Q8—21no—
262C2×Q8#6322712yes—
263C2×D4—341no—
264C2×D4—341no—
265C2×D4—682no—
266C22×C4—341no—
267C22×C4—681no—
268C22×C4—681no—
269C22×C4—681no—
270C22×C4—681no—
271C22×C4—681no—
272C22×C4—681no—
273C22×C4C2×C4×D1711yescharacteristic
274C22×C4#6325211yescharacteristic
275C22×C4C2×C22⋊D1711yescharacteristic
276SD16—684no—
277M16—41no—
278M16—41no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—22no—
284C2×C8—21no—
285C2×C8—342no—
286C2×C8—681no—
287C2×C8—681no—
288C2×C8—681no—
289C2×C8—681no—
290C2×C8#6323012yescomplemented
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—341no—
297C4⋊C4—341no—
298C4⋊C4#6322712yes—
299C22⋊C4—22no—
300C22⋊C4—681no—
301C22⋊C4—681no—
302C42—22no—
303C42C2×D6811yescharacteristic
304C42#6325211yescharacteristic
305C42C2×C22⋊D1711yescharacteristic
306C42C2×C22⋊D1711yescharacteristic
307C23—342no—
308C23—681no—
309C23—681no—
310C23—681no—
311C23—681no—
312C23—681no—
313C23—681no—
314C23C4×C22⋊D1711yescharacteristic
315Q8—42no—
316Q8—81no—
317D4—342no—
318D4—342no—
319D4—681no—
320D4—681no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—681no—
326C2×C4—681no—
327C2×C4—681no—
328C2×C4—1361no—
329C2×C4—1361no—
330C2×C4—1361no—
331C2×C4—1361no—
332C2×C4C2×#6322711yescharacteristic
333C2×C4C4×C22⋊D1711yescharacteristic
334C2×C4#1058761511yescharacteristic
335C2×C4#1058761611yescharacteristic
336C2×C4#1058761611yescharacteristic
337C2×C4C2×#6323011yescharacteristic
338C2×C4#1058762811yescharacteristic
339C2×C4#1058763511yescharacteristic
340C2×C4#1058763611yescharacteristic
341C2×C4#1058763911yescharacteristic
342C8—22no—
343C8—41no—
344C8—42no—
345C8—682no—
346C8—1361no—
347C8—1361no—
348C22—21no—
349C22—21no—
350C22—682no—
351C22—682no—
352C22—682no—
353C22—1361no—
354C22—1361no—
355C22—1361no—
356C22—1361no—
357C22#1176268811yescharacteristic
358C22C4×#6323011yescharacteristic
359C22#1176290711yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—42no—
366C4—1361no—
367C4#1176294811yescharacteristic
368C4#1176295411yescharacteristic
369C4#1176300911yescharacteristic
370C4#1176303111yescharacteristic
371C2—21no—
372C2—21no—
373C2—1362no—
374C2#1452913911yescharacteristic
375C2#1452914611yescharacteristic
376C2#1452920211yescharacteristic
subgroupG/H
centerC2×C4#10587639
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2961C2
socleC22×C17#386
prime radicalC22×D68C2×C4
cosocleC2×C42×C17C23
hypercenter#2961D17
hypocenterC17#9050
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2961

Complements

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

NH ≅ G/Ntype
3. #14527441C2semidirect
5. #14526679C2semidirect
6. #14526629C2semidirect
7. C17×#2961C2semidirect
95. C2×C8×C17SD16semidirect
161. #2961D17semidirect
259. C17#9050semidirect
290. C2×C8#63230semidirect

Maximal subgroups

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

subgroupindex
#145387882
#145295822
#145274412
#145272082
#145266792
#145266292
C17×#29612
#905017