Finite Group Databasebeta

← #16931077

Subgroups — #16931077

Order 4352.

488 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538581C211yesmaximal, characteristic
2#14537808C211yesmaximal, characteristic
3#14527347C211yesmaximal, characteristic, complemented
4#14527186C211yesmaximal, characteristic, complemented
5#14526681C211yesmaximal, characteristic, complemented
6#14526642C211yesmaximal, characteristic, complemented
7C17×#1804C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9#11763109—22no—
10#11763099C412yescomplemented
11#11763089C412yescomplemented
12D4×#3622—22no—
13D4×#3622—22no—
14#11762862C2211yescharacteristic
15#11762862C2211yescharacteristic
16#11762849—21no—
17#11762833C2211yescharacteristic
18#11762814—21no—
19C2×C22⋊#3622—22no—
20#11762545—22no—
21#11762539—22no—
22C2×C4×D4×C17C2211yescharacteristic
23C2×C17×C4⋊C8C2211yescharacteristic
24C2×C17×#102—21no—
25C17×#382C2211yescharacteristic
26C17×#340—21no—
27C22×D4×C17D411yescharacteristic
28C23×C4×C17—21no—
29C22×C8×C17—21no—
30C4×D4×C17—21no—
31C4×D4×C17—21no—
32C4×D4×C17C2×C412yes—
33C4×D4×C17D412yes—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17D411yescharacteristic
36C2×C22⋊C4×C17—21no—
37C2×C42×C17C2311yescharacteristic
38#10587612—21no—
39#10587610—21no—
40#10587610—21no—
41C2×#63223—21no—
42C22×#3622—24no—
43#10587556—21no—
44#10587555C2×C411yescharacteristic
45#10587555C2×C411yescharacteristic
46C4×Dic34—21no—
47C4×Dic34—21no—
48C17×C4⋊C8—21no—
49C17×C4⋊C8—21no—
50C17×#102—42no—
51C17×#95—21no—
52C17×#95—21no—
53#10587503—22no—
54#10587503—22no—
55C22⋊#3622—24no—
56C22⋊#3622—21no—
57C22⋊#3622D412yes—
58#10587479—22no—
59#10587478—22no—
60C4⋊#3622—21no—
61C4⋊#3622—21no—
62C4⋊#3622—21no—
63C4⋊#3622C2×C412yes—
64C4×#3622—21no—
65C4×#3622D412yes—
66C24×C17—21no—
67C2×D4×C17—21no—
68C2×D4×C17—21no—
69C2×D4×C17—21no—
70C2×D4×C17C22⋊C412yes—
71C2×D4×C17SD1612yes—
72C2×D4×C17Q1612yes—
73C22×C4×C17—21no—
74C22×C4×C17—22no—
75C22×C4×C17—22no—
76C22×C4×C17—41no—
77C22×C4×C17—82no—
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17C2×D411yescharacteristic
80C22×C4×C17#4111yescharacteristic
81C2×Dic34—21no—
82C2×Dic34—21no—
83C2×C8×C17—41no—
84C2×C8×C17—41no—
85C2×C8×C17—41no—
86C4⋊C4×C17—21no—
87C4⋊C4×C17—41no—
88C4⋊C4×C17—41no—
89C4⋊C4×C17C22⋊C412yes—
90C22⋊C4×C17—22no—
91C22⋊C4×C17—22no—
92C42×C17C22×C411yescharacteristic
93C42×C17C2×D411yescharacteristic
94C42×C17C2×D411yescharacteristic
95C42×C17#4111yescharacteristic
96C22⋊Dic17—41no—
97C4⋊Dic17—21no—
98C4⋊Dic17—21no—
99C4⋊Dic17—21no—
100C4⋊Dic17—21no—
101#63225—41no—
102#63225—41no—
103C4×Dic17—41no—
104#63223—41no—
105#63223—41no—
106C2×#3622—22no—
107C2×#3622—22no—
108C2×#3622—22no—
109C2×#3622—84no—
110#9303—171nomaximal, Sylow
111C23×C17—22no—
112C23×C17—22no—
113C23×C17—22no—
114C23×C17—81no—
115C23×C17—81no—
116C23×C17#12111yescharacteristic
117D4×C17—22no—
118D4×C17—22no—
119D4×C17—22no—
120D4×C17#10314yes—
121C2×C4×C17—22no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—44no—
125C2×C4×C17—82no—
126C2×C4×C17—81no—
127C2×C4×C17—81no—
128C2×C4×C17—81no—
129C2×C4×C17—81no—
130C2×C4×C17C2×C22⋊C411yescharacteristic
131C2×C4×C17C4×D411yescharacteristic
132C2×C4×C17C4×D411yescharacteristic
133C2×C4×C17#12011yescharacteristic
134C2×C4×C17#12111yescharacteristic
135C2×C4×C17#12311yescharacteristic
136C2×C4×C17C2×SD1611yescharacteristic
137C2×C4×C17C2×Q1611yescharacteristic
138C2×C4×C17#13511yescharacteristic
139C2×C4×C17#13511yescharacteristic
140C2×Dic17—41no—
141C2×Dic17—41no—
142Dic34—42no—
143Dic34—81no—
144C8×C17—81no—
145#3622—42no—
146#3622—42no—
147#3622—42no—
148#3077—171no—
149#2972—171no—
150#1804D1711yescharacteristic
151#1518—171no—
152#1481—171no—
153#1301—171no—
154#1286—171no—
155C22×C17—21no—
156C22×C17—21no—
157C22×C17—24no—
158C22×C17—42no—
159C22×C17—42no—
160C22×C17—82no—
161C22×C17—82no—
162C22×C17#38611yescharacteristic
163C22×C17#46511yescharacteristic
164C22×C17#46711yescharacteristic
165C4×C17—21no—
166C4×C17—21no—
167C4×C17—21no—
168C4×C17—21no—
169C4×C17—42no—
170C4×C17—161no—
171C4×C17C2×#10311yescharacteristic
172C4×C17#41611yescharacteristic
173C4×C17#46511yescharacteristic
174C4×C17#46711yescharacteristic
175Dic17—81no—
176Dic17—81no—
177#533—171no—
178C2×C4×D4C2×D1711yescharacteristic
179#478—342no—
180#476—172no—
181#474—172no—
182C8×D4—342no—
183C8×D4—342no—
184#431—171no—
185#431—171no—
186#428—341no—
187#423—171no—
188C2×C4⋊C8C2×D1711yescharacteristic
189#418—341no—
190C2×#102—21no—
191C2×C22⋊C8—342no—
192#382C2×D1711yescharacteristic
193#340—21no—
194#328—342no—
195Q8⋊C8—342no—
196C2×C17—21no—
197C2×C17—21no—
198C2×C17—44no—
199C2×C17#188111yescharacteristic
200C2×C17#189211yescharacteristic
201C2×C17#190411yescharacteristic
202C22×D4C22⋊D1711yescharacteristic
203C23×C4—21no—
204C2×M16—341no—
205C22×C8—21no—
206C22×C8—344no—
207C4⋊Q8—171no—
208C4⋊Q8—171no—
209#125—341no—
210C22⋊Q8—341no—
211C22⋊Q8—341no—
212C4×Q8—341no—
213C4×Q8—341no—
214C4×D4—21no—
215C4×D4—21no—
216C4×D4C4×D1712yes—
217C4×D4D6812yes—
218#117—341no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C22⋊D1711yescharacteristic
221C2×C22⋊C4—21no—
222C2×C42C22×D1711yescharacteristic
223#107—342no—
224#106—342no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—172no—
228C4⋊C8—341no—
229C4⋊C8—341no—
230C4⋊C8—341no—
231#102—42no—
232#102—342no—
233#102—342no—
234C22⋊C8—172no—
235C22⋊C8—344no—
236C22⋊C8—341no—
237C4×C8—172no—
238C4×C8—341no—
239#95—21no—
240#95—21no—
241C17#930311yescharacteristic, complemented, Sylow
242C24—21no—
243C2×Q8—341no—
244C2×Q8—341no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4#6322712yes—
249C2×D4#6322912yes—
250C2×D4#6323112yes—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—41no—
255C22×C4—82no—
256C22×C4D4×D1711yescharacteristic
257C22×C4#6325411yescharacteristic
258C22×C4C2×C22⋊D1711yescharacteristic
259M16—681no—
260M16—681no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—342no—
265C2×C8—342no—
266C2×C8—342no—
267C2×C8—1364no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—341no—
272C4⋊C4—341no—
273C4⋊C4—341no—
274C4⋊C4—341no—
275C4⋊C4—681no—
276C4⋊C4—681no—
277C4⋊C4#6322712yes—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C22⋊C4—681no—
281C42—681no—
282C42C2×C4×D1711yescharacteristic
283C42C2×D6811yescharacteristic
284C42D4×D1711yescharacteristic
285C42#6325411yescharacteristic
286C23—22no—
287C23—22no—
288C23—22no—
289C23—81no—
290C23—81no—
291C23#1058762511yescharacteristic
292Q8—682no—
293Q8—1361no—
294D4—22no—
295D4—22no—
296D4—22no—
297D4#1058748114yes—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—44no—
302C2×C4—82no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—681no—
308C2×C4—681no—
309C2×C4#1058756711yescharacteristic
310C2×C4#1058756711yescharacteristic
311C2×C4#1058756811yescharacteristic
312C2×C4#1058757211yescharacteristic
313C2×C4C2×#6322711yescharacteristic
314C2×C4C2×#6322911yescharacteristic
315C2×C4#1058762511yescharacteristic
316C2×C4C2×#6323111yescharacteristic
317C2×C4#1058763611yescharacteristic
318C2×C4#1058763611yescharacteristic
319C8—81no—
320C8—682no—
321C8—682no—
322C8—682no—
323C22—21no—
324C22—21no—
325C22—24no—
326C22—42no—
327C22—42no—
328C22—82no—
329C22—82no—
330C22#1176268611yescharacteristic
331C22#1176303611yescharacteristic
332C22#1176304811yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—161no—
339C4—1361no—
340C4—1361no—
341C4C2×#1058748111yescharacteristic
342C4#1176280311yescharacteristic
343C4#1176303611yescharacteristic
344C4#1176304811yescharacteristic
345C2—21no—
346C2—21no—
347C2—44no—
348C2#1452914411yescharacteristic
349C2#1452920511yescharacteristic
350C2#1452926911yescharacteristic
subgroupG/H
centerC22#11762686
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1804C2
socleC22×C17#386
prime radicalC22×D4×C17D4
cosocleC2×C42×C17C23
hypercenter#1804D17
hypocenterC17#9303
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
3. #14527347C2semidirect
4. #14527186C2semidirect
5. #14526681C2semidirect
6. #14526642C2semidirect
10. #11763099C4semidirect
11. #11763089C4semidirect
241. C17#9303semidirect

Maximal subgroups

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

subgroupindex
#145385812
#145378082
#145273472
#145271862
#145266812
#145266422
C17×#18042
#930317