Finite Group Databasebeta

← #16930862

Subgroups — #16930862

Order 4352.

428 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539925C211yesmaximal, characteristic
2#14529628C211yesmaximal, characteristic
3#14527474C211yesmaximal, characteristic
4C2×#11762556C211yesmaximal, characteristic
5#14526681C211yesmaximal, characteristic
6#14526635C211yesmaximal, characteristic
7C17×#2962C211yesmaximal, characteristic
8C2×#10587555C2211yescharacteristic
9#11763205—21no—
10#11763159—21no—
11#11763137C414yes—
12#11763094—22no—
13#11762862C2211yescharacteristic
14#11762833C2211yescharacteristic
15C2×C4⋊#3622C2211yescharacteristic
16C2×#10587495—21no—
17C2×#10587495—21no—
18#11762558—21no—
19#11762556—21no—
20#11762556—21no—
21#11762555—21no—
22C17×#533C2211yescharacteristic
23C17×#446—22no—
24C17×#446—21no—
25C8×Q8×C17—21no—
26C17×#424—21no—
27C2×C17×C4⋊C8C2211yescharacteristic
28C17×#405—21no—
29C4×M16×C17C2211yescharacteristic
30C22×Dic34—21no—
31C2×M16×C17D411yescharacteristic
32C2×M16×C17D411yescharacteristic
33C22×C8×C17—21no—
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×C4⋊Dic17—21no—
44C2×C4⋊Dic17C2×C412yes—
45C2×#63223—21no—
46C22×#3622—21no—
47#10587555—21no—
48#10587555—21no—
49#10587555—21no—
50#10587555—21no—
51C17×C4⋊C8—22no—
52C17×C4⋊C8—22no—
53C17×C4⋊C8—21no—
54C17×C4⋊C8D411yescharacteristic
55C17×C4⋊C8D411yescharacteristic
56C17×#97—22no—
57C17×#97—21no—
58C4×C8×C17—22no—
59C4×C8×C17—21no—
60#10587506—24no—
61C22⋊#3622C2×C412yes—
62#10587495—42no—
63#10587495—42no—
64#10587479—24no—
65C4⋊#3622—21no—
66C4⋊#3622—21no—
67C4⋊#3622—21no—
68C4⋊#3622—21no—
69C4⋊#3622—21no—
70C4×#3622—21no—
71C2×Q8×C17—21no—
72C2×Q8×C17C22⋊C412yes—
73C22×C4×C17C22×C411yescharacteristic
74C22×C4×C17C2×D411yescharacteristic
75C22×C4×C17#4111yescharacteristic
76C22×Dic17—22no—
77C2×Dic34—41no—
78C2×Dic34—41no—
79C2×Dic34—41no—
80C2×Dic34—41no—
81C2×Dic34—41no—
82C2×Dic34—41no—
83M16×C17—21no—
84M16×C17—21no—
85M16×C17—21no—
86M16×C17SD1612yes—
87C2×C8×C17—21no—
88C2×C8×C17—21no—
89C2×C8×C17—21no—
90C2×C8×C17—21no—
91C2×C8×C17—41no—
92C2×C8×C17—41no—
93C4⋊C4×C17—22no—
94C4⋊C4×C17—21no—
95C4⋊C4×C17—21no—
96C4⋊C4×C17—21no—
97C4⋊C4×C17—22no—
98C4⋊C4×C17C22⋊C412yes—
99C22⋊C4×C17—22no—
100C42×C17—22no—
101C42×C17C2×D411yescharacteristic
102C42×C17C2×D411yescharacteristic
103C42×C17C2×D411yescharacteristic
104C42×C17#4111yescharacteristic
105C4⋊Dic17—22no—
106C4⋊Dic17—22no—
107C4⋊Dic17—41no—
108C4⋊Dic17—41no—
109#63223—41no—
110#63223—41no—
111C2×#3622—22no—
112C2×#3622—41no—
113C2×#3622—41no—
114C2×#3622—81no—
115#9272—171nomaximal, Sylow
116C23×C17C4×D411yescharacteristic
117Q8×C17—42no—
118Q8×C17—41no—
119Q8×C17—41no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—22no—
123C2×C4×C17—22no—
124C2×C4×C17—41no—
125C2×C4×C17C2×C22⋊C411yescharacteristic
126C2×C4×C17C4×D411yescharacteristic
127C2×C4×C17#12011yescharacteristic
128C2×C4×C17#12111yescharacteristic
129C2×C4×C17#12111yescharacteristic
130C2×C4×C17#12311yescharacteristic
131C2×C4×C17C2×SD1611yescharacteristic
132C2×C4×C17#13511yescharacteristic
133C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C17#13711yescharacteristic
135C2×Dic17—42no—
136C2×Dic17—42no—
137C2×Dic17—42no—
138Dic34—81no—
139Dic34—81no—
140Dic34—81no—
141Dic34—81no—
142C8×C17—22no—
143C8×C17—41no—
144C8×C17—41no—
145C8×C17—41no—
146#3622—42no—
147#3622—81no—
148#3622—81no—
149#3229—171no—
150#2962D1711yescharacteristic
151#1966—171no—
152#1550—171no—
153C2×#332—171no—
154#1301—171no—
155#1283—171no—
156C22×C17—21no—
157C22×C17—21no—
158C22×C17#38611yescharacteristic
159C22×C17C4×SD1611yescharacteristic
160C22×C17#44011yescharacteristic
161C4×C17—21no—
162C4×C17—21no—
163C4×C17—21no—
164C4×C17—42no—
165C4×C17—42no—
166C4×C17#44811yescharacteristic
167C4×C17#44911yescharacteristic
168C4×C17#46011yescharacteristic
169C4×C17#46411yescharacteristic
170C4×C17#47111yescharacteristic
171C4×C17#47311yescharacteristic
172Dic17—82no—
173#533C2×D1711yescharacteristic
174C2×C4⋊Q8—171no—
175#498—341no—
176#487—341no—
177#483—174no—
178#475—342no—
179#446—22no—
180#446—21no—
181C8×Q8—21no—
182#431—171no—
183#424—21no—
184#423—171no—
185C2×C4⋊C8—171no—
186C2×C4⋊C8C2×D1711yescharacteristic
187C2×#101—341no—
188C2×#101—341no—
189#405—21no—
190C4×M16C2×D1711yescharacteristic
191#333—341no—
192#332—341no—
193#332—341no—
194#332—341no—
195C2×C17—21no—
196C2×C17—21no—
197C2×C17#188011yescharacteristic
198C2×C17#190811yescharacteristic
199C2×C17#191511yescharacteristic
200C22×Q8—341no—
201C2×M16—341no—
202C2×M16C22⋊D1711yescharacteristic
203C2×M16C22⋊D1711yescharacteristic
204C22×C8—21no—
205C22×C8—341no—
206C4⋊Q8—341no—
207C4⋊Q8—341no—
208C4⋊Q8—341no—
209C4⋊Q8—341no—
210C4⋊Q8D6811yescharacteristic
211C4⋊Q8D6811yescharacteristic
212#125—21no—
213C22⋊Q8—21no—
214C22⋊Q8C4×D1712yes—
215C4×Q8—21no—
216C4×Q8C22⋊D1712yes—
217#117—21no—
218C2×C4⋊C4—172no—
219C2×C4⋊C4—341no—
220C2×C42C22×D1711yescharacteristic
221#106—344no—
222C4⋊C8—22no—
223C4⋊C8—22no—
224C4⋊C8—21no—
225C4⋊C8—341no—
226C4⋊C8—341no—
227C4⋊C8—341no—
228C4⋊C8—341no—
229C4⋊C8—341no—
230C4⋊C8C22⋊D1711yescharacteristic
231C4⋊C8C22⋊D1711yescharacteristic
232#103—344no—
233#101—682no—
234#101—682no—
235C22⋊C8—172no—
236#97—22no—
237#97—21no—
238C4×C8—22no—
239C4×C8—21no—
240C4×C8—341no—
241C17#927211yescharacteristic, complemented, Sylow
242C2×Q8—21no—
243C2×Q8—681no—
244C2×Q8—681no—
245C2×Q8—681no—
246C2×Q8—681no—
247C2×Q8—681no—
248C2×Q8—681no—
249C2×Q8#6322712yes—
250C22×C4—342no—
251C22×C4C2×C4×D1711yescharacteristic
252C22×C4#6325211yescharacteristic
253C22×C4C2×C22⋊D1711yescharacteristic
254M16—21no—
255M16—21no—
256M16—21no—
257M16—681no—
258M16—681no—
259M16#6323012yes—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—342no—
267C2×C8—681no—
268C2×C8—681no—
269C2×C8—1361no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—342no—
276C4⋊C4—342no—
277C4⋊C4—681no—
278C4⋊C4—681no—
279C4⋊C4#6322712yes—
280C22⋊C4—22no—
281C42—22no—
282C42C2×D6811yescharacteristic
283C42#6325211yescharacteristic
284C42C2×C22⋊D1711yescharacteristic
285C42C2×C22⋊D1711yescharacteristic
286C23C4×C22⋊D1711yescharacteristic
287Q8—42no—
288Q8—41no—
289Q8—41no—
290Q8—1361no—
291Q8—1361no—
292Q8—1361no—
293Q8—1361no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—682no—
300C2×C4—682no—
301C2×C4—682no—
302C2×C4C2×#6322711yescharacteristic
303C2×C4C4×C22⋊D1711yescharacteristic
304C2×C4#1058761511yescharacteristic
305C2×C4#1058761611yescharacteristic
306C2×C4#1058761611yescharacteristic
307C2×C4C2×#6323011yescharacteristic
308C2×C4#1058762811yescharacteristic
309C2×C4#1058763511yescharacteristic
310C2×C4#1058763611yescharacteristic
311C2×C4#1058763911yescharacteristic
312C8—22no—
313C8—41no—
314C8—41no—
315C8—41no—
316C8—682no—
317C8—1361no—
318C8—1361no—
319C22—21no—
320C22—21no—
321C22#1176268811yescharacteristic
322C22C4×#6323011yescharacteristic
323C22#1176290711yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—42no—
328C4—42no—
329C4—1362no—
330C4#1176294811yescharacteristic
331C4#1176295411yescharacteristic
332C4#1176300911yescharacteristic
333C4#1176303111yescharacteristic
334C4#1176307211yescharacteristic
335C4#1176308411yescharacteristic
336C2—21no—
337C2—21no—
338C2#1452913911yescharacteristic
339C2#1452929911yescharacteristic
340C2#1452933611yescharacteristic
subgroupG/H
centerC22#11762688
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2962C2
socleC22×C17#386
prime radicalC23×C17C4×D4
cosocleC2×C42×C17C23
hypercenter#2962D17
hypocenterC17#9272
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
241. C17#9272semidirect

Maximal subgroups

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

subgroupindex
#145399252
#145296282
#145274742
C2×#117625562
#145266812
#145266352
C17×#29622
#927217