Finite Group Databasebeta

← #16922938

Subgroups — #16922938

Order 4352.

464 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537123C211yesmaximal, characteristic
2#14528764C211yesmaximal, characteristic
3#14526609C212yesmaximal, complemented
4#14526608C212yesmaximal, complemented
5C17×#1797C211yesmaximal, characteristic
6C2×#10587610C411yescharacteristic
7C2×C4⋊#3622—21no—
8C2×C22⋊#3622—21no—
9#11762715C411yescharacteristic
10#11762715C2211yescharacteristic
11#11762707C411yescharacteristic
12#11762707C2211yescharacteristic
13#11762693—21no—
14#11762693—21no—
15#11762682—21no—
16#11762672—21no—
17#11762669C411yescharacteristic
18#11762564C2212yes—
19C22×C42×C17C2211yescharacteristic
20C2×C17×C4⋊C8—21no—
21C2×C17×C22⋊C8—21no—
22C17×#336C2212yes—
23C23×C4×C17C2×C411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C22×Dic34C2×C411yescharacteristic
27C22×C8×C17—22no—
28C2×C42×C17—42no—
29C2×C42×C17C2×C411yescharacteristic
30C2×C42×C17D411yescharacteristic
31C2×C42×C17D411yescharacteristic
32C2×C42×C17C2311yescharacteristic
33C2×C22⋊Dic17—21no—
34C2×C22⋊Dic17—21no—
35C2×C4⋊Dic17C2×C411yescharacteristic
36C2×C4⋊Dic17C2×C411yescharacteristic
37C2×C4⋊Dic17C2×C411yescharacteristic
38#10587610—42no—
39C2×#63225—21no—
40C2×#63225—21no—
41C2×#63225—21no—
42C22×#3622—22no—
43C17×C4⋊C8—42no—
44C17×C22⋊C8—42no—
45#10587502—21no—
46#10587502—21no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52C22⋊#3622—42no—
53C4⋊#3622—42no—
54C24×C17C22⋊C411yescharacteristic
55C22×C4×C17—22no—
56C22×C4×C17—22no—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—41no—
60C22×C4×C17—41no—
61C22×C4×C17—41no—
62C22×C4×C17—41no—
63C22×C4×C17—41no—
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17SD1612yes—
68C22×C4×C17Q1612yes—
69C22×C4×C17C22×C411yescharacteristic
70C22×C4×C17C2×D411yescharacteristic
71C22×C4×C17C2×D411yescharacteristic
72C22×Dic17—21no—
73C22×Dic17—21no—
74C22×Dic17—21no—
75C22×Dic17—21no—
76C2×Dic34—22no—
77C2×Dic34—41no—
78C2×Dic34—41no—
79C2×C8×C17—42no—
80C2×C8×C17—42no—
81C2×C8×C17—42no—
82C42×C17—22no—
83C42×C17—22no—
84C42×C17—41no—
85C42×C17—41no—
86C22⋊Dic17—42no—
87C22⋊Dic17—42no—
88C4⋊Dic17—22no—
89C4⋊Dic17—41no—
90C4⋊Dic17—41no—
91#63225—42no—
92#63225—42no—
93#63225—41no—
94#63225—41no—
95C2×#3622—42no—
96C2×#3622—42no—
97C2×#3622—42no—
98#7715—171nomaximal, Sylow
99C23×C17—21no—
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—21no—
105C23×C17#10312yes—
106C23×C17C2×C22⋊C411yescharacteristic
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—42no—
121C2×C4×C17—42no—
122C2×C4×C17—44no—
123C2×C4×C17—42no—
124C2×C4×C17—42no—
125C2×C4×C17#9912yes—
126C2×C4×C17#10312yes—
127C2×C4×C17#13112yes—
128C2×C4×C17C2×SD1611yescharacteristic
129C2×C4×C17C2×Q1611yescharacteristic
130C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C17#13711yescharacteristic
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144Dic34—82no—
145C8×C17—82no—
146#3622—82no—
147#2855—171no—
148#1797—171no—
149#1797D1711yescharacteristic
150#1272—172no—
151#1271—172no—
152C22×C17—22no—
153C22×C17—22no—
154C22×C17—22no—
155C22×C17—41no—
156C22×C17—41no—
157C22×C17—41no—
158C22×C17—41no—
159C22×C17#40811yescharacteristic
160C22×C17C2×#9911yescharacteristic
161C22×C17#41311yescharacteristic
162C22×C17C2×#10311yescharacteristic
163C22×C17#41711yescharacteristic
164C22×C17#42111yescharacteristic
165C22×C17#42111yescharacteristic
166C4×C17—22no—
167C4×C17—22no—
168C4×C17—21no—
169C4×C17—21no—
170C4×C17—21no—
171C4×C17—22no—
172C4×C17—21no—
173C4×C17—41no—
174Dic17—81no—
175Dic17—81no—
176Dic17—81no—
177Dic17—81no—
178C2×C22⋊Q8—171no—
179C22×C42C2×D1711yescharacteristic
180C2×C4⋊C8—21no—
181C2×C4⋊C8—341no—
182C2×C22⋊C8—21no—
183C2×C22⋊C8—341no—
184#391—171no—
185#391—171no—
186#389—171no—
187#389—171no—
188#387—341no—
189#387—341no—
190#385—341no—
191#381—341no—
192#380—171no—
193#336—172no—
194#336C2×D1712yes—
195C2×C17—42no—
196C2×C17#146811yescharacteristic
197C2×C17#148111yescharacteristic
198C2×C17#149511yescharacteristic
199C2×C17#151311yescharacteristic
200C2×C17#152011yescharacteristic
201C2×C17#153511yescharacteristic
202C2×C17#155011yescharacteristic
203C22×Q8—171no—
204C23×C4C4×D1711yescharacteristic
205C23×C4D6811yescharacteristic
206C23×C4C22⋊D1711yescharacteristic
207C22×C8—22no—
208C22×C8—342no—
209C22⋊Q8—682no—
210C2×C4⋊C4—171no—
211C2×C4⋊C4—171no—
212C2×C4⋊C4—171no—
213C2×C4⋊C4—341no—
214C2×C4⋊C4—341no—
215C2×C4⋊C4—341no—
216C2×C22⋊C4—341no—
217C2×C22⋊C4—341no—
218C2×C42—42no—
219C2×C42C4×D1711yescharacteristic
220C2×C42D6811yescharacteristic
221C2×C42C22⋊D1711yescharacteristic
222C2×C42C22×D1711yescharacteristic
223C4⋊C8—42no—
224C4⋊C8—682no—
225C22⋊C8—42no—
226C22⋊C8—682no—
227#95—341no—
228#95—341no—
229#95—341no—
230#95—341no—
231#95—341no—
232#95—341no—
233#95—341no—
234C17#771511yescharacteristic, complemented, Sylow
235C24#6322711yescharacteristic
236C2×Q8—342no—
237C2×Q8—681no—
238C2×Q8—681no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—341no—
249C22×C4—341no—
250C22×C4—341no—
251C22×C4—341no—
252C22×C4#6321912yes—
253C22×C4Dic6812yes—
254C22×C4#6322711yescharacteristic
255C22×C4#6322711yescharacteristic
256C22×C4#6322711yescharacteristic
257C22×C4C2×C4×D1711yescharacteristic
258C22×C4C2×D6811yescharacteristic
259C22×C4C2×C22⋊D1711yescharacteristic
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—682no—
264C2×C8—682no—
265C2×C8—682no—
266C4⋊C4—342no—
267C4⋊C4—681no—
268C4⋊C4—681no—
269C4⋊C4—682no—
270C4⋊C4—682no—
271C4⋊C4—681no—
272C4⋊C4—681no—
273C22⋊C4—682no—
274C22⋊C4—682no—
275C42—22no—
276C42—22no—
277C42—41no—
278C42—41no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23#1058748712yes—
286C23C2×#6322711yescharacteristic
287Q8—1362no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—44no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—681no—
307C2×C4—681no—
308C2×C4—681no—
309C2×C4—681no—
310C2×C4—681no—
311C2×C4—681no—
312C2×C4—681no—
313C2×C4—681no—
314C2×C4—681no—
315C2×C4—681no—
316C2×C4—681no—
317C2×C4—681no—
318C2×C4#1058747712yes—
319C2×C4#1058748712yes—
320C2×C4C2×#6321911yescharacteristic
321C2×C4C2×Dic6811yescharacteristic
322C2×C4#1058759312yes—
323C2×C4#1058761811yescharacteristic
324C2×C4#1058762811yescharacteristic
325C8—82no—
326C8—1362no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22#1176277711yescharacteristic
335C22C2×#1058747711yescharacteristic
336C22#1176279111yescharacteristic
337C22C2×#1058748711yescharacteristic
338C22#1176280811yescharacteristic
339C22#1176282511yescharacteristic
340C22#1176282711yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—22no—
345C4—21no—
346C4—22no—
347C4—22no—
348C4—41no—
349C4—1361no—
350C4—1361no—
351C4—1361no—
352C4—1361no—
353C2—42no—
354C2#1452713311yescharacteristic
355C2#1452718811yescharacteristic
356C2#1452724711yescharacteristic
357C2#1452732511yescharacteristic
358C2#1452735711yescharacteristic
359C2#1452741311yescharacteristic
360C2#1452747211yescharacteristic
subgroupG/H
centerC23C2×#63227
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1797C2
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C42×C17C23
hypercenter#1797D17
hypocenterC17#7715
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #14526609C2semidirect
4. #14526608C2semidirect
234. C17#7715semidirect

Maximal subgroups

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

subgroupindex
#145371232
#145287642
#145266092
#145266082
C17×#17972
#771517