Finite Group Databasebeta

← #16945484

Subgroups — #16945484

Order 4352.

440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533960C211yesmaximal, characteristic
2#14528776C211yesmaximal, characteristic
3#14526815C212yesmaximal, complemented
4#14526812C212yesmaximal, complemented
5C17×#1459C211yesmaximal, characteristic
6C2×#10587610C411yescharacteristic
7#11762833—21no—
8C2×#10587504—21no—
9#11762748C2211yescharacteristic
10#11762745C411yescharacteristic
11#11762729C2211yescharacteristic
12#11762721C411yescharacteristic
13#11762693—21no—
14#11762689—21no—
15#11762682—21no—
16#11762667—21no—
17C2×#10587502C411yescharacteristic
18#11762578C2212yes—
19C2×C4×D4×C17C2211yescharacteristic
20C2×C17×C22⋊C8—21no—
21C17×#324C2212yes—
22C17×#323—21no—
23C22×D4×C17D411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C23×Dic17—21no—
27C22×Dic34C2×C411yescharacteristic
28C22×C8×C17—41no—
29C4×D4×C17—41no—
30C4×D4×C17—41no—
31C2×C4⋊C4×C17C2311yescharacteristic
32C2×C22⋊C4×C17C2×C411yescharacteristic
33C2×C22⋊C4×C17D411yescharacteristic
34C2×C42×C17D411yescharacteristic
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38C2×C4⋊Dic17C2×C411yescharacteristic
39#10587610—41no—
40#10587610—41no—
41C2×#63225—21no—
42C2×#63225—21no—
43C2×#63225—21no—
44C2×#63223—22no—
45C17×C22⋊C8—22no—
46C17×C22⋊C8—41no—
47#10587504—42no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502C2×C411yescharacteristic
54#10587502C2×C411yescharacteristic
55C4⋊#3622—41no—
56C4⋊#3622—41no—
57C24×C17C22⋊C411yescharacteristic
58C24×C17C22⋊C411yescharacteristic
59C2×D4×C17—41no—
60C2×D4×C17—41no—
61C2×D4×C17SD1612yes—
62C2×D4×C17Q1612yes—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—81no—
68C22×C4×C17—81no—
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22×C411yescharacteristic
72C22×C4×C17C2×D411yescharacteristic
73C22×C4×C17C2×D411yescharacteristic
74C22×Dic17—21no—
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17—21no—
78C22×Dic17—42no—
79C22×Dic17—42no—
80C22×Dic17—81no—
81C2×Dic34—41no—
82C2×Dic34—81no—
83C2×C8×C17—42no—
84C2×C8×C17—82no—
85C4⋊C4×C17—41no—
86C22⋊C4×C17—41no—
87C22⋊C4×C17—41no—
88C42×C17—21no—
89C42×C17—21no—
90C22⋊Dic17—42no—
91C22⋊Dic17—42no—
92C22⋊Dic17—81no—
93C4⋊Dic17—41no—
94#63225—42no—
95#63225—41no—
96#63225—41no—
97#63225—81no—
98#63223—42no—
99#63223—42no—
100C2×#3622—42no—
101#11906—171nomaximal, Sylow
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—21no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17—41no—
110C23×C17#10312yes—
111C23×C17#10312yes—
112C23×C17C2×C22⋊C411yescharacteristic
113D4×C17—42no—
114D4×C17—42no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—41no—
121C2×C4×C17—42no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—81no—
126C2×C4×C17—81no—
127C2×C4×C17—81no—
128C2×C4×C17#9911yescharacteristic
129C2×C4×C17#9911yescharacteristic
130C2×C4×C17C2×SD1611yescharacteristic
131C2×C4×C17C2×Q1611yescharacteristic
132C2×Dic17—22no—
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—
144C2×Dic17—84no—
145Dic34—82no—
146C8×C17—82no—
147#3622—82no—
148#2564—171no—
149#1800—171no—
150#1459D1711yescharacteristic
151#1354—172no—
152#1353—172no—
153C22×C17—21no—
154C22×C17—21no—
155C22×C17—22no—
156C22×C17—22no—
157C22×C17—42no—
158C22×C17—42no—
159C22×C17—42no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17—41no—
164C22×C17—81no—
165C22×C17C2×#9911yescharacteristic
166C22×C17C2×#10311yescharacteristic
167C22×C17#42111yescharacteristic
168C4×C17—21no—
169C4×C17—21no—
170C4×C17—21no—
171C4×C17—21no—
172C4×C17—41no—
173C4×C17—41no—
174C4×C17—41no—
175Dic17—42no—
176Dic17—81no—
177Dic17—81no—
178Dic17—81no—
179C2×C22⋊Q8—171no—
180C2×C4×D4C2×D1711yescharacteristic
181#423—341no—
182C2×#100—341no—
183C2×C22⋊C8—21no—
184#400—171no—
185#399—171no—
186#395—171no—
187#393—171no—
188#387—341no—
189#386—341no—
190#385—341no—
191#380—341no—
192C2×#95—171no—
193#343—172no—
194#324C2×D1712yes—
195#323—21no—
196C2×C17—21no—
197C2×C17—21no—
198C2×C17—42no—
199C2×C17—42no—
200C2×C17#152011yescharacteristic
201C2×C17#212111yescharacteristic
202C2×C17#213211yescharacteristic
203C22×Q8—171no—
204C22×D4D6811yescharacteristic
205C23×C4—341no—
206C23×C4C4×D1711yescharacteristic
207C23×C4C22⋊D1711yescharacteristic
208C2×M16—342no—
209C22×C8—41no—
210C22⋊Q8—681no—
211C22⋊Q8—681no—
212C4×D4—41no—
213C4×D4—41no—
214C2×C4⋊C4—171no—
215C2×C4⋊C4—341no—
216C2×C4⋊C4—341no—
217C2×C4⋊C4—341no—
218C2×C4⋊C4C22×D1711yescharacteristic
219C2×C22⋊C4—341no—
220C2×C22⋊C4—341no—
221C2×C22⋊C4—341no—
222C2×C22⋊C4C4×D1711yescharacteristic
223C2×C22⋊C4C22⋊D1711yescharacteristic
224C2×C42D6811yescharacteristic
225C4⋊C8—681no—
226C4⋊C8—681no—
227#100—682no—
228C22⋊C8—22no—
229C22⋊C8—41no—
230#95—171no—
231#95—171no—
232#95—341no—
233#95—341no—
234#95—341no—
235#95—341no—
236#95—341no—
237C17#1190611yescharacteristic, complemented, Sylow
238C24#6322711yescharacteristic
239C24#6322711yescharacteristic
240C2×Q8—681no—
241C2×Q8—1361no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4#6321912yes—
245C2×D4Dic6812yes—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—341no—
253C22×C4—341no—
254C22×C4—341no—
255C22×C4—341no—
256C22×C4—682no—
257C22×C4—682no—
258C22×C4—1361no—
259C22×C4#6322711yescharacteristic
260C22×C4#6322711yescharacteristic
261C22×C4C2×C4×D1711yescharacteristic
262C22×C4C2×D6811yescharacteristic
263C22×C4C2×C22⋊D1711yescharacteristic
264M16—682no—
265M16—682no—
266C2×C8—42no—
267C2×C8—82no—
268C2×C8—682no—
269C4⋊C4—41no—
270C4⋊C4—681no—
271C4⋊C4—682no—
272C4⋊C4—681no—
273C4⋊C4—681no—
274C4⋊C4—1361no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—682no—
278C22⋊C4—682no—
279C22⋊C4—1361no—
280C42—21no—
281C42—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23#1058748712yes—
291C23#1058748712yes—
292C23C2×#6322711yescharacteristic
293Q8—1362no—
294D4—42no—
295D4—42no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—342no—
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—681no—
319C2×C4—681no—
320C2×C4—681no—
321C2×C4—1364no—
322C2×C4#1058747711yescharacteristic
323C2×C4#1058747711yescharacteristic
324C2×C4C2×#6321911yescharacteristic
325C2×C4C2×Dic6811yescharacteristic
326C8—82no—
327C8—1362no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—22no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—81no—
340C22C2×#1058747711yescharacteristic
341C22C2×#1058748711yescharacteristic
342C22#1176282511yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—682no—
351C4—1361no—
352C4—1361no—
353C4—1361no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—42no—
358C2#1452735711yescharacteristic
359C2#1453042811yescharacteristic
360C2#1453046711yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1459C2
socleC22×C17C2×#99
prime radicalC22×D4×C17D4
cosocleC2×C4⋊C4×C17C23
hypercenter#1459D17
hypocenterC17#11906
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #14526815C2semidirect
4. #14526812C2semidirect
237. C17#11906semidirect

Maximal subgroups

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

subgroupindex
#145339602
#145287762
#145268152
#145268122
C17×#14592
#1190617