Finite Group Databasebeta

← #16945463

Subgroups — #16945463

Order 4352.

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

normal subgroups only

This group has 452 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#14527105C211yesmaximal, characteristic
3#14526807C212yesmaximal, complemented
4#14526804C212yesmaximal, complemented
5C17×#1799C211yesmaximal, characteristic
6C2×#10587610C411yescharacteristic, complemented
7#11762862—21no—
8#11762748C411yescharacteristic, complemented
9#11762745C2211yescharacteristic
10#11762729C411yescharacteristic, complemented
11#11762721C2211yescharacteristic
12#11762693—21no—
13#11762689—21no—
14#11762682—21no—
15#11762667—21no—
16C2×#10587502C411yescharacteristic, complemented
17#11762533—21no—
18#11762533C2212yes—
19C2×C4×D4×C17C2211yescharacteristic
20C2×C17×#99—21no—
21C17×#380—21no—
22C17×#342C2212yes—
23C22×D4×C17D411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C23×Dic17—21no—
27C22×Dic34C2×C411yescharacteristic
28C4×D4×C17—41no—
29C4×D4×C17—41no—
30C2×C4⋊C4×C17—41no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C22⋊C4×C17—22no—
33C2×C22⋊C4×C17D411yescharacteristic
34C2×C22⋊C4×C17C2311yescharacteristic
35C2×C42×C17D411yescharacteristic
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38C2×C22⋊Dic17—21no—
39C2×C4⋊Dic17C2×C411yescharacteristic
40#10587610—41no—
41#10587610—41no—
42C2×#63225—21no—
43C2×#63225—21no—
44C2×#63225—21no—
45C17×#99—42no—
46C17×#95—41no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502C2×C411yescharacteristic
53#10587502C2×C411yescharacteristic
54C22⋊#3622—22no—
55C4⋊#3622—41no—
56C4×#3622—41no—
57C24×C17C22⋊C411yescharacteristic
58C24×C17C2×D411yescharacteristic
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—42no—
68C22×C4×C17—81no—
69C22×C4×C17—81no—
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22×C411yescharacteristic
74C22×C4×C17C2×D411yescharacteristic
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17—21no—
78C22×Dic17—21no—
79C22×Dic17—42no—
80C22×Dic17—42no—
81C22×Dic17—81no—
82C2×Dic34—41no—
83C2×Dic34—81no—
84C4⋊C4×C17—41no—
85C4⋊C4×C17—82no—
86C22⋊C4×C17—41no—
87C22⋊C4×C17—41no—
88C22⋊C4×C17—42no—
89C22⋊C4×C17—42no—
90C42×C17—21no—
91C42×C17—21no—
92C22⋊Dic17—42no—
93C22⋊Dic17—42no—
94C22⋊Dic17—81no—
95C4⋊Dic17—41no—
96#63225—42no—
97#63225—41no—
98#63225—41no—
99#63225—81no—
100C2×#3622—42no—
101#11902—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×C17C2×C22⋊C411yescharacteristic
112C23×C17C2×SD1611yescharacteristic
113C23×C17C2×Q1611yescharacteristic
114D4×C17—42no—
115D4×C17—42no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—41no—
122C2×C4×C17—42no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—81no—
127C2×C4×C17—81no—
128C2×C4×C17—81no—
129C2×C4×C17—82no—
130C2×C4×C17—82no—
131C2×C4×C17—82no—
132C2×C4×C17#9911yescharacteristic
133C2×C4×C17#9911yescharacteristic
134C2×C4×C17#10312yes—
135C2×Dic17—22no—
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—41no—
145C2×Dic17—41no—
146C2×Dic17—41no—
147C2×Dic17—84no—
148Dic34—82no—
149#3622—82no—
150#2564—171no—
151#1799D1711yescharacteristic
152#1460—171no—
153#1352—172no—
154#1351—172no—
155C22×C17—21no—
156C22×C17—21no—
157C22×C17—21no—
158C22×C17—22no—
159C22×C17—21no—
160C22×C17—42no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17—42no—
164C22×C17—41no—
165C22×C17—41no—
166C22×C17—41no—
167C22×C17—41no—
168C22×C17—81no—
169C22×C17C2×#9911yescharacteristic
170C22×C17C2×#10311yescharacteristic
171C22×C17#42111yescharacteristic
172C4×C17—21no—
173C4×C17—21no—
174C4×C17—22no—
175C4×C17—41no—
176C4×C17—41no—
177C4×C17—41no—
178C4×C17—162no—
179Dic17—42no—
180Dic17—81no—
181Dic17—81no—
182Dic17—81no—
183C2×C22⋊Q8—171no—
184C2×C4×D4C2×D1711yescharacteristic
185#431—341no—
186C2×#99—21no—
187#400—171no—
188#399—171no—
189#395—171no—
190#393—171no—
191#387—341no—
192#386—341no—
193#385—341no—
194#380—21no—
195#380—341no—
196C2×#95—171no—
197#342C2×D1712yes—
198#323—172no—
199#323—341no—
200C2×C17—21no—
201C2×C17—21no—
202C2×C17—41no—
203C2×C17—42no—
204C2×C17—41no—
205C2×C17#152011yescharacteristic
206C2×C17#212111yescharacteristic
207C2×C17#212611yescharacteristic
208C22×Q8—171no—
209C22×D4C22⋊D1711yescharacteristic
210C23×C4—341no—
211C23×C4C4×D1711yescharacteristic
212C23×C4C22⋊D1711yescharacteristic
213C22⋊Q8—681no—
214C22⋊Q8—681no—
215C4×D4—41no—
216C4×D4—41no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4—171no—
219C2×C4⋊C4—341no—
220C2×C4⋊C4—341no—
221C2×C4⋊C4—341no—
222C2×C4⋊C4C4×D1711yescharacteristic
223C2×C22⋊C4—22no—
224C2×C22⋊C4—341no—
225C2×C22⋊C4—341no—
226C2×C22⋊C4—341no—
227C2×C22⋊C4D6811yescharacteristic
228C2×C22⋊C4C22×D1711yescharacteristic
229C2×C42D6811yescharacteristic
230C4⋊C8—681no—
231#99—42no—
232C22⋊C8—342no—
233C4×C8—681no—
234#95—41no—
235#95—171no—
236#95—171no—
237#95—341no—
238#95—341no—
239#95—341no—
240#95—341no—
241#95—341no—
242C17#1190211yescharacteristic, complemented, Sylow
243C24#6322711yescharacteristic
244C24C2×C22⋊D1711yescharacteristic
245C2×Q8—681no—
246C2×Q8—1361no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4#6322912yes—
250C2×D4#6323112yes—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4—341no—
259C22×C4—341no—
260C22×C4—341no—
261C22×C4—341no—
262C22×C4—682no—
263C22×C4—682no—
264C22×C4—1361no—
265C22×C4#6322711yescharacteristic
266C22×C4#6322711yescharacteristic
267C22×C4#6322711yescharacteristic
268C22×C4C2×C4×D1711yescharacteristic
269C22×C4C2×D6811yescharacteristic
270C2×C8—682no—
271C4⋊C4—41no—
272C4⋊C4—82no—
273C4⋊C4—681no—
274C4⋊C4—682no—
275C4⋊C4—681no—
276C4⋊C4—681no—
277C4⋊C4—1361no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—682no—
283C22⋊C4—682no—
284C22⋊C4—1361no—
285C42—21no—
286C42—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23#1058748112yes—
296C23C2×#6322711yescharacteristic
297C23C2×#6322911yescharacteristic
298C23C2×#6323111yescharacteristic
299Q8—1362no—
300D4—42no—
301D4—42no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—82no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4—342no—
319C2×C4—681no—
320C2×C4—681no—
321C2×C4—681no—
322C2×C4—681no—
323C2×C4—681no—
324C2×C4—681no—
325C2×C4—681no—
326C2×C4—681no—
327C2×C4—681no—
328C2×C4—681no—
329C2×C4—681no—
330C2×C4—1364no—
331C2×C4#1058747711yescharacteristic
332C2×C4#1058747711yescharacteristic
333C2×C4#1058748112yes—
334C8—1362no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—21no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—42no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—81no—
349C22C2×#1058747711yescharacteristic
350C22C2×#1058748111yescharacteristic
351C22#1176282711yescharacteristic
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—162no—
359C4—682no—
360C4—1361no—
361C4—1361no—
362C4—1361no—
363C2—21no—
364C2—21no—
365C2—41no—
366C2—42no—
367C2—41no—
368C2#1452735511yescharacteristic
369C2#1453042811yescharacteristic
370C2#1453044711yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1799C2
socleC22×C17C2×#99
prime radicalC22×D4×C17D4
cosocleC2×C22⋊C4×C17C23
hypercenter#1799D17
hypocenterC17#11902
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #14526807C2semidirect
4. #14526804C2semidirect
6. C2×#10587610C4semidirect
8. #11762748C4semidirect
10. #11762729C4semidirect
16. C2×#10587502C4semidirect
242. C17#11902semidirect

Maximal subgroups

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

subgroupindex
#145339602
#145271052
#145268072
#145268042
C17×#17992
#1190217