Finite Group Databasebeta

← #16944803

Subgroups — #16944803

Order 4352.

486 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 83 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#14534471C211yesmaximal, characteristic
2#14527118C211yesmaximal, characteristic, complemented
3#14526804C212yesmaximal, complemented
4#14526780C212yesmaximal
5C17×#1740C211yesmaximal, characteristic, complemented
6C2×#10587561C411yescharacteristic, complemented
7#11762866—21no—
8#11762729C411yescharacteristic, complemented
9#11762726C411yescharacteristic, complemented
10#11762721C2211yescharacteristic
11#11762718C2211yescharacteristic
12#11762709—21no—
13#11762700—21no—
14#11762699—21no—
15#11762688—21no—
16#11762655C411yescharacteristic, complemented
17#11762535—21no—
18#11762533C2212yes—
19C2×C17×#117—21no—
20C2×C17×#117C2211yescharacteristic
21C17×#342—21no—
22C17×#342C2212yes—
23C23×C4×C17D411yescharacteristic
24C22×C22⋊D17—21no—
25C22×D68C2×C411yescharacteristic
26C22×Dic34C2×C411yescharacteristic
27C17×#117—24no—
28C17×#117—41no—
29C17×#117—41no—
30C17×#117—42no—
31C2×C4⋊C4×C17—41no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C22⋊C4×C17—22no—
35C2×C22⋊C4×C17D411yescharacteristic
36C2×C22⋊C4×C17C2311yescharacteristic
37C2×C42×C17—41no—
38C2×C42×C17C2×C411yescharacteristic
39C2×C42×C17D411yescharacteristic
40C2×C22⋊Dic17—21no—
41C2×#63227—21no—
42C2×#63227—21no—
43C2×#63227—21no—
44C2×#63227—21no—
45C2×#63227—21no—
46C2×#63225—21no—
47C2×C4×Dic17—21no—
48#10587561—41no—
49#10587561—41no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502C2×C411yescharacteristic
54#10587502C2×C411yescharacteristic
55C22⋊#3622—22no—
56C4⋊#3622—41no—
57#10587474—41no—
58C24×C17C2×D411yescharacteristic
59C23×D17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—22no—
65C22×C4×C17—42no—
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C22⋊C411yescharacteristic
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22×C411yescharacteristic
71C22×C4×C17C2×D411yescharacteristic
72C2×C22⋊D17—42no—
73C2×C22⋊D17—41no—
74C2×C22⋊D17—41no—
75C2×C22⋊D17—81no—
76C22×Dic17—21no—
77C22×Dic17—21no—
78C22×Dic17—21no—
79C2×D68—41no—
80C2×D68—81no—
81C2×Dic34—41no—
82C2×Dic34—81no—
83C4⋊C4×C17—41no—
84C4⋊C4×C17—41no—
85C4⋊C4×C17—44no—
86C22⋊C4×C17—24no—
87C22⋊C4×C17—41no—
88C22⋊C4×C17—41no—
89C22⋊C4×C17—42no—
90C42×C17—21no—
91C42×C17—21no—
92C42×C17—21no—
93C42×C17—21no—
94C42×C17—44no—
95C22⋊Dic17—81no—
96#63227—42no—
97#63227—42no—
98#63227—41no—
99#63227—41no—
100#63227—42no—
101#63227—81no—
102#63225—81no—
103C4×Dic17—42no—
104C2×#3622—42no—
105#11758—171nomaximal, Sylow
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—41no—
109C23×C17—41no—
110C23×C17C2×C22⋊C411yescharacteristic
111C23×C17AGL(1,ℤ/8)11yescharacteristic
112C23×C17#13711yescharacteristic
113C22×D17—41no—
114C22×D17—41no—
115C22×D17—41no—
116C22×D17—41no—
117C22×D17—41no—
118C22×D17—41no—
119C22×D17—41no—
120C2×C4×C17—22no—
121C2×C4×C17—22no—
122C2×C4×C17—22no—
123C2×C4×C17—22no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—44no—
137C2×C4×C17—82no—
138C2×C4×C17—82no—
139C2×C4×C17#9911yescharacteristic
140C2×C4×C17#9911yescharacteristic
141C2×C4×C17#10412yes—
142C22⋊D17—82no—
143C22⋊D17—82no—
144C2×Dic17—22no—
145C2×Dic17—41no—
146C2×Dic17—41no—
147C2×Dic17—41no—
148C2×Dic17—41no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153D68—82no—
154Dic34—82no—
155#3622—82no—
156#2610—171no—
157#1740D1711yescharacteristic, complemented
158#1464—171no—
159#1351—172no—
160#1343—172no—
161C22×C17—21no—
162C22×C17—21no—
163C22×C17—21no—
164C22×C17—21no—
165C22×C17—41no—
166C22×C17—41no—
167C22×C17—41no—
168C22×C17—41no—
169C22×C17—81no—
170C22×C17C2×#9911yescharacteristic
171C22×C17#41711yescharacteristic
172C22×C17C2×#10411yescharacteristic
173C2×D17—81no—
174C2×D17—81no—
175C2×D17—81no—
176C2×D17—81no—
177C2×D17—81no—
178C2×D17—81no—
179C2×D17—81no—
180C4×C17—21no—
181C4×C17—21no—
182C4×C17—22no—
183C4×C17—41no—
184C4×C17—41no—
185C4×C17—41no—
186C4×C17—41no—
187C4×C17—84no—
188Dic17—42no—
189Dic17—81no—
190Dic17—81no—
191C2×#124—171no—
192C2×#117—21no—
193C2×#117C2×D1711yescharacteristic
194#432—341no—
195#395—171no—
196#394—171no—
197#393—171no—
198#392—171no—
199#390—341no—
200#388—341no—
201#388—341no—
202#386—341no—
203#376—171no—
204#342—21no—
205#342C2×D1712yes—
206#324—341no—
207#323—172no—
208C2×C17—21no—
209C2×C17—21no—
210C2×C17—41no—
211C2×C17—41no—
212C2×C17#150411yescharacteristic
213C2×C17#212211yescharacteristic
214C2×C17#212611yescharacteristic
215D17—161no—
216C22×Q8—171no—
217C22×D4—171no—
218C22×D4—341no—
219C23×C4C22⋊D1711yescharacteristic
220#124—681no—
221#124—681no—
222#117—24no—
223#117—41no—
224#117—41no—
225#117—42no—
226C2×C4⋊C4—41no—
227C2×C4⋊C4—341no—
228C2×C4⋊C4C4×D1711yescharacteristic
229C2×C4⋊C4D6811yescharacteristic
230C2×C22⋊C4—22no—
231C2×C22⋊C4—341no—
232C2×C22⋊C4—341no—
233C2×C22⋊C4—341no—
234C2×C22⋊C4—341no—
235C2×C22⋊C4—341no—
236C2×C22⋊C4—341no—
237C2×C22⋊C4C22⋊D1711yescharacteristic
238C2×C22⋊C4C22×D1711yescharacteristic
239C2×C42—41no—
240C2×C42—341no—
241C2×C42C4×D1711yescharacteristic
242C2×C42D6811yescharacteristic
243C4⋊C8—681no—
244C22⋊C8—342no—
245#97—681no—
246#95—171no—
247#95—171no—
248#95—341no—
249#95—341no—
250#95—341no—
251C17#1175811yescharacteristic, complemented, Sylow
252C24—341no—
253C24C2×C22⋊D1711yescharacteristic
254C2×Q8—681no—
255C2×Q8—1361no—
256C2×D4—681no—
257C2×D4—682no—
258C2×D4—681no—
259C2×D4—681no—
260C2×D4—1361no—
261C2×D4—1361no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—42no—
268C22×C4—341no—
269C22×C4—341no—
270C22×C4—341no—
271C22×C4#6322711yescharacteristic
272C22×C4#6322711yescharacteristic
273C22×C4#6322711yescharacteristic
274C22×C4#6322711yescharacteristic
275C22×C4C2×C4×D1711yescharacteristic
276C22×C4C2×D6811yescharacteristic
277C2×C8—682no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—44no—
281C4⋊C4—1361no—
282C22⋊C4—24no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—42no—
286C22⋊C4—682no—
287C22⋊C4—682no—
288C22⋊C4—682no—
289C22⋊C4—681no—
290C22⋊C4—681no—
291C22⋊C4—1361no—
292C22⋊C4—1361no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—21no—
297C42—44no—
298C42—682no—
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23—681no—
304C23—681no—
305C23—681no—
306C23—681no—
307C23—681no—
308C23—681no—
309C23—681no—
310C23C2×#6322711yescharacteristic
311C23#1058761811yescharacteristic
312C23#1058762811yescharacteristic
313Q8—1362no—
314D4—1362no—
315D4—1362no—
316D4—1362no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—44no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—342no—
337C2×C4—681no—
338C2×C4—681no—
339C2×C4—681no—
340C2×C4—681no—
341C2×C4—681no—
342C2×C4—681no—
343C2×C4—681no—
344C2×C4—681no—
345C2×C4#1058747612yes—
346C2×C4#1058747711yescharacteristic
347C2×C4#1058747711yescharacteristic
348C8—1362no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—81no—
358C22—1361no—
359C22—1361no—
360C22—1361no—
361C22—1361no—
362C22—1361no—
363C22—1361no—
364C22—1361no—
365C22C2×#1058747711yescharacteristic
366C22#1176280811yescharacteristic
367C22C2×#1058747611yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—84no—
376C4—682no—
377C4—1361no—
378C4—1361no—
379C2—21no—
380C2—21no—
381C2—41no—
382C2—41no—
383C2—2721no—
384C2#1452728611yescharacteristic
385C2#1453043311yescharacteristic
386C2#1453044711yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1740C2
socleC22×C17C2×#99
prime radical#11762718C22
cosocleC2×C22⋊C4×C17C23
hypercenter#1740D17
hypocenterC17#11758
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1740

Complements

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

NH ≅ G/Ntype
2. #14527118C2semidirect
3. #14526804C2semidirect
5. C17×#1740C2semidirect
6. C2×#10587561C4semidirect
8. #11762729C4semidirect
9. #11762726C4semidirect
16. #11762655C4semidirect
157. #1740D17semidirect
251. C17#11758semidirect

Maximal subgroups

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

subgroupindex
#145344712
#145271182
#145268042
#145267802
C17×#17402
#1175817