Finite Group Databasebeta

← #16945353

Subgroups — #16945353

Order 4352.

522 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 103 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#14528772C211yesmaximal, characteristic, complemented
2#14527105C211yesmaximal, characteristic, complemented
3#14526784C212yesmaximal, complemented
4#14526781C212yesmaximal, complemented
5C17×#2543C211yesmaximal, characteristic
6#11762862—21no—
7C2×#10587505—21no—
8#11762669—21no—
9#11762576C2212yes—
10#11762533—21no—
11#11762533C2212yes—
12C2×C17×#121—21no—
13C2×C17×#121C411yescharacteristic, complemented
14C2×C4×D4×C17C2211yescharacteristic
15C17×#398C411yescharacteristic, complemented
16C17×#397C2211yescharacteristic
17C17×#394C411yescharacteristic, complemented
18C17×#392C2211yescharacteristic
19C17×#388—21no—
20C17×#386—21no—
21C17×#386—21no—
22C2×C17×#95C411yescharacteristic, complemented
23C22×D4×C17—21no—
24C22×D4×C17—21no—
25C22×D4×C17C2×C411yescharacteristic
26C22×D4×C17D411yescharacteristic
27C23×C4×C17—21no—
28C23×C4×C17C2×C411yescharacteristic
29C23×C4×C17D411yescharacteristic
30C17×#121—42no—
31C17×#121—42no—
32C17×#121—41no—
33C17×#121—41no—
34C4×D4×C17—41no—
35C4×D4×C17—41no—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17C2×C411yescharacteristic
38C2×C4⋊C4×C17C2×C411yescharacteristic
39C2×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17—21no—
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17—21no—
43C2×C22⋊C4×C17—21no—
44C2×C22⋊C4×C17D411yescharacteristic
45C2×C22⋊C4×C17C2311yescharacteristic
46C2×C42×C17D411yescharacteristic
47C2×C22⋊Dic17—22no—
48C2×C4⋊Dic17—41no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95—21no—
52C17×#95C2×C411yescharacteristic
53C17×#95C2×C411yescharacteristic
54#10587505—42no—
55#10587502—41no—
56C22⋊#3622—22no—
57C4⋊#3622—41no—
58C4×#3622—41no—
59C24×C17—21no—
60C24×C17C22⋊C411yescharacteristic
61C24×C17C2×D411yescharacteristic
62C2×D4×C17—41no—
63C2×D4×C17—41no—
64C2×D4×C17—41no—
65C2×D4×C17—42no—
66C2×D4×C17—42no—
67C2×D4×C17—42no—
68C2×D4×C17—42no—
69C2×D4×C17—41no—
70C2×D4×C17—41no—
71C2×D4×C17—81no—
72C2×D4×C17—81no—
73C2×D4×C17D812yes—
74C2×D4×C17SD1612yes—
75C22×C4×C17—21no—
76C22×C4×C17—21no—
77C22×C4×C17—21no—
78C22×C4×C17—21no—
79C22×C4×C17—21no—
80C22×C4×C17—21no—
81C22×C4×C17—21no—
82C22×C4×C17—42no—
83C22×C4×C17—42no—
84C22×C4×C17—81no—
85C22×C4×C17—81no—
86C22×C4×C17—81no—
87C22×C4×C17C22⋊C411yescharacteristic
88C22×C4×C17C22⋊C411yescharacteristic
89C22×C4×C17C22⋊C411yescharacteristic
90C22×C4×C17C22×C411yescharacteristic
91C22×C4×C17C2×D411yescharacteristic
92C22×Dic17—42no—
93C4⋊C4×C17—41no—
94C4⋊C4×C17—41no—
95C4⋊C4×C17—42no—
96C22⋊C4×C17—41no—
97C22⋊C4×C17—41no—
98C22⋊C4×C17—42no—
99C22⋊C4×C17—41no—
100C22⋊C4×C17—41no—
101C22⋊C4×C17—41no—
102C22⋊C4×C17—41no—
103C22⋊C4×C17—42no—
104C22⋊C4×C17—81no—
105C42×C17—21no—
106C42×C17—21no—
107C22⋊Dic17—42no—
108C22⋊Dic17—42no—
109C4⋊Dic17—82no—
110C2×#3622—42no—
111#11876—171nomaximal, Sylow
112C23×C17—21no—
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—41no—
117C23×C17—41no—
118C23×C17—41no—
119C23×C17—41no—
120C23×C17—41no—
121C23×C17—41no—
122C23×C17—41no—
123C23×C17—41no—
124C23×C17—41no—
125C23×C17—41no—
126C23×C17—41no—
127C23×C17#10212yes—
128C23×C17C2×C22⋊C411yescharacteristic
129C23×C17C2×D811yescharacteristic
130C23×C17C2×SD1611yescharacteristic
131D4×C17—42no—
132D4×C17—42no—
133D4×C17—82no—
134D4×C17—82no—
135D4×C17—82no—
136D4×C17—84no—
137C2×C4×C17—21no—
138C2×C4×C17—21no—
139C2×C4×C17—22no—
140C2×C4×C17—21no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—41no—
144C2×C4×C17—42no—
145C2×C4×C17—41no—
146C2×C4×C17—41no—
147C2×C4×C17—41no—
148C2×C4×C17—41no—
149C2×C4×C17—41no—
150C2×C4×C17—41no—
151C2×C4×C17—41no—
152C2×C4×C17—41no—
153C2×C4×C17—41no—
154C2×C4×C17—41no—
155C2×C4×C17—41no—
156C2×C4×C17—81no—
157C2×C4×C17—81no—
158C2×C4×C17—81no—
159C2×C4×C17—84no—
160C2×C4×C17#9911yescharacteristic
161C2×C4×C17#9911yescharacteristic
162C2×C4×C17#10212yes—
163C2×Dic17—82no—
164C2×Dic17—82no—
165C2×Dic17—82no—
166#3622—82no—
167#2543D1711yescharacteristic
168#1799—171no—
169#1460—171no—
170#1344—172no—
171#1343—172no—
172C22×C17—21no—
173C22×C17—21no—
174C22×C17—21no—
175C22×C17—22no—
176C22×C17—21no—
177C22×C17—42no—
178C22×C17—41no—
179C22×C17—41no—
180C22×C17—42no—
181C22×C17—41no—
182C22×C17—41no—
183C22×C17—41no—
184C22×C17—41no—
185C22×C17—81no—
186C22×C17—81no—
187C22×C17—81no—
188C22×C17—81no—
189C22×C17—81no—
190C22×C17—81no—
191C22×C17—81no—
192C22×C17—81no—
193C22×C17C2×#9911yescharacteristic
194C22×C17C2×#10211yescharacteristic
195C22×C17#42111yescharacteristic
196C4×C17—21no—
197C4×C17—21no—
198C4×C17—22no—
199C4×C17—42no—
200C4×C17—41no—
201C4×C17—41no—
202C4×C17—41no—
203C4×C17—81no—
204C4×C17—81no—
205Dic17—162no—
206C2×#121—21no—
207C2×#121Dic1711yescharacteristic, complemented
208C2×C4×D4C2×D1711yescharacteristic
209#431—341no—
210C2×#99—341no—
211#398Dic1711yescharacteristic, complemented
212#397C2×D1711yescharacteristic
213#394Dic1711yescharacteristic, complemented
214#392C2×D1711yescharacteristic
215#388—21no—
216#386—21no—
217#386—21no—
218#380—341no—
219C2×#95Dic1711yescharacteristic, complemented
220#342—172no—
221#323—172no—
222#323—341no—
223C2×C17—21no—
224C2×C17—21no—
225C2×C17—41no—
226C2×C17—42no—
227C2×C17—41no—
228C2×C17—161no—
229C2×C17#151911yescharacteristic
230C2×C17#212111yescharacteristic
231C2×C17#212611yescharacteristic
232C22×D4—21no—
233C22×D4—21no—
234C22×D4C2×Dic1711yescharacteristic
235C22×D4C22⋊D1711yescharacteristic
236C23×C4—21no—
237C23×C4C2×Dic1711yescharacteristic
238C23×C4C22⋊D1711yescharacteristic
239#121—42no—
240#121—42no—
241#121—41no—
242#121—41no—
243C4×D4—41no—
244C4×D4—41no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—681no—
247C2×C4⋊C4C2×Dic1711yescharacteristic
248C2×C4⋊C4C2×Dic1711yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—342no—
255C2×C22⋊C4C22⋊D1711yescharacteristic
256C2×C22⋊C4C22×D1711yescharacteristic
257C2×C42C22⋊D1711yescharacteristic
258C4⋊C8—681no—
259#99—682no—
260C22⋊C8—342no—
261C4×C8—681no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—681no—
266#95C2×Dic1711yescharacteristic
267#95C2×Dic1711yescharacteristic
268C17#1187611yescharacteristic, complemented, Sylow
269C24—21no—
270C24C22⋊Dic1711yescharacteristic
271C24C2×C22⋊D1711yescharacteristic
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—81no—
282C2×D4—81no—
283C2×D4#6322812yes—
284C2×D4#6322912yes—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—81no—
295C22×C4—81no—
296C22×C4—81no—
297C22×C4—682no—
298C22×C4C22⋊Dic1711yescharacteristic
299C22×C4C22⋊Dic1711yescharacteristic
300C22×C4C22⋊Dic1711yescharacteristic
301C22×C4C22×Dic1711yescharacteristic
302C22×C4C2×C22⋊D1711yescharacteristic
303C2×C8—682no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—42no—
307C4⋊C4—1362no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—81no—
317C22⋊C4—682no—
318C22⋊C4—682no—
319C42—21no—
320C42—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23#1058750312yes—
337C23C2×#6322811yescharacteristic
338C23C2×#6322911yescharacteristic
339C23C2×C22⋊Dic1711yescharacteristic
340D4—42no—
341D4—42no—
342D4—82no—
343D4—82no—
344D4—82no—
345D4—84no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—84no—
369C2×C4—1362no—
370C2×C4—1362no—
371C2×C4—1362no—
372C2×C4#1058750312yes—
373C2×C4#1058750511yescharacteristic
374C2×C4#1058750511yescharacteristic
375C8—1362no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—21no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22C2×#1058750511yescharacteristic
398C22C2×#1058750311yescharacteristic
399C22#1176282611yescharacteristic
400C4—22no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—81no—
408C4—81no—
409C4—2722no—
410C2—21no—
411C2—21no—
412C2—41no—
413C2—42no—
414C2—41no—
415C2—161no—
416C2#1452735211yescharacteristic
417C2#1453043011yescharacteristic
418C2#1453044911yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
Fitting, prime radicalC17×#2543C2
socleC22×C17C2×#99
cosocleC2×C22⋊C4×C17C23
hypercenter#2543D17
hypocenterC17#11876
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2543

Complements

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

NH ≅ G/Ntype
1. #14528772C2semidirect
2. #14527105C2semidirect
3. #14526784C2semidirect
4. #14526781C2semidirect
13. C2×C17×#121C4semidirect
15. C17×#398C4semidirect
17. C17×#394C4semidirect
22. C2×C17×#95C4semidirect
207. C2×#121Dic17semidirect
211. #398Dic17semidirect
213. #394Dic17semidirect
219. C2×#95Dic17semidirect
268. C17#11876semidirect

Maximal subgroups

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

subgroupindex
#145287722
#145271052
#145267842
#145267812
C17×#25432
#1187617