Finite Group Databasebeta

← #16945348

Subgroups — #16945348

Order 4352.

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

normal subgroups only

This group has 536 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#14527102C211yesmaximal, characteristic, complemented
3#14526784C212yesmaximal, complemented
4#14526781C212yesmaximal, complemented
5C17×#2535C211yesmaximal, characteristic
6C2×#10587505—21no—
7C2×C22⋊#3622—21no—
8#11762669—21no—
9#11762576C2212yes—
10#11762535—21no—
11#11762533C2212yes—
12C2×C17×#121—21no—
13C2×C4×D4×C17C411yescharacteristic, complemented
14C2×C4×D4×C17C2211yescharacteristic
15C17×#397C411yescharacteristic, complemented
16C17×#397C2211yescharacteristic
17C17×#392C411yescharacteristic, complemented
18C17×#392C2211yescharacteristic
19C17×#386—21no—
20C17×#386—21no—
21C17×#382C411yescharacteristic, complemented
22C17×#380—21no—
23C22×D4×C17—21no—
24C22×D4×C17—21no—
25C22×D4×C17C2×C411yescharacteristic
26C22×D4×C17D411yescharacteristic
27C23×C4×C17—21no—
28C23×C4×C17D411yescharacteristic
29C23×C4×C17D411yescharacteristic
30C17×#121—42no—
31C17×#121—42no—
32C4×D4×C17—41no—
33C4×D4×C17—41no—
34C4×D4×C17—41no—
35C4×D4×C17—41no—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17C2×C411yescharacteristic
38C2×C4⋊C4×C17D411yescharacteristic
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×C17C2×C411yescharacteristic
45C2×C22⋊C4×C17C2311yescharacteristic
46C2×C42×C17C2×C411yescharacteristic
47C2×C22⋊Dic17—22no—
48C2×C4⋊Dic17—41no—
49C22×#3622—41no—
50C17×#95—21no—
51C17×#95—21no—
52C17×#95—21no—
53C17×#95C2×C411yescharacteristic
54C17×#95C2×C411yescharacteristic
55#10587505—42no—
56#10587502—41no—
57C22⋊#3622—22no—
58C22⋊#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—42no—
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—81no—
104C22⋊C4×C17—81no—
105C42×C17—21no—
106C42×C17—21no—
107C22⋊Dic17—42no—
108C22⋊Dic17—42no—
109C4⋊Dic17—82no—
110C2×#3622—42no—
111C2×#3622—82no—
112#11875—171nomaximal, Sylow
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—22no—
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—41no—
128C23×C17#10212yes—
129C23×C17C2×C22⋊C411yescharacteristic
130C23×C17C2×D811yescharacteristic
131C23×C17C2×SD1611yescharacteristic
132D4×C17—42no—
133D4×C17—42no—
134D4×C17—42no—
135D4×C17—42no—
136D4×C17—84no—
137D4×C17—82no—
138D4×C17—82no—
139C2×C4×C17—21no—
140C2×C4×C17—21no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—21no—
144C2×C4×C17—41no—
145C2×C4×C17—42no—
146C2×C4×C17—42no—
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—41no—
157C2×C4×C17—41no—
158C2×C4×C17—41no—
159C2×C4×C17—81no—
160C2×C4×C17—81no—
161C2×C4×C17—84no—
162C2×C4×C17#9911yescharacteristic
163C2×C4×C17#9911yescharacteristic
164C2×C4×C17#10212yes—
165C2×Dic17—82no—
166C2×Dic17—82no—
167C2×Dic17—82no—
168#3622—82no—
169#2535D1711yescharacteristic
170#1799—171no—
171#1459—171no—
172#1344—172no—
173#1343—172no—
174C22×C17—21no—
175C22×C17—21no—
176C22×C17—21no—
177C22×C17—22no—
178C22×C17—21no—
179C22×C17—42no—
180C22×C17—41no—
181C22×C17—41no—
182C22×C17—42no—
183C22×C17—42no—
184C22×C17—41no—
185C22×C17—41no—
186C22×C17—41no—
187C22×C17—41no—
188C22×C17—42no—
189C22×C17—81no—
190C22×C17—81no—
191C22×C17—81no—
192C22×C17—81no—
193C22×C17—81no—
194C22×C17—81no—
195C22×C17C2×#9911yescharacteristic
196C22×C17C2×#10211yescharacteristic
197C22×C17#42111yescharacteristic
198C4×C17—21no—
199C4×C17—21no—
200C4×C17—22no—
201C4×C17—41no—
202C4×C17—41no—
203C4×C17—41no—
204C4×C17—81no—
205C4×C17—81no—
206C4×C17—81no—
207Dic17—162no—
208C2×#121—21no—
209C2×C4×D4Dic1711yescharacteristic, complemented
210C2×C4×D4C2×D1711yescharacteristic
211C2×#99—341no—
212C2×C22⋊C8—341no—
213#397Dic1711yescharacteristic, complemented
214#397C2×D1711yescharacteristic
215#392Dic1711yescharacteristic, complemented
216#392C2×D1711yescharacteristic
217#386—21no—
218#386—21no—
219#382Dic1711yescharacteristic, complemented
220#380—21no—
221#380—341no—
222#342—172no—
223#324—341no—
224#323—172no—
225C2×C17—21no—
226C2×C17—21no—
227C2×C17—41no—
228C2×C17—42no—
229C2×C17—41no—
230C2×C17—82no—
231C2×C17#151911yescharacteristic
232C2×C17#212011yescharacteristic
233C2×C17#212711yescharacteristic
234C22×D4—21no—
235C22×D4—21no—
236C22×D4C2×Dic1711yescharacteristic
237C22×D4C22⋊D1711yescharacteristic
238C23×C4—21no—
239C23×C4C22⋊D1711yescharacteristic
240C23×C4C22⋊D1711yescharacteristic
241C22×C8—681no—
242#121—42no—
243#121—42no—
244C4×D4—41no—
245C4×D4—41no—
246C4×D4—41no—
247C4×D4—41no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—681no—
250C2×C4⋊C4C2×Dic1711yescharacteristic
251C2×C4⋊C4C22⋊D1711yescharacteristic
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—342no—
258C2×C22⋊C4C2×Dic1711yescharacteristic
259C2×C22⋊C4C22×D1711yescharacteristic
260C2×C42C2×Dic1711yescharacteristic
261#99—682no—
262C22⋊C8—342no—
263C22⋊C8—681no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—681no—
268#95C2×Dic1711yescharacteristic
269#95C2×Dic1711yescharacteristic
270C17#1187511yescharacteristic, complemented, Sylow
271C24—21no—
272C24C22⋊Dic1711yescharacteristic
273C24C2×C22⋊D1711yescharacteristic
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—81no—
284C2×D4—81no—
285C2×D4#6322812yes—
286C2×D4#6322912yes—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—81no—
298C22×C4—81no—
299C22×C4—682no—
300C22×C4C22⋊Dic1711yescharacteristic
301C22×C4C22⋊Dic1711yescharacteristic
302C22×C4C22⋊Dic1711yescharacteristic
303C22×C4C22×Dic1711yescharacteristic
304C22×C4C2×C22⋊D1711yescharacteristic
305C2×C8—682no—
306C2×C8—1362no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—42no—
310C4⋊C4—1362no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—81no—
319C22⋊C4—81no—
320C22⋊C4—682no—
321C22⋊C4—682no—
322C42—21no—
323C42—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—22no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23#1058750312yes—
340C23C2×#6322811yescharacteristic
341C23C2×#6322911yescharacteristic
342C23C2×C22⋊Dic1711yescharacteristic
343D4—42no—
344D4—42no—
345D4—42no—
346D4—42no—
347D4—84no—
348D4—82no—
349D4—82no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—84no—
373C2×C4—1362no—
374C2×C4—1362no—
375C2×C4—1362no—
376C2×C4#1058750312yes—
377C2×C4#1058750511yescharacteristic
378C2×C4#1058750511yescharacteristic
379C8—1362no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—21no—
385C22—42no—
386C22—41no—
387C22—41no—
388C22—42no—
389C22—42no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—42no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22C2×#1058750511yescharacteristic
402C22C2×#1058750311yescharacteristic
403C22#1176282611yescharacteristic
404C4—22no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4—2722no—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—42no—
418C2—41no—
419C2—82no—
420C2#1452735211yescharacteristic
421C2#1453042511yescharacteristic
422C2#1453045311yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
Fitting, prime radicalC17×#2535C2
socleC22×C17C2×#99
cosocleC2×C22⋊C4×C17C23
hypercenter#2535D17
hypocenterC17#11875
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. #14528772C2semidirect
2. #14527102C2semidirect
3. #14526784C2semidirect
4. #14526781C2semidirect
13. C2×C4×D4×C17C4semidirect
15. C17×#397C4semidirect
17. C17×#392C4semidirect
21. C17×#382C4semidirect
209. C2×C4×D4Dic17semidirect
213. #397Dic17semidirect
215. #392Dic17semidirect
219. #382Dic17semidirect
270. C17#11875semidirect

Maximal subgroups

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

subgroupindex
#145287722
#145271022
#145267842
#145267812
C17×#25352
#1187517