Finite Group Databasebeta

← #16929751

Subgroups — #16929751

Order 4352.

564 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537808C211yesmaximal, characteristic, complemented
2#14527175C211yesmaximal, characteristic, complemented
3#14527175C211yesmaximal, characteristic, complemented
4#14527105C211yesmaximal, characteristic, complemented
5#14526629C211yesmaximal, characteristic, complemented
6#14526615C211yesmaximal, characteristic, complemented
7C2×C17×#442C211yesmaximal, characteristic
8D4×#3622—22no—
9D4×#3622—22no—
10#11762862C2211yescharacteristic
11#11762862C2211yescharacteristic
12#11762862C2211yescharacteristic
13#11762862C2211yescharacteristic
14C2×C22⋊#3622—22no—
15D4⋊#3622—22no—
16D4⋊#3622—22no—
17#11762533—22no—
18C22×D8×C17C411yescharacteristic
19C2×C4×D4×C17C2211yescharacteristic
20C2×C4×D4×C17C2211yescharacteristic
21C17×#442—22no—
22C17×#442—22no—
23C2×C17×#106C411yescharacteristic
24C2×C17×#102C411yescharacteristic
25C2×C17×#102C411yescharacteristic
26C2×C17×#97C2211yescharacteristic
27C22×D4×C17C2×C411yescharacteristic
28C22×D4×C17C2×C411yescharacteristic
29C23×C4×C17—21no—
30C23×C4×C17—21no—
31C2×D8×C17—22no—
32C2×D8×C17—22no—
33C2×D8×C17C814yescomplemented
34C22×C8×C17C2×C411yescharacteristic
35C22×C8×C17C2×C411yescharacteristic
36C4×D4×C17—21no—
37C4×D4×C17—21no—
38C4×D4×C17—21no—
39C4×D4×C17—21no—
40C4×D4×C17—21no—
41C4×D4×C17—21no—
42C4×D4×C17D412yes—
43C4×D4×C17D412yes—
44C2×C4⋊C4×C17C2×C411yescharacteristic
45C2×C4⋊C4×C17C2×C411yescharacteristic
46C2×C22⋊C4×C17—21no—
47C2×C22⋊C4×C17—21no—
48C2×C42×C17C2311yescharacteristic
49C22×#3622—24no—
50C17×#106—22no—
51C17×#102—22no—
52C17×#102—22no—
53C17×#97—21no—
54C17×#97—21no—
55C22⋊#3622—24no—
56C22⋊#3622—21no—
57C22⋊#3622—21no—
58C22⋊#3622—21no—
59C22⋊#3622D412yes—
60C4⋊#3622—21no—
61C4⋊#3622—21no—
62C4⋊#3622—21no—
63C4⋊#3622—21no—
64C4×#3622—21no—
65C4×#3622—21no—
66C4×#3622—21no—
67C4×#3622D412yes—
68C24×C17—21no—
69C24×C17—21no—
70C2×D4×C17—21no—
71C2×D4×C17—21no—
72C2×D4×C17—21no—
73C2×D4×C17—21no—
74C2×D4×C17—21no—
75C2×D4×C17—21no—
76C2×D4×C17—21no—
77C2×D4×C17—21no—
78C2×D4×C17C22⋊C412yes—
79C2×D4×C17C2×C812yes—
80C2×D4×C17C2×C812yescomplemented
81C2×D4×C17M1612yes—
82C22×C4×C17—21no—
83C22×C4×C17—22no—
84C22×C4×C17—22no—
85C22×C4×C17—21no—
86C22×C4×C17—41no—
87C22×C4×C17—41no—
88C22×C4×C17—82no—
89C22×C4×C17—82no—
90C22×C4×C17C22×C411yescharacteristic
91C22×C4×C17C2×D411yescharacteristic
92C22×C4×C17#4111yescharacteristic
93D8×C17—28no—
94C2×C8×C17—21no—
95C2×C8×C17—21no—
96C2×C8×C17—21no—
97C2×C8×C17—21no—
98C2×C8×C17—21no—
99C2×C8×C17C2×C812yescomplemented
100C4⋊C4×C17—21no—
101C4⋊C4×C17—21no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17C22⋊C412yes—
104C22⋊C4×C17—22no—
105C22⋊C4×C17—22no—
106C22⋊C4×C17—41no—
107C22⋊C4×C17—41no—
108C42×C17C2×D411yescharacteristic
109C42×C17C2×D411yescharacteristic
110C42×C17C2×D411yescharacteristic
111C42×C17#4111yescharacteristic
112C2×#3622—22no—
113C2×#3622—22no—
114C2×#3622—41no—
115C2×#3622—41no—
116C2×#3622—84no—
117#9089—171nomaximal, Sylow
118C23×C17—22no—
119C23×C17—22no—
120C23×C17—22no—
121C23×C17—22no—
122C23×C17—41no—
123C23×C17—41no—
124C23×C17—81no—
125C23×C17—81no—
126C23×C17—81no—
127C23×C17—81no—
128C23×C17C4×D411yescharacteristic
129D4×C17—22no—
130D4×C17—22no—
131D4×C17—22no—
132D4×C17—22no—
133D4×C17—22no—
134D4×C17—41no—
135D4×C17—41no—
136D4×C17C22⋊C814yes—
137C2×C4×C17—22no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—44no—
141C2×C4×C17—41no—
142C2×C4×C17—82no—
143C2×C4×C17—82no—
144C2×C4×C17—82no—
145C2×C4×C17—81no—
146C2×C4×C17—81no—
147C2×C4×C17C2×C22⋊C411yescharacteristic
148C2×C4×C17C4×D411yescharacteristic
149C2×C4×C17#12011yescharacteristic
150C2×C4×C17#12111yescharacteristic
151C2×C4×C17#12111yescharacteristic
152C2×C4×C17#12311yescharacteristic
153C2×C4×C17C22×C811yescharacteristic
154C2×C4×C17C2×M1611yescharacteristic
155C2×C4×C17#13111yescharacteristic
156C2×C4×C17#13111yescharacteristic
157C8×C17—22no—
158C8×C17—41no—
159#3622—42no—
160#3622—42no—
161#3622—81no—
162#3622—81no—
163#2972—171no—
164C2×#442D1711yescharacteristic
165#1478—171no—
166#1478—171no—
167#1460—171no—
168#1281—171no—
169#1275—171no—
170C22×C17—21no—
171C22×C17—21no—
172C22×C17—24no—
173C22×C17—42no—
174C22×C17—42no—
175C22×C17—42no—
176C22×C17—82no—
177C22×C17—82no—
178C22×C17—82no—
179C22×C17—82no—
180C22×C17—81no—
181C22×C17—81no—
182C22×C17#38611yescharacteristic
183C22×C17C8×D411yescharacteristic
184C22×C17#43511yescharacteristic
185C4×C17—21no—
186C4×C17—21no—
187C4×C17—21no—
188C4×C17—21no—
189C4×C17—42no—
190C4×C17—81no—
191C4×C17C2×C22⋊C811yescharacteristic
192C4×C17#40811yescharacteristic
193C4×C17C8×D411yescharacteristic
194C4×C17#43511yescharacteristic
195C22×D8Dic1711yescharacteristic
196C2×C4×D4C2×D1711yescharacteristic
197C2×C4×D4C2×D1711yescharacteristic
198#442—22no—
199#442—22no—
200C8×D4—342no—
201C8×D4—342no—
202#431—171no—
203#431—171no—
204#431—171no—
205#431—171no—
206C2×#106Dic1711yescharacteristic
207C2×#102Dic1711yescharacteristic
208C2×#102Dic1711yescharacteristic
209C2×C22⋊C8—342no—
210C2×#97C2×D1711yescharacteristic
211D4⋊C8—342no—
212D4⋊C8—342no—
213#323—342no—
214C2×C17—21no—
215C2×C17—21no—
216C2×C17—44no—
217C2×C17—82no—
218C2×C17#186911yescharacteristic
219C2×C17#190311yescharacteristic
220C2×C17#190411yescharacteristic
221C22×D4C2×Dic1711yescharacteristic
222C22×D4C2×Dic1711yescharacteristic
223C23×C4—21no—
224C23×C4—21no—
225C2×D8—22no—
226C2×D8—22no—
227C2×D8#362214yescomplemented
228C22×C8—344no—
229C22×C8C2×Dic1711yescharacteristic
230C22×C8C2×Dic1711yescharacteristic
231C4×D4—21no—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4C22⋊D1712yes—
238C4×D4C22⋊D1712yes—
239C2×C4⋊C4C2×Dic1711yescharacteristic
240C2×C4⋊C4C2×Dic1711yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C42C22×D1711yescharacteristic
244#106—22no—
245C4⋊C8—341no—
246C4⋊C8—341no—
247C4⋊C8—341no—
248C4⋊C8—341no—
249#102—22no—
250#102—22no—
251C22⋊C8—172no—
252C22⋊C8—344no—
253C22⋊C8—341no—
254C22⋊C8—341no—
255C22⋊C8—341no—
256#97—21no—
257#97—21no—
258C4×C8—172no—
259C4×C8—341no—
260C4×C8—341no—
261C4×C8—341no—
262C17#908911yescharacteristic, complemented, Sylow
263C24—21no—
264C24—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4C2×#362212yes—
274C2×D4C2×#362212yescomplemented
275C2×D4#6322312yes—
276C2×D4C22⋊Dic1712yes—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—82no—
284C22×C4—82no—
285C22×C4D4×D1711yescharacteristic
286C22×C4#6325411yescharacteristic
287C22×C4C22×Dic1711yescharacteristic
288D8—28no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—342no—
295C2×C8—342no—
296C2×C8—681no—
297C2×C8—681no—
298C2×C8—1364no—
299C2×C8C2×#362212yescomplemented
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4C22⋊Dic1712yes—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42D4×D1711yescharacteristic
309C42#6325411yescharacteristic
310C42C2×C22⋊D1711yescharacteristic
311C42C2×C22⋊D1711yescharacteristic
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—41no—
317C23—41no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23D4×Dic1711yescharacteristic
323D4—22no—
324D4—22no—
325D4—22no—
326D4—22no—
327D4—22no—
328D4—41no—
329D4—41no—
330D4C22⋊#362214yes—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—44no—
335C2×C4—41no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4C22×#362211yescharacteristic
342C2×C4C2×#6322311yescharacteristic
343C2×C4D4×Dic1711yescharacteristic
344C2×C4#1058762111yescharacteristic
345C2×C4#1058762311yescharacteristic
346C2×C4#1058762511yescharacteristic
347C2×C4#1058762511yescharacteristic
348C2×C4#1058763411yescharacteristic
349C2×C4#1058763411yescharacteristic
350C2×C4C2×C22⋊Dic1711yescharacteristic
351C8—22no—
352C8—41no—
353C8—682no—
354C8—682no—
355C8—1361no—
356C8—1361no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—81no—
368C22—81no—
369C22#1176268911yescharacteristic
370C22D4×#362211yescharacteristic
371C22#1176288111yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—42no—
377C4—81no—
378C4C2×C22⋊#362211yescharacteristic
379C4#1176277611yescharacteristic
380C4D4×#362211yescharacteristic
381C4#1176288111yescharacteristic
382C2—21no—
383C2—21no—
384C2—44no—
385C2—82no—
386C2#1452907711yescharacteristic
387C2#1452926611yescharacteristic
388C2#1452927311yescharacteristic
subgroupG/H
centerC22#11762689
commutatorC2×C4×C17C22×C8
FrattiniC2×C42C22×D17
FittingC2×C17×#442C2
socleC22×C17#386
prime radicalC22×D8×C17C4
cosocleC2×C42×C17C23
hypercenterC2×#442D17
hypocenterC17#9089
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. #14537808C2semidirect
2. #14527175C2semidirect
3. #14527175C2semidirect
4. #14527105C2semidirect
5. #14526629C2semidirect
6. #14526615C2semidirect
33. C2×D8×C17C8semidirect
80. C2×D4×C17C2×C8semidirect
99. C2×C8×C17C2×C8semidirect
227. C2×D8#3622semidirect
262. C17#9089semidirect
274. C2×D4C2×#3622semidirect
299. C2×C8C2×#3622semidirect

Maximal subgroups

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

subgroupindex
#145378082
#145271752
#145271052
#145266292
#145266152
C2×C17×#4422
#908917