Finite Group Databasebeta

← #16943880

Subgroups — #16943880

Order 4352.

496 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 91 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#14527114C211yesmaximal, characteristic, complemented
2C2×#11762535C211yesmaximal, characteristic, complemented
3#14526730C212yesmaximal, complemented
4#14526716C212yesmaximal, complemented
5C17×#2501C211yesmaximal, characteristic
6#11762773—21no—
7C2×C22⋊#3622—21no—
8#11762535—21no—
9#11762535—21no—
10#11762535C2212yes—
11#11762535C2212yes—
12C2×C17×#123—21no—
13C2×C17×#123—21no—
14C2×C17×#121C411yescharacteristic
15C22×C4⋊C4×C17C2211yescharacteristic
16C17×#399—21no—
17C17×#399—21no—
18C17×#390C411yescharacteristic
19C17×#390C2211yescharacteristic
20C17×#384C411yescharacteristic
21C17×#384C2211yescharacteristic
22C4×C22⋊C4×C17C411yescharacteristic
23C22×D4×C17—21no—
24C22×D4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17D411yescharacteristic
27C23×C4×C17D411yescharacteristic
28C17×#123—44no—
29C17×#123—44no—
30C17×#121—41no—
31C17×#121—41no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17—41no—
37C2×C4⋊C4×C17—41no—
38C2×C4⋊C4×C17C2×C411yescharacteristic
39C2×C4⋊C4×C17C2×C411yescharacteristic
40C2×C4⋊C4×C17D411yescharacteristic
41C2×C4⋊C4×C17D411yescharacteristic
42C2×C4⋊C4×C17C2311yescharacteristic
43C2×C22⋊C4×C17—21no—
44C2×C22⋊C4×C17—21no—
45C2×C22⋊C4×C17—21no—
46C2×C22⋊C4×C17—21no—
47C2×C22⋊C4×C17—21no—
48C2×C22⋊C4×C17—21no—
49C2×C42×C17C2×C411yescharacteristic
50C2×C42×C17C2×C411yescharacteristic
51C2×#63223—41no—
52C22×#3622—41no—
53C17×#95—21no—
54C22⋊#3622—22no—
55C22⋊#3622—22no—
56C22⋊#3622—41no—
57C22⋊#3622—41no—
58C24×C17—21no—
59C24×C17C22⋊C411yescharacteristic
60C2×D4×C17—22no—
61C2×D4×C17—41no—
62C2×D4×C17—41no—
63C2×D4×C17—42no—
64C2×D4×C17—42no—
65C2×D4×C17—41no—
66C2×D4×C17—41no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17—21no—
74C22×C4×C17—21no—
75C22×C4×C17—22no—
76C22×C4×C17—21no—
77C22×C4×C17—41no—
78C22×C4×C17—42no—
79C22×C4×C17—42no—
80C22×C4×C17C22⋊C411yescharacteristic
81C22×C4×C17C22⋊C411yescharacteristic
82C22×C4×C17C22⋊C411yescharacteristic
83C22×C4×C17C22×C411yescharacteristic
84C22×C4×C17C2×D411yescharacteristic
85C22×C4×C17C2×D411yescharacteristic
86C4⋊C4×C17—41no—
87C4⋊C4×C17—41no—
88C4⋊C4×C17—41no—
89C4⋊C4×C17—41no—
90C4⋊C4×C17—41no—
91C4⋊C4×C17—42no—
92C4⋊C4×C17—42no—
93C4⋊C4×C17—42no—
94C4⋊C4×C17—42no—
95C22⋊C4×C17—24no—
96C22⋊C4×C17—42no—
97C22⋊C4×C17—42no—
98C22⋊C4×C17—42no—
99C22⋊C4×C17—42no—
100C22⋊C4×C17—42no—
101C42×C17—22no—
102C42×C17—41no—
103#63223—82no—
104C2×#3622—42no—
105C2×#3622—42no—
106C2×#3622—82no—
107#11549—171nomaximal, Sylow
108C23×C17—22no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—41no—
112C23×C17—41no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17—41no—
116C23×C17—41no—
117C23×C17—41no—
118C23×C17—41no—
119C23×C17#9911yescharacteristic
120C23×C17#9911yescharacteristic
121C23×C17C2×C22⋊C411yescharacteristic
122D4×C17—82no—
123D4×C17—82no—
124D4×C17—82no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—22no—
128C2×C4×C17—22no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—42no—
137C2×C4×C17—42no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—42no—
141C2×C4×C17—42no—
142C2×C4×C17—41no—
143C2×C4×C17—41no—
144C2×C4×C17—41no—
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—81no—
152C2×C4×C17—81no—
153C2×C4×C17#13112yes—
154#3622—82no—
155#3622—82no—
156#2501D1711yescharacteristic
157#1463—171no—
158C2×#324—171no—
159#1325—172no—
160#1318—172no—
161C22×C17—21no—
162C22×C17—21no—
163C22×C17—21no—
164C22×C17—21no—
165C22×C17—21no—
166C22×C17—21no—
167C22×C17—21no—
168C22×C17—42no—
169C22×C17—42no—
170C22×C17—81no—
171C22×C17—81no—
172C22×C17—81no—
173C22×C17—81no—
174C22×C17—81no—
175C22×C17—81no—
176C22×C17—81no—
177C22×C17#35312yes—
178C22×C17#40811yescharacteristic
179C22×C17C2×#9911yescharacteristic
180C22×C17#41311yescharacteristic
181C4×C17—22no—
182C4×C17—42no—
183C4×C17—42no—
184C4×C17—41no—
185C4×C17—41no—
186C4×C17—41no—
187C4×C17—41no—
188C4×C17—41no—
189C4×C17—81no—
190C2×#123—21no—
191C2×#123—21no—
192C2×#121Dic1711yescharacteristic
193C22×C4⋊C4C2×D1711yescharacteristic
194#407—341no—
195C2×C22⋊C8—341no—
196#399—21no—
197#399—21no—
198#390Dic1711yescharacteristic
199#390C2×D1711yescharacteristic
200#384Dic1711yescharacteristic
201#384C2×D1711yescharacteristic
202C4×C22⋊C4Dic1711yescharacteristic
203#324—172no—
204#324—172no—
205#324—341no—
206#324—341no—
207C2×C17—21no—
208C2×C17—21no—
209C2×C17—22no—
210C2×C17—41no—
211C2×C17—161no—
212C2×C17#146811yescharacteristic
213C2×C17C2×#35311yescharacteristic
214C2×C17#213311yescharacteristic
215C22×D4—21no—
216C22×D4C2×Dic1711yescharacteristic
217C23×C4C2×Dic1711yescharacteristic
218C23×C4C22⋊D1711yescharacteristic
219C23×C4C22⋊D1711yescharacteristic
220C2×M16—681no—
221C22×C8—681no—
222#123—44no—
223#123—44no—
224#121—41no—
225#121—41no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—41no—
231C2×C4⋊C4—41no—
232C2×C4⋊C4C2×Dic1711yescharacteristic
233C2×C4⋊C4C2×Dic1711yescharacteristic
234C2×C4⋊C4C22⋊D1711yescharacteristic
235C2×C4⋊C4C22⋊D1711yescharacteristic
236C2×C4⋊C4C22×D1711yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C42C2×Dic1711yescharacteristic
244C2×C42C2×Dic1711yescharacteristic
245C22⋊C8—342no—
246C22⋊C8—342no—
247C22⋊C8—681no—
248C22⋊C8—681no—
249#95—21no—
250C17#1154911yescharacteristic, complemented, Sylow
251C24—21no—
252C24C22⋊Dic1711yescharacteristic
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4—41no—
259C2×D4—41no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4C22⋊Dic1711yescharacteristic
274C22×C4C22⋊Dic1711yescharacteristic
275C22×C4C22⋊Dic1711yescharacteristic
276C22×C4C22×Dic1711yescharacteristic
277C22×C4C2×C22⋊D1711yescharacteristic
278C22×C4C2×C22⋊D1711yescharacteristic
279M16—1362no—
280C2×C8—682no—
281C2×C8—682no—
282C2×C8—1362no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C22⋊C4—24no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C42—22no—
299C42—41no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23#1058750511yescharacteristic
312C23#1058750511yescharacteristic
313C23C2×C22⋊Dic1711yescharacteristic
314D4—82no—
315D4—82no—
316D4—82no—
317C2×C4—21no—
318C2×C4—21no—
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—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4#1058763412yes—
346C8—1362no—
347C8—1362no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—42no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22#1176260212yes—
365C22#1176277611yescharacteristic
366C22C2×#1058750511yescharacteristic
367C22#1176279311yescharacteristic
368C4—22no—
369C4—42no—
370C4—42no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—81no—
377C2—21no—
378C2—21no—
379C2—22no—
380C2—41no—
381C2—161no—
382C2#1452713211yescharacteristic
383C2C2×#1176260211yescharacteristic
384C2#1453047311yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2501C2
socleC22×C17C2×#99
prime radicalC2×C17×#121C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2501D17
hypocenterC17#11549
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2501

Complements

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

NH ≅ G/Ntype
1. #14527114C2semidirect
2. C2×#11762535C2semidirect
3. #14526730C2semidirect
4. #14526716C2semidirect
250. C17#11549semidirect

Maximal subgroups

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

subgroupindex
#145271142
C2×#117625352
#145267302
#145267162
C17×#25012
#1154917