Finite Group Databasebeta

← #17958567

Subgroups — #17958567

Order 4352.

496 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 72 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#14544032C211yesmaximal, characteristic, complemented
2C2×#11763654C211yesmaximal, characteristic, complemented
3#14543727C212yesmaximal, complemented
4#14543712C212yesmaximal, complemented
5#14533256C211yesmaximal, characteristic
6#11763779—21no—
7C2×C22⋊#3624—21no—
8#11763654—21no—
9#11763654—21no—
10#11763654C2212yes—
11#11763654C2212yes—
12C2×#10587621—21no—
13C2×#10587621—21no—
14C22×C4⋊Dic17C2211yescharacteristic
15#11762745—21no—
16#11762745—21no—
17#11762712C411yescharacteristic
18#11762712C2211yescharacteristic
19#11762678C411yescharacteristic
20#11762678C2211yescharacteristic
21C4×C22⋊Dic17C411yescharacteristic
22C2×C17×#121C411yescharacteristic
23C22×D4×C17—21no—
24C22×D4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×Dic17D411yescharacteristic
27C23×Dic17D411yescharacteristic
28C2×#63247—41no—
29C22×#3624—41no—
30C17×#121—41no—
31C17×#121—41no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C22⋊C4×C17—21no—
34C2×C22⋊Dic17—21no—
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38C2×C22⋊Dic17—21no—
39#10587621—44no—
40#10587621—44no—
41C2×C4⋊Dic17—41no—
42C2×C4⋊Dic17—41no—
43C2×C4⋊Dic17C2×C411yescharacteristic
44C2×C4⋊Dic17D411yescharacteristic
45C2×C4⋊Dic17D411yescharacteristic
46C2×C4⋊Dic17C2311yescharacteristic
47C2×#63225—21no—
48C2×#63225—21no—
49C2×#63225—21no—
50C2×#63225—21no—
51C2×C4×Dic17C2×C411yescharacteristic
52C2×C4×Dic17C2×C411yescharacteristic
53C22⋊#3624—22no—
54C22⋊#3624—22no—
55C22⋊#3624—41no—
56C22⋊#3624—41no—
57#10587502—21no—
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—22no—
70C22×C4×C17—21no—
71C22×C4×C17—41no—
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22×C411yescharacteristic
74C22×Dic17—21no—
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17—21no—
78C22×Dic17—21no—
79C22×Dic17—21no—
80C22×Dic17—42no—
81C22×Dic17—42no—
82C22×Dic17C22⋊C411yescharacteristic
83C22×Dic17C22⋊C411yescharacteristic
84C22×Dic17C2×D411yescharacteristic
85C22×Dic17C2×D411yescharacteristic
86#63247—82no—
87C2×#3624—42no—
88C2×#3624—42no—
89C2×#3624—82no—
90C4⋊C4×C17—41no—
91C22⋊C4×C17—42no—
92C22⋊Dic17—24no—
93C22⋊Dic17—42no—
94C22⋊Dic17—42no—
95C22⋊Dic17—42no—
96C22⋊Dic17—42no—
97C4⋊Dic17—41no—
98C4⋊Dic17—41no—
99C4⋊Dic17—41no—
100C4⋊Dic17—41no—
101#63225—42no—
102#63225—42no—
103#63225—42no—
104#63225—42no—
105C4×Dic17—22no—
106C4×Dic17—41no—
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—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—42no—
131C2×C4×C17—42no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17#13112yes—
136C2×Dic17—22no—
137C2×Dic17—22no—
138C2×Dic17—21no—
139C2×Dic17—21no—
140C2×Dic17—21no—
141C2×Dic17—21no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—42no—
145C2×Dic17—42no—
146C2×Dic17—41no—
147C2×Dic17—41no—
148C2×Dic17—41no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—81no—
153C2×Dic17—81no—
154#3624—82no—
155#3624—82no—
156#2501—171no—
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—41no—
183C4×C17—81no—
184Dic17—42no—
185Dic17—42no—
186Dic17—41no—
187Dic17—41no—
188Dic17—41no—
189Dic17—41no—
190C2×#123—341no—
191C2×#123—341no—
192C2×#121#59511yescharacteristic
193C22×C4⋊C4—171no—
194#407—341no—
195C2×C22⋊C8—341no—
196#399—341no—
197#399—341no—
198#390—171no—
199#390—171no—
200#384—171no—
201#384—171no—
202C4×C22⋊C4—171no—
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×#59511yescharacteristic
217C23×C4—171no—
218C23×C4—171no—
219C23×C4C2×#59511yescharacteristic
220C2×M16—681no—
221C22×C8—681no—
222#123—684no—
223#123—684no—
224#121—41no—
225#121—41no—
226C2×C4⋊C4—171no—
227C2×C4⋊C4—171no—
228C2×C4⋊C4—171no—
229C2×C4⋊C4—171no—
230C2×C4⋊C4—341no—
231C2×C4⋊C4—341no—
232C2×C4⋊C4—341no—
233C2×C4⋊C4—341no—
234C2×C4⋊C4—681no—
235C2×C4⋊C4—681no—
236C2×C4⋊C4C2×#59511yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—341no—
239C2×C22⋊C4—341no—
240C2×C22⋊C4—341no—
241C2×C22⋊C4—341no—
242C2×C22⋊C4—341no—
243C2×C42—171no—
244C2×C42—171no—
245C22⋊C8—342no—
246C22⋊C8—342no—
247C22⋊C8—681no—
248C22⋊C8—681no—
249#95—341no—
250C17#1154911yescharacteristic, complemented, Sylow
251C24—21no—
252C24C22⋊#59511yescharacteristic
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—22no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—171no—
266C22×C4—171no—
267C22×C4—171no—
268C22×C4—171no—
269C22×C4—341no—
270C22×C4—341no—
271C22×C4—341no—
272C22×C4—341no—
273C22×C4—341no—
274C22×C4—341no—
275C22×C4—682no—
276C22×C4—682no—
277C22×C4C22⋊#59511yescharacteristic
278C22×C4C22×#59511yescharacteristic
279M16—1362no—
280C2×C8—682no—
281C2×C8—682no—
282C2×C8—1362no—
283C4⋊C4—41no—
284C4⋊C4—681no—
285C4⋊C4—681no—
286C4⋊C4—681no—
287C4⋊C4—681no—
288C4⋊C4—682no—
289C4⋊C4—682no—
290C4⋊C4—682no—
291C4⋊C4—682no—
292C22⋊C4—42no—
293C22⋊C4—344no—
294C22⋊C4—682no—
295C22⋊C4—682no—
296C22⋊C4—682no—
297C22⋊C4—682no—
298C42—342no—
299C42—681no—
300C23—22no—
301C23—21no—
302C23—21no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23#1058755111yescharacteristic
312C23#1058755111yescharacteristic
313C23C2×C22⋊#59511yescharacteristic
314D4—82no—
315D4—82no—
316D4—82no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—342no—
328C2×C4—342no—
329C2×C4—341no—
330C2×C4—341no—
331C2×C4—341no—
332C2×C4—341no—
333C2×C4—681no—
334C2×C4—681no—
335C2×C4—682no—
336C2×C4—682no—
337C2×C4—681no—
338C2×C4—681no—
339C2×C4—681no—
340C2×C4—681no—
341C2×C4—681no—
342C2×C4—681no—
343C2×C4—1361no—
344C2×C4—1361no—
345C2×C4#1058767812yes—
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#1176371312yes—
365C22#1176378211yescharacteristic
366C22C2×#1058755111yescharacteristic
367C22#1176379611yescharacteristic
368C4—22no—
369C4—41no—
370C4—81no—
371C4—682no—
372C4—682no—
373C4—681no—
374C4—681no—
375C4—681no—
376C4—681no—
377C2—21no—
378C2—21no—
379C2—22no—
380C2—41no—
381C2—161no—
382C2#1454404911yescharacteristic
383C2C2×#1176371311yescharacteristic
384C2#1454507911yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
Fitting, prime radicalC2×C17×#121C4
socleC22×C17C2×#99
cosocleC2×C4⋊Dic17C23
hypercenterC2×#121#595
hypocenterC17#11549
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #14544032C2semidirect
2. C2×#11763654C2semidirect
3. #14543727C2semidirect
4. #14543712C2semidirect
250. C17#11549semidirect

Maximal subgroups

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

subgroupindex
#145440322
C2×#117636542
#145437272
#145437122
#145332562
#1154917