Finite Group Databasebeta

← #16930390

Subgroups — #16930390

Order 4352.

622 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 127 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#14534526C211yesmaximal, characteristic
2#14531402C211yesmaximal, characteristic, complemented
3#14527353C212yesmaximal
4#14526652C212yesmaximal, complemented
5C2×C17×#324C211yesmaximal, characteristic, complemented
6C2×#10587615—21no—
7C2×#10587616C2211yescharacteristic
8C2×#10587612—21no—
9#11762739C412yescomplemented
10#11762731—22no—
11#11762726C412yescomplemented
12#11762708—24no—
13#11762688—21no—
14#11762669—21no—
15#11762669C2211yescharacteristic
16#11762669C2212yes—
17#11762544—24no—
18C22×C4⋊C4×C17C2211yescharacteristic
19C2×C17×C22⋊C8C2212yes—
20C17×#324—22no—
21C23×C4×C17D411yescharacteristic
22C23×C4×C17D411yescharacteristic
23C23×C4×C17C2311yescharacteristic
24C22×C22⋊D17—21no—
25C22×D68C2×C411yescharacteristic
26C22×C8×C17—22no—
27C2×C4⋊C4×C17—22no—
28C2×C4⋊C4×C17—22no—
29C2×C4⋊C4×C17C2×C412yes—
30C2×C4⋊C4×C17D412yes—
31C2×C22⋊Dic17—21no—
32C2×C22⋊Dic17—22no—
33#10587616—22no—
34#10587616—22no—
35#10587615—42no—
36#10587615—42no—
37C2×#63227—22no—
38C2×#63227—22no—
39C2×#63227—21no—
40#10587612—42no—
41#10587612—42no—
42C2×C4⋊Dic17—22no—
43C2×C4⋊Dic17—22no—
44C2×C4⋊Dic17—22no—
45C2×C4⋊Dic17—21no—
46C2×C4⋊Dic17C2×C411yescharacteristic
47C2×#63225—22no—
48C2×C4×Dic17—22no—
49C17×C22⋊C8—22no—
50C17×C22⋊C8—22no—
51#10587502—22no—
52#10587502—22no—
53#10587502C2×C412yes—
54#10587502D414yes—
55C24×C17C2×D411yescharacteristic
56C23×D17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—81no—
64C22×C4×C17—81no—
65C22×C4×C17C22⋊C412yes—
66C22×C4×C17C22⋊C412yes—
67C22×C4×C17D812yes—
68C22×C4×C17SD1612yes—
69C22×C4×C17C22×C411yescharacteristic
70C22×C4×C17C2×D412yes—
71C22×C4×C17C2×D411yescharacteristic
72C22×C4×C17#4112yes—
73C2×C22⋊D17—41no—
74C2×C22⋊D17—41no—
75C2×C22⋊D17—41no—
76C2×C22⋊D17—41no—
77C2×C22⋊D17—41no—
78C2×C22⋊D17—41no—
79C22×Dic17—21no—
80C22×Dic17—22no—
81C22×Dic17—24no—
82C2×D68—22no—
83C2×D68—81no—
84C2×C8×C17—42no—
85C2×C8×C17—82no—
86C4⋊C4×C17—24no—
87C4⋊C4×C17—24no—
88C22⋊Dic17—42no—
89C22⋊Dic17—41no—
90C22⋊Dic17—41no—
91C22⋊Dic17—42no—
92#63227—44no—
93#63227—42no—
94#63227—82no—
95C4⋊Dic17—22no—
96C4⋊Dic17—44no—
97C4⋊Dic17—82no—
98C4⋊Dic17—82no—
99C4⋊Dic17—81no—
100#63225—44no—
101C4×Dic17—44no—
102#9204—171nomaximal, Sylow
103C23×C17—41no—
104C23×C17—41no—
105C23×C17C2×C22⋊C411yescharacteristic
106C23×C17#12011yescharacteristic
107C23×C17#12311yescharacteristic
108C23×C17C2×D811yescharacteristic
109C23×C17C2×SD1611yescharacteristic
110C23×C17AGL(1,ℤ/8)11yescharacteristic
111C23×C17#13711yescharacteristic
112C22×D17—42no—
113C22×D17—42no—
114C22×D17—41no—
115C22×D17—41no—
116C22×D17—41no—
117C2×C4×C17—22no—
118C2×C4×C17—22no—
119C2×C4×C17—22no—
120C2×C4×C17—22no—
121C2×C4×C17—22no—
122C2×C4×C17—22no—
123C2×C4×C17—22no—
124C2×C4×C17—42no—
125C2×C4×C17—41no—
126C2×C4×C17—42no—
127C2×C4×C17—41no—
128C2×C4×C17—42no—
129C2×C4×C17—42no—
130C2×C4×C17—81no—
131C2×C4×C17#10214yes—
132C2×C4×C17C4×D412yes—
133C2×C4×C17#12112yes—
134C22⋊D17—81no—
135C22⋊D17—81no—
136C22⋊D17—81no—
137C22⋊D17—81no—
138C2×Dic17—44no—
139C2×Dic17—42no—
140C2×Dic17—44no—
141C2×Dic17—42no—
142C2×Dic17—41no—
143C2×Dic17—42no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146C2×Dic17—44no—
147D68—82no—
148C8×C17—82no—
149#2618—171no—
150#2316—171no—
151#1519—172no—
152C2×#324D1711yescharacteristic, complemented
153#1289—172no—
154C22×C17—21no—
155C22×C17—21no—
156C22×C17—21no—
157C22×C17—21no—
158C22×C17—21no—
159C22×C17—21no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17—41no—
164C22×C17#38611yescharacteristic
165C22×C17C2×#10211yescharacteristic
166C22×C17#41711yescharacteristic
167C22×C17#44711yescharacteristic
168C22×C17#44811yescharacteristic
169C22×C17#48011yescharacteristic
170C22×C17#48111yescharacteristic
171C2×D17—82no—
172C2×D17—82no—
173C2×D17—81no—
174C2×D17—81no—
175C2×D17—81no—
176C4×C17—24no—
177C4×C17—22no—
178C4×C17—22no—
179C4×C17—42no—
180Dic17—84no—
181Dic17—82no—
182Dic17—81no—
183C2×#123—341no—
184C2×#121—171no—
185C2×#117—341no—
186C22×C4⋊C4C2×D1711yescharacteristic
187C2×C22⋊C8C2×D1712yes—
188#398—172no—
189#396—342no—
190#394—172no—
191#389—344no—
192#386—341no—
193#380—171no—
194#380—172no—
195#380—341no—
196#327—344no—
197#324—22no—
198C2×C17—21no—
199C2×C17—21no—
200C2×C17—21no—
201C2×C17—21no—
202C2×C17—21no—
203C2×C17—21no—
204C2×C17#187411yescharacteristic
205C2×C17#191211yescharacteristic
206C2×C17#191311yescharacteristic
207D17—161no—
208C22×D4—171no—
209C22×D4—341no—
210C23×C4D6811yescharacteristic
211C23×C4D6811yescharacteristic
212C23×C4C22×D1711yescharacteristic
213C22×C8—22no—
214#123—682no—
215#123—682no—
216#121—342no—
217#121—342no—
218#117—682no—
219#117—682no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—171no—
223C2×C4⋊C4—342no—
224C2×C4⋊C4—342no—
225C2×C4⋊C4—342no—
226C2×C4⋊C4—342no—
227C2×C4⋊C4—341no—
228C2×C4⋊C4C4×D1712yes—
229C2×C4⋊C4C22⋊D1712yes—
230C2×C22⋊C4—342no—
231C2×C22⋊C4—341no—
232C2×C22⋊C4—341no—
233C2×C22⋊C4—342no—
234C2×C22⋊C4—342no—
235C2×C42—342no—
236C22⋊C8—22no—
237C22⋊C8—22no—
238#95—172no—
239#95—174no—
240#95—342no—
241#95—342no—
242C17#920411yescharacteristic, complemented, Sylow
243C24—341no—
244C24C2×D6811yescharacteristic
245C2×D4—342no—
246C2×D4—681no—
247C2×D4—681no—
248C2×D4—681no—
249C2×D4—681no—
250C2×D4—681no—
251C2×D4—681no—
252C2×D4—1361no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—81no—
260C22×C4—81no—
261C22×C4—344no—
262C22×C4—342no—
263C22×C4—341no—
264C22×C4#6321912yes—
265C22×C4D13612yes—
266C22×C4#6322712yes—
267C22×C4#6322712yes—
268C22×C4C2×C4×D1711yescharacteristic
269C22×C4D4×D1712yes—
270C22×C4#6325412yes—
271C22×C4C2×C22⋊D1711yescharacteristic
272C2×C8—42no—
273C2×C8—82no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—342no—
277C4⋊C4—684no—
278C4⋊C4—684no—
279C4⋊C4—1362no—
280C4⋊C4—1361no—
281C4⋊C4—1362no—
282C22⋊C4—681no—
283C22⋊C4—682no—
284C22⋊C4—681no—
285C22⋊C4—682no—
286C22⋊C4—684no—
287C22⋊C4—682no—
288C22⋊C4—1362no—
289C42—684no—
290C23—41no—
291C23—41no—
292C23—682no—
293C23—682no—
294C23—681no—
295C23—681no—
296C23—681no—
297C23#1058756811yescharacteristic
298C23#1058757211yescharacteristic
299C23C2×#6321911yescharacteristic
300C23C2×D13611yescharacteristic
301C23#1058759411yescharacteristic
302C23#1058759511yescharacteristic
303C23C2×#6322711yescharacteristic
304D4—1362no—
305D4—1361no—
306D4—1361no—
307D4—1361no—
308D4—1361no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—682no—
324C2×C4—684no—
325C2×C4—684no—
326C2×C4—682no—
327C2×C4—684no—
328C2×C4—682no—
329C2×C4—681no—
330C2×C4—681no—
331C2×C4—681no—
332C2×C4#1058749214yes—
333C2×C4#1058756712yes—
334C2×C4#1058762512yes—
335C8—82no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—1362no—
347C22—1362no—
348C22—1361no—
349C22—1361no—
350C22—1361no—
351C22#1176268611yescharacteristic
352C22C2×#1058749211yescharacteristic
353C22#1176281111yescharacteristic
354C22#1176294511yescharacteristic
355C22#1176295011yescharacteristic
356C22#1176312311yescharacteristic
357C22#1176312811yescharacteristic
358C4—22no—
359C4—22no—
360C4—24no—
361C4—42no—
362C4—1364no—
363C4—1362no—
364C4—1361no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2—2721no—
372C2#1452909911yescharacteristic
373C2#1452931911yescharacteristic
374C2#1452932411yescharacteristic
subgroupG/H
centerC22#11762686
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC2×C17×#324C2
socleC22×C17#386
prime radicalC2×#10587616C22
cosocleC23×C4×C17C23
hypercenterC2×#324D17
hypocenterC17#9204
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #14531402C2semidirect
4. #14526652C2semidirect
5. C2×C17×#324C2semidirect
9. #11762739C4semidirect
11. #11762726C4semidirect
152. C2×#324D17semidirect
242. C17#9204semidirect

Maximal subgroups

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

subgroupindex
#145345262
#145314022
#145273532
#145266522
C2×C17×#3242
#920417