Finite Group Databasebeta

← #17958287

Subgroups — #17958287

Order 4352.

488 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 90 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#14544023C211yesmaximal, characteristic
2#14544019C211yesmaximal, characteristic
3#14543729C212yesmaximal, complemented
4#14543710C212yesmaximal, complemented
5C4×#10587615C211yesmaximal, characteristic
6#11763826—21no—
7#11763777—21no—
8#11763655—21no—
9#11763653—21no—
10#11763652C2212yes—
11#11763652C2212yes—
12C2×#10587615C411yescharacteristic
13C2×C4×C22⋊D17C2211yescharacteristic
14#11762700—21no—
15#11762693—21no—
16#11762688C411yescharacteristic
17#11762682C2211yescharacteristic
18#11762672C2211yescharacteristic
19C4×#63225—21no—
20C4×#63227—21no—
21C4×C22⋊Dic17C411yescharacteristic
22C22×C42×C17C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C22×C22⋊D17C2×C411yescharacteristic
27C22×C4×D17D411yescharacteristic
28C2×#63242—41no—
29C2×C42×C17—21no—
30C2×C42×C17—21no—
31C2×C42×C17—41no—
32C2×C42×C17—41no—
33C2×C22⋊Dic17C2×C411yescharacteristic
34C2×C22⋊Dic17C2×C411yescharacteristic
35C2×C22⋊Dic17C2311yescharacteristic
36#10587615—22no—
37#10587615C814yescomplemented
38C4×C22⋊D17—41no—
39C4×C22⋊D17—41no—
40C2×#63227—21no—
41C2×#63227—21no—
42C2×#63227D411yescharacteristic
43C2×#63225—21no—
44C2×#63225—21no—
45C2×#63225D411yescharacteristic
46C2×C4×Dic17—21no—
47C2×C4×Dic17D411yescharacteristic
48C22⋊#3624—22no—
49C22⋊#3624—22no—
50#10587544—41no—
51#10587543—41no—
52C4×#3624—41no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58C24×C17C22×C411yescharacteristic
59C23×D17C22⋊C411yescharacteristic
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—42no—
66C22×C4×C17—42no—
67C22×C4×C17—41no—
68C22×C4×C17—41no—
69C22×C4×C17—41no—
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C2×C812yescomplemented
73C2×C22⋊D17—41no—
74C2×C22⋊D17—41no—
75C2×C22⋊D17C2×C812yes—
76C2×C22⋊D17M1612yes—
77C22×Dic17—21no—
78C22×Dic17—21no—
79C22×Dic17C22⋊C411yescharacteristic
80C22×Dic17C2×D411yescharacteristic
81C22×Dic17C2×D411yescharacteristic
82C2×C4×D17—21no—
83C2×C4×D17—21no—
84C2×C4×D17—42no—
85C2×#3624—42no—
86C2×#3624—42no—
87#63242—82no—
88C42×C17—42no—
89C42×C17—41no—
90C42×C17—41no—
91C22⋊Dic17—21no—
92C22⋊Dic17—41no—
93C22⋊Dic17—41no—
94C22⋊Dic17C2×C812yescomplemented
95#63227—24no—
96#63227—41no—
97#63227—42no—
98#63225—24no—
99#63225—41no—
100#63225—42no—
101C4×Dic17—21no—
102C4×Dic17—21no—
103C4×Dic17—42no—
104#11472—171nomaximal, Sylow
105C23×C17—21no—
106C23×C17—21no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17C2×C22⋊C411yescharacteristic
110C23×C17C22×C811yescharacteristic
111C23×C17C2×M1611yescharacteristic
112C22×D17—21no—
113C22×D17—21no—
114C22×D17—41no—
115C22×D17—41no—
116C22×D17C22⋊C812yes—
117C2×C4×C17—22no—
118C2×C4×C17—22no—
119C2×C4×C17—22no—
120C2×C4×C17—21no—
121C2×C4×C17—42no—
122C2×C4×C17—41no—
123C2×C4×C17—42no—
124C2×C4×C17—42no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—42no—
129C2×C4×C17—41no—
130C2×C4×C17—42no—
131C2×C4×C17—42no—
132C2×C4×C17#9911yescharacteristic
133C2×C4×C17#9911yescharacteristic
134C22⋊D17—42no—
135C22⋊D17—42no—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—22no—
139C2×Dic17—21no—
140C2×Dic17—21no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146C2×Dic17—41no—
147C2×Dic17—41no—
148C2×Dic17C22⋊C812yes—
149C4×D17—42no—
150C4×D17—81no—
151#3624—82no—
152#3624—82no—
153C4×#123—171no—
154#1460—171no—
155#1459—171no—
156#1326—172no—
157#1317—172no—
158C22×C17—21no—
159C22×C17—21no—
160C22×C17—21no—
161C22×C17—21no—
162C22×C17—41no—
163C22×C17—41no—
164C22×C17—42no—
165C22×C17—41no—
166C22×C17—41no—
167C22×C17C2×C22⋊C811yescharacteristic
168C22×C17C2×#9911yescharacteristic
169C22×C17#41311yescharacteristic
170C2×D17—22no—
171C2×D17—41no—
172C2×D17—41no—
173C2×D17—42no—
174C2×D17—81no—
175C4×C17—21no—
176C4×C17—41no—
177C4×C17—42no—
178C4×C17—42no—
179C4×C17#35212yes—
180Dic17—22no—
181Dic17—42no—
182Dic17—41no—
183Dic17—41no—
184Dic17—81no—
185C2×#123—171no—
186C2×C4×D4—171no—
187C22×C42#59511yescharacteristic
188#431—341no—
189C2×C22⋊C8—341no—
190#388—341no—
191#387—341no—
192#386—171no—
193#385—171no—
194#381—171no—
195C4×C4⋊C4—341no—
196C4×C22⋊C4—171no—
197C4×C22⋊C4—341no—
198#324—341no—
199#323—172no—
200#323—172no—
201#323—341no—
202C2×C17—21no—
203C2×C17—21no—
204C2×C17—41no—
205C2×C17—41no—
206C2×C17#145911yescharacteristic
207C2×C17C2×#35211yescharacteristic
208C2×C17#212011yescharacteristic
209D17—42no—
210C22×D4—171no—
211C23×C4—171no—
212C23×C4C2×#59511yescharacteristic
213C23×C4C2×#59511yescharacteristic
214C23×C4C2×#59511yescharacteristic
215C22×C8—681no—
216#123—174no—
217#123—342no—
218C4×D4—681no—
219C4×D4—681no—
220C2×C4⋊C4—171no—
221C2×C4⋊C4—341no—
222C2×C4⋊C4—341no—
223C2×C22⋊C4—171no—
224C2×C22⋊C4—171no—
225C2×C22⋊C4—171no—
226C2×C22⋊C4—171no—
227C2×C22⋊C4—341no—
228C2×C22⋊C4—341no—
229C2×C42—21no—
230C2×C42—21no—
231C2×C42—41no—
232C2×C42—41no—
233C2×C42—171no—
234C2×C42—341no—
235C4⋊C8—681no—
236C22⋊C8—342no—
237C22⋊C8—342no—
238C22⋊C8—681no—
239C4×C8—681no—
240#95—341no—
241#95—341no—
242#95—341no—
243#95—341no—
244#95—341no—
245C17#1147211yescharacteristic, complemented, Sylow
246C24—171no—
247C24C22×#59511yescharacteristic
248C2×D4—172no—
249C2×D4—172no—
250C2×D4—681no—
251C2×D4—681no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—171no—
263C22×C4—171no—
264C22×C4—171no—
265C22×C4—341no—
266C22×C4—341no—
267C22×C4—341no—
268C22×C4—341no—
269C22×C4—682no—
270C22×C4#6324212yescomplemented
271C22×C4C22⋊#59511yescharacteristic
272C22×C4C22⋊#59511yescharacteristic
273C2×C8—682no—
274C2×C8—682no—
275C2×C8—1362no—
276C4⋊C4—344no—
277C4⋊C4—681no—
278C4⋊C4—682no—
279C22⋊C4—172no—
280C22⋊C4—344no—
281C22⋊C4—341no—
282C22⋊C4—681no—
283C22⋊C4—682no—
284C22⋊C4—681no—
285C22⋊C4—681no—
286C42—42no—
287C42—41no—
288C42—41no—
289C42—341no—
290C42—341no—
291C42—682no—
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—172no—
297C23—341no—
298C23—341no—
299C23—681no—
300C23—681no—
301C23C2×#6324211yescharacteristic
302C23D17⋊M1611yescharacteristic
303C23C2×C22⋊#59511yescharacteristic
304D4—682no—
305D4—682no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—172no—
322C2×C4—341no—
323C2×C4—341no—
324C2×C4—342no—
325C2×C4—341no—
326C2×C4—341no—
327C2×C4—681no—
328C2×C4—681no—
329C2×C4—682no—
330C2×C4—681no—
331C2×C4—681no—
332C2×C4—681no—
333C2×C4—681no—
334C2×C4—681no—
335C2×C4—1361no—
336C2×C4#1058755111yescharacteristic
337C2×C4#1058755111yescharacteristic
338C8—1362no—
339C8—1362no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—342no—
350C22—682no—
351C22—681no—
352C22—681no—
353C22—1361no—
354C22#1176377711yescharacteristic
355C22C2×#1058755111yescharacteristic
356C22#1176379511yescharacteristic
357C4—21no—
358C4—41no—
359C4—42no—
360C4—42no—
361C4—342no—
362C4—682no—
363C4—681no—
364C4—681no—
365C4—1361no—
366C4#1176371112yes—
367C2—21no—
368C2—21no—
369C2—41no—
370C2—41no—
371C2—682no—
372C2#1454401911yescharacteristic
373C2C2×#1176371111yescharacteristic
374C2#1454503511yescharacteristic
subgroupG/H
centerC2×C4#10587551
commutatorC23×C17C22×C8
FrattiniC24C22×#595
FittingC22×C42×C17C4
socleC22×C17C2×#99
prime radicalC22×C22⋊D17C2×C4
cosocleC2×C22⋊Dic17C23
hypercenterC22×C42#595
hypocenterC17#11472
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
3. #14543729C2semidirect
4. #14543710C2semidirect
37. #10587615C8semidirect
72. C22×C4×C17C2×C8semidirect
94. C22⋊Dic17C2×C8semidirect
245. C17#11472semidirect
270. C22×C4#63242semidirect

Maximal subgroups

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

subgroupindex
#145440232
#145440192
#145437292
#145437102
C4×#105876152
#1147217