Finite Group Databasebeta

← #17949859

Subgroups — #17949859

Order 4352.

590 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 94 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#14544675C211yesmaximal, characteristic, complemented
2#14544510C211yesmaximal, characteristic, complemented
3#14543603C212yesmaximal, complemented
4#14543601C212yesmaximal, complemented
5#14531290C211yesmaximal, characteristic
6C2×C22⋊#3624—21no—
7C2×C22⋊#3624—21no—
8C2×#10587542—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587616C411yescharacteristic
13C2×#10587579C411yescharacteristic
14C2×#10587567—21no—
15C22×C4×Dic17C2211yescharacteristic
16#11762710C2211yescharacteristic
17#11762705C2211yescharacteristic
18#11762698—21no—
19#11762686—21no—
20C4⋊C4×Dic17C411yescharacteristic
21#11762656—21no—
22C17×#380C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C22×C22⋊D17—21no—
25C23×Dic17D411yescharacteristic
26C23×Dic17D411yescharacteristic
27C22×D68C2×C411yescharacteristic
28C22×C4×D17—21no—
29C22×#3624—22no—
30C22×#3624—22no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C22⋊C4×C17—21no—
34#10587616—22no—
35#10587616—22no—
36C2×#63227—21no—
37C2×#63227—21no—
38C2×#63227—21no—
39C2×#63227—21no—
40C2×C4⋊Dic17C2×C411yescharacteristic
41C2×#63225—21no—
42C2×C4×Dic17—21no—
43C2×C4×Dic17—42no—
44C2×C4×Dic17C2×C411yescharacteristic
45C2×C4×Dic17D411yescharacteristic
46C2×C4×Dic17D411yescharacteristic
47C2×C4×Dic17C2311yescharacteristic
48#10587579—42no—
49#10587567—44no—
50C22⋊#3624—24no—
51C22⋊#3624—42no—
52#10587542—42no—
53C17×#95—21no—
54#10587502—21no—
55#10587502—21no—
56C24×C17C22⋊C411yescharacteristic
57C23×D17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—41no—
63C22×C4×C17—41no—
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C22×C411yescharacteristic
66C2×C22⋊D17—24no—
67C2×C22⋊D17—42no—
68C2×C22⋊D17—42no—
69C22×Dic17—22no—
70C22×Dic17—21no—
71C22×Dic17—22no—
72C22×Dic17—22no—
73C22×Dic17—22no—
74C22×Dic17—41no—
75C22×Dic17—41no—
76C22×Dic17C22⋊C411yescharacteristic
77C22×Dic17C22⋊C411yescharacteristic
78C22×Dic17C2×D411yescharacteristic
79C22×Dic17C2×D411yescharacteristic
80C2×D68—21no—
81C2×D68—41no—
82C2×D68—41no—
83C2×D68M1612yes—
84C2×C4×D17—42no—
85C2×C4×D17—42no—
86C2×C4×D17—42no—
87C2×#3624—24no—
88C2×#3624—42no—
89C2×#3624—42no—
90C2×#3624—42no—
91C2×#3624—42no—
92C2×#3624—42no—
93C4⋊C4×C17—41no—
94C4⋊C4×C17—41no—
95C22⋊C4×C17—42no—
96#63227—24no—
97#63227—42no—
98#63227—42no—
99#63227—42no—
100C4⋊Dic17—21no—
101C4⋊Dic17M1612yes—
102#63225—42no—
103C4×Dic17—22no—
104C4×Dic17—22no—
105C4×Dic17—41no—
106C4×Dic17—41no—
107C4×Dic17—42no—
108#7620—171nomaximal, Sylow
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—21no—
114C23×C17—21no—
115C23×C17#10412yes—
116C23×C17C2×C22⋊C411yescharacteristic
117C22×D17—22no—
118C22×D17—41no—
119C22×D17—41no—
120C22×D17—41no—
121C22×D17—41no—
122C22×D17—41no—
123C22×D17—41no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—42no—
130C2×C4×C17—42no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17C2×M1611yescharacteristic
138C2×C4×C17C2×M1611yescharacteristic
139C22⋊D17—48no—
140C2×Dic17—21no—
141C2×Dic17—21no—
142C2×Dic17—21no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17—22no—
147C2×Dic17—21no—
148C2×Dic17—21no—
149C2×Dic17—21no—
150C2×Dic17—44no—
151C2×Dic17—44no—
152C2×Dic17—41no—
153C2×Dic17—41no—
154C2×Dic17#9912yes—
155C2×Dic17#13512yes—
156C2×Dic17AGL(1,ℤ/8)12yes—
157D68—42no—
158D68—42no—
159C4×D17—84no—
160#3624—44no—
161#3624—82no—
162C4×#121—171no—
163#1817—171no—
164#1749—171no—
165#1271—172no—
166#1270—172no—
167C22×C17—22no—
168C22×C17—22no—
169C22×C17—22no—
170C22×C17—41no—
171C22×C17—41no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17#40711yescharacteristic
175C22×C17C2×#9911yescharacteristic
176C22×C17#41311yescharacteristic
177C22×C17#41611yescharacteristic
178C22×C17#41811yescharacteristic
179C22×C17C2×#10411yescharacteristic
180C22×C17#42111yescharacteristic
181C2×D17—42no—
182C2×D17—42no—
183C2×D17—42no—
184C2×D17—81no—
185C2×D17—81no—
186C2×D17—81no—
187C2×D17—81no—
188C4×C17—21no—
189C4×C17—21no—
190C4×C17—41no—
191C4×C17—81no—
192C4×C17—81no—
193Dic17—22no—
194Dic17—22no—
195Dic17—22no—
196Dic17—42no—
197Dic17—41no—
198C2×#121—171no—
199C2×C4×D4—171no—
200C2×C4×D4—341no—
201C22×C42—171no—
202C2×C22⋊C8—341no—
203C2×C22⋊C8—341no—
204C2×#97—341no—
205#390—171no—
206#389—171no—
207#388—341no—
208#386—341no—
209#380#59511yescharacteristic
210C4×C4⋊C4—171no—
211C4×C22⋊C4—341no—
212#336—172no—
213#336—172no—
214#336—341no—
215C2×C17—42no—
216C2×C17#146511yescharacteristic
217C2×C17#148811yescharacteristic
218C2×C17#149011yescharacteristic
219C2×C17#150111yescharacteristic
220C2×C17#151011yescharacteristic
221C2×C17#153211yescharacteristic
222C2×C17#155311yescharacteristic
223D17—82no—
224C22×D4—171no—
225C22×D4—341no—
226C23×C4—171no—
227C23×C4—171no—
228C23×C4—341no—
229C23×C4C2×#59511yescharacteristic
230C22×C8—342no—
231C22×C8—342no—
232#121—342no—
233#121—342no—
234C4×D4—682no—
235C4×D4—684no—
236C2×C4⋊C4—171no—
237C2×C4⋊C4—341no—
238C2×C4⋊C4C2×#59511yescharacteristic
239C2×C4⋊C4C2×#59511yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—341no—
242C2×C22⋊C4—341no—
243C2×C22⋊C4—341no—
244C2×C22⋊C4—341no—
245C2×C42—171no—
246C2×C42—171no—
247C2×C42—171no—
248C2×C42—171no—
249C2×C42—341no—
250C2×C42—682no—
251C22⋊C8—344no—
252C22⋊C8—682no—
253#97—682no—
254#95—21no—
255#95—341no—
256#95—341no—
257C17#762011yescharacteristic, complemented, Sylow
258C24—341no—
259C24C22⋊#59511yescharacteristic
260C2×D4—172no—
261C2×D4—344no—
262C2×D4—341no—
263C2×D4—681no—
264C2×D4—681no—
265C2×D4—682no—
266C2×D4—682no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—171no—
274C22×C4—171no—
275C22×C4—171no—
276C22×C4—171no—
277C22×C4—342no—
278C22×C4—342no—
279C22×C4—342no—
280C22×C4—341no—
281C22×C4—342no—
282C22×C4—682no—
283C22×C4—682no—
284C22×C4—682no—
285C22×C4—681no—
286C22×C4—681no—
287C22×C4C22⋊#59511yescharacteristic
288C22×C4C22×#59511yescharacteristic
289C2×C8—344no—
290C2×C8—682no—
291C2×C8—682no—
292C2×C8—682no—
293C2×C8—682no—
294C2×C8—682no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—172no—
298C4⋊C4—341no—
299C4⋊C4—682no—
300C22⋊C4—42no—
301C22⋊C4—344no—
302C22⋊C4—682no—
303C22⋊C4—682no—
304C22⋊C4—682no—
305C42—342no—
306C42—342no—
307C42—681no—
308C42—681no—
309C42—682no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—342no—
317C23—681no—
318C23—681no—
319C23—681no—
320C23—681no—
321C23—681no—
322C23—681no—
323C23#1058755012yes—
324C23C2×C22⋊#59511yescharacteristic
325D4—682no—
326D4—682no—
327D4—688no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—172no—
342C2×C4—172no—
343C2×C4—172no—
344C2×C4—341no—
345C2×C4—341no—
346C2×C4—341no—
347C2×C4—341no—
348C2×C4—341no—
349C2×C4—341no—
350C2×C4—342no—
351C2×C4—341no—
352C2×C4—341no—
353C2×C4—341no—
354C2×C4—684no—
355C2×C4—684no—
356C2×C4—681no—
357C2×C4—681no—
358C2×C4—1364no—
359C2×C4D17⋊M1611yescharacteristic
360C2×C4D17⋊M1611yescharacteristic
361C8—684no—
362C8—1362no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—682no—
371C22—682no—
372C22—682no—
373C22—1361no—
374C22—1361no—
375C22—1361no—
376C22—1361no—
377C22#1176378111yescharacteristic
378C22D17⋊#9911yescharacteristic
379C22#1176379611yescharacteristic
380C22#1176379911yescharacteristic
381C22#1176380111yescharacteristic
382C22C2×#1058755011yescharacteristic
383C22#1176380611yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—81no—
388C4—81no—
389C4—342no—
390C4—342no—
391C4—342no—
392C4—681no—
393C4—682no—
394C2—42no—
395C2—1362no—
396C2#1454404211yescharacteristic
397C2#1454411711yescharacteristic
398C2#1454412511yescharacteristic
399C2#1454416211yescharacteristic
400C2#1454419011yescharacteristic
401C2#1454426211yescharacteristic
402C2#1454430811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#380C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587616C4
cosocleC2×C4×Dic17C23
hypercenter#380#595
hypocenterC17#7620
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. #14544675C2semidirect
2. #14544510C2semidirect
3. #14543603C2semidirect
4. #14543601C2semidirect
257. C17#7620semidirect

Maximal subgroups

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

subgroupindex
#145446752
#145445102
#145436032
#145436012
#145312902
#762017