Finite Group Databasebeta

← #17949783

Subgroups — #17949783

Order 4352.

588 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 110 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#14544674C211yesmaximal, characteristic, complemented
2#14544638C211yesmaximal, characteristic, complemented
3#14543603C212yesmaximal, complemented
4#14543601C212yesmaximal, complemented
5#14531290C211yesmaximal, characteristic
6C2×C4⋊#3624—21no—
7C2×C22⋊#3624—21no—
8C2×C22⋊#3624—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#10587616C814yescomplemented
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—42no—
51C22⋊#3624—42no—
52C4⋊#3624—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—41no—
61C22×C4×C17—41no—
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C2×C812yes—
64C22×C4×C17M1612yes—
65C22×C4×C17C22×C411yescharacteristic
66C2×C22⋊D17—24no—
67C2×C22⋊D17—42no—
68C2×C22⋊D17—42no—
69C22×Dic17—21no—
70C22×Dic17—22no—
71C22×Dic17—21no—
72C22×Dic17—22no—
73C22×Dic17—21no—
74C22×Dic17—41no—
75C22×Dic17—41no—
76C22×Dic17—41no—
77C22×Dic17C22⋊C411yescharacteristic
78C22×Dic17C22⋊C411yescharacteristic
79C22×Dic17C2×D411yescharacteristic
80C22×Dic17C2×D411yescharacteristic
81C2×D68—21no—
82C2×D68—41no—
83C2×D68—41no—
84C2×D68C2×C812yes—
85C2×C4×D17—42no—
86C2×C4×D17—42no—
87C2×C4×D17—42no—
88C2×#3624—42no—
89C2×#3624—42no—
90C2×#3624—42no—
91C2×#3624—42no—
92C2×#3624—42no—
93C2×#3624—42no—
94C4⋊C4×C17—41no—
95C4⋊C4×C17—41no—
96C22⋊C4×C17—42no—
97#63227—24no—
98#63227—42no—
99#63227—42no—
100#63227—41no—
101#63227—41no—
102C4⋊Dic17—21no—
103C4⋊Dic17C2×C812yes—
104#63225—42no—
105C4×Dic17—22no—
106C4×Dic17—22no—
107C4×Dic17—41no—
108C4×Dic17—41no—
109C4×Dic17—42no—
110#7599—171nomaximal, Sylow
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17C22⋊C812yes—
118C23×C17C2×C22⋊C411yescharacteristic
119C22×D17—22no—
120C22×D17—41no—
121C22×D17—41no—
122C22×D17—41no—
123C22×D17—41no—
124C22×D17—41no—
125C22×D17—41no—
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—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17C22⋊C812yes—
139C2×C4×C17C22×C811yescharacteristic
140C2×C4×C17C2×M1611yescharacteristic
141C22⋊D17—48no—
142C2×Dic17—21no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17—21no—
147C2×Dic17—21no—
148C2×Dic17—22no—
149C2×Dic17—21no—
150C2×Dic17—21no—
151C2×Dic17—21no—
152C2×Dic17—44no—
153C2×Dic17—42no—
154C2×Dic17—42no—
155C2×Dic17—41no—
156C2×Dic17—41no—
157C2×Dic17#9912yes—
158C2×Dic17AGL(1,ℤ/8)11yescharacteristic
159C2×Dic17AGL(1,ℤ/8)12yes—
160C2×Dic17#13711yescharacteristic
161D68—42no—
162D68—42no—
163C4×D17—84no—
164#3624—82no—
165#3624—82no—
166C4×#121—171no—
167#1817—171no—
168#1797—171no—
169#1271—172no—
170#1270—172no—
171C22×C17—22no—
172C22×C17—22no—
173C22×C17—22no—
174C22×C17—41no—
175C22×C17—41no—
176C22×C17—41no—
177C22×C17—41no—
178C22×C17C2×C22⋊C811yescharacteristic
179C22×C17C2×#9911yescharacteristic
180C22×C17#41311yescharacteristic
181C22×C17#41711yescharacteristic
182C22×C17#41811yescharacteristic
183C22×C17#42111yescharacteristic
184C22×C17#42111yescharacteristic
185C2×D17—42no—
186C2×D17—42no—
187C2×D17—42no—
188C2×D17—81no—
189C2×D17—81no—
190C2×D17—81no—
191C2×D17—81no—
192C4×C17—21no—
193C4×C17—21no—
194C4×C17—22no—
195C4×C17—81no—
196C4×C17—81no—
197Dic17—22no—
198Dic17—22no—
199Dic17—21no—
200Dic17—21no—
201Dic17—42no—
202Dic17—41no—
203C2×#121—171no—
204C2×C4×D4—171no—
205C2×C4×D4—341no—
206C22×C42—171no—
207C2×C4⋊C8—341no—
208C2×C22⋊C8—341no—
209C2×C22⋊C8—341no—
210#390—171no—
211#389—171no—
212#388—341no—
213#386—341no—
214#380#59511yescharacteristic
215C4×C4⋊C4—171no—
216C4×C22⋊C4—341no—
217#336—172no—
218#336—172no—
219#336—341no—
220C2×C17—42no—
221C2×C17#145911yescharacteristic
222C2×C17#147711yescharacteristic
223C2×C17#147811yescharacteristic
224C2×C17#151011yescharacteristic
225C2×C17#151311yescharacteristic
226C2×C17#153511yescharacteristic
227C2×C17#155711yescharacteristic
228D17—82no—
229C22×D4—171no—
230C22×D4—341no—
231C23×C4—171no—
232C23×C4—171no—
233C23×C4—341no—
234C23×C4C2×#59511yescharacteristic
235C22×C8—342no—
236C22×C8—342no—
237#121—174no—
238#121—342no—
239C4×D4—682no—
240C4×D4—684no—
241C2×C4⋊C4—171no—
242C2×C4⋊C4—341no—
243C2×C4⋊C4C2×#59511yescharacteristic
244C2×C4⋊C4C2×#59511yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—341no—
247C2×C22⋊C4—341no—
248C2×C22⋊C4—341no—
249C2×C22⋊C4—341no—
250C2×C42—171no—
251C2×C42—171no—
252C2×C42—171no—
253C2×C42—171no—
254C2×C42—341no—
255C2×C42—682no—
256C4⋊C8—682no—
257C22⋊C8—682no—
258C22⋊C8—682no—
259#95—21no—
260#95—341no—
261#95—341no—
262C17#759911yescharacteristic, complemented, Sylow
263C24—341no—
264C24C22⋊#59511yescharacteristic
265C2×D4—172no—
266C2×D4—344no—
267C2×D4—341no—
268C2×D4—681no—
269C2×D4—681no—
270C2×D4—682no—
271C2×D4—682no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—171no—
277C22×C4—171no—
278C22×C4—171no—
279C22×C4—171no—
280C22×C4—341no—
281C22×C4—342no—
282C22×C4—342no—
283C22×C4—341no—
284C22×C4—341no—
285C22×C4—682no—
286C22×C4—682no—
287C22×C4—682no—
288C22×C4—681no—
289C22×C4—681no—
290C22×C4—681no—
291C22×C4#6324212yes—
292C22×C4#6324312yes—
293C22×C4C22⋊#59511yescharacteristic
294C22×C4C22×#59511yescharacteristic
295C2×C8—682no—
296C2×C8—682no—
297C2×C8—682no—
298C2×C8—682no—
299C2×C8—682no—
300C2×C8—682no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—172no—
304C4⋊C4—341no—
305C4⋊C4—682no—
306C22⋊C4—42no—
307C22⋊C4—344no—
308C22⋊C4—682no—
309C22⋊C4—681no—
310C22⋊C4—681no—
311C22⋊C4—682no—
312C42—342no—
313C42—342no—
314C42—681no—
315C42—681no—
316C42—682no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—342no—
324C23—681no—
325C23—681no—
326C23—681no—
327C23—681no—
328C23—681no—
329C23—681no—
330C23#1058754312yes—
331C23C2×C22⋊#59511yescharacteristic
332D4—682no—
333D4—682no—
334D4—688no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—172no—
348C2×C4—171no—
349C2×C4—171no—
350C2×C4—172no—
351C2×C4—341no—
352C2×C4—341no—
353C2×C4—341no—
354C2×C4—341no—
355C2×C4—341no—
356C2×C4—341no—
357C2×C4—342no—
358C2×C4—341no—
359C2×C4—341no—
360C2×C4—341no—
361C2×C4—684no—
362C2×C4—682no—
363C2×C4—682no—
364C2×C4—681no—
365C2×C4—681no—
366C2×C4—1364no—
367C2×C4#1058754312yes—
368C2×C4C2×#6324211yescharacteristic
369C2×C4C2×#6324311yescharacteristic
370C8—1362no—
371C8—1362no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—682no—
380C22—682no—
381C22—682no—
382C22—1361no—
383C22—1361no—
384C22—1361no—
385C22—1361no—
386C22C2×#1058754311yescharacteristic
387C22D17⋊#9911yescharacteristic
388C22#1176379611yescharacteristic
389C22#1176380011yescharacteristic
390C22#1176380111yescharacteristic
391C22#1176380611yescharacteristic
392C22#1176380811yescharacteristic
393C4—21no—
394C4—21no—
395C4—22no—
396C4—81no—
397C4—81no—
398C4—342no—
399C4—342no—
400C4—341no—
401C4—341no—
402C4—681no—
403C4—682no—
404C2—42no—
405C2—1362no—
406C2#1454402211yescharacteristic
407C2#1454408111yescharacteristic
408C2#1454408511yescharacteristic
409C2#1454419011yescharacteristic
410C2#1454420211yescharacteristic
411C2#1454427111yescharacteristic
412C2#1454431611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#380C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587616C4
cosocleC2×C4×Dic17C23
hypercenter#380#595
hypocenterC17#7599
LCSG ▷ C2×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. #14544674C2semidirect
2. #14544638C2semidirect
3. #14543603C2semidirect
4. #14543601C2semidirect
35. #10587616C8semidirect
262. C17#7599semidirect

Maximal subgroups

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

subgroupindex
#145446742
#145446382
#145436032
#145436012
#145312902
#759917