Finite Group Databasebeta

← #17956941

Subgroups — #17956941

Order 4352.

802 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763689C212yesmaximal
2C2×#11763689C212yesmaximal
3#14544447C212yesmaximal
4C2×#11762660C211yesmaximal, characteristic
5C22×#63247C2214yes—
6#11763689—24no—
7#11763689C418yescomplemented
8#11763675—22no—
9#11763675—22no—
10C22×#63225C2211yescharacteristic
11C22×#63225C2211yescharacteristic
12C22×C4×Dic17C411yescharacteristic
13C22×C4×Dic17C411yescharacteristic
14C22×C4×Dic17C2211yescharacteristic
15#11762660—22no—
16#11762660—22no—
17C2×#10587502C411yescharacteristic
18C2×C17×#95C411yescharacteristic
19C23×C4×C17C2×C411yescharacteristic
20C23×C4×C17C2×C411yescharacteristic
21C23×C4×C17C2×C411yescharacteristic
22C23×Dic17C2×C411yescharacteristic
23C23×Dic17C2×C411yescharacteristic
24C23×Dic17C2×C411yescharacteristic
25C23×Dic17C2311yescharacteristic
26C2×#63247—24no—
27C2×#63247—24no—
28C2×#63247—24no—
29C2×#63247—24no—
30C2×#63247—24no—
31C2×#63247C2×C418yes—
32C22×#3624—24no—
33C2×#63225—22no—
34C2×#63225—22no—
35C2×#63225—22no—
36C2×#63225—22no—
37C2×#63225C2×C414yes—
38C2×#63225D412yes—
39C2×#63225Q812yes—
40C2×C4×Dic17—21no—
41C2×C4×Dic17—21no—
42C2×C4×Dic17—21no—
43C2×C4×Dic17—21no—
44C2×C4×Dic17—22no—
45C2×C4×Dic17—22no—
46C2×C4×Dic17—42no—
47C2×C4×Dic17—42no—
48C2×C4×Dic17D412yes—
49C2×C4×Dic17D412yes—
50C17×#95—22no—
51#10587502—22no—
52C24×C17C22×C411yescharacteristic
53C22×C4×C17—21no—
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—41no—
60C22×C4×C17—41no—
61C22×C4×C17—41no—
62C22×C4×C17—41no—
63C22×C4×C17—41no—
64C22×C4×C17—41no—
65C22×C4×C17C4212yes—
66C22×C4×C17C22⋊C412yes—
67C22×C4×C17C4⋊C412yes—
68C22×Dic17—21no—
69C22×Dic17—21no—
70C22×Dic17—22no—
71C22×Dic17—22no—
72C22×Dic17—21no—
73C22×Dic17—21no—
74C22×Dic17—21no—
75C22×Dic17—21no—
76C22×Dic17—41no—
77C22×Dic17—41no—
78C22×Dic17—41no—
79C22×Dic17—41no—
80C22×Dic17C4212yes—
81C22×Dic17C22⋊C411yescharacteristic
82C22×Dic17C22⋊C411yescharacteristic
83C22×Dic17C4⋊C412yes—
84C22×Dic17C22×C412yes—
85C22×Dic17C2×D411yescharacteristic
86C22×Dic17C2×D412yes—
87C22×Dic17C2×Q811yescharacteristic
88C22×Dic17#4112yes—
89C22×Dic17#4112yes—
90C22×Dic17#4112yes—
91C22×Dic17#4112yes—
92#63247—28no—
93#63247—28no—
94#63247—44no—
95#63247—44no—
96C2×#3624—28no—
97C2×#3624—44no—
98C2×#3624—44no—
99#63225—28no—
100#63225—24no—
101#63225—24no—
102C4×Dic17—24no—
103C4×Dic17—24no—
104C4×Dic17—42no—
105C4×Dic17—42no—
106C4×Dic17—42no—
107C4×Dic17—42no—
108#10802—171nomaximal, Sylow
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—21no—
113C23×C17C2×C4211yescharacteristic
114C23×C17C2×C22⋊C411yescharacteristic
115C23×C17C2×C4⋊C411yescharacteristic
116C23×C17#11711yescharacteristic
117C23×C17#11711yescharacteristic
118C23×C17#11711yescharacteristic
119C23×C17#11711yescharacteristic
120C2×C4×C17—22no—
121C2×C4×C17—22no—
122C2×C4×C17—22no—
123C2×C4×C17—22no—
124C2×C4×C17—22no—
125C2×C4×C17—42no—
126C2×C4×C17—42no—
127C2×C4×C17—42no—
128C2×C4×C17—42no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—42no—
134C2×C4×C17—42no—
135C2×Dic17—24no—
136C2×Dic17—24no—
137C2×Dic17—21no—
138C2×Dic17—21no—
139C2×Dic17—21no—
140C2×Dic17—21no—
141C2×Dic17—22no—
142C2×Dic17—22no—
143C2×Dic17—42no—
144C2×Dic17—42no—
145C2×Dic17—41no—
146C2×Dic17—41no—
147C2×Dic17—41no—
148C2×Dic17—41no—
149C2×Dic17—42no—
150C2×Dic17—42no—
151C2×Dic17#10012yes—
152C2×Dic17#10112yes—
153C2×Dic17#11714yes—
154C2×Dic17C4×D414yes—
155C2×Dic17C4×D412yes—
156C2×Dic17C4×Q812yes—
157C2×Dic17#12112yes—
158C2×Dic17C22⋊Q812yes—
159C2×Dic17#12314yes—
160C2×Dic17#12412yes—
161C2×Dic17#12512yes—
162C2×Dic17#12614yes—
163#3624—48no—
164C2×C4×C4⋊C4—171no—
165C2×#343—172no—
166C2×#343—172no—
167#1728—172no—
168C22×C17—21no—
169C22×C17—21no—
170C22×C17—21no—
171C22×C17—21no—
172C22×C17—21no—
173C22×C17—21no—
174C22×C17—21no—
175C22×C17—21no—
176C22×C17—21no—
177C22×C17—21no—
178C22×C17—21no—
179C22×C17—21no—
180C22×C17#37611yescharacteristic
181C22×C17C4×C22⋊C411yescharacteristic
182C22×C17C4×C4⋊C411yescharacteristic
183C22×C17#38011yescharacteristic
184C22×C17#38111yescharacteristic
185C22×C17#38211yescharacteristic
186C22×C17#38311yescharacteristic
187C22×C17C2×#10011yescharacteristic
188C22×C17C2×#10111yescharacteristic
189C22×C17#41311yescharacteristic
190C22×C17#41311yescharacteristic
191C4×C17—42no—
192C4×C17—42no—
193C4×C17—42no—
194Dic17—22no—
195Dic17—22no—
196Dic17—42no—
197Dic17—42no—
198Dic17#38714yes—
199Dic17#38814yes—
200C22×M16—174no—
201C22×C4⋊C4—171no—
202C22×C4⋊C4—171no—
203C22×C42—171no—
204C22×C42—171no—
205C22×C42—171no—
206C4×C4⋊C4—342no—
207C4×C4⋊C4—342no—
208C2×#95—171no—
209C2×#95#59511yescharacteristic
210#343—178no—
211#343—344no—
212#336—342no—
213#336—342no—
214C2×C17—21no—
215C2×C17—21no—
216C2×C17—21no—
217C2×C17—21no—
218C2×C17#143411yescharacteristic
219C2×C17C4×#10011yescharacteristic
220C2×C17C4×#10111yescharacteristic
221C2×C17#180011yescharacteristic
222C2×C17#180111yescharacteristic
223C2×C17#182111yescharacteristic
224C2×C17#182211yescharacteristic
225C23×C4—171no—
226C23×C4—171no—
227C23×C4—171no—
228C23×C4—171no—
229C23×C4C2×#59511yescharacteristic
230C23×C4C2×#59511yescharacteristic
231C23×C4C2×#59511yescharacteristic
232C2×M16—178no—
233C2×M16—344no—
234C2×M16—344no—
235C2×M16—344no—
236C2×M16—344no—
237C2×M16—344no—
238C22×C8—344no—
239C2×C4⋊C4—174no—
240C2×C4⋊C4—172no—
241C2×C4⋊C4—172no—
242C2×C4⋊C4—342no—
243C2×C4⋊C4—342no—
244C2×C4⋊C4—342no—
245C2×C4⋊C4—342no—
246C2×C42—172no—
247C2×C42—172no—
248C2×C42—342no—
249C2×C42—342no—
250C2×C42—341no—
251C2×C42—341no—
252C2×C42—341no—
253C2×C42—341no—
254C2×C42—682no—
255C2×C42—682no—
256#95—22no—
257#95—342no—
258C17#1080211yescharacteristic, complemented, Sylow
259C24C22×#59511yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—172no—
273C22×C4—171no—
274C22×C4—171no—
275C22×C4—172no—
276C22×C4—172no—
277C22×C4—172no—
278C22×C4—172no—
279C22×C4—172no—
280C22×C4—171no—
281C22×C4—171no—
282C22×C4—172no—
283C22×C4—172no—
284C22×C4—342no—
285C22×C4—342no—
286C22×C4—341no—
287C22×C4—341no—
288C22×C4—341no—
289C22×C4—341no—
290C22×C4—341no—
291C22×C4—341no—
292C22×C4—681no—
293C22×C4—681no—
294C22×C4—681no—
295C22×C4—681no—
296C22×C4C4×#59512yes—
297C22×C4C4⋊#59512yes—
298C22×C4C22⋊#59512yes—
299M16—348no—
300M16—348no—
301M16—684no—
302M16—684no—
303C2×C8—348no—
304C2×C8—684no—
305C2×C8—684no—
306C4⋊C4—348no—
307C4⋊C4—344no—
308C4⋊C4—344no—
309C42—344no—
310C42—344no—
311C42—682no—
312C42—682no—
313C42—682no—
314C42—682no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23C2×C4×#59511yescharacteristic
320C23C2×C4⋊#59511yescharacteristic
321C23#1058767711yescharacteristic
322C23#1058767711yescharacteristic
323C23#1058767711yescharacteristic
324C23#1058767711yescharacteristic
325C23C2×C22⋊#59511yescharacteristic
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—174no—
342C2×C4—174no—
343C2×C4—172no—
344C2×C4—172no—
345C2×C4—172no—
346C2×C4—172no—
347C2×C4—174no—
348C2×C4—172no—
349C2×C4—172no—
350C2×C4—174no—
351C2×C4—172no—
352C2×C4—172no—
353C2×C4—344no—
354C2×C4—344no—
355C2×C4—341no—
356C2×C4—341no—
357C2×C4—341no—
358C2×C4—341no—
359C2×C4—342no—
360C2×C4—342no—
361C2×C4—682no—
362C2×C4—682no—
363C2×C4—681no—
364C2×C4—681no—
365C2×C4—681no—
366C2×C4—681no—
367C2×C4—682no—
368C2×C4—682no—
369C8—688no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22#1176374511yescharacteristic
383C22C4×C22⋊#59511yescharacteristic
384C22C4×C4⋊#59511yescharacteristic
385C22#1176375111yescharacteristic
386C22#1176375211yescharacteristic
387C22#1176375311yescharacteristic
388C22#1176375411yescharacteristic
389C22D17⋊#10011yescharacteristic
390C22D17⋊#10111yescharacteristic
391C22#1176379611yescharacteristic
392C22#1176379611yescharacteristic
393C4—42no—
394C4—42no—
395C4—42no—
396C4—174no—
397C4—174no—
398C4—342no—
399C4—342no—
400C4—682no—
401C4—682no—
402C2—21no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2#1454396011yescharacteristic
407C2#1454453411yescharacteristic
408C2#1454453711yescharacteristic
409C2#1454464911yescharacteristic
410C2#1454465111yescharacteristic
411C2#1454468411yescharacteristic
412C2#1454468611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC23×C17C2×C42
FrattiniC24C22×#595
FittingC2×C17×#95C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22×C4
cosocleC23×Dic17C23
hypercenterC2×#95#595
hypocenterC17#10802
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
7. #11763689C4semidirect
258. C17#10802semidirect

Maximal subgroups

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

subgroupindex
C2×#117636892
#145444472
C2×#117626602
#1080217