Finite Group Databasebeta

← #17951765

Subgroups — #17951765

Order 4352.

914 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14544510C212yesmaximal, complemented
2C2×#11763653C212yesmaximal
3#14543622C212yesmaximal, complemented
4C2×#11762656C211yesmaximal, characteristic
5C2×C22⋊#3624C2214yes—
6C2×#10587542—22no—
7#11763675—22no—
8#11763653C418yescomplemented
9C23×C4×D17C411yescharacteristic
10C22×#63227C411yescharacteristic
11C22×#63227C2211yescharacteristic
12C22×C4×Dic17C411yescharacteristic
13C22×C4×Dic17C2211yescharacteristic
14#11762656—22no—
15#11762656—22no—
16C2×#10587502C2211yescharacteristic
17C2×C17×#95C411yescharacteristic
18C24×D17C2×C411yescharacteristic
19C23×C4×C17C2×C411yescharacteristic
20C23×C4×C17C2×C411yescharacteristic
21C23×C4×C17C2×C411yescharacteristic
22C23×Dic17C2×C411yescharacteristic
23C23×Dic17C2×C411yescharacteristic
24C23×Dic17C2311yescharacteristic
25C22×C4×D17—22no—
26C22×C4×D17—22no—
27C22×C4×D17—21no—
28C22×C4×D17—21no—
29C22×C4×D17—42no—
30C22×C4×D17—42no—
31C22×#3624—24no—
32C2×#63227—22no—
33C2×#63227—22no—
34C2×#63227—22no—
35C2×#63227—22no—
36C2×#63227—22no—
37C2×#63227C2×C414yes—
38C2×C4×Dic17—21no—
39C2×C4×Dic17—21no—
40C2×C4×Dic17—42no—
41C2×C4×Dic17—42no—
42C2×C4×Dic17D412yes—
43C2×C4×Dic17D412yes—
44C22⋊#3624—24no—
45C22⋊#3624C2×C418yescomplemented
46#10587542—44no—
47C17×#95—22no—
48#10587502—22no—
49C24×C17C22×C411yescharacteristic
50C23×D17—21no—
51C23×D17—21no—
52C23×D17—21no—
53C23×D17—21no—
54C23×D17—41no—
55C23×D17—41no—
56C23×D17—41no—
57C23×D17—41no—
58C23×D17C4212yes—
59C23×D17M1612yes—
60C23×D17M1612yes—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—41no—
68C22×C4×C17—41no—
69C22×C4×C17—41no—
70C22×C4×C17—41no—
71C22×C4×C17—41no—
72C22×C4×C17—41no—
73C22×C4×C17C4212yes—
74C22×C4×C17C22⋊C412yes—
75C22×C4×C17M1612yes—
76C22×Dic17—21no—
77C22×Dic17—21no—
78C22×Dic17—22no—
79C22×Dic17—22no—
80C22×Dic17—21no—
81C22×Dic17—21no—
82C22×Dic17—41no—
83C22×Dic17—41no—
84C22×Dic17—41no—
85C22×Dic17—41no—
86C22×Dic17C22⋊C411yescharacteristic
87C22×Dic17C22⋊C411yescharacteristic
88C22×Dic17M1612yes—
89C22×Dic17C22×C412yes—
90C22×Dic17C2×D412yes—
91C22×Dic17#4112yes—
92C2×C4×D17—24no—
93C2×C4×D17—24no—
94C2×C4×D17—48no—
95C2×C4×D17—48no—
96C2×C4×D17—42no—
97C2×C4×D17—42no—
98C2×C4×D17—42no—
99C2×C4×D17—42no—
100C2×#3624—28no—
101C2×#3624—44no—
102C2×#3624—44no—
103#63227—28no—
104#63227—28no—
105C4×Dic17—24no—
106C4×Dic17—42no—
107C4×Dic17—42no—
108C4×Dic17—42no—
109#8152—171nomaximal, Sylow
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—21no—
114C23×C17C2×C4211yescharacteristic
115C23×C17C2×C22⋊C411yescharacteristic
116C23×C17#11711yescharacteristic
117C23×C17C2×M1611yescharacteristic
118C23×C17C2×M1611yescharacteristic
119C23×C17C2×M1611yescharacteristic
120C23×C17C2×M1611yescharacteristic
121C22×D17—22no—
122C22×D17—22no—
123C22×D17—22no—
124C22×D17—22no—
125C22×D17—22no—
126C22×D17—22no—
127C22×D17—42no—
128C22×D17—42no—
129C22×D17—42no—
130C22×D17—42no—
131C22×D17—42no—
132C22×D17—42no—
133C22×D17—41no—
134C22×D17—41no—
135C22×D17—41no—
136C22×D17—41no—
137C22×D17—42no—
138C22×D17—42no—
139C22×D17—42no—
140C22×D17—42no—
141C22×D17—42no—
142C22×D17—42no—
143C22×D17#9714yescomplemented
144C2×C4×C17—22no—
145C2×C4×C17—22no—
146C2×C4×C17—22no—
147C2×C4×C17—22no—
148C2×C4×C17—22no—
149C2×C4×C17—42no—
150C2×C4×C17—42no—
151C2×C4×C17—42no—
152C2×C4×C17—42no—
153C2×C4×C17—41no—
154C2×C4×C17—41no—
155C2×C4×C17—41no—
156C2×C4×C17—41no—
157C2×C4×C17—42no—
158C2×C4×C17—42no—
159C2×Dic17—24no—
160C2×Dic17—24no—
161C2×Dic17—21no—
162C2×Dic17—21no—
163C2×Dic17—22no—
164C2×Dic17—21no—
165C2×Dic17—22no—
166C2×Dic17—21no—
167C2×Dic17—22no—
168C2×Dic17—42no—
169C2×Dic17—42no—
170C2×Dic17—42no—
171C2×Dic17—41no—
172C2×Dic17—41no—
173C2×Dic17—42no—
174C2×Dic17#9912yes—
175C2×Dic17#10012yes—
176C2×Dic17C4×D414yes—
177C4×D17—48no—
178C4×D17—48no—
179#3624—48no—
180C2×C4×C22⋊C4—171no—
181#1749—172no—
182C2×#323—172no—
183#1280—172no—
184C22×C17—21no—
185C22×C17—21no—
186C22×C17—21no—
187C22×C17—21no—
188C22×C17—21no—
189C22×C17—21no—
190C22×C17—21no—
191C22×C17—21no—
192C22×C17—21no—
193C22×C17—21no—
194C22×C17—21no—
195C22×C17—21no—
196C22×C17C4×C22⋊C411yescharacteristic
197C22×C17C2×#9711yescharacteristic
198C22×C17C4×M1611yescharacteristic
199C22×C17#40711yescharacteristic
200C22×C17#40711yescharacteristic
201C22×C17C2×#9911yescharacteristic
202C22×C17#41011yescharacteristic
203C22×C17C2×#10011yescharacteristic
204C22×C17#41311yescharacteristic
205C22×C17#43211yescharacteristic
206C22×C17#43211yescharacteristic
207C2×D17—24no—
208C2×D17—44no—
209C2×D17—44no—
210C2×D17—44no—
211C2×D17—42no—
212C2×D17—42no—
213C2×D17—42no—
214C2×D17—42no—
215C2×D17—42no—
216C2×D17—42no—
217C2×D17—44no—
218C4×C17—42no—
219C4×C17—42no—
220C4×C17—42no—
221Dic17—22no—
222Dic17—22no—
223Dic17—24no—
224Dic17—42no—
225C24×C4—171no—
226C22×C22⋊C4—171no—
227C22×C22⋊C4—171no—
228C22×C42—171no—
229C22×C42—171no—
230C2×C22⋊C8—174no—
231C2×#97—342no—
232C4×C22⋊C4—342no—
233C4×C22⋊C4—342no—
234C2×#95—171no—
235C2×#95#59511yescharacteristic
236#336—342no—
237#323—178no—
238C2×C17—21no—
239C2×C17—21no—
240C2×C17—21no—
241C2×C17—21no—
242C2×C17#146211yescharacteristic
243C2×C17#146411yescharacteristic
244C2×C17#146511yescharacteristic
245C2×C17#146611yescharacteristic
246C2×C17#174911yescharacteristic
247C2×C17C4×#9911yescharacteristic
248C2×C17C4×#10011yescharacteristic
249D17—44no—
250C25—171no—
251C23×C4—171no—
252C23×C4—171no—
253C23×C4—171no—
254C23×C4—341no—
255C23×C4—341no—
256C23×C4—342no—
257C23×C4—342no—
258C23×C4—682no—
259C23×C4—682no—
260C23×C4C2×#59511yescharacteristic
261C23×C4C2×#59511yescharacteristic
262C23×C4C2×#59511yescharacteristic
263C22×C8—344no—
264C2×C22⋊C4—174no—
265C2×C22⋊C4—342no—
266C2×C22⋊C4—342no—
267C2×C22⋊C4—342no—
268C2×C22⋊C4—342no—
269C2×C22⋊C4—342no—
270C2×C42—172no—
271C2×C42—172no—
272C2×C42—341no—
273C2×C42—341no—
274C2×C42—682no—
275C2×C42—682no—
276C22⋊C8—178no—
277C22⋊C8—344no—
278#97—684no—
279#95—22no—
280#95—342no—
281C17#815211yescharacteristic, complemented, Sylow
282C24—172no—
283C24—172no—
284C24—172no—
285C24—341no—
286C24—341no—
287C24—341no—
288C24—341no—
289C24—681no—
290C24—681no—
291C24—681no—
292C24—681no—
293C24C22×#59511yescharacteristic
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—171no—
307C22×C4—171no—
308C22×C4—172no—
309C22×C4—172no—
310C22×C4—172no—
311C22×C4—172no—
312C22×C4—344no—
313C22×C4—344no—
314C22×C4—342no—
315C22×C4—342no—
316C22×C4—341no—
317C22×C4—341no—
318C22×C4—341no—
319C22×C4—341no—
320C22×C4—682no—
321C22×C4—682no—
322C22×C4—688no—
323C22×C4—682no—
324C22×C4—682no—
325C22×C4—688no—
326C22×C4—681no—
327C22×C4—681no—
328C22×C4—681no—
329C22×C4—681no—
330C22×C4#6324312yes—
331C22×C4C4×#59512yes—
332C22×C4C22⋊#59512yes—
333C2×C8—348no—
334C2×C8—684no—
335C2×C8—684no—
336C22⋊C4—348no—
337C22⋊C4—348no—
338C42—344no—
339C42—682no—
340C42—682no—
341C42—682no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—174no—
347C23—342no—
348C23—342no—
349C23—342no—
350C23—342no—
351C23—342no—
352C23—342no—
353C23—682no—
354C23—682no—
355C23—682no—
356C23—682no—
357C23—682no—
358C23—682no—
359C23—682no—
360C23—682no—
361C23—682no—
362C23—682no—
363C23—682no—
364C23—682no—
365C23—681no—
366C23—681no—
367C23—681no—
368C23—681no—
369C23C2×#6324311yescharacteristic
370C23D17⋊M1611yescharacteristic
371C23D17⋊M1611yescharacteristic
372C23D17⋊M1611yescharacteristic
373C23C2×C4×#59511yescharacteristic
374C23#1058767711yescharacteristic
375C23C2×C22⋊#59511yescharacteristic
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—174no—
392C2×C4—172no—
393C2×C4—172no—
394C2×C4—344no—
395C2×C4—344no—
396C2×C4—341no—
397C2×C4—341no—
398C2×C4—342no—
399C2×C4—341no—
400C2×C4—342no—
401C2×C4—341no—
402C2×C4—342no—
403C2×C4—688no—
404C2×C4—688no—
405C2×C4—682no—
406C2×C4—682no—
407C2×C4—682no—
408C2×C4—681no—
409C2×C4—681no—
410C2×C4—682no—
411C8—688no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—344no—
425C22—684no—
426C22—684no—
427C22—684no—
428C22—684no—
429C22—682no—
430C22—682no—
431C22—682no—
432C22—682no—
433C22—682no—
434C22—682no—
435C22C4×C22⋊#59511yescharacteristic
436C22#1176376811yescharacteristic
437C22C4×#6324311yescharacteristic
438C22#1176378011yescharacteristic
439C22#1176378111yescharacteristic
440C22D17⋊#9911yescharacteristic
441C22#1176379011yescharacteristic
442C22D17⋊#10011yescharacteristic
443C22#1176379611yescharacteristic
444C22#1176383111yescharacteristic
445C22#1176383211yescharacteristic
446C4—42no—
447C4—42no—
448C4—42no—
449C4—344no—
450C4—342no—
451C4—342no—
452C4—682no—
453C2—21no—
454C2—21no—
455C2—21no—
456C2—21no—
457C2—684no—
458C2#1454403011yescharacteristic
459C2#1454403811yescharacteristic
460C2#1454404211yescharacteristic
461C2#1454404511yescharacteristic
462C2#1454451111yescharacteristic
463C2#1454452911yescharacteristic
464C2#1454453411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC23×C17C2×C42
FrattiniC24C22×#595
FittingC2×C17×#95C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17C2×C4
cosocleC23×Dic17C23
hypercenterC2×#95#595
hypocenterC17#8152
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
1. #14544510C2semidirect
3. #14543622C2semidirect
8. #11763653C4semidirect
45. C22⋊#3624C2×C4semidirect
143. C22×D17#97semidirect
281. C17#8152semidirect

Maximal subgroups

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

subgroupindex
#145445102
C2×#117636532
#145436222
C2×#117626562
#815217