Finite Group Databasebeta

← #17952430

Subgroups — #17952430

Order 4352.

1502 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14544607C212yesmaximal
2C2×#11763655C212yesmaximal, complemented
3C2×#11763654C212yesmaximal, complemented
4C22×C4⋊C4×D17C211yesmaximal, characteristic
5C2×#10587543—24no—
6C2×C22⋊#3624C2214yes—
7#11763655—24no—
8#11763654—24no—
9C23×C4×D17C411yescharacteristic
10C23×C4×D17C411yescharacteristic
11C23×C4×D17C2211yescharacteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×#63225C411yescharacteristic
14C22×#63225C2211yescharacteristic
15C2×C4⋊C4×D17—24no—
16C2×C4⋊C4×D17—24no—
17C2×C4⋊C4×D17—24no—
18C22×C4⋊C4×C17C411yescharacteristic
19C24×D17C2×C411yescharacteristic
20C23×C4×C17C2×C411yescharacteristic
21C23×C4×C17C2×C411yescharacteristic
22C23×C4×C17C2×C411yescharacteristic
23C23×Dic17C2×C411yescharacteristic
24C23×Dic17C2×C411yescharacteristic
25C23×Dic17C2311yescharacteristic
26C22×C4×D17—22no—
27C22×C4×D17—22no—
28C22×C4×D17—22no—
29C22×C4×D17—22no—
30C22×C4×D17—22no—
31C22×C4×D17—22no—
32C22×C4×D17—22no—
33C22×C4×D17—22no—
34C22×C4×D17—22no—
35C22×C4×D17—22no—
36C22×C4×D17—22no—
37C22×C4×D17—44no—
38C22×C4×D17—44no—
39C22×C4×D17C814yescomplemented
40C22×C4×D17D414yes—
41C22×#3624—24no—
42C2×C4⋊C4×C17—22no—
43C2×C4⋊C4×C17—22no—
44C2×C4⋊C4×C17—22no—
45C2×C4⋊Dic17—22no—
46C2×C4⋊Dic17—22no—
47C2×C4⋊Dic17D414yes—
48C2×#63225—22no—
49C2×#63225—22no—
50C2×#63225—22no—
51C2×#63225—22no—
52C2×#63225—22no—
53C2×#63225D414yes—
54C4⋊C4×D17—232no—
55C22⋊#3624—24no—
56C22⋊#3624—24no—
57#10587543—48no—
58C24×C17C22×C411yescharacteristic
59C23×D17—21no—
60C23×D17—21no—
61C23×D17—21no—
62C23×D17—21no—
63C23×D17—24no—
64C23×D17—24no—
65C23×D17C22⋊C412yes—
66C23×D17C2×C812yes—
67C23×D17M1612yes—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17—21no—
74C22×C4×C17—21no—
75C22×C4×C17—21no—
76C22×C4×C17—42no—
77C22×C4×C17—42no—
78C22×C4×C17C22⋊C412yes—
79C22×C4×C17C22⋊C412yes—
80C22×C4×C17C22⋊C412yes—
81C22×C4×C17C2×C812yes—
82C22×C4×C17M1612yes—
83C22×Dic17—21no—
84C22×Dic17—21no—
85C22×Dic17—21no—
86C22×Dic17—21no—
87C22×Dic17—21no—
88C22×Dic17—21no—
89C22×Dic17—42no—
90C22×Dic17—42no—
91C22×Dic17C22⋊C412yes—
92C22×Dic17C22⋊C412yes—
93C22×Dic17C2×C812yes—
94C22×Dic17M1612yes—
95C22×Dic17C2×D412yes—
96C22×Dic17C2×D412yes—
97C22×Dic17C2×D412yes—
98C2×C4×D17—28no—
99C2×C4×D17—28no—
100C2×C4×D17—28no—
101C2×C4×D17—28no—
102C2×C4×D17—28no—
103C2×C4×D17—28no—
104C2×C4×D17—28no—
105C2×C4×D17—28no—
106C2×C4×D17—28no—
107C2×C4×D17—28no—
108C2×C4×D17—44no—
109C2×C4×D17—48no—
110C2×C4×D17—48no—
111C2×C4×D17—48no—
112C2×C4×D17—44no—
113C2×C4×D17—48no—
114C2×C4×D17—44no—
115C2×#3624—48no—
116C2×#3624—44no—
117C4⋊C4×C17—28no—
118C4⋊Dic17—28no—
119#63225—28no—
120#63225—28no—
121#8299—171nomaximal, Sylow
122C23×C17—22no—
123C23×C17—22no—
124C23×C17C2×C22⋊C411yescharacteristic
125C23×C17C2×C22⋊C411yescharacteristic
126C23×C17C2×C22⋊C411yescharacteristic
127C23×C17C22×C811yescharacteristic
128C23×C17C2×M1611yescharacteristic
129C23×C17C2×M1611yescharacteristic
130C23×C17C2×M1611yescharacteristic
131C22×D17—24no—
132C22×D17—24no—
133C22×D17—28no—
134C22×D17—28no—
135C22×D17—24no—
136C22×D17—24no—
137C22×D17—22no—
138C22×D17—22no—
139C22×D17—22no—
140C22×D17—22no—
141C22×D17—22no—
142C22×D17—22no—
143C22×D17—22no—
144C22×D17—22no—
145C22×D17—28no—
146C22×D17—28no—
147C22×D17C22⋊C814yes—
148C22×D17#9914yes—
149C22×D17#10114yes—
150C2×C4×C17—22no—
151C2×C4×C17—22no—
152C2×C4×C17—22no—
153C2×C4×C17—22no—
154C2×C4×C17—22no—
155C2×C4×C17—22no—
156C2×C4×C17—22no—
157C2×C4×C17—22no—
158C2×C4×C17—24no—
159C2×C4×C17—42no—
160C2×C4×C17—42no—
161C2×C4×C17—42no—
162C2×C4×C17—42no—
163C2×C4×C17—42no—
164C2×C4×C17C22⋊C814yescomplemented
165C2×Dic17—22no—
166C2×Dic17—22no—
167C2×Dic17—22no—
168C2×Dic17—22no—
169C2×Dic17—22no—
170C2×Dic17—22no—
171C2×Dic17—24no—
172C2×Dic17—22no—
173C2×Dic17—42no—
174C2×Dic17—42no—
175C2×Dic17—42no—
176C2×Dic17—42no—
177C2×Dic17—42no—
178C2×Dic17C22⋊C814yescomplemented
179C2×Dic17#12014yes—
180C4×D17—232no—
181C4×D17—416no—
182C4×D17—416no—
183#3624—84no—
184C23×C4⋊C4—171no—
185#1779—172no—
186C2×#324—172no—
187C2×#324—172no—
188C22×C17—22no—
189C22×C17—22no—
190C22×C17—22no—
191C22×C17—22no—
192C22×C17—21no—
193C22×C17—21no—
194C22×C17—21no—
195C22×C17—21no—
196C22×C17#37911yescharacteristic
197C22×C17C2×C22⋊C811yescharacteristic
198C22×C17C2×C22⋊C811yescharacteristic
199C22×C17C2×C22⋊C811yescharacteristic
200C22×C17#40711yescharacteristic
201C22×C17#40711yescharacteristic
202C22×C17#40711yescharacteristic
203C22×C17C2×#9912yes—
204C22×C17C2×#10112yes—
205C2×D17—28no—
206C2×D17—28no—
207C2×D17—28no—
208C2×D17—28no—
209C2×D17—24no—
210C2×D17—24no—
211C2×D17—24no—
212C2×D17—24no—
213C2×D17—24no—
214C2×D17—24no—
215C2×D17#32418yescomplemented
216C4×C17—24no—
217C4×C17—42no—
218C4×C17—42no—
219Dic17—24no—
220Dic17—24no—
221Dic17—42no—
222C24×C4—171no—
223C24×C4—171no—
224C24×C4—171no—
225C22×C4⋊C4—171no—
226C22×C4⋊C4—171no—
227C22×C4⋊C4—171no—
228C22×C4⋊C4—344no—
229C22×C4⋊C4—344no—
230C22×C4⋊C4—344no—
231C22×C4⋊C4#59511yescharacteristic
232C2×C22⋊C8—174no—
233C2×C22⋊C8—344no—
234#324—344no—
235#324—344no—
236C2×C17—21no—
237C2×C17—21no—
238C2×C17—21no—
239C2×C17—21no—
240C2×C17C2×#32412yes—
241C2×C17#146312yes—
242C2×C17#177911yescharacteristic
243C2×C17#178111yescharacteristic
244C2×C17#178411yescharacteristic
245D17—28no—
246C25—171no—
247C23×C4—171no—
248C23×C4—171no—
249C23×C4—171no—
250C23×C4—174no—
251C23×C4—174no—
252C23×C4—342no—
253C23×C4—342no—
254C23×C4—342no—
255C23×C4—342no—
256C23×C4—342no—
257C23×C4—342no—
258C23×C4—342no—
259C23×C4—342no—
260C23×C4—342no—
261C23×C4—342no—
262C23×C4—342no—
263C23×C4—684no—
264C23×C4—684no—
265C23×C4C2×#59511yescharacteristic
266C23×C4C2×#59511yescharacteristic
267C23×C4C2×#59511yescharacteristic
268C22×C8—344no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—174no—
273C2×C4⋊C4—174no—
274C2×C4⋊C4—3432no—
275C2×C4⋊C4—342no—
276C2×C4⋊C4—342no—
277C2×C4⋊C4—342no—
278C2×C4⋊C4—342no—
279C2×C4⋊C4—342no—
280C2×C4⋊C4—342no—
281C2×C4⋊C4—342no—
282C22⋊C8—344no—
283C22⋊C8—344no—
284C22⋊C8—688no—
285C17#829911yescharacteristic, complemented, Sylow
286C24—172no—
287C24—172no—
288C24—172no—
289C24—344no—
290C24—344no—
291C24—341no—
292C24—341no—
293C24—341no—
294C24—341no—
295C24C22×#59511yescharacteristic
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—172no—
307C22×C4—172no—
308C22×C4—172no—
309C22×C4—172no—
310C22×C4—172no—
311C22×C4—172no—
312C22×C4—172no—
313C22×C4—348no—
314C22×C4—348no—
315C22×C4—348no—
316C22×C4—348no—
317C22×C4—348no—
318C22×C4—348no—
319C22×C4—348no—
320C22×C4—348no—
321C22×C4—348no—
322C22×C4—341no—
323C22×C4—341no—
324C22×C4—341no—
325C22×C4—341no—
326C22×C4—348no—
327C22×C4—341no—
328C22×C4—341no—
329C22×C4—684no—
330C22×C4—684no—
331C22×C4—688no—
332C22×C4—688no—
333C22×C4—688no—
334C22×C4—684no—
335C22×C4—688no—
336C22×C4—682no—
337C22×C4—682no—
338C22×C4#6324212yes—
339C22×C4#6324312yes—
340C22×C4C22⋊#59512yes—
341C22×C4C22⋊#59512yes—
342C22×C4C22⋊#59512yes—
343C2×C8—684no—
344C2×C8—688no—
345C4⋊C4—28no—
346C4⋊C4—348no—
347C4⋊C4—348no—
348C4⋊C4—348no—
349C23—22no—
350C23—22no—
351C23—174no—
352C23—174no—
353C23—174no—
354C23—348no—
355C23—348no—
356C23—344no—
357C23—344no—
358C23—348no—
359C23—348no—
360C23—344no—
361C23—344no—
362C23—342no—
363C23—342no—
364C23—342no—
365C23—342no—
366C23—342no—
367C23—342no—
368C23—342no—
369C23—342no—
370C23C2×#6324211yescharacteristic
371C23C2×#6324311yescharacteristic
372C23D17⋊M1611yescharacteristic
373C23D17⋊M1611yescharacteristic
374C23C2×C22⋊#59511yescharacteristic
375C23C2×C22⋊#59511yescharacteristic
376C23C2×C22⋊#59511yescharacteristic
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—174no—
392C2×C4—174no—
393C2×C4—3432no—
394C2×C4—342no—
395C2×C4—342no—
396C2×C4—342no—
397C2×C4—342no—
398C2×C4—342no—
399C2×C4—342no—
400C2×C4—344no—
401C2×C4—342no—
402C2×C4—6816no—
403C2×C4—6816no—
404C2×C4—682no—
405C2×C4—682no—
406C2×C4—682no—
407C2×C4—682no—
408C2×C4—682no—
409C2×C4#1058754314yescomplemented
410C8—1364no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—178no—
420C22—348no—
421C22—348no—
422C22—348no—
423C22—348no—
424C22—344no—
425C22—344no—
426C22—344no—
427C22—344no—
428C22—344no—
429C22—344no—
430C22#1176375011yescharacteristic
431C22#1176377711yescharacteristic
432C22#1176377711yescharacteristic
433C22C2×#1058754311yescharacteristic
434C22#1176378011yescharacteristic
435C22#1176378011yescharacteristic
436C22#1176378111yescharacteristic
437C22D17⋊#9912yes—
438C22D17⋊#10112yes—
439C4—24no—
440C4—42no—
441C4—42no—
442C4—344no—
443C4—344no—
444C4—682no—
445C2—21no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—348no—
450C2#1454401312yes—
451C2#1454403312yes—
452C2#1454460711yescharacteristic
453C2#1454461111yescharacteristic
454C2#1454461911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC23×C17C22×C8
FrattiniC24C22×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17C2×C4
cosocleC23×Dic17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#8299
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11763655C2semidirect
3. C2×#11763654C2semidirect
39. C22×C4×D17C8semidirect
164. C2×C4×C17C22⋊C8semidirect
178. C2×Dic17C22⋊C8semidirect
215. C2×D17#324semidirect
285. C17#8299semidirect
409. C2×C4#10587543semidirect

Maximal subgroups

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

subgroupindex
#145446072
C2×#117636552
C2×#117636542
C22×C4⋊C4×D172
#829917