Finite Group Databasebeta

← #17953134

Subgroups — #17953134

Order 4352.

898 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14544640C212yesmaximal, complemented
2C2×#11763652C212yesmaximal
3#14543622C212yesmaximal, complemented
4C2×C4×C22⋊Dic17C211yesmaximal, characteristic
5C2×#10587544—22no—
6C2×C22⋊#3624C2214yes—
7#11763675—22no—
8#11763652—24no—
9C22×C22⋊Dic17C411yescharacteristic
10C22×C22⋊Dic17C2211yescharacteristic
11C22×C4×Dic17C411yescharacteristic
12C22×C4×Dic17C2211yescharacteristic
13C4×C22⋊Dic17—22no—
14C4×C22⋊Dic17—22no—
15C2×#10587502C411yescharacteristic
16C2×#10587502C2211yescharacteristic
17C24×C4×C17C411yescharacteristic
18C25×C17C2×C411yescharacteristic
19C23×C4×C17—22no—
20C23×C4×C17—21no—
21C23×C4×C17—21no—
22C23×C4×C17—22no—
23C23×C4×C17—42no—
24C23×C4×C17—42no—
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17C2×C411yescharacteristic
27C23×Dic17C2×C411yescharacteristic
28C23×Dic17C2×C411yescharacteristic
29C23×Dic17C2×C411yescharacteristic
30C23×Dic17C2311yescharacteristic
31C22×#3624—24no—
32C2×C22⋊Dic17—22no—
33C2×C22⋊Dic17—22no—
34C2×C22⋊Dic17—22no—
35C2×C22⋊Dic17—22no—
36C2×C22⋊Dic17C814yescomplemented
37C2×C22⋊Dic17D412yes—
38C2×C22⋊Dic17Q812yes—
39C2×C4×Dic17—21no—
40C2×C4×Dic17—21no—
41C2×C4×Dic17—42no—
42C2×C4×Dic17—42no—
43C2×C4×Dic17D412yes—
44C2×C4×Dic17D412yes—
45C22⋊#3624—24no—
46C22⋊#3624—24no—
47#10587544—44no—
48#10587502—22no—
49#10587502—22no—
50C24×C17—21no—
51C24×C17—21no—
52C24×C17—21no—
53C24×C17—21no—
54C24×C17—41no—
55C24×C17—41no—
56C24×C17—41no—
57C24×C17—41no—
58C24×C17C4⋊C412yes—
59C24×C17C2×C812yes—
60C24×C17M1612yes—
61C24×C17C22×C411yescharacteristic
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—22no—
65C22×C4×C17—22no—
66C22×C4×C17—24no—
67C22×C4×C17—24no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—48no—
71C22×C4×C17—48no—
72C22×C4×C17—42no—
73C22×C4×C17—42no—
74C22×C4×C17—42no—
75C22×C4×C17—42no—
76C22×C4×C17—41no—
77C22×C4×C17—41no—
78C22×C4×C17C22⋊C411yescharacteristic
79C22×C4×C17C22⋊C411yescharacteristic
80C22×C4×C17M1612yes—
81C22×Dic17—21no—
82C22×Dic17—21no—
83C22×Dic17—21no—
84C22×Dic17—21no—
85C22×Dic17—41no—
86C22×Dic17—41no—
87C22×Dic17—41no—
88C22×Dic17—41no—
89C22×Dic17—41no—
90C22×Dic17—41no—
91C22×Dic17—41no—
92C22×Dic17—41no—
93C22×Dic17C22⋊C412yes—
94C22×Dic17C4⋊C412yes—
95C22×Dic17C2×C812yes—
96C22×Dic17C2×C812yes—
97C22×Dic17M1612yes—
98C22×Dic17C2×D412yes—
99C22×Dic17C2×D411yescharacteristic
100C22×Dic17C2×Q811yescharacteristic
101C22×Dic17#4112yes—
102C2×#3624—44no—
103C2×#3624—44no—
104C2×#3624—44no—
105C22⋊Dic17—28no—
106C22⋊Dic17—24no—
107C22⋊Dic17—24no—
108C4×Dic17—24no—
109C4×Dic17—42no—
110C4×Dic17—42no—
111C4×Dic17—42no—
112#8559—171nomaximal, Sylow
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—22no—
118C23×C17—22no—
119C23×C17—22no—
120C23×C17—22no—
121C23×C17—22no—
122C23×C17—22no—
123C23×C17—42no—
124C23×C17—42no—
125C23×C17—42no—
126C23×C17—42no—
127C23×C17—42no—
128C23×C17—42no—
129C23×C17—42no—
130C23×C17—42no—
131C23×C17—42no—
132C23×C17—42no—
133C23×C17—42no—
134C23×C17—42no—
135C23×C17—41no—
136C23×C17—41no—
137C23×C17—41no—
138C23×C17—41no—
139C23×C17C4⋊C814yescomplemented
140C23×C17C2×C22⋊C411yescharacteristic
141C23×C17C2×C4⋊C411yescharacteristic
142C23×C17#11711yescharacteristic
143C23×C17C22×C811yescharacteristic
144C23×C17C2×M1611yescharacteristic
145C23×C17C2×M1611yescharacteristic
146C23×C17C2×M1611yescharacteristic
147C2×C4×C17—24no—
148C2×C4×C17—24no—
149C2×C4×C17—21no—
150C2×C4×C17—21no—
151C2×C4×C17—21no—
152C2×C4×C17—21no—
153C2×C4×C17—22no—
154C2×C4×C17—48no—
155C2×C4×C17—48no—
156C2×C4×C17—42no—
157C2×C4×C17—41no—
158C2×C4×C17—41no—
159C2×C4×C17—42no—
160C2×C4×C17#9912yes—
161C2×C4×C17#10012yes—
162C2×Dic17—22no—
163C2×Dic17—22no—
164C2×Dic17—22no—
165C2×Dic17—22no—
166C2×Dic17—22no—
167C2×Dic17—22no—
168C2×Dic17—42no—
169C2×Dic17—42no—
170C2×Dic17—41no—
171C2×Dic17—41no—
172C2×Dic17—42no—
173C2×Dic17—42no—
174C2×Dic17—42no—
175C2×Dic17—41no—
176C2×Dic17—41no—
177C2×Dic17—41no—
178C2×Dic17—41no—
179C2×Dic17—42no—
180C2×Dic17—42no—
181C2×Dic17C22⋊C814yes—
182C2×Dic17#12112yes—
183C2×Dic17C22⋊Q812yes—
184#3624—84no—
185C2×C4×C22⋊C4—171no—
186#1797—172no—
187C2×#323—172no—
188#1280—172no—
189C22×C17—21no—
190C22×C17—21no—
191C22×C17—21no—
192C22×C17—21no—
193C22×C17—21no—
194C22×C17—21no—
195C22×C17—21no—
196C22×C17—21no—
197C22×C17—21no—
198C22×C17—21no—
199C22×C17—21no—
200C22×C17—21no—
201C22×C17—24no—
202C22×C17—44no—
203C22×C17—44no—
204C22×C17—44no—
205C22×C17—44no—
206C22×C17—42no—
207C22×C17—42no—
208C22×C17—42no—
209C22×C17—42no—
210C22×C17—42no—
211C22×C17—42no—
212C22×C17#38011yescharacteristic
213C22×C17C2×C22⋊C811yescharacteristic
214C22×C17#40711yescharacteristic
215C22×C17C2×#9911yescharacteristic
216C22×C17#41011yescharacteristic
217C22×C17C2×#10011yescharacteristic
218C22×C17#41311yescharacteristic
219C22×C17C2×C4⋊C811yescharacteristic
220C22×C17#42311yescharacteristic
221C22×C17#43111yescharacteristic
222C22×C17#43211yescharacteristic
223C4×C17—22no—
224C4×C17—22no—
225C4×C17—42no—
226Dic17—22no—
227Dic17—22no—
228Dic17—24no—
229Dic17—42no—
230Dic17—42no—
231C24×C4#59511yescharacteristic
232C22×C22⋊C4—171no—
233C22×C22⋊C4—171no—
234C22×C42—171no—
235C22×C42—171no—
236C2×C4⋊C8—342no—
237C2×C22⋊C8—174no—
238C4×C22⋊C4—342no—
239C4×C22⋊C4—342no—
240C2×#95—171no—
241C2×#95—171no—
242#336—342no—
243#323—344no—
244C2×C17—21no—
245C2×C17—21no—
246C2×C17—21no—
247C2×C17—21no—
248C2×C17—44no—
249C2×C17#145911yescharacteristic
250C2×C17#146011yescharacteristic
251C2×C17#146211yescharacteristic
252C2×C17#146411yescharacteristic
253C2×C17#179711yescharacteristic
254C2×C17#179911yescharacteristic
255C2×C17#180011yescharacteristic
256C25C2×#59511yescharacteristic
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—171no—
264C23×C4—171no—
265C23×C4—171no—
266C23×C4—171no—
267C23×C4C2×#59511yescharacteristic
268C23×C4C2×#59511yescharacteristic
269C22×C8—344no—
270C2×C22⋊C4—174no—
271C2×C22⋊C4—172no—
272C2×C22⋊C4—172no—
273C2×C22⋊C4—342no—
274C2×C22⋊C4—342no—
275C2×C22⋊C4—342no—
276C2×C22⋊C4—342no—
277C2×C42—172no—
278C2×C42—172no—
279C2×C42—341no—
280C2×C42—341no—
281C2×C42—682no—
282C2×C42—682no—
283C4⋊C8—684no—
284C22⋊C8—344no—
285C22⋊C8—344no—
286#95—342no—
287#95—342no—
288C17#855911yescharacteristic, complemented, Sylow
289C24—21no—
290C24—21no—
291C24—21no—
292C24—21no—
293C24—41no—
294C24—41no—
295C24—41no—
296C24—41no—
297C24#6324212yes—
298C24C4⋊#59512yes—
299C24#6324712yes—
300C24C22×#59511yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—48no—
310C22×C4—48no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—172no—
318C22×C4—172no—
319C22×C4—172no—
320C22×C4—172no—
321C22×C4—171no—
322C22×C4—171no—
323C22×C4—172no—
324C22×C4—172no—
325C22×C4—172no—
326C22×C4—341no—
327C22×C4—341no—
328C22×C4—341no—
329C22×C4—341no—
330C22×C4—681no—
331C22×C4—681no—
332C22×C4—681no—
333C22×C4—681no—
334C22×C4—681no—
335C22×C4—681no—
336C22×C4—681no—
337C22×C4—681no—
338C22×C4#6324712yes—
339C22×C4C22⋊#59511yescharacteristic
340C22×C4C22⋊#59511yescharacteristic
341C2×C8—684no—
342C2×C8—684no—
343C2×C8—684no—
344C22⋊C4—344no—
345C22⋊C4—344no—
346C22⋊C4—348no—
347C42—344no—
348C42—682no—
349C42—682no—
350C42—682no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23#1058754414yescomplemented
378C23C2×#6324211yescharacteristic
379C23D17⋊M1611yescharacteristic
380C23C2×C4⋊#59511yescharacteristic
381C23#1058767711yescharacteristic
382C23C2×#6324711yescharacteristic
383C23C2×#6324711yescharacteristic
384C23C2×C22⋊#59511yescharacteristic
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—48no—
393C2×C4—48no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—172no—
399C2×C4—172no—
400C2×C4—174no—
401C2×C4—342no—
402C2×C4—342no—
403C2×C4—342no—
404C2×C4—342no—
405C2×C4—342no—
406C2×C4—342no—
407C2×C4—681no—
408C2×C4—682no—
409C2×C4—681no—
410C2×C4—682no—
411C2×C4—682no—
412C2×C4—682no—
413C2×C4—682no—
414C2×C4—681no—
415C2×C4—681no—
416C2×C4—681no—
417C2×C4—681no—
418C2×C4—682no—
419C2×C4—682no—
420C2×C4#1058755112yes—
421C2×C4#1058755312yes—
422C8—1364no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—24no—
436C22—44no—
437C22—44no—
438C22—44no—
439C22—44no—
440C22—42no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22#1176375111yescharacteristic
447C22#1176377711yescharacteristic
448C22#1176377911yescharacteristic
449C22C2×#1058755111yescharacteristic
450C22#1176378811yescharacteristic
451C22C2×#1058755311yescharacteristic
452C22#1176379511yescharacteristic
453C22C2×#1058754411yescharacteristic
454C22#1176381211yescharacteristic
455C22#1176382611yescharacteristic
456C22#1176382911yescharacteristic
457C4—22no—
458C4—22no—
459C4—42no—
460C4—342no—
461C4—342no—
462C4—344no—
463C4—682no—
464C4—682no—
465C2—21no—
466C2—21no—
467C2—21no—
468C2—21no—
469C2—44no—
470C2#1454401911yescharacteristic
471C2#1454402311yescharacteristic
472C2#1454402911yescharacteristic
473C2#1454403511yescharacteristic
474C2#1454464011yescharacteristic
475C2#1454464411yescharacteristic
476C2#1454464811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC23×C17C22×C8
FrattiniC24C22×#595
FittingC24×C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC25×C17C2×C4
cosocleC23×Dic17C23
hypercenterC24×C4#595
hypocenterC17#8559
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. #14544640C2semidirect
3. #14543622C2semidirect
36. C2×C22⋊Dic17C8semidirect
139. C23×C17C4⋊C8semidirect
288. C17#8559semidirect
377. C23#10587544semidirect

Maximal subgroups

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

subgroupindex
#145446402
C2×#117636522
#145436222
C2×C4×C22⋊Dic172
#855917