Finite Group Databasebeta

← #16933455

Subgroups — #16933455

Order 4352.

742 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537085C211yesmaximal, characteristic
2#14528764C211yesmaximal, characteristic, complemented
3C2×#11762545C212yesmaximal, complemented
4C2×#11762542C212yesmaximal
5C4×C17×#95C211yesmaximal, characteristic, complemented
6C2×#10587561C411yescharacteristic, complemented
7C2×#10587610C2211yescharacteristic
8C2×#10587616C2211yescharacteristic
9C2×C4⋊#3622—21no—
10C2×C22⋊#3622C2212yes—
11#11762715C411yescharacteristic, complemented
12#11762711C411yescharacteristic, complemented
13#11762700—21no—
14#11762700—21no—
15#11762688—21no—
16#11762688—21no—
17#11762675C411yescharacteristic, complemented
18#11762564—21no—
19#11762545—24no—
20#11762542—24no—
21C22×C42×C17—21no—
22C22×C42×C17C2211yescharacteristic
23C2×C17×#95—21no—
24C2×C17×#95C2212yes—
25C23×C4×C17—22no—
26C23×C4×C17D411yescharacteristic
27C23×C4×C17D411yescharacteristic
28C23×C4×C17C2311yescharacteristic
29C22×C22⋊D17—21no—
30C22×D68C2×C411yescharacteristic
31C22×Dic34C2×C411yescharacteristic
32C2×C42×C17—24no—
33C2×C42×C17—42no—
34C2×C42×C17—42no—
35C2×C42×C17—42no—
36C2×C42×C17C2×C411yescharacteristic
37C2×C42×C17C2×C411yescharacteristic
38C2×C42×C17D411yescharacteristic
39C2×C42×C17D411yescharacteristic
40C2×C22⋊Dic17—21no—
41#10587616—22no—
42#10587616—22no—
43C2×#63227—21no—
44C2×#63227—21no—
45C2×#63227—21no—
46C2×#63227—21no—
47C2×#63227—21no—
48C2×C4⋊Dic17C2×C411yescharacteristic
49C2×C4⋊Dic17C2×C411yescharacteristic
50#10587610—22no—
51#10587610—22no—
52C2×#63225—21no—
53C22×#3622—22no—
54#10587561—42no—
55C17×#95—24no—
56C17×#95—22no—
57C17×#95D414yes—
58#10587502—21no—
59#10587502—21no—
60#10587502—21no—
61#10587502—21no—
62C22⋊#3622—22no—
63C22⋊#3622—22no—
64C4⋊#3622—42no—
65C24×C17C2×D411yescharacteristic
66C23×D17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—22no—
70C22×C4×C17—22no—
71C22×C4×C17—24no—
72C22×C4×C17—24no—
73C22×C4×C17—24no—
74C22×C4×C17—22no—
75C22×C4×C17—22no—
76C22×C4×C17—41no—
77C22×C4×C17—41no—
78C22×C4×C17—41no—
79C22×C4×C17—42no—
80C22×C4×C17—42no—
81C22×C4×C17—42no—
82C22×C4×C17—42no—
83C22×C4×C17C22⋊C411yescharacteristic
84C22×C4×C17C22⋊C411yescharacteristic
85C22×C4×C17C22⋊C411yescharacteristic
86C22×C4×C17C22⋊C411yescharacteristic
87C22×C4×C17C22×C411yescharacteristic
88C22×C4×C17C2×D411yescharacteristic
89C22×C4×C17C2×D412yes—
90C22×C4×C17#4112yes—
91C2×C22⋊D17—42no—
92C2×C22⋊D17—42no—
93C2×C22⋊D17—41no—
94C2×C22⋊D17—41no—
95C22×Dic17—21no—
96C22×Dic17—21no—
97C22×Dic17—21no—
98C2×D68—22no—
99C2×D68—41no—
100C2×D68—41no—
101C2×Dic34—22no—
102C2×Dic34—41no—
103C2×Dic34—41no—
104C42×C17—22no—
105C42×C17—22no—
106C42×C17—41no—
107C42×C17—41no—
108C42×C17—48no—
109C22⋊Dic17—42no—
110#63227—42no—
111#63227—42no—
112#63227—42no—
113#63227—42no—
114#63227—41no—
115#63227—41no—
116C4⋊Dic17—22no—
117C4⋊Dic17—22no—
118#63225—41no—
119#63225—41no—
120C2×#3622—42no—
121C2×#3622—42no—
122C2×#3622—42no—
123#9713—171nomaximal, Sylow
124C23×C17—21no—
125C23×C17—21no—
126C23×C17—21no—
127C23×C17—21no—
128C23×C17C2×C22⋊C411yescharacteristic
129C23×C17#12112yes—
130C23×C17#13512yes—
131C23×C17AGL(1,ℤ/8)11yescharacteristic
132C23×C17#13711yescharacteristic
133C22×D17—41no—
134C22×D17—41no—
135C22×D17—41no—
136C22×D17—41no—
137C22×D17—41no—
138C22×D17—41no—
139C22×D17—41no—
140C2×C4×C17—24no—
141C2×C4×C17—24no—
142C2×C4×C17—21no—
143C2×C4×C17—21no—
144C2×C4×C17—21no—
145C2×C4×C17—21no—
146C2×C4×C17—21no—
147C2×C4×C17—21no—
148C2×C4×C17—21no—
149C2×C4×C17—21no—
150C2×C4×C17—21no—
151C2×C4×C17—21no—
152C2×C4×C17—28no—
153C2×C4×C17—21no—
154C2×C4×C17—21no—
155C2×C4×C17—21no—
156C2×C4×C17—42no—
157C2×C4×C17—42no—
158C2×C4×C17—44no—
159C2×C4×C17—44no—
160C2×C4×C17—44no—
161C2×C4×C17—44no—
162C2×C4×C17—44no—
163C2×C4×C17—44no—
164C2×C4×C17—44no—
165C2×C4×C17#9912yes—
166C2×C4×C17#10412yes—
167C2×C4×C17#10412yes—
168C2×C4×C17C4×D412yes—
169C2×C4×C17#12411yescharacteristic
170C2×C4×C17#12711yescharacteristic
171C22⋊D17—82no—
172C22⋊D17—82no—
173C2×Dic17—41no—
174C2×Dic17—41no—
175C2×Dic17—41no—
176C2×Dic17—41no—
177C2×Dic17—41no—
178C2×Dic17—41no—
179C2×Dic17—41no—
180C2×Dic17—41no—
181C2×Dic17—41no—
182D68—82no—
183Dic34—82no—
184#3622—82no—
185#2850—171no—
186#1797—171no—
187C2×#328—172no—
188C2×#327—172no—
189C4×#95D1711yescharacteristic, complemented
190C22×C17—22no—
191C22×C17—22no—
192C22×C17—22no—
193C22×C17—22no—
194C22×C17—21no—
195C22×C17—21no—
196C22×C17—21no—
197C22×C17—21no—
198C22×C17#39011yescharacteristic
199C22×C17C2×#9911yescharacteristic
200C22×C17#41011yescharacteristic
201C22×C17#41611yescharacteristic
202C22×C17#41711yescharacteristic
203C22×C17C2×#10411yescharacteristic
204C22×C17C2×#10411yescharacteristic
205C22×C17#46312yes—
206C22×C17#46412yes—
207C2×D17—81no—
208C2×D17—81no—
209C2×D17—81no—
210C2×D17—81no—
211C2×D17—81no—
212C2×D17—81no—
213C2×D17—81no—
214C4×C17—21no—
215C4×C17—22no—
216C4×C17—21no—
217C4×C17—22no—
218C4×C17—22no—
219C4×C17—22no—
220C4×C17—48no—
221C4×C17—41no—
222Dic17—81no—
223Dic17—81no—
224Dic17—81no—
225C2×#124—171no—
226C2×C22⋊Q8—171no—
227C2×#121—171no—
228C22×C42—21no—
229C22×C42C2×D1711yescharacteristic
230C2×C4⋊C8—341no—
231C2×C22⋊C8—172no—
232#391—171no—
233#390—171no—
234#388—341no—
235#388—341no—
236#386—341no—
237#386—341no—
238#382—171no—
239C2×#95—21no—
240C2×#95C2×D1712yes—
241#336—341no—
242#328—344no—
243#327—344no—
244C2×C17—22no—
245C2×C17—22no—
246C2×C17#150011yescharacteristic
247C2×C17#150111yescharacteristic
248C2×C17#150411yescharacteristic
249C2×C17#150911yescharacteristic
250C2×C17#196211yescharacteristic
251C2×C17#196411yescharacteristic
252C2×C17#198311yescharacteristic
253D17—161no—
254C22×Q8—171no—
255C22×D4—171no—
256C22×D4—341no—
257C23×C4—22no—
258C23×C4C22⋊D1711yescharacteristic
259C23×C4C22⋊D1711yescharacteristic
260C23×C4C22×D1711yescharacteristic
261C22×C8—342no—
262#124—682no—
263C22⋊Q8—342no—
264C22⋊Q8—342no—
265#121—342no—
266#121—342no—
267C2×C4⋊C4—171no—
268C2×C4⋊C4—171no—
269C2×C4⋊C4—341no—
270C2×C22⋊C4—341no—
271C2×C22⋊C4—341no—
272C2×C22⋊C4—341no—
273C2×C22⋊C4—341no—
274C2×C22⋊C4—341no—
275C2×C22⋊C4—341no—
276C2×C42—24no—
277C2×C42—42no—
278C2×C42—42no—
279C2×C42—42no—
280C2×C42C4×D1711yescharacteristic
281C2×C42C4×D1711yescharacteristic
282C2×C42D6811yescharacteristic
283C2×C42D6811yescharacteristic
284C4⋊C8—682no—
285C22⋊C8—342no—
286C22⋊C8—342no—
287#95—24no—
288#95—22no—
289#95—341no—
290#95—341no—
291#95—341no—
292#95—341no—
293#95D6814yes—
294C17#971311yescharacteristic, complemented, Sylow
295C24—341no—
296C24C2×C22⋊D1711yescharacteristic
297C2×Q8—342no—
298C2×Q8—681no—
299C2×Q8—681no—
300C2×D4—342no—
301C2×D4—681no—
302C2×D4—681no—
303C2×D4—682no—
304C2×D4—681no—
305C2×D4—681no—
306C2×D4—682no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—341no—
324C22×C4—341no—
325C22×C4—341no—
326C22×C4#6322711yescharacteristic
327C22×C4#6322711yescharacteristic
328C22×C4#6322711yescharacteristic
329C22×C4#6322711yescharacteristic
330C22×C4C2×C4×D1711yescharacteristic
331C22×C4C2×D6811yescharacteristic
332C22×C4C2×D6812yes—
333C22×C4#6325212yes—
334C2×C8—682no—
335C2×C8—682no—
336C2×C8—682no—
337C4⋊C4—342no—
338C4⋊C4—342no—
339C4⋊C4—681no—
340C4⋊C4—681no—
341C22⋊C4—682no—
342C22⋊C4—682no—
343C22⋊C4—682no—
344C22⋊C4—682no—
345C22⋊C4—682no—
346C22⋊C4—681no—
347C22⋊C4—681no—
348C42—22no—
349C42—22no—
350C42—41no—
351C42—41no—
352C42—48no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—681no—
358C23—681no—
359C23—681no—
360C23—681no—
361C23—681no—
362C23—681no—
363C23—681no—
364C23C2×#6322711yescharacteristic
365C23#1058761612yes—
366C23#1058761811yescharacteristic
367C23#1058762811yescharacteristic
368C23#1058763612yes—
369Q8—1362no—
370D4—1362no—
371D4—1362no—
372D4—1362no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—28no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—681no—
399C2×C4—681no—
400C2×C4—681no—
401C2×C4—681no—
402C2×C4—681no—
403C2×C4—681no—
404C2×C4—681no—
405C2×C4—681no—
406C2×C4—681no—
407C2×C4#1058747612yes—
408C2×C4#1058747612yes—
409C2×C4#1058747712yes—
410C2×C4C4×D6812yes—
411C2×C4#1058756011yescharacteristic
412C2×C4#1058756111yescharacteristic
413C8—1362no—
414C22—22no—
415C22—22no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—22no—
421C22—22no—
422C22—1361no—
423C22—1361no—
424C22—1361no—
425C22—1361no—
426C22—1361no—
427C22—1361no—
428C22—1361no—
429C22#1176271111yescharacteristic
430C22C2×#1058747711yescharacteristic
431C22#1176278211yescharacteristic
432C22#1176280311yescharacteristic
433C22#1176280811yescharacteristic
434C22C2×#1058747611yescharacteristic
435C22C2×#1058747611yescharacteristic
436C22#1176302412yes—
437C22#1176303112yes—
438C4—22no—
439C4—22no—
440C4—22no—
441C4—21no—
442C4—22no—
443C4—21no—
444C4—48no—
445C4—41no—
446C4—1361no—
447C4—1361no—
448C4—1361no—
449C2—22no—
450C2—22no—
451C2—2721no—
452C2#1452726811yescharacteristic
453C2#1452727311yescharacteristic
454C2#1452728611yescharacteristic
455C2#1452730711yescharacteristic
456C2#1452961211yescharacteristic
457C2#1452962011yescharacteristic
458C2#1452971611yescharacteristic
subgroupG/H
centerC23C2×#63227
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC4×C17×#95C2
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587616C22
cosocleC23×C4×C17C23
hypercenterC4×#95D17
hypocenterC17#9713
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. #14528764C2semidirect
3. C2×#11762545C2semidirect
5. C4×C17×#95C2semidirect
6. C2×#10587561C4semidirect
11. #11762715C4semidirect
12. #11762711C4semidirect
17. #11762675C4semidirect
189. C4×#95D17semidirect
294. C17#9713semidirect

Maximal subgroups

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

subgroupindex
#145370852
#145287642
C2×#117625452
C2×#117625422
C4×C17×#952
#971317