Finite Group Databasebeta

← #14536902

Subgroups — #14536902

Order 2176.

508 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11762750C211yesmaximal, characteristic, complemented
2#11762738C211yesmaximal, characteristic, complemented
3#11762737C211yesmaximal, characteristic, complemented
4#11762724C211yesmaximal, characteristic, complemented
5#11762724C211yesmaximal, characteristic, complemented
6#11762723C211yesmaximal, characteristic, complemented
7#11762723C211yesmaximal, characteristic, complemented
8#11762723C211yesmaximal, characteristic, complemented
9#11762717C211yesmaximal, characteristic, complemented
10#11762717C211yesmaximal, characteristic, complemented
11#11762717C211yesmaximal, characteristic, complemented
12#11762709C211yesmaximal, characteristic, complemented
13#11762703C211yesmaximal, characteristic, complemented
14#11762697C211yesmaximal, characteristic, complemented
15C17×#392C211yesmaximal, characteristic, complemented
16C22×D4×C17C2211yescharacteristic
17C22×D4×C17C2211yescharacteristic
18C22×D4×C17C2211yescharacteristic
19C22×C22⋊D17C2211yescharacteristic
20C22×C22⋊D17C2211yescharacteristic
21C22×C22⋊D17C2211yescharacteristic
22C2×C22⋊C4×C17C2211yescharacteristic
23C2×C22⋊C4×C17C2211yescharacteristic
24C2×C22⋊C4×C17C2211yescharacteristic
25C2×C22⋊Dic17C2211yescharacteristic
26C2×C22⋊Dic17C2211yescharacteristic
27C2×C22⋊Dic17C2211yescharacteristic
28C2×C22⋊Dic17C2211yescharacteristic
29C2×C22⋊Dic17C2211yescharacteristic
30C2×C22⋊Dic17C2211yescharacteristic
31C2×C22⋊Dic17C2211yescharacteristic
32C2×C22⋊Dic17C2211yescharacteristic
33C2×C22⋊Dic17C2211yescharacteristic
34C2×#63227C2211yescharacteristic
35C2×#63227C2211yescharacteristic
36C2×#63227C2211yescharacteristic
37C2×#63227C2211yescharacteristic
38C2×#63225C2211yescharacteristic
39C2×#63225C2211yescharacteristic
40C2×#63225C2211yescharacteristic
41C2×#63225C2211yescharacteristic
42C2×C4×Dic17C2211yescharacteristic
43C17×#95C2211yescharacteristic
44#10587502C2211yescharacteristic
45#10587502C2211yescharacteristic
46#10587502C2211yescharacteristic
47#10587502C2211yescharacteristic
48#10587502C2211yescharacteristic
49#10587502C2211yescharacteristic
50#10587502C2211yescharacteristic
51C24×C17C2311yescharacteristic
52C24×C17C2311yescharacteristic
53C24×C17C2311yescharacteristic
54C23×D17C2311yescharacteristic
55C2×D4×C17—41no—
56C2×D4×C17—41no—
57C2×D4×C17—41no—
58C2×D4×C17—41no—
59C2×D4×C17—41no—
60C2×D4×C17—41no—
61C2×D4×C17—41no—
62C2×D4×C17—41no—
63C2×D4×C17—41no—
64C22×C4×C17C2311yescharacteristic
65C22×C4×C17C2311yescharacteristic
66C22×C4×C17C2311yescharacteristic
67C22×C4×C17C2311yescharacteristic
68C2×C22⋊D17—22no—
69C2×C22⋊D17—41no—
70C2×C22⋊D17—41no—
71C2×C22⋊D17—41no—
72C2×C22⋊D17—41no—
73C2×C22⋊D17—41no—
74C2×C22⋊D17—41no—
75C2×C22⋊D17—41no—
76C2×C22⋊D17—41no—
77C22×Dic17C2311yescharacteristic
78C22×Dic17C2311yescharacteristic
79C22×Dic17C2311yescharacteristic
80C22×Dic17C2311yescharacteristic
81C22×Dic17C2311yescharacteristic
82C22×Dic17C2311yescharacteristic
83C22×Dic17C2311yescharacteristic
84C22⋊C4×C17—41no—
85C22⋊C4×C17—41no—
86C22⋊C4×C17—41no—
87C22⋊Dic17—22no—
88C22⋊Dic17—22no—
89C22⋊Dic17—41no—
90C22⋊Dic17—41no—
91C22⋊Dic17—41no—
92C22⋊Dic17—41no—
93C22⋊Dic17—41no—
94C22⋊Dic17—41no—
95C22⋊Dic17—41no—
96#63227—41no—
97#63227—41no—
98#63227—41no—
99#63227—41no—
100#63225—41no—
101#63225—41no—
102#63225—41no—
103#63225—41no—
104C4×Dic17—41no—
105C23×C17—21no—
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—21no—
118C23×C17—21no—
119C23×C17—21no—
120C23×C17—21no—
121C23×C17—21no—
122C23×C17—21no—
123C23×C17—21no—
124C23×C17—21no—
125C23×C17—21no—
126C23×C17C2411yescharacteristic
127C22×D17—21no—
128C22×D17—21no—
129C22×D17—21no—
130C22×D17—21no—
131C22×D17—21no—
132C22×D17—21no—
133C22×D17—21no—
134D4×C17—44no—
135D4×C17—44no—
136D4×C17—44no—
137C2×C4×C17—21no—
138C2×C4×C17—21no—
139C2×C4×C17—21no—
140C2×C4×C17—21no—
141C2×C4×C17—21no—
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—
149C22⋊D17—44no—
150C22⋊D17—44no—
151C22⋊D17—44no—
152C2×Dic17—21no—
153C2×Dic17—21no—
154C2×Dic17—21no—
155C2×Dic17—21no—
156C2×Dic17—21no—
157C2×Dic17—21no—
158C2×Dic17—21no—
159C2×Dic17—21no—
160C2×Dic17—21no—
161C2×Dic17—21no—
162C2×Dic17—21no—
163C2×Dic17—21no—
164C2×Dic17—21no—
165C2×Dic17—21no—
166C2×Dic17—21no—
167C2×Dic17—21no—
168C2×Dic17—21no—
169C2×Dic17—21no—
170C2×Dic17—21no—
171C2×Dic17—21no—
172C2×Dic17#4112yes—
173#2828—171nomaximal, Sylow
174C22×C17—41no—
175C22×C17—41no—
176C22×C17—41no—
177C22×C17—41no—
178C22×C17—41no—
179C22×C17—41no—
180C22×C17—41no—
181C22×C17—41no—
182C22×C17—41no—
183C22×C17—41no—
184C22×C17—41no—
185C22×C17—41no—
186C22×C17—41no—
187C22×C17—41no—
188C22×C17—41no—
189C22×C17—41no—
190C22×C17—41no—
191C22×C17—41no—
192C22×C17—41no—
193C22×C17—41no—
194C22×C17—41no—
195C22×C17C2×#4111yescharacteristic
196C22×C17H(5,𝔽2)11yescharacteristic
197C22×C17H(5,𝔽2)11yescharacteristic
198C22×C17H(5,𝔽2)11yescharacteristic
199C22×C17H(5,𝔽2)11yescharacteristic
200C22×C17H(5,𝔽2)11yescharacteristic
201C22×C17H(5,𝔽2)11yescharacteristic
202C2×D17—41no—
203C2×D17—41no—
204C2×D17—41no—
205C2×D17—41no—
206C2×D17—41no—
207C2×D17—41no—
208C2×D17—41no—
209C4×C17—41no—
210C4×C17—41no—
211C4×C17—41no—
212C4×C17—41no—
213Dic17—22no—
214Dic17—41no—
215Dic17—41no—
216Dic17—41no—
217Dic17—41no—
218Dic17—41no—
219Dic17—41no—
220#400—171no—
221#397—171no—
222#397—171no—
223#394—171no—
224#394—171no—
225#394—171no—
226#394—171no—
227#394—171no—
228#392—171no—
229#392—171no—
230#392—171no—
231#392D1711yescharacteristic, complemented
232#390—171no—
233#388—171no—
234#388—171no—
235C2×C17—81no—
236C2×C17—81no—
237C2×C17—81no—
238C2×C17#53811yescharacteristic
239C2×C17#54011yescharacteristic
240C2×C17#54011yescharacteristic
241C2×C17#56011yescharacteristic
242C2×C17#56011yescharacteristic
243C2×C17#56011yescharacteristic
244C2×C17H(3,𝔽4)11yescharacteristic
245D17—81no—
246C22×D4—171no—
247C22×D4—171no—
248C22×D4—171no—
249C22×D4C2×D1711yescharacteristic
250C22×D4C2×D1711yescharacteristic
251C22×D4C2×D1711yescharacteristic
252C2×C4⋊C4—171no—
253C2×C4⋊C4—171no—
254C2×C4⋊C4—171no—
255C2×C4⋊C4—171no—
256C2×C22⋊C4—171no—
257C2×C22⋊C4—171no—
258C2×C22⋊C4—171no—
259C2×C22⋊C4—171no—
260C2×C22⋊C4—171no—
261C2×C22⋊C4—171no—
262C2×C22⋊C4—171no—
263C2×C22⋊C4—171no—
264C2×C22⋊C4—171no—
265C2×C22⋊C4—171no—
266C2×C22⋊C4—171no—
267C2×C22⋊C4—171no—
268C2×C22⋊C4—171no—
269C2×C22⋊C4C2×D1711yescharacteristic
270C2×C22⋊C4C2×D1711yescharacteristic
271C2×C22⋊C4C2×D1711yescharacteristic
272C2×C42—171no—
273#95—171no—
274#95—171no—
275#95—171no—
276#95—171no—
277#95—171no—
278#95—171no—
279#95—171no—
280#95C2×D1711yescharacteristic
281C17#282811yescharacteristic, complemented, Sylow
282C24—171no—
283C24C22×D1711yescharacteristic
284C24C22×D1711yescharacteristic
285C24C22×D1711yescharacteristic
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—342no—
296C2×D4—681no—
297C2×D4—681no—
298C2×D4—681no—
299C2×D4—681no—
300C2×D4—681no—
301C2×D4—681no—
302C2×D4—681no—
303C2×D4—681no—
304C22×C4—171no—
305C22×C4—171no—
306C22×C4—171no—
307C22×C4—171no—
308C22×C4—171no—
309C22×C4—171no—
310C22×C4—171no—
311C22×C4C22×D1711yescharacteristic
312C22×C4C22×D1711yescharacteristic
313C22×C4C22×D1711yescharacteristic
314C22×C4C22×D1711yescharacteristic
315C4⋊C4—681no—
316C4⋊C4—681no—
317C4⋊C4—681no—
318C4⋊C4—681no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—342no—
323C22⋊C4—342no—
324C22⋊C4—681no—
325C22⋊C4—681no—
326C22⋊C4—681no—
327C22⋊C4—681no—
328C22⋊C4—681no—
329C22⋊C4—681no—
330C22⋊C4—681no—
331C22⋊C4—681no—
332C22⋊C4—681no—
333C22⋊C4—681no—
334C22⋊C4—681no—
335C42—681no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—341no—
358C23—341no—
359C23—341no—
360C23—341no—
361C23—341no—
362C23—341no—
363C23—341no—
364C23C23×D1711yescharacteristic
365D4—44no—
366D4—44no—
367D4—44no—
368D4—684no—
369D4—684no—
370D4—684no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
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—172no—
384C2×C4—341no—
385C2×C4—341no—
386C2×C4—341no—
387C2×C4—341no—
388C2×C4—341no—
389C2×C4—341no—
390C2×C4—341no—
391C2×C4—341no—
392C2×C4—341no—
393C2×C4—341no—
394C2×C4—341no—
395C2×C4—341no—
396C2×C4—341no—
397C2×C4—341no—
398C2×C4—341no—
399C2×C4—341no—
400C2×C4—341no—
401C2×C4—341no—
402C2×C4—341no—
403C2×C4—341no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—681no—
426C22—681no—
427C22—681no—
428C22—681no—
429C22—681no—
430C22—681no—
431C22—681no—
432C22#1058769111yescharacteristic
433C22#1058769111yescharacteristic
434C22#1058769111yescharacteristic
435C22#1058769111yescharacteristic
436C22#1058769111yescharacteristic
437C22#1058769111yescharacteristic
438C22#41×D1711yescharacteristic
439C4—41no—
440C4—41no—
441C4—41no—
442C4—41no—
443C4—342no—
444C4—681no—
445C4—681no—
446C4—681no—
447C4—681no—
448C4—681no—
449C4—681no—
450C2—81no—
451C2—81no—
452C2—81no—
453C2—1361no—
454C2#1176339111yescharacteristic
455C2#1176340911yescharacteristic
456C2#1176340911yescharacteristic
457C2#1176354611yescharacteristic
458C2#1176354811yescharacteristic
459C2#1176354811yescharacteristic
460C2#1176355211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, cosocleC23×C17C24
FittingC17×#392C2
hypercenter#392D17
hypocenterC17#2828
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #11762750C2semidirect
2. #11762738C2semidirect
3. #11762737C2semidirect
4. #11762724C2semidirect
5. #11762724C2semidirect
6. #11762723C2semidirect
7. #11762723C2semidirect
8. #11762723C2semidirect
9. #11762717C2semidirect
10. #11762717C2semidirect
11. #11762717C2semidirect
12. #11762709C2semidirect
13. #11762703C2semidirect
14. #11762697C2semidirect
15. C17×#392C2semidirect
231. #392D17semidirect
281. C17#2828semidirect

Maximal subgroups

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

subgroupindex
#117627502
#117627382
#117627372
#117627242
#117627232
#117627172
#117627092
#117627032
#117626972
C17×#3922
#282817