Finite Group Databasebeta

← #44558485

Subgroups — #44558485

Order 32128.

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#30631625C211yesmaximal, characteristic, complemented
2#30631616C211yesmaximal, characteristic, complemented
3#30631612C211yesmaximal, characteristic, complemented
4#30631604C211yesmaximal, characteristic, complemented
5#30631603C211yesmaximal, characteristic, complemented
6#30631602C211yesmaximal, characteristic, complemented
7#30631602C211yesmaximal, characteristic, complemented
8#30631596C211yesmaximal, characteristic, complemented
9#30631596C211yesmaximal, characteristic, complemented
10#30631595C211yesmaximal, characteristic, complemented
11#30631595C211yesmaximal, characteristic, complemented
12#30631587C211yesmaximal, characteristic, complemented
13#30631581C211yesmaximal, characteristic, complemented
14#30631579C211yesmaximal, characteristic, complemented
15#394×C251C211yesmaximal, characteristic, complemented
16C22×D1004C2211yescharacteristic
17C22×C22⋊D251C2211yescharacteristic
18C22×C22⋊D251C2211yescharacteristic
19C22×C22⋊D251C2211yescharacteristic
20C22×C22⋊D251C2211yescharacteristic
21C2×C4⋊Dic251C2211yescharacteristic
22C2×Dic251⋊C4C2211yescharacteristic
23C2×Dic251⋊C4C2211yescharacteristic
24C2×C22⋊Dic251C2211yescharacteristic
25C2×C22⋊Dic251C2211yescharacteristic
26C2×C22⋊Dic251C2211yescharacteristic
27C2×C22⋊Dic251C2211yescharacteristic
28C2×(C2×D251)⋊C4C2211yescharacteristic
29C2×(C2×D251)⋊C4C2211yescharacteristic
30C2×(C2×D251)⋊C4C2211yescharacteristic
31C2×(C2×D251)⋊C4C2211yescharacteristic
32C2×(C2×D251)⋊C4C2211yescharacteristic
33C2×(C2×D251)⋊C4C2211yescharacteristic
34C2×(C2×D251)⋊C4C2211yescharacteristic
35C2×(C2×D251)⋊C4C2211yescharacteristic
36C2×C4×Dic251C2211yescharacteristic
37C251⋊#95C2211yescharacteristic
38C251⋊#95C2211yescharacteristic
39C251⋊#95C2211yescharacteristic
40C251⋊#95C2211yescharacteristic
41C251⋊#95C2211yescharacteristic
42C251⋊#95C2211yescharacteristic
43C251⋊#95C2211yescharacteristic
44C22×D4×C251C2211yescharacteristic
45C2×C4⋊C4×C251C2211yescharacteristic
46C2×C22⋊C4×C251C2211yescharacteristic
47C2×C22⋊C4×C251C2211yescharacteristic
48C2×C22⋊C4×C251C2211yescharacteristic
49C2×C22⋊C4×C251C2211yescharacteristic
50#95×C251C2211yescharacteristic
51C23×D251C2311yescharacteristic
52C23×D251C2311yescharacteristic
53C2×D1004—41no—
54C2×D1004—41no—
55C2×D1004—41no—
56C2×C22⋊D251—22no—
57C2×C22⋊D251—41no—
58C2×C22⋊D251—41no—
59C2×C22⋊D251—41no—
60C2×C22⋊D251—41no—
61C2×C22⋊D251—41no—
62C2×C22⋊D251—41no—
63C2×C22⋊D251—41no—
64C2×C22⋊D251—41no—
65C2×C22⋊D251—41no—
66C2×C22⋊D251—41no—
67C2×C22⋊D251—41no—
68C22×Dic251C2311yescharacteristic
69C22×Dic251C2311yescharacteristic
70C22×Dic251C2311yescharacteristic
71C22×Dic251C2311yescharacteristic
72C22×Dic251C2311yescharacteristic
73C22×Dic251C2311yescharacteristic
74C4⋊Dic251—41no—
75Dic251⋊C4—41no—
76Dic251⋊C4—41no—
77C22⋊Dic251—22no—
78C22⋊Dic251—41no—
79C22⋊Dic251—41no—
80C22⋊Dic251—41no—
81(C2×D251)⋊C4—22no—
82(C2×D251)⋊C4—41no—
83(C2×D251)⋊C4—41no—
84(C2×D251)⋊C4—41no—
85(C2×D251)⋊C4—41no—
86(C2×D251)⋊C4—41no—
87(C2×D251)⋊C4—41no—
88(C2×D251)⋊C4—41no—
89C4×Dic251—41no—
90C24×C251C2311yescharacteristic
91C24×C251C2311yescharacteristic
92C2×D4×C251—41no—
93C2×D4×C251—41no—
94C2×D4×C251—41no—
95C22×C4×C251C2311yescharacteristic
96C22×C4×C251C2311yescharacteristic
97C22×C4×C251C2311yescharacteristic
98C22×C4×C251C2311yescharacteristic
99C22×C4×C251C2311yescharacteristic
100C4⋊C4×C251—41no—
101C22⋊C4×C251—41no—
102C22⋊C4×C251—41no—
103C22⋊C4×C251—41no—
104C22⋊C4×C251—41no—
105C22×D251—21no—
106C22×D251—21no—
107C22×D251—21no—
108C22×D251—21no—
109C22×D251—21no—
110C22×D251—21no—
111C22×D251—21no—
112C22×D251—21no—
113C22×D251—21no—
114C22×D251—21no—
115C22×D251—21no—
116C22×D251—21no—
117C22×D251—21no—
118C22×D251—21no—
119D1004—44no—
120C22⋊D251—44no—
121C22⋊D251—44no—
122C22⋊D251—44no—
123C22⋊D251—44no—
124C2×Dic251—21no—
125C2×Dic251—21no—
126C2×Dic251—21no—
127C2×Dic251—21no—
128C2×Dic251—21no—
129C2×Dic251—21no—
130C2×Dic251—21no—
131C2×Dic251—21no—
132C2×Dic251—21no—
133C2×Dic251—21no—
134C2×Dic251—21no—
135C2×Dic251—21no—
136C2×Dic251—21no—
137C2×Dic251—21no—
138C2×Dic251—21no—
139C2×Dic251—21no—
140C2×Dic251—21no—
141C2×Dic251#4112yes—
142C23×C251—21no—
143C23×C251—21no—
144C23×C251—21no—
145C23×C251—21no—
146C23×C251—21no—
147C23×C251—21no—
148C23×C251—21no—
149C23×C251—21no—
150C23×C251—21no—
151C23×C251—21no—
152C23×C251—21no—
153C23×C251—21no—
154C23×C251—21no—
155C23×C251—21no—
156C23×C251C2411yescharacteristic
157D4×C251—44no—
158C2×C4×C251—21no—
159C2×C4×C251—21no—
160C2×C4×C251—21no—
161C2×C4×C251—21no—
162C2×C4×C251—21no—
163C2×C4×C251—21no—
164C2×C4×C251—21no—
165C2×C4×C251—21no—
166C2×C4×C251—21no—
167C2×C4×C251—21no—
168C2×C4×C251—21no—
169C2×C4×C251—21no—
170C2×C4×C251—21no—
171C2×C4×C251—21no—
172C2×C4×C251—21no—
173C22×C251—41no—
174C22×C251—41no—
175C22×C251—41no—
176C22×C251—41no—
177C22×C251—41no—
178C22×C251—41no—
179C22×C251—41no—
180C22×C251—41no—
181C22×C251—41no—
182C22×C251—41no—
183C22×C251—41no—
184C22×C251—41no—
185C22×C251—41no—
186C22×C251—41no—
187C22×C251C2×#4111yescharacteristic
188C22×C251H(5,𝔽2)11yescharacteristic
189C22×C251H(5,𝔽2)11yescharacteristic
190C22×C251H(5,𝔽2)11yescharacteristic
191C22×C251H(5,𝔽2)11yescharacteristic
192C22×C251H(5,𝔽2)11yescharacteristic
193C22×C251H(5,𝔽2)11yescharacteristic
194C2×D251—41no—
195C2×D251—41no—
196C2×D251—41no—
197C2×D251—41no—
198C2×D251—41no—
199C2×D251—41no—
200C2×D251—41no—
201C2×D251—41no—
202C2×D251—41no—
203C2×D251—41no—
204C2×D251—41no—
205C2×D251—41no—
206C2×D251—41no—
207C2×D251—41no—
208C4×C251—41no—
209C4×C251—41no—
210C4×C251—41no—
211C4×C251—41no—
212C4×C251—41no—
213Dic251—22no—
214Dic251—41no—
215Dic251—41no—
216Dic251—41no—
217Dic251—41no—
218Dic251—41no—
219C2×C251—81no—
220C2×C251—81no—
221C2×C251#53811yescharacteristic
222C2×C251#54011yescharacteristic
223C2×C251#54011yescharacteristic
224C2×C251#56011yescharacteristic
225C2×C251#56011yescharacteristic
226C2×C251#56011yescharacteristic
227C2×C251H(3,𝔽4)11yescharacteristic
228D251—81no—
229D251—81no—
230C251#282811yescharacteristic, complemented, Sylow
231#2828—2511nomaximal, Sylow
232#400—2511no—
233#397—2511no—
234#397—2511no—
235#394—2511no—
236#394—2511no—
237#394—2511no—
238#394—2511no—
239#394D25111yescharacteristic, complemented
240#392—2511no—
241#392—2511no—
242#392—2511no—
243#392—2511no—
244#390—2511no—
245#388—2511no—
246#388—2511no—
247C22×D4—2511no—
248C22×D4—2511no—
249C22×D4—2511no—
250C22×D4—2511no—
251C22×D4—2511no—
252C22×D4C2×D25111yescharacteristic
253C2×C4⋊C4—2511no—
254C2×C4⋊C4—2511no—
255C2×C4⋊C4—2511no—
256C2×C4⋊C4C2×D25111yescharacteristic
257C2×C22⋊C4—2511no—
258C2×C22⋊C4—2511no—
259C2×C22⋊C4—2511no—
260C2×C22⋊C4—2511no—
261C2×C22⋊C4—2511no—
262C2×C22⋊C4—2511no—
263C2×C22⋊C4—2511no—
264C2×C22⋊C4—2511no—
265C2×C22⋊C4—2511no—
266C2×C22⋊C4—2511no—
267C2×C22⋊C4—2511no—
268C2×C22⋊C4—2511no—
269C2×C22⋊C4C2×D25111yescharacteristic
270C2×C22⋊C4C2×D25111yescharacteristic
271C2×C22⋊C4C2×D25111yescharacteristic
272C2×C22⋊C4C2×D25111yescharacteristic
273C2×C42—2511no—
274#95—2511no—
275#95—2511no—
276#95—2511no—
277#95—2511no—
278#95—2511no—
279#95—2511no—
280#95—2511no—
281#95C2×D25111yescharacteristic
282C24—2511no—
283C24—2511no—
284C24C22×D25111yescharacteristic
285C24C22×D25111yescharacteristic
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—10041no—
290C2×D4—10041no—
291C2×D4—10041no—
292C2×D4—10041no—
293C2×D4—10041no—
294C2×D4—10041no—
295C2×D4—10041no—
296C2×D4—10041no—
297C2×D4—10041no—
298C2×D4—10041no—
299C2×D4—10041no—
300C2×D4—10041no—
301C2×D4—10041no—
302C2×D4—10041no—
303C2×D4—5022no—
304C22×C4—2511no—
305C22×C4—2511no—
306C22×C4—2511no—
307C22×C4—2511no—
308C22×C4—2511no—
309C22×C4—2511no—
310C22×C4C22×D25111yescharacteristic
311C22×C4C22×D25111yescharacteristic
312C22×C4C22×D25111yescharacteristic
313C22×C4C22×D25111yescharacteristic
314C22×C4C22×D25111yescharacteristic
315C4⋊C4—41no—
316C4⋊C4—10041no—
317C4⋊C4—10041no—
318C4⋊C4—10041no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—10041no—
324C22⋊C4—10041no—
325C22⋊C4—10041no—
326C22⋊C4—10041no—
327C22⋊C4—10041no—
328C22⋊C4—10041no—
329C22⋊C4—10041no—
330C22⋊C4—10041no—
331C22⋊C4—10041no—
332C22⋊C4—10041no—
333C22⋊C4—5022no—
334C22⋊C4—5022no—
335C42—10041no—
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—5021no—
351C23—5021no—
352C23—5021no—
353C23—5021no—
354C23—5021no—
355C23—5021no—
356C23—5021no—
357C23—5021no—
358C23—5021no—
359C23—5021no—
360C23—5021no—
361C23—5021no—
362C23—5021no—
363C23—5021no—
364C23C23×D25111yescharacteristic
365D4—44no—
366D4—10044no—
367D4—10044no—
368D4—10044no—
369D4—10044no—
370D4—10044no—
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—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—5021no—
387C2×C4—5021no—
388C2×C4—5021no—
389C2×C4—5021no—
390C2×C4—5021no—
391C2×C4—5021no—
392C2×C4—5021no—
393C2×C4—5021no—
394C2×C4—5021no—
395C2×C4—5021no—
396C2×C4—5021no—
397C2×C4—5021no—
398C2×C4—5021no—
399C2×C4—5021no—
400C2×C4—5021no—
401C2×C4—5021no—
402C2×C4—5021no—
403C2×C4—2512no—
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—10041no—
419C22—10041no—
420C22—10041no—
421C22—10041no—
422C22—10041no—
423C22—10041no—
424C22—10041no—
425C22—10041no—
426C22—10041no—
427C22—10041no—
428C22—10041no—
429C22—10041no—
430C22—10041no—
431C22—10041no—
432C22#41×D25111yescharacteristic
433C22#2254876011yescharacteristic
434C22#2254876011yescharacteristic
435C22#2254876011yescharacteristic
436C22#2254876011yescharacteristic
437C22#2254876111yescharacteristic
438C22#2254876111yescharacteristic
439C4—41no—
440C4—41no—
441C4—41no—
442C4—41no—
443C4—41no—
444C4—10041no—
445C4—10041no—
446C4—10041no—
447C4—10041no—
448C4—10041no—
449C4—5022no—
450C2—81no—
451C2—81no—
452C2—20081no—
453C2—20081no—
454C2#3063227111yescharacteristic
455C2#3063228711yescharacteristic
456C2#3063228911yescharacteristic
457C2#3063242511yescharacteristic
458C2#3063242511yescharacteristic
459C2#3063242711yescharacteristic
460C2#3063243011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D251
commutator, socle, cosocleC23×C251C24
Fitting#394×C251C2
hypercenter#394D251
hypocenterC251#2828
LCSG ▷ C23×C251 ▷ C251
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #30631625C2semidirect
2. #30631616C2semidirect
3. #30631612C2semidirect
4. #30631604C2semidirect
5. #30631603C2semidirect
6. #30631602C2semidirect
7. #30631602C2semidirect
8. #30631596C2semidirect
9. #30631596C2semidirect
10. #30631595C2semidirect
11. #30631595C2semidirect
12. #30631587C2semidirect
13. #30631581C2semidirect
14. #30631579C2semidirect
15. #394×C251C2semidirect
230. C251#2828semidirect
239. #394D251semidirect

Maximal subgroups

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

subgroupindex
#306316252
#306316162
#306316122
#306316042
#306316032
#306316022
#306315962
#306315952
#306315872
#306315812
#306315792
#394×C2512
#2828251