Finite Group Databasebeta

← #44558461

Subgroups — #44558461

Order 32128.

464 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30631628C211yesmaximal, characteristic, complemented
2#30631626C211yesmaximal, characteristic, complemented
3#30631622C211yesmaximal, characteristic, complemented
4#30631615C211yesmaximal, characteristic, complemented
5#30631612C211yesmaximal, characteristic, complemented
6#30631610C211yesmaximal, characteristic, complemented
7#30631610C211yesmaximal, characteristic, complemented
8#30631603C211yesmaximal, characteristic, complemented
9#30631602C211yesmaximal, characteristic, complemented
10#30631601C211yesmaximal, characteristic, complemented
11#30631595C211yesmaximal, characteristic
12#30631563C211yesmaximal, characteristic, complemented
13#30631563C211yesmaximal, characteristic, complemented
14#30631561C211yesmaximal, characteristic, complemented
15#394×C251C211yesmaximal, characteristic, complemented
16C22×C22⋊D251C2211yescharacteristic
17C22×C22⋊D251C2211yescharacteristic
18C22×C4×D251C2211yescharacteristic
19C2×C4⋊Dic251C2211yescharacteristic
20C2×C4⋊Dic251C2211yescharacteristic
21C2×Dic251⋊C4C2211yescharacteristic
22C2×Dic251⋊C4C2211yescharacteristic
23C2×Dic251⋊C4C2211yescharacteristic
24C2×Dic251⋊C4C2211yescharacteristic
25C2×C22⋊Dic251C2211yescharacteristic
26C2×C22⋊Dic251C2211yescharacteristic
27C2×C22⋊Dic251C2211yescharacteristic
28C2×C22⋊Dic251C2211yescharacteristic
29C2×C22⋊Dic251C2211yescharacteristic
30C2×C22⋊Dic251C2211yescharacteristic
31C2×(C2×D251)⋊C4C2211yescharacteristic
32C2×(C2×D251)⋊C4C2211yescharacteristic
33C2×(C2×D251)⋊C4C2211yescharacteristic
34C2×(C2×D251)⋊C4C2211yescharacteristic
35C251⋊#95C2211yescharacteristic
36C251⋊#95C2211yescharacteristic
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
52C2×C22⋊D251—22no—
53C2×C22⋊D251—22no—
54C2×C22⋊D251—41no—
55C2×C22⋊D251—41no—
56C2×C22⋊D251—41no—
57C2×C22⋊D251—41no—
58C22×Dic251C2311yescharacteristic
59C22×Dic251C2311yescharacteristic
60C22×Dic251C2311yescharacteristic
61C22×Dic251C2311yescharacteristic
62C22×Dic251C2311yescharacteristic
63C22×Dic251C2311yescharacteristic
64C22×Dic251C2311yescharacteristic
65C2×C4×D251—41no—
66C2×C4×D251—41no—
67C2×C4×D251—41no—
68C4⋊Dic251—41no—
69C4⋊Dic251—41no—
70Dic251⋊C4—41no—
71Dic251⋊C4—41no—
72Dic251⋊C4—41no—
73Dic251⋊C4—41no—
74C22⋊Dic251—41no—
75C22⋊Dic251—41no—
76C22⋊Dic251—41no—
77C22⋊Dic251—41no—
78C22⋊Dic251—41no—
79C22⋊Dic251—41no—
80(C2×D251)⋊C4—22no—
81(C2×D251)⋊C4—41no—
82(C2×D251)⋊C4—41no—
83(C2×D251)⋊C4—41no—
84C24×C251C2311yescharacteristic
85C24×C251C2311yescharacteristic
86C2×D4×C251—41no—
87C2×D4×C251—41no—
88C2×D4×C251—41no—
89C22×C4×C251C2311yescharacteristic
90C22×C4×C251C2311yescharacteristic
91C22×C4×C251C2311yescharacteristic
92C22×C4×C251C2311yescharacteristic
93C22×C4×C251C2311yescharacteristic
94C4⋊C4×C251—41no—
95C22⋊C4×C251—41no—
96C22⋊C4×C251—41no—
97C22⋊C4×C251—41no—
98C22⋊C4×C251—41no—
99C22×D251—21no—
100C22×D251—21no—
101C22×D251—21no—
102C22×D251—21no—
103C22×D251—21no—
104C22×D251—21no—
105C22×D251#4112yes—
106C22⋊D251—44no—
107C22⋊D251—44no—
108C2×Dic251—21no—
109C2×Dic251—21no—
110C2×Dic251—21no—
111C2×Dic251—21no—
112C2×Dic251—21no—
113C2×Dic251—21no—
114C2×Dic251—21no—
115C2×Dic251—21no—
116C2×Dic251—21no—
117C2×Dic251—21no—
118C2×Dic251—21no—
119C2×Dic251—21no—
120C2×Dic251—21no—
121C2×Dic251—21no—
122C2×Dic251—21no—
123C2×Dic251—21no—
124C2×Dic251—21no—
125C2×Dic251—21no—
126C2×Dic251—21no—
127C2×Dic251—21no—
128C2×Dic251—21no—
129C4×D251—44no—
130C23×C251—21no—
131C23×C251—21no—
132C23×C251—21no—
133C23×C251—21no—
134C23×C251—21no—
135C23×C251—21no—
136C23×C251—21no—
137C23×C251—21no—
138C23×C251—21no—
139C23×C251—21no—
140C23×C251—21no—
141C23×C251—21no—
142C23×C251—21no—
143C23×C251—21no—
144C23×C251C2411yescharacteristic
145D4×C251—44no—
146C2×C4×C251—21no—
147C2×C4×C251—21no—
148C2×C4×C251—21no—
149C2×C4×C251—21no—
150C2×C4×C251—21no—
151C2×C4×C251—21no—
152C2×C4×C251—21no—
153C2×C4×C251—21no—
154C2×C4×C251—21no—
155C2×C4×C251—21no—
156C2×C4×C251—21no—
157C2×C4×C251—21no—
158C2×C4×C251—21no—
159C2×C4×C251—21no—
160C2×C4×C251—21no—
161C22×C251—41no—
162C22×C251—41no—
163C22×C251—41no—
164C22×C251—41no—
165C22×C251—41no—
166C22×C251—41no—
167C22×C251—41no—
168C22×C251—41no—
169C22×C251—41no—
170C22×C251—41no—
171C22×C251—41no—
172C22×C251—41no—
173C22×C251—41no—
174C22×C251—41no—
175C22×C251C2×#4111yescharacteristic
176C22×C251H(5,𝔽2)11yescharacteristic
177C22×C251H(5,𝔽2)11yescharacteristic
178C22×C251H(5,𝔽2)11yescharacteristic
179C22×C251H(5,𝔽2)11yescharacteristic
180C22×C251H(5,𝔽2)11yescharacteristic
181C22×C2512−1+411yescharacteristic
182C2×D251—22no—
183C2×D251—22no—
184C2×D251—22no—
185C2×D251—41no—
186C2×D251—41no—
187C2×D251—41no—
188C2×D251—41no—
189C4×C251—41no—
190C4×C251—41no—
191C4×C251—41no—
192C4×C251—41no—
193C4×C251—41no—
194Dic251—41no—
195Dic251—41no—
196Dic251—41no—
197Dic251—41no—
198Dic251—41no—
199Dic251—41no—
200Dic251—41no—
201C2×C251—81no—
202C2×C251—81no—
203C2×C251#53811yescharacteristic
204C2×C251#53811yescharacteristic
205C2×C251#53911yescharacteristic
206C2×C251#56011yescharacteristic
207C2×C251#56011yescharacteristic
208C2×C251#56211yescharacteristic
209C2×C251#56211yescharacteristic
210D251—42no—
211C251#282611yescharacteristic, complemented, Sylow
212#2826—2511nomaximal, Sylow
213#400—2511no—
214#400—2511no—
215#399—2511no—
216#397—2511no—
217#397—2511no—
218#396—2511no—
219#396—2511no—
220#394—2511no—
221#394—2511no—
222#394—2511no—
223#394D25111yescharacteristic, complemented
224#392—2511no—
225#386—2511no—
226#386—2511no—
227#385—2511no—
228C22×D4—2511no—
229C22×D4—2511no—
230C22×D4C2×D25111yescharacteristic
231C23×C4—2511no—
232C2×C4⋊C4—2511no—
233C2×C4⋊C4—2511no—
234C2×C4⋊C4—2511no—
235C2×C4⋊C4—2511no—
236C2×C4⋊C4—2511no—
237C2×C4⋊C4—2511no—
238C2×C4⋊C4C2×D25111yescharacteristic
239C2×C22⋊C4—2511no—
240C2×C22⋊C4—2511no—
241C2×C22⋊C4—2511no—
242C2×C22⋊C4—2511no—
243C2×C22⋊C4—2511no—
244C2×C22⋊C4—2511no—
245C2×C22⋊C4—2511no—
246C2×C22⋊C4—2511no—
247C2×C22⋊C4—2511no—
248C2×C22⋊C4—2511no—
249C2×C22⋊C4C2×D25111yescharacteristic
250C2×C22⋊C4C2×D25111yescharacteristic
251C2×C22⋊C4C2×D25111yescharacteristic
252C2×C22⋊C4C2×D25111yescharacteristic
253#95—2511no—
254#95—2511no—
255#95—2511no—
256#95—2511no—
257#95—2511no—
258#95—2511no—
259#95—2511no—
260#95—2511no—
261#95—2511no—
262#95C2×D25111yescharacteristic
263C24—2511no—
264C24C22×D25111yescharacteristic
265C24C22×D25111yescharacteristic
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—10041no—
270C2×D4—10041no—
271C2×D4—10041no—
272C2×D4—10041no—
273C2×D4—5022no—
274C2×D4—5022no—
275C22×C4—10041no—
276C22×C4—10041no—
277C22×C4—10041no—
278C22×C4—2511no—
279C22×C4—2511no—
280C22×C4—2511no—
281C22×C4—2511no—
282C22×C4—2511no—
283C22×C4—2511no—
284C22×C4—2511no—
285C22×C4C22×D25111yescharacteristic
286C22×C4C22×D25111yescharacteristic
287C22×C4C22×D25111yescharacteristic
288C22×C4C22×D25111yescharacteristic
289C22×C4C22×D25111yescharacteristic
290C4⋊C4—41no—
291C4⋊C4—10041no—
292C4⋊C4—10041no—
293C4⋊C4—10041no—
294C4⋊C4—10041no—
295C4⋊C4—10041no—
296C4⋊C4—10041no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—10041no—
302C22⋊C4—10041no—
303C22⋊C4—10041no—
304C22⋊C4—10041no—
305C22⋊C4—10041no—
306C22⋊C4—10041no—
307C22⋊C4—10041no—
308C22⋊C4—10041no—
309C22⋊C4—10041no—
310C22⋊C4—5022no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—5021no—
326C23—5021no—
327C23—5021no—
328C23—5021no—
329C23—5021no—
330C23—5021no—
331C23—2512no—
332C23C23×D25111yescharacteristic
333D4—44no—
334D4—10044no—
335D4—10044no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—10044no—
352C2×C4—5021no—
353C2×C4—5021no—
354C2×C4—5021no—
355C2×C4—5021no—
356C2×C4—5021no—
357C2×C4—5021no—
358C2×C4—5021no—
359C2×C4—5021no—
360C2×C4—5021no—
361C2×C4—5021no—
362C2×C4—5021no—
363C2×C4—5021no—
364C2×C4—5021no—
365C2×C4—5021no—
366C2×C4—5021no—
367C2×C4—5021no—
368C2×C4—5021no—
369C2×C4—5021no—
370C2×C4—5021no—
371C2×C4—5021no—
372C2×C4—5021no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—10041no—
388C22—10041no—
389C22—10041no—
390C22—10041no—
391C22—5022no—
392C22—5022no—
393C22—5022no—
394C22#41×D25111yescharacteristic
395C22#2254876011yescharacteristic
396C22#2254876011yescharacteristic
397C22#2254876011yescharacteristic
398C22#2254876011yescharacteristic
399C22#2254876111yescharacteristic
400C22#2254876211yescharacteristic
401C4—41no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—10041no—
407C4—10041no—
408C4—10041no—
409C4—10041no—
410C4—10041no—
411C4—10041no—
412C4—10041no—
413C2—81no—
414C2—81no—
415C2—10042no—
416C2#3063226911yescharacteristic
417C2#3063227111yescharacteristic
418C2#3063228011yescharacteristic
419C2#3063242511yescharacteristic
420C2#3063242611yescharacteristic
421C2#3063243211yescharacteristic
422C2#3063243411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D251
commutator, socle, cosocleC23×C251C24
Fitting#394×C251C2
prime radical#30631595C2
hypercenter#394D251
hypocenterC251#2826
LCSG ▷ C23×C251 ▷ C251
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #30631628C2semidirect
2. #30631626C2semidirect
3. #30631622C2semidirect
4. #30631615C2semidirect
5. #30631612C2semidirect
6. #30631610C2semidirect
7. #30631610C2semidirect
8. #30631603C2semidirect
9. #30631602C2semidirect
10. #30631601C2semidirect
12. #30631563C2semidirect
13. #30631563C2semidirect
14. #30631561C2semidirect
15. #394×C251C2semidirect
211. C251#2826semidirect
223. #394D251semidirect

Maximal subgroups

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

subgroupindex
#306316282
#306316262
#306316222
#306316152
#306316122
#306316102
#306316032
#306316022
#306316012
#306315952
#306315632
#306315612
#394×C2512
#2826251