Finite Group Databasebeta

← #44510086

Subgroups — #44510086

Order 30848.

540 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21440602C211yesmaximal, characteristic
2#29507617C211yesmaximal, characteristic
3#29507617C211yesmaximal, characteristic
4#29507614C211yesmaximal, characteristic, complemented
5#29507612C211yesmaximal, characteristic, complemented
6#29507610C211yesmaximal, characteristic, complemented
7#29507608C211yesmaximal, characteristic, complemented
8#29507606C211yesmaximal, characteristic, complemented
9#29507579C211yesmaximal, characteristic, complemented
10#29507578C211yesmaximal, characteristic, complemented
11#29507575C211yesmaximal, characteristic, complemented
12#29507574C211yesmaximal, characteristic, complemented
13C4×#16838749C211yesmaximal, characteristic, complemented
14#29507562C211yesmaximal, characteristic, complemented
15#388×C241C211yesmaximal, characteristic, complemented
16C22×C22⋊D241C2211yescharacteristic
17C23×Dic241C2211yescharacteristic
18C22×C4×D241C2211yescharacteristic
19#21440602C418yescomplemented
20C2×C4⋊Dic241C2211yescharacteristic
21C2×#16838749C2211yescharacteristic
22C2×#16838749C2211yescharacteristic
23C2×#16838749C2211yescharacteristic
24C2×#16838749C2211yescharacteristic
25C2×#16838749C2211yescharacteristic
26C2×C22⋊Dic241C2211yescharacteristic
27C2×C22⋊Dic241C2211yescharacteristic
28C2×#16838747C2211yescharacteristic
29C2×#16838747C2211yescharacteristic
30C2×#16838747C2211yescharacteristic
31C2×#16838747C2211yescharacteristic
32C2×#16838747C2211yescharacteristic
33C2×C4×Dic241C2211yescharacteristic
34C2×C4×Dic241C2211yescharacteristic
35C2×C4×Dic241C2211yescharacteristic
36C2×C4×Dic241C2211yescharacteristic
37#21440549C2211yescharacteristic
38#21440549C2211yescharacteristic
39#21440549C2211yescharacteristic
40#21440549C2211yescharacteristic
41#21440549C2211yescharacteristic
42#21440549C2211yescharacteristic
43#21440549C2211yescharacteristic
44#21440549C2211yescharacteristic
45C2×C4⋊C4×C241C2211yescharacteristic
46C2×C22⋊C4×C241C2211yescharacteristic
47C2×C22⋊C4×C241C2211yescharacteristic
48C2×C22⋊C4×C241C2211yescharacteristic
49C2×C42×C241C2211yescharacteristic
50#95×C241C2211yescharacteristic
51#95×C241C2211yescharacteristic
52C23×D241C2311yescharacteristic
53C2×C22⋊D241—22no—
54C2×C22⋊D241—22no—
55C2×C22⋊D241C2×C414yes—
56C22×Dic241—41no—
57C22×Dic241—41no—
58C22×Dic241C2×C414yes—
59C22×Dic241C2311yescharacteristic
60C22×Dic241C2311yescharacteristic
61C22×Dic241C2311yescharacteristic
62C22×Dic241C2311yescharacteristic
63C22×Dic241C2311yescharacteristic
64C22×Dic241C2311yescharacteristic
65C22×Dic241C2311yescharacteristic
66C2×C4×D241—41no—
67C2×C4×D241—41no—
68C2×C4×D241C2×C414yes—
69C4⋊Dic241—41no—
70#16838749—22no—
71#16838749—22no—
72#16838749—41no—
73#16838749—41no—
74#16838749C2×C414yes—
75C22⋊Dic241—41no—
76C22⋊Dic241—41no—
77#16838747—41no—
78#16838747—41no—
79#16838747—41no—
80#16838747—41no—
81#16838747C2×C414yes—
82C4×Dic241—22no—
83C4×Dic241—22no—
84C4×Dic241—41no—
85C4×Dic241C2×C414yes—
86C24×C241C2311yescharacteristic
87C22×C4×C241C2311yescharacteristic
88C22×C4×C241C2311yescharacteristic
89C22×C4×C241C2311yescharacteristic
90C22×C4×C241C2311yescharacteristic
91C22×C4×C241C2311yescharacteristic
92C22×C4×C241C2311yescharacteristic
93C4⋊C4×C241—41no—
94C22⋊C4×C241—41no—
95C22⋊C4×C241—41no—
96C22⋊C4×C241C2×C414yes—
97C42×C241—41no—
98C22×D241—21no—
99C22×D241—21no—
100C22×D241—21no—
101C22×D241—21no—
102C22×D241—21no—
103C22×D241—21no—
104C22×D241C22×C412yes—
105C22⋊D241—28no—
106C2×Dic241—21no—
107C2×Dic241—21no—
108C2×Dic241—21no—
109C2×Dic241—21no—
110C2×Dic241—21no—
111C2×Dic241—21no—
112C2×Dic241—21no—
113C2×Dic241—21no—
114C2×Dic241—21no—
115C2×Dic241—21no—
116C2×Dic241—21no—
117C2×Dic241—21no—
118C2×Dic241—21no—
119C2×Dic241—21no—
120C2×Dic241—21no—
121C2×Dic241—21no—
122C2×Dic241—44no—
123C2×Dic241C22×C412yes—
124C2×Dic241C22×C412yes—
125C2×Dic241C22×C412yes—
126C2×Dic241#4112yes—
127C2×Dic241#4112yes—
128C4×D241—44no—
129C23×C241—21no—
130C23×C241—21no—
131C23×C241—21no—
132C23×C241—21no—
133C23×C241—21no—
134C23×C241—21no—
135C23×C241C22×C412yes—
136C23×C241C2411yescharacteristic
137C2×C4×C241—21no—
138C2×C4×C241—21no—
139C2×C4×C241—21no—
140C2×C4×C241—21no—
141C2×C4×C241—21no—
142C2×C4×C241—21no—
143C2×C4×C241—21no—
144C2×C4×C241—21no—
145C2×C4×C241—21no—
146C2×C4×C241—21no—
147C2×C4×C241—21no—
148C2×C4×C241—21no—
149C2×C4×C241—21no—
150C2×C4×C241—21no—
151C2×C4×C241—21no—
152C2×C4×C241—21no—
153C2×C4×C241C22×C412yes—
154C2×C4×C241C22×C412yes—
155C22×C241—22no—
156C22×C241—22no—
157C22×C241—22no—
158C22×C241—41no—
159C22×C241—41no—
160C22×C241—41no—
161C22×C241—41no—
162C22×C241C23×C411yescharacteristic
163C22×C241C2×#4111yescharacteristic
164C22×C241C2×#4111yescharacteristic
165C22×C241H(5,𝔽2)11yescharacteristic
166C22×C241H(5,𝔽2)11yescharacteristic
167C22×C241H(5,𝔽2)11yescharacteristic
168C22×C2412−1+411yescharacteristic
169C2×D241—22no—
170C2×D241—22no—
171C2×D241—22no—
172C2×D241—41no—
173C2×D241—41no—
174C2×D241—41no—
175C2×D241—41no—
176C4×C241—22no—
177C4×C241—22no—
178C4×C241—41no—
179C4×C241—41no—
180C4×C241—41no—
181C4×C241—41no—
182Dic241—22no—
183Dic241—22no—
184Dic241—41no—
185Dic241—41no—
186Dic241—41no—
187Dic241—41no—
188Dic241#11714yes—
189C2×C241—42no—
190C2×C241C2×#11711yescharacteristic
191C2×C241#51811yescharacteristic
192C2×C241#52011yescharacteristic
193C2×C241#54011yescharacteristic
194C2×C241#54011yescharacteristic
195C2×C241#54211yescharacteristic
196C2×C241#54211yescharacteristic
197D241—42no—
198C241#231911yescharacteristic, complemented, Sylow
199#2319—2411nomaximal, Sylow
200C2×C4×D4—2411no—
201#390—2411no—
202#390—2411no—
203#389—2411no—
204#389—2411no—
205#388—2411no—
206#388—2411no—
207#388—2411no—
208#388D24111yescharacteristic, complemented
209#381—2411no—
210#381—2411no—
211#380—2411no—
212#380—2411no—
213C4×C4⋊C4—2411no—
214#376—2411no—
215C22×D4—2411no—
216C23×C4—2411no—
217C23×C4—2411no—
218C4×D4—2418no—
219C2×C4⋊C4—2411no—
220C2×C4⋊C4—2411no—
221C2×C4⋊C4—2411no—
222C2×C4⋊C4—2411no—
223C2×C4⋊C4—2411no—
224C2×C4⋊C4—2411no—
225C2×C4⋊C4C2×D24111yescharacteristic
226C2×C22⋊C4—2411no—
227C2×C22⋊C4—2411no—
228C2×C22⋊C4—2411no—
229C2×C22⋊C4—2411no—
230C2×C22⋊C4—2411no—
231C2×C22⋊C4—2411no—
232C2×C22⋊C4—2411no—
233C2×C22⋊C4C2×D24111yescharacteristic
234C2×C22⋊C4C2×D24111yescharacteristic
235C2×C22⋊C4C2×D24111yescharacteristic
236C2×C42—2411no—
237C2×C42—2411no—
238C2×C42—2411no—
239C2×C42—2411no—
240C2×C42C2×D24111yescharacteristic
241#95—2411no—
242#95—2411no—
243#95—2411no—
244#95—2411no—
245#95—2411no—
246#95—2411no—
247#95—2411no—
248#95—2411no—
249#95C2×D24111yescharacteristic
250#95C2×D24111yescharacteristic
251C24—2411no—
252C24C22×D24111yescharacteristic
253C2×D4—4822no—
254C2×D4—4822no—
255C2×D4—2414no—
256C22×C4—9641no—
257C22×C4—9641no—
258C22×C4—9641no—
259C22×C4—9641no—
260C22×C4—2414no—
261C22×C4—2414no—
262C22×C4—2411no—
263C22×C4—2411no—
264C22×C4—2411no—
265C22×C4—2411no—
266C22×C4—2411no—
267C22×C4—2411no—
268C22×C4—2411no—
269C22×C4C22×D24111yescharacteristic
270C22×C4C22×D24111yescharacteristic
271C22×C4C22×D24111yescharacteristic
272C22×C4C22×D24111yescharacteristic
273C22×C4C22×D24111yescharacteristic
274C22×C4C22×D24111yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—9641no—
277C4⋊C4—9641no—
278C4⋊C4—9641no—
279C4⋊C4—4822no—
280C4⋊C4—4822no—
281C4⋊C4—2414no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—9641no—
285C22⋊C4—9641no—
286C22⋊C4—9641no—
287C22⋊C4—9641no—
288C22⋊C4—9641no—
289C22⋊C4—9641no—
290C22⋊C4—2414no—
291C22⋊C4C4×D24114yes—
292C42—41no—
293C42—9641no—
294C42—4822no—
295C42—4822no—
296C42—2414no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—4821no—
304C23—4821no—
305C23—4821no—
306C23—4821no—
307C23—4821no—
308C23—4821no—
309C23—2412no—
310C23C2×C4×D24112yes—
311C23C23×D24111yescharacteristic
312D4—4828no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—9644no—
330C2×C4—9644no—
331C2×C4—4821no—
332C2×C4—4821no—
333C2×C4—4821no—
334C2×C4—4821no—
335C2×C4—4821no—
336C2×C4—4821no—
337C2×C4—4821no—
338C2×C4—4821no—
339C2×C4—4821no—
340C2×C4—4821no—
341C2×C4—4821no—
342C2×C4—4821no—
343C2×C4—4821no—
344C2×C4—4821no—
345C2×C4—4821no—
346C2×C4—4821no—
347C2×C4—2412no—
348C2×C4—2412no—
349C2×C4—2412no—
350C2×C4—2412no—
351C2×C4—2412no—
352C2×C4C2×C4×D24112yes—
353C2×C4C2×C4×D24112yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—9641no—
362C22—9641no—
363C22—9641no—
364C22—9641no—
365C22—4822no—
366C22—4822no—
367C22—4822no—
368C22C22×C4×D24111yescharacteristic
369C22#41×D24111yescharacteristic
370C22#41×D24111yescharacteristic
371C22#2144068711yescharacteristic
372C22#2144068711yescharacteristic
373C22#2144068811yescharacteristic
374C22#2144068911yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—9641no—
382C4—9641no—
383C4—9641no—
384C4—9641no—
385C4—4822no—
386C4—4822no—
387C4—2414no—
388C2—42no—
389C2—9642no—
390C2#117×D24111yescharacteristic
391C2#2950818911yescharacteristic
392C2#2950819611yescharacteristic
393C2#2950831711yescharacteristic
394C2#2950831911yescharacteristic
395C2#2950833111yescharacteristic
396C2#2950833311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D241
commutatorC22×C241C23×C4
Fitting#388×C241C2
socle, cosocleC23×C241C24
prime radicalC22×C22⋊D241C22
hypercenter#388D241
hypocenterC241#2319
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
4. #29507614C2semidirect
5. #29507612C2semidirect
6. #29507610C2semidirect
7. #29507608C2semidirect
8. #29507606C2semidirect
9. #29507579C2semidirect
10. #29507578C2semidirect
11. #29507575C2semidirect
12. #29507574C2semidirect
13. C4×#16838749C2semidirect
14. #29507562C2semidirect
15. #388×C241C2semidirect
19. #21440602C4semidirect
198. C241#2319semidirect
208. #388D241semidirect

Maximal subgroups

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

subgroupindex
C2×#214406022
#295076172
#295076142
#295076122
#295076102
#295076082
#295076062
#295075792
#295075782
#295075752
#295075742
C4×#168387492
#295075622
#388×C2412
#2319241