Finite Group Databasebeta

← C2×#14557433 #17997050

Subgroups — C2×#14557433 #17997050

Order 4736.

1360 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊D37C211yesmaximal, characteristic
2C22×#10596936C211yesmaximal, characteristic, complemented
3C22×C22⋊Dic37C211yesmaximal, characteristic, complemented
4C22×#10596938C211yesmaximal, characteristic, complemented
5C22×#10596938C211yesmaximal, characteristic, complemented
6C22×C4×Dic37C211yesmaximal, characteristic, complemented
7#14557433C218yesmaximal, direct product factor
8C22×C22⋊C4×C37C211yesmaximal, characteristic, complemented
9C24×D37C2211yescharacteristic
10C22×C22⋊D37—24no—
11C22×C22⋊D37—24no—
12C22×C22⋊D37C418yescomplemented
13C22×C22⋊D37C2214yes—
14C23×Dic37C2211yescharacteristic
15C23×Dic37C2211yescharacteristic
16C23×Dic37C2211yescharacteristic
17C2×#10596936—24no—
18C2×#10596936C2214yescomplemented
19C2×C22⋊Dic37—24no—
20C2×C22⋊Dic37C2214yescomplemented
21C2×#10596938—24no—
22C2×#10596938—24no—
23C2×#10596938C2214yescomplemented
24C2×#10596938C2214yescomplemented
25C2×C4×Dic37—24no—
26C2×C4×Dic37C2214yescomplemented
27C25×C37C2211yescharacteristic
28C23×C4×C37C2211yescharacteristic
29C23×C4×C37C2211yescharacteristic
30C2×C22⋊C4×C37—24no—
31C2×C22⋊C4×C37C2214yescomplemented
32C24×C37—22no—
33C24×C37—22no—
34C24×C37—22no—
35C24×C37—22no—
36C24×C37—22no—
37C24×C37—22no—
38C24×C37C2×C414yes—
39C24×C37C2312yes—
40C24×C37C2311yescharacteristic
41C23×D37—22no—
42C23×D37—22no—
43C23×D37—22no—
44C23×D37—22no—
45C23×D37—22no—
46C23×D37—22no—
47C23×D37C2×C414yes—
48C23×D37C2312yes—
49C22×C4×C37—22no—
50C22×C4×C37—22no—
51C22×C4×C37—22no—
52C22×C4×C37—22no—
53C22×C4×C37—22no—
54C22×C4×C37D414yescomplemented
55C22×C4×C37C2312yes—
56C22×C4×C37C2312yes—
57C2×C22⋊D37—232no—
58C2×C22⋊D37—28no—
59C2×C22⋊D37—28no—
60C2×C22⋊D37C2×C4116yescomplemented
61C22×Dic37—22no—
62C22×Dic37—22no—
63C22×Dic37—22no—
64C22×Dic37—22no—
65C22×Dic37—22no—
66C22×Dic37C2×C414yes—
67C22×Dic37D414yes—
68C22×Dic37D414yes—
69C22×Dic37D414yescomplemented
70C22×Dic37C2312yes—
71C22×Dic37C2312yes—
72C22×Dic37C2312yes—
73C22⋊C4×C37—28no—
74C22⋊Dic37—28no—
75#10596938—28no—
76#10596938—28no—
77#10596936—28no—
78C4×Dic37—28no—
79C23×C37—28no—
80C23×C37—28no—
81C23×C37—28no—
82C23×C37—22no—
83C23×C37—22no—
84C23×C37—22no—
85C23×C37—22no—
86C23×C37—22no—
87C23×C37—22no—
88C23×C37—44no—
89C23×C37—44no—
90C23×C37—44no—
91C23×C37—44no—
92C23×C37C22×C414yes—
93C23×C37C22×C412yes—
94C23×C37C2×D412yes—
95C23×C37C2×D412yes—
96C23×C37C2×D412yes—
97C23×C37C2×D412yes—
98C23×C37#4112yes—
99C23×C37#4112yes—
100C23×C37C2411yescharacteristic
101C22×D37—28no—
102C22×D37—28no—
103C22×D37—28no—
104C22×D37—22no—
105C22×D37—22no—
106C22×D37—22no—
107C22×D37—22no—
108C22×D37—22no—
109C22×D37—22no—
110C22×D37—44no—
111C22×D37—44no—
112C22×D37—44no—
113C22×D37—44no—
114C22×D37C22×C414yes—
115C2×C4×C37—28no—
116C2×C4×C37—22no—
117C2×C4×C37—22no—
118C2×C4×C37—22no—
119C2×C4×C37—22no—
120C2×C4×C37—22no—
121C2×C4×C37—44no—
122C2×C4×C37C2×D414yescomplemented
123C22⋊D37—232no—
124C2×Dic37—28no—
125C2×Dic37—22no—
126C2×Dic37—22no—
127C2×Dic37—22no—
128C2×Dic37—22no—
129C2×Dic37—22no—
130C2×Dic37—44no—
131C2×Dic37C22⋊C4116yescomplemented
132C2×Dic37C22×C414yes—
133C2×Dic37C2×D414yes—
134C2×Dic37C2×D414yes—
135C2×Dic37C2×D414yescomplemented
136C22×C37—24no—
137C22×C37—24no—
138C22×C37—24no—
139C22×C37—42no—
140C22×C37—42no—
141C22×C37—42no—
142C22×C37—42no—
143C22×C37—416no—
144C22×C37C2×C22⋊C414yes—
145C22×C37C4×D414yes—
146C22×C37C4×D414yes—
147C22×C37#12114yes—
148C22×C37#12114yes—
149C22×C37#12414yes—
150C22×C37#12714yes—
151C22×C37C23×C411yescharacteristic
152C22×C37C22×D411yescharacteristic
153C22×C37C22×D411yescharacteristic
154C22×C37C22×D411yescharacteristic
155C22×C37C22×D411yescharacteristic
156C22×C37C2×#4111yescharacteristic
157C22×C37C2×#4111yescharacteristic
158C2×D37—24no—
159C2×D37—24no—
160C2×D37—24no—
161C2×D37—42no—
162C2×D37—42no—
163C2×D37—42no—
164C2×D37—42no—
165C2×D37—416no—
166C4×C37—24no—
167C4×C37—42no—
168Dic37—24no—
169Dic37—42no—
170Dic37C2×C22⋊C418yescomplemented
171C2×#390—371nomaximal, Sylow
172C2×C37—44no—
173C2×C37#39018yescomplemented
174C2×C37C22×C22⋊C411yescharacteristic
175C2×C37C2×C4×D411yescharacteristic
176C2×C37C2×C4×D411yescharacteristic
177C2×C37C2×#12111yescharacteristic
178C2×C37C2×#12111yescharacteristic
179C2×C37C2×#12411yescharacteristic
180C2×C37C2×#12711yescharacteristic
181D37—44no—
182C23×D4—371no—
183C22×C4⋊C4—371no—
184C22×C22⋊C4—371no—
185C22×C22⋊C4—371no—
186C22×C22⋊C4—371no—
187C22×C22⋊C4D3711yescharacteristic, complemented
188C22×C42—371no—
189#390—378no—
190C37C2×#39011yescharacteristic, complemented, Sylow
191C25—371no—
192C25C2×D3711yescharacteristic
193C22×D4—378no—
194C22×D4—374no—
195C22×D4—744no—
196C22×D4—744no—
197C23×C4—371no—
198C23×C4—371no—
199C23×C4—371no—
200C23×C4C2×D3711yescharacteristic
201C23×C4C2×D3711yescharacteristic
202C2×C4⋊C4—374no—
203C2×C4⋊C4—744no—
204C2×C22⋊C4—24no—
205C2×C22⋊C4—374no—
206C2×C22⋊C4—374no—
207C2×C22⋊C4—374no—
208C2×C22⋊C4—744no—
209C2×C22⋊C4—744no—
210C2×C22⋊C4—744no—
211C2×C22⋊C4C2×D3714yescomplemented
212C2×C42—374no—
213C2×C42—744no—
214C24—22no—
215C24—22no—
216C24—22no—
217C24—22no—
218C24—22no—
219C24—22no—
220C24—374no—
221C24—372no—
222C24—742no—
223C24—742no—
224C24—742no—
225C24—742no—
226C24—742no—
227C24—742no—
228C24C4×D3714yes—
229C24C22×D3712yes—
230C24C22×D3711yescharacteristic
231C2×D4—3716no—
232C2×D4—7432no—
233C2×D4—748no—
234C2×D4—748no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—374no—
241C22×C4—374no—
242C22×C4—374no—
243C22×C4—372no—
244C22×C4—374no—
245C22×C4—372no—
246C22×C4—372no—
247C22×C4—742no—
248C22×C4—742no—
249C22×C4—742no—
250C22×C4—742no—
251C22×C4—742no—
252C22×C4C22⋊D3714yescomplemented
253C22×C4C22×D3712yes—
254C22×C4C22×D3712yes—
255C4⋊C4—748no—
256C22⋊C4—28no—
257C22⋊C4—748no—
258C22⋊C4—748no—
259C22⋊C4—748no—
260C42—748no—
261C23—28no—
262C23—28no—
263C23—28no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—22no—
269C23—22no—
270C23—44no—
271C23—44no—
272C23—44no—
273C23—44no—
274C23—374no—
275C23—748no—
276C23—748no—
277C23—748no—
278C23—742no—
279C23—742no—
280C23—742no—
281C23—742no—
282C23—742no—
283C23—742no—
284C23—1484no—
285C23—1484no—
286C23—1484no—
287C23—1484no—
288C23C2×C4×D3714yes—
289C23C2×C4×D3712yes—
290C23#1059696212yes—
291C23D4×D3712yes—
292C23D4×D3712yes—
293C23D4×D3712yes—
294C23#1059696412yes—
295C23C2×C22⋊D3712yes—
296C23C23×D3711yescharacteristic
297D4—7432no—
298C2×C4—28no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—44no—
305C2×C4—3716no—
306C2×C4—374no—
307C2×C4—374no—
308C2×C4—374no—
309C2×C4—374no—
310C2×C4—748no—
311C2×C4—742no—
312C2×C4—742no—
313C2×C4—742no—
314C2×C4—742no—
315C2×C4—742no—
316C2×C4—1484no—
317C2×C4C2×C22⋊D3714yescomplemented
318C22—24no—
319C22—24no—
320C22—24no—
321C22—42no—
322C22—42no—
323C22—42no—
324C22—42no—
325C22—416no—
326C22—744no—
327C22—744no—
328C22—744no—
329C22—1482no—
330C22—1482no—
331C22—1482no—
332C22—1482no—
333C22—14816no—
334C22C22⋊C4×D3714yes—
335C22#1192449614yes—
336C22C4×C22⋊D3714yes—
337C22#1192450814yes—
338C22#1192450914yes—
339C22#1192452214yes—
340C22#1192453214yes—
341C22C22×C4×D3711yescharacteristic
342C22C2×D4×D3711yescharacteristic
343C22C2×D4×D3711yescharacteristic
344C22C2×D4×D3711yescharacteristic
345C22C22×C22⋊D3711yescharacteristic
346C22C2×#1059696411yescharacteristic
347C22C2×#1059696211yescharacteristic
348C4—24no—
349C4—42no—
350C4—378no—
351C4—744no—
352C4—1482no—
353C2—44no—
354C2—1484no—
355C2#1455743318yesdirect product factor
356C2C2×C22⋊C4×D3711yescharacteristic
357C2C2×#1192449611yescharacteristic
358C2C2×C4×C22⋊D3711yescharacteristic
359C2C2×#1192450811yescharacteristic
360C2C2×#1192450911yescharacteristic
361C2C2×#1192452211yescharacteristic
362C2C2×#1192453211yescharacteristic
subgroupG/H
centerC24C22×D37
commutatorC22×C37C23×C4
FrattiniC23C23×D37
FittingC22×C22⋊C4×C37C2
socleC24×C37C23
prime radicalC23×C22⋊D37C2
cosocleC23×C37C24
hypercenterC22×C22⋊C4D37
hypocenterC37C2×#390
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#10596936C2semidirect
3. C22×C22⋊Dic37C2semidirect
4. C22×#10596938C2semidirect
5. C22×#10596938C2semidirect
6. C22×C4×Dic37C2semidirect
7. #14557433C2direct (N × H)
8. C22×C22⋊C4×C37C2semidirect
12. C22×C22⋊D37C4semidirect
18. C2×#10596936C22semidirect
20. C2×C22⋊Dic37C22semidirect
23. C2×#10596938C22semidirect
24. C2×#10596938C22semidirect
26. C2×C4×Dic37C22semidirect
31. C2×C22⋊C4×C37C22semidirect
54. C22×C4×C37D4semidirect
60. C2×C22⋊D37C2×C4semidirect
69. C22×Dic37D4semidirect
122. C2×C4×C37C2×D4semidirect
131. C2×Dic37C22⋊C4semidirect
135. C2×Dic37C2×D4semidirect
170. Dic37C2×C22⋊C4semidirect
173. C2×C37#390semidirect
187. C22×C22⋊C4D37semidirect
190. C37C2×#390semidirect
211. C2×C22⋊C4C2×D37semidirect
252. C22×C4C22⋊D37semidirect
317. C2×C4C2×C22⋊D37semidirect
355. C2#14557433direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D372
C22×#105969362
C22×C22⋊Dic372
C22×#105969382
C22×C4×Dic372
#145574332
C22×C22⋊C4×C372
C2×#39037