Finite Group Databasebeta

← C2×#10621038 #13059871

Subgroups — C2×#10621038 #13059871

Order 1344.

1324 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×D7C211yesmaximal, characteristic, complemented
2C22×D84C211yesmaximal, characteristic, complemented
3C22×#4247C211yesmaximal, characteristic, complemented
4C22×#4246C211yesmaximal, characteristic, complemented
5C2×C7×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
7C2×#66575C211yesmaximal, characteristic, complemented
8#10621038C218yesmaximal, direct product factor
9C2×#6445—31nomaximal, Hall
10C23×D21C2211yescharacteristic
11C23×D21C2211yescharacteristic, complemented
12C23×D3×C7C2211yescharacteristic
13C23×C3×D7C2211yescharacteristic
14C22×D3×D7—24no—
15C22×D3×D7—24no—
16C22×D3×D7—24no—
17C22×D3×D7C2214yescomplemented
18C22×C3×C4×C7C2211yescharacteristic, complemented
19C2×D84—24no—
20C2×D84C2214yescomplemented
21C22×C7×Dic3C2211yescharacteristic, complemented
22C22×C3×Dic7C2211yescharacteristic, complemented
23C2×#4247—24no—
24C2×#4247C2214yescomplemented
25C2×#4246—24no—
26C2×#4246C2214yescomplemented
27C7×(C2×D3)⋊C4C2214yescomplemented
28C3×(C2×D7)⋊C4C2214yescomplemented
29#66575C2214yescomplemented
30C24×D7—31no—
31C22×C22⋊D7—31no—
32C22×D28—31no—
33C22×D28—31no—
34C2×C7×C22⋊C4—31no—
35C2×(C2×D7)⋊C4—31no—
36C2×(C2×D7)⋊C4D311yescharacteristic, complemented
37#6445—38no—
38C2×#882—71nomaximal, Hall
39C23×C3×C7C2311yescharacteristic
40C22×D21—22no—
41C22×D21—22no—
42C22×D21—22no—
43C22×D21—22no—
44C22×D21—22no—
45C22×D21D414yescomplemented
46C22×D21C2312yes—
47C22×D21C2312yescomplemented
48C22×D3×C7—22no—
49C22×D3×C7—22no—
50C22×D3×C7D414yescomplemented
51C22×D3×C7C2312yes—
52C22×C3×D7—22no—
53C22×C3×D7—22no—
54C22×C3×D7D414yescomplemented
55C22×C3×D7C2312yes—
56C2×D3×D7—232no—
57C2×D3×D7—28no—
58C2×D3×D7—28no—
59C2×D3×D7—28no—
60C2×C3×C4×C7—22no—
61C2×C3×C4×C7C2312yescomplemented
62D84—28no—
63C2×C7×Dic3—22no—
64C2×C7×Dic3C2312yescomplemented
65C2×C3×Dic7—22no—
66C2×C3×Dic7C2312yescomplemented
67#4247—28no—
68#4246—28no—
69C24×C7—31no—
70C23×D7—31no—
71C23×D7—31no—
72C23×D7—34no—
73C23×D7—64no—
74C23×D7—64no—
75C23×D7—64no—
76C23×D7C2×D311yescharacteristic
77C22×C4×C7—31no—
78C22×C4×C7C2×D311yescharacteristic, complemented
79C2×C22⋊D7—34no—
80C2×C22⋊D7—64no—
81C22×Dic7C2×D311yescharacteristic, complemented
82C2×D28—34no—
83C2×D28—34no—
84C2×D28—64no—
85C2×D28—64no—
86C7×C22⋊C4—34no—
87(C2×D7)⋊C4—34no—
88(C2×D7)⋊C4C2×D314yescomplemented
89C24×D3—71no—
90C22×#67—71no—
91C22×D12—71no—
92C22×D12—71no—
93C2×C3×C22⋊C4—71no—
94C2×(C2×D3)⋊C4—71no—
95C2×(C2×D3)⋊C4D711yescharacteristic, complemented
96#882—78no—
97C22×C3×C7C2×D412yes—
98C22×C3×C7C2×D412yes—
99C22×C3×C7C2×D412yes—
100C22×C3×C7C2411yescharacteristic
101C2×D21—28no—
102C2×D21—22no—
103C2×D21—22no—
104C2×D21—22no—
105C2×D21—22no—
106C2×D21—22no—
107C2×D21—44no—
108C2×D21C2×D414yescomplemented
109C2×D3×C7—28no—
110C2×D3×C7—22no—
111C2×D3×C7—22no—
112C2×D3×C7C2×D414yescomplemented
113C2×C3×D7—28no—
114C2×C3×D7—22no—
115C2×C3×D7—22no—
116C2×C3×D7C2×D414yescomplemented
117D3×D7—232no—
118C3×C4×C7—22no—
119C3×Dic7—22no—
120C7×Dic3—22no—
121C2×#120—211noSylow
122C23×C7—34no—
123C23×C7—32no—
124C23×C7—62no—
125C23×C7—62no—
126C23×C7C22×D311yescharacteristic
127C22×D7—22no—
128C22×D7—22no—
129C22×D7—34no—
130C22×D7—32no—
131C22×D7—32no—
132C22×D7—68no—
133C22×D7—68no—
134C22×D7—632no—
135C22×D7—62no—
136C22×D7—62no—
137C22×D7—68no—
138C22×D7—62no—
139C22×D7—62no—
140C22×D7—62no—
141C22×D7D1214yescomplemented
142C22×D7C22×D312yes—
143C2×C4×C7—22no—
144C2×C4×C7—32no—
145C2×C4×C7—62no—
146C2×C4×C7C22×D312yescomplemented
147C22⋊D7—68no—
148C2×Dic7—22no—
149C2×Dic7C22×D312yescomplemented
150D28—68no—
151D28—68no—
152C24×C3—71no—
153C23×D3—71no—
154C23×D3—71no—
155C23×D3—74no—
156C23×D3—144no—
157C23×D3—144no—
158C23×D3—144no—
159C23×D3C2×D711yescharacteristic
160C22×C3×C4—71no—
161C22×C3×C4C2×D711yescharacteristic, complemented
162C2×#67—74no—
163C2×#67—144no—
164C22×Dic3C2×D711yescharacteristic, complemented
165C2×D12—74no—
166C2×D12—74no—
167C2×D12—144no—
168C2×D12—144no—
169C3×C22⋊C4—74no—
170(C2×D3)⋊C4—74no—
171(C2×D3)⋊C4C2×D714yescomplemented
172C2×C3×C7#12014yescomplemented
173C2×C3×C7C22×D411yescharacteristic
174C2×C3×C7C22×D411yescharacteristic
175C2×C3×C7C22×D411yescharacteristic
176D21—24no—
177D21—42no—
178C3×D7—24no—
179D3×C7—24no—
180C25—211no—
181C22×D4—211no—
182C22×D4—211no—
183C22×D4—211no—
184#120—218no—
185C2×C22⋊C4—31no—
186C2×C22⋊C4—71no—
187C2×C22⋊C4—211no—
188C22×C7—34no—
189C22×C7—68no—
190C22×C7—62no—
191C22×C7—62no—
192C22×C7C2×D1212yes—
193C22×C7D3×D412yes—
194C22×C7D3×D412yes—
195C22×C7C23×D311yescharacteristic
196C2×D7—28no—
197C2×D7—22no—
198C2×D7—22no—
199C2×D7—34no—
200C2×D7—632no—
201C2×D7—68no—
202C2×D7—62no—
203C2×D7—62no—
204C2×D7—62no—
205C2×D7—62no—
206C2×D7—62no—
207C2×D7—124no—
208C2×D7C2×D1214yescomplemented
209C4×C7—22no—
210C4×C7—62no—
211Dic7—22no—
212C23×C3—74no—
213C23×C3—72no—
214C23×C3—142no—
215C23×C3—142no—
216C23×C3C22×D711yescharacteristic
217C22×D3—22no—
218C22×D3—22no—
219C22×D3—74no—
220C22×D3—72no—
221C22×D3—72no—
222C22×D3—148no—
223C22×D3—148no—
224C22×D3—1432no—
225C22×D3—142no—
226C22×D3—142no—
227C22×D3—148no—
228C22×D3—142no—
229C22×D3—142no—
230C22×D3—142no—
231C22×D3D2814yescomplemented
232C22×D3C22×D712yes—
233C2×C3×C4—22no—
234C2×C3×C4—72no—
235C2×C3×C4—142no—
236C2×C3×C4C22×D712yescomplemented
237#67—148no—
238C2×Dic3—22no—
239C2×Dic3C22×D712yescomplemented
240D12—148no—
241D12—148no—
242C3×C7C2×#12011yescharacteristic, complemented, Hall
243C24—31no—
244C24—71no—
245C24—214no—
246C24—211no—
247C24—211no—
248C24—424no—
249C24—424no—
250C24—424no—
251C2×D4—214no—
252C2×D4—214no—
253C2×D4—214no—
254C2×D4—424no—
255C2×D4—424no—
256C2×D4—424no—
257C22×C4—31no—
258C22×C4—71no—
259C22×C4D3×D711yescharacteristic, complemented
260C22⋊C4—34no—
261C22⋊C4—74no—
262C22⋊C4—214no—
263C2×C7—64no—
264C2×C7#88214yescomplemented
265C2×C7C22×D1211yescharacteristic
266C2×C7C2×D3×D411yescharacteristic
267C2×C7C2×D3×D411yescharacteristic
268D7—24no—
269D7—64no—
270D7—122no—
271C22×C3—74no—
272C22×C3—148no—
273C22×C3—142no—
274C22×C3—142no—
275C22×C3C2×D2812yes—
276C22×C3D4×D712yes—
277C22×C3D4×D712yes—
278C22×C3C23×D711yescharacteristic
279C2×D3—28no—
280C2×D3—22no—
281C2×D3—22no—
282C2×D3—74no—
283C2×D3—1432no—
284C2×D3—148no—
285C2×D3—142no—
286C2×D3—142no—
287C2×D3—142no—
288C2×D3—142no—
289C2×D3—142no—
290C2×D3—284no—
291C2×D3C2×D2814yescomplemented
292C3×C4—22no—
293C3×C4—142no—
294Dic3—22no—
295C23—34no—
296C23—32no—
297C23—62no—
298C23—62no—
299C23—74no—
300C23—72no—
301C23—142no—
302C23—142no—
303C23—214no—
304C23—212no—
305C23—212no—
306C23—428no—
307C23—428no—
308C23—428no—
309C23—4232no—
310C23—422no—
311C23—422no—
312C23—422no—
313C23—422no—
314C23—422no—
315C23C2×D3×D711yescharacteristic
316D4—428no—
317D4—428no—
318D4—428no—
319C2×C4—22no—
320C2×C4—32no—
321C2×C4—62no—
322C2×C4—72no—
323C2×C4—142no—
324C2×C4C2×D3×D712yescomplemented
325C7C2×#88211yescharacteristic, complemented, Sylow
326C2×C3—144no—
327C2×C3#644514yescomplemented
328C2×C3C22×D2811yescharacteristic
329C2×C3C2×D4×D711yescharacteristic
330C2×C3C2×D4×D711yescharacteristic
331D3—24no—
332D3—144no—
333D3—282no—
334C22—34no—
335C22—68no—
336C22—62no—
337C22—62no—
338C22—74no—
339C22—148no—
340C22—142no—
341C22—142no—
342C22—214no—
343C22—4232no—
344C22—428no—
345C22—422no—
346C22—422no—
347C22—422no—
348C22—422no—
349C22—422no—
350C22—844no—
351C22D7×D1212yes—
352C22D3×D2812yes—
353C22#6669412yes—
354C22C22×D3×D711yescharacteristic
355C4—22no—
356C4—62no—
357C4—142no—
358C3C2×#644511yescharacteristic, complemented, Sylow
359C2—64no—
360C2—144no—
361C2—424no—
362C2—842no—
363C2#1062103814yesdirect product factor
364C2C2×D7×D1211yescharacteristic
365C2C2×D3×D2811yescharacteristic
366C2C2×#6669411yescharacteristic
subgroupG/H
centerC23C2×D3×D7
commutator, cosocleC22×C3×C7C24
FrattiniC22C22×D3×D7
FittingC22×C3×C4×C7C22
socleC23×C3×C7C23
hypercenterC22×C4D3×D7
hypocenterC3×C7C2×#120
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C23×D3×D7C2semidirect
2. C22×D84C2semidirect
3. C22×#4247C2semidirect
4. C22×#4246C2semidirect
5. C2×C7×(C2×D3)⋊C4C2semidirect
6. C2×C3×(C2×D7)⋊C4C2semidirect
7. C2×#66575C2semidirect
8. #10621038C2direct (N × H)
11. C23×D21C22semidirect
17. C22×D3×D7C22semidirect
18. C22×C3×C4×C7C22semidirect
20. C2×D84C22semidirect
21. C22×C7×Dic3C22semidirect
22. C22×C3×Dic7C22semidirect
24. C2×#4247C22semidirect
26. C2×#4246C22semidirect
27. C7×(C2×D3)⋊C4C22semidirect
28. C3×(C2×D7)⋊C4C22semidirect
29. #66575C22semidirect
36. C2×(C2×D7)⋊C4D3semidirect
45. C22×D21D4semidirect
47. C22×D21C23semidirect
50. C22×D3×C7D4semidirect
54. C22×C3×D7D4semidirect
61. C2×C3×C4×C7C23semidirect
64. C2×C7×Dic3C23semidirect
66. C2×C3×Dic7C23semidirect
78. C22×C4×C7C2×D3semidirect
81. C22×Dic7C2×D3semidirect
88. (C2×D7)⋊C4C2×D3semidirect
95. C2×(C2×D3)⋊C4D7semidirect
108. C2×D21C2×D4semidirect
112. C2×D3×C7C2×D4semidirect
116. C2×C3×D7C2×D4semidirect
141. C22×D7D12semidirect
146. C2×C4×C7C22×D3semidirect
149. C2×Dic7C22×D3semidirect
161. C22×C3×C4C2×D7semidirect
164. C22×Dic3C2×D7semidirect
171. (C2×D3)⋊C4C2×D7semidirect
172. C2×C3×C7#120semidirect
208. C2×D7C2×D12semidirect
231. C22×D3D28semidirect
236. C2×C3×C4C22×D7semidirect
239. C2×Dic3C22×D7semidirect
242. C3×C7C2×#120semidirect
259. C22×C4D3×D7semidirect
264. C2×C7#882semidirect
291. C2×D3C2×D28semidirect
324. C2×C4C2×D3×D7semidirect
325. C7C2×#882semidirect
327. C2×C3#6445semidirect
358. C3C2×#6445semidirect
363. C2#10621038direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3×D72
C22×D842
C22×#42472
C22×#42462
C2×C7×(C2×D3)⋊C42
C2×C3×(C2×D7)⋊C42
C2×#665752
#106210382
C2×#64453
C2×#8827