Finite Group Databasebeta

← #21455178

Subgroups — #21455178

Order 7808.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#14519823C211yesmaximal, characteristic, complemented
2#16840562C211yesmaximal, characteristic, complemented
3#16840560C211yesmaximal, characteristic, complemented
4#16840331C211yesmaximal, characteristic, complemented
5#16839941C214yesmaximal, complemented
6#16839931C214yesmaximal, complemented
7#16839780C211yesmaximal, characteristic, complemented
8C2×#14519693C211yesmaximal, characteristic, complemented
9C61×#421C211yesmaximal, characteristic, complemented
10#14519823—22no—
11#14519823—22no—
12#14519823—22no—
13#14519823C2214yes—
14C2×#11758226—21no—
15C2×#11758222—21no—
16C2×#11758222C2211yescharacteristic
17C2×#11758222C2211yescharacteristic, complemented
18C22×D244—21no—
19C22×D244C2211yescharacteristic
20C2×D4×D61—22no—
21C2×D4×D61—21no—
22#14519810—21no—
23#14519810C2212yescomplemented
24#14519808—21no—
25#14519807C2212yescomplemented
26#14519805—21no—
27#14519805C2212yescomplemented
28#14519803—21no—
29#14519802C2212yescomplemented
30#14519799—22no—
31#14519797—22no—
32C2×#11758194C2211yescharacteristic, complemented
33#14519774C2212yescomplemented
34#14519765C2212yescomplemented
35#14519752—22no—
36#14519747—22no—
37#14519705C2214yescomplemented
38#14519693C2214yescomplemented
39C2×#41×C61C2211yescharacteristic
40C2×M16×C61C2211yescharacteristic, complemented
41#117×C61C2211yescharacteristic, complemented
42#104×C61C2214yescomplemented
43C23×D61—22no—
44C23×D61D412yes—
45#41×C61—21no—
46#41×C61—21no—
47#41×C61D412yescomplemented
48#41×C61C2312yes—
49C2×Q8×C61D411yescharacteristic, complemented
50C2×D4×C61—21no—
51C2×D4×C61D411yescharacteristic, complemented
52C22×C4×C61—21no—
53C22×C4×C61C2311yescharacteristic
54C2×C22⋊D61—22no—
55C2×C22⋊D61—21no—
56C2×C22⋊D61—21no—
57#11758226—24no—
58#11758226—24no—
59D4×D61—28no—
60D4×D61—24no—
61D4×D61—28no—
62D4×D61—24no—
63#11758222—24no—
64#11758222—21no—
65#11758222—21no—
66#11758222—21no—
67#11758222—21no—
68#11758222—21no—
69#11758222—21no—
70#11758222—24no—
71#11758222D412yescomplemented
72#11758222C2312yes—
73C2×D244—22no—
74C2×D244—24no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—24no—
80C2×D244—24no—
81C2×D244D412yes—
82C2×D244D411yescharacteristic, complemented
83C2×D244C2312yes—
84C2×D244C2311yescharacteristic, complemented
85C2×C4×D61—22no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×Dic122D411yescharacteristic, complemented
89C2×Dic122C2311yescharacteristic, complemented
90M16×C61—21no—
91M16×C61C2312yescomplemented
92C2×C8×C61—21no—
93C4⋊C4×C61—21no—
94C22⋊C4×C61—21no—
95C42×C61C2312yescomplemented
96#11758202—22no—
97#11758201—22no—
98#11758200—22no—
99#11758199—22no—
100#11758198—24no—
101#11758194—21no—
102#11758194C2312yescomplemented
103C2×#92418—21no—
104Dic244—22no—
105D488—22no—
106#11758190—22no—
107#11758190—22no—
108C23×C61—21no—
109C23×C61C2×D411yescharacteristic
110C22×D61—22no—
111C22×D61—21no—
112C22×D61—28no—
113C22×D61—22no—
114C22×D61—21no—
115C22×D61—82no—
116C22×D61—84no—
117C22×D61C2×D414yes—
118Q8×C61—21no—
119Q8×C61C2×D412yes—
120D4×C61—22no—
121D4×C61—22no—
122D4×C61—21no—
123D4×C61C2×D412yes—
124C2×C4×C61—21no—
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C2×C4×C61—22no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2411yescharacteristic
134C22⋊D61—28no—
135C22⋊D61—22no—
136C22⋊D61—22no—
137C22⋊D61—41no—
138C22⋊D61—41no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141D244—28no—
142D244—22no—
143D244—21no—
144D244—22no—
145D244—22no—
146D244—22no—
147D244—21no—
148D244—21no—
149D244—84no—
150D244C2×D412yes—
151C4×D61—28no—
152C4×D61—22no—
153C4×D61—22no—
154C4×D61—41no—
155C4×D61—41no—
156Dic122—21no—
157Dic122—21no—
158Dic122—21no—
159Dic122C2×D412yes—
160C8×C61—22no—
161#92418—22no—
162C22×C61—22no—
163C22×C61—41no—
164C22×C61—42no—
165C22×C61#12011yescharacteristic
166C22×C61#12011yescharacteristic
167C22×C61C22×D411yescharacteristic
168C2×D61—24no—
169C2×D61—22no—
170C2×D61—44no—
171C2×D61—42no—
172C2×D61—44no—
173C2×D61—42no—
174C2×D61—41no—
175C2×D61—82no—
176C2×D61—88no—
177C4×C61—22no—
178C4×C61—42no—
179C4×C61#12011yescharacteristic
180C4×C61#12011yescharacteristic
181C4×C61C22×D411yescharacteristic
182C4×C61C22×D411yescharacteristic
183Dic61—22no—
184Dic61—41no—
185#3019—611nomaximal, Sylow
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61—42no—
190C2×C61C2×#12011yescharacteristic
191D61—44no—
192D61—42no—
193D61—81no—
194C2×H(5,𝔽2)—611no—
195#575—611no—
196#575—611no—
197#535—611no—
198#455—614no—
199#453—614no—
200#421—611no—
201#421D6111yescharacteristic, complemented
202C2×#100—611no—
203C61#301911yescharacteristic, complemented, Sylow
204H(5,𝔽2)—614no—
205H(5,𝔽2)—1222no—
206H(5,𝔽2)—1222no—
207H(5,𝔽2)—1222no—
208C2×#41—611no—
209C2×#41—611no—
210C2×#41—1221no—
211C2×#41—1221no—
212C2×#41C2×D6111yescharacteristic
213C22×D4—611no—
214C22×D4—1221no—
215C22×D4—1222no—
216C22×D4—1221no—
217#137—612no—
218#137—612no—
219#137—1221no—
220#137—1221no—
221AGL(1,ℤ/8)—612no—
222AGL(1,ℤ/8)—612no—
223AGL(1,ℤ/8)—1221no—
224AGL(1,ℤ/8)—1221no—
225#135—1222no—
226#135—1222no—
227C2×M16—611no—
228C2×M16C2×D6111yescharacteristic, complemented
229#127—612no—
230#124—612no—
231#121—1222no—
232#120—1222no—
233#117C2×D6111yescharacteristic, complemented
234#104—614no—
235#104C2×D6114yescomplemented
236#100—614no—
237C24—612no—
238C24—1222no—
239#41—21no—
240#41—21no—
241#41—612no—
242#41—612no—
243#41—1224no—
244#41—1224no—
245#41—1224no—
246#41—1224no—
247#41—1221no—
248#41—1221no—
249#41—1221no—
250#41—1221no—
251#41—1221no—
252#41—1221no—
253#41D24412yescomplemented
254#41C22×D6112yes—
255C2×Q8—611no—
256C2×Q8—611no—
257C2×Q8D24411yescharacteristic, complemented
258C2×D4—21no—
259C2×D4—611no—
260C2×D4—612no—
261C2×D4—612no—
262C2×D4—611no—
263C2×D4—1224no—
264C2×D4—1222no—
265C2×D4—1224no—
266C2×D4—1224no—
267C2×D4—1228no—
268C2×D4—1228no—
269C2×D4—1224no—
270C2×D4—1222no—
271C2×D4—1221no—
272C2×D4—1224no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4D24411yescharacteristic, complemented
279C22×C4—21no—
280C22×C4—1222no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4C22×D6111yescharacteristic
284Q16—1222no—
285Q16—1222no—
286SD16—1222no—
287SD16—1222no—
288SD16—1222no—
289SD16—1222no—
290D8—1222no—
291D8—1222no—
292M16—21no—
293M16—612no—
294M16—1221no—
295M16C22×D6112yescomplemented
296C2×C8—21no—
297C2×C8—1221no—
298C4⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—1224no—
301C42C22×D6112yescomplemented
302C23—21no—
303C23—614no—
304C23—1228no—
305C23—1222no—
306C23—1221no—
307C23—1222no—
308C23—1221no—
309C23—4884no—
310C23—4882no—
311C23D4×D6111yescharacteristic
312Q8—21no—
313Q8—612no—
314Q8—1221no—
315Q8—1221no—
316Q8—1221no—
317Q8C2×D24412yes—
318D4—22no—
319D4—22no—
320D4—21no—
321D4—612no—
322D4—1228no—
323D4—1228no—
324D4—1222no—
325D4—1222no—
326D4—1222no—
327D4—1221no—
328D4—1222no—
329D4—1221no—
330D4—1221no—
331D4—1222no—
332D4—1222no—
333D4—4884no—
334D4—2441no—
335D4—2441no—
336D4C2×D24412yes—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—1228no—
342C2×C4—1221no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1221no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4C2×D24411yescharacteristic
349C2×C4C2×D24411yescharacteristic
350C2×C4D4×D6111yescharacteristic
351C2×C4D4×D6111yescharacteristic
352C2×C4D4×D6111yescharacteristic
353C2×C4C23×D6111yescharacteristic
354C8—22no—
355C8—1222no—
356C22—22no—
357C22—41no—
358C22—42no—
359C22—1222no—
360C22—1224no—
361C22—4882no—
362C22—4888no—
363C22—2442no—
364C22—2444no—
365C22—2442no—
366C22—2444no—
367C22—2441no—
368C22#1451974711yescharacteristic
369C22#1451974711yescharacteristic
370C22C2×D4×D6111yescharacteristic
371C4—22no—
372C4—42no—
373C4—1222no—
374C4—2441no—
375C4#1451974711yescharacteristic
376C4#1451974711yescharacteristic
377C4C2×D4×D6111yescharacteristic
378C4C22×D24411yescharacteristic
379C2—21no—
380C2—21no—
381C2—21no—
382C2—42no—
383C2—4881no—
384C2—2442no—
385C2—2444no—
386C2C2×#1451974711yescharacteristic
subgroupG/H
centerC2C2×#14519747
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#421C2
socleC2×C61C2×#120
hypercenter#421D61
hypocenterC61#3019
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. C2×#14519823C2semidirect
2. #16840562C2semidirect
3. #16840560C2semidirect
4. #16840331C2semidirect
5. #16839941C2semidirect
6. #16839931C2semidirect
7. #16839780C2semidirect
8. C2×#14519693C2semidirect
9. C61×#421C2semidirect
17. C2×#11758222C22semidirect
23. #14519810C22semidirect
25. #14519807C22semidirect
27. #14519805C22semidirect
29. #14519802C22semidirect
32. C2×#11758194C22semidirect
33. #14519774C22semidirect
34. #14519765C22semidirect
37. #14519705C22semidirect
38. #14519693C22semidirect
40. C2×M16×C61C22semidirect
41. #117×C61C22semidirect
42. #104×C61C22semidirect
47. #41×C61D4semidirect
49. C2×Q8×C61D4semidirect
51. C2×D4×C61D4semidirect
71. #11758222D4semidirect
82. C2×D244D4semidirect
84. C2×D244C23semidirect
88. C2×Dic122D4semidirect
89. C2×Dic122C23semidirect
91. M16×C61C23semidirect
95. C42×C61C23semidirect
102. #11758194C23semidirect
201. #421D61semidirect
203. C61#3019semidirect
228. C2×M16C2×D61semidirect
233. #117C2×D61semidirect
235. #104C2×D61semidirect
253. #41D244semidirect
257. C2×Q8D244semidirect
278. C2×D4D244semidirect
295. M16C22×D61semidirect
301. C42C22×D61semidirect