Finite Group Databasebeta

← #21455177

Subgroups — #21455177

Order 7808.

762 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 133 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
1H(5,𝔽2)×D61C211yesmaximal, characteristic, complemented
2#16840561C212yesmaximal, complemented
3#16840330C211yesmaximal, characteristic, complemented
4#16839939C211yesmaximal, characteristic, complemented
5#16839938C212yesmaximal, complemented
6#16839932C211yesmaximal, characteristic, complemented
7#16839931C212yesmaximal, complemented
8#16839930C211yesmaximal, characteristic, complemented
9#16839777C212yesmaximal, complemented
10#100×D61C211yesmaximal, characteristic, complemented
11C61×#455C211yesmaximal, characteristic, complemented
12#14519823—22no—
13#14519823C2212yes—
14#14519822—22no—
15#14519822—22no—
16#14519822C2211yescharacteristic
17C2×#11758226C2211yescharacteristic, complemented
18#41×D61—22no—
19#41×D61C2212yes—
20C2×D4×D61—22no—
21C2×D4×D61—22no—
22C2×D4×D61C2211yescharacteristic
23#14519809—22no—
24#14519808C2212yescomplemented
25#14519805C2212yescomplemented
26#14519804—22no—
27#14519802C2212yescomplemented
28#14519800—22no—
29#14519798—22no—
30M16×D61C2212yescomplemented
31#14519774C2211yescharacteristic, complemented
32#14519773C2211yescharacteristic, complemented
33#14519766C2211yescharacteristic, complemented
34#14519750—22no—
35#14519747—22no—
36#14519734C2211yescharacteristic, complemented
37#14519705C2212yescomplemented
38#14519704C2212yescomplemented
39#14519703C2212yescomplemented
40#14519694C2211yescharacteristic, complemented
41#14519693C2212yescomplemented
42H(5,𝔽2)×C61C2211yescharacteristic
43#137×C61C2212yescomplemented
44#124×C61C2211yescharacteristic, complemented
45#104×C61C2212yescomplemented
46#100×C61C2211yescharacteristic, complemented
47C23×D61—22no—
48C23×D61D412yes—
49#41×C61—22no—
50#41×C61C2312yes—
51C2×Q8×C61C2311yescharacteristic, complemented
52C2×D4×C61—22no—
53C2×D4×C61—22no—
54C2×D4×C61C2311yescharacteristic
55C2×C22⋊D61—22no—
56C2×C22⋊D61—24no—
57C2×C22⋊D61—22no—
58C2×C22⋊D61—22no—
59C2×C22⋊D61D412yes—
60#11758226—22no—
61#11758226—22no—
62#11758226—22no—
63#11758226D412yescomplemented
64Q8×D61D412yescomplemented
65#11758224—24no—
66#11758224—22no—
67#11758224—22no—
68#11758224D412yescomplemented
69D4×D61—24no—
70D4×D61—24no—
71D4×D61—24no—
72D4×D61—22no—
73D4×D61—24no—
74D4×D61—22no—
75D4×D61—22no—
76D4×D61—22no—
77D4×D61—22no—
78D4×D61D412yescomplemented
79#11758222—24no—
80#11758222—22no—
81#11758222—22no—
82#11758222C2312yes—
83C2×D244—22no—
84C2×D244—22no—
85C2×D244—21no—
86C2×D244—22no—
87C2×D244C2311yescharacteristic
88C2×D244C2311yescharacteristic, complemented
89C2×C4×D61—22no—
90C2×C4×D61—22no—
91C2×C4×D61—21no—
92C2×C4×D61C2311yescharacteristic
93Q16×C61—22no—
94SD16×C61—22no—
95M16×C61C2312yescomplemented
96C22⋊C4×C61—22no—
97C42×C61C2311yescharacteristic, complemented
98#11758202—22no—
99#11758201—22no—
100#11758201—22no—
101#11758199—22no—
102#11758198—21no—
103#11758198—22no—
104#11758196—21no—
105C4×Dic61C2311yescharacteristic, complemented
106#11758194C2312yescomplemented
107D488—22no—
108#11758190—22no—
109#11758189—22no—
110C8×D61—22no—
111C23×C61—22no—
112C23×C61C2×D412yes—
113C22×D61—24no—
114C22×D61—22no—
115C22×D61—22no—
116C22×D61—22no—
117C22×D61—22no—
118C22×D61—21no—
119C22×D61—82no—
120C22×D61—84no—
121C22×D61C2×D412yes—
122C22×D61C2×D411yescharacteristic
123Q8×C61—22no—
124Q8×C61C2×D412yes—
125D4×C61—24no—
126D4×C61—22no—
127D4×C61—22no—
128D4×C61C2×D412yes—
129C2×C4×C61—22no—
130C2×C4×C61—22no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61C2411yescharacteristic
134C22⋊D61—24no—
135C22⋊D61—24no—
136C22⋊D61—22no—
137C22⋊D61—22no—
138C22⋊D61—24no—
139C22⋊D61—22no—
140C22⋊D61—82no—
141C2×Dic61—22no—
142C2×Dic61—22no—
143C2×Dic61—21no—
144C2×Dic61C2×D411yescharacteristic
145D244—24no—
146D244—22no—
147D244—22no—
148D244—22no—
149D244—41no—
150D244—41no—
151D244—82no—
152D244C2×D412yes—
153C4×D61—24no—
154C4×D61—22no—
155C4×D61—22no—
156C4×D61—22no—
157C4×D61—42no—
158C4×D61C2×D412yes—
159C4×D61C2×D412yes—
160Dic122—22no—
161Dic122C2×D412yes—
162C8×C61—22no—
163#92418—22no—
164C22×C61—22no—
165C22×C61—22no—
166C22×C61—42no—
167C22×C61—82no—
168C22×C61C22×D411yescharacteristic
169C2×D61—22no—
170C2×D61—22no—
171C2×D61—41no—
172C2×D61—44no—
173C2×D61—44no—
174C2×D61—42no—
175C2×D61—42no—
176C2×D61—41no—
177C2×D61—82no—
178C2×D61—84no—
179C2×D61—82no—
180C2×D61#12011yescharacteristic
181C2×D61#12011yescharacteristic
182C4×C61—22no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61C22×D412yes—
186Dic61—22no—
187Dic61—41no—
188Dic61#12012yes—
189#3019—611nomaximal, Sylow
190C2×C61—21no—
191C2×C61—42no—
192C2×C61—42no—
193C2×C61C2×#12011yescharacteristic
194D61—21no—
195D61—21no—
196D61—42no—
197D61—42no—
198D61—81no—
199C2×H(5,𝔽2)—611no—
200#575—612no—
201#535—611no—
202#455—612no—
203#455—611no—
204#455D6111yescharacteristic, complemented
205#453—611no—
206#453—612no—
207#453—611no—
208#421—612no—
209C2×#100—611no—
210C61#301911yescharacteristic, complemented, Sylow
211H(5,𝔽2)—612no—
212H(5,𝔽2)—611no—
213H(5,𝔽2)—1222no—
214H(5,𝔽2)—1222no—
215H(5,𝔽2)—1222no—
216H(5,𝔽2)C2×D6111yescharacteristic
217C2×#41—612no—
218C2×#41—611no—
219C2×#41—1222no—
220C22×D4—611no—
221C22×D4—1222no—
222C22×D4—1222no—
223#137—612no—
224#137—1222no—
225#137C2×D6112yescomplemented
226AGL(1,ℤ/8)—612no—
227AGL(1,ℤ/8)—612no—
228AGL(1,ℤ/8)—1222no—
229#135—1222no—
230#135—1222no—
231C2×M16—612no—
232#127—611no—
233#127—611no—
234#124—611no—
235#124C2×D6111yescharacteristic, complemented
236#121—1222no—
237#120—1222no—
238#117—611no—
239#104—612no—
240#104—612no—
241#104—612no—
242#104C2×D6112yescomplemented
243#100—611no—
244#100—612no—
245#100C2×D6111yescharacteristic, complemented
246C24—612no—
247C24—1222no—
248#41—22no—
249#41—612no—
250#41—612no—
251#41—612no—
252#41—1222no—
253#41—1222no—
254#41—1224no—
255#41—1222no—
256#41—1222no—
257#41—1222no—
258#41—1222no—
259#41—1224no—
260#41—1222no—
261#41C22×D6112yes—
262C2×Q8—612no—
263C2×Q8C22×D6111yescharacteristic, complemented
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—612no—
267C2×D4—612no—
268C2×D4—611no—
269C2×D4—611no—
270C2×D4—1222no—
271C2×D4—1222no—
272C2×D4—1222no—
273C2×D4—1221no—
274C2×D4—1222no—
275C2×D4—1222no—
276C2×D4—1222no—
277C2×D4—1222no—
278C2×D4—1224no—
279C2×D4—1224no—
280C2×D4—1224no—
281C2×D4—1224no—
282C2×D4—1224no—
283C2×D4—1222no—
284C2×D4—1222no—
285C2×D4—1222no—
286C2×D4—1222no—
287C2×D4C22×D6111yescharacteristic
288C22×C4—611no—
289C22×C4—1222no—
290C22×C4—1221no—
291C22×C4—1222no—
292Q16—22no—
293Q16—1222no—
294SD16—22no—
295SD16—1222no—
296SD16—1222no—
297SD16—1222no—
298D8—1222no—
299D8—1222no—
300M16—612no—
301M16—1222no—
302M16C22×D6112yescomplemented
303C2×C8—1222no—
304C4⋊C4—1221no—
305C22⋊C4—22no—
306C22⋊C4—1221no—
307C22⋊C4—1222no—
308C42—611no—
309C42C22×D6111yescharacteristic, complemented
310C23—22no—
311C23—611no—
312C23—612no—
313C23—1222no—
314C23—1222no—
315C23—1222no—
316C23—1222no—
317C23—1224no—
318C23—1221no—
319C23—4882no—
320C23—4884no—
321C23D4×D6112yes—
322Q8—22no—
323Q8—612no—
324Q8—1222no—
325Q8D4×D6112yes—
326D4—24no—
327D4—22no—
328D4—22no—
329D4—612no—
330D4—1222no—
331D4—1224no—
332D4—1224no—
333D4—1222no—
334D4—1222no—
335D4—1224no—
336D4—1224no—
337D4—1222no—
338D4—1222no—
339D4—1222no—
340D4—4882no—
341D4—4882no—
342D4—2441no—
343D4—2441no—
344D4D4×D6112yes—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—611no—
350C2×C4—612no—
351C2×C4—612no—
352C2×C4—1222no—
353C2×C4—1222no—
354C2×C4—1224no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1221no—
359C2×C4—2442no—
360C2×C4C23×D6111yescharacteristic
361C8—22no—
362C8—1222no—
363C22—22no—
364C22—22no—
365C22—42no—
366C22—82no—
367C22—611no—
368C22—611no—
369C22—1222no—
370C22—1222no—
371C22—4882no—
372C22—4882no—
373C22—4884no—
374C22—2441no—
375C22—2442no—
376C22—2442no—
377C22—2444no—
378C22—2444no—
379C22—2441no—
380C22C2×D4×D6111yescharacteristic
381C4—22no—
382C4—41no—
383C4—41no—
384C4—612no—
385C4—1222no—
386C4—2441no—
387C4C2×D4×D6112yes—
388C2—21no—
389C2—42no—
390C2—42no—
391C2—1221no—
392C2—1221no—
393C2—4881no—
394C2—2442no—
395C2—2442no—
396C2#120×D6111yescharacteristic
subgroupG/H
centerC2#120×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#455C2
socleC2×C61C2×#120
hypercenter#455D61
hypocenterC61#3019
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. H(5,𝔽2)×D61C2semidirect
2. #16840561C2semidirect
3. #16840330C2semidirect
4. #16839939C2semidirect
5. #16839938C2semidirect
6. #16839932C2semidirect
7. #16839931C2semidirect
8. #16839930C2semidirect
9. #16839777C2semidirect
10. #100×D61C2semidirect
11. C61×#455C2semidirect
17. C2×#11758226C22semidirect
24. #14519808C22semidirect
25. #14519805C22semidirect
27. #14519802C22semidirect
30. M16×D61C22semidirect
31. #14519774C22semidirect
32. #14519773C22semidirect
33. #14519766C22semidirect
36. #14519734C22semidirect
37. #14519705C22semidirect
38. #14519704C22semidirect
39. #14519703C22semidirect
40. #14519694C22semidirect
41. #14519693C22semidirect
43. #137×C61C22semidirect
44. #124×C61C22semidirect
45. #104×C61C22semidirect
46. #100×C61C22semidirect
51. C2×Q8×C61C23semidirect
63. #11758226D4semidirect
64. Q8×D61D4semidirect
68. #11758224D4semidirect
78. D4×D61D4semidirect
88. C2×D244C23semidirect
95. M16×C61C23semidirect
97. C42×C61C23semidirect
105. C4×Dic61C23semidirect
106. #11758194C23semidirect
204. #455D61semidirect
210. C61#3019semidirect
225. #137C2×D61semidirect
235. #124C2×D61semidirect
242. #104C2×D61semidirect
245. #100C2×D61semidirect
263. C2×Q8C22×D61semidirect
302. M16C22×D61semidirect
309. C42C22×D61semidirect