Finite Group Databasebeta

← #21455192

Subgroups — #21455192

Order 7808.

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

normal subgroups only

This group has 736 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
1#16840598C211yesmaximal, characteristic, complemented
2C2×#14519805C211yesmaximal, characteristic, complemented
3C2×#14519802C211yesmaximal, characteristic, complemented
4#16840331C211yesmaximal, characteristic, complemented
5#16839936C214yesmaximal, complemented
6#16839931C214yesmaximal, complemented
7#16839780C211yesmaximal, characteristic, complemented
8#16839744C211yesmaximal, characteristic, complemented
9C61×#421C211yesmaximal, characteristic, complemented
10#14519825—21no—
11#14519824—21no—
12#14519824C2212yescomplemented
13#14519823—21no—
14#14519823C2212yescomplemented
15#14519822—21no—
16#14519822—22no—
17C2×#11758222—22no—
18C2×#11758222C2211yescharacteristic
19C2×#11758222C2211yescharacteristic
20#41×D61—22no—
21#41×D61—22no—
22C22×D244C2211yescharacteristic, complemented
23#14519805—22no—
24#14519805C2214yescomplemented
25#14519802—22no—
26#14519802C2214yescomplemented
27C2×#11758190—21no—
28C2×#11758201—21no—
29C2×D488—21no—
30C2×#11758199—21no—
31C2×#11758194C2211yescharacteristic, complemented
32#14519774C2212yescomplemented
33#14519765C2212yescomplemented
34#14519752—22no—
35#14519747—22no—
36#14519705C2214yescomplemented
37#14519695C2212yescomplemented
38#14519693C2212yescomplemented
39C2×#41×C61C2211yescharacteristic
40C2×M16×C61C2211yescharacteristic, complemented
41#117×C61C2211yescharacteristic, complemented
42#104×C61C2214yescomplemented
43C23×D61—21no—
44#41×C61—21no—
45#41×C61—21no—
46#41×C61D412yescomplemented
47#41×C61C2312yes—
48C2×Q8×C61D411yescharacteristic, complemented
49C2×D4×C61—21no—
50C2×D4×C61D411yescharacteristic, complemented
51C22×C4×C61—21no—
52C22×C4×C61C2311yescharacteristic
53C2×C22⋊D61—24no—
54C2×C22⋊D61—21no—
55C2×C22⋊D61D412yes—
56#11758226—22no—
57#11758226—22no—
58Q8×D61—22no—
59Q8×D61—22no—
60#11758224—24no—
61#11758224—22no—
62#11758224—22no—
63#11758224—24no—
64D4×D61—24no—
65D4×D61—22no—
66D4×D61—24no—
67D4×D61—22no—
68#11758222—24no—
69#11758222—24no—
70#11758222—21no—
71#11758222—21no—
72#11758222—21no—
73#11758222—21no—
74#11758222—21no—
75#11758222—21no—
76#11758222—22no—
77#11758222—22no—
78#11758222D412yescomplemented
79#11758222C2312yes—
80C2×D244—22no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—24no—
87C2×D244D411yescharacteristic, complemented
88C2×D244C2312yes—
89C2×D244C2311yescharacteristic
90C2×C4×D61—24no—
91C2×C4×D61—21no—
92C2×C4×D61D412yes—
93C2×Dic122—22no—
94C2×Dic122D411yescharacteristic, complemented
95C2×Dic122C2311yescharacteristic
96M16×C61—21no—
97M16×C61C2312yes—
98C2×C8×C61—21no—
99C4⋊C4×C61—21no—
100C22⋊C4×C61—21no—
101C42×C61C2312yes—
102#11758201—24no—
103#11758199—24no—
104#11758198—24no—
105#11758194—21no—
106#11758194C2312yes—
107C2×#92418—21no—
108D488—24no—
109#11758190—24no—
110C23×C61—21no—
111C23×C61C2×D411yescharacteristic
112C22×D61—24no—
113C22×D61—21no—
114C22×D61—22no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—82no—
118C22×D61C2×D412yes—
119Q8×C61—21no—
120Q8×C61C2×D412yes—
121D4×C61—22no—
122D4×C61—22no—
123D4×C61—21no—
124D4×C61C2×D412yes—
125C2×C4×C61—21no—
126C2×C4×C61—22no—
127C2×C4×C61—22no—
128C2×C4×C61—22no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—24no—
136C22⋊D61—24no—
137C22⋊D61—22no—
138C22⋊D61—22no—
139C22⋊D61—22no—
140C22⋊D61—22no—
141C2×Dic61—24no—
142C2×Dic61—21no—
143C2×Dic61C2×D412yes—
144D244—24no—
145D244—21no—
146D244—21no—
147D244—21no—
148D244—22no—
149D244—22no—
150D244—41no—
151D244—41no—
152D244—84no—
153D244C2×D412yes—
154C4×D61—24no—
155C4×D61—24no—
156C4×D61—22no—
157C4×D61—22no—
158C4×D61—22no—
159C4×D61—22no—
160Dic122—24no—
161Dic122—21no—
162Dic122—21no—
163Dic122—21no—
164Dic122C2×D412yes—
165C8×C61—22no—
166#92418—22no—
167C22×C61—22no—
168C22×C61—41no—
169C22×C61—81no—
170C22×C61#12011yescharacteristic
171C22×C61#12011yescharacteristic
172C22×C61C22×D411yescharacteristic
173C2×D61—22no—
174C2×D61—22no—
175C2×D61—42no—
176C2×D61—44no—
177C2×D61—42no—
178C2×D61—81no—
179C2×D61—84no—
180C2×D61—82no—
181C2×D61—82no—
182C4×C61—22no—
183C4×C61—42no—
184C4×C61#12011yescharacteristic
185C4×C61#12011yescharacteristic
186C4×C61C22×D411yescharacteristic
187C4×C61C22×D411yescharacteristic
188Dic61—22no—
189Dic61—22no—
190#3021—611nomaximal, Sylow
191C2×C61—21no—
192C2×C61—21no—
193C2×C61—21no—
194C2×C61—42no—
195C2×C61C2×#12011yescharacteristic
196D61—42no—
197D61—42no—
198D61—82no—
199#585—611no—
200C2×AGL(1,ℤ/8)—611no—
201C2×AGL(1,ℤ/8)—611no—
202#535—611no—
203#454—614no—
204#453—614no—
205#421—611no—
206#421D6111yescharacteristic, complemented
207#413—611no—
208C61#302111yescharacteristic, complemented, Sylow
2092−1+4—612no—
2102−1+4—1221no—
2112−1+4—1221no—
212H(5,𝔽2)—612no—
213H(5,𝔽2)—1222no—
214H(5,𝔽2)—1221no—
215H(5,𝔽2)—1221no—
216C2×#41—611no—
217C2×#41—611no—
218C2×#41—1222no—
219C2×#41—1222no—
220C2×#41—1222no—
221C2×#41C2×D6111yescharacteristic
222C22×D4—611no—
223AGL(1,ℤ/8)—614no—
224AGL(1,ℤ/8)—614no—
225AGL(1,ℤ/8)—1222no—
226AGL(1,ℤ/8)—1222no—
227C2×SD16—1221no—
228C2×SD16—1221no—
229C2×D8—1221no—
230C2×D8—1221no—
231C2×M16—611no—
232C2×M16C2×D6111yescharacteristic, complemented
233#127—612no—
234#124—612no—
235#121—1222no—
236#120—1222no—
237#117C2×D6111yescharacteristic, complemented
238#104—614no—
239#104C2×D6114yescomplemented
240#101—612no—
241#100—612no—
242C24—1221no—
243#41—21no—
244#41—21no—
245#41—612no—
246#41—612no—
247#41—1222no—
248#41—1222no—
249#41—1224no—
250#41—1224no—
251#41—1224no—
252#41—1224no—
253#41—1222no—
254#41—1222no—
255#41—1222no—
256#41—1222no—
257#41—1221no—
258#41—1221no—
259#41—1221no—
260#41—1221no—
261#41—1221no—
262#41—1221no—
263#41D24412yescomplemented
264#41C22×D6112yes—
265C2×Q8—611no—
266C2×Q8—611no—
267C2×Q8—1222no—
268C2×Q8—1222no—
269C2×Q8—1222no—
270C2×Q8D24411yescharacteristic, complemented
271C2×D4—21no—
272C2×D4—612no—
273C2×D4—611no—
274C2×D4—611no—
275C2×D4—612no—
276C2×D4—1222no—
277C2×D4—1224no—
278C2×D4—1224no—
279C2×D4—1224no—
280C2×D4—1222no—
281C2×D4—1224no—
282C2×D4—1221no—
283C2×D4—1222no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4D24411yescharacteristic, complemented
290C22×C4—21no—
291C22×C4—612no—
292C22×C4—1224no—
293C22×C4—1221no—
294C22×C4C22×D6111yescharacteristic
295SD16—1224no—
296SD16—1224no—
297D8—1224no—
298D8—1224no—
299M16—21no—
300M16—612no—
301M16—1221no—
302M16C22×D6112yes—
303C2×C8—21no—
304C2×C8—1221no—
305C4⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—1224no—
308C42C22×D6112yes—
309C23—21no—
310C23—612no—
311C23—1224no—
312C23—1221no—
313C23—1222no—
314C23—4882no—
315C23—2441no—
316C23—2441no—
317C23D4×D6111yescharacteristic
318Q8—21no—
319Q8—612no—
320Q8—1224no—
321Q8—1221no—
322Q8—1221no—
323Q8—1221no—
324Q8C2×D24412yes—
325D4—22no—
326D4—22no—
327D4—21no—
328D4—612no—
329D4—1224no—
330D4—1224no—
331D4—1224no—
332D4—1222no—
333D4—1222no—
334D4—1222no—
335D4—1222no—
336D4—1221no—
337D4—1222no—
338D4—1221no—
339D4—1222no—
340D4—1221no—
341D4—4884no—
342D4—2441no—
343D4—2441no—
344D4C2×D24412yes—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—612no—
350C2×C4—1224no—
351C2×C4—1224no—
352C2×C4—1224no—
353C2×C4—1221no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4C2×D24411yescharacteristic
359C2×C4C2×D24411yescharacteristic
360C2×C4D4×D6111yescharacteristic
361C2×C4D4×D6111yescharacteristic
362C2×C4D4×D6111yescharacteristic
363C2×C4C23×D6111yescharacteristic
364C8—22no—
365C8—1222no—
366C22—22no—
367C22—41no—
368C22—81no—
369C22—1222no—
370C22—1222no—
371C22—4882no—
372C22—4882no—
373C22—4881no—
374C22—4884no—
375C22—2444no—
376C22—2442no—
377C22—2442no—
378C22#1451974711yescharacteristic
379C22#1451974711yescharacteristic
380C22C2×D4×D6111yescharacteristic
381C4—22no—
382C4—42no—
383C4—1222no—
384C4—1222no—
385C4#1451974711yescharacteristic
386C4#1451974711yescharacteristic
387C4C2×D4×D6111yescharacteristic
388C4C22×D24411yescharacteristic
389C2—21no—
390C2—21no—
391C2—21no—
392C2—42no—
393C2—4882no—
394C2—2442no—
395C2—2442no—
396C2C2×#1451974711yescharacteristic
subgroupG/H
centerC2C2×#14519747
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#421C2
socleC2×C61C2×#120
hypercenter#421D61
hypocenterC61#3021
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. #16840598C2semidirect
2. C2×#14519805C2semidirect
3. C2×#14519802C2semidirect
4. #16840331C2semidirect
5. #16839936C2semidirect
6. #16839931C2semidirect
7. #16839780C2semidirect
8. #16839744C2semidirect
9. C61×#421C2semidirect
12. #14519824C22semidirect
14. #14519823C22semidirect
22. C22×D244C22semidirect
24. #14519805C22semidirect
26. #14519802C22semidirect
31. C2×#11758194C22semidirect
32. #14519774C22semidirect
33. #14519765C22semidirect
36. #14519705C22semidirect
37. #14519695C22semidirect
38. #14519693C22semidirect
40. C2×M16×C61C22semidirect
41. #117×C61C22semidirect
42. #104×C61C22semidirect
46. #41×C61D4semidirect
48. C2×Q8×C61D4semidirect
50. C2×D4×C61D4semidirect
78. #11758222D4semidirect
87. C2×D244D4semidirect
94. C2×Dic122D4semidirect
206. #421D61semidirect
208. C61#3021semidirect
232. C2×M16C2×D61semidirect
237. #117C2×D61semidirect
239. #104C2×D61semidirect
263. #41D244semidirect
270. C2×Q8D244semidirect
289. C2×D4D244semidirect