Finite Group Databasebeta

← #21455185

Subgroups — #21455185

Order 7808.

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

normal subgroups only

This group has 698 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×#14519824C211yesmaximal, characteristic, complemented
2#16840562C211yesmaximal, characteristic, complemented
3#16840560C211yesmaximal, characteristic, complemented
4#16840338C211yesmaximal, characteristic, complemented
5#16839946C214yesmaximal, complemented
6#16839936C214yesmaximal, complemented
7#16839780C211yesmaximal, characteristic, complemented
8C2×#14519695C211yesmaximal, characteristic, complemented
9C61×#421C211yesmaximal, characteristic, complemented
10#14519824—22no—
11#14519824—22no—
12#14519824—22no—
13#14519824C2214yes—
14C2×#11758222—21no—
15C2×#11758222C2211yescharacteristic
16C2×#11758222C2211yescharacteristic
17C2×#11758224—21no—
18C2×#11758224—22no—
19C22×Dic122—21no—
20C22×Dic122C2211yescharacteristic
21C2×Q8×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
33#14519777C2212yescomplemented
34#14519765C2212yescomplemented
35#14519761—22no—
36#14519757—22no—
37#14519705C2214yescomplemented
38#14519695C2214yescomplemented
39C2×#41×C61C2211yescharacteristic
40C2×M16×C61C2211yescharacteristic
41#117×C61C2211yescharacteristic
42#104×C61C2214yescomplemented
43#41×C61—21no—
44#41×C61—21no—
45#41×C61D412yes—
46#41×C61C2312yes—
47C2×Q8×C61D411yescharacteristic
48C2×D4×C61—21no—
49C2×D4×C61D411yescharacteristic
50C22×C4×C61—21no—
51C22×C4×C61C2311yescharacteristic
52C2×C22⋊D61—22no—
53C2×C22⋊D61—21no—
54C2×C22⋊D61—21no—
55C22×Dic61—22no—
56C22×Dic61D412yes—
57Q8×D61—24no—
58Q8×D61—24no—
59#11758224—28no—
60#11758224—24no—
61#11758224—24no—
62#11758224—28no—
63#11758222—24no—
64#11758222—21no—
65#11758222—21no—
66#11758222—24no—
67#11758222—21no—
68#11758222—21no—
69#11758222—21no—
70#11758222—21no—
71#11758222D412yes—
72#11758222C2312yes—
73C2×D244D411yescharacteristic
74C2×D244C2311yescharacteristic
75C2×C4×D61—22no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×Dic122—22no—
79C2×Dic122—24no—
80C2×Dic122—21no—
81C2×Dic122—21no—
82C2×Dic122—21no—
83C2×Dic122—21no—
84C2×Dic122—24no—
85C2×Dic122D412yes—
86C2×Dic122D411yescharacteristic
87C2×Dic122C2311yescharacteristic
88C2×Dic122C2312yes—
89M16×C61—21no—
90M16×C61C2312yes—
91C2×C8×C61—21no—
92C4⋊C4×C61—21no—
93C22⋊C4×C61—21no—
94C42×C61C2312yes—
95#11758202—22no—
96#11758201—22no—
97#11758200—22no—
98#11758199—22no—
99#11758198—24no—
100C4⋊Dic61—24no—
101#11758194—21no—
102#11758194C2312yes—
103C2×#92418—21no—
104Dic244—22no—
105D488—22no—
106#11758190—22no—
107#11758190—22no—
108C23×C61—21no—
109C23×C61C2×D411yescharacteristic
110C22×D61—21no—
111C22×D61—21no—
112Q8×C61—21no—
113Q8×C61C2×D412yes—
114D4×C61—22no—
115D4×C61—22no—
116D4×C61—21no—
117D4×C61C2×D412yes—
118C2×C4×C61—21no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2411yescharacteristic
128C22⋊D61—28no—
129C22⋊D61—22no—
130C22⋊D61—22no—
131C22⋊D61—41no—
132C22⋊D61—41no—
133C2×Dic61—28no—
134C2×Dic61—22no—
135C2×Dic61—21no—
136C2×Dic61—22no—
137C2×Dic61—21no—
138C2×Dic61C2×D414yes—
139D244—21no—
140D244—21no—
141D244—21no—
142D244C2×D412yes—
143C4×D61—28no—
144C4×D61—22no—
145C4×D61—22no—
146C4×D61—41no—
147C4×D61—41no—
148Dic122—28no—
149Dic122—22no—
150Dic122—21no—
151Dic122—22no—
152Dic122—22no—
153Dic122—22no—
154Dic122—21no—
155Dic122—21no—
156Dic122C2×D412yes—
157C8×C61—22no—
158#92418—22no—
159C22×C61—22no—
160C22×C61—41no—
161C22×C61—42no—
162C22×C61#12011yescharacteristic
163C22×C61#12011yescharacteristic
164C22×C61C22×D411yescharacteristic
165C2×D61—22no—
166C2×D61—42no—
167C2×D61—42no—
168C2×D61—41no—
169C4×C61—22no—
170C4×C61—42no—
171C4×C61#12011yescharacteristic
172C4×C61#12011yescharacteristic
173C4×C61C22×D411yescharacteristic
174C4×C61C22×D411yescharacteristic
175Dic61—24no—
176Dic61—22no—
177Dic61—41no—
178#3020—611nomaximal, Sylow
179C2×C61—21no—
180C2×C61—21no—
181C2×C61—21no—
182C2×C61—42no—
183C2×C61C2×#12011yescharacteristic
184D61—42no—
185D61—81no—
186C2×2−1+4—611no—
187#575—611no—
188#575—611no—
189#536—611no—
190#456—614no—
191#454—614no—
192#421—611no—
193#421D6111yescharacteristic, complemented
194C2×#101—611no—
195C61#302011yescharacteristic, complemented, Sylow
1962−1+4—614no—
1972−1+4—1222no—
1982−1+4—1222no—
1992−1+4—1222no—
200C2×#41—611no—
201C2×#41—611no—
202C2×#41—1221no—
203C2×#41—1222no—
204C2×#41—1221no—
205C2×#41C2×D6111yescharacteristic
206C22×Q8—611no—
207C22×Q8—1221no—
208C22×Q8—1221no—
209#137—612no—
210#137—612no—
211#137—1221no—
212#137—1221no—
213AGL(1,ℤ/8)—612no—
214AGL(1,ℤ/8)—612no—
215AGL(1,ℤ/8)—1221no—
216AGL(1,ℤ/8)—1221no—
217#135—1222no—
218#135—1222no—
219C2×M16—611no—
220C2×M16C2×D6111yescharacteristic
221C4⋊Q8—612no—
222#124—612no—
223#123—1222no—
224C22⋊Q8—1222no—
225#117C2×D6111yescharacteristic
226#104—614no—
227#104C2×D6114yescomplemented
228#101—614no—
229#41—21no—
230#41—21no—
231#41—612no—
232#41—612no—
233#41—1224no—
234#41—1224no—
235#41—1228no—
236#41—1228no—
237#41—1224no—
238#41—1224no—
239#41—1221no—
240#41—1221no—
241#41—1221no—
242#41—1221no—
243#41—1221no—
244#41—1221no—
245#41D24412yes—
246#41C22×D6112yes—
247C2×Q8—612no—
248C2×Q8—612no—
249C2×Q8—611no—
250C2×Q8—611no—
251C2×Q8—1224no—
252C2×Q8—1222no—
253C2×Q8—1224no—
254C2×Q8—1224no—
255C2×Q8—1224no—
256C2×Q8—1221no—
257C2×Q8—1221no—
258C2×Q8—1221no—
259C2×Q8—1221no—
260C2×Q8D24411yescharacteristic
261C2×D4—21no—
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—1222no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4D24411yescharacteristic
268C22×C4—21no—
269C22×C4—612no—
270C22×C4—1222no—
271C22×C4—1222no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4C22×D6111yescharacteristic
275Q16—1222no—
276Q16—1222no—
277SD16—1222no—
278SD16—1222no—
279SD16—1222no—
280SD16—1222no—
281D8—1222no—
282D8—1222no—
283M16—21no—
284M16—612no—
285M16—1221no—
286M16C22×D6112yes—
287C2×C8—21no—
288C2×C8—1221no—
289C4⋊C4—21no—
290C4⋊C4—1224no—
291C22⋊C4—21no—
292C22⋊C4—1224no—
293C42C22×D6112yes—
294C23—21no—
295C23—1221no—
296C23—1221no—
297C23D4×D6111yescharacteristic
298Q8—21no—
299Q8—612no—
300Q8—1228no—
301Q8—1222no—
302Q8—1222no—
303Q8—1222no—
304Q8—1222no—
305Q8—1221no—
306Q8—1221no—
307Q8—1221no—
308Q8C2×D24412yes—
309D4—22no—
310D4—22no—
311D4—21no—
312D4—612no—
313D4—1228no—
314D4—1222no—
315D4—1222no—
316D4—1221no—
317D4—1221no—
318D4—1221no—
319D4—2441no—
320D4—2441no—
321D4C2×D24412yes—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—614no—
327C2×C4—1228no—
328C2×C4—1228no—
329C2×C4—1222no—
330C2×C4—1222no—
331C2×C4—1221no—
332C2×C4—1222no—
333C2×C4—1222no—
334C2×C4—1221no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4C2×D24411yescharacteristic
338C2×C4C2×D24411yescharacteristic
339C2×C4D4×D6111yescharacteristic
340C2×C4D4×D6111yescharacteristic
341C2×C4D4×D6111yescharacteristic
342C2×C4C23×D6111yescharacteristic
343C8—22no—
344C8—1222no—
345C22—22no—
346C22—41no—
347C22—42no—
348C22—1222no—
349C22—2442no—
350C22—2442no—
351C22—2441no—
352C22#1451974711yescharacteristic
353C22#1451974711yescharacteristic
354C22C2×D4×D6111yescharacteristic
355C4—22no—
356C4—42no—
357C4—1224no—
358C4—1222no—
359C4—2441no—
360C4#1451974711yescharacteristic
361C4#1451974711yescharacteristic
362C4C2×D4×D6111yescharacteristic
363C4C22×D24411yescharacteristic
364C2—21no—
365C2—21no—
366C2—21no—
367C2—42no—
368C2—4881no—
369C2—2442no—
370C2C2×#1451974711yescharacteristic
subgroupG/H
centerC2C2×#14519747
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#421C2
socleC2×C61C2×#120
hypercenter#421D61
hypocenterC61#3020
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×#14519824C2semidirect
2. #16840562C2semidirect
3. #16840560C2semidirect
4. #16840338C2semidirect
5. #16839946C2semidirect
6. #16839936C2semidirect
7. #16839780C2semidirect
8. C2×#14519695C2semidirect
9. C61×#421C2semidirect
23. #14519810C22semidirect
25. #14519807C22semidirect
27. #14519805C22semidirect
29. #14519802C22semidirect
33. #14519777C22semidirect
34. #14519765C22semidirect
37. #14519705C22semidirect
38. #14519695C22semidirect
42. #104×C61C22semidirect
193. #421D61semidirect
195. C61#3020semidirect
227. #104C2×D61semidirect