Finite Group Databasebeta

← C4×#14519809 #21454639

Subgroups — C4×#14519809 #21454639

Order 7808.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519809C211yesmaximal, characteristic
2C4×#11758226C211yesmaximal, characteristic
3C4×Q8×D61C211yesmaximal, characteristic, complemented
4#16839869C211yesmaximal, characteristic, complemented
5#16839866C211yesmaximal, characteristic, complemented
6#16839865C211yesmaximal, characteristic, complemented
7#16839861C211yesmaximal, characteristic, complemented
8C4×#11758202C211yesmaximal, characteristic, complemented
9C4×#11758190C211yesmaximal, characteristic, complemented
10C4×#11758201C211yesmaximal, characteristic, complemented
11#16839803C211yesmaximal, characteristic, complemented
12#16839769C211yesmaximal, characteristic, complemented
13#16839762C211yesmaximal, characteristic
14C4×#11758189C211yesmaximal, characteristic, complemented
15C4×Q16×C61C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18#14519809C418yesdirect product factor
19C2×#11758202C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21C2×#11758201C2211yescharacteristic
22C2×#11758189C2211yescharacteristic
23C2×#11758189C2211yescharacteristic
24Q8×Dic61C2211yescharacteristic
25Q8×Dic61C2211yescharacteristic
26C4×Dic122—21no—
27C4×Dic122C2211yescharacteristic
28#14519742—21no—
29#14519742C2211yescharacteristic
30C4×D244—21no—
31C4×D244C2211yescharacteristic
32#14519739—21no—
33#14519739C2211yescharacteristic
34#14519735—21no—
35#14519735C2211yescharacteristic
36C4⋊C4×D61—21no—
37C4⋊C4×D61C2211yescharacteristic
38C42×D61—21no—
39C42×D61—21no—
40C42×D61C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519709C2211yescharacteristic
43#14519708C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519687C2211yescharacteristic
51#14519687C2211yescharacteristic
52C4×#92418C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic
55C4×Q8×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C4×C8×C61C2211yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62#11758226—22no—
63#11758226C2×C414yes—
64Q8×D61—22no—
65Q8×D61C2×C414yescomplemented
66C2×D244—21no—
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61D411yescharacteristic
74C2×C4×D61D411yescharacteristic
75C2×C4×D61C2311yescharacteristic
76C2×Dic122—21no—
77C2×Dic122C2311yescharacteristic
78Q16×C61C2×C414yescomplemented
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C42×C61—21no—
86C42×C61—21no—
87C42×C61C2311yescharacteristic
88#11758202C2×C414yescomplemented
89#11758201C2×C414yescomplemented
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61D411yescharacteristic
106C4×Dic61D411yescharacteristic
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758190C2×C414yescomplemented
111#11758189—22no—
112#11758189C2×C414yescomplemented
113C22×D61—21no—
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61C22×C412yes—
118Q8×C61C22×C412yes—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132D244—24no—
133D244—21no—
134D244C22×C412yes—
135C4×D61—24no—
136C4×D61—22no—
137C4×D61—24no—
138C4×D61—41no—
139C4×D61—42no—
140C4×D61—42no—
141C4×D61—42no—
142C4×D61C22×C412yes—
143C4×D61#4112yes—
144Dic122—21no—
145Dic122—24no—
146Dic122C22×C412yes—
147C8×C61—21no—
148C8×C61C22×C412yes—
149#92418—21no—
150#92418C22×C412yes—
151C22×C61C22×D411yescharacteristic
152C2×D61—21no—
153C2×D61—21no—
154C2×D61—22no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61C4×D412yes—
158C4×C61—22no—
159C4×C61—22no—
160C4×C61—21no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61#13712yescomplemented
164C4×C61C23×C411yescharacteristic
165C4×C61C2×#4111yescharacteristic
166Dic61—22no—
167Dic61—21no—
168Dic61—21no—
169Dic61—41no—
170Dic61—41no—
171Dic61C4×D412yes—
172C4×#137—611nomaximal, Sylow
173C2×C61C2×C4×D411yescharacteristic
174C2×C61C2×#13711yescharacteristic
175C2×C61#57511yescharacteristic
176D61—22no—
177D61—42no—
178C2×#137—611no—
179C4×#41—611no—
180C2×C4×Q8—611no—
181#441—611no—
182#441—611no—
183#440—611no—
184#440—611no—
185C4×Q16—611no—
186C4×Q16D6111yescharacteristic, complemented
187C4×SD16—611no—
188C4×SD16—611no—
189#428—611no—
190#419—611no—
191#417—611no—
192C4×M16—611no—
193C61C4×#13711yescharacteristic, complemented, Sylow
194C2×#41—611no—
195C22×Q8—611no—
196#137—618no—
197C2×Q16—611no—
198C2×Q16C2×D6111yescharacteristic
199C2×SD16—611no—
200C2×SD16—611no—
201C2×M16—611no—
202C2×M16—611no—
203C4×Q8—611no—
204C4×Q8—611no—
205C4×Q8—611no—
206C4×Q8—611no—
207C4×Q8—1221no—
208C4×Q8—1221no—
209C4×Q8C2×D6111yescharacteristic
210C4×Q8C2×D6111yescharacteristic
211C4×D4—611no—
212C4×D4—611no—
213C4×D4—1221no—
214C4×D4—1221no—
215#117—611no—
216#117—1221no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—1221no—
219C2×C42—611no—
220C2×C42—1221no—
221C2×C42—1221no—
222#107—611no—
223#107C2×D6111yescharacteristic
224#106—611no—
225#106—611no—
226#103—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103C2×D6111yescharacteristic
231#103C2×D6111yescharacteristic
232#102—611no—
233#102—611no—
234#97—611no—
235#97—611no—
236C4×C8—611no—
237C4×C8C2×D6111yescharacteristic
238#41—614no—
239#41—1222no—
240C2×Q8—614no—
241C2×Q8—611no—
242C2×Q8—1221no—
243C2×Q8—1222no—
244C2×Q8C22×D6111yescharacteristic
245C2×Q8C22×D6111yescharacteristic
246C2×D4—611no—
247C2×D4—1221no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256Q16—614no—
257Q16C4×D6114yescomplemented
258SD16—614no—
259SD16—614no—
260M16—614no—
261M16—1222no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8C22×D6111yescharacteristic
265C2×C8C22×D6111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—611no—
269C4⋊C4—611no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4C22×D6111yescharacteristic
276C4⋊C4C22×D6111yescharacteristic
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C42—21no—
281C42—21no—
282C42—611no—
283C42—611no—
284C42—611no—
285C42—1221no—
286C42—1221no—
287C42—1221no—
288C42—1221no—
289C42—1221no—
290C42C22×D6111yescharacteristic
291C23—611no—
292C23—1221no—
293Q8—21no—
294Q8—21no—
295Q8—612no—
296Q8—1224no—
297Q8—1221no—
298Q8C2×C4×D6112yes—
299Q8C2×C4×D6112yes—
300D4—612no—
301D4—1224no—
302D4—1221no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—611no—
308C2×C4—612no—
309C2×C4—612no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—1224no—
313C2×C4—1224no—
314C2×C4—1221no—
315C2×C4—1222no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—2441no—
319C2×C4—2442no—
320C2×C4—2442no—
321C2×C4—2442no—
322C2×C4D4×D6111yescharacteristic
323C2×C4D4×D6111yescharacteristic
324C2×C4C23×D6111yescharacteristic
325C8—21no—
326C8—612no—
327C8—1221no—
328C8C2×C4×D6112yes—
329C22—612no—
330C22—1221no—
331C22—1221no—
332C22—1222no—
333C22—2441no—
334C22—2441no—
335C22C2×D4×D6111yescharacteristic
336C4—22no—
337C4—22no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—612no—
342C4—1222no—
343C4—1221no—
344C4—1221no—
345C4—2441no—
346C4—2441no—
347C4#1451980912yesdirect product factor
348C4C22×C4×D6111yescharacteristic
349C4#41×D6111yescharacteristic
350C2—1222no—
351C2—2442no—
352C2C4×D4×D6111yescharacteristic
353C2C2×#1451980911yescharacteristic
354C2#1684055911yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC4×C61C23×C4
FrattiniC2×C4C23×D61
FittingC4×Q16×C61C2
socleC22×C61C22×D4
hypercenterC4×Q16D61
hypocenterC61C4×#137
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D61C2semidirect
4. #16839869C2semidirect
5. #16839866C2semidirect
6. #16839865C2semidirect
7. #16839861C2semidirect
8. C4×#11758202C2semidirect
9. C4×#11758190C2semidirect
10. C4×#11758201C2semidirect
11. #16839803C2semidirect
12. #16839769C2semidirect
14. C4×#11758189C2semidirect
15. C4×Q16×C61C2semidirect
18. #14519809C4direct (N × H)
65. Q8×D61C2×C4semidirect
78. Q16×C61C2×C4semidirect
88. #11758202C2×C4semidirect
89. #11758201C2×C4semidirect
110. #11758190C2×C4semidirect
112. #11758189C2×C4semidirect
163. C4×C61#137semidirect
186. C4×Q16D61semidirect
193. C61C4×#137semidirect
257. Q16C4×D61semidirect
347. C4#14519809direct (N × H)