Finite Group Databasebeta

← #21457522

Subgroups — #21457522

Order 7808.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519797C211yesmaximal, characteristic, complemented
2C22×#11758200C211yesmaximal, characteristic, complemented
3#16840421C211yesmaximal, characteristic, complemented
4#16840144C211yesmaximal, characteristic, complemented
5#16839993C211yesmaximal, characteristic, complemented
6#16839989C211yesmaximal, characteristic, complemented
7#16839981C211yesmaximal, characteristic, complemented
8#16839977C211yesmaximal, characteristic, complemented
9#16839924C211yesmaximal, characteristic, complemented
10#16839917C211yesmaximal, characteristic, complemented
11#16839905C211yesmaximal, characteristic, complemented
12#16839896C211yesmaximal, characteristic, complemented
13C4×#11758200C211yesmaximal, characteristic, complemented
14D4×#92418C211yesmaximal, characteristic, complemented
15C61×#546C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic, complemented
17C22×Dic122C2211yescharacteristic
18#14519797—24no—
19C2×#11758202C2211yescharacteristic, complemented
20C2×#11758202C2211yescharacteristic, complemented
21C2×#11758200—24no—
22C2×#11758200C2211yescharacteristic
23C2×#11758200C2211yescharacteristic
24C2×#11758200C2211yescharacteristic
25C2×#11758200C2211yescharacteristic
26C2×#11758201C2211yescharacteristic, complemented
27C2×#11758199C2211yescharacteristic
28C2×#11758199C2211yescharacteristic
29C22×#92418C2211yescharacteristic
30C22×#92418C2211yescharacteristic, complemented
31#14519765C2211yescharacteristic, complemented
32#14519763—21no—
33#14519756C2211yescharacteristic, complemented
34#14519755—21no—
35#14519751C2211yescharacteristic
36#14519749—21no—
37C4×Dic122C2211yescharacteristic, complemented
38#14519737—21no—
39#14519708C2211yescharacteristic, complemented
40C4⋊#92418C2211yescharacteristic, complemented
41#14519701C2211yescharacteristic, complemented
42#14519700C2211yescharacteristic, complemented
43#14519700C2211yescharacteristic, complemented
44#14519698C2211yescharacteristic
45#14519698C2211yescharacteristic
46#14519697C2211yescharacteristic, complemented
47C22⋊#92418C2211yescharacteristic
48C22⋊#92418C2211yescharacteristic, complemented
49C4×#92418C2211yescharacteristic, complemented
50C2×#41×C61C2211yescharacteristic
51C22×D4×C61C2211yescharacteristic
52#124×C61C2211yescharacteristic
53#123×C61—21no—
54C22⋊Q8×C61C2211yescharacteristic
55#121×C61—21no—
56#121×C61C2211yescharacteristic
57#120×C61—21no—
58C4×D4×C61C2211yescharacteristic
59C4×D4×C61C2211yescharacteristic
60C2×C22⋊C4×C61—21no—
61C24×C61—21no—
62#41×C61—22no—
63#41×C61—41no—
64C2×Q8×C61C2311yescharacteristic
65C2×D4×C61—22no—
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61—41no—
70C2×D4×C61D411yescharacteristic
71C2×D4×C61C2311yescharacteristic
72C2×D4×C61C2311yescharacteristic
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61C2311yescharacteristic
76C22×C4×C61C2311yescharacteristic
77C2×C22⋊D61—21no—
78C2×C22⋊D61—21no—
79C22×Dic61—21no—
80#11758222—22no—
81#11758222—41no—
82C2×D244C2311yescharacteristic
83C2×C4×D61—21no—
84C2×Dic122—22no—
85C2×Dic122—21no—
86C2×Dic122—41no—
87C2×Dic122C2311yescharacteristic
88C2×Dic122C2311yescharacteristic
89C4⋊C4×C61—21no—
90C4⋊C4×C61D411yescharacteristic
91C4⋊C4×C61C2311yescharacteristic
92C22⋊C4×C61—21no—
93C22⋊C4×C61—21no—
94C22⋊C4×C61—21no—
95C22⋊C4×C61—21no—
96C22⋊C4×C61—21no—
97C22⋊C4×C61D411yescharacteristic
98C22⋊C4×C61D411yescharacteristic
99C42×C61C2311yescharacteristic
100C22⋊Dic61—21no—
101#11758202—22no—
102#11758202—41no—
103#11758201—22no—
104#11758200—22no—
105#11758200—22no—
106#11758200—22no—
107#11758200D414yescomplemented
108#11758199—22no—
109#11758199—41no—
110#11758198—21no—
111#11758198—21no—
112#11758198—21no—
113C4⋊Dic61C2311yescharacteristic
114#11758196—21no—
115#11758196—21no—
116C4×Dic61—21no—
117C2×#92418—22no—
118C2×#92418—22no—
119C2×#92418C2311yescharacteristic
120C2×#92418C2311yescharacteristic
121C2×#92418C2311yescharacteristic
122C2×#92418C2311yescharacteristic
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—42no—
126C23×C61—42no—
127C23×C61—81no—
128C23×C61C2×D411yescharacteristic
129C23×C61C2×D411yescharacteristic
130C22×D61—21no—
131Q8×C61—21no—
132Q8×C61—21no—
133D4×C61—22no—
134D4×C61—21no—
135D4×C61—21no—
136D4×C61—21no—
137D4×C61—42no—
138D4×C61—42no—
139D4×C61—81no—
140D4×C61C2×D412yes—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—42no—
148C2×C4×C61—81no—
149C2×C4×C61C2×D411yescharacteristic
150C2×C4×C61C2×D411yescharacteristic
151C2×C4×C61C2×D411yescharacteristic
152C2×C4×C61C2×D411yescharacteristic
153C2×C4×C61C2411yescharacteristic
154C22⋊D61—42no—
155C22⋊D61—42no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—42no—
160D244—21no—
161D244—21no—
162C4×D61—42no—
163Dic122—21no—
164Dic122—21no—
165Dic122—21no—
166Dic122—42no—
167Dic122C2×D412yes—
168#92418—21no—
169#92418—21no—
170#92418—21no—
171#92418C2×D412yes—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—22no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—84no—
184C22×C61#13512yescomplemented
185C22×C61C22×D411yescharacteristic
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—41no—
194C4×C61—41no—
195C4×C61C22×D411yescharacteristic
196C4×C61H(5,𝔽2)11yescharacteristic
197Dic61—22no—
198Dic61—41no—
199Dic61—41no—
200#3282—611nomaximal, Sylow
201C2×C61—22no—
202C2×C61—41no—
203C2×C61—42no—
204C2×C61—81no—
205C2×C61D4211yescharacteristic
206C2×C61C2×#13511yescharacteristic
207C2×C61#57711yescharacteristic
208D61—81no—
209C2×#135—611no—
210C22×SD16—611no—
211#548—611no—
212#546D6111yescharacteristic, complemented
213#495—611no—
214#465—611no—
215#465—611no—
216#464—611no—
217#463—611no—
218#452—611no—
219#451—611no—
220#449—611no—
221#447—611no—
222C4×SD16—611no—
223C8×D4—611no—
224C61#328211yescharacteristic, complemented, Sylow
225C2×#41—611no—
226C2×#41C2×D6111yescharacteristic
227C22×Q8—611no—
228C22×D4C2×D6111yescharacteristic
229#135—1224no—
230C2×Q16—611no—
231C2×Q16—611no—
232C2×SD16—611no—
233C2×SD16—611no—
234C2×SD16—611no—
235C2×SD16—611no—
236C2×SD16—611no—
237C2×SD16—1224no—
238C2×D8—611no—
239C2×D8—611no—
240C22×C8—611no—
241C22×C8—611no—
242#124—611no—
243#124—1221no—
244#124C2×D6111yescharacteristic
245#123—21no—
246C22⋊Q8—611no—
247C22⋊Q8—1221no—
248C22⋊Q8C2×D6111yescharacteristic
249#121—21no—
250#121—611no—
251#121—1221no—
252#121C2×D6111yescharacteristic
253#120—21no—
254C4×Q8—611no—
255C4×D4—1221no—
256C4×D4C2×D6111yescharacteristic
257C4×D4C2×D6111yescharacteristic
258C2×C22⋊C4—21no—
259#106—611no—
260C4⋊C8—611no—
261#103—611no—
262#103—611no—
263#103—611no—
264#102—611no—
265#102—611no—
266#102—611no—
267C22⋊C8—611no—
268C22⋊C8—611no—
269C4×C8—611no—
270C24—21no—
271#41—22no—
272#41—41no—
273#41—1222no—
274#41—2441no—
275C2×Q8—611no—
276C2×Q8—611no—
277C2×Q8—1222no—
278C2×Q8—1221no—
279C2×Q8—2441no—
280C2×Q8C22×D6111yescharacteristic
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—611no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4C22⋊D6111yescharacteristic
290C2×D4C22×D6111yescharacteristic
291C2×D4C22×D6111yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4C22×D6111yescharacteristic
297C22×C4C22×D6111yescharacteristic
298Q16—1222no—
299Q16—2441no—
300SD16—614no—
301SD16—1222no—
302SD16—1222no—
303SD16—1222no—
304SD16—1222no—
305D8—1222no—
306D8—2441no—
307C2×C8—611no—
308C2×C8—611no—
309C2×C8—611no—
310C2×C8—611no—
311C2×C8—1222no—
312C2×C8—1222no—
313C4⋊C4—21no—
314C4⋊C4—611no—
315C4⋊C4—1221no—
316C4⋊C4—1221no—
317C4⋊C4C22⋊D6111yescharacteristic
318C4⋊C4C22×D6111yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C22⋊C4C22⋊D6111yescharacteristic
329C22⋊C4C22⋊D6111yescharacteristic
330C42—1221no—
331C42C22×D6111yescharacteristic
332C23—21no—
333C23—21no—
334C23—42no—
335C23—42no—
336C23—81no—
337C23—1221no—
338C23C2×C22⋊D6111yescharacteristic
339C23C2×C22⋊D6111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—612no—
343Q8—1221no—
344Q8—1221no—
345Q8—1221no—
346Q8—2442no—
347D4—22no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—42no—
353D4—81no—
354D4—1221no—
355D4—1221no—
356D4—2442no—
357D4—2442no—
358D4D4×D6112yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—81no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—2442no—
371C2×C4—2442no—
372C2×C4C2×C22⋊D6111yescharacteristic
373C2×C4C2×C22⋊D6111yescharacteristic
374C2×C4C2×C22⋊D6111yescharacteristic
375C2×C4C2×C22⋊D6111yescharacteristic
376C2×C4C23×D6111yescharacteristic
377C8—612no—
378C8—1221no—
379C8—1221no—
380C8—1221no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—22no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—84no—
393C22—2441no—
394C22—2441no—
395C22—2441no—
396C22#1451979712yescomplemented
397C22C22×C22⋊D6111yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—1222no—
405C4—2441no—
406C4—2441no—
407C4C2×D4×D6111yescharacteristic
408C4#1451982211yescharacteristic
409C2—22no—
410C2—41no—
411C2—42no—
412C2—81no—
413C2—4881no—
414C2D4×C22⋊D6111yescharacteristic
415C2C2×#1451979711yescharacteristic
416C2#1684057311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#546C2
socleC22×C61C22×D4
hypercenter#546D61
hypocenterC61#3282
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#14519797C2semidirect
2. C22×#11758200C2semidirect
3. #16840421C2semidirect
4. #16840144C2semidirect
5. #16839993C2semidirect
6. #16839989C2semidirect
7. #16839981C2semidirect
8. #16839977C2semidirect
9. #16839924C2semidirect
10. #16839917C2semidirect
11. #16839905C2semidirect
12. #16839896C2semidirect
13. C4×#11758200C2semidirect
14. D4×#92418C2semidirect
15. C61×#546C2semidirect
16. C2×#11758222C22semidirect
19. C2×#11758202C22semidirect
20. C2×#11758202C22semidirect
26. C2×#11758201C22semidirect
30. C22×#92418C22semidirect
31. #14519765C22semidirect
33. #14519756C22semidirect
37. C4×Dic122C22semidirect
39. #14519708C22semidirect
40. C4⋊#92418C22semidirect
41. #14519701C22semidirect
42. #14519700C22semidirect
43. #14519700C22semidirect
46. #14519697C22semidirect
48. C22⋊#92418C22semidirect
49. C4×#92418C22semidirect
107. #11758200D4semidirect
184. C22×C61#135semidirect
212. #546D61semidirect
224. C61#3282semidirect
396. C22#14519797semidirect