Finite Group Databasebeta

← #21455040

Subgroups — #21455040

Order 7808.

764 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D61C211yesmaximal, characteristic, complemented
2C2×#14519800C211yesmaximal, characteristic, complemented
3C2×#14519798C211yesmaximal, characteristic, complemented
4#16840275C211yesmaximal, characteristic, complemented
5#16839922C211yesmaximal, characteristic, complemented
6#16839916C211yesmaximal, characteristic, complemented
7#16839911C211yesmaximal, characteristic, complemented
8#16839909C211yesmaximal, characteristic, complemented
9#16839907C211yesmaximal, characteristic, complemented
10#16839902C211yesmaximal, characteristic, complemented
11#16839897C211yesmaximal, characteristic, complemented
12#16839757C211yesmaximal, characteristic, complemented
13#16839755C211yesmaximal, characteristic, complemented
14C22⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#452C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758226C2211yescharacteristic, complemented
18C2×#11758222—21no—
19C2×#11758222C2211yescharacteristic
20C2×#11758224—21no—
21C2×#11758224C2211yescharacteristic
22#41×D61—24no—
23#41×D61—24no—
24C2×Q8×D61C2211yescharacteristic
25C2×D4×D61—21no—
26C2×D4×D61C2211yescharacteristic
27C22×C4×D61—21no—
28C22×C4×D61C2211yescharacteristic
29#14519800—24no—
30#14519798—24no—
31C2×#11758202C2211yescharacteristic, complemented
32C2×#11758190C2211yescharacteristic, complemented
33C2×#11758201C2211yescharacteristic, complemented
34C2×#11758201C2211yescharacteristic, complemented
35C2×D488C2211yescharacteristic, complemented
36C2×#11758199C2211yescharacteristic, complemented
37C2×C8×D61C2211yescharacteristic, complemented
38C2×C8×D61C2211yescharacteristic, complemented
39#14519762—21no—
40#14519753C2211yescharacteristic
41#14519752C2211yescharacteristic
42#14519751C2211yescharacteristic, complemented
43#14519747—21no—
44#14519739—21no—
45#14519737—21no—
46#14519735C2211yescharacteristic, complemented
47#14519702C2211yescharacteristic, complemented
48#14519701C2211yescharacteristic, complemented
49#14519700C2211yescharacteristic, complemented
50#14519699C2211yescharacteristic, complemented
51#14519698C2211yescharacteristic, complemented
52#14519697C2211yescharacteristic, complemented
53C22⋊#92418C2211yescharacteristic, complemented
54#14519689C2211yescharacteristic
55#14519689C2211yescharacteristic
56C2×#41×C61C2211yescharacteristic
57C2×Q16×C61C2211yescharacteristic, complemented
58C2×SD16×C61C2211yescharacteristic, complemented
59C22⋊Q8×C61C2211yescharacteristic, complemented
60#103×C61C2211yescharacteristic, complemented
61#102×C61C2211yescharacteristic, complemented
62C22⋊C8×C61C2211yescharacteristic, complemented
63C23×D61—21no—
64C23×D61D411yescharacteristic
65#41×C61—22no—
66#41×C61—22no—
67C2×Q8×C61C2311yescharacteristic
68C2×Q8×C61C2311yescharacteristic
69C2×D4×C61—21no—
70C2×D4×C61C2311yescharacteristic
71C22×C4×C61—21no—
72C22×C4×C61C2311yescharacteristic
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C2×C22⋊D61—21no—
77C22×Dic61—21no—
78C22×Dic61D411yescharacteristic
79#11758226—22no—
80#11758226—22no—
81#11758226—22no—
82#11758226D414yescomplemented
83Q8×D61—22no—
84Q8×D61—22no—
85#11758224—28no—
86#11758224—22no—
87#11758224D414yescomplemented
88D4×D61—28no—
89D4×D61—22no—
90D4×D61—22no—
91#11758222—28no—
92#11758222—22no—
93#11758222—22no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—21no—
97C2×D244C2311yescharacteristic
98C2×D244C2311yescharacteristic
99C2×C4×D61—28no—
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—22no—
104C2×C4×D61—22no—
105C2×C4×D61—21no—
106C2×C4×D61D411yescharacteristic
107C2×C4×D61D411yescharacteristic
108C2×C4×D61C2311yescharacteristic
109C2×C4×D61C2311yescharacteristic
110C2×Dic122—21no—
111C2×Dic122C2311yescharacteristic
112Q16×C61—22no—
113SD16×C61—22no—
114C2×C8×C61C2311yescharacteristic
115C2×C8×C61C2311yescharacteristic
116C4⋊C4×C61—21no—
117C4⋊C4×C61C2311yescharacteristic
118C22⋊C4×C61—21no—
119#11758202—22no—
120#11758201—22no—
121#11758201—22no—
122#11758199—22no—
123#11758198—21no—
124#11758198—21no—
125#11758198—21no—
126#11758198—21no—
127C4⋊Dic61C2311yescharacteristic
128#11758196—21no—
129C4×Dic61—21no—
130C2×#92418C2311yescharacteristic
131C2×#92418C2311yescharacteristic
132D488—22no—
133#11758190—22no—
134C8×D61—22no—
135C8×D61—22no—
136C23×C61—21no—
137C23×C61C2×D411yescharacteristic
138C22×D61—24no—
139C22×D61—21no—
140C22×D61—22no—
141C22×D61—22no—
142C22×D61—21no—
143C22×D61—41no—
144C22×D61—42no—
145C22×D61—42no—
146C22×D61C2×D411yescharacteristic
147C22×D61C2×D411yescharacteristic
148Q8×C61—21no—
149Q8×C61—21no—
150Q8×C61—21no—
151Q8×C61C2×D412yes—
152D4×C61—24no—
153D4×C61—21no—
154D4×C61C2×D412yes—
155C2×C4×C61—24no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61C2×D411yescharacteristic
162C2×C4×C61C2411yescharacteristic
163C22⋊D61—24no—
164C22⋊D61—24no—
165C22⋊D61—24no—
166C22⋊D61—42no—
167C2×Dic61—21no—
168C2×Dic61—22no—
169C2×Dic61—24no—
170C2×Dic61—21no—
171C2×Dic61C2×D411yescharacteristic
172C2×Dic61C2×D411yescharacteristic
173D244—24no—
174D244—21no—
175D244—21no—
176D244—21no—
177D244—42no—
178D244—42no—
179D244C2×D412yes—
180C4×D61—24no—
181C4×D61—24no—
182C4×D61—22no—
183C4×D61—21no—
184C4×D61—21no—
185C4×D61—22no—
186C4×D61—24no—
187C4×D61—42no—
188C4×D61C2×D412yes—
189C4×D61C2×D412yes—
190Dic122—24no—
191Dic122—21no—
192Dic122C2×D412yes—
193C8×C61—21no—
194C8×C61—21no—
195#92418—21no—
196#92418—21no—
197C22×C61—21no—
198C22×C61—22no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61C22×D411yescharacteristic
204C2×D61—21no—
205C2×D61—21no—
206C2×D61—21no—
207C2×D61—21no—
208C2×D61—22no—
209C2×D61—44no—
210C2×D61—48no—
211C2×D61—41no—
212C2×D61—41no—
213C2×D61—41no—
214C2×D61—41no—
215C2×D61—41no—
216C2×D61#12012yes—
217C2×D61#13512yescomplemented
218C4×C61—22no—
219C4×C61—21no—
220C4×C61—41no—
221C4×C61—41no—
222C4×C61C22×D411yescharacteristic
223C4×C61C22×D411yescharacteristic
224Dic61—21no—
225Dic61—22no—
226Dic61—41no—
227Dic61#12012yes—
228#3002—611nomaximal, Sylow
229C2×C61—41no—
230C2×C61—42no—
231C2×C61C2×#12011yescharacteristic
232C2×C61C2×#13511yescharacteristic
233C2×C61#57511yescharacteristic
234D61—22no—
235D61—22no—
236D61—42no—
237D61—81no—
238C22×#41—611no—
239C2×#135—611no—
240C2×#135—611no—
241#525—611no—
242#452—611no—
243#452D6111yescharacteristic, complemented
244#451—611no—
245#450—611no—
246#449—611no—
247#449—611no—
248#448—611no—
249#447—611no—
250#416—611no—
251#416—611no—
252C2×C22⋊C8—611no—
253C61#300211yescharacteristic, complemented, Sylow
254C2×#41—611no—
255C2×#41—611no—
256C2×#41—611no—
257C2×#41—611no—
258C2×#41—1221no—
259C2×#41—1221no—
260C2×#41—1224no—
261C2×#41—1224no—
262C2×#41C2×D6111yescharacteristic
263C22×Q8—611no—
264C22×D4—611no—
265C22×D4—1221no—
266C23×C4—611no—
267C23×C4—1221no—
268#135—1224no—
269#135—1224no—
270C2×Q16—611no—
271C2×Q16C2×D6111yescharacteristic, complemented
272C2×SD16—611no—
273C2×SD16—611no—
274C2×SD16—611no—
275C2×SD16C2×D6111yescharacteristic, complemented
276C2×D8—611no—
277C2×D8—611no—
278C22×C8—611no—
279C22×C8—611no—
280#123—1221no—
281C22⋊Q8—611no—
282C22⋊Q8C2×D6111yescharacteristic, complemented
283#121—611no—
284#121—611no—
285#120—1221no—
286C4×D4—1221no—
287C4×D4—1221no—
288#117—611no—
289#103—611no—
290#103—611no—
291#103—611no—
292#103C2×D6111yescharacteristic, complemented
293#102—611no—
294#102—611no—
295#102—611no—
296#102C2×D6111yescharacteristic, complemented
297C22⋊C8—611no—
298C22⋊C8—611no—
299C22⋊C8—611no—
300C22⋊C8C2×D6111yescharacteristic, complemented
301C24—611no—
302C24—1221no—
303#41—22no—
304#41—22no—
305#41—614no—
306#41—614no—
307#41—1222no—
308#41—1222no—
309#41—1228no—
310#41—1222no—
311#41—1222no—
312#41—1222no—
313#41—1222no—
314#41—1228no—
315C2×Q8—611no—
316C2×Q8—1221no—
317C2×Q8—1222no—
318C2×Q8—1222no—
319C2×Q8C22×D6111yescharacteristic
320C2×Q8C22×D6111yescharacteristic
321C2×D4—21no—
322C2×D4—611no—
323C2×D4—611no—
324C2×D4—1221no—
325C2×D4—1221no—
326C2×D4—1221no—
327C2×D4—1221no—
328C2×D4—1222no—
329C2×D4—1228no—
330C2×D4—1221no—
331C2×D4—1221no—
332C2×D4—1222no—
333C2×D4—1221no—
334C2×D4C22×D6111yescharacteristic
335C22×C4—21no—
336C22×C4—611no—
337C22×C4—611no—
338C22×C4—611no—
339C22×C4—611no—
340C22×C4—611no—
341C22×C4—1222no—
342C22×C4—1222no—
343C22×C4—1221no—
344C22×C4—1221no—
345C22×C4—1221no—
346C22×C4—1228no—
347C22×C4—1221no—
348C22×C4—1221no—
349C22×C4C22×D6111yescharacteristic
350Q16—22no—
351Q16—1222no—
352SD16—22no—
353SD16—1222no—
354SD16—1222no—
355SD16—1222no—
356D8—1222no—
357D8—1222no—
358C2×C8—611no—
359C2×C8—611no—
360C2×C8—1222no—
361C2×C8—1222no—
362C2×C8C22×D6111yescharacteristic
363C2×C8C22×D6111yescharacteristic
364C4⋊C4—21no—
365C4⋊C4—611no—
366C4⋊C4—1221no—
367C4⋊C4C22×D6111yescharacteristic
368C22⋊C4—21no—
369C22⋊C4—1221no—
370C22⋊C4—1221no—
371C22⋊C4—1221no—
372C22⋊C4—1221no—
373C42—1221no—
374C23—21no—
375C23—611no—
376C23—611no—
377C23—1222no—
378C23—1222no—
379C23—1224no—
380C23—1221no—
381C23—1221no—
382C23—2441no—
383C23—2442no—
384C23—2442no—
385C23D4×D6111yescharacteristic
386Q8—21no—
387Q8—21no—
388Q8—21no—
389Q8—612no—
390Q8—1224no—
391Q8—1221no—
392Q8D4×D6112yes—
393D4—24no—
394D4—21no—
395D4—612no—
396D4—1224no—
397D4—1224no—
398D4—1224no—
399D4—1224no—
400D4—1221no—
401D4—1221no—
402D4—1221no—
403D4—2442no—
404D4—2442no—
405D4—2442no—
406D4D4×D6112yes—
407C2×C4—24no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—611no—
414C2×C4—612no—
415C2×C4—612no—
416C2×C4—611no—
417C2×C4—1222no—
418C2×C4—1224no—
419C2×C4—1222no—
420C2×C4—1224no—
421C2×C4—1224no—
422C2×C4—1222no—
423C2×C4—1224no—
424C2×C4—1221no—
425C2×C4—1221no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—2442no—
429C2×C4D4×D6111yescharacteristic
430C2×C4C23×D6111yescharacteristic
431C8—21no—
432C8—21no—
433C8—1221no—
434C8—1221no—
435C22—21no—
436C22—22no—
437C22—21no—
438C22—21no—
439C22—41no—
440C22—41no—
441C22—612no—
442C22—612no—
443C22—1221no—
444C22—1221no—
445C22—1221no—
446C22—1221no—
447C22—1222no—
448C22—2444no—
449C22—2448no—
450C22—2441no—
451C22—2441no—
452C22—2441no—
453C22—2441no—
454C22—2441no—
455C22C2×D4×D6111yescharacteristic
456C4—21no—
457C4—22no—
458C4—41no—
459C4—41no—
460C4—612no—
461C4—1221no—
462C4—1222no—
463C4—2441no—
464C4C2×D4×D6111yescharacteristic
465C4C2×D4×D6111yescharacteristic
466C2—41no—
467C2—42no—
468C2—1222no—
469C2—1222no—
470C2—4881no—
471C2—2442no—
472C2#120×D6111yescharacteristic
473C2#135×D6111yescharacteristic
474C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#452C2
socleC22×C61C22×D4
hypercenter#452D61
hypocenterC61#3002
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#41×D61C2semidirect
2. C2×#14519800C2semidirect
3. C2×#14519798C2semidirect
4. #16840275C2semidirect
5. #16839922C2semidirect
6. #16839916C2semidirect
7. #16839911C2semidirect
8. #16839909C2semidirect
9. #16839907C2semidirect
10. #16839902C2semidirect
11. #16839897C2semidirect
12. #16839757C2semidirect
13. #16839755C2semidirect
14. C22⋊C8×D61C2semidirect
15. C61×#452C2semidirect
17. C2×#11758226C22semidirect
31. C2×#11758202C22semidirect
32. C2×#11758190C22semidirect
33. C2×#11758201C22semidirect
34. C2×#11758201C22semidirect
35. C2×D488C22semidirect
36. C2×#11758199C22semidirect
37. C2×C8×D61C22semidirect
38. C2×C8×D61C22semidirect
42. #14519751C22semidirect
46. #14519735C22semidirect
47. #14519702C22semidirect
48. #14519701C22semidirect
49. #14519700C22semidirect
50. #14519699C22semidirect
51. #14519698C22semidirect
52. #14519697C22semidirect
53. C22⋊#92418C22semidirect
57. C2×Q16×C61C22semidirect
58. C2×SD16×C61C22semidirect
59. C22⋊Q8×C61C22semidirect
60. #103×C61C22semidirect
61. #102×C61C22semidirect
62. C22⋊C8×C61C22semidirect
82. #11758226D4semidirect
87. #11758224D4semidirect
217. C2×D61#135semidirect
243. #452D61semidirect
253. C61#3002semidirect
271. C2×Q16C2×D61semidirect
275. C2×SD16C2×D61semidirect
282. C22⋊Q8C2×D61semidirect
292. #103C2×D61semidirect
296. #102C2×D61semidirect
300. C22⋊C8C2×D61semidirect