Finite Group Databasebeta

← #21455551

Subgroups — #21455551

Order 7808.

446 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840558C211yesmaximal, characteristic
2C2×#14519806C211yesmaximal, characteristic, complemented
3#137×D61C211yesmaximal, characteristic, complemented
4#16840527C211yesmaximal, characteristic, complemented
5#16840038C211yesmaximal, characteristic, complemented
6#16840037C211yesmaximal, characteristic, complemented
7#16840036C211yesmaximal, characteristic, complemented
8#16840035C211yesmaximal, characteristic, complemented
9#16840024C211yesmaximal, characteristic, complemented
10#16840023C211yesmaximal, characteristic, complemented
11#16840022C211yesmaximal, characteristic, complemented
12#16839809C211yesmaximal, characteristic, complemented
13#16839743C211yesmaximal, characteristic, complemented
14#101×D61C211yesmaximal, characteristic, complemented
15C61×#471C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17#41×D61C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19#14519810C2211yescharacteristic
20#14519810C2211yescharacteristic
21#14519809—21no—
22#14519808C2211yescharacteristic
23#14519807C2211yescharacteristic
24#14519807C2211yescharacteristic
25#14519806—21no—
26#14519806—21no—
27#14519806—21no—
28#14519806—21no—
29#14519806—21no—
30#14519806—21no—
31#14519803C2211yescharacteristic
32#14519801—21no—
33#14519798—21no—
34#14519796—21no—
35C2×Dic244C2211yescharacteristic, complemented
36C2×#11758202C2211yescharacteristic, complemented
37Q16×D61—21no—
38C2×#11758200C2211yescharacteristic, complemented
39SD16×D61—21no—
40#14519785—21no—
41#14519785C2211yescharacteristic
42#14519784C2211yescharacteristic
43#14519783—21no—
44#14519783C2211yescharacteristic
45C2×#11758189—21no—
46C2×#11758189C2211yescharacteristic
47M16×D61—21no—
48M16×D61C2211yescharacteristic
49M16×D61C2211yescharacteristic
50M16×D61C2211yescharacteristic
51#14519713C2211yescharacteristic, complemented
52#14519712C2211yescharacteristic, complemented
53#14519712C2211yescharacteristic, complemented
54#14519696C2211yescharacteristic, complemented
55#14519695C2211yescharacteristic, complemented
56#14519695C2211yescharacteristic, complemented
57#14519695C2211yescharacteristic, complemented
58#14519695C2211yescharacteristic, complemented
59#14519694C2211yescharacteristic, complemented
60#137×C61C2211yescharacteristic
61AGL(1,ℤ/8)×C61C2211yescharacteristic
62C2×SD16×C61C2211yescharacteristic, complemented
63#131×C61C2211yescharacteristic
64#108×C61C2211yescharacteristic, complemented
65#101×C61C2211yescharacteristic, complemented
66#100×C61C2211yescharacteristic, complemented
67#41×C61C2311yescharacteristic
68C2×Q8×C61C2311yescharacteristic
69C2×D4×C61C2311yescharacteristic
70C2×C22⋊D61—21no—
71C22×Dic61—21no—
72#11758226D411yescharacteristic
73Q8×D61—21no—
74Q8×D61—21no—
75Q8×D61—21no—
76Q8×D61—21no—
77Q8×D61D411yescharacteristic
78#11758224—21no—
79#11758224—21no—
80#11758224—21no—
81#11758224—21no—
82#11758224—21no—
83#11758224D411yescharacteristic
84D4×D61—21no—
85D4×D61D411yescharacteristic
86#11758222—21no—
87#11758222C2311yescharacteristic
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61C2311yescharacteristic
91C2×Dic122—21no—
92C2×Dic122C2311yescharacteristic
93C2×Dic122C2311yescharacteristic
94Q16×C61—21no—
95SD16×C61—21no—
96SD16×C61—21no—
97SD16×C61—21no—
98SD16×C61—21no—
99D8×C61—21no—
100M16×C61—21no—
101M16×C61C2311yescharacteristic
102M16×C61C2311yescharacteristic
103M16×C61C2311yescharacteristic
104C2×C8×C61—21no—
105C2×C8×C61C2311yescharacteristic
106#11758202—21no—
107#11758202—21no—
108#11758202—21no—
109#11758202—21no—
110#11758202—21no—
111#11758201—21no—
112#11758200—21no—
113#11758200—21no—
114#11758200—21no—
115#11758200—21no—
116#11758200—21no—
117#11758199—21no—
118#11758194—21no—
119#11758194C2311yescharacteristic
120#11758194C2311yescharacteristic
121#11758194C2311yescharacteristic
122C2×#92418—21no—
123C2×#92418C2311yescharacteristic
124Dic244—21no—
125Dic244—21no—
126Dic244—21no—
127Dic244—21no—
128#11758190—21no—
129#11758190—21no—
130#11758189—21no—
131#11758189—21no—
132#11758189—21no—
133#11758189—21no—
134#11758189—21no—
135#11758189D411yescharacteristic
136#11758189D411yescharacteristic
137#11758189D411yescharacteristic
138#11758189D411yescharacteristic
139C8×D61—21no—
140C8×D61—21no—
141C8×D61—21no—
142C8×D61—21no—
143C8×D61—21no—
144C23×C61—21no—
145C22×D61—21no—
146C22×D61#4111yescharacteristic
147Q8×C61—21no—
148Q8×C61—21no—
149Q8×C61C2×D411yescharacteristic
150D4×C61—21no—
151D4×C61—21no—
152D4×C61—21no—
153D4×C61C2×D411yescharacteristic
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61C2411yescharacteristic
157C22⋊D61—21no—
158C22⋊D61—21no—
159C22⋊D61—21no—
160C22⋊D61—41no—
161C22⋊D61—41no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61#4111yescharacteristic
168D244—21no—
169D244C2×D411yescharacteristic
170C4×D61—21no—
171C4×D61—21no—
172C4×D61—21no—
173C4×D61—41no—
174C4×D61—41no—
175C4×D61C2×D411yescharacteristic
176C4×D61C2×D411yescharacteristic
177C4×D61C2×D411yescharacteristic
178C4×D61C2×D411yescharacteristic
179Dic122—21no—
180Dic122—21no—
181Dic122—21no—
182Dic122—21no—
183Dic122—21no—
184Dic122—41no—
185Dic122—41no—
186Dic122C2×D411yescharacteristic
187C8×C61—21no—
188C8×C61—21no—
189C8×C61—21no—
190C8×C61C2×D411yescharacteristic
191C8×C61C2×D411yescharacteristic
192#92418—21no—
193#92418—21no—
194#92418—21no—
195#92418C2×D411yescharacteristic
196#92418C2×D411yescharacteristic
197C22×C61—21no—
198C22×C61—41no—
199C22×C61—81no—
200C22×C61C2×#4111yescharacteristic
201C2×D61—21no—
202C2×D61—41no—
203C2×D61—81no—
204C2×D61#12111yescharacteristic
205C2×D61#12111yescharacteristic
206C4×C61—21no—
207C4×C61—41no—
208C4×C61C22×D411yescharacteristic
209C4×C61C22×D411yescharacteristic
210Dic61—21no—
211Dic61—41no—
212Dic61—41no—
213Dic61#12111yescharacteristic
214Dic61#12111yescharacteristic
215#3069—611nomaximal, Sylow
216C2×C61—21no—
217C2×C61—41no—
218C2×C61—81no—
219C2×C61C2×#12111yescharacteristic
220D61—21no—
221D61—21no—
222D61—41no—
223#575—611no—
224C2×#137—611no—
225C2×#137—611no—
226#568—611no—
227#473—611no—
228#473—611no—
229#473—611no—
230#473—611no—
231#471—611no—
232#471—611no—
233#471—611no—
234#471D6111yescharacteristic, complemented
235#430—611no—
236#413—611no—
237C2×#101—611no—
238C61#306911yescharacteristic, complemented, Sylow
239C2×#41—611no—
240C2×#41—611no—
241C22×Q8—611no—
242#137—611no—
243#137—611no—
244#137—611no—
245#137—611no—
246#137—611no—
247#137—1221no—
248#137—1221no—
249#137—1221no—
250#137—1221no—
251#137—1221no—
252#137—1221no—
253#137—1221no—
254#137C2×D6111yescharacteristic
255AGL(1,ℤ/8)—611no—
256AGL(1,ℤ/8)—1221no—
257AGL(1,ℤ/8)C2×D6111yescharacteristic
258#135—1221no—
259#135—1221no—
260C2×Q16—611no—
261C2×Q16—611no—
262C2×Q16—1221no—
263C2×SD16—611no—
264C2×SD16—1221no—
265C2×SD16C2×D6111yescharacteristic, complemented
266#131—611no—
267#131—611no—
268#131—611no—
269#131—1221no—
270#131—1221no—
271#131C2×D6111yescharacteristic
272C2×M16—611no—
273C2×M16—611no—
274C2×M16—611no—
275C2×M16—611no—
276C2×M16—1221no—
277C2×M16—1221no—
278#108—611no—
279#108—611no—
280#108—611no—
281#108C2×D6111yescharacteristic, complemented
282#101—611no—
283#101—611no—
284#101—611no—
285#101—611no—
286#101—611no—
287#101C2×D6111yescharacteristic, complemented
288#100—611no—
289#100C2×D6111yescharacteristic, complemented
290#41—611no—
291#41—611no—
292#41—611no—
293#41—1221no—
294#41—1221no—
295#41—1221no—
296#41—1221no—
297#41—1221no—
298#41—1221no—
299#41C22×D6111yescharacteristic
300C2×Q8—611no—
301C2×Q8—611no—
302C2×Q8—611no—
303C2×Q8—1221no—
304C2×Q8—1221no—
305C2×Q8—1221no—
306C2×Q8—1221no—
307C2×Q8—1221no—
308C2×Q8C22×D6111yescharacteristic
309C2×D4—611no—
310C2×D4—1221no—
311C2×D4—1221no—
312C2×D4C22×D6111yescharacteristic
313C22×C4—611no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—1221no—
317Q16—21no—
318Q16—1221no—
319Q16—1221no—
320Q16—1221no—
321Q16—1221no—
322Q16—1221no—
323Q16—1221no—
324Q16—1221no—
325Q16—1221no—
326Q16—1221no—
327SD16—21no—
328SD16—21no—
329SD16—21no—
330SD16—21no—
331SD16—1221no—
332SD16—1221no—
333SD16—1221no—
334SD16—1221no—
335SD16—1221no—
336SD16—1221no—
337SD16—1221no—
338SD16—1221no—
339D8—21no—
340D8—1221no—
341M16—21no—
342M16—611no—
343M16—611no—
344M16—611no—
345M16—611no—
346M16—611no—
347M16—611no—
348M16—611no—
349M16—1221no—
350M16—1221no—
351M16—1221no—
352M16—1221no—
353M16—1221no—
354M16—1221no—
355M16C22×D6111yescharacteristic
356M16C22×D6111yescharacteristic
357M16C22×D6111yescharacteristic
358C2×C8—21no—
359C2×C8—611no—
360C2×C8—1221no—
361C2×C8—1221no—
362C2×C8—1221no—
363C2×C8—1221no—
364C2×C8—1221no—
365C2×C8—1221no—
366C2×C8C22×D6111yescharacteristic
367C23—21no—
368C23—611no—
369C23—1221no—
370Q8—21no—
371Q8—21no—
372Q8—611no—
373Q8—1221no—
374Q8—1221no—
375Q8—1221no—
376Q8—1221no—
377Q8—1221no—
378Q8—2441no—
379Q8—2441no—
380Q8D4×D6111yescharacteristic
381D4—21no—
382D4—21no—
383D4—21no—
384D4—611no—
385D4—1221no—
386D4—1221no—
387D4—1221no—
388D4—1221no—
389D4—2441no—
390D4—2441no—
391D4D4×D6111yescharacteristic
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—611no—
395C2×C4—611no—
396C2×C4—611no—
397C2×C4—611no—
398C2×C4—611no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4C23×D6111yescharacteristic
410C8—21no—
411C8—21no—
412C8—21no—
413C8—611no—
414C8—611no—
415C8—1221no—
416C8—1221no—
417C8—1221no—
418C8D4×D6111yescharacteristic
419C8D4×D6111yescharacteristic
420C22—21no—
421C22—41no—
422C22—81no—
423C22—611no—
424C22—611no—
425C22—1221no—
426C22—4881no—
427C22—2441no—
428C22#41×D6111yescharacteristic
429C4—21no—
430C4—41no—
431C4—611no—
432C4—611no—
433C4—1221no—
434C4—2441no—
435C4—2441no—
436C4C2×D4×D6111yescharacteristic
437C4C2×D4×D6111yescharacteristic
438C2—21no—
439C2—41no—
440C2—81no—
441C2—1221no—
442C2—1221no—
443C2—2441no—
444C2#121×D6111yescharacteristic
subgroupG/H
centerC2#121×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#471C2
socleC2×C61C2×#121
hypercenter#471D61
hypocenterC61#3069
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
2. C2×#14519806C2semidirect
3. #137×D61C2semidirect
4. #16840527C2semidirect
5. #16840038C2semidirect
6. #16840037C2semidirect
7. #16840036C2semidirect
8. #16840035C2semidirect
9. #16840024C2semidirect
10. #16840023C2semidirect
11. #16840022C2semidirect
12. #16839809C2semidirect
13. #16839743C2semidirect
14. #101×D61C2semidirect
15. C61×#471C2semidirect
35. C2×Dic244C22semidirect
36. C2×#11758202C22semidirect
38. C2×#11758200C22semidirect
51. #14519713C22semidirect
52. #14519712C22semidirect
53. #14519712C22semidirect
54. #14519696C22semidirect
55. #14519695C22semidirect
56. #14519695C22semidirect
57. #14519695C22semidirect
58. #14519695C22semidirect
59. #14519694C22semidirect
62. C2×SD16×C61C22semidirect
64. #108×C61C22semidirect
65. #101×C61C22semidirect
66. #100×C61C22semidirect
234. #471D61semidirect
238. C61#3069semidirect
265. C2×SD16C2×D61semidirect
281. #108C2×D61semidirect
287. #101C2×D61semidirect
289. #100C2×D61semidirect