Finite Group Databasebeta

← #23766243

Subgroups — #23766243

Order 10112.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579118C211yesmaximal, characteristic, complemented
2C22×(C2×D79)⋊C4C211yesmaximal, characteristic
3C2×C22⋊C4×D79C211yesmaximal, characteristic
4#19098454C211yesmaximal, characteristic, complemented
5#19098454C211yesmaximal, characteristic, complemented
6#19098452C211yesmaximal, characteristic, complemented
7#19098452C211yesmaximal, characteristic, complemented
8#19098436C211yesmaximal, characteristic, complemented
9#19098435C211yesmaximal, characteristic, complemented
10#19098425C211yesmaximal, characteristic, complemented
11#19098422C211yesmaximal, characteristic, complemented
12#19098418C211yesmaximal, characteristic
13C22⋊C4×Dic79C211yesmaximal, characteristic, complemented
14C4×(C2×D79)⋊C4C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C79C211yesmaximal, characteristic, complemented
16C24×D79C2211yescharacteristic
17C23×Dic79C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20#14579118—24no—
21C2×Dic79⋊C4C2211yescharacteristic, complemented
22C2×Dic79⋊C4C2211yescharacteristic, complemented
23C2×Dic79⋊C4C2211yescharacteristic, complemented
24C2×Dic79⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic79C2211yescharacteristic
26C2×C22⋊Dic79C2211yescharacteristic
27C2×(C2×D79)⋊C4—24no—
28C2×(C2×D79)⋊C4C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×(C2×D79)⋊C4C2211yescharacteristic
35C2×(C2×D79)⋊C4C2211yescharacteristic
36C2×(C2×D79)⋊C4C2211yescharacteristic
37C2×(C2×D79)⋊C4C2211yescharacteristic
38C22⋊C4×D79C418yescomplemented
39C2×C4×Dic79C2211yescharacteristic, complemented
40C2×C4×Dic79C2211yescharacteristic, complemented
41C79⋊#95C2211yescharacteristic, complemented
42C79⋊#95C2211yescharacteristic, complemented
43C79⋊#95C2211yescharacteristic, complemented
44C79⋊#95C2211yescharacteristic, complemented
45C79⋊#95C2211yescharacteristic, complemented
46C79⋊#95C2211yescharacteristic, complemented
47C23×C4×C79C2211yescharacteristic
48C2×C22⋊C4×C79C2211yescharacteristic
49C2×C22⋊C4×C79C2211yescharacteristic
50C2×C42×C79C2211yescharacteristic, complemented
51C2×C42×C79C2211yescharacteristic, complemented
52#95×C79C2211yescharacteristic, complemented
53#95×C79C2211yescharacteristic, complemented
54C23×D79—22no—
55C23×D79—22no—
56C23×D79—22no—
57C23×D79—22no—
58C23×D79—41no—
59C23×D79—41no—
60C23×D79C2×C414yes—
61C23×D79C2311yescharacteristic
62C23×D79C2311yescharacteristic
63C22×Dic79—22no—
64C22×Dic79—22no—
65C22×Dic79—41no—
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C22×Dic79C2311yescharacteristic
69C22×Dic79C2311yescharacteristic
70C22×Dic79C2311yescharacteristic
71C22×Dic79C2311yescharacteristic
72C2×C4×D79—22no—
73C2×C4×D79—22no—
74C2×C4×D79—41no—
75C2×C4×D79—41no—
76C2×C4×D79C2×C414yescomplemented
77C2×C4×D79C2×C414yescomplemented
78Dic79⋊C4—22no—
79Dic79⋊C4—22no—
80Dic79⋊C4—41no—
81Dic79⋊C4—41no—
82C22⋊Dic79—22no—
83C22⋊Dic79C2×C414yes—
84(C2×D79)⋊C4—22no—
85(C2×D79)⋊C4—22no—
86(C2×D79)⋊C4—22no—
87(C2×D79)⋊C4—22no—
88(C2×D79)⋊C4—22no—
89(C2×D79)⋊C4—41no—
90(C2×D79)⋊C4—41no—
91(C2×D79)⋊C4C2×C414yescomplemented
92(C2×D79)⋊C4C2×C414yescomplemented
93(C2×D79)⋊C4D414yes—
94C4×Dic79—22no—
95C4×Dic79—41no—
96C24×C79C2311yescharacteristic
97C22×C4×C79—22no—
98C22×C4×C79—22no—
99C22×C4×C79—41no—
100C22×C4×C79C2311yescharacteristic
101C22×C4×C79C2311yescharacteristic
102C22×C4×C79C2311yescharacteristic
103C22×C4×C79C2311yescharacteristic
104C22×C4×C79C2311yescharacteristic
105C22×C4×C79C2311yescharacteristic
106C22⋊C4×C79—22no—
107C22⋊C4×C79C2×C414yes—
108C42×C79—22no—
109C42×C79—41no—
110C23×C79—21no—
111C23×C79—21no—
112C23×C79—21no—
113C23×C79—21no—
114C23×C79C22×C412yes—
115C23×C79#4112yes—
116C23×C79#4112yes—
117C23×C79C2411yescharacteristic
118C22×D79—21no—
119C22×D79—21no—
120C22×D79—21no—
121C22×D79—21no—
122C22×D79—28no—
123C22×D79—21no—
124C22×D79—21no—
125C22×D79—21no—
126C22×D79—21no—
127C22×D79—21no—
128C22×D79—21no—
129C22×D79—28no—
130C22×D79—44no—
131C22×D79—44no—
132C22×D79—44no—
133C22×D79—44no—
134C22×D79—44no—
135C22×D79C22×C412yes—
136C22×D79C22×C412yes—
137C22×D79C2×D412yes—
138C22×D79#4112yes—
139C2×C4×C79—21no—
140C2×C4×C79—21no—
141C2×C4×C79—21no—
142C2×C4×C79—21no—
143C2×C4×C79—21no—
144C2×C4×C79—21no—
145C2×C4×C79—21no—
146C2×C4×C79—21no—
147C2×C4×C79—21no—
148C2×C4×C79—21no—
149C2×C4×C79—21no—
150C2×C4×C79—21no—
151C2×C4×C79—21no—
152C2×C4×C79—21no—
153C2×C4×C79—21no—
154C2×C4×C79—44no—
155C2×C4×C79C22×C412yes—
156C2×C4×C79C22×C412yes—
157C2×C4×C79C2×D412yes—
158C2×Dic79—21no—
159C2×Dic79—21no—
160C2×Dic79—21no—
161C2×Dic79—21no—
162C2×Dic79—21no—
163C2×Dic79—21no—
164C2×Dic79—21no—
165C2×Dic79—21no—
166C2×Dic79—21no—
167C2×Dic79—21no—
168C2×Dic79—21no—
169C2×Dic79—21no—
170C2×Dic79—21no—
171C2×Dic79—21no—
172C2×Dic79—21no—
173C2×Dic79—44no—
174C2×Dic79C22×C412yes—
175C2×Dic79C22×C412yes—
176C2×Dic79C2×D412yes—
177C4×D79—28no—
178C4×D79—44no—
179C22×C79—22no—
180C22×C79—22no—
181C22×C79—22no—
182C22×C79—22no—
183C22×C79—22no—
184C22×C79—22no—
185C22×C79#11714yescomplemented
186C22×C79C23×C411yescharacteristic
187C22×C79C22×D411yescharacteristic
188C22×C79C2×#4111yescharacteristic
189C22×C79C2×#4111yescharacteristic
190C22×C79C2×#4111yescharacteristic
191C22×C79H(5,𝔽2)11yescharacteristic
192C22×C79H(5,𝔽2)11yescharacteristic
193C2×D79—22no—
194C2×D79—22no—
195C2×D79—22no—
196C2×D79—22no—
197C2×D79—22no—
198C2×D79—22no—
199C2×D79—22no—
200C2×D79—22no—
201C2×D79—22no—
202C2×D79—416no—
203C2×D79—41no—
204C2×D79—41no—
205C2×D79—41no—
206C2×D79—41no—
207C2×D79C4×D414yes—
208C4×C79—22no—
209C4×C79—22no—
210C4×C79—22no—
211C4×C79—41no—
212C4×C79—41no—
213C4×C79—41no—
214Dic79—22no—
215Dic79—22no—
216Dic79—22no—
217Dic79—41no—
218Dic79—41no—
219Dic79—41no—
220C2×C79—24no—
221C2×C79C2×#11711yescharacteristic
222C2×C79C2×C4×D411yescharacteristic
223C2×C79#51811yescharacteristic
224C2×C79#54611yescharacteristic
225C2×C79#54611yescharacteristic
226C2×C79#55111yescharacteristic
227C2×C79#55111yescharacteristic
228D79—24no—
229D79—42no—
230#2342—791nomaximal, Sylow
231C79#234211yescharacteristic, complemented, Sylow
232C2×#117—791no—
233C22×C22⋊C4—791no—
234C22×C22⋊C4—791no—
235#388—791no—
236#388—791no—
237#388—791no—
238#388—791no—
239#385—791no—
240#385—791no—
241#381—791no—
242#380—791no—
243#379—791no—
244C4×C22⋊C4—791no—
245C4×C22⋊C4—791no—
246C4×C22⋊C4D7911yescharacteristic, complemented
247C25—791no—
248C23×C4—791no—
249C23×C4—791no—
250C23×C4—791no—
251C23×C4C2×D7911yescharacteristic
252#117—1584no—
253C2×C4⋊C4—791no—
254C2×C4⋊C4—791no—
255C2×C4⋊C4—791no—
256C2×C4⋊C4—791no—
257C2×C22⋊C4—791no—
258C2×C22⋊C4—791no—
259C2×C22⋊C4—791no—
260C2×C22⋊C4—791no—
261C2×C22⋊C4—791no—
262C2×C22⋊C4—791no—
263C2×C22⋊C4—798no—
264C2×C22⋊C4—791no—
265C2×C22⋊C4—791no—
266C2×C22⋊C4—791no—
267C2×C22⋊C4—791no—
268C2×C22⋊C4—791no—
269C2×C22⋊C4—791no—
270C2×C22⋊C4—1584no—
271C2×C22⋊C4C2×D7911yescharacteristic
272C2×C22⋊C4C2×D7911yescharacteristic
273C2×C42—791no—
274C2×C42—791no—
275C2×C42C2×D7911yescharacteristic, complemented
276C2×C42C2×D7911yescharacteristic, complemented
277#95—791no—
278#95—791no—
279#95—791no—
280#95—791no—
281#95—791no—
282#95—791no—
283#95C2×D7911yescharacteristic, complemented
284#95C2×D7911yescharacteristic, complemented
285C24—3161no—
286C24—3161no—
287C24—794no—
288C24—791no—
289C24—791no—
290C24—1582no—
291C24—1582no—
292C24—1582no—
293C24—1582no—
294C24C22×D7911yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—41no—
298C22×C4—3161no—
299C22×C4—3161no—
300C22×C4—3161no—
301C22×C4—794no—
302C22×C4—791no—
303C22×C4—791no—
304C22×C4—791no—
305C22×C4—794no—
306C22×C4—791no—
307C22×C4—791no—
308C22×C4—791no—
309C22×C4—1582no—
310C22×C4—1582no—
311C22×C4—1582no—
312C22×C4—1582no—
313C22×C4C22×D7911yescharacteristic
314C22×C4C22×D7911yescharacteristic
315C22×C4C22×D7911yescharacteristic
316C22×C4C22×D7911yescharacteristic
317C22×C4C22×D7911yescharacteristic
318C22×C4C22×D7911yescharacteristic
319C4⋊C4—3161no—
320C4⋊C4—3161no—
321C4⋊C4—1582no—
322C4⋊C4—1582no—
323C22⋊C4—22no—
324C22⋊C4—3161no—
325C22⋊C4—3161no—
326C22⋊C4—794no—
327C22⋊C4—794no—
328C22⋊C4—794no—
329C22⋊C4—794no—
330C22⋊C4—1582no—
331C22⋊C4—1582no—
332C22⋊C4—1582no—
333C22⋊C4—1582no—
334C22⋊C4—1582no—
335C22⋊C4—1582no—
336C22⋊C4C4×D7914yes—
337C42—22no—
338C42—41no—
339C42—3161no—
340C42—1582no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—3164no—
346C23—3164no—
347C23—3164no—
348C23—3164no—
349C23—3164no—
350C23—792no—
351C23—792no—
352C23—792no—
353C23—792no—
354C23—1588no—
355C23—1581no—
356C23—1581no—
357C23—1581no—
358C23—1581no—
359C23—1581no—
360C23—1588no—
361C23—1581no—
362C23—1581no—
363C23—1581no—
364C23—1581no—
365C23—1581no—
366C23C2×C4×D7912yes—
367C23#1192962412yes—
368C23#1192962412yes—
369C23C23×D7911yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—44no—
386C2×C4—3164no—
387C2×C4—3164no—
388C2×C4—792no—
389C2×C4—792no—
390C2×C4—792no—
391C2×C4—1588no—
392C2×C4—1581no—
393C2×C4—1581no—
394C2×C4—1581no—
395C2×C4—1581no—
396C2×C4—1581no—
397C2×C4—1581no—
398C2×C4—1581no—
399C2×C4—1581no—
400C2×C4—1581no—
401C2×C4—1581no—
402C2×C4—1581no—
403C2×C4—1581no—
404C2×C4—1581no—
405C2×C4—1581no—
406C2×C4—1581no—
407C2×C4C2×C4×D7912yes—
408C2×C4C2×C4×D7912yes—
409C2×C4D4×D7912yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—31616no—
417C22—3161no—
418C22—3161no—
419C22—3161no—
420C22—3161no—
421C22—794no—
422C22—1582no—
423C22—1582no—
424C22—1582no—
425C22—1582no—
426C22—1582no—
427C22—1582no—
428C22—1582no—
429C22—1582no—
430C22—1582no—
431C22#1457911814yescomplemented
432C22C22×C4×D7911yescharacteristic
433C22C2×D4×D7911yescharacteristic
434C22#41×D7911yescharacteristic
435C22C2×#1192962411yescharacteristic
436C22C2×#1192962411yescharacteristic
437C22#1457920611yescharacteristic
438C22#1457920711yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—3161no—
446C4—3161no—
447C4—3161no—
448C4—1582no—
449C4—1582no—
450C4—1582no—
451C2—24no—
452C2—3162no—
453C2—1584no—
454C2C2×#1457911811yescharacteristic
455C2C4×D4×D7911yescharacteristic
456C2#1909903511yescharacteristic
457C2#1909920311yescharacteristic
458C2#1909920911yescharacteristic
459C2#1909923711yescharacteristic
460C2#1909924211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
FittingC4×C22⋊C4×C79C2
socle, cosocleC23×C79C24
prime radicalC24×D79C22
hypercenterC4×C22⋊C4D79
hypocenterC79#2342
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14579118C2semidirect
4. #19098454C2semidirect
5. #19098454C2semidirect
6. #19098452C2semidirect
7. #19098452C2semidirect
8. #19098436C2semidirect
9. #19098435C2semidirect
10. #19098425C2semidirect
11. #19098422C2semidirect
13. C22⋊C4×Dic79C2semidirect
14. C4×(C2×D79)⋊C4C2semidirect
15. C4×C22⋊C4×C79C2semidirect
21. C2×Dic79⋊C4C22semidirect
22. C2×Dic79⋊C4C22semidirect
23. C2×Dic79⋊C4C22semidirect
24. C2×Dic79⋊C4C22semidirect
38. C22⋊C4×D79C4semidirect
39. C2×C4×Dic79C22semidirect
40. C2×C4×Dic79C22semidirect
41. C79⋊#95C22semidirect
42. C79⋊#95C22semidirect
43. C79⋊#95C22semidirect
44. C79⋊#95C22semidirect
45. C79⋊#95C22semidirect
46. C79⋊#95C22semidirect
50. C2×C42×C79C22semidirect
51. C2×C42×C79C22semidirect
52. #95×C79C22semidirect
53. #95×C79C22semidirect
76. C2×C4×D79C2×C4semidirect
77. C2×C4×D79C2×C4semidirect
91. (C2×D79)⋊C4C2×C4semidirect
92. (C2×D79)⋊C4C2×C4semidirect
185. C22×C79#117semidirect
231. C79#2342semidirect
246. C4×C22⋊C4D79semidirect
275. C2×C42C2×D79semidirect
276. C2×C42C2×D79semidirect
283. #95C2×D79semidirect
284. #95C2×D79semidirect
431. C22#14579118semidirect