Finite Group Databasebeta

← #388×D79 #23765828

Subgroups — #388×D79 #23765828

Order 10112.

928 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D79C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D79C211yesmaximal, characteristic
3C2×C22⋊C4×D79C211yesmaximal, characteristic
4C2×C22⋊C4×D79C211yesmaximal, characteristic
5C2×C42×D79C211yesmaximal, characteristic, complemented
6#19098457C211yesmaximal, characteristic, complemented
7#19098456C211yesmaximal, characteristic, complemented
8#19098455C211yesmaximal, characteristic, complemented
9#19098454C211yesmaximal, characteristic, complemented
10#19098453C211yesmaximal, characteristic, complemented
11#19098452C211yesmaximal, characteristic, complemented
12#19098451C211yesmaximal, characteristic, complemented
13#95×D79C211yesmaximal, characteristic, complemented
14#95×D79C211yesmaximal, characteristic, complemented
15#388×C79C211yesmaximal, characteristic, complemented
16C24×D79C2211yescharacteristic
17C22×C4×D79C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20C22×C4×D79C2211yescharacteristic
21C22×C4×D79C2211yescharacteristic
22C22×C4×D79C2211yescharacteristic
23C2×C4⋊Dic79C2211yescharacteristic, complemented
24C2×Dic79⋊C4C2211yescharacteristic, complemented
25C2×Dic79⋊C4C2211yescharacteristic, complemented
26C4⋊C4×D79—24no—
27C2×C22⋊Dic79C2211yescharacteristic
28C2×C22⋊Dic79C2211yescharacteristic
29C2×C22⋊Dic79C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×(C2×D79)⋊C4C2211yescharacteristic
35C2×(C2×D79)⋊C4C2211yescharacteristic
36C22⋊C4×D79—24no—
37C22⋊C4×D79—24no—
38C22⋊C4×D79C418yescomplemented
39C2×C4×Dic79C2211yescharacteristic, complemented
40C2×C4×Dic79C2211yescharacteristic, complemented
41C2×C4×Dic79C2211yescharacteristic, complemented
42C42×D79—24no—
43C79⋊#95C2211yescharacteristic, complemented
44C79⋊#95C2211yescharacteristic, complemented
45C79⋊#95C2211yescharacteristic, complemented
46C79⋊#95C2211yescharacteristic, complemented
47C79⋊#95C2211yescharacteristic, complemented
48C79⋊#95C2211yescharacteristic, complemented
49C2×C4⋊C4×C79C2211yescharacteristic, complemented
50C2×C22⋊C4×C79C2211yescharacteristic
51C2×C22⋊C4×C79C2211yescharacteristic
52C2×C22⋊C4×C79C2211yescharacteristic
53C2×C42×C79C2211yescharacteristic, complemented
54#95×C79C2211yescharacteristic, complemented
55#95×C79C2211yescharacteristic, complemented
56C23×D79—22no—
57C23×D79—22no—
58C23×D79—22no—
59C23×D79—22no—
60C23×D79—22no—
61C23×D79—22no—
62C23×D79C2×C414yes—
63C23×D79C2311yescharacteristic
64C23×D79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C22×Dic79C2311yescharacteristic
69C22×Dic79C2311yescharacteristic
70C22×Dic79C2311yescharacteristic
71C2×C4×D79—22no—
72C2×C4×D79—22no—
73C2×C4×D79—22no—
74C2×C4×D79—22no—
75C2×C4×D79—22no—
76C2×C4×D79—22no—
77C2×C4×D79—22no—
78C2×C4×D79—22no—
79C2×C4×D79—22no—
80C2×C4×D79—22no—
81C2×C4×D79—22no—
82C2×C4×D79—22no—
83C2×C4×D79—22no—
84C2×C4×D79—22no—
85C2×C4×D79C2×C414yes—
86C2×C4×D79C2×C414yes—
87C2×C4×D79D414yes—
88C2×C4×D79D414yes—
89C4⋊Dic79—22no—
90Dic79⋊C4—22no—
91Dic79⋊C4—22no—
92C22⋊Dic79—22no—
93C22⋊Dic79—22no—
94C22⋊Dic79C2×C414yescomplemented
95(C2×D79)⋊C4—22no—
96(C2×D79)⋊C4—22no—
97(C2×D79)⋊C4—22no—
98(C2×D79)⋊C4—22no—
99(C2×D79)⋊C4C2×C414yescomplemented
100(C2×D79)⋊C4C2×C414yescomplemented
101C4×Dic79—22no—
102C4×Dic79—22no—
103C4×Dic79—22no—
104C24×C79C2311yescharacteristic
105C22×C4×C79C2311yescharacteristic
106C22×C4×C79C2311yescharacteristic
107C22×C4×C79C2311yescharacteristic
108C22×C4×C79C2311yescharacteristic
109C22×C4×C79C2311yescharacteristic
110C22×C4×C79C2311yescharacteristic
111C4⋊C4×C79—22no—
112C22⋊C4×C79—22no—
113C22⋊C4×C79—22no—
114C22⋊C4×C79C2×C414yescomplemented
115C42×C79—22no—
116C23×C79—21no—
117C23×C79—21no—
118C23×C79—21no—
119C23×C79—21no—
120C23×C79—21no—
121C23×C79—21no—
122C23×C79C22×C412yes—
123C23×C79C2411yescharacteristic
124C22×D79—21no—
125C22×D79—21no—
126C22×D79—21no—
127C22×D79—21no—
128C22×D79—21no—
129C22×D79—21no—
130C22×D79—28no—
131C22×D79—28no—
132C22×D79—28no—
133C22×D79—44no—
134C22×D79—44no—
135C22×D79—44no—
136C22×D79—44no—
137C22×D79C22×C412yes—
138C22×D79C22×C412yes—
139C22×D79C2×D412yes—
140C22×D79C2×D412yes—
141C22×D79#4112yes—
142C22×D79#4112yes—
143C22×D79#4112yes—
144C22×D79#4112yes—
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—21no—
155C2×C4×C79—21no—
156C2×C4×C79—21no—
157C2×C4×C79—21no—
158C2×C4×C79—21no—
159C2×C4×C79C22×C412yes—
160C2×C4×C79C22×C412yes—
161C2×C4×C79C2×D412yes—
162C2×C4×C79C2×D412yes—
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—21no—
174C2×Dic79—21no—
175C2×Dic79—21no—
176C2×Dic79—21no—
177C2×Dic79C22×C412yes—
178C2×Dic79C22×C412yes—
179C2×Dic79C2×D412yes—
180C2×Dic79C2×D412yes—
181C4×D79—28no—
182C4×D79—28no—
183C4×D79—28no—
184C4×D79—28no—
185C4×D79—44no—
186C4×D79—44no—
187C22×C79—22no—
188C22×C79—22no—
189C22×C79—22no—
190C22×C79—41no—
191C22×C79—41no—
192C22×C79—41no—
193C22×C79—41no—
194C22×C79C23×C411yescharacteristic
195C22×C79C22×D411yescharacteristic
196C22×C79C22×D411yescharacteristic
197C22×C79C2×#4111yescharacteristic
198C22×C79C2×#4111yescharacteristic
199C22×C79C2×#4111yescharacteristic
200C22×C79C2×#4111yescharacteristic
201C2×D79—22no—
202C2×D79—22no—
203C2×D79—22no—
204C2×D79—41no—
205C2×D79—41no—
206C2×D79—41no—
207C2×D79—41no—
208C2×D79—416no—
209C2×D79#11714yes—
210C2×D79C4×D414yes—
211C2×D79C4×D414yes—
212C2×D79#12114yes—
213C2×D79#12314yes—
214C2×D79#12414yes—
215C2×D79#12614yes—
216C4×C79—22no—
217C4×C79—22no—
218C4×C79—22no—
219C4×C79—22no—
220C4×C79—41no—
221C4×C79—41no—
222Dic79—22no—
223Dic79—22no—
224Dic79—22no—
225Dic79—22no—
226Dic79—41no—
227Dic79—41no—
228C2×C79—42no—
229C2×C79C2×#11711yescharacteristic
230C2×C79C2×C4×D411yescharacteristic
231C2×C79C2×C4×D411yescharacteristic
232C2×C79C2×#12111yescharacteristic
233C2×C79C2×#12311yescharacteristic
234C2×C79C2×#12411yescharacteristic
235C2×C79C2×#12611yescharacteristic
236D79—42no—
237D79#38818yesdirect product factor
238C2×#388—791nomaximal, Sylow
239C79C2×#38811yescharacteristic, complemented, Sylow
240C22×C4⋊C4—791no—
241C22×C22⋊C4—791no—
242C22×C22⋊C4—791no—
243C22×C22⋊C4—791no—
244C22×C42—791no—
245#388—791no—
246#388—791no—
247#388—791no—
248#388—791no—
249#388—791no—
250#388—791no—
251#388—791no—
252#388D7911yescharacteristic, direct product factor
253C2×#95—791no—
254C2×#95—791no—
255C25—791no—
256C23×C4—791no—
257C23×C4—791no—
258C23×C4—791no—
259C23×C4—791no—
260C23×C4—791no—
261C23×C4—791no—
262C2×C4⋊C4—791no—
263C2×C4⋊C4—791no—
264C2×C4⋊C4—791no—
265C2×C4⋊C4—1584no—
266C2×C4⋊C4C2×D7911yescharacteristic, complemented
267C2×C22⋊C4—791no—
268C2×C22⋊C4—791no—
269C2×C22⋊C4—791no—
270C2×C22⋊C4—798no—
271C2×C22⋊C4—791no—
272C2×C22⋊C4—791no—
273C2×C22⋊C4—791no—
274C2×C22⋊C4—791no—
275C2×C22⋊C4—791no—
276C2×C22⋊C4—791no—
277C2×C22⋊C4—1584no—
278C2×C22⋊C4—1584no—
279C2×C22⋊C4C2×D7911yescharacteristic
280C2×C22⋊C4C2×D7911yescharacteristic
281C2×C22⋊C4C2×D7911yescharacteristic
282C2×C42—791no—
283C2×C42—791no—
284C2×C42—791no—
285C2×C42—1584no—
286C2×C42C2×D7911yescharacteristic, complemented
287#95—791no—
288#95—791no—
289#95—791no—
290#95—791no—
291#95—791no—
292#95—791no—
293#95C2×D7911yescharacteristic, complemented
294#95C2×D7911yescharacteristic, complemented
295C24—791no—
296C24—794no—
297C24—791no—
298C24—1582no—
299C24—1582no—
300C24—1582no—
301C24—1582no—
302C24—1582no—
303C24—1582no—
304C24C22×D7911yescharacteristic
305C22×C4—791no—
306C22×C4—791no—
307C22×C4—791no—
308C22×C4—791no—
309C22×C4—794no—
310C22×C4—794no—
311C22×C4—794no—
312C22×C4—794no—
313C22×C4—791no—
314C22×C4—791no—
315C22×C4—1582no—
316C22×C4—1582no—
317C22×C4—1582no—
318C22×C4—1582no—
319C22×C4—1582no—
320C22×C4—1582no—
321C22×C4—1582no—
322C22×C4—1582no—
323C22×C4—1582no—
324C22×C4—1582no—
325C22×C4—1582no—
326C22×C4—1582no—
327C22×C4—1582no—
328C22×C4—1582no—
329C22×C4C22×D7911yescharacteristic
330C22×C4C22×D7911yescharacteristic
331C22×C4C22×D7911yescharacteristic
332C22×C4C22×D7911yescharacteristic
333C22×C4C22×D7911yescharacteristic
334C22×C4C22×D7911yescharacteristic
335C4⋊C4—22no—
336C4⋊C4—1582no—
337C4⋊C4—1582no—
338C4⋊C4—1582no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—794no—
342C22⋊C4—794no—
343C22⋊C4—794no—
344C22⋊C4—1582no—
345C22⋊C4—1582no—
346C22⋊C4—1582no—
347C22⋊C4—1582no—
348C22⋊C4—1582no—
349C22⋊C4—1582no—
350C22⋊C4C4×D7914yescomplemented
351C42—22no—
352C42—1582no—
353C42—1582no—
354C42—1582no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—3164no—
362C23—3164no—
363C23—3164no—
364C23—3164no—
365C23—792no—
366C23—792no—
367C23—792no—
368C23—792no—
369C23—792no—
370C23—792no—
371C23—792no—
372C23—792no—
373C23—1588no—
374C23—1588no—
375C23—1588no—
376C23—1581no—
377C23—1581no—
378C23—1581no—
379C23—1581no—
380C23—1581no—
381C23—1581no—
382C23C2×C4×D7912yes—
383C23C23×D7911yescharacteristic
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—3164no—
399C2×C4—3164no—
400C2×C4—792no—
401C2×C4—792no—
402C2×C4—792no—
403C2×C4—792no—
404C2×C4—1588no—
405C2×C4—1588no—
406C2×C4—1588no—
407C2×C4—1588no—
408C2×C4—1581no—
409C2×C4—1581no—
410C2×C4—1581no—
411C2×C4—1581no—
412C2×C4—1581no—
413C2×C4—1581no—
414C2×C4—1581no—
415C2×C4—1581no—
416C2×C4—1581no—
417C2×C4—1581no—
418C2×C4—1581no—
419C2×C4—1581no—
420C2×C4—1581no—
421C2×C4—1581no—
422C2×C4C2×C4×D7912yes—
423C2×C4C2×C4×D7912yes—
424C2×C4D4×D7912yes—
425C2×C4D4×D7912yes—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—31616no—
434C22—3161no—
435C22—3161no—
436C22—3161no—
437C22—3161no—
438C22—794no—
439C22—794no—
440C22—794no—
441C22—794no—
442C22—794no—
443C22—794no—
444C22—794no—
445C22—1582no—
446C22—1582no—
447C22—1582no—
448C22C22×C4×D7911yescharacteristic
449C22C2×D4×D7911yescharacteristic
450C22C2×D4×D7911yescharacteristic
451C22#41×D7911yescharacteristic
452C22#41×D7911yescharacteristic
453C22#41×D7911yescharacteristic
454C22#41×D7911yescharacteristic
455C4—22no—
456C4—22no—
457C4—22no—
458C4—22no—
459C4—41no—
460C4—41no—
461C4—3161no—
462C4—3161no—
463C4—1582no—
464C4—1582no—
465C4—1582no—
466C4—1582no—
467C2—42no—
468C2—3162no—
469C2—798no—
470C2#117×D7911yescharacteristic
471C2C4×D4×D7911yescharacteristic
472C2C4×D4×D7911yescharacteristic
473C2#121×D7911yescharacteristic
474C2#123×D7911yescharacteristic
475C2#124×D7911yescharacteristic
476C2#126×D7911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
Fitting#388×C79C2
socle, cosocleC23×C79C24
prime radicalC24×D79C22
hypercenter#388D79
hypocenterC79C2×#388
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D79C2semidirect
5. C2×C42×D79C2semidirect
6. #19098457C2semidirect
7. #19098456C2semidirect
8. #19098455C2semidirect
9. #19098454C2semidirect
10. #19098453C2semidirect
11. #19098452C2semidirect
12. #19098451C2semidirect
13. #95×D79C2semidirect
14. #95×D79C2semidirect
15. #388×C79C2semidirect
23. C2×C4⋊Dic79C22semidirect
24. C2×Dic79⋊C4C22semidirect
25. C2×Dic79⋊C4C22semidirect
38. C22⋊C4×D79C4semidirect
39. C2×C4×Dic79C22semidirect
40. C2×C4×Dic79C22semidirect
41. C2×C4×Dic79C22semidirect
43. C79⋊#95C22semidirect
44. C79⋊#95C22semidirect
45. C79⋊#95C22semidirect
46. C79⋊#95C22semidirect
47. C79⋊#95C22semidirect
48. C79⋊#95C22semidirect
49. C2×C4⋊C4×C79C22semidirect
53. C2×C42×C79C22semidirect
54. #95×C79C22semidirect
55. #95×C79C22semidirect
94. C22⋊Dic79C2×C4semidirect
99. (C2×D79)⋊C4C2×C4semidirect
100. (C2×D79)⋊C4C2×C4semidirect
114. C22⋊C4×C79C2×C4semidirect
237. D79#388direct (N × H)
239. C79C2×#388semidirect
252. #388D79direct (N × H)
266. C2×C4⋊C4C2×D79semidirect
286. C2×C42C2×D79semidirect
293. #95C2×D79semidirect
294. #95C2×D79semidirect
350. C22⋊C4C4×D79semidirect