Finite Group Databasebeta

← #23769210

Subgroups — #23769210

Order 10112.

668 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579139C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D79C211yesmaximal, characteristic
3#19098499C211yesmaximal, characteristic, complemented
4#19098498C211yesmaximal, characteristic, complemented
5#19098486C211yesmaximal, characteristic, complemented
6#19098485C211yesmaximal, characteristic, complemented
7#19098485C211yesmaximal, characteristic, complemented
8#19098476C211yesmaximal, characteristic, complemented
9#19098475C211yesmaximal, characteristic, complemented
10#19098437C211yesmaximal, characteristic, complemented
11#19098434C211yesmaximal, characteristic, complemented
12#19098420C211yesmaximal, characteristic, complemented
13#19098418C211yesmaximal, characteristic
14#19098418C211yesmaximal, characteristic
15#396×C79C211yesmaximal, characteristic, complemented
16C24×D79C2211yescharacteristic
17C22×Dic158C2211yescharacteristic, complemented
18C22×C4×D79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20#14579139—24no—
21C2×C4⋊Dic79C2211yescharacteristic, complemented
22C2×C4⋊Dic79C2211yescharacteristic, complemented
23C2×Dic79⋊C4C2211yescharacteristic, complemented
24C2×Dic79⋊C4C2211yescharacteristic, complemented
25C2×Dic79⋊C4C2211yescharacteristic, complemented
26C2×Dic79⋊C4C2211yescharacteristic, complemented
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
36C2×(C2×D79)⋊C4C2211yescharacteristic
37C2×(C2×D79)⋊C4C2211yescharacteristic
38C2×(C2×D79)⋊C4C2211yescharacteristic
39C2×(C2×D79)⋊C4C2211yescharacteristic
40C22⋊C4×D79—24no—
41C79⋊#95C2211yescharacteristic, complemented
42C79⋊#95C2211yescharacteristic, complemented
43C79⋊#95C2211yescharacteristic, complemented
44C79⋊#95C2211yescharacteristic, complemented
45C79⋊#95C2211yescharacteristic, complemented
46C2×C4⋊C4×C79C2211yescharacteristic, complemented
47C2×C4⋊C4×C79C2211yescharacteristic, complemented
48C2×C4⋊C4×C79C2211yescharacteristic, complemented
49C2×C22⋊C4×C79C2211yescharacteristic
50C2×C22⋊C4×C79C2211yescharacteristic
51C2×C22⋊C4×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic, complemented
53C23×D79—22no—
54C23×D79—22no—
55C23×D79—41no—
56C23×D79—41no—
57C23×D79—41no—
58C23×D79—41no—
59C23×D79Q814yescomplemented
60C23×D79C2311yescharacteristic
61C23×D79C2311yescharacteristic
62C2×Dic158—22no—
63C2×Dic158—41no—
64C2×Dic158—41no—
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C22×Dic79C2311yescharacteristic
69C22×Dic79C2311yescharacteristic
70C22×Dic79C2311yescharacteristic
71C2×C4×D79—22no—
72C2×C4×D79—41no—
73C2×C4×D79—41no—
74C2×C4×D79—41no—
75C2×C4×D79—41no—
76C2×C4×D79D414yes—
77C4⋊Dic79—41no—
78C4⋊Dic79—41no—
79Dic79⋊C4—22no—
80Dic79⋊C4—22no—
81Dic79⋊C4—41no—
82Dic79⋊C4—41no—
83C22⋊Dic79—22no—
84C22⋊Dic79—41no—
85C22⋊Dic79—41no—
86(C2×D79)⋊C4—22no—
87(C2×D79)⋊C4—22no—
88(C2×D79)⋊C4—22no—
89(C2×D79)⋊C4—22no—
90(C2×D79)⋊C4—22no—
91(C2×D79)⋊C4—22no—
92(C2×D79)⋊C4—41no—
93(C2×D79)⋊C4—41no—
94(C2×D79)⋊C4—41no—
95(C2×D79)⋊C4—41no—
96C24×C79C2311yescharacteristic
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101C22×C4×C79C2311yescharacteristic
102C22×C4×C79C2311yescharacteristic
103C4⋊C4×C79—22no—
104C4⋊C4×C79—41no—
105C4⋊C4×C79—41no—
106C22⋊C4×C79—22no—
107C22⋊C4×C79—41no—
108C22⋊C4×C79—41no—
109C23×C79—21no—
110C23×C79—21no—
111C23×C79—21no—
112C23×C79—21no—
113C23×C79—21no—
114C23×C79—21no—
115C23×C79C2×Q812yes—
116C23×C79C2411yescharacteristic
117C22×D79—21no—
118C22×D79—21no—
119C22×D79—21no—
120C22×D79—21no—
121C22×D79—21no—
122C22×D79—21no—
123C22×D79—21no—
124C22×D79—21no—
125C22×D79—21no—
126C22×D79—21no—
127C22×D79—28no—
128C22×D79—44no—
129C22×D79—44no—
130C22×D79—44no—
131C22×D79—44no—
132C22×D79—44no—
133C22×D79—44no—
134C22×D79C2×D412yes—
135C22×D79C2×Q812yes—
136C22×D79C2×Q812yes—
137C22×D79#4112yes—
138C2×C4×C79—21no—
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—21no—
155C2×C4×C79C2×D412yes—
156C2×Dic79—21no—
157C2×Dic79—21no—
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×Dic79C2×D412yes—
174C4×D79—44no—
175C4×D79—44no—
176Dic158—44no—
177C22×C79—22no—
178C22×C79—22no—
179C22×C79—22no—
180C22×C79—41no—
181C22×C79—41no—
182C22×C79—41no—
183C22×C79—41no—
184C22×C79C22×D411yescharacteristic
185C22×C79C22×Q811yescharacteristic
186C22×C79C2×#4111yescharacteristic
187C22×C79H(5,𝔽2)11yescharacteristic
188C22×C79H(5,𝔽2)11yescharacteristic
189C22×C79H(5,𝔽2)11yescharacteristic
190C22×C79H(5,𝔽2)11yescharacteristic
191C2×D79—22no—
192C2×D79—22no—
193C2×D79—22no—
194C2×D79—22no—
195C2×D79—22no—
196C2×D79—22no—
197C2×D79—22no—
198C2×D79—22no—
199C2×D79—22no—
200C2×D79—416no—
201C2×D79—41no—
202C2×D79—41no—
203C2×D79—41no—
204C2×D79—41no—
205C2×D79C22⋊Q814yes—
206C4×C79—22no—
207C4×C79—41no—
208C4×C79—41no—
209C4×C79—41no—
210C4×C79—41no—
211C4×C79—41no—
212Dic79—22no—
213Dic79—41no—
214Dic79—41no—
215Dic79—41no—
216Dic79—41no—
217Dic79—41no—
218C2×C79—42no—
219C2×C79C2×C22⋊Q811yescharacteristic
220C2×C79#53411yescharacteristic
221C2×C79#53511yescharacteristic
222C2×C79#53811yescharacteristic
223C2×C79#53811yescharacteristic
224C2×C79#54311yescharacteristic
225C2×C79#54311yescharacteristic
226D79—24no—
227D79—42no—
228#2626—791nomaximal, Sylow
229C79#262611yescharacteristic, complemented, Sylow
230C2×C22⋊Q8—791no—
231C22×C22⋊C4—791no—
232#399—791no—
233#399—791no—
234#396—791no—
235#396—791no—
236#396—791no—
237#396D7911yescharacteristic, complemented
238#393—791no—
239#393—791no—
240#385—791no—
241#385—791no—
242#380—791no—
243#379—791no—
244#379—791no—
245C25—791no—
246C22×Q8—791no—
247C23×C4—791no—
248C23×C4—791no—
249C22⋊Q8—1584no—
250C2×C4⋊C4—791no—
251C2×C4⋊C4—791no—
252C2×C4⋊C4—791no—
253C2×C4⋊C4—791no—
254C2×C4⋊C4—791no—
255C2×C4⋊C4—791no—
256C2×C4⋊C4C2×D7911yescharacteristic, complemented
257C2×C4⋊C4C2×D7911yescharacteristic, complemented
258C2×C4⋊C4C2×D7911yescharacteristic, complemented
259C2×C22⋊C4—791no—
260C2×C22⋊C4—791no—
261C2×C22⋊C4—791no—
262C2×C22⋊C4—791no—
263C2×C22⋊C4—791no—
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—791no—
271C2×C22⋊C4—791no—
272C2×C22⋊C4—1584no—
273C2×C22⋊C4C2×D7911yescharacteristic
274C2×C22⋊C4C2×D7911yescharacteristic
275C2×C22⋊C4C2×D7911yescharacteristic
276#95—791no—
277#95—791no—
278#95—791no—
279#95—791no—
280#95—791no—
281#95C2×D7911yescharacteristic, complemented
282C24—3161no—
283C24—3161no—
284C24—3161no—
285C24—3161no—
286C24—794no—
287C24—791no—
288C24—791no—
289C24—1582no—
290C24—1582no—
291C24C22×D7911yescharacteristic
292C2×Q8—3161no—
293C2×Q8—3161no—
294C2×Q8—1582no—
295C22×C4—3161no—
296C22×C4—3161no—
297C22×C4—3161no—
298C22×C4—3161no—
299C22×C4—794no—
300C22×C4—791no—
301C22×C4—791no—
302C22×C4—791no—
303C22×C4—791no—
304C22×C4—791no—
305C22×C4—791no—
306C22×C4—1582no—
307C22×C4C22×D7911yescharacteristic
308C22×C4C22×D7911yescharacteristic
309C22×C4C22×D7911yescharacteristic
310C22×C4C22×D7911yescharacteristic
311C22×C4C22×D7911yescharacteristic
312C22×C4C22×D7911yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—3161no—
317C4⋊C4—3161no—
318C4⋊C4—3161no—
319C4⋊C4—3161no—
320C4⋊C4—1582no—
321C4⋊C4—1582no—
322C22⋊C4—22no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—3161no—
326C22⋊C4—3161no—
327C22⋊C4—3161no—
328C22⋊C4—3161no—
329C22⋊C4—3161no—
330C22⋊C4—3161no—
331C22⋊C4—1582no—
332C22⋊C4—1582no—
333C22⋊C4—1582no—
334C22⋊C4—1582no—
335C22⋊C4—1582no—
336C22⋊C4—1582no—
337C22⋊C4—1582no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—3164no—
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—1581no—
361C23—1581no—
362C23—1581no—
363C23—1581no—
364C23—1581no—
365C23Q8×D7912yes—
366C23C23×D7911yescharacteristic
367Q8—3164no—
368C2×C4—21no—
369C2×C4—21no—
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—3164no—
386C2×C4—3164no—
387C2×C4—792no—
388C2×C4—1581no—
389C2×C4—1581no—
390C2×C4—1581no—
391C2×C4—1581no—
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×C4D4×D7912yes—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—31616no—
414C22—3161no—
415C22—3161no—
416C22—3161no—
417C22—3161no—
418C22—794no—
419C22—1582no—
420C22—1582no—
421C22—1582no—
422C22—1582no—
423C22—1582no—
424C22—1582no—
425C22—1582no—
426C22—1582no—
427C22—1582no—
428C22C2×D4×D7911yescharacteristic
429C22C2×Q8×D7911yescharacteristic
430C22#41×D7911yescharacteristic
431C22#1457920611yescharacteristic
432C22#1457920611yescharacteristic
433C22#1457920711yescharacteristic
434C22#1457920711yescharacteristic
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—3161no—
442C4—3161no—
443C4—3161no—
444C4—3161no—
445C4—3161no—
446C4—1582no—
447C2—42no—
448C2—3162no—
449C2—1584no—
450C2C22⋊Q8×D7911yescharacteristic
451C2#1909912111yescharacteristic
452C2#1909912911yescharacteristic
453C2#1909914511yescharacteristic
454C2#1909915211yescharacteristic
455C2#1909918811yescharacteristic
456C2#1909918811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#396×C79C2
prime radicalC24×D79C22
hypercenter#396D79
hypocenterC79#2626
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#14579139C2semidirect
3. #19098499C2semidirect
4. #19098498C2semidirect
5. #19098486C2semidirect
6. #19098485C2semidirect
7. #19098485C2semidirect
8. #19098476C2semidirect
9. #19098475C2semidirect
10. #19098437C2semidirect
11. #19098434C2semidirect
12. #19098420C2semidirect
15. #396×C79C2semidirect
17. C22×Dic158C22semidirect
21. C2×C4⋊Dic79C22semidirect
22. C2×C4⋊Dic79C22semidirect
23. C2×Dic79⋊C4C22semidirect
24. C2×Dic79⋊C4C22semidirect
25. C2×Dic79⋊C4C22semidirect
26. C2×Dic79⋊C4C22semidirect
41. C79⋊#95C22semidirect
42. C79⋊#95C22semidirect
43. C79⋊#95C22semidirect
44. C79⋊#95C22semidirect
45. C79⋊#95C22semidirect
46. C2×C4⋊C4×C79C22semidirect
47. C2×C4⋊C4×C79C22semidirect
48. C2×C4⋊C4×C79C22semidirect
52. #95×C79C22semidirect
59. C23×D79Q8semidirect
229. C79#2626semidirect
237. #396D79semidirect
256. C2×C4⋊C4C2×D79semidirect
257. C2×C4⋊C4C2×D79semidirect
258. C2×C4⋊C4C2×D79semidirect
281. #95C2×D79semidirect