Finite Group Databasebeta

← #23766449

Subgroups — #23766449

Order 10112.

716 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579132C211yesmaximal, characteristic
2C2×C4×C22⋊D79C211yesmaximal, characteristic, complemented
3C2×(C22⋊D79)⋊C4C211yesmaximal, characteristic, complemented
4#19098457C211yesmaximal, characteristic, complemented
5#19098451C211yesmaximal, characteristic, complemented
6#19098448C211yesmaximal, characteristic, complemented
7#19098446C211yesmaximal, characteristic, complemented
8#19098443C211yesmaximal, characteristic, complemented
9#19098439C211yesmaximal, characteristic, complemented
10#19098439C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic79C211yesmaximal, characteristic, complemented
12C4×C22⋊Dic79C211yesmaximal, characteristic, complemented
13#19098410C211yesmaximal, characteristic, complemented
14#95×D79C211yesmaximal, characteristic, complemented
15#386×C79C211yesmaximal, characteristic, complemented
16C22×C22⋊D79C2211yescharacteristic
17C22×C22⋊D79C2211yescharacteristic
18C23×Dic79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20C22×C4×D79C2211yescharacteristic
21C22×C4×D79C2211yescharacteristic
22#14579132C418yescomplemented
23C4×C22⋊D79—24no—
24(C22⋊D79)⋊C4—24no—
25C2×C4⋊Dic79C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×C22⋊Dic79C2211yescharacteristic
29C2×C22⋊Dic79C2211yescharacteristic
30C2×C22⋊Dic79C2211yescharacteristic
31C2×C22⋊Dic79C2211yescharacteristic
32C2×C22⋊Dic79C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×(C2×D79)⋊C4C2211yescharacteristic
35C2×C4×Dic79C2211yescharacteristic
36C2×C4×Dic79C2211yescharacteristic
37C2×C4×Dic79C2211yescharacteristic
38C2×C4×Dic79C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C79⋊#95C2211yescharacteristic
46C79⋊#95C2211yescharacteristic
47C22×D4×C79C2211yescharacteristic
48C23×C4×C79C2211yescharacteristic
49C2×C22⋊C4×C79C2211yescharacteristic
50C2×C22⋊C4×C79C2211yescharacteristic
51C2×C22⋊C4×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic
53#95×C79C2211yescharacteristic
54C23×D79C2311yescharacteristic
55C2×C22⋊D79—22no—
56C2×C22⋊D79—22no—
57C2×C22⋊D79—22no—
58C2×C22⋊D79—22no—
59C2×C22⋊D79C2×C414yescomplemented
60C2×C22⋊D79C2×C414yescomplemented
61C22×Dic79—22no—
62C22×Dic79—22no—
63C22×Dic79—41no—
64C22×Dic79C2311yescharacteristic
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—41no—
76C2×C4×D79—41no—
77C2×C4×D79—41no—
78C2×C4×D79—41no—
79C2×C4×D79C2×C414yescomplemented
80C4⋊Dic79C2×C414yescomplemented
81Dic79⋊C4—22no—
82Dic79⋊C4—22no—
83C22⋊Dic79—22no—
84C22⋊Dic79—22no—
85C22⋊Dic79—41no—
86C22⋊Dic79C2×C414yescomplemented
87C22⋊Dic79C2×C414yescomplemented
88(C2×D79)⋊C4—22no—
89(C2×D79)⋊C4D414yescomplemented
90C4×Dic79—22no—
91C4×Dic79—22no—
92C4×Dic79—41no—
93C4×Dic79—41no—
94C24×C79C2311yescharacteristic
95C24×C79C2311yescharacteristic
96C2×D4×C79—41no—
97C2×D4×C79—41no—
98C2×D4×C79C2×C414yescomplemented
99C22×C4×C79—22no—
100C22×C4×C79—22no—
101C22×C4×C79—41no—
102C22×C4×C79C2311yescharacteristic
103C22×C4×C79C2311yescharacteristic
104C22×C4×C79C2311yescharacteristic
105C22×C4×C79C2311yescharacteristic
106C22×C4×C79C2311yescharacteristic
107C22⋊C4×C79—22no—
108C22⋊C4×C79—22no—
109C22⋊C4×C79—41no—
110C23×C79—21no—
111C23×C79—21no—
112C23×C79—21no—
113C23×C79—21no—
114C23×C79—21no—
115C23×C79—21no—
116C23×C79—21no—
117C23×C79—21no—
118C23×C79—21no—
119C23×C79—21no—
120C23×C79—21no—
121C23×C79—21no—
122C23×C79C22×C412yes—
123C23×C79C22×C412yes—
124C23×C79C2411yescharacteristic
125C22×D79—21no—
126C22×D79—21no—
127C22×D79—21no—
128C22×D79—21no—
129C22×D79C22×C412yes—
130C22×D79C2×D412yes—
131C22×D79#4112yes—
132D4×C79—44no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
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—44no—
146C2×C4×C79C22×C412yes—
147C2×C4×C79C2×D412yes—
148C2×C4×C79#4112yes—
149C22⋊D79—28no—
150C22⋊D79—28no—
151C2×Dic79—21no—
152C2×Dic79—21no—
153C2×Dic79—21no—
154C2×Dic79—21no—
155C2×Dic79—21no—
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—44no—
168C2×Dic79C22×C412yes—
169C2×Dic79C22×C412yes—
170C2×Dic79C22×C412yes—
171C2×Dic79C2×D412yes—
172C2×Dic79#4112yes—
173C4×D79—44no—
174C4×D79—44no—
175C4×D79—44no—
176C22×C79—22no—
177C22×C79—22no—
178C22×C79—22no—
179C22×C79—22no—
180C22×C79—22no—
181C22×C79—22no—
182C22×C79—41no—
183C22×C79—41no—
184C22×C79—41no—
185C22×C79—41no—
186C22×C79—41no—
187C22×C79—41no—
188C22×C79—41no—
189C22×C79—41no—
190C22×C79C23×C411yescharacteristic
191C22×C79C22×D411yescharacteristic
192C22×C79C2×#4111yescharacteristic
193C22×C79C2×#4111yescharacteristic
194C22×C79C2×#4111yescharacteristic
195C22×C79H(5,𝔽2)11yescharacteristic
196C22×C79H(5,𝔽2)11yescharacteristic
197C2×D79—22no—
198C2×D79—22no—
199C2×D79—22no—
200C2×D79—22no—
201C2×D79—22no—
202C2×D79—22no—
203C2×D79C4×D414yes—
204C4×C79—22no—
205C4×C79—22no—
206C4×C79—22no—
207C4×C79—41no—
208C4×C79—41no—
209Dic79—22no—
210Dic79—22no—
211Dic79—22no—
212Dic79—22no—
213Dic79—22no—
214Dic79—41no—
215Dic79—41no—
216C2×C79—42no—
217C2×C79—42no—
218C2×C79C2×C4×D411yescharacteristic
219C2×C79C4×#4111yescharacteristic
220C2×C79#51811yescharacteristic
221C2×C79#54611yescharacteristic
222C2×C79#54611yescharacteristic
223C2×C79#55311yescharacteristic
224C2×C79#55311yescharacteristic
225D79—24no—
226#2364—791nomaximal, Sylow
227C79#236411yescharacteristic, complemented, Sylow
228C2×#121—791no—
229C2×C4×D4—791no—
230C2×C4×D4—791no—
231#388—791no—
232#388—791no—
233#387—791no—
234#387—791no—
235#386—791no—
236#386—791no—
237#386—791no—
238#386D7911yescharacteristic, complemented
239C4×C22⋊C4—791no—
240C4×C22⋊C4—791no—
241C4×C22⋊C4—791no—
242C2×#95—791no—
243C22×D4—791no—
244C22×D4—791no—
245C22×D4C2×D7911yescharacteristic
246C23×C4—791no—
247C23×C4—791no—
248C23×C4—791no—
249C23×C4—791no—
250C23×C4C2×D7911yescharacteristic
251#121—798no—
252C4×D4—1584no—
253C4×D4—1584no—
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—791no—
264C2×C22⋊C4C2×D7911yescharacteristic
265C2×C22⋊C4C2×D7911yescharacteristic
266C2×C22⋊C4C2×D7911yescharacteristic
267C2×C42—791no—
268C2×C42—791no—
269C2×C42—791no—
270C2×C42—791no—
271#95—791no—
272#95—791no—
273#95—791no—
274#95—791no—
275#95—791no—
276#95—791no—
277#95—791no—
278#95—791no—
279#95C2×D7911yescharacteristic
280#95C2×D7911yescharacteristic
281C24—791no—
282C24C22×D7911yescharacteristic
283C24C22×D7911yescharacteristic
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—794no—
287C2×D4—794no—
288C2×D4—1582no—
289C2×D4—1582no—
290C2×D4—1582no—
291C2×D4—1582no—
292C2×D4C4×D7914yescomplemented
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—41no—
296C22×C4—3161no—
297C22×C4—3161no—
298C22×C4—3161no—
299C22×C4—3161no—
300C22×C4—3161no—
301C22×C4—794no—
302C22×C4—791no—
303C22×C4—791no—
304C22×C4—791no—
305C22×C4—791no—
306C22×C4—791no—
307C22×C4—791no—
308C22×C4—791no—
309C22×C4—1582no—
310C22×C4—1582no—
311C22×C4—1582no—
312C22×C4—1582no—
313C22×C4—1582no—
314C22×C4—1582no—
315C22×C4C22×D7911yescharacteristic
316C22×C4C22×D7911yescharacteristic
317C22×C4C22×D7911yescharacteristic
318C22×C4C22×D7911yescharacteristic
319C22×C4C22×D7911yescharacteristic
320C4⋊C4—794no—
321C4⋊C4—1582no—
322C4⋊C4—1582no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—41no—
326C22⋊C4—3161no—
327C22⋊C4—794no—
328C22⋊C4—794no—
329C22⋊C4—794no—
330C22⋊C4—1582no—
331C22⋊C4—1582no—
332C22⋊C4—1582no—
333C42—3161no—
334C42—3161no—
335C42—1582no—
336C42—1582no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—792no—
350C23—792no—
351C23—792no—
352C23—1581no—
353C23—1581no—
354C23—1581no—
355C23—1581no—
356C23C2×C4×D7912yes—
357C23C2×C4×D7912yes—
358C23C23×D7911yescharacteristic
359D4—44no—
360D4—1588no—
361D4—1588no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—44no—
375C2×C4—3164no—
376C2×C4—3164no—
377C2×C4—3164no—
378C2×C4—3164no—
379C2×C4—792no—
380C2×C4—792no—
381C2×C4—792no—
382C2×C4—792no—
383C2×C4—792no—
384C2×C4—1581no—
385C2×C4—1581no—
386C2×C4—1581no—
387C2×C4—1581no—
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×C4C2×C4×D7912yes—
401C2×C4D4×D7912yes—
402C2×C4#1192962312yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—794no—
418C22—1582no—
419C22—1582no—
420C22—1582no—
421C22—1582no—
422C22—1582no—
423C22—1582no—
424C22C22×C4×D7911yescharacteristic
425C22C2×D4×D7911yescharacteristic
426C22#41×D7911yescharacteristic
427C22#41×D7911yescharacteristic
428C22C2×#1192962311yescharacteristic
429C22#1457920611yescharacteristic
430C22#1457920611yescharacteristic
431C4—22no—
432C4—22no—
433C4—22no—
434C4—41no—
435C4—41no—
436C4—3161no—
437C4—3161no—
438C4—1582no—
439C4—1582no—
440C4—1582no—
441C4—1582no—
442C4—1582no—
443C2—42no—
444C2—42no—
445C2—1584no—
446C2C4×D4×D7911yescharacteristic
447C2C4×#1192962311yescharacteristic
448C2#1909903611yescharacteristic
449C2#1909920011yescharacteristic
450C2#1909921011yescharacteristic
451C2#1909925811yescharacteristic
452C2#1909926011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
Fitting#386×C79C2
socle, cosocleC23×C79C24
prime radicalC2×#14579132C2
hypercenter#386D79
hypocenterC79#2364
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D79C2semidirect
3. C2×(C22⋊D79)⋊C4C2semidirect
4. #19098457C2semidirect
5. #19098451C2semidirect
6. #19098448C2semidirect
7. #19098446C2semidirect
8. #19098443C2semidirect
9. #19098439C2semidirect
10. #19098439C2semidirect
11. C22⋊C4×Dic79C2semidirect
12. C4×C22⋊Dic79C2semidirect
13. #19098410C2semidirect
14. #95×D79C2semidirect
15. #386×C79C2semidirect
22. #14579132C4semidirect
59. C2×C22⋊D79C2×C4semidirect
60. C2×C22⋊D79C2×C4semidirect
79. C2×C4×D79C2×C4semidirect
80. C4⋊Dic79C2×C4semidirect
86. C22⋊Dic79C2×C4semidirect
87. C22⋊Dic79C2×C4semidirect
89. (C2×D79)⋊C4D4semidirect
98. C2×D4×C79C2×C4semidirect
227. C79#2364semidirect
238. #386D79semidirect
292. C2×D4C4×D79semidirect