Finite Group Databasebeta

← #22591802

Subgroups — #22591802

Order 9088.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556110C211yesmaximal, characteristic, complemented
2C2×#14556097C211yesmaximal, characteristic
3C2×C4×C22⋊D71C211yesmaximal, characteristic, complemented
4#17985935C211yesmaximal, characteristic, complemented
5#17985927C211yesmaximal, characteristic, complemented
6#17985915C211yesmaximal, characteristic, complemented
7#17985914C211yesmaximal, characteristic, complemented
8#17985893C211yesmaximal, characteristic, complemented
9#17985892C211yesmaximal, characteristic, complemented
10#17985878C211yesmaximal, characteristic, complemented
11#17985875C211yesmaximal, characteristic, complemented
12#17985872C211yesmaximal, characteristic, complemented
13#17985859C211yesmaximal, characteristic, complemented
14#17985855C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C71C211yesmaximal, characteristic, complemented
16C22×C22⋊D71C2211yescharacteristic
17C22×C22⋊D71C2211yescharacteristic
18C22×C22⋊D71C2211yescharacteristic
19C22×C4×D71C2211yescharacteristic, complemented
20#14556110—24no—
21#14556097—24no—
22C4×C22⋊D71—24no—
23C2×C4⋊Dic71C2211yescharacteristic, complemented
24C2×C4⋊Dic71C2211yescharacteristic, complemented
25C2×Dic71⋊C4C2211yescharacteristic, complemented
26C2×Dic71⋊C4C2211yescharacteristic, complemented
27C2×Dic71⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic71C2211yescharacteristic
29C2×C22⋊Dic71C2211yescharacteristic
30C2×C22⋊Dic71C2211yescharacteristic
31C2×C22⋊Dic71C2211yescharacteristic
32C2×C22⋊Dic71C2211yescharacteristic
33C2×C22⋊Dic71C2211yescharacteristic
34C2×C22⋊Dic71C2211yescharacteristic
35C2×C22⋊Dic71C2211yescharacteristic
36C2×C22⋊Dic71C2211yescharacteristic
37C2×(C2×D71)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D71)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D71)⋊C4C2211yescharacteristic, complemented
40C2×C4×Dic71C2211yescharacteristic, complemented
41C71⋊#95C2211yescharacteristic, complemented
42C71⋊#95C2211yescharacteristic, complemented
43C71⋊#95C2211yescharacteristic, complemented
44C71⋊#95C2211yescharacteristic, complemented
45C71⋊#95C2211yescharacteristic, complemented
46C71⋊#95C2211yescharacteristic, complemented
47C25×C71C2211yescharacteristic
48C23×C4×C71C2211yescharacteristic
49C23×C4×C71C2211yescharacteristic
50C2×C22⋊C4×C71—24no—
51C2×C22⋊C4×C71C2211yescharacteristic
52C2×C22⋊C4×C71C2211yescharacteristic
53C2×C22⋊C4×C71C2211yescharacteristic
54C2×C22⋊C4×C71C2211yescharacteristic
55C23×D71C2311yescharacteristic
56C2×C22⋊D71—22no—
57C2×C22⋊D71—22no—
58C2×C22⋊D71—22no—
59C2×C22⋊D71—22no—
60C2×C22⋊D71—22no—
61C2×C22⋊D71—22no—
62C2×C22⋊D71—41no—
63C2×C22⋊D71—41no—
64C2×C22⋊D71D414yes—
65C22×Dic71C2311yescharacteristic
66C22×Dic71C2311yescharacteristic
67C22×Dic71C2311yescharacteristic
68C22×Dic71C2311yescharacteristic
69C22×Dic71C2311yescharacteristic
70C22×Dic71C2311yescharacteristic
71C22×Dic71C2311yescharacteristic
72C2×C4×D71—22no—
73C2×C4×D71—22no—
74C2×C4×D71—41no—
75C4⋊Dic71—22no—
76C4⋊Dic71—41no—
77Dic71⋊C4—22no—
78Dic71⋊C4—22no—
79Dic71⋊C4—41no—
80C22⋊Dic71—22no—
81C22⋊Dic71—22no—
82C22⋊Dic71—22no—
83C22⋊Dic71—22no—
84C22⋊Dic71—22no—
85C22⋊Dic71—22no—
86C22⋊Dic71—22no—
87C22⋊Dic71—41no—
88C22⋊Dic71—41no—
89(C2×D71)⋊C4—22no—
90(C2×D71)⋊C4—22no—
91(C2×D71)⋊C4—41no—
92C4×Dic71—22no—
93C24×C71—22no—
94C24×C71—22no—
95C24×C71—22no—
96C24×C71—22no—
97C24×C71—22no—
98C24×C71—41no—
99C24×C71—41no—
100C24×C71C2311yescharacteristic
101C24×C71C2311yescharacteristic
102C24×C71C2311yescharacteristic
103C22×C4×C71—22no—
104C22×C4×C71—22no—
105C22×C4×C71—22no—
106C22×C4×C71—22no—
107C22×C4×C71—41no—
108C22×C4×C71—41no—
109C22×C4×C71C2311yescharacteristic
110C22×C4×C71C2311yescharacteristic
111C22×C4×C71C2311yescharacteristic
112C22×C4×C71C2311yescharacteristic
113C22⋊C4×C71—22no—
114C22⋊C4×C71—22no—
115C22⋊C4×C71—22no—
116C22⋊C4×C71D414yescomplemented
117C23×C71—21no—
118C23×C71—21no—
119C23×C71—21no—
120C23×C71—21no—
121C23×C71—28no—
122C23×C71—21no—
123C23×C71—21no—
124C23×C71—21no—
125C23×C71—21no—
126C23×C71—21no—
127C23×C71—21no—
128C23×C71—21no—
129C23×C71—21no—
130C23×C71—21no—
131C23×C71—21no—
132C23×C71—21no—
133C23×C71—21no—
134C23×C71—44no—
135C23×C71—44no—
136C23×C71—44no—
137C23×C71—44no—
138C23×C71—44no—
139C23×C71—44no—
140C23×C71C2×D412yes—
141C23×C71C2×D412yes—
142C23×C71#4112yes—
143C23×C71#4112yes—
144C23×C71#4112yes—
145C23×C71C2411yescharacteristic
146C22×D71—21no—
147C22×D71—21no—
148C22×D71—21no—
149C22×D71—21no—
150C22×D71—21no—
151C22×D71—21no—
152C22×D71C2×D412yes—
153C2×C4×C71—21no—
154C2×C4×C71—21no—
155C2×C4×C71—21no—
156C2×C4×C71—21no—
157C2×C4×C71—21no—
158C2×C4×C71—21no—
159C2×C4×C71—21no—
160C2×C4×C71—21no—
161C2×C4×C71—21no—
162C2×C4×C71—21no—
163C2×C4×C71—44no—
164C2×C4×C71—44no—
165C2×C4×C71C2×D412yes—
166C2×C4×C71C2×D412yes—
167C22⋊D71—28no—
168C22⋊D71—44no—
169C22⋊D71—44no—
170C2×Dic71—21no—
171C2×Dic71—21no—
172C2×Dic71—21no—
173C2×Dic71—21no—
174C2×Dic71—21no—
175C2×Dic71—21no—
176C2×Dic71—21no—
177C2×Dic71—21no—
178C2×Dic71—21no—
179C2×Dic71—21no—
180C2×Dic71—21no—
181C2×Dic71—21no—
182C2×Dic71—21no—
183C2×Dic71—21no—
184C2×Dic71—21no—
185C2×Dic71—21no—
186C2×Dic71—21no—
187C2×Dic71—21no—
188C2×Dic71—21no—
189C2×Dic71—21no—
190C2×Dic71C2×D412yes—
191C4×D71—44no—
192C22×C71—22no—
193C22×C71—22no—
194C22×C71—22no—
195C22×C71—22no—
196C22×C71—22no—
197C22×C71—22no—
198C22×C71—22no—
199C22×C71—22no—
200C22×C71—22no—
201C22×C71—22no—
202C22×C71—22no—
203C22×C71—22no—
204C22×C71—416no—
205C22×C71—41no—
206C22×C71—41no—
207C22×C71—41no—
208C22×C71—41no—
209C22×C71—41no—
210C22×C71—41no—
211C22×C71—41no—
212C22×C71—41no—
213C22×C71#12314yescomplemented
214C22×C71C22×D411yescharacteristic
215C22×C71C22×D411yescharacteristic
216C22×C71C2×#4111yescharacteristic
217C22×C71C2×#4111yescharacteristic
218C22×C71C2×#4111yescharacteristic
219C22×C71H(5,𝔽2)11yescharacteristic
220C22×C71H(5,𝔽2)11yescharacteristic
221C2×D71—22no—
222C2×D71—22no—
223C2×D71—22no—
224C2×D71—41no—
225C2×D71—41no—
226C2×D71—41no—
227C2×D71—41no—
228C4×C71—22no—
229C4×C71—22no—
230C4×C71—41no—
231C4×C71—41no—
232Dic71—22no—
233Dic71—41no—
234Dic71—41no—
235Dic71—41no—
236Dic71—41no—
237Dic71—41no—
238Dic71—41no—
239C2×C71—24no—
240C2×C71—42no—
241C2×C71—42no—
242C2×C71C2×#12311yescharacteristic
243C2×C71#52511yescharacteristic
244C2×C71#53811yescharacteristic
245C2×C71D4211yescharacteristic
246C2×C71#54611yescharacteristic
247C2×C71#54611yescharacteristic
248C2×C71#55111yescharacteristic
249D71—42no—
250#2418—711nomaximal, Sylow
251C71#241811yescharacteristic, complemented, Sylow
252C2×#123—711no—
253C2×#120—711no—
254C2×C4×D4—711no—
255C22×C22⋊C4D7111yescharacteristic, complemented
256#399—711no—
257#397—711no—
258#394—711no—
259#394—711no—
260#388—711no—
261#388—711no—
262#386—711no—
263#386—711no—
264#385—711no—
265#380—711no—
266#379—711no—
267C25C2×D7111yescharacteristic
268C22×D4—711no—
269C22×D4—711no—
270C22×D4—711no—
271C23×C4—711no—
272C23×C4C2×D7111yescharacteristic
273C23×C4C2×D7111yescharacteristic
274#123—1424no—
275#120—1424no—
276C4×D4—1424no—
277C2×C4⋊C4—711no—
278C2×C4⋊C4—711no—
279C2×C4⋊C4—711no—
280C2×C4⋊C4—711no—
281C2×C4⋊C4—711no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—711no—
284C2×C22⋊C4—711no—
285C2×C22⋊C4—711no—
286C2×C22⋊C4—711no—
287C2×C22⋊C4—711no—
288C2×C22⋊C4—711no—
289C2×C22⋊C4—711no—
290C2×C22⋊C4—711no—
291C2×C22⋊C4—711no—
292C2×C22⋊C4—711no—
293C2×C22⋊C4—711no—
294C2×C22⋊C4—711no—
295C2×C22⋊C4C2×D7111yescharacteristic
296C2×C22⋊C4C2×D7111yescharacteristic
297C2×C22⋊C4C2×D7111yescharacteristic
298C2×C22⋊C4C2×D7111yescharacteristic
299C2×C42—711no—
300#95—711no—
301#95—711no—
302#95—711no—
303#95—711no—
304#95—711no—
305#95—711no—
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—22no—
311C24—41no—
312C24—41no—
313C24—711no—
314C24C22×D7111yescharacteristic
315C24C22×D7111yescharacteristic
316C24C22×D7111yescharacteristic
317C2×D4—2841no—
318C2×D4—2841no—
319C2×D4—714no—
320C2×D4—1422no—
321C2×D4—1422no—
322C2×D4—1422no—
323C2×D4—1422no—
324C2×D4—1422no—
325C2×D4—1422no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—2841no—
333C22×C4—711no—
334C22×C4—711no—
335C22×C4—711no—
336C22×C4—711no—
337C22×C4—711no—
338C22×C4—711no—
339C22×C4—711no—
340C22×C4—1422no—
341C22×C4—1422no—
342C22×C4C22×D7111yescharacteristic
343C22×C4C22×D7111yescharacteristic
344C22×C4C22×D7111yescharacteristic
345C22×C4C22×D7111yescharacteristic
346C4⋊C4—2841no—
347C4⋊C4—2841no—
348C4⋊C4—1422no—
349C4⋊C4—1422no—
350C4⋊C4—1422no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—2841no—
355C22⋊C4—2841no—
356C22⋊C4—2841no—
357C22⋊C4—1422no—
358C22⋊C4—1422no—
359C22⋊C4—1422no—
360C22⋊C4—1422no—
361C22⋊C4—1422no—
362C22⋊C4—1422no—
363C22⋊C4—1422no—
364C22⋊C4—1422no—
365C22⋊C4—1422no—
366C22⋊C4C22⋊D7114yescomplemented
367C42—1422no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—44no—
386C23—44no—
387C23—44no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—712no—
392C23—1421no—
393C23—1421no—
394C23—1421no—
395C23—1421no—
396C23—1421no—
397C23—1421no—
398C23D4×D7112yes—
399C23C2×C22⋊D7112yes—
400C23#1176586412yes—
401C23#1176586512yes—
402C23#1176586512yes—
403C23C23×D7111yescharacteristic
404D4—2844no—
405D4—2844no—
406D4—1428no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—2844no—
420C2×C4—712no—
421C2×C4—1421no—
422C2×C4—1421no—
423C2×C4—1421no—
424C2×C4—1421no—
425C2×C4—1421no—
426C2×C4—1421no—
427C2×C4—1421no—
428C2×C4—1421no—
429C2×C4—1421no—
430C2×C4—1421no—
431C2×C4—1421no—
432C2×C4—1421no—
433C2×C4—1421no—
434C2×C4—1421no—
435C2×C4—1421no—
436C2×C4—1421no—
437C2×C4—1421no—
438C2×C4—1421no—
439C2×C4—1421no—
440C2×C4—1421no—
441C2×C4C2×C22⋊D7112yes—
442C2×C4C2×C22⋊D7112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—416no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—2841no—
465C22—2841no—
466C22—2841no—
467C22—2841no—
468C22—1422no—
469C22—1422no—
470C22—1422no—
471C22#1455611014yescomplemented
472C22C2×D4×D7111yescharacteristic
473C22C22×C22⋊D7111yescharacteristic
474C22C2×#1176586411yescharacteristic
475C22C2×#1176586511yescharacteristic
476C22C2×#1176586511yescharacteristic
477C22#1455617311yescharacteristic
478C22#1455617311yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—2841no—
484C4—2841no—
485C4—2841no—
486C4—2841no—
487C4—2841no—
488C4—2841no—
489C4—1422no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—2842no—
494C2C2×#1455611011yescharacteristic
495C2#1798651011yescharacteristic
496C2#1798658711yescharacteristic
497C2D4×C22⋊D7111yescharacteristic
498C2#1798663911yescharacteristic
499C2#1798664311yescharacteristic
500C2#1798667511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
FittingC22×C22⋊C4×C71C2
hypercenterC22×C22⋊C4D71
hypocenterC71#2418
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14556110C2semidirect
3. C2×C4×C22⋊D71C2semidirect
4. #17985935C2semidirect
5. #17985927C2semidirect
6. #17985915C2semidirect
7. #17985914C2semidirect
8. #17985893C2semidirect
9. #17985892C2semidirect
10. #17985878C2semidirect
11. #17985875C2semidirect
12. #17985872C2semidirect
13. #17985859C2semidirect
14. #17985855C2semidirect
15. C22×C22⋊C4×C71C2semidirect
19. C22×C4×D71C22semidirect
23. C2×C4⋊Dic71C22semidirect
24. C2×C4⋊Dic71C22semidirect
25. C2×Dic71⋊C4C22semidirect
26. C2×Dic71⋊C4C22semidirect
27. C2×Dic71⋊C4C22semidirect
37. C2×(C2×D71)⋊C4C22semidirect
38. C2×(C2×D71)⋊C4C22semidirect
39. C2×(C2×D71)⋊C4C22semidirect
40. C2×C4×Dic71C22semidirect
41. C71⋊#95C22semidirect
42. C71⋊#95C22semidirect
43. C71⋊#95C22semidirect
44. C71⋊#95C22semidirect
45. C71⋊#95C22semidirect
46. C71⋊#95C22semidirect
116. C22⋊C4×C71D4semidirect
213. C22×C71#123semidirect
251. C71#2418semidirect
255. C22×C22⋊C4D71semidirect
366. C22⋊C4C22⋊D71semidirect
471. C22#14556110semidirect