Finite Group Databasebeta

← #22592464

Subgroups — #22592464

Order 9088.

786 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×#14556114C211yesmaximal, characteristic, complemented
2C2×#14556108C211yesmaximal, characteristic, complemented
3C2×#14556098C211yesmaximal, characteristic
4C2×C22⋊C4×D71C211yesmaximal, characteristic, complemented
5#17985924C211yesmaximal, characteristic, complemented
6#17985916C211yesmaximal, characteristic, complemented
7#17985915C211yesmaximal, characteristic, complemented
8#17985912C211yesmaximal, characteristic, complemented
9#17985901C211yesmaximal, characteristic, complemented
10#17985891C211yesmaximal, characteristic, complemented
11#17985877C211yesmaximal, characteristic, complemented
12#17985877C211yesmaximal, characteristic, complemented
13#17985854C211yesmaximal, characteristic, complemented
14C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
15#388×C71C211yesmaximal, characteristic, complemented
16C24×D71C2211yescharacteristic
17C22×Dic142C2211yescharacteristic, complemented
18C22×D284C2211yescharacteristic
19C22×D284C2211yescharacteristic
20C22×C22⋊D71C2211yescharacteristic
21C22×C4×D71C2211yescharacteristic
22C22×C4×D71C2211yescharacteristic
23#14556114—24no—
24#14556108—24no—
25#14556098—24no—
26C2×C4⋊Dic71C2211yescharacteristic, complemented
27C2×C4⋊Dic71C2211yescharacteristic, complemented
28C2×C22⋊Dic71C2211yescharacteristic
29C2×C22⋊Dic71C2211yescharacteristic
30C2×(C2×D71)⋊C4C2211yescharacteristic
31C2×(C2×D71)⋊C4C2211yescharacteristic
32C2×(C2×D71)⋊C4C2211yescharacteristic
33C2×(C2×D71)⋊C4C2211yescharacteristic
34C2×(C2×D71)⋊C4C2211yescharacteristic
35C2×(C2×D71)⋊C4C2211yescharacteristic
36C2×(C2×D71)⋊C4C2211yescharacteristic
37C2×(C2×D71)⋊C4C2211yescharacteristic
38C2×(C2×D71)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D71)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D71)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D71)⋊C4C2211yescharacteristic, complemented
42C22⋊C4×D71—24no—
43C2×C4×Dic71C2211yescharacteristic, complemented
44C71⋊#95C2211yescharacteristic, complemented
45C71⋊#95C2211yescharacteristic, complemented
46C71⋊#95C2211yescharacteristic, complemented
47C71⋊#95C2211yescharacteristic, complemented
48C2×C4⋊C4×C71C2211yescharacteristic, complemented
49C2×C22⋊C4×C71C2211yescharacteristic
50C2×C22⋊C4×C71C2211yescharacteristic
51C2×C22⋊C4×C71C2211yescharacteristic
52C2×C42×C71C2211yescharacteristic, complemented
53#95×C71C2211yescharacteristic, complemented
54#95×C71C2211yescharacteristic, complemented
55C23×D71—22no—
56C23×D71—22no—
57C23×D71—22no—
58C23×D71—22no—
59C23×D71—22no—
60C23×D71—41no—
61C23×D71—41no—
62C23×D71C2311yescharacteristic
63C23×D71C2311yescharacteristic
64C23×D71C2311yescharacteristic
65C2×Dic142—22no—
66C2×Dic142—22no—
67C2×Dic142—41no—
68C2×D284—22no—
69C2×D284—22no—
70C2×D284—22no—
71C2×D284—22no—
72C2×D284—22no—
73C2×D284—41no—
74C2×C22⋊D71—22no—
75C2×C22⋊D71—22no—
76C2×C22⋊D71—41no—
77C22×Dic71C2311yescharacteristic
78C22×Dic71C2311yescharacteristic
79C22×Dic71C2311yescharacteristic
80C22×Dic71C2311yescharacteristic
81C22×Dic71C2311yescharacteristic
82C2×C4×D71—22no—
83C2×C4×D71—22no—
84C2×C4×D71—22no—
85C2×C4×D71—22no—
86C2×C4×D71—41no—
87C2×C4×D71—41no—
88C4⋊Dic71—22no—
89C4⋊Dic71—22no—
90C22⋊Dic71—22no—
91C22⋊Dic71—22no—
92(C2×D71)⋊C4—22no—
93(C2×D71)⋊C4—22no—
94(C2×D71)⋊C4—22no—
95(C2×D71)⋊C4—22no—
96(C2×D71)⋊C4—22no—
97(C2×D71)⋊C4—22no—
98(C2×D71)⋊C4—22no—
99(C2×D71)⋊C4—22no—
100(C2×D71)⋊C4—41no—
101(C2×D71)⋊C4—41no—
102(C2×D71)⋊C4—41no—
103(C2×D71)⋊C4D414yes—
104C4×Dic71—22no—
105C24×C71C2311yescharacteristic
106C22×C4×C71C2311yescharacteristic
107C22×C4×C71C2311yescharacteristic
108C22×C4×C71C2311yescharacteristic
109C22×C4×C71C2311yescharacteristic
110C22×C4×C71C2311yescharacteristic
111C22×C4×C71C2311yescharacteristic
112C4⋊C4×C71—22no—
113C22⋊C4×C71—22no—
114C22⋊C4×C71—41no—
115C22⋊C4×C71D414yescomplemented
116C42×C71—41no—
117C23×C71—21no—
118C23×C71—21no—
119C23×C71—21no—
120C23×C71—21no—
121C23×C71—21no—
122C23×C71—21no—
123C23×C71C2×D412yes—
124C23×C71C2411yescharacteristic
125C22×D71—21no—
126C22×D71—21no—
127C22×D71—21no—
128C22×D71—21no—
129C22×D71—28no—
130C22×D71—21no—
131C22×D71—21no—
132C22×D71—21no—
133C22×D71—21no—
134C22×D71—21no—
135C22×D71—21no—
136C22×D71—21no—
137C22×D71—21no—
138C22×D71—21no—
139C22×D71—21no—
140C22×D71—21no—
141C22×D71—21no—
142C22×D71—21no—
143C22×D71—44no—
144C22×D71—44no—
145C22×D71—44no—
146C22×D71—44no—
147C22×D71—44no—
148C22×D71—44no—
149C22×D71C2×D412yes—
150C22×D71#4112yes—
151C22×D71#4112yes—
152C22×D71#4112yes—
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—21no—
164C2×C4×C71—21no—
165C2×C4×C71—21no—
166C2×C4×C71—21no—
167C2×C4×C71—21no—
168C2×C4×C71C2×D412yes—
169C2×C4×C71C2×D412yes—
170C2×C4×C71C2×D412yes—
171C22⋊D71—44no—
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×Dic71C2×D412yes—
187D284—44no—
188D284—44no—
189C4×D71—44no—
190C4×D71—44no—
191Dic142—44no—
192C22×C71—22no—
193C22×C71—22no—
194C22×C71—22no—
195C22×C71—41no—
196C22×C71—41no—
197C22×C71—41no—
198C22×C71—41no—
199C22×C71C22×D411yescharacteristic
200C22×C71C22×D411yescharacteristic
201C22×C71C2×#4111yescharacteristic
202C22×C71C2×#4111yescharacteristic
203C22×C71C2×#4111yescharacteristic
204C22×C71H(5,𝔽2)11yescharacteristic
205C22×C71H(5,𝔽2)11yescharacteristic
206C2×D71—22no—
207C2×D71—22no—
208C2×D71—22no—
209C2×D71—22no—
210C2×D71—22no—
211C2×D71—22no—
212C2×D71—22no—
213C2×D71—22no—
214C2×D71—22no—
215C2×D71—416no—
216C2×D71—41no—
217C2×D71—41no—
218C2×D71—41no—
219C2×D71—41no—
220C2×D71—41no—
221C2×D71—41no—
222C2×D71—41no—
223C2×D71—41no—
224C2×D71—41no—
225C2×D71—41no—
226C2×D71—41no—
227C2×D71#12414yescomplemented
228C4×C71—22no—
229C4×C71—22no—
230C4×C71—22no—
231C4×C71—41no—
232C4×C71—41no—
233C4×C71—41no—
234Dic71—22no—
235Dic71—41no—
236Dic71—41no—
237Dic71—41no—
238Dic71—41no—
239C2×C71—42no—
240C2×C71#52511yescharacteristic
241C2×C71C2×#12411yescharacteristic
242C2×C71#53811yescharacteristic
243C2×C71D4211yescharacteristic
244C2×C71#54611yescharacteristic
245C2×C71#54611yescharacteristic
246C2×C71#55111yescharacteristic
247D71—24no—
248D71—42no—
249D71—81no—
250#2472—711nomaximal, Sylow
251C71#247211yescharacteristic, complemented, Sylow
252C2×#124—711no—
253C2×C22⋊Q8—711no—
254C2×#120—711no—
255C22×C22⋊C4—711no—
256#397—711no—
257#394—711no—
258#394—711no—
259#393—711no—
260#390—711no—
261#388—711no—
262#388D7111yescharacteristic, complemented
263#386—711no—
264#386—711no—
265#379—711no—
266C4×C22⋊C4—711no—
267C25—711no—
268C22×Q8—711no—
269C22×D4—711no—
270C22×D4—711no—
271C22×D4—711no—
272C23×C4—711no—
273C23×C4—711no—
274#124—1424no—
275C22⋊Q8—1424no—
276#120—1424no—
277C2×C4⋊C4—711no—
278C2×C4⋊C4—711no—
279C2×C4⋊C4C2×D7111yescharacteristic, complemented
280C2×C22⋊C4—711no—
281C2×C22⋊C4—711no—
282C2×C22⋊C4—711no—
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—1424no—
295C2×C22⋊C4C2×D7111yescharacteristic
296C2×C22⋊C4C2×D7111yescharacteristic
297C2×C22⋊C4C2×D7111yescharacteristic
298C2×C42—711no—
299C2×C42C2×D7111yescharacteristic, complemented
300#95—711no—
301#95—711no—
302#95—711no—
303#95—711no—
304#95C2×D7111yescharacteristic, complemented
305#95C2×D7111yescharacteristic, complemented
306C24—2841no—
307C24—2841no—
308C24—711no—
309C24—711no—
310C24—711no—
311C24—1422no—
312C24—1422no—
313C24—1422no—
314C24—1422no—
315C24—1422no—
316C24C22×D7111yescharacteristic
317C2×Q8—2841no—
318C2×Q8—1422no—
319C2×Q8—1422no—
320C2×D4—2841no—
321C2×D4—2841no—
322C2×D4—1422no—
323C2×D4—1422no—
324C2×D4—1422no—
325C2×D4—1422no—
326C2×D4—1422no—
327C2×D4—1422no—
328C2×D4—1422no—
329C22×C4—2841no—
330C22×C4—2841no—
331C22×C4—711no—
332C22×C4—711no—
333C22×C4—711no—
334C22×C4—711no—
335C22×C4—711no—
336C22×C4—1422no—
337C22×C4—1422no—
338C22×C4—1422no—
339C22×C4—1422no—
340C22×C4C22×D7111yescharacteristic
341C22×C4C22×D7111yescharacteristic
342C22×C4C22×D7111yescharacteristic
343C22×C4C22×D7111yescharacteristic
344C22×C4C22×D7111yescharacteristic
345C22×C4C22×D7111yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—1422no—
348C4⋊C4—1422no—
349C22⋊C4—22no—
350C22⋊C4—41no—
351C22⋊C4—2841no—
352C22⋊C4—2841no—
353C22⋊C4—2841no—
354C22⋊C4—714no—
355C22⋊C4—1422no—
356C22⋊C4—1422no—
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⋊C4D28414yescomplemented
366C42—41no—
367C42—1422no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—2844no—
375C23—2844no—
376C23—2844no—
377C23—2844no—
378C23—2844no—
379C23—2844no—
380C23—712no—
381C23—712no—
382C23—712no—
383C23—712no—
384C23—1428no—
385C23—1421no—
386C23—1421no—
387C23—1421no—
388C23—1421no—
389C23—1421no—
390C23—1421no—
391C23—1421no—
392C23—1421no—
393C23—1421no—
394C23—1421no—
395C23—1421no—
396C23—1421no—
397C23—1421no—
398C23—1421no—
399C23—1421no—
400C23—1421no—
401C23—1421no—
402C23C2×D28412yes—
403C23C23×D7111yescharacteristic
404Q8—2844no—
405D4—2844no—
406D4—2844no—
407D4—2844no—
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—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—2844no—
424C2×C4—2844no—
425C2×C4—712no—
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×C4D4×D7112yes—
441C2×C4C2×D28412yes—
442C2×C4C2×D28412yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—28416no—
451C22—2841no—
452C22—2841no—
453C22—2841no—
454C22—2841no—
455C22—2841no—
456C22—2841no—
457C22—2841no—
458C22—2841no—
459C22—2841no—
460C22—2841no—
461C22—2841no—
462C22—714no—
463C22—1422no—
464C22—1422no—
465C22—1422no—
466C22—1422no—
467C22—1422no—
468C22—1422no—
469C22—1422no—
470C22—1422no—
471C22—1422no—
472C22C2×D4×D7111yescharacteristic
473C22C22×D28411yescharacteristic
474C22#41×D7111yescharacteristic
475C22#41×D7111yescharacteristic
476C22#41×D7111yescharacteristic
477C22#1455617311yescharacteristic
478C22#1455617411yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—2841no—
486C4—2841no—
487C4—2841no—
488C4—2841no—
489C4—1422no—
490C2—42no—
491C2—2842no—
492C2—5681no—
493C2—1424no—
494C2#1798651111yescharacteristic
495C2#124×D7111yescharacteristic
496C2#1798658511yescharacteristic
497C2D4×D28411yescharacteristic
498C2#1798663811yescharacteristic
499C2#1798664411yescharacteristic
500C2#1798667411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#388×C71C2
hypercenter#388D71
hypocenterC71#2472
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14556114C2semidirect
2. C2×#14556108C2semidirect
4. C2×C22⋊C4×D71C2semidirect
5. #17985924C2semidirect
6. #17985916C2semidirect
7. #17985915C2semidirect
8. #17985912C2semidirect
9. #17985901C2semidirect
10. #17985891C2semidirect
11. #17985877C2semidirect
12. #17985877C2semidirect
13. #17985854C2semidirect
14. C4×(C2×D71)⋊C4C2semidirect
15. #388×C71C2semidirect
17. C22×Dic142C22semidirect
26. C2×C4⋊Dic71C22semidirect
27. C2×C4⋊Dic71C22semidirect
38. C2×(C2×D71)⋊C4C22semidirect
39. C2×(C2×D71)⋊C4C22semidirect
40. C2×(C2×D71)⋊C4C22semidirect
41. C2×(C2×D71)⋊C4C22semidirect
43. C2×C4×Dic71C22semidirect
44. C71⋊#95C22semidirect
45. C71⋊#95C22semidirect
46. C71⋊#95C22semidirect
47. C71⋊#95C22semidirect
48. C2×C4⋊C4×C71C22semidirect
52. C2×C42×C71C22semidirect
53. #95×C71C22semidirect
54. #95×C71C22semidirect
115. C22⋊C4×C71D4semidirect
227. C2×D71#124semidirect
251. C71#2472semidirect
262. #388D71semidirect
279. C2×C4⋊C4C2×D71semidirect
299. C2×C42C2×D71semidirect
304. #95C2×D71semidirect
305. #95C2×D71semidirect
365. C22⋊C4D284semidirect