Finite Group Databasebeta

← #22614051

Subgroups — #22614051

Order 9344.

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×#14556577C211yesmaximal, characteristic, complemented
2C2×#14556570C211yesmaximal, characteristic, complemented
3C2×#14556560C211yesmaximal, characteristic
4#17988515C211yesmaximal, characteristic, complemented
5#17988503C211yesmaximal, characteristic, complemented
6#17988502C211yesmaximal, characteristic, complemented
7#17988499C211yesmaximal, characteristic, complemented
8#17988487C211yesmaximal, characteristic, complemented
9#17988480C211yesmaximal, characteristic, complemented
10#17988475C211yesmaximal, characteristic, complemented
11#17988466C211yesmaximal, characteristic, complemented
12#17988466C211yesmaximal, characteristic, complemented
13#17988443C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic73C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic, complemented
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic
20#14556577—24no—
21#14556570—24no—
22#14556560—24no—
23C2×C4⋊Dic73C2211yescharacteristic, complemented
24C2×#11924007C2211yescharacteristic, complemented
25C2×#11924007C2211yescharacteristic, complemented
26C2×C22⋊Dic73C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33C2×C22⋊Dic73C2211yescharacteristic
34C2×C22⋊Dic73C2211yescharacteristic
35C2×#11924005C2211yescharacteristic, complemented
36C2×#11924005C2211yescharacteristic, complemented
37C2×#11924005C2211yescharacteristic, complemented
38C2×#11924005C2211yescharacteristic, complemented
39C2×C4×Dic73C2211yescharacteristic, complemented
40C2×C4×Dic73C2211yescharacteristic, complemented
41#14556498C2211yescharacteristic, complemented
42#14556498C2211yescharacteristic, complemented
43#14556498C2211yescharacteristic, complemented
44#14556498C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46#14556498C2211yescharacteristic, complemented
47C25×C73C2211yescharacteristic
48C23×C4×C73C2211yescharacteristic
49C23×C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73—24no—
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C22⋊C4×C73C2211yescharacteristic
53C2×C22⋊C4×C73C2211yescharacteristic
54C2×C22⋊C4×C73C2211yescharacteristic
55C23×D73C2311yescharacteristic
56C2×Dic146—22no—
57C2×Dic146—22no—
58C2×Dic146—41no—
59C2×C22⋊D73—22no—
60C2×C22⋊D73—22no—
61C2×C22⋊D73—22no—
62C2×C22⋊D73—22no—
63C2×C22⋊D73—22no—
64C2×C22⋊D73—22no—
65C2×C22⋊D73—22no—
66C2×C22⋊D73—41no—
67C2×C22⋊D73—41no—
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C22×Dic73C2311yescharacteristic
71C22×Dic73C2311yescharacteristic
72C22×Dic73C2311yescharacteristic
73C22×Dic73C2311yescharacteristic
74C22×Dic73C2311yescharacteristic
75C4⋊Dic73—22no—
76#11924007—22no—
77#11924007—22no—
78C22⋊Dic73—22no—
79C22⋊Dic73—22no—
80C22⋊Dic73—22no—
81C22⋊Dic73—22no—
82C22⋊Dic73—22no—
83C22⋊Dic73—22no—
84C22⋊Dic73—41no—
85C22⋊Dic73—41no—
86C22⋊Dic73D414yes—
87#11924005—22no—
88#11924005—22no—
89#11924005—41no—
90#11924005—41no—
91C4×Dic73—22no—
92C4×Dic73—41no—
93C24×C73—22no—
94C24×C73—22no—
95C24×C73—22no—
96C24×C73—22no—
97C24×C73—22no—
98C24×C73—41no—
99C24×C73—41no—
100C24×C73C2311yescharacteristic
101C24×C73C2311yescharacteristic
102C24×C73C2311yescharacteristic
103C22×C4×C73—22no—
104C22×C4×C73—22no—
105C22×C4×C73—22no—
106C22×C4×C73—22no—
107C22×C4×C73—41no—
108C22×C4×C73—41no—
109C22×C4×C73C2311yescharacteristic
110C22×C4×C73C2311yescharacteristic
111C22×C4×C73C2311yescharacteristic
112C22×C4×C73C2311yescharacteristic
113C22⋊C4×C73—22no—
114C22⋊C4×C73—22no—
115C22⋊C4×C73—22no—
116C22⋊C4×C73D414yescomplemented
117C23×C73—21no—
118C23×C73—21no—
119C23×C73—21no—
120C23×C73—21no—
121C23×C73—28no—
122C23×C73—21no—
123C23×C73—21no—
124C23×C73—21no—
125C23×C73—21no—
126C23×C73—21no—
127C23×C73—21no—
128C23×C73—21no—
129C23×C73—21no—
130C23×C73—21no—
131C23×C73—21no—
132C23×C73—21no—
133C23×C73—21no—
134C23×C73—44no—
135C23×C73—44no—
136C23×C73—44no—
137C23×C73—44no—
138C23×C73—44no—
139C23×C73—44no—
140C23×C73C2×D412yes—
141C23×C73C2×D412yes—
142C23×C73#4112yes—
143C23×C73#4112yes—
144C23×C73#4112yes—
145C23×C73C2411yescharacteristic
146C22×D73—21no—
147C22×D73—21no—
148C22×D73—21no—
149C22×D73—21no—
150C22×D73—21no—
151C22×D73—21no—
152C22×D73—21no—
153C2×C4×C73—21no—
154C2×C4×C73—21no—
155C2×C4×C73—21no—
156C2×C4×C73—21no—
157C2×C4×C73—21no—
158C2×C4×C73—21no—
159C2×C4×C73—21no—
160C2×C4×C73—21no—
161C2×C4×C73—21no—
162C2×C4×C73—21no—
163C2×C4×C73—44no—
164C2×C4×C73—44no—
165C2×C4×C73C2×D412yes—
166C2×C4×C73C2×D412yes—
167C22⋊D73—44no—
168C22⋊D73—44no—
169C22⋊D73—44no—
170C2×Dic73—21no—
171C2×Dic73—21no—
172C2×Dic73—21no—
173C2×Dic73—21no—
174C2×Dic73—21no—
175C2×Dic73—21no—
176C2×Dic73—21no—
177C2×Dic73—21no—
178C2×Dic73—21no—
179C2×Dic73—21no—
180C2×Dic73—21no—
181C2×Dic73—21no—
182C2×Dic73—21no—
183C2×Dic73—21no—
184C2×Dic73—21no—
185C2×Dic73—21no—
186C2×Dic73—21no—
187C2×Dic73—21no—
188C2×Dic73—21no—
189C2×Dic73C2×D412yes—
190C2×Dic73C2×D412yes—
191Dic146—44no—
192C22×C73—22no—
193C22×C73—22no—
194C22×C73—22no—
195C22×C73—22no—
196C22×C73—22no—
197C22×C73—22no—
198C22×C73—22no—
199C22×C73—22no—
200C22×C73—22no—
201C22×C73—22no—
202C22×C73—22no—
203C22×C73—22no—
204C22×C73—416no—
205C22×C73—41no—
206C22×C73—41no—
207C22×C73—41no—
208C22×C73—41no—
209C22×C73—41no—
210C22×C73—41no—
211C22×C73—41no—
212C22×C73—41no—
213C22×C73#12414yescomplemented
214C22×C73C22×D411yescharacteristic
215C22×C73C22×D411yescharacteristic
216C22×C73C2×#4111yescharacteristic
217C22×C73C2×#4111yescharacteristic
218C22×C73C2×#4111yescharacteristic
219C22×C73H(5,𝔽2)11yescharacteristic
220C22×C73H(5,𝔽2)11yescharacteristic
221C2×D73—41no—
222C2×D73—41no—
223C2×D73—41no—
224C2×D73—41no—
225C2×D73—41no—
226C2×D73—41no—
227C2×D73—41no—
228C4×C73—22no—
229C4×C73—22no—
230C4×C73—41no—
231C4×C73—41no—
232Dic73—22no—
233Dic73—22no—
234Dic73—41no—
235Dic73—41no—
236Dic73—41no—
237Dic73—41no—
238Dic73—41no—
239C2×C73—24no—
240C2×C73—42no—
241C2×C73—42no—
242C2×C73#52511yescharacteristic
243C2×C73C2×#12411yescharacteristic
244C2×C73#53811yescharacteristic
245C2×C73D4211yescharacteristic
246C2×C73#54611yescharacteristic
247C2×C73#54611yescharacteristic
248C2×C73#55111yescharacteristic
249D73—81no—
250#2472—731nomaximal, Sylow
251C73#247211yescharacteristic, complemented, Sylow
252C2×#124—731no—
253C2×C22⋊Q8—731no—
254C2×#120—731no—
255C22×C22⋊C4D7311yescharacteristic, complemented
256#397—731no—
257#394—731no—
258#394—731no—
259#393—731no—
260#390—731no—
261#388—731no—
262#388—731no—
263#386—731no—
264#386—731no—
265#379—731no—
266C4×C22⋊C4—731no—
267C25C2×D7311yescharacteristic
268C22×Q8—731no—
269C22×D4—731no—
270C22×D4—731no—
271C22×D4—731no—
272C23×C4C2×D7311yescharacteristic
273C23×C4C2×D7311yescharacteristic
274#124—1464no—
275C22⋊Q8—1464no—
276#120—1464no—
277C2×C4⋊C4—731no—
278C2×C4⋊C4—731no—
279C2×C4⋊C4—731no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—731no—
282C2×C22⋊C4—731no—
283C2×C22⋊C4—731no—
284C2×C22⋊C4—731no—
285C2×C22⋊C4—731no—
286C2×C22⋊C4—731no—
287C2×C22⋊C4—731no—
288C2×C22⋊C4—731no—
289C2×C22⋊C4—731no—
290C2×C22⋊C4—731no—
291C2×C22⋊C4—731no—
292C2×C22⋊C4—731no—
293C2×C22⋊C4—731no—
294C2×C22⋊C4C2×D7311yescharacteristic
295C2×C22⋊C4C2×D7311yescharacteristic
296C2×C22⋊C4C2×D7311yescharacteristic
297C2×C22⋊C4C2×D7311yescharacteristic
298C2×C42—731no—
299C2×C42—731no—
300#95—731no—
301#95—731no—
302#95—731no—
303#95—731no—
304#95—731no—
305#95—731no—
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—22no—
311C24—41no—
312C24—41no—
313C24—731no—
314C24C22×D7311yescharacteristic
315C24C22×D7311yescharacteristic
316C24C22×D7311yescharacteristic
317C2×Q8—2921no—
318C2×Q8—1462no—
319C2×Q8—1462no—
320C2×D4—2921no—
321C2×D4—2921no—
322C2×D4—1462no—
323C2×D4—1462no—
324C2×D4—1462no—
325C2×D4—1462no—
326C2×D4—1462no—
327C2×D4—1462no—
328C2×D4—1462no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—731no—
336C22×C4—731no—
337C22×C4—731no—
338C22×C4—731no—
339C22×C4—731no—
340C22×C4—731no—
341C22×C4—731no—
342C22×C4C22×D7311yescharacteristic
343C22×C4C22×D7311yescharacteristic
344C22×C4C22×D7311yescharacteristic
345C22×C4C22×D7311yescharacteristic
346C4⋊C4—1462no—
347C4⋊C4—1462no—
348C4⋊C4—1462no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—2921no—
353C22⋊C4—2921no—
354C22⋊C4—2921no—
355C22⋊C4—2921no—
356C22⋊C4—734no—
357C22⋊C4—1462no—
358C22⋊C4—1462no—
359C22⋊C4—1462no—
360C22⋊C4—1462no—
361C22⋊C4—1462no—
362C22⋊C4—1462no—
363C22⋊C4—1462no—
364C22⋊C4—1462no—
365C22⋊C4C22⋊D7314yescomplemented
366C42—2921no—
367C42—1462no—
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—1461no—
392C23—1461no—
393C23—1461no—
394C23—1461no—
395C23—1461no—
396C23—1461no—
397C23—1461no—
398C23D4×D7312yes—
399C23C2×C22⋊D7312yes—
400C23#1192402712yes—
401C23#1192402812yes—
402C23#1192402812yes—
403C23C23×D7311yescharacteristic
404Q8—2924no—
405D4—2924no—
406D4—2924no—
407D4—2924no—
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—44no—
419C2×C4—44no—
420C2×C4—732no—
421C2×C4—732no—
422C2×C4—1461no—
423C2×C4—1461no—
424C2×C4—1461no—
425C2×C4—1461no—
426C2×C4—1461no—
427C2×C4—1461no—
428C2×C4—1461no—
429C2×C4—1461no—
430C2×C4—1461no—
431C2×C4—1461no—
432C2×C4—1461no—
433C2×C4—1461no—
434C2×C4—1461no—
435C2×C4—1461no—
436C2×C4—1461no—
437C2×C4—1461no—
438C2×C4—1461no—
439C2×C4—1461no—
440C2×C4—1461no—
441C2×C4C2×C22⋊D7312yes—
442C2×C4C2×C22⋊D7312yes—
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—2921no—
465C22—2921no—
466C22—2921no—
467C22—2921no—
468C22—2921no—
469C22—2921no—
470C22—2921no—
471C22#1455657714yescomplemented
472C22C2×D4×D7311yescharacteristic
473C22C22×C22⋊D7311yescharacteristic
474C22C2×#1192402711yescharacteristic
475C22C2×#1192402811yescharacteristic
476C22C2×#1192402811yescharacteristic
477C22#1455663611yescharacteristic
478C22#1455663611yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—2921no—
484C4—2921no—
485C4—2921no—
486C4—2921no—
487C4—2921no—
488C4—1462no—
489C4—1462no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—5841no—
494C2#1798909811yescharacteristic
495C2C2×#1455657711yescharacteristic
496C2#1798917511yescharacteristic
497C2D4×C22⋊D7311yescharacteristic
498C2#1798922711yescharacteristic
499C2#1798923111yescharacteristic
500C2#1798926311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC22×C22⋊C4×C73C2
hypercenterC22×C22⋊C4D73
hypocenterC73#2472
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14556577C2semidirect
2. C2×#14556570C2semidirect
4. #17988515C2semidirect
5. #17988503C2semidirect
6. #17988502C2semidirect
7. #17988499C2semidirect
8. #17988487C2semidirect
9. #17988480C2semidirect
10. #17988475C2semidirect
11. #17988466C2semidirect
12. #17988466C2semidirect
13. #17988443C2semidirect
14. C4×C22⋊Dic73C2semidirect
15. C22×C22⋊C4×C73C2semidirect
16. C22×Dic146C22semidirect
23. C2×C4⋊Dic73C22semidirect
24. C2×#11924007C22semidirect
25. C2×#11924007C22semidirect
35. C2×#11924005C22semidirect
36. C2×#11924005C22semidirect
37. C2×#11924005C22semidirect
38. C2×#11924005C22semidirect
39. C2×C4×Dic73C22semidirect
40. C2×C4×Dic73C22semidirect
41. #14556498C22semidirect
42. #14556498C22semidirect
43. #14556498C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
46. #14556498C22semidirect
116. C22⋊C4×C73D4semidirect
213. C22×C73#124semidirect
251. C73#2472semidirect
255. C22×C22⋊C4D73semidirect
365. C22⋊C4C22⋊D73semidirect
471. C22#14556577semidirect