Finite Group Databasebeta

← #22621545

Subgroups — #22621545

Order 9344.

556 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556618C211yesmaximal, characteristic, complemented
2#17989256C211yesmaximal, characteristic, complemented
3D4×C22⋊D73C211yesmaximal, characteristic, complemented
4#17988962C211yesmaximal, characteristic, complemented
5#17988840C211yesmaximal, characteristic, complemented
6#17988837C211yesmaximal, characteristic, complemented
7#17988785C211yesmaximal, characteristic, complemented
8#17988780C211yesmaximal, characteristic, complemented
9#17988732C211yesmaximal, characteristic, complemented
10#17988731C211yesmaximal, characteristic, complemented
11#17988721C211yesmaximal, characteristic, complemented
12#17988719C211yesmaximal, characteristic, complemented
13SD16×Dic73C211yesmaximal, characteristic, complemented
14#17988663C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic, complemented
17C22×C22⋊D73—21no—
18C2×D4×D73C2211yescharacteristic
19#14556618—24no—
20C2×#11924015C2211yescharacteristic, complemented
21C2×D584C2211yescharacteristic, complemented
22C2×#11924013C2211yescharacteristic
23C2×#11924013C2211yescharacteristic, complemented
24C2×#11924013C2211yescharacteristic, complemented
25C2×#11924011C2211yescharacteristic, complemented
26#14556587—21no—
27#14556587C2211yescharacteristic
28#14556587C2211yescharacteristic, complemented
29#14556565—21no—
30#14556565C2211yescharacteristic
31#14556565C2211yescharacteristic, complemented
32#14556563—21no—
33#14556562—21no—
34#14556562C2211yescharacteristic
35#14556562C2211yescharacteristic, complemented
36#14556560—21no—
37#14556559—21no—
38Q8×Dic73C2211yescharacteristic, complemented
39D4×Dic73C2211yescharacteristic
40C4×C22⋊D73—21no—
41C4×C22⋊D73C2211yescharacteristic
42#14556523C2211yescharacteristic, complemented
43#14556520C2211yescharacteristic, complemented
44#14556515C2211yescharacteristic, complemented
45#14556513C2211yescharacteristic, complemented
46#14556513C2211yescharacteristic, complemented
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic, complemented
49#14556512C2211yescharacteristic, complemented
50C22⋊#10596831C2211yescharacteristic, complemented
51#14556503C2211yescharacteristic, complemented
52C8×Dic73C2211yescharacteristic, complemented
53C2×#41×C73C2211yescharacteristic, complemented
54C22×D4×C73C2211yescharacteristic
55AGL(1,ℤ/8)×C73—24no—
56C2×SD16×C73C2211yescharacteristic
57C2×SD16×C73C2211yescharacteristic, complemented
58C2×D8×C73C2211yescharacteristic
59C2×D8×C73C2211yescharacteristic, complemented
60C2×M16×C73C2211yescharacteristic, complemented
61C23×D73—21no—
62#11924029—22no—
63#11924029—41no—
64C2×D292—21no—
65C2×D292C2311yescharacteristic
66C2×D292C2311yescharacteristic
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C22⋊D73—21no—
73C2×C22⋊D73—21no—
74C2×C22⋊D73—21no—
75C2×C22⋊D73—21no—
76C2×C22⋊D73—44no—
77C2×C22⋊D73D411yescharacteristic
78D4×D73—22no—
79D4×D73—41no—
80C22×Dic73—21no—
81C2×C4×D73—21no—
82C2×C4×D73C2311yescharacteristic
83#11924015—22no—
84D584—22no—
85#11924013—22no—
86#11924013—41no—
87#11924013—41no—
88#11924011—22no—
89C2×#10596831C2311yescharacteristic
90C2×#10596831C2311yescharacteristic
91C4⋊Dic73—21no—
92C4⋊Dic73C2311yescharacteristic
93C4⋊Dic73C2311yescharacteristic
94#11924007D411yescharacteristic
95C22⋊Dic73—21no—
96C22⋊Dic73—21no—
97C22⋊Dic73—21no—
98C22⋊Dic73D411yescharacteristic
99#11924005—21no—
100#11924005—21no—
101#11924005D411yescharacteristic
102C4×Dic73—21no—
103C4×Dic73C2311yescharacteristic
104C24×C73—21no—
105#41×C73—22no—
106#41×C73—41no—
107C2×Q8×C73C2311yescharacteristic
108C2×D4×C73—22no—
109C2×D4×C73—21no—
110C2×D4×C73—21no—
111C2×D4×C73—41no—
112C2×D4×C73C2311yescharacteristic
113C2×D4×C73C2311yescharacteristic
114C2×D4×C73C2311yescharacteristic
115C22×C4×C73—21no—
116C22×C4×C73C2311yescharacteristic
117SD16×C73—22no—
118SD16×C73D414yescomplemented
119D8×C73—22no—
120D8×C73—22no—
121M16×C73—22no—
122C2×C8×C73C2311yescharacteristic
123C2×C8×C73C2311yescharacteristic
124C23×C73—21no—
125C23×C73—21no—
126C23×C73—21no—
127C23×C73—42no—
128C23×C73—42no—
129C23×C73—81no—
130C23×C73C2×D411yescharacteristic
131C22×D73—21no—
132C22×D73—21no—
133C22×D73—42no—
134C22×D73—42no—
135C22×D73—81no—
136C22×D73C2×D411yescharacteristic
137Q8×C73—21no—
138Q8×C73C2×D412yescomplemented
139D4×C73—21no—
140D4×C73—21no—
141D4×C73—21no—
142D4×C73—21no—
143D4×C73—21no—
144D4×C73—42no—
145D4×C73—42no—
146D4×C73C2×D412yes—
147C2×C4×C73—21no—
148C2×C4×C73—21no—
149C2×C4×C73—21no—
150C2×C4×C73—42no—
151C2×C4×C73C2×D411yescharacteristic
152C2×C4×C73C2411yescharacteristic
153C22⋊D73—22no—
154C22⋊D73—42no—
155C22⋊D73—42no—
156C22⋊D73—42no—
157C22⋊D73—42no—
158C22⋊D73—42no—
159C22⋊D73—81no—
160C22⋊D73—81no—
161C22⋊D73—81no—
162C22⋊D73—81no—
163C2×Dic73—21no—
164C2×Dic73—21no—
165C2×Dic73—42no—
166C2×Dic73C2×D411yescharacteristic
167C2×Dic73C2×D411yescharacteristic
168C2×Dic73C2×D411yescharacteristic
169D292—21no—
170D292—21no—
171D292—21no—
172D292—21no—
173D292—42no—
174C4×D73—21no—
175C4×D73—21no—
176C4×D73—42no—
177C8×C73—21no—
178C8×C73C2×D412yescomplemented
179#10596831—21no—
180#10596831—21no—
181C22×C73—22no—
182C22×C73—21no—
183C22×C73—21no—
184C22×C73—21no—
185C22×C73—41no—
186C22×C73—41no—
187C22×C73—41no—
188C22×C73—41no—
189C22×C73—41no—
190C22×C73—41no—
191C22×C73—41no—
192C22×C73—41no—
193C22×C73—84no—
194C22×C73C22×D411yescharacteristic
195C2×D73—21no—
196C2×D73—21no—
197C2×D73—21no—
198C2×D73—41no—
199C2×D73—41no—
200C2×D73—41no—
201C2×D73—41no—
202C2×D73—41no—
203C2×D73—41no—
204C2×D73—84no—
205C4×C73—22no—
206C4×C73—21no—
207C4×C73C22×D411yescharacteristic
208C4×C73H(5,𝔽2)11yescharacteristic
209Dic73—21no—
210Dic73—21no—
211Dic73—41no—
212Dic73—41no—
213Dic73AGL(1,ℤ/8)12yescomplemented
214C2×C73—42no—
215C2×C73—41no—
216C2×C73—81no—
217C2×C73—81no—
218C2×C73D4211yescharacteristic
219C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C73#57611yescharacteristic
221D73—41no—
222D73—81no—
223D73—81no—
224#3274—731nomaximal, Sylow
225C73#327411yescharacteristic, complemented, Sylow
226C2×AGL(1,ℤ/8)—731no—
227C2×AGL(1,ℤ/8)D7311yescharacteristic, complemented
228#550—731no—
229D42—731no—
230#493—731no—
231#469—731no—
232#469—731no—
233#460—731no—
234#459—731no—
235#449—731no—
236#449—731no—
237#447—731no—
238#447—731no—
239C4×SD16—731no—
240#436—731no—
241C2×#41—731no—
242C2×#41C2×D7311yescharacteristic, complemented
243C22×D4—731no—
244C22×D4—1461no—
245C22×D4C2×D7311yescharacteristic
246AGL(1,ℤ/8)—24no—
247AGL(1,ℤ/8)—1464no—
248C2×SD16—731no—
249C2×SD16C2×D7311yescharacteristic
250C2×SD16C2×D7311yescharacteristic, complemented
251C2×D8—731no—
252C2×D8—731no—
253C2×D8—731no—
254C2×D8—731no—
255C2×D8C2×D7311yescharacteristic
256C2×D8C2×D7311yescharacteristic, complemented
257C2×M16—731no—
258C2×M16C2×D7311yescharacteristic, complemented
259#127—731no—
260#127—731no—
261#127—1461no—
262#121—731no—
263#121—731no—
264#121—731no—
265#121—731no—
266#121—1461no—
267#121—1461no—
268#121—1461no—
269#120—1461no—
270#120—1461no—
271C4×Q8—731no—
272C4×D4—731no—
273C4×D4—731no—
274C4×D4—1461no—
275#106—731no—
276C4⋊C8—731no—
277#103—731no—
278#102—731no—
279#102—731no—
280#102—731no—
281#102—731no—
282#102—731no—
283C22⋊C8—731no—
284C22⋊C8—731no—
285C4×C8—731no—
286C24—21no—
287C24—1461no—
288#41—22no—
289#41—41no—
290#41—2921no—
291#41—1462no—
292C2×Q8C22×D7311yescharacteristic
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—2924no—
298C2×D4—2921no—
299C2×D4—731no—
300C2×D4—731no—
301C2×D4—731no—
302C2×D4—1461no—
303C2×D4—1461no—
304C2×D4—1461no—
305C2×D4—1461no—
306C2×D4—1461no—
307C2×D4—1461no—
308C2×D4—1461no—
309C2×D4—1461no—
310C2×D4—1462no—
311C2×D4—1461no—
312C2×D4—1461no—
313C2×D4C22×D7311yescharacteristic
314C2×D4C22×D7311yescharacteristic
315C2×D4C22×D7311yescharacteristic
316C22×C4—21no—
317C22×C4—731no—
318C22×C4—1461no—
319C22×C4—1461no—
320C22×C4C22×D7311yescharacteristic
321SD16—22no—
322SD16—1462no—
323SD16C22⋊D7314yescomplemented
324D8—22no—
325D8—22no—
326D8—2921no—
327D8—2921no—
328D8—1462no—
329D8—1462no—
330M16—22no—
331M16—1462no—
332C2×C8—731no—
333C2×C8—731no—
334C2×C8C22×D7311yescharacteristic
335C2×C8C22×D7311yescharacteristic
336C4⋊C4—731no—
337C4⋊C4—731no—
338C4⋊C4—731no—
339C4⋊C4—1461no—
340C22⋊C4—731no—
341C22⋊C4—731no—
342C22⋊C4—1461no—
343C22⋊C4—1461no—
344C22⋊C4—1461no—
345C22⋊C4—1461no—
346C22⋊C4—1461no—
347C42—731no—
348C42—1461no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—42no—
353C23—42no—
354C23—81no—
355C23—2922no—
356C23—2922no—
357C23—5841no—
358C23—731no—
359C23—1461no—
360C23—1461no—
361C23D4×D7311yescharacteristic
362Q8—21no—
363Q8C2×C22⋊D7312yescomplemented
364D4—21no—
365D4—21no—
366D4—21no—
367D4—21no—
368D4—21no—
369D4—42no—
370D4—42no—
371D4—2922no—
372D4—2922no—
373D4—2922no—
374D4—2922no—
375D4—2922no—
376D4—2922no—
377D4—5841no—
378D4—5841no—
379D4—5841no—
380D4—5841no—
381D4—1462no—
382D4—1461no—
383D4—1461no—
384D4—1461no—
385D4—1461no—
386D4C2×C22⋊D7312yes—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—2922no—
392C2×C4—2922no—
393C2×C4—731no—
394C2×C4—731no—
395C2×C4—731no—
396C2×C4—1461no—
397C2×C4—1461no—
398C2×C4—1461no—
399C2×C4—1461no—
400C2×C4D4×D7311yescharacteristic
401C2×C4C23×D7311yescharacteristic
402C8—21no—
403C8—1461no—
404C8—1461no—
405C8C2×C22⋊D7312yescomplemented
406C22—21no—
407C22—21no—
408C22—22no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—84no—
419C22—2921no—
420C22—2921no—
421C22—2921no—
422C22—2921no—
423C22—2921no—
424C22—2921no—
425C22—5844no—
426C22—1461no—
427C22—1461no—
428C22—1461no—
429C22C2×D4×D7311yescharacteristic
430C4—21no—
431C4—22no—
432C4—2921no—
433C4—2921no—
434C4—732no—
435C4—1461no—
436C4—1461no—
437C4C22×C22⋊D7311yescharacteristic
438C4#1455663611yescharacteristic
439C2—41no—
440C2—42no—
441C2—81no—
442C2—81no—
443C2—2921no—
444C2—5841no—
445C2—5841no—
446C2D4×C22⋊D7311yescharacteristic
447C2AGL(1,ℤ/8)×D7311yescharacteristic
448C2#1798939111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×AGL(1,ℤ/8)×C73C2
socleC22×C73C22×D4
hypercenterC2×AGL(1,ℤ/8)D73
hypocenterC73#3274
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#14556618C2semidirect
2. #17989256C2semidirect
3. D4×C22⋊D73C2semidirect
4. #17988962C2semidirect
5. #17988840C2semidirect
6. #17988837C2semidirect
7. #17988785C2semidirect
8. #17988780C2semidirect
9. #17988732C2semidirect
10. #17988731C2semidirect
11. #17988721C2semidirect
12. #17988719C2semidirect
13. SD16×Dic73C2semidirect
14. #17988663C2semidirect
15. C2×AGL(1,ℤ/8)×C73C2semidirect
16. C2×#11924029C22semidirect
20. C2×#11924015C22semidirect
21. C2×D584C22semidirect
23. C2×#11924013C22semidirect
24. C2×#11924013C22semidirect
25. C2×#11924011C22semidirect
28. #14556587C22semidirect
31. #14556565C22semidirect
35. #14556562C22semidirect
38. Q8×Dic73C22semidirect
42. #14556523C22semidirect
43. #14556520C22semidirect
44. #14556515C22semidirect
45. #14556513C22semidirect
46. #14556513C22semidirect
48. #14556512C22semidirect
49. #14556512C22semidirect
50. C22⋊#10596831C22semidirect
51. #14556503C22semidirect
52. C8×Dic73C22semidirect
53. C2×#41×C73C22semidirect
57. C2×SD16×C73C22semidirect
59. C2×D8×C73C22semidirect
60. C2×M16×C73C22semidirect
118. SD16×C73D4semidirect
138. Q8×C73C2×D4semidirect
178. C8×C73C2×D4semidirect
213. Dic73AGL(1,ℤ/8)semidirect
225. C73#3274semidirect
227. C2×AGL(1,ℤ/8)D73semidirect
242. C2×#41C2×D73semidirect
250. C2×SD16C2×D73semidirect
256. C2×D8C2×D73semidirect
258. C2×M16C2×D73semidirect
323. SD16C22⋊D73semidirect
363. Q8C2×C22⋊D73semidirect
405. C8C2×C22⋊D73semidirect