Finite Group Databasebeta

← #22621525

Subgroups — #22621525

Order 9344.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556615C211yesmaximal, characteristic, complemented
2#17989236C211yesmaximal, characteristic, complemented
3D4×C22⋊D73C211yesmaximal, characteristic, complemented
4#17988958C211yesmaximal, characteristic, complemented
5#17988833C211yesmaximal, characteristic, complemented
6#17988830C211yesmaximal, characteristic, complemented
7#17988790C211yesmaximal, characteristic, complemented
8#17988780C211yesmaximal, characteristic, complemented
9#17988738C211yesmaximal, characteristic, complemented
10#17988736C211yesmaximal, characteristic, complemented
11#17988732C211yesmaximal, characteristic, complemented
12#17988729C211yesmaximal, characteristic, complemented
13D8×Dic73C211yesmaximal, characteristic, complemented
14#17988663C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic, complemented
17C22×C22⋊D73—21no—
18C2×D4×D73C2211yescharacteristic
19#14556615—24no—
20C2×#11924017C2211yescharacteristic, complemented
21C2×#11924016C2211yescharacteristic
22C2×#11924016C2211yescharacteristic, complemented
23C2×#11924015C2211yescharacteristic, complemented
24C2×#11924013C2211yescharacteristic, complemented
25C2×#11924011C2211yescharacteristic, complemented
26#14556589C2211yescharacteristic, complemented
27#14556587C2211yescharacteristic
28#14556574—21no—
29#14556572—21no—
30#14556570C2211yescharacteristic, complemented
31#14556567C2211yescharacteristic, complemented
32#14556565C2211yescharacteristic
33#14556563—21no—
34#14556563—21no—
35#14556562C2211yescharacteristic
36#14556560—21no—
37#14556559—21no—
38D4×Dic73C2211yescharacteristic
39D4×Dic73C2211yescharacteristic, complemented
40C4×C22⋊D73C2211yescharacteristic
41C2×#11924007—21no—
42#14556525C2211yescharacteristic, complemented
43#14556520C2211yescharacteristic, complemented
44#14556516C2211yescharacteristic, complemented
45#14556515C2211yescharacteristic, 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#11924027—22no—
63#11924027—41no—
64C2×Dic146C2311yescharacteristic
65C2×D292C2311yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C22⋊D73—44no—
73C2×C22⋊D73D411yescharacteristic
74D4×D73—22no—
75D4×D73—41no—
76C22×Dic73—21no—
77C22×Dic73—21no—
78C22×Dic73—21no—
79C2×C4×D73C2311yescharacteristic
80#11924017—22no—
81#11924016—22no—
82#11924016—41no—
83#11924015—41no—
84#11924013—22no—
85#11924011—22no—
86C2×#10596831C2311yescharacteristic
87C2×#10596831C2311yescharacteristic
88C4⋊Dic73C2311yescharacteristic
89C4⋊Dic73C2311yescharacteristic
90#11924007—21no—
91#11924007—21no—
92#11924007—21no—
93#11924007—21no—
94#11924007D411yescharacteristic
95C22⋊Dic73—21no—
96C22⋊Dic73—21no—
97C22⋊Dic73—21no—
98C22⋊Dic73—21no—
99C22⋊Dic73D411yescharacteristic
100#11924005—21no—
101#11924005—21no—
102#11924005D411yescharacteristic
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×C73—22no—
119D8×C73—22no—
120D8×C73D414yescomplemented
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—42no—
133C22×D73—42no—
134C22×D73—81no—
135C22×D73C2×D411yescharacteristic
136Q8×C73—21no—
137Q8×C73—21no—
138D4×C73—21no—
139D4×C73—21no—
140D4×C73—21no—
141D4×C73—21no—
142D4×C73—42no—
143D4×C73—42no—
144D4×C73C2×D412yes—
145D4×C73C2×D412yescomplemented
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—21no—
149C2×C4×C73—42no—
150C2×C4×C73C2×D411yescharacteristic
151C2×C4×C73C2411yescharacteristic
152C22⋊D73—22no—
153C22⋊D73—42no—
154C22⋊D73—42no—
155C22⋊D73—42no—
156C22⋊D73—42no—
157C22⋊D73—42no—
158C22⋊D73—81no—
159C2×Dic73—21no—
160C2×Dic73—21no—
161C2×Dic73—21no—
162C2×Dic73—42no—
163C2×Dic73—42no—
164C2×Dic73—42no—
165C2×Dic73C2×D411yescharacteristic
166C2×Dic73C2×D411yescharacteristic
167C2×Dic73C2×D411yescharacteristic
168D292—21no—
169D292—21no—
170C4×D73—21no—
171C4×D73—21no—
172Dic146—21no—
173Dic146—21no—
174C8×C73—21no—
175C8×C73C2×D412yescomplemented
176#10596831—21no—
177#10596831—21no—
178C22×C73—22no—
179C22×C73—22no—
180C22×C73—21no—
181C22×C73—21no—
182C22×C73—21no—
183C22×C73—41no—
184C22×C73—41no—
185C22×C73—41no—
186C22×C73—41no—
187C22×C73—41no—
188C22×C73—41no—
189C22×C73—41no—
190C22×C73—84no—
191C22×C73C22×D411yescharacteristic
192C2×D73—21no—
193C2×D73—21no—
194C2×D73—21no—
195C2×D73—41no—
196C2×D73—41no—
197C2×D73—41no—
198C2×D73—84no—
199C4×C73—21no—
200C4×C73—41no—
201C4×C73C22×D411yescharacteristic
202C4×C73H(5,𝔽2)11yescharacteristic
203Dic73—21no—
204Dic73—21no—
205Dic73—41no—
206Dic73—41no—
207Dic73—41no—
208Dic73AGL(1,ℤ/8)12yescomplemented
209C2×C73—42no—
210C2×C73—41no—
211C2×C73—42no—
212C2×C73—81no—
213C2×C73D4211yescharacteristic
214C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C73#57711yescharacteristic
216D73—41no—
217D73—81no—
218#3272—731nomaximal, Sylow
219C73#327211yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)—731no—
221C2×AGL(1,ℤ/8)D7311yescharacteristic, complemented
222#547—731no—
223D42—731no—
224#492—731no—
225#468—731no—
226#468—731no—
227#461—731no—
228#459—731no—
229#450—731no—
230#450—731no—
231#449—731no—
232#449—731no—
233C4×D8—731no—
234#436—731no—
235C2×#41—731no—
236C2×#41C2×D7311yescharacteristic, complemented
237C22×D4—731no—
238C22×D4—1461no—
239C22×D4C2×D7311yescharacteristic
240AGL(1,ℤ/8)—24no—
241AGL(1,ℤ/8)—1464no—
242C2×SD16—731no—
243C2×SD16—731no—
244C2×SD16—731no—
245C2×SD16—731no—
246C2×SD16C2×D7311yescharacteristic
247C2×SD16C2×D7311yescharacteristic, complemented
248C2×D8—731no—
249C2×D8C2×D7311yescharacteristic
250C2×D8C2×D7311yescharacteristic, complemented
251C2×M16—731no—
252C2×M16C2×D7311yescharacteristic, complemented
253C4⋊Q8—731no—
254#127—731no—
255#123—1461no—
256#123—1461no—
257C22⋊Q8—731no—
258C22⋊Q8—731no—
259#121—731no—
260#121—731no—
261#121—1461no—
262#121—1461no—
263#120—1461no—
264#120—1461no—
265C4×D4—731no—
266C4×D4—731no—
267C4×D4—731no—
268C2×C4⋊C4—1461no—
269#107—731no—
270C4⋊C8—731no—
271#103—731no—
272#103—731no—
273#102—731no—
274#102—731no—
275#102—731no—
276#102—731no—
277C22⋊C8—731no—
278C22⋊C8—731no—
279C4×C8—731no—
280C24—21no—
281C24—1461no—
282#41—22no—
283#41—41no—
284#41—2921no—
285#41—1462no—
286C2×Q8—731no—
287C2×Q8C22×D7311yescharacteristic
288C2×D4—22no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—2924no—
293C2×D4—2921no—
294C2×D4—731no—
295C2×D4—731no—
296C2×D4—1461no—
297C2×D4—1461no—
298C2×D4—1461no—
299C2×D4—1461no—
300C2×D4—1461no—
301C2×D4—1461no—
302C2×D4—1462no—
303C2×D4C22×D7311yescharacteristic
304C2×D4C22×D7311yescharacteristic
305C2×D4C22×D7311yescharacteristic
306C22×C4—21no—
307C22×C4—731no—
308C22×C4—1461no—
309C22×C4—1461no—
310C22×C4—1461no—
311C22×C4C22×D7311yescharacteristic
312SD16—22no—
313SD16—22no—
314SD16—2921no—
315SD16—2921no—
316SD16—1462no—
317SD16—1462no—
318D8—22no—
319D8—1462no—
320D8C22⋊D7314yescomplemented
321M16—22no—
322M16—1462no—
323C2×C8—731no—
324C2×C8—731no—
325C2×C8C22×D7311yescharacteristic
326C2×C8C22×D7311yescharacteristic
327C4⋊C4—731no—
328C4⋊C4—731no—
329C4⋊C4—731no—
330C4⋊C4—1461no—
331C4⋊C4—1461no—
332C4⋊C4—1461no—
333C4⋊C4—1461no—
334C22⋊C4—731no—
335C22⋊C4—731no—
336C22⋊C4—1461no—
337C22⋊C4—1461no—
338C22⋊C4—1461no—
339C22⋊C4—1461no—
340C22⋊C4—1461no—
341C22⋊C4—1461no—
342C42—731no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—81no—
349C23—2922no—
350C23—2922no—
351C23—5841no—
352C23—731no—
353C23—1461no—
354C23D4×D7311yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—1461no—
358Q8—1461no—
359D4—21no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—42no—
365D4—2922no—
366D4—2922no—
367D4—2922no—
368D4—2922no—
369D4—2922no—
370D4—5841no—
371D4—1462no—
372D4—1461no—
373D4—1461no—
374D4C2×C22⋊D7312yes—
375D4C2×C22⋊D7312yescomplemented
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—2922no—
381C2×C4—2922no—
382C2×C4—2922no—
383C2×C4—731no—
384C2×C4—731no—
385C2×C4—731no—
386C2×C4—1461no—
387C2×C4—1461no—
388C2×C4—1461no—
389C2×C4—1461no—
390C2×C4—1461no—
391C2×C4D4×D7311yescharacteristic
392C2×C4C23×D7311yescharacteristic
393C8—21no—
394C8—1461no—
395C8—1461no—
396C8C2×C22⋊D7312yescomplemented
397C22—21no—
398C22—21no—
399C22—22no—
400C22—22no—
401C22—21no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—84no—
410C22—2921no—
411C22—2921no—
412C22—2921no—
413C22—5844no—
414C22—1461no—
415C22—1461no—
416C22—1461no—
417C22C2×D4×D7311yescharacteristic
418C4—21no—
419C4—41no—
420C4—2921no—
421C4—2921no—
422C4—2921no—
423C4—732no—
424C4—1461no—
425C4—1461no—
426C4C22×C22⋊D7311yescharacteristic
427C4#1455663611yescharacteristic
428C2—41no—
429C2—42no—
430C2—42no—
431C2—81no—
432C2—2921no—
433C2—5841no—
434C2D4×C22⋊D7311yescharacteristic
435C2AGL(1,ℤ/8)×D7311yescharacteristic
436C2#1798939711yescharacteristic
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#3272
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×#14556615C2semidirect
2. #17989236C2semidirect
3. D4×C22⋊D73C2semidirect
4. #17988958C2semidirect
5. #17988833C2semidirect
6. #17988830C2semidirect
7. #17988790C2semidirect
8. #17988780C2semidirect
9. #17988738C2semidirect
10. #17988736C2semidirect
11. #17988732C2semidirect
12. #17988729C2semidirect
13. D8×Dic73C2semidirect
14. #17988663C2semidirect
15. C2×AGL(1,ℤ/8)×C73C2semidirect
16. C2×#11924027C22semidirect
20. C2×#11924017C22semidirect
22. C2×#11924016C22semidirect
23. C2×#11924015C22semidirect
24. C2×#11924013C22semidirect
25. C2×#11924011C22semidirect
26. #14556589C22semidirect
30. #14556570C22semidirect
31. #14556567C22semidirect
39. D4×Dic73C22semidirect
42. #14556525C22semidirect
43. #14556520C22semidirect
44. #14556516C22semidirect
45. #14556515C22semidirect
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
120. D8×C73D4semidirect
145. D4×C73C2×D4semidirect
175. C8×C73C2×D4semidirect
208. Dic73AGL(1,ℤ/8)semidirect
219. C73#3272semidirect
221. C2×AGL(1,ℤ/8)D73semidirect
236. C2×#41C2×D73semidirect
247. C2×SD16C2×D73semidirect
250. C2×D8C2×D73semidirect
252. C2×M16C2×D73semidirect
320. D8C22⋊D73semidirect
375. D4C2×C22⋊D73semidirect
396. C8C2×C22⋊D73semidirect