Finite Group Databasebeta

← #22621536

Subgroups — #22621536

Order 9344.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556615C211yesmaximal, characteristic, complemented
2#17989231C211yesmaximal, characteristic, complemented
3#17989225C211yesmaximal, characteristic, complemented
4#17988968C211yesmaximal, characteristic, complemented
5#17988833C211yesmaximal, characteristic, complemented
6#17988830C211yesmaximal, characteristic, complemented
7#17988804C211yesmaximal, characteristic, complemented
8#17988800C211yesmaximal, characteristic, complemented
9#17988749C211yesmaximal, characteristic, complemented
10#17988746C211yesmaximal, characteristic, complemented
11#17988721C211yesmaximal, characteristic, complemented
12#17988719C211yesmaximal, characteristic, complemented
13D8×Dic73C211yesmaximal, characteristic, complemented
14#17988663C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×D4×D73C2211yescharacteristic, complemented
18#14556615—24no—
19C2×#11924018C2211yescharacteristic, complemented
20C2×#11924017C2211yescharacteristic, complemented
21C2×#11924016C2211yescharacteristic, complemented
22C2×#11924013C2211yescharacteristic
23C2×#11924013C2211yescharacteristic
24C2×#11924011C2211yescharacteristic, complemented
25#14556580C2211yescharacteristic, complemented
26#14556578C2211yescharacteristic, complemented
27#14556574—21no—
28#14556572—21no—
29#14556570C2211yescharacteristic, complemented
30#14556567C2211yescharacteristic, complemented
31#14556565C2211yescharacteristic
32#14556563—21no—
33#14556563—21no—
34#14556562C2211yescharacteristic
35#14556560—21no—
36#14556559—21no—
37D4×Dic73C2211yescharacteristic, complemented
38D4×Dic73C2211yescharacteristic, complemented
39C4×C22⋊D73C2211yescharacteristic
40C2×C22⋊Dic73—21no—
41C2×#11924005—21no—
42#14556525C2211yescharacteristic, complemented
43#14556520C2211yescharacteristic, complemented
44#14556516C2211yescharacteristic, complemented
45#14556515C2211yescharacteristic, complemented
46#14556513C2211yescharacteristic, complemented
47#14556512C2211yescharacteristic, complemented
48#14556512C2211yescharacteristic, complemented
49#14556512C2211yescharacteristic, complemented
50C22⋊#10596831C2211yescharacteristic, complemented
51#14556503C2211yescharacteristic, complemented
52C8×Dic73C2211yescharacteristic, complemented
53C2×#41×C73C2211yescharacteristic
54C22×D4×C73C2211yescharacteristic, complemented
55AGL(1,ℤ/8)×C73—24no—
56C2×SD16×C73C2211yescharacteristic, complemented
57C2×SD16×C73C2211yescharacteristic, complemented
58C2×D8×C73C2211yescharacteristic
59C2×D8×C73C2211yescharacteristic
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⋊D73D411yescharacteristic
71D4×D73—22no—
72D4×D73—41no—
73C22×Dic73—21no—
74C22×Dic73—21no—
75C22×Dic73—21no—
76C2×C4×D73C2311yescharacteristic
77#11924018—41no—
78#11924017—22no—
79#11924016—22no—
80#11924013—22no—
81#11924013—41no—
82#11924011—22no—
83C2×#10596831C2311yescharacteristic
84C2×#10596831C2311yescharacteristic
85C4⋊Dic73C2311yescharacteristic
86C4⋊Dic73C2311yescharacteristic
87#11924007—21no—
88#11924007—21no—
89#11924007D411yescharacteristic
90C22⋊Dic73—21no—
91C22⋊Dic73—21no—
92C22⋊Dic73—21no—
93C22⋊Dic73—21no—
94C22⋊Dic73—21no—
95C22⋊Dic73—21no—
96C22⋊Dic73D411yescharacteristic
97#11924005—21no—
98#11924005—21no—
99#11924005—21no—
100#11924005—21no—
101#11924005D411yescharacteristic
102C4×Dic73C2311yescharacteristic
103C24×C73—21no—
104#41×C73—22no—
105#41×C73—41no—
106C2×Q8×C73C2311yescharacteristic
107C2×D4×C73—22no—
108C2×D4×C73—21no—
109C2×D4×C73—21no—
110C2×D4×C73—41no—
111C2×D4×C73C2311yescharacteristic
112C2×D4×C73C2311yescharacteristic
113C2×D4×C73C2311yescharacteristic
114C22×C4×C73—21no—
115C22×C4×C73C2311yescharacteristic
116SD16×C73—22no—
117SD16×C73—22no—
118D8×C73—22no—
119D8×C73D414yescomplemented
120M16×C73—22no—
121C2×C8×C73C2311yescharacteristic
122C2×C8×C73C2311yescharacteristic
123C23×C73—21no—
124C23×C73—21no—
125C23×C73—21no—
126C23×C73—42no—
127C23×C73—42no—
128C23×C73—81no—
129C23×C73C2×D411yescharacteristic
130C22×D73—21no—
131C22×D73—42no—
132C22×D73—42no—
133C22×D73—81no—
134C22×D73C2×D411yescharacteristic
135Q8×C73—21no—
136Q8×C73—21no—
137D4×C73—21no—
138D4×C73—21no—
139D4×C73—21no—
140D4×C73—21no—
141D4×C73—42no—
142D4×C73—42no—
143D4×C73C2×D412yes—
144D4×C73C2×D412yes—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—42no—
149C2×C4×C73C2×D411yescharacteristic
150C2×C4×C73C2411yescharacteristic
151C22⋊D73—41no—
152C22⋊D73—42no—
153C22⋊D73—42no—
154C22⋊D73—81no—
155C22⋊D73—81no—
156C2×Dic73—21no—
157C2×Dic73—21no—
158C2×Dic73—21no—
159C2×Dic73—42no—
160C2×Dic73—81no—
161C2×Dic73—81no—
162C2×Dic73C2×D411yescharacteristic
163C2×Dic73C2×D411yescharacteristic
164C2×Dic73C2×D411yescharacteristic
165D292—21no—
166D292—21no—
167C4×D73—21no—
168C4×D73—21no—
169Dic146—21no—
170Dic146—21no—
171C8×C73—21no—
172C8×C73C2×D412yes—
173#10596831—21no—
174#10596831—21no—
175C22×C73—22no—
176C22×C73—22no—
177C22×C73—21no—
178C22×C73—21no—
179C22×C73—21no—
180C22×C73—41no—
181C22×C73—41no—
182C22×C73—41no—
183C22×C73—41no—
184C22×C73—41no—
185C22×C73—41no—
186C22×C73—41no—
187C22×C73—84no—
188C22×C73C22×D411yescharacteristic
189C2×D73—21no—
190C2×D73—21no—
191C2×D73—21no—
192C2×D73—41no—
193C2×D73—41no—
194C2×D73—41no—
195C2×D73—84no—
196C4×C73—21no—
197C4×C73—41no—
198C4×C73C22×D411yescharacteristic
199C4×C73H(5,𝔽2)11yescharacteristic
200Dic73—21no—
201Dic73—21no—
202Dic73—21no—
203Dic73—41no—
204Dic73—41no—
205Dic73—41no—
206C2×C73—42no—
207C2×C73—41no—
208C2×C73—42no—
209C2×C73—81no—
210C2×C73D4211yescharacteristic
211C2×C73#57511yescharacteristic
212C2×C73#57611yescharacteristic
213D73—41no—
214D73—81no—
215#3273—731nomaximal, Sylow
216C73#327311yescharacteristic, complemented, Sylow
217C2×AGL(1,ℤ/8)—731no—
218C2×AGL(1,ℤ/8)D7311yescharacteristic, complemented
219#546—731no—
220#546—731no—
221#495—731no—
222#468—731no—
223#468—731no—
224#463—731no—
225#463—731no—
226#452—731no—
227#452—731no—
228#447—731no—
229#447—731no—
230C4×D8—731no—
231#436—731no—
232C2×#41—731no—
233C2×#41C2×D7311yescharacteristic
234C22×D4—731no—
235C22×D4C2×D7311yescharacteristic, complemented
236AGL(1,ℤ/8)—24no—
237AGL(1,ℤ/8)—1464no—
238C2×Q16—731no—
239C2×SD16—731no—
240C2×SD16—731no—
241C2×SD16C2×D7311yescharacteristic, complemented
242C2×SD16C2×D7311yescharacteristic, complemented
243C2×D8—731no—
244C2×D8—731no—
245C2×D8C2×D7311yescharacteristic
246C2×D8C2×D7311yescharacteristic
247C2×M16—731no—
248C2×M16C2×D7311yescharacteristic, complemented
249#124—731no—
250#124—731no—
251#123—1461no—
252#123—1461no—
253C22⋊Q8—731no—
254C22⋊Q8—731no—
255#121—731no—
256#121—731no—
257#121—1461no—
258#121—1461no—
259#120—1461no—
260#120—1461no—
261C4×D4—731no—
262C4×D4—731no—
263C4×D4—731no—
264C2×C22⋊C4—1461no—
265C2×C22⋊C4—1461no—
266#107—731no—
267C4⋊C8—731no—
268#103—731no—
269#103—731no—
270#102—731no—
271#102—731no—
272#102—731no—
273#102—731no—
274C22⋊C8—731no—
275C22⋊C8—731no—
276C4×C8—731no—
277C24—21no—
278C24—1461no—
279#41—22no—
280#41—41no—
281#41—2921no—
282#41—1462no—
283C2×Q8—731no—
284C2×Q8C22×D7311yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—2921no—
290C2×D4—731no—
291C2×D4—731no—
292C2×D4—1461no—
293C2×D4—1461no—
294C2×D4—1462no—
295C2×D4—1461no—
296C2×D4—1461no—
297C2×D4C22×D7311yescharacteristic
298C2×D4C22×D7311yescharacteristic
299C2×D4C22×D7311yescharacteristic
300C22×C4—21no—
301C22×C4—731no—
302C22×C4—1461no—
303C22×C4—1461no—
304C22×C4—1461no—
305C22×C4C22×D7311yescharacteristic
306Q16—2921no—
307SD16—22no—
308SD16—22no—
309SD16—1462no—
310SD16—1462no—
311D8—22no—
312D8—2921no—
313D8—1462no—
314D8C22⋊D7314yescomplemented
315M16—22no—
316M16—1462no—
317C2×C8—731no—
318C2×C8—731no—
319C2×C8C22×D7311yescharacteristic
320C2×C8C22×D7311yescharacteristic
321C4⋊C4—731no—
322C4⋊C4—731no—
323C4⋊C4—731no—
324C4⋊C4—1461no—
325C4⋊C4—1461no—
326C22⋊C4—731no—
327C22⋊C4—731no—
328C22⋊C4—1461no—
329C22⋊C4—1461no—
330C22⋊C4—1461no—
331C22⋊C4—1461no—
332C22⋊C4—1461no—
333C22⋊C4—1461no—
334C22⋊C4—1461no—
335C22⋊C4—1461no—
336C22⋊C4—1461no—
337C22⋊C4—1461no—
338C42—731no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—42no—
343C23—42no—
344C23—81no—
345C23—2922no—
346C23—2922no—
347C23—5841no—
348C23—731no—
349C23—1461no—
350C23D4×D7311yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—1461no—
354Q8—1461no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—21no—
359D4—42no—
360D4—42no—
361D4—2922no—
362D4—2922no—
363D4—2921no—
364D4—5841no—
365D4—5841no—
366D4—1461no—
367D4—1461no—
368D4C2×C22⋊D7312yes—
369D4C2×C22⋊D7312yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—2922no—
375C2×C4—5841no—
376C2×C4—5841no—
377C2×C4—731no—
378C2×C4—731no—
379C2×C4—731no—
380C2×C4—1461no—
381C2×C4—1461no—
382C2×C4—1461no—
383C2×C4—1461no—
384C2×C4—1461no—
385C2×C4D4×D7311yescharacteristic
386C2×C4C23×D7311yescharacteristic
387C8—21no—
388C8—1461no—
389C8—1461no—
390C8C2×C22⋊D7312yes—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—22no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—84no—
404C22—2921no—
405C22—2921no—
406C22—2921no—
407C22—5844no—
408C22—1461no—
409C22—1461no—
410C22—1461no—
411C22C2×D4×D7311yescharacteristic
412C4—21no—
413C4—41no—
414C4—2921no—
415C4—2921no—
416C4—2921no—
417C4—1461no—
418C4—1461no—
419C4—1461no—
420C4C22×C22⋊D7311yescharacteristic
421C4#1455663611yescharacteristic
422C2—41no—
423C2—42no—
424C2—42no—
425C2—81no—
426C2—2921no—
427C2—5841no—
428C2D4×C22⋊D7311yescharacteristic
429C2#1798938311yescharacteristic
430C2#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#3273
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. #17989231C2semidirect
3. #17989225C2semidirect
4. #17988968C2semidirect
5. #17988833C2semidirect
6. #17988830C2semidirect
7. #17988804C2semidirect
8. #17988800C2semidirect
9. #17988749C2semidirect
10. #17988746C2semidirect
11. #17988721C2semidirect
12. #17988719C2semidirect
13. D8×Dic73C2semidirect
14. #17988663C2semidirect
15. C2×AGL(1,ℤ/8)×C73C2semidirect
17. C2×D4×D73C22semidirect
19. C2×#11924018C22semidirect
20. C2×#11924017C22semidirect
21. C2×#11924016C22semidirect
24. C2×#11924011C22semidirect
25. #14556580C22semidirect
26. #14556578C22semidirect
29. #14556570C22semidirect
30. #14556567C22semidirect
37. D4×Dic73C22semidirect
38. D4×Dic73C22semidirect
42. #14556525C22semidirect
43. #14556520C22semidirect
44. #14556516C22semidirect
45. #14556515C22semidirect
46. #14556513C22semidirect
47. #14556512C22semidirect
48. #14556512C22semidirect
49. #14556512C22semidirect
50. C22⋊#10596831C22semidirect
51. #14556503C22semidirect
52. C8×Dic73C22semidirect
54. C22×D4×C73C22semidirect
56. C2×SD16×C73C22semidirect
57. C2×SD16×C73C22semidirect
60. C2×M16×C73C22semidirect
119. D8×C73D4semidirect
216. C73#3273semidirect
218. C2×AGL(1,ℤ/8)D73semidirect
235. C22×D4C2×D73semidirect
241. C2×SD16C2×D73semidirect
242. C2×SD16C2×D73semidirect
248. C2×M16C2×D73semidirect
314. D8C22⋊D73semidirect