Finite Group Databasebeta

← #22621524

Subgroups — #22621524

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×#14556616C211yesmaximal, characteristic, complemented
2C2×#14556615C211yesmaximal, characteristic, complemented
3#17989236C211yesmaximal, characteristic, complemented
4#17989221C211yesmaximal, characteristic, complemented
5#17988958C211yesmaximal, characteristic, complemented
6#17988836C211yesmaximal, characteristic, complemented
7#17988831C211yesmaximal, characteristic, complemented
8#17988791C211yesmaximal, characteristic, complemented
9#17988780C211yesmaximal, characteristic, complemented
10#17988740C211yesmaximal, characteristic, complemented
11#17988736C211yesmaximal, characteristic, complemented
12#17988733C211yesmaximal, characteristic, complemented
13#17988667C211yesmaximal, characteristic, complemented
14#17988662C211yesmaximal, characteristic, complemented
15#449×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic, complemented
17C22×D292C2211yescharacteristic
18C2×D4×D73—21no—
19C2×D4×D73C2211yescharacteristic
20#14556616—24no—
21#14556615—24no—
22C2×#11924017C2211yescharacteristic
23C2×#11924017C2211yescharacteristic, complemented
24C2×#11924016C2211yescharacteristic, complemented
25C2×#11924015C2211yescharacteristic
26C2×#11924015C2211yescharacteristic, complemented
27C2×#11924013C2211yescharacteristic
28C2×#11924013C2211yescharacteristic, complemented
29C2×#11924012C2211yescharacteristic, complemented
30C2×#11924011C2211yescharacteristic, complemented
31#14556589C2211yescharacteristic, complemented
32#14556587C2211yescharacteristic
33#14556574—21no—
34#14556572—21no—
35#14556570C2211yescharacteristic, complemented
36#14556567C2211yescharacteristic, complemented
37#14556566C2211yescharacteristic
38#14556564—21no—
39#14556563—21no—
40#14556561—21no—
41#14556559—21no—
42D4×Dic73C2211yescharacteristic, complemented
43#14556553C2211yescharacteristic
44C4×C22⋊D73C2211yescharacteristic
45C2×#11924007—21no—
46#14556524C2211yescharacteristic, complemented
47#14556520C2211yescharacteristic, complemented
48#14556514C2211yescharacteristic, complemented
49#14556513C2211yescharacteristic
50#14556513C2211yescharacteristic, complemented
51#14556512C2211yescharacteristic, complemented
52#14556503C2211yescharacteristic, complemented
53C8×Dic73C2211yescharacteristic, complemented
54C2×#41×C73C2211yescharacteristic, complemented
55C2×SD16×C73C2211yescharacteristic, complemented
56C2×D8×C73C2211yescharacteristic, complemented
57#121×C73C2211yescharacteristic
58#103×C73C2211yescharacteristic, complemented
59#102×C73C2211yescharacteristic, complemented
60C22⋊C8×C73C2211yescharacteristic, complemented
61C23×D73—21no—
62C23×D73—21no—
63#11924027—22no—
64#11924027—41no—
65C2×Dic146C2311yescharacteristic
66C2×D292—22no—
67C2×D292—21no—
68C2×D292—21no—
69C2×D292—41no—
70C2×D292C2311yescharacteristic
71C2×D292C2311yescharacteristic
72C2×C22⋊D73—21no—
73C2×C22⋊D73—21no—
74C2×C22⋊D73—21no—
75C2×C22⋊D73—21no—
76C2×C22⋊D73D411yescharacteristic
77D4×D73—22no—
78D4×D73—41no—
79D4×D73—44no—
80C22×Dic73—21no—
81C22×Dic73—21no—
82C2×C4×D73—21no—
83C2×C4×D73C2311yescharacteristic
84#11924017—22no—
85#11924017—41no—
86#11924016—22no—
87#11924015—22no—
88#11924015—22no—
89#11924013—22no—
90#11924013D414yescomplemented
91#11924012—22no—
92#11924011—22no—
93C2×#10596831C2311yescharacteristic
94C2×#10596831C2311yescharacteristic
95C4⋊Dic73C2311yescharacteristic
96#11924007—21no—
97#11924007—21no—
98#11924007—21no—
99#11924007—21no—
100#11924007D411yescharacteristic
101C22⋊Dic73—21no—
102C22⋊Dic73—21no—
103C22⋊Dic73D411yescharacteristic
104#11924005—21no—
105#11924005—21no—
106#11924005—21no—
107#11924005D411yescharacteristic
108C4×Dic73C2311yescharacteristic
109#41×C73—22no—
110#41×C73—41no—
111C2×Q8×C73C2311yescharacteristic
112C2×D4×C73—21no—
113C2×D4×C73—21no—
114C2×D4×C73C2311yescharacteristic
115C2×D4×C73C2311yescharacteristic
116C22×C4×C73—21no—
117C22×C4×C73C2311yescharacteristic
118SD16×C73—41no—
119D8×C73—22no—
120C2×C8×C73C2311yescharacteristic
121C2×C8×C73C2311yescharacteristic
122C4⋊C4×C73C2311yescharacteristic
123C22⋊C4×C73—21no—
124C23×C73—21no—
125C23×C73—21no—
126C23×C73C2×D411yescharacteristic
127C22×D73—21no—
128C22×D73—21no—
129C22×D73—42no—
130C22×D73—42no—
131C22×D73—42no—
132C22×D73—42no—
133C22×D73—81no—
134C22×D73—81no—
135C22×D73C2×D411yescharacteristic
136Q8×C73—21no—
137Q8×C73—21no—
138D4×C73—21no—
139D4×C73—21no—
140D4×C73—21no—
141D4×C73—42no—
142D4×C73—42no—
143D4×C73C2×D412yescomplemented
144C2×C4×C73—21no—
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—22no—
152C22⋊D73—42no—
153C22⋊D73—42no—
154C22⋊D73—42no—
155C22⋊D73—81no—
156C2×Dic73—21no—
157C2×Dic73—21no—
158C2×Dic73—42no—
159C2×Dic73—42no—
160C2×Dic73C2×D411yescharacteristic
161C2×Dic73C2×D411yescharacteristic
162C2×Dic73C2×D411yescharacteristic
163D292—21no—
164D292—21no—
165D292—21no—
166D292—42no—
167D292—42no—
168D292C2×D412yes—
169C4×D73—21no—
170C4×D73—21no—
171C4×D73—42no—
172Dic146—21no—
173Dic146—21no—
174C8×C73—21no—
175C8×C73—21no—
176#10596831—21no—
177#10596831C2×D412yescomplemented
178C22×C73—22no—
179C22×C73—21no—
180C22×C73—21no—
181C22×C73—21no—
182C22×C73—41no—
183C22×C73—41no—
184C22×C73—41no—
185C22×C73—41no—
186C22×C73—41no—
187C22×C73C22×D411yescharacteristic
188C2×D73—21no—
189C2×D73—22no—
190C2×D73—21no—
191C2×D73—21no—
192C2×D73—41no—
193C2×D73—41no—
194C2×D73—41no—
195C2×D73—41no—
196C2×D73—41no—
197C2×D73—84no—
198C2×D73—84no—
199C4×C73—21no—
200C4×C73—41no—
201C4×C73—41no—
202C4×C73C22×D411yescharacteristic
203C4×C73H(5,𝔽2)11yescharacteristic
204Dic73—21no—
205Dic73—21no—
206Dic73—41no—
207Dic73—41no—
208Dic73AGL(1,ℤ/8)12yescomplemented
209C2×C73—41no—
210C2×C73—42no—
211C2×C73—81no—
212C2×C73D4211yescharacteristic
213C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
214C2×C73#57711yescharacteristic
215D73—41no—
216D73—42no—
217D73—81no—
218#3272—731nomaximal, Sylow
219C73#327211yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)—731no—
221C2×AGL(1,ℤ/8)—731no—
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#449D7311yescharacteristic, complemented
233C4×D8—731no—
234#436—731no—
235C2×#41—731no—
236C2×#41C2×D7311yescharacteristic, complemented
237C22×D4—731no—
238C22×D4—731no—
239C22×D4—1461no—
240AGL(1,ℤ/8)—1464no—
241AGL(1,ℤ/8)—1464no—
242C2×SD16—731no—
243C2×SD16—731no—
244C2×SD16—731no—
245C2×SD16—731no—
246C2×SD16—731no—
247C2×SD16C2×D7311yescharacteristic, complemented
248C2×D8—731no—
249C2×D8—731no—
250C2×D8C2×D7311yescharacteristic, complemented
251C2×M16—731no—
252C2×M16—731no—
253C4⋊Q8—731no—
254#127—731no—
255#123—1461no—
256#123—1461no—
257C22⋊Q8—731no—
258C22⋊Q8—731no—
259#121—731no—
260#121—1461no—
261#121—1461no—
262#121C2×D7311yescharacteristic
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#103C2×D7311yescharacteristic, complemented
273#102—731no—
274#102—731no—
275#102—731no—
276#102C2×D7311yescharacteristic, complemented
277C22⋊C8—731no—
278C22⋊C8C2×D7311yescharacteristic, complemented
279C4×C8—731no—
280C24—1461no—
281C24—1461no—
282#41—22no—
283#41—41no—
284#41—2921no—
285#41—1462no—
286C2×Q8—731no—
287C2×Q8C22×D7311yescharacteristic
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—2921no—
291C2×D4—2924no—
292C2×D4—2921no—
293C2×D4—731no—
294C2×D4—731no—
295C2×D4—731no—
296C2×D4—1461no—
297C2×D4—1462no—
298C2×D4—1461no—
299C2×D4—1461no—
300C2×D4—1461no—
301C2×D4—1462no—
302C2×D4—1461no—
303C2×D4—1461no—
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—41no—
313SD16—2921no—
314SD16—1462no—
315SD16—1462no—
316SD16—1462no—
317SD16—1462no—
318D8—22no—
319D8—734no—
320D8—1462no—
321M16—1462no—
322M16—1462no—
323C2×C8—731no—
324C2×C8—731no—
325C2×C8C22×D7311yescharacteristic
326C2×C8C22×D7311yescharacteristic
327C4⋊C4—731no—
328C4⋊C4—731no—
329C4⋊C4—1461no—
330C4⋊C4—1461no—
331C4⋊C4—1461no—
332C4⋊C4—1461no—
333C4⋊C4C22×D7311yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—731no—
336C22⋊C4—731no—
337C22⋊C4—1461no—
338C22⋊C4—1461no—
339C22⋊C4—1461no—
340C22⋊C4—1461no—
341C22⋊C4—1461no—
342C42—731no—
343C23—21no—
344C23—21no—
345C23—2922no—
346C23—2922no—
347C23—2922no—
348C23—2922no—
349C23—5841no—
350C23—5841no—
351C23—731no—
352C23—1461no—
353C23—1461no—
354C23D4×D7311yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—1461no—
358Q8—1461no—
359D4—21no—
360D4—21no—
361D4—21no—
362D4—42no—
363D4—42no—
364D4—2922no—
365D4—2922no—
366D4—2922no—
367D4—2922no—
368D4—2922no—
369D4—5841no—
370D4—732no—
371D4—1462no—
372D4—1461no—
373D4—1461no—
374D4—1461no—
375D4D4×D7312yescomplemented
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—2922no—
382C2×C4—2922no—
383C2×C4—2922no—
384C2×C4—731no—
385C2×C4—731no—
386C2×C4—731no—
387C2×C4—1461no—
388C2×C4—1461no—
389C2×C4—1461no—
390C2×C4—1461no—
391C2×C4D4×D7311yescharacteristic
392C2×C4C23×D7311yescharacteristic
393C8—21no—
394C8—21no—
395C8—732no—
396C8—1461no—
397C22—21no—
398C22—21no—
399C22—22no—
400C22—21no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—2921no—
407C22—2921no—
408C22—2921no—
409C22—2921no—
410C22—2921no—
411C22—5844no—
412C22—5844no—
413C22—1461no—
414C22—1461no—
415C22—1462no—
416C22—1461no—
417C22C2×D4×D7311yescharacteristic
418C4—21no—
419C4—41no—
420C4—41no—
421C4—2921no—
422C4—2921no—
423C4—732no—
424C4—1461no—
425C4—1461no—
426C4C2×D4×D7311yescharacteristic
427C4#1455663611yescharacteristic
428C2—41no—
429C2—42no—
430C2—81no—
431C2—2922no—
432C2—2921no—
433C2—5841no—
434C2#1798921911yescharacteristic
435C2AGL(1,ℤ/8)×D7311yescharacteristic
436C2#1798939411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#449×C73C2
socleC22×C73C22×D4
hypercenter#449D73
hypocenterC73#3272
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#14556616C2semidirect
2. C2×#14556615C2semidirect
3. #17989236C2semidirect
4. #17989221C2semidirect
5. #17988958C2semidirect
6. #17988836C2semidirect
7. #17988831C2semidirect
8. #17988791C2semidirect
9. #17988780C2semidirect
10. #17988740C2semidirect
11. #17988736C2semidirect
12. #17988733C2semidirect
13. #17988667C2semidirect
14. #17988662C2semidirect
15. #449×C73C2semidirect
16. C2×#11924027C22semidirect
23. C2×#11924017C22semidirect
24. C2×#11924016C22semidirect
26. C2×#11924015C22semidirect
28. C2×#11924013C22semidirect
29. C2×#11924012C22semidirect
30. C2×#11924011C22semidirect
31. #14556589C22semidirect
35. #14556570C22semidirect
36. #14556567C22semidirect
42. D4×Dic73C22semidirect
46. #14556524C22semidirect
47. #14556520C22semidirect
48. #14556514C22semidirect
50. #14556513C22semidirect
51. #14556512C22semidirect
52. #14556503C22semidirect
53. C8×Dic73C22semidirect
54. C2×#41×C73C22semidirect
55. C2×SD16×C73C22semidirect
56. C2×D8×C73C22semidirect
58. #103×C73C22semidirect
59. #102×C73C22semidirect
60. C22⋊C8×C73C22semidirect
90. #11924013D4semidirect
143. D4×C73C2×D4semidirect
177. #10596831C2×D4semidirect
208. Dic73AGL(1,ℤ/8)semidirect
219. C73#3272semidirect
232. #449D73semidirect
236. C2×#41C2×D73semidirect
247. C2×SD16C2×D73semidirect
250. C2×D8C2×D73semidirect
272. #103C2×D73semidirect
276. #102C2×D73semidirect
278. C22⋊C8C2×D73semidirect
375. D4D4×D73semidirect