Finite Group Databasebeta

← #22619545

Subgroups — #22619545

Order 9344.

548 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556618C211yesmaximal, characteristic, complemented
2C2×M16×D73C211yesmaximal, characteristic, complemented
3#17989100C211yesmaximal, characteristic, complemented
4#121×D73C211yesmaximal, characteristic, complemented
5#17988840C211yesmaximal, characteristic, complemented
6#17988838C211yesmaximal, characteristic, complemented
7#17988835C211yesmaximal, characteristic, complemented
8#17988824C211yesmaximal, characteristic, complemented
9#17988822C211yesmaximal, characteristic, complemented
10#17988819C211yesmaximal, characteristic, complemented
11#17988813C211yesmaximal, characteristic, complemented
12#17988628C211yesmaximal, characteristic, complemented
13#17988590C211yesmaximal, characteristic, complemented
14#17988587C211yesmaximal, characteristic, complemented
15#468×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×D4×D73—21no—
18C2×D4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20#14556618—24no—
21C2×#11924015C2211yescharacteristic, complemented
22C2×D584C2211yescharacteristic, complemented
23C2×#11924013C2211yescharacteristic, complemented
24C2×#11924012C2211yescharacteristic, complemented
25C2×#11924011C2211yescharacteristic
26C2×#11924011C2211yescharacteristic
27M16×D73—24no—
28C2×C8×D73C2211yescharacteristic, complemented
29C2×C8×D73C2211yescharacteristic, complemented
30#14556576—21no—
31#14556567C2211yescharacteristic, complemented
32#14556566C2211yescharacteristic
33#14556566C2211yescharacteristic, complemented
34#14556565C2211yescharacteristic
35#14556565C2211yescharacteristic, complemented
36#14556564—21no—
37#14556563—21no—
38#14556562C2211yescharacteristic
39#14556561—21no—
40#14556553—21no—
41#14556551—21no—
42#14556549C2211yescharacteristic
43C4⋊C4×D73C2211yescharacteristic
44C22⋊C4×D73—21no—
45#14556524C2211yescharacteristic, complemented
46#14556523C2211yescharacteristic, complemented
47#14556522C2211yescharacteristic, complemented
48#14556515C2211yescharacteristic, complemented
49#14556513C2211yescharacteristic, complemented
50#14556513C2211yescharacteristic, complemented
51#14556512C2211yescharacteristic, complemented
52#14556511C2211yescharacteristic, complemented
53#14556511C2211yescharacteristic, complemented
54C2×SD16×C73C2211yescharacteristic, complemented
55C2×M16×C73C2211yescharacteristic, complemented
56C22⋊Q8×C73C2211yescharacteristic, complemented
57#121×C73C2211yescharacteristic
58#107×C73C2211yescharacteristic, complemented
59#103×C73C2211yescharacteristic, complemented
60#102×C73C2211yescharacteristic, complemented
61C23×D73—21no—
62C23×D73D411yescharacteristic
63#11924029—22no—
64#11924029—22no—
65C2×D292—21no—
66C2×D292—21no—
67C2×D292—21no—
68C2×D292C2311yescharacteristic
69C2×D292C2311yescharacteristic
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C22⋊D73—21no—
73C2×C22⋊D73—21no—
74D4×D73—22no—
75D4×D73—22no—
76D4×D73—44no—
77C22×Dic73D411yescharacteristic
78C2×C4×D73—22no—
79C2×C4×D73—22no—
80C2×C4×D73—21no—
81C2×C4×D73—21no—
82C2×C4×D73D411yescharacteristic
83C2×C4×D73D411yescharacteristic
84C2×C4×D73C2311yescharacteristic
85C2×C4×D73C2311yescharacteristic
86#11924015—22no—
87D584—22no—
88#11924013—22no—
89#11924012—22no—
90#11924011—22no—
91#11924011D414yescomplemented
92C2×#10596831C2311yescharacteristic
93C2×#10596831C2311yescharacteristic
94C8×D73—22no—
95C8×D73—22no—
96C4⋊Dic73C2311yescharacteristic
97C4⋊Dic73C2311yescharacteristic
98#11924007—21no—
99#11924007—21no—
100C22⋊Dic73—21no—
101#11924005—21no—
102#11924005—21no—
103#11924005—21no—
104#11924005—21no—
105#11924005—21no—
106#11924005—21no—
107C4×Dic73—21no—
108C2×Q8×C73C2311yescharacteristic
109C2×D4×C73—21no—
110C2×D4×C73C2311yescharacteristic
111C22×C4×C73C2311yescharacteristic
112SD16×C73—22no—
113M16×C73—22no—
114C2×C8×C73C2311yescharacteristic
115C2×C8×C73C2311yescharacteristic
116C4⋊C4×C73—21no—
117C4⋊C4×C73C2311yescharacteristic
118C4⋊C4×C73C2311yescharacteristic
119C22⋊C4×C73—21no—
120C22⋊C4×C73—21no—
121C23×C73—21no—
122C23×C73C2×D411yescharacteristic
123C22×D73—22no—
124C22×D73—22no—
125C22×D73—21no—
126C22×D73—21no—
127C22×D73—41no—
128C22×D73—42no—
129C22×D73—42no—
130C22×D73—42no—
131C22×D73C2×D411yescharacteristic
132C22×D73C2×D411yescharacteristic
133Q8×C73—21no—
134Q8×C73—21no—
135D4×C73—21no—
136D4×C73—21no—
137D4×C73—42no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73C2×D411yescharacteristic
144C2×C4×C73C2411yescharacteristic
145C22⋊D73—42no—
146C22⋊D73—42no—
147C22⋊D73—42no—
148C22⋊D73—42no—
149C2×Dic73—22no—
150C2×Dic73—21no—
151C2×Dic73—21no—
152C2×Dic73C2×D411yescharacteristic
153C2×Dic73C2×D411yescharacteristic
154D292—21no—
155D292—21no—
156D292—21no—
157D292—21no—
158D292—42no—
159D292—42no—
160D292—42no—
161C4×D73—22no—
162C4×D73—21no—
163C4×D73—21no—
164C4×D73—22no—
165C4×D73—42no—
166C4×D73—42no—
167C4×D73C2×D412yes—
168C4×D73#4112yes—
169C8×C73—21no—
170C8×C73C2×D412yescomplemented
171#10596831—21no—
172#10596831C2×D412yescomplemented
173C22×C73—21no—
174C22×C73—21no—
175C22×C73—21no—
176C22×C73—41no—
177C22×C73—41no—
178C22×C73—41no—
179C22×C73C22×D411yescharacteristic
180C2×D73—21no—
181C2×D73—21no—
182C2×D73—21no—
183C2×D73—21no—
184C2×D73—44no—
185C2×D73—41no—
186C2×D73—41no—
187C2×D73—41no—
188C2×D73—41no—
189C2×D73—41no—
190C2×D73—41no—
191C2×D73—84no—
192C2×D73#12112yes—
193C2×D73AGL(1,ℤ/8)12yescomplemented
194C4×C73—21no—
195C4×C73—41no—
196C4×C73—41no—
197C4×C73—41no—
198C4×C73C22×D411yescharacteristic
199C4×C73C2×#4111yescharacteristic
200Dic73—21no—
201Dic73—41no—
202Dic73—41no—
203Dic73#12112yes—
204C2×C73—41no—
205C2×C73—81no—
206C2×C73C2×#12111yescharacteristic
207C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
208C2×C73#57511yescharacteristic
209D73—22no—
210D73—22no—
211D73—81no—
212D73—81no—
213#3055—731nomaximal, Sylow
214C73#305511yescharacteristic, complemented, Sylow
215C2×AGL(1,ℤ/8)—731no—
216C22×M16—731no—
217#525—731no—
218C2×#121—731no—
219#469—731no—
220#469—731no—
221#468—731no—
222#468D7311yescharacteristic, complemented
223#466—731no—
224#466—731no—
225#465—731no—
226#465—731no—
227#428—731no—
228#418—731no—
229#417—731no—
230C2×#41—731no—
231C22×D4—731no—
232C22×D4—1461no—
233C23×C4—731no—
234AGL(1,ℤ/8)—1464no—
235C2×SD16—731no—
236C2×SD16C2×D7311yescharacteristic, complemented
237C2×D8—731no—
238C2×D8—731no—
239C2×M16—731no—
240C2×M16—731no—
241C2×M16—731no—
242C2×M16—1464no—
243C2×M16C2×D7311yescharacteristic, complemented
244C22×C8—731no—
245C22×C8—731no—
246#123—1461no—
247C22⋊Q8—731no—
248C22⋊Q8C2×D7311yescharacteristic, complemented
249#121—731no—
250#121—731no—
251#121—731no—
252#121—731no—
253#121—731no—
254#121—1461no—
255#121—1461no—
256#121C2×D7311yescharacteristic
257#120—1461no—
258C4×D4—1461no—
259C4×D4—1461no—
260#117—731no—
261C2×C4⋊C4—731no—
262C2×C22⋊C4—1461no—
263#107—731no—
264#107C2×D7311yescharacteristic, complemented
265#106—731no—
266#106—731no—
267#103—731no—
268#103C2×D7311yescharacteristic, complemented
269#102—731no—
270#102—731no—
271#102—731no—
272#102—731no—
273#102—731no—
274#102C2×D7311yescharacteristic, complemented
275C24—731no—
276C24—1461no—
277#41—1462no—
278#41—1462no—
279C2×Q8C22×D7311yescharacteristic
280C2×D4—21no—
281C2×D4—2924no—
282C2×D4—731no—
283C2×D4—731no—
284C2×D4—1461no—
285C2×D4—1461no—
286C2×D4—1461no—
287C2×D4—1462no—
288C2×D4—1462no—
289C2×D4—1461no—
290C2×D4—1461no—
291C2×D4—1461no—
292C2×D4—1461no—
293C2×D4C22×D7311yescharacteristic
294C22×C4—731no—
295C22×C4—731no—
296C22×C4—731no—
297C22×C4—731no—
298C22×C4—731no—
299C22×C4—1461no—
300C22×C4—1461no—
301C22×C4—1462no—
302C22×C4—1462no—
303C22×C4C22×D7311yescharacteristic
304SD16—22no—
305SD16—1462no—
306D8—1462no—
307D8—1462no—
308M16—22no—
309M16—734no—
310M16—1462no—
311M16—1462no—
312C2×C8—731no—
313C2×C8—731no—
314C2×C8—1462no—
315C2×C8—1462no—
316C2×C8C22×D7311yescharacteristic
317C2×C8C22×D7311yescharacteristic
318C4⋊C4—21no—
319C4⋊C4—731no—
320C4⋊C4—731no—
321C4⋊C4—1461no—
322C4⋊C4—1461no—
323C4⋊C4C22×D7311yescharacteristic
324C4⋊C4C22×D7311yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—1461no—
328C22⋊C4—1461no—
329C22⋊C4—1461no—
330C22⋊C4—1461no—
331C22⋊C4—1461no—
332C22⋊C4—1461no—
333C22⋊C4—1461no—
334C42—1461no—
335C23—21no—
336C23—2921no—
337C23—2922no—
338C23—2922no—
339C23—2922no—
340C23—731no—
341C23—731no—
342C23—1462no—
343C23—1462no—
344C23—1461no—
345C23—1461no—
346C23D4×D7311yescharacteristic
347Q8—21no—
348Q8—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—2922no—
353D4—2922no—
354D4—2922no—
355D4—2922no—
356D4—2922no—
357D4—2922no—
358D4—2922no—
359D4—1461no—
360D4—1461no—
361D4—1461no—
362D4—1461no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—2922no—
369C2×C4—2922no—
370C2×C4—731no—
371C2×C4—732no—
372C2×C4—732no—
373C2×C4—731no—
374C2×C4—1462no—
375C2×C4—1462no—
376C2×C4—1461no—
377C2×C4—1461no—
378C2×C4—1462no—
379C2×C4—1461no—
380C2×C4—1461no—
381C2×C4D4×D7311yescharacteristic
382C2×C4C23×D7311yescharacteristic
383C8—21no—
384C8—732no—
385C8—1461no—
386C8D4×D7312yescomplemented
387C22—21no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—2924no—
394C22—2921no—
395C22—2921no—
396C22—2921no—
397C22—2921no—
398C22—2921no—
399C22—2921no—
400C22—5844no—
401C22—732no—
402C22—732no—
403C22—1461no—
404C22—1461no—
405C22—1461no—
406C22—1461no—
407C22C2×D4×D7311yescharacteristic
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—2921no—
413C4—2921no—
414C4—732no—
415C4—1461no—
416C4C2×D4×D7311yescharacteristic
417C4#41×D7311yescharacteristic
418C2—41no—
419C2—81no—
420C2—5841no—
421C2—5841no—
422C2—1462no—
423C2—1462no—
424C2#121×D7311yescharacteristic
425C2AGL(1,ℤ/8)×D7311yescharacteristic
426C2#1798938611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#468×C73C2
socleC22×C73C22×D4
hypercenter#468D73
hypocenterC73#3055
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#14556618C2semidirect
2. C2×M16×D73C2semidirect
3. #17989100C2semidirect
4. #121×D73C2semidirect
5. #17988840C2semidirect
6. #17988838C2semidirect
7. #17988835C2semidirect
8. #17988824C2semidirect
9. #17988822C2semidirect
10. #17988819C2semidirect
11. #17988813C2semidirect
12. #17988628C2semidirect
13. #17988590C2semidirect
14. #17988587C2semidirect
15. #468×C73C2semidirect
21. C2×#11924015C22semidirect
22. C2×D584C22semidirect
23. C2×#11924013C22semidirect
24. C2×#11924012C22semidirect
28. C2×C8×D73C22semidirect
29. C2×C8×D73C22semidirect
31. #14556567C22semidirect
33. #14556566C22semidirect
35. #14556565C22semidirect
45. #14556524C22semidirect
46. #14556523C22semidirect
47. #14556522C22semidirect
48. #14556515C22semidirect
49. #14556513C22semidirect
50. #14556513C22semidirect
51. #14556512C22semidirect
52. #14556511C22semidirect
53. #14556511C22semidirect
54. C2×SD16×C73C22semidirect
55. C2×M16×C73C22semidirect
56. C22⋊Q8×C73C22semidirect
58. #107×C73C22semidirect
59. #103×C73C22semidirect
60. #102×C73C22semidirect
91. #11924011D4semidirect
170. C8×C73C2×D4semidirect
172. #10596831C2×D4semidirect
193. C2×D73AGL(1,ℤ/8)semidirect
214. C73#3055semidirect
222. #468D73semidirect
236. C2×SD16C2×D73semidirect
243. C2×M16C2×D73semidirect
248. C22⋊Q8C2×D73semidirect
264. #107C2×D73semidirect
268. #103C2×D73semidirect
274. #102C2×D73semidirect
386. C8D4×D73semidirect