Finite Group Databasebeta

← #22623610

Subgroups — #22623610

Order 9344.

1522 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556639C211yesmaximal, characteristic, complemented
2C2×#41×D73C211yesmaximal, characteristic, complemented
3Q8×D292C211yesmaximal, characteristic, complemented
4Q8×C22⋊D73C211yesmaximal, characteristic, complemented
5#17989244C211yesmaximal, characteristic, complemented
6#17989242C213yesmaximal, complemented
7#17989239C213yesmaximal, complemented
8#17989234C213yesmaximal, complemented
9#17989230C213yesmaximal, complemented
10#17989166C213yesmaximal, complemented
11#17989157C213yesmaximal, complemented
12#17989096C213yesmaximal, complemented
13C22⋊Q8×D73C213yesmaximal, complemented
14#17989069C211yesmaximal, characteristic, complemented
15#548×C73C211yesmaximal, characteristic, complemented
16#14556639—28no—
17C2×#11924029C2211yescharacteristic
18C2×#11924029C2213yescomplemented
19C2×#11924028C2213yes—
20C2×#11924028C2213yescomplemented
21C2×#11924028C2213yescomplemented
22C2×#11924027C2213yes—
23#41×D73—28no—
24C2×Q8×D73C2211yescharacteristic
25C2×Q8×D73C2213yescomplemented
26C2×Q8×D73C2211yescharacteristic, complemented
27C2×D4×D73C2213yes—
28C22×C4×D73C2213yes—
29#14556591C2213yescomplemented
30#14556589C2213yescomplemented
31#14556578C2213yescomplemented
32#14556576C2213yescomplemented
33#14556573C2216yescomplemented
34#14556573C2216yescomplemented
35#14556573C2213yescomplemented
36#14556571C2213yes—
37#14556571C2213yescomplemented
38#14556570C2213yescomplemented
39#14556570C2213yescomplemented
40#14556569C2213yes—
41#14556568C2213yescomplemented
42#14556568C2216yescomplemented
43#14556567C2213yes—
44#14556564C2211yescharacteristic
45#14556564C2216yescomplemented
46#14556563C2213yescomplemented
47#14556562C2213yescomplemented
48#14556562C2216yescomplemented
49#14556561C2213yes—
50#14556559C2213yes—
51Q8×Dic73C2211yescharacteristic, complemented
52C4×D292C2213yes—
53C4×D292C2213yescomplemented
54#14556553C2213yescomplemented
55C4×C22⋊D73C2213yes—
56C4×C22⋊D73C2213yescomplemented
57#14556548C2213yescomplemented
58C4⋊C4×D73C2213yescomplemented
59C4⋊C4×D73C2216yescomplemented
60C22⋊C4×D73C2216yes—
61C2×#41×C73C2211yescharacteristic
62C22×Q8×C73C2211yescharacteristic, complemented
63#124×C73C2213yescomplemented
64C22⋊Q8×C73C2213yescomplemented
65#121×C73C2213yescomplemented
66C4×Q8×C73C2211yescharacteristic, complemented
67C4×D4×C73C2213yescomplemented
68C23×D73C2313yes—
69#11924029—212no—
70#11924029D418yescomplemented
71#11924028—212no—
72#11924028—212no—
73#11924028—212no—
74#11924027—212no—
75C2×Dic146C2313yes—
76C2×Dic146C2313yes—
77C2×Dic146C2313yes—
78Q8×D73—24no—
79Q8×D73—24no—
80Q8×D73—212no—
81C2×D292C2311yescharacteristic
82C2×D292C2313yes—
83C2×D292C2313yes—
84C2×C22⋊D73C2311yescharacteristic
85C2×C22⋊D73C2313yes—
86C2×C22⋊D73C2316yes—
87C2×C22⋊D73C2311yescharacteristic
88C2×C22⋊D73C2313yes—
89D4×D73—212no—
90C22×Dic73C2313yes—
91C2×C4×D73—212no—
92C2×C4×D73C2316yes—
93C2×C4×D73C2313yes—
94C2×C4×D73C2313yes—
95C2×C4×D73C2313yes—
96C2×C4×D73C2311yescharacteristic
97C2×C4×D73C2316yes—
98C2×C4×D73C2313yes—
99C4⋊Dic73C2313yes—
100C4⋊Dic73C2316yes—
101C4⋊Dic73C2313yes—
102#11924007C2313yes—
103#11924007C2313yes—
104#11924007C2316yes—
105#11924007C2311yescharacteristic
106#11924007C2313yes—
107C22⋊Dic73C2316yes—
108C22⋊Dic73C2313yes—
109C22⋊Dic73C2313yes—
110#11924005C2313yes—
111#11924005C2313yes—
112#11924005C2313yes—
113#11924005C2313yes—
114#11924005C2311yescharacteristic
115#11924005C2313yes—
116C4×Dic73C2313yes—
117#41×C73—24no—
118C2×Q8×C73—24no—
119C2×Q8×C73C2313yes—
120C2×Q8×C73C2311yescharacteristic
121C2×D4×C73C2313yes—
122C2×D4×C73C2313yes—
123C22×C4×C73C2313yes—
124C22×C4×C73C2313yes—
125C4⋊C4×C73C2313yes—
126C4⋊C4×C73C2313yes—
127C22⋊C4×C73C2311yescharacteristic
128C22⋊C4×C73C2313yes—
129C22⋊C4×C73C2316yes—
130C42×C73C2313yes—
131C23×C73C2413yes—
132C23×C73C2411yescharacteristic
133C22×D73—26no—
134C22×D73—26no—
135C22×D73—43no—
136C22×D73C2411yescharacteristic
137C22×D73C2413yes—
138C22×D73C2411yescharacteristic
139Q8×C73—26no—
140Q8×C73C2×D414yes—
141D4×C73—26no—
142D4×C73—43no—
143C2×C4×C73—26no—
144C2×C4×C73—26no—
145C2×C4×C73C2411yescharacteristic
146C2×C4×C73C2413yes—
147C2×C4×C73C2413yes—
148C2×C4×C73C2411yescharacteristic
149C2×C4×C73C2413yes—
150C22⋊D73—212no—
151C22⋊D73—26no—
152C22⋊D73—22no—
153C22⋊D73—22no—
154C22⋊D73—43no—
155C2×Dic73—26no—
156C2×Dic73C2411yescharacteristic
157C2×Dic73C2413yes—
158C2×Dic73C2413yes—
159C2×Dic73C2413yes—
160C2×Dic73C2411yescharacteristic
161D292—26no—
162D292—22no—
163D292C2×D4112yes—
164C4×D73—26no—
165C4×D73—212no—
166C4×D73—26no—
167C4×D73—26no—
168C4×D73—22no—
169C4×D73—46no—
170C4×D73C2×D4112yes—
171Dic146—26no—
172Dic146—26no—
173Dic146—26no—
174C22×C73—23no—
175C22×C73—21no—
176C22×C73—21no—
177C22×C73—23no—
178C22×C73—23no—
179C22×C73—21no—
180C22×C73C2511yescharacteristic
181C2×D73—21no—
182C2×D73—23no—
183C2×D73—23no—
184C2×D73—21no—
185C2×D73—21no—
186C2×D73—21no—
187C2×D73—21no—
188C2×D73—412no—
189C2×D73C22×D416yes—
190C2×D732−1+412yescomplemented
191C4×C73—23no—
192C4×C73—21no—
193C4×C73—21no—
194C4×C73—23no—
195C4×C73C22×D416yes—
196Dic73—23no—
197Dic73—23no—
198Dic73—21no—
199Dic73—23no—
200Dic73C22×D412yes—
201C2×C73—43no—
202C2×C73—41no—
203C2×C73C23×D411yescharacteristic
204C2×C73C2×2−1+411yescharacteristic
205C2×C73#58511yescharacteristic
206D73—22no—
207D73—26no—
208D73—41no—
209#3489—731nomaximal, Sylow
210C73#348911yescharacteristic, complemented, Sylow
211C2×2−1+4—731no—
212C22×#41—731no—
213D4×Q8—731no—
214D4×Q8—731no—
215#548—731no—
216#548D7311yescharacteristic, complemented
217#547—733no—
218#547—733no—
219#546—733no—
220#546—733no—
221#537—733no—
222#536—733no—
223#525—733no—
224C2×C22⋊Q8—733no—
225#520—731no—
2262−1+4—1468no—
227C2×#41—731no—
228C2×#41—733no—
229C2×#41—733no—
230C2×#41—733no—
231C2×#41—733no—
232C2×#41—733no—
233C2×#41—1468no—
234C2×#41C2×D7311yescharacteristic
235C22×Q8—733no—
236C22×Q8—731no—
237C22×Q8—731no—
238C22×Q8C2×D7311yescharacteristic, complemented
239C22×D4—733no—
240C23×C4—733no—
241C4⋊Q8—733no—
242C4⋊Q8—733no—
243#124—733no—
244#124C2×D7313yescomplemented
245#123—733no—
246#123—733no—
247#123—736no—
248#123—736no—
249C22⋊Q8—733no—
250C22⋊Q8—733no—
251C22⋊Q8—733no—
252C22⋊Q8—733no—
253C22⋊Q8—733no—
254C22⋊Q8—733no—
255C22⋊Q8—736no—
256C22⋊Q8—733no—
257C22⋊Q8C2×D7313yescomplemented
258#121—733no—
259#121—736no—
260#121—733no—
261#121—731no—
262#121—736no—
263#121C2×D7313yescomplemented
264#120—733no—
265#120—733no—
266C4×Q8—731no—
267C4×Q8C2×D7311yescharacteristic, complemented
268C4×D4—733no—
269C4×D4—733no—
270C4×D4—733no—
271C4×D4—733no—
272C4×D4—733no—
273C4×D4C2×D7313yescomplemented
274#117—733no—
275C2×C4⋊C4—733no—
276C2×C4⋊C4—736no—
277C2×C22⋊C4—736no—
278C24—733no—
279#41—24no—
280#41—738no—
281#41—14612no—
282#41—14612no—
283#41—14612no—
284#41—14612no—
285#41—14612no—
286C2×Q8—24no—
287C2×Q8—733no—
288C2×Q8—733no—
289C2×Q8—733no—
290C2×Q8—14612no—
291C2×Q8—1464no—
292C2×Q8—1464no—
293C2×Q8C22×D7313yes—
294C2×Q8C22×D7311yescharacteristic
295C2×D4—733no—
296C2×D4—731no—
297C2×D4—733no—
298C2×D4—731no—
299C2×D4—736no—
300C2×D4—733no—
301C2×D4—731no—
302C2×D4—733no—
303C2×D4—14612no—
304C2×D4C22×D7313yes—
305C2×D4C22×D7313yes—
306C22×C4—736no—
307C22×C4—733no—
308C22×C4—733no—
309C22×C4—736no—
310C22×C4—733no—
311C22×C4—733no—
312C22×C4—733no—
313C22×C4—731no—
314C22×C4—14612no—
315C22×C4C22×D7313yes—
316C22×C4C22×D7313yes—
317C4⋊C4—733no—
318C4⋊C4—733no—
319C4⋊C4—736no—
320C4⋊C4—731no—
321C4⋊C4—733no—
322C4⋊C4—733no—
323C4⋊C4—736no—
324C4⋊C4—733no—
325C4⋊C4C22×D7313yes—
326C4⋊C4C22×D7313yes—
327C22⋊C4—736no—
328C22⋊C4—733no—
329C22⋊C4—733no—
330C22⋊C4—733no—
331C22⋊C4—733no—
332C22⋊C4—733no—
333C22⋊C4—733no—
334C22⋊C4—731no—
335C22⋊C4—733no—
336C22⋊C4C22×D7316yes—
337C22⋊C4C22×D7311yescharacteristic
338C22⋊C4C22×D7313yes—
339C42—733no—
340C42C22×D7313yes—
341C23—2923no—
342C23—731no—
343C23—733no—
344C23—731no—
345C23—1466no—
346C23—1466no—
347C23C23×D7313yes—
348C23C23×D7311yescharacteristic
349Q8—26no—
350Q8—1466no—
351Q8—1466no—
352Q8—1466no—
353Q8D4×D7314yes—
354D4—26no—
355D4—43no—
356D4—2923no—
357D4—7312no—
358D4—1466no—
359D4—1462no—
360D4—1462no—
361D4—14612no—
362D4—1466no—
363D4—1462no—
364C2×C4—26no—
365C2×C4—26no—
366C2×C4—2926no—
367C2×C4—731no—
368C2×C4—7312no—
369C2×C4—731no—
370C2×C4—733no—
371C2×C4—733no—
372C2×C4—733no—
373C2×C4—1462no—
374C2×C4—1466no—
375C2×C4—14612no—
376C2×C4—1466no—
377C2×C4—1466no—
378C2×C4—1466no—
379C2×C4C23×D7311yescharacteristic
380C2×C4C23×D7313yes—
381C2×C4C23×D7313yes—
382C2×C4C23×D7311yescharacteristic
383C2×C4C23×D7313yes—
384C22—21no—
385C22—23no—
386C22—21no—
387C22—23no—
388C22—21no—
389C22—23no—
390C22—29212no—
391C22—736no—
392C22—732no—
393C22—1461no—
394C22—1461no—
395C22—1461no—
396C22—1461no—
397C22—1463no—
398C22—1463no—
399C22—1461no—
400C22C24×D7311yescharacteristic
401C4—21no—
402C4—23no—
403C4—21no—
404C4—23no—
405C4—732no—
406C4—1463no—
407C4—1463no—
408C4—1461no—
409C4—1463no—
410C4C2×D4×D7316yes—
411C2—43no—
412C2—41no—
413C2—2921no—
414C2—1462no—
415C2—1466no—
416C2C22×D4×D7311yescharacteristic
417C22−1+4×D7311yescharacteristic
418C2#1798942311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D73
commutator, socleC22×C73C25
Fitting#548×C73C2
hypercenter#548D73
hypocenterC73#3489
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#14556639C2semidirect
2. C2×#41×D73C2semidirect
3. Q8×D292C2semidirect
4. Q8×C22⋊D73C2semidirect
5. #17989244C2semidirect
6. #17989242C2semidirect
7. #17989239C2semidirect
8. #17989234C2semidirect
9. #17989230C2semidirect
10. #17989166C2semidirect
11. #17989157C2semidirect
12. #17989096C2semidirect
13. C22⋊Q8×D73C2semidirect
14. #17989069C2semidirect
15. #548×C73C2semidirect
18. C2×#11924029C22semidirect
20. C2×#11924028C22semidirect
21. C2×#11924028C22semidirect
25. C2×Q8×D73C22semidirect
26. C2×Q8×D73C22semidirect
29. #14556591C22semidirect
30. #14556589C22semidirect
31. #14556578C22semidirect
32. #14556576C22semidirect
33. #14556573C22semidirect
34. #14556573C22semidirect
35. #14556573C22semidirect
37. #14556571C22semidirect
38. #14556570C22semidirect
39. #14556570C22semidirect
41. #14556568C22semidirect
42. #14556568C22semidirect
45. #14556564C22semidirect
46. #14556563C22semidirect
47. #14556562C22semidirect
48. #14556562C22semidirect
51. Q8×Dic73C22semidirect
53. C4×D292C22semidirect
54. #14556553C22semidirect
56. C4×C22⋊D73C22semidirect
57. #14556548C22semidirect
58. C4⋊C4×D73C22semidirect
59. C4⋊C4×D73C22semidirect
62. C22×Q8×C73C22semidirect
63. #124×C73C22semidirect
64. C22⋊Q8×C73C22semidirect
65. #121×C73C22semidirect
66. C4×Q8×C73C22semidirect
67. C4×D4×C73C22semidirect
70. #11924029D4semidirect
190. C2×D732−1+4semidirect
210. C73#3489semidirect
216. #548D73semidirect
238. C22×Q8C2×D73semidirect
244. #124C2×D73semidirect
257. C22⋊Q8C2×D73semidirect
263. #121C2×D73semidirect
267. C4×Q8C2×D73semidirect
273. C4×D4C2×D73semidirect