Finite Group Databasebeta

← #22614173

Subgroups — #22614173

Order 9344.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×D73C211yesmaximal, characteristic
2#17988515C211yesmaximal, characteristic, complemented
3#17988515C211yesmaximal, characteristic, complemented
4#17988513C211yesmaximal, characteristic, complemented
5#17988509C211yesmaximal, characteristic, complemented
6#17988480C211yesmaximal, characteristic, complemented
7#17988478C211yesmaximal, characteristic, complemented
8#17988477C211yesmaximal, characteristic, complemented
9#17988458C211yesmaximal, characteristic, complemented
10#17988458C211yesmaximal, characteristic, complemented
11#17988444C211yesmaximal, characteristic, complemented
12#17988442C211yesmaximal, characteristic
13#17988442C211yesmaximal, characteristic
14C4×#11924005C211yesmaximal, characteristic, complemented
15C2×#126×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19C2×C4⋊Dic73C2211yescharacteristic, complemented
20C2×#11924007C2211yescharacteristic, complemented
21C2×#11924007C2211yescharacteristic, complemented
22C2×C22⋊Dic73C2211yescharacteristic
23C2×C22⋊Dic73C2211yescharacteristic
24C2×C22⋊Dic73C2211yescharacteristic
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C22⋊C4×D73—24no—
36C2×C4×Dic73C2211yescharacteristic, complemented
37#14556498C2211yescharacteristic, complemented
38#14556498C2211yescharacteristic, complemented
39#14556498C2211yescharacteristic, complemented
40#14556498C2211yescharacteristic, complemented
41#14556498C2211yescharacteristic, complemented
42#14556498C2211yescharacteristic, complemented
43#14556498C2211yescharacteristic, complemented
44#14556498C2211yescharacteristic, complemented
45#126×C73—24no—
46C2×C4⋊C4×C73C2211yescharacteristic, complemented
47C2×C4⋊C4×C73C2211yescharacteristic, complemented
48C2×C4⋊C4×C73C2211yescharacteristic, complemented
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C42×C73C2211yescharacteristic, complemented
53C23×D73—22no—
54C23×D73—22no—
55C23×D73—22no—
56C23×D73—22no—
57C23×D73—22no—
58C23×D73—41no—
59C23×D73—41no—
60C23×D73C2311yescharacteristic
61C23×D73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C2×C4×D73—22no—
69C2×C4×D73—22no—
70C2×C4×D73—22no—
71C2×C4×D73—22no—
72C2×C4×D73—41no—
73C2×C4×D73—41no—
74C4⋊Dic73—41no—
75#11924007—41no—
76#11924007—41no—
77C22⋊Dic73—22no—
78C22⋊Dic73—41no—
79C22⋊Dic73—41no—
80#11924005—22no—
81#11924005—22no—
82#11924005—22no—
83#11924005—22no—
84#11924005—22no—
85#11924005—22no—
86#11924005—22no—
87#11924005—22no—
88#11924005—41no—
89#11924005—41no—
90C4×Dic73—41no—
91C24×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C22×C4×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96C22×C4×C73C2311yescharacteristic
97C22×C4×C73C2311yescharacteristic
98C4⋊C4×C73—22no—
99C4⋊C4×C73—22no—
100C4⋊C4×C73—22no—
101C22⋊C4×C73—22no—
102C22⋊C4×C73—22no—
103C22⋊C4×C73D414yes—
104C42×C73—22no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73C2×D412yes—
112C23×C73C2411yescharacteristic
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—28no—
118C22×D73—21no—
119C22×D73—21no—
120C22×D73—21no—
121C22×D73—21no—
122C22×D73—21no—
123C22×D73—21no—
124C22×D73—44no—
125C22×D73—44no—
126C22×D73—44no—
127C22×D73—44no—
128C22×D73—44no—
129C22×D73—44no—
130C22×D73#4112yes—
131C22×D73#4112yes—
132C22×D73#4112yes—
133C22×D73#4112yes—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—21no—
149C2×C4×C73—21no—
150C2×C4×C73C2×D412yes—
151C2×C4×C73C2×D412yes—
152C2×Dic73—21no—
153C2×Dic73—21no—
154C2×Dic73—21no—
155C2×Dic73—21no—
156C2×Dic73—21no—
157C2×Dic73—21no—
158C2×Dic73—21no—
159C2×Dic73—21no—
160C2×Dic73—21no—
161C2×Dic73—21no—
162C2×Dic73—21no—
163C2×Dic73—21no—
164C2×Dic73—21no—
165C2×Dic73—21no—
166C2×Dic73—21no—
167C2×Dic73—21no—
168C2×Dic73—21no—
169C2×Dic73—21no—
170C4×D73—44no—
171C4×D73—44no—
172C22×C73—22no—
173C22×C73—22no—
174C22×C73—22no—
175C22×C73—41no—
176C22×C73—41no—
177C22×C73—41no—
178C22×C73—41no—
179C22×C73C22×D411yescharacteristic
180C22×C73C2×#4111yescharacteristic
181C22×C73C2×#4111yescharacteristic
182C22×C73C2×#4111yescharacteristic
183C22×C73C2×#4111yescharacteristic
184C22×C73H(5,𝔽2)11yescharacteristic
185C22×C73H(5,𝔽2)11yescharacteristic
186C2×D73—22no—
187C2×D73—22no—
188C2×D73—22no—
189C2×D73—22no—
190C2×D73—22no—
191C2×D73—22no—
192C2×D73—22no—
193C2×D73—22no—
194C2×D73—22no—
195C2×D73—416no—
196C2×D73—41no—
197C2×D73—41no—
198C2×D73—41no—
199C2×D73—41no—
200C2×D73#12614yescomplemented
201C4×C73—22no—
202C4×C73—22no—
203C4×C73—41no—
204C4×C73—41no—
205C4×C73—41no—
206C4×C73—41no—
207Dic73—41no—
208Dic73—41no—
209Dic73—41no—
210Dic73—41no—
211Dic73—41no—
212Dic73—41no—
213C2×C73—42no—
214C2×C73#52511yescharacteristic
215C2×C73C2×#12611yescharacteristic
216C2×C73#53811yescharacteristic
217C2×C73#54611yescharacteristic
218C2×C73#54611yescharacteristic
219C2×C73#55111yescharacteristic
220C2×C73#55111yescharacteristic
221D73—24no—
222D73—42no—
223#2480—731nomaximal, Sylow
224C73#248011yescharacteristic, complemented, Sylow
225C2×#126D7311yescharacteristic, complemented
226C22×C22⋊C4—731no—
227#397—731no—
228#397—731no—
229#397—731no—
230#396—731no—
231#388—731no—
232#388—731no—
233#388—731no—
234#385—731no—
235#385—731no—
236#380—731no—
237#379—731no—
238#379—731no—
239C4×C22⋊C4—731no—
240C25—731no—
241C23×C4—731no—
242C23×C4—731no—
243#126—24no—
244C2×C4⋊C4—731no—
245C2×C4⋊C4—731no—
246C2×C4⋊C4—731no—
247C2×C4⋊C4C2×D7311yescharacteristic, complemented
248C2×C4⋊C4C2×D7311yescharacteristic, complemented
249C2×C4⋊C4C2×D7311yescharacteristic, complemented
250C2×C22⋊C4—731no—
251C2×C22⋊C4—731no—
252C2×C22⋊C4—731no—
253C2×C22⋊C4—731no—
254C2×C22⋊C4—731no—
255C2×C22⋊C4—731no—
256C2×C22⋊C4—731no—
257C2×C22⋊C4—731no—
258C2×C22⋊C4—731no—
259C2×C22⋊C4—731no—
260C2×C22⋊C4—731no—
261C2×C22⋊C4—731no—
262C2×C22⋊C4—731no—
263C2×C22⋊C4—1464no—
264C2×C22⋊C4C2×D7311yescharacteristic
265C2×C22⋊C4C2×D7311yescharacteristic
266C2×C22⋊C4C2×D7311yescharacteristic
267C2×C42—731no—
268C2×C42C2×D7311yescharacteristic, complemented
269#95—731no—
270#95—731no—
271#95—731no—
272#95—731no—
273#95—731no—
274#95—731no—
275#95—731no—
276#95—731no—
277C24—2921no—
278C24—2921no—
279C24—731no—
280C24—731no—
281C24—1462no—
282C24—1462no—
283C24—1462no—
284C24—1462no—
285C24—1462no—
286C24C22×D7311yescharacteristic
287C22×C4—2921no—
288C22×C4—2921no—
289C22×C4—731no—
290C22×C4—731no—
291C22×C4—731no—
292C22×C4—731no—
293C22×C4—731no—
294C22×C4—731no—
295C22×C4—1462no—
296C22×C4—1462no—
297C22×C4—1462no—
298C22×C4—1462no—
299C22×C4C22×D7311yescharacteristic
300C22×C4C22×D7311yescharacteristic
301C22×C4C22×D7311yescharacteristic
302C22×C4C22×D7311yescharacteristic
303C22×C4C22×D7311yescharacteristic
304C22×C4C22×D7311yescharacteristic
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—2921no—
309C4⋊C4—2921no—
310C4⋊C4—2921no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—2921no—
314C22⋊C4—2921no—
315C22⋊C4—2921no—
316C22⋊C4—2921no—
317C22⋊C4—1462no—
318C22⋊C4—1462no—
319C22⋊C4—1462no—
320C22⋊C4—1462no—
321C22⋊C4—1462no—
322C22⋊C4—1462no—
323C22⋊C4—1462no—
324C22⋊C4—1462no—
325C22⋊C4—1462no—
326C22⋊C4C22⋊D7314yes—
327C42—22no—
328C42—2921no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—2924no—
336C23—2924no—
337C23—2924no—
338C23—2924no—
339C23—2924no—
340C23—2924no—
341C23—732no—
342C23—732no—
343C23—732no—
344C23—732no—
345C23—1468no—
346C23—1461no—
347C23—1461no—
348C23—1461no—
349C23—1461no—
350C23—1461no—
351C23—1461no—
352C23—1461no—
353C23—1461no—
354C23—1461no—
355C23—1461no—
356C23C2×C22⋊D7312yes—
357C23C23×D7311yescharacteristic
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—2924no—
375C2×C4—2924no—
376C2×C4—1461no—
377C2×C4—1461no—
378C2×C4—1461no—
379C2×C4—1461no—
380C2×C4—1461no—
381C2×C4—1461no—
382C2×C4—1461no—
383C2×C4—1461no—
384C2×C4—1461no—
385C2×C4—1461no—
386C2×C4—1461no—
387C2×C4—1461no—
388C2×C4—1461no—
389C2×C4—1461no—
390C2×C4—1461no—
391C2×C4—1461no—
392C2×C4—1461no—
393C2×C4—1461no—
394C2×C4C2×C22⋊D7312yes—
395C2×C4C2×C22⋊D7312yes—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—29216no—
404C22—2921no—
405C22—2921no—
406C22—2921no—
407C22—2921no—
408C22—734no—
409C22—1462no—
410C22—1462no—
411C22—1462no—
412C22—1462no—
413C22—1462no—
414C22—1462no—
415C22—1462no—
416C22—1462no—
417C22—1462no—
418C22C22×C22⋊D7311yescharacteristic
419C22#41×D7311yescharacteristic
420C22#41×D7311yescharacteristic
421C22#41×D7311yescharacteristic
422C22#41×D7311yescharacteristic
423C22#1455663711yescharacteristic
424C22#1455663711yescharacteristic
425C4—22no—
426C4—22no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—2921no—
432C4—2921no—
433C4—2921no—
434C4—2921no—
435C4—2921no—
436C4—2921no—
437C2—42no—
438C2—2922no—
439C2—1464no—
440C2#1798909411yescharacteristic
441C2#126×D7311yescharacteristic
442C2#1798917611yescharacteristic
443C2#1798922511yescharacteristic
444C2#1798922511yescharacteristic
445C2#1798926211yescharacteristic
446C2#1798926211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#126×C73C2
hypercenterC2×#126D73
hypocenterC73#2480
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
2. #17988515C2semidirect
3. #17988515C2semidirect
4. #17988513C2semidirect
5. #17988509C2semidirect
6. #17988480C2semidirect
7. #17988478C2semidirect
8. #17988477C2semidirect
9. #17988458C2semidirect
10. #17988458C2semidirect
11. #17988444C2semidirect
14. C4×#11924005C2semidirect
15. C2×#126×C73C2semidirect
19. C2×C4⋊Dic73C22semidirect
20. C2×#11924007C22semidirect
21. C2×#11924007C22semidirect
36. C2×C4×Dic73C22semidirect
37. #14556498C22semidirect
38. #14556498C22semidirect
39. #14556498C22semidirect
40. #14556498C22semidirect
41. #14556498C22semidirect
42. #14556498C22semidirect
43. #14556498C22semidirect
44. #14556498C22semidirect
46. C2×C4⋊C4×C73C22semidirect
47. C2×C4⋊C4×C73C22semidirect
48. C2×C4⋊C4×C73C22semidirect
52. C2×C42×C73C22semidirect
200. C2×D73#126semidirect
224. C73#2480semidirect
225. C2×#126D73semidirect
247. C2×C4⋊C4C2×D73semidirect
248. C2×C4⋊C4C2×D73semidirect
249. C2×C4⋊C4C2×D73semidirect
268. C2×C42C2×D73semidirect