Finite Group Databasebeta

← #22616317

Subgroups — #22616317

Order 9344.

666 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556586C211yesmaximal, characteristic, complemented
2C2×#14556559C211yesmaximal, characteristic
3#17988522C211yesmaximal, characteristic, complemented
4#17988510C211yesmaximal, characteristic, complemented
5#17988503C211yesmaximal, characteristic, complemented
6#17988502C211yesmaximal, characteristic, complemented
7#17988502C211yesmaximal, characteristic, complemented
8#17988501C211yesmaximal, characteristic, complemented
9#17988487C211yesmaximal, characteristic, complemented
10#17988481C211yesmaximal, characteristic, complemented
11#17988478C211yesmaximal, characteristic, complemented
12#17988478C211yesmaximal, characteristic, complemented
13#17988442C211yesmaximal, characteristic, complemented
14#17988442C211yesmaximal, characteristic, complemented
15#390×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19#14556586—24no—
20#14556559—24no—
21C2×C4⋊Dic73C2211yescharacteristic, complemented
22C2×#11924007C2211yescharacteristic, complemented
23C2×#11924007C2211yescharacteristic, complemented
24C2×#11924007C2211yescharacteristic, complemented
25C2×#11924007C2211yescharacteristic, complemented
26C2×C22⋊Dic73C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic, complemented
30C2×C22⋊Dic73C2211yescharacteristic, complemented
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic
39C2×#11924005C2211yescharacteristic
40C2×#11924005C2211yescharacteristic
41C2×C4×Dic73C2211yescharacteristic, complemented
42#14556498C2211yescharacteristic, complemented
43#14556498C2211yescharacteristic, complemented
44#14556498C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46C22×D4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic, complemented
48C2×C22⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic, complemented
51C2×C22⋊C4×C73C2211yescharacteristic, complemented
52C2×C42×C73C2211yescharacteristic, complemented
53C23×D73—22no—
54C23×D73—22no—
55C23×D73—22no—
56C23×D73—41no—
57C23×D73—41no—
58C23×D73—41no—
59C23×D73—41no—
60C23×D73C2311yescharacteristic
61C23×D73C2311yescharacteristic
62C2×C22⋊D73—22no—
63C2×C22⋊D73—22no—
64C2×C22⋊D73—22no—
65C2×C22⋊D73—41no—
66C2×C22⋊D73—41no—
67C2×C22⋊D73—41no—
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C22×Dic73C2311yescharacteristic
71C22×Dic73C2311yescharacteristic
72C22×Dic73C2311yescharacteristic
73C22×Dic73C2311yescharacteristic
74C4⋊Dic73—22no—
75#11924007—22no—
76#11924007—41no—
77#11924007—41no—
78#11924007—41no—
79C22⋊Dic73—22no—
80C22⋊Dic73—22no—
81C22⋊Dic73—41no—
82C22⋊Dic73—41no—
83C22⋊Dic73—41no—
84#11924005—22no—
85#11924005—22no—
86#11924005—22no—
87#11924005—22no—
88#11924005—41no—
89#11924005—41no—
90#11924005—41no—
91#11924005—41no—
92#11924005—41no—
93#11924005D414yes—
94C4×Dic73—22no—
95C24×C73C2311yescharacteristic
96C24×C73C2311yescharacteristic
97C2×D4×C73—22no—
98C2×D4×C73—22no—
99C2×D4×C73—41no—
100C22×C4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102C22×C4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104C22×C4×C73C2311yescharacteristic
105C4⋊C4×C73—22no—
106C22⋊C4×C73—41no—
107C22⋊C4×C73—41no—
108C22⋊C4×C73—41no—
109C22⋊C4×C73—41no—
110C42×C73—41no—
111C23×C73—21no—
112C23×C73—21no—
113C23×C73—21no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—21no—
118C23×C73—21no—
119C23×C73—21no—
120C23×C73—21no—
121C23×C73—21no—
122C23×C73—21no—
123C23×C73—21no—
124C23×C73#4112yes—
125C23×C73C2411yescharacteristic
126C22×D73—21no—
127C22×D73—21no—
128C22×D73—21no—
129C22×D73—21no—
130C22×D73—21no—
131C22×D73—21no—
132C22×D73—21no—
133C22×D73—21no—
134C22×D73—21no—
135C22×D73—21no—
136C22×D73—21no—
137C22×D73—21no—
138C22×D73—44no—
139C22×D73—44no—
140C22×D73—44no—
141C22×D73—44no—
142C22×D73—44no—
143C22×D73—44no—
144C22×D73—44no—
145C22×D73C2×D412yes—
146C22×D73#4112yes—
147D4×C73—44no—
148C2×C4×C73—21no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—21no—
152C2×C4×C73—21no—
153C2×C4×C73—21no—
154C2×C4×C73—21no—
155C2×C4×C73—21no—
156C2×C4×C73—21no—
157C2×C4×C73—21no—
158C2×C4×C73—21no—
159C2×C4×C73—21no—
160C2×C4×C73—21no—
161C2×C4×C73—21no—
162C2×C4×C73C2×D412yes—
163C22⋊D73—44no—
164C22⋊D73—44no—
165C2×Dic73—21no—
166C2×Dic73—21no—
167C2×Dic73—21no—
168C2×Dic73—21no—
169C2×Dic73—21no—
170C2×Dic73—21no—
171C2×Dic73—21no—
172C2×Dic73—21no—
173C2×Dic73—21no—
174C2×Dic73—21no—
175C2×Dic73—21no—
176C2×Dic73—21no—
177C2×Dic73—21no—
178C2×Dic73—21no—
179C2×Dic73—21no—
180C2×Dic73—21no—
181C2×Dic73—21no—
182C2×Dic73C2×D412yes—
183C22×C73—22no—
184C22×C73—22no—
185C22×C73—22no—
186C22×C73—41no—
187C22×C73—41no—
188C22×C73—41no—
189C22×C73—41no—
190C22×C73—41no—
191C22×C73—41no—
192C22×C73—41no—
193C22×C73—41no—
194C22×C73—41no—
195C22×C73—41no—
196C22×C73—41no—
197C22×C73C22×D411yescharacteristic
198C22×C73C2×#4111yescharacteristic
199C22×C73C2×#4111yescharacteristic
200C22×C73H(5,𝔽2)11yescharacteristic
201C22×C73H(5,𝔽2)11yescharacteristic
202C22×C73H(5,𝔽2)11yescharacteristic
203C22×C73H(5,𝔽2)11yescharacteristic
204C2×D73—22no—
205C2×D73—22no—
206C2×D73—22no—
207C2×D73—22no—
208C2×D73—22no—
209C2×D73—22no—
210C2×D73—416no—
211C2×D73—41no—
212C2×D73—41no—
213C2×D73—41no—
214C2×D73—41no—
215C2×D73—41no—
216C2×D73—41no—
217C2×D73—41no—
218C2×D73—41no—
219C4×C73—22no—
220C4×C73—41no—
221C4×C73—41no—
222C4×C73—41no—
223C4×C73—41no—
224Dic73—22no—
225Dic73—41no—
226Dic73—41no—
227Dic73—41no—
228Dic73—41no—
229Dic73—41no—
230C2×C73—42no—
231C2×C73—81no—
232C2×C73#53511yescharacteristic
233C2×C73#53811yescharacteristic
234C2×C73#53811yescharacteristic
235C2×C73#54611yescharacteristic
236C2×C73#54611yescharacteristic
237C2×C73#55111yescharacteristic
238C2×C73#56011yescharacteristic
239D73—42no—
240D73—42no—
241#2685—731nomaximal, Sylow
242C73#268511yescharacteristic, complemented, Sylow
243C2×#126—731no—
244C2×#120—731no—
245#399—731no—
246#396—731no—
247#394—731no—
248#394—731no—
249#394—731no—
250#394—731no—
251#390—731no—
252#390D7311yescharacteristic, complemented
253#388—731no—
254#388—731no—
255#388—731no—
256#379—731no—
257#379—731no—
258C25—731no—
259C22×D4—731no—
260C22×D4—731no—
261C22×D4C2×D7311yescharacteristic
262#126—1464no—
263#120—1464no—
264C2×C4⋊C4—731no—
265C2×C4⋊C4—731no—
266C2×C4⋊C4—731no—
267C2×C4⋊C4—731no—
268C2×C4⋊C4—731no—
269C2×C4⋊C4C2×D7311yescharacteristic, complemented
270C2×C22⋊C4—731no—
271C2×C22⋊C4—731no—
272C2×C22⋊C4—731no—
273C2×C22⋊C4—731no—
274C2×C22⋊C4—731no—
275C2×C22⋊C4—731no—
276C2×C22⋊C4—731no—
277C2×C22⋊C4—731no—
278C2×C22⋊C4—731no—
279C2×C22⋊C4—731no—
280C2×C22⋊C4—731no—
281C2×C22⋊C4—731no—
282C2×C22⋊C4—731no—
283C2×C22⋊C4—731no—
284C2×C22⋊C4—731no—
285C2×C22⋊C4C2×D7311yescharacteristic
286C2×C22⋊C4C2×D7311yescharacteristic
287C2×C22⋊C4C2×D7311yescharacteristic, complemented
288C2×C22⋊C4C2×D7311yescharacteristic, complemented
289C2×C42—731no—
290C2×C42C2×D7311yescharacteristic, complemented
291#95—731no—
292#95—731no—
293#95—731no—
294#95—731no—
295C24—2921no—
296C24—2921no—
297C24—2921no—
298C24—2921no—
299C24—731no—
300C24—731no—
301C24—1462no—
302C24—1462no—
303C24—1462no—
304C24C22×D7311yescharacteristic
305C24C22×D7311yescharacteristic
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—41no—
309C2×D4—2921no—
310C2×D4—2921no—
311C2×D4—2921no—
312C2×D4—1462no—
313C2×D4—1462no—
314C2×D4—1462no—
315C22×C4—731no—
316C22×C4—731no—
317C22×C4—731no—
318C22×C4—731no—
319C22×C4—731no—
320C22×C4—731no—
321C22×C4C22×D7311yescharacteristic
322C22×C4C22×D7311yescharacteristic
323C22×C4C22×D7311yescharacteristic
324C22×C4C22×D7311yescharacteristic
325C22×C4C22×D7311yescharacteristic
326C4⋊C4—22no—
327C4⋊C4—2921no—
328C4⋊C4—2921no—
329C4⋊C4—2921no—
330C4⋊C4—1462no—
331C4⋊C4—1462no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—2921no—
337C22⋊C4—2921no—
338C22⋊C4—2921no—
339C22⋊C4—2921no—
340C22⋊C4—2921no—
341C22⋊C4—2921no—
342C22⋊C4—2921no—
343C22⋊C4—2921no—
344C22⋊C4—734no—
345C22⋊C4—1462no—
346C22⋊C4—1462no—
347C22⋊C4—1462no—
348C22⋊C4—1462no—
349C22⋊C4—1462no—
350C22⋊C4—1462no—
351C42—41no—
352C42—1462no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—2924no—
367C23—2924no—
368C23—2924no—
369C23—2924no—
370C23—2924no—
371C23—2924no—
372C23—2924no—
373C23—732no—
374C23—732no—
375C23—1461no—
376C23—1461no—
377C23—1461no—
378C23—1461no—
379C23—1461no—
380C23—1461no—
381C23—1461no—
382C23—1461no—
383C23—1461no—
384C23—1461no—
385C23—1461no—
386C23—1461no—
387C23#1192402812yes—
388C23C23×D7311yescharacteristic
389D4—44no—
390D4—2924no—
391D4—2924no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—732no—
407C2×C4—1461no—
408C2×C4—1461no—
409C2×C4—1461no—
410C2×C4—1461no—
411C2×C4—1461no—
412C2×C4—1461no—
413C2×C4—1461no—
414C2×C4—1461no—
415C2×C4—1461no—
416C2×C4—1461no—
417C2×C4—1461no—
418C2×C4—1461no—
419C2×C4—1461no—
420C2×C4—1461no—
421C2×C4—1461no—
422C2×C4—1461no—
423C2×C4—1461no—
424C2×C4D4×D7312yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—29216no—
440C22—2921no—
441C22—2921no—
442C22—2921no—
443C22—2921no—
444C22—2921no—
445C22—2921no—
446C22—2921no—
447C22—2921no—
448C22—1462no—
449C22—1462no—
450C22—1462no—
451C22—1462no—
452C22—1462no—
453C22—1462no—
454C22C2×D4×D7311yescharacteristic
455C22#41×D7311yescharacteristic
456C22C2×#1192402811yescharacteristic
457C22#1455663611yescharacteristic
458C22#1455663611yescharacteristic
459C22#1455663611yescharacteristic
460C22#1455663711yescharacteristic
461C4—22no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—2921no—
467C4—2921no—
468C4—2921no—
469C4—2921no—
470C4—2921no—
471C4—1462no—
472C2—42no—
473C2—81no—
474C2—2922no—
475C2—2922no—
476C2#1798915011yescharacteristic
477C2#1798916911yescharacteristic
478C2#1798917011yescharacteristic
479C2#1798922711yescharacteristic
480C2#1798923011yescharacteristic
481C2#1798926611yescharacteristic
482C2#1798932511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#390×C73C2
hypercenter#390D73
hypocenterC73#2685
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14556586C2semidirect
3. #17988522C2semidirect
4. #17988510C2semidirect
5. #17988503C2semidirect
6. #17988502C2semidirect
7. #17988502C2semidirect
8. #17988501C2semidirect
9. #17988487C2semidirect
10. #17988481C2semidirect
11. #17988478C2semidirect
12. #17988478C2semidirect
13. #17988442C2semidirect
14. #17988442C2semidirect
15. #390×C73C2semidirect
21. C2×C4⋊Dic73C22semidirect
22. C2×#11924007C22semidirect
23. C2×#11924007C22semidirect
24. C2×#11924007C22semidirect
25. C2×#11924007C22semidirect
29. C2×C22⋊Dic73C22semidirect
30. C2×C22⋊Dic73C22semidirect
41. C2×C4×Dic73C22semidirect
42. #14556498C22semidirect
43. #14556498C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
47. C2×C4⋊C4×C73C22semidirect
50. C2×C22⋊C4×C73C22semidirect
51. C2×C22⋊C4×C73C22semidirect
52. C2×C42×C73C22semidirect
242. C73#2685semidirect
252. #390D73semidirect
269. C2×C4⋊C4C2×D73semidirect
287. C2×C22⋊C4C2×D73semidirect
288. C2×C22⋊C4C2×D73semidirect
290. C2×C42C2×D73semidirect