Finite Group Databasebeta

← #22616311

Subgroups — #22616311

Order 9344.

688 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556577C211yesmaximal, characteristic, complemented
2C2×#14556560C211yesmaximal, characteristic
3#17988515C211yesmaximal, characteristic, complemented
4#17988512C211yesmaximal, characteristic, complemented
5#17988503C211yesmaximal, characteristic, complemented
6#17988502C211yesmaximal, characteristic, complemented
7#17988499C211yesmaximal, characteristic, complemented
8#17988499C211yesmaximal, characteristic, complemented
9#17988481C211yesmaximal, characteristic, complemented
10#17988480C211yesmaximal, characteristic, complemented
11#17988463C211yesmaximal, characteristic, complemented
12#17988463C211yesmaximal, characteristic, complemented
13#17988463C211yesmaximal, characteristic, complemented
14#17988443C211yesmaximal, characteristic, complemented
15#379×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic, complemented
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic
20C22×C4×D73C2211yescharacteristic, complemented
21#14556577—24no—
22#14556560—24no—
23C2×C4⋊Dic73C2211yescharacteristic, complemented
24C2×#11924007C2211yescharacteristic, complemented
25C2×C22⋊Dic73C2211yescharacteristic
26C2×C22⋊Dic73C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33C2×C22⋊Dic73C2211yescharacteristic
34C2×#11924005C2211yescharacteristic, complemented
35C2×#11924005C2211yescharacteristic, complemented
36C2×#11924005C2211yescharacteristic, complemented
37C2×C4×Dic73C2211yescharacteristic, complemented
38#14556498C2211yescharacteristic, complemented
39#14556498C2211yescharacteristic, complemented
40#14556498C2211yescharacteristic, complemented
41#14556498C2211yescharacteristic, complemented
42#14556498C2211yescharacteristic, complemented
43#14556498C2211yescharacteristic, complemented
44#14556498C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46C25×C73C2211yescharacteristic
47C2×C22⋊C4×C73C2211yescharacteristic
48C2×C22⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C22⋊C4×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C2×Dic146—22no—
55C2×Dic146—41no—
56C2×Dic146—41no—
57C2×C22⋊D73—22no—
58C2×C22⋊D73—22no—
59C2×C22⋊D73—22no—
60C2×C22⋊D73—22no—
61C2×C22⋊D73—41no—
62C2×C22⋊D73—41no—
63C2×C22⋊D73—41no—
64C2×C22⋊D73—41no—
65C2×C22⋊D73D414yes—
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C22×Dic73C2311yescharacteristic
71C22×Dic73C2311yescharacteristic
72C22×Dic73C2311yescharacteristic
73C2×C4×D73—41no—
74C2×C4×D73—41no—
75C2×C4×D73—41no—
76C4⋊Dic73—41no—
77#11924007—41no—
78C22⋊Dic73—22no—
79C22⋊Dic73—22no—
80C22⋊Dic73—22no—
81C22⋊Dic73—22no—
82C22⋊Dic73—22no—
83C22⋊Dic73—41no—
84C22⋊Dic73—41no—
85C22⋊Dic73—41no—
86C22⋊Dic73—41no—
87#11924005—22no—
88#11924005—22no—
89#11924005—41no—
90C4×Dic73—22no—
91C24×C73—22no—
92C24×C73—22no—
93C24×C73—22no—
94C24×C73—41no—
95C24×C73—41no—
96C24×C73—41no—
97C24×C73—41no—
98C24×C73C2311yescharacteristic
99C24×C73C2311yescharacteristic
100C24×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102C22×C4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104C22×C4×C73C2311yescharacteristic
105C22⋊C4×C73—22no—
106C22⋊C4×C73—22no—
107C22⋊C4×C73—41no—
108C22⋊C4×C73—41no—
109C22⋊C4×C73—41no—
110C22⋊C4×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—21no—
125C23×C73—21no—
126C23×C73—21no—
127C23×C73—21no—
128C23×C73—21no—
129C23×C73—44no—
130C23×C73—44no—
131C23×C73—44no—
132C23×C73—44no—
133C23×C73—44no—
134C23×C73—44no—
135C23×C73—44no—
136C23×C73C2×D412yes—
137C23×C73#4112yes—
138C23×C73#4112yes—
139C23×C73C2411yescharacteristic
140C22×D73—21no—
141C22×D73—21no—
142C22×D73—21no—
143C22×D73—21no—
144C22×D73—21no—
145C22×D73—21no—
146C22×D73C2×D412yes—
147C2×C4×C73—21no—
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—
159C22⋊D73—44no—
160C22⋊D73—44no—
161C22⋊D73—44no—
162C2×Dic73—21no—
163C2×Dic73—21no—
164C2×Dic73—21no—
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—
183C4×D73—44no—
184Dic146—44no—
185C22×C73—22no—
186C22×C73—22no—
187C22×C73—22no—
188C22×C73—22no—
189C22×C73—22no—
190C22×C73—22no—
191C22×C73—22no—
192C22×C73—22no—
193C22×C73—22no—
194C22×C73—416no—
195C22×C73—41no—
196C22×C73—41no—
197C22×C73—41no—
198C22×C73—41no—
199C22×C73—41no—
200C22×C73—41no—
201C22×C73—41no—
202C22×C73—41no—
203C22×C73—41no—
204C22×C73—41no—
205C22×C73—41no—
206C22×C73—41no—
207C22×C73C22×D411yescharacteristic
208C22×C73C2×#4111yescharacteristic
209C22×C73C2×#4111yescharacteristic
210C22×C73H(5,𝔽2)11yescharacteristic
211C22×C73H(5,𝔽2)11yescharacteristic
212C22×C73H(5,𝔽2)11yescharacteristic
213C22×C73H(5,𝔽2)11yescharacteristic
214C2×D73—22no—
215C2×D73—22no—
216C2×D73—22no—
217C2×D73—41no—
218C2×D73—41no—
219C2×D73—41no—
220C2×D73—41no—
221C4×C73—41no—
222C4×C73—41no—
223C4×C73—41no—
224C4×C73—41no—
225Dic73—22no—
226Dic73—41no—
227Dic73—41no—
228Dic73—41no—
229Dic73—41no—
230Dic73—41no—
231Dic73—41no—
232C2×C73—42no—
233C2×C73—42no—
234C2×C73—42no—
235C2×C73#53411yescharacteristic
236C2×C73#53811yescharacteristic
237C2×C73#53811yescharacteristic
238C2×C73#54611yescharacteristic
239C2×C73#54611yescharacteristic
240C2×C73#55111yescharacteristic
241C2×C73H(3,𝔽4)11yescharacteristic
242D73—42no—
243#2684—731nomaximal, Sylow
244C73#268411yescharacteristic, complemented, Sylow
245C2×#124—731no—
246C2×#120—731no—
247#397—731no—
248#397—731no—
249#394—731no—
250#394—731no—
251#393—731no—
252#393—731no—
253#388—731no—
254#388—731no—
255#386—731no—
256#386—731no—
257#386—731no—
258#379—731no—
259#379D7311yescharacteristic, complemented
260C25C2×D7311yescharacteristic
261C22×Q8—731no—
262C22×D4—731no—
263C22×D4—731no—
264C22×D4—731no—
265C23×C4—731no—
266#124—1464no—
267#120—1464no—
268C2×C4⋊C4—731no—
269C2×C4⋊C4—731no—
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⋊C4C2×D7311yescharacteristic
283C2×C22⋊C4C2×D7311yescharacteristic
284C2×C22⋊C4C2×D7311yescharacteristic
285C2×C22⋊C4C2×D7311yescharacteristic
286C2×C22⋊C4C2×D7311yescharacteristic
287C2×C22⋊C4C2×D7311yescharacteristic
288C2×C42—731no—
289#95—731no—
290#95—731no—
291#95—731no—
292#95—731no—
293#95—731no—
294#95—731no—
295#95—731no—
296#95—731no—
297C24—22no—
298C24—22no—
299C24—22no—
300C24—41no—
301C24—41no—
302C24—41no—
303C24—41no—
304C24—731no—
305C24C22×D7311yescharacteristic
306C24C22×D7311yescharacteristic
307C24C22×D7311yescharacteristic
308C2×Q8—2921no—
309C2×Q8—2921no—
310C2×Q8—1462no—
311C2×D4—2921no—
312C2×D4—2921no—
313C2×D4—2921no—
314C2×D4—2921no—
315C2×D4—734no—
316C2×D4—1462no—
317C2×D4—1462no—
318C2×D4—1462no—
319C2×D4—1462no—
320C22×C4—2921no—
321C22×C4—2921no—
322C22×C4—2921no—
323C22×C4—731no—
324C22×C4—731no—
325C22×C4—731no—
326C22×C4—731no—
327C22×C4—731no—
328C22×C4—731no—
329C22×C4—731no—
330C22×C4C22×D7311yescharacteristic
331C22×C4C22×D7311yescharacteristic
332C22×C4C22×D7311yescharacteristic
333C22×C4C22×D7311yescharacteristic
334C4⋊C4—2921no—
335C4⋊C4—2921no—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—2921no—
343C22⋊C4—2921no—
344C22⋊C4—2921no—
345C22⋊C4—2921no—
346C22⋊C4—2921no—
347C22⋊C4—1462no—
348C22⋊C4—1462no—
349C22⋊C4—1462no—
350C22⋊C4—1462no—
351C22⋊C4—1462no—
352C22⋊C4—1462no—
353C22⋊C4—1462no—
354C42—1462no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—44no—
374C23—44no—
375C23—44no—
376C23—44no—
377C23—44no—
378C23—44no—
379C23—44no—
380C23—732no—
381C23—1461no—
382C23—1461no—
383C23—1461no—
384C23—1461no—
385C23—1461no—
386C23—1461no—
387C23D4×D7312yes—
388C23#1192402712yes—
389C23#1192402812yes—
390C23C23×D7311yescharacteristic
391Q8—2924no—
392D4—2924no—
393D4—2924no—
394D4—2924no—
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—21no—
407C2×C4—2924no—
408C2×C4—732no—
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×C4—1461no—
425C2×C4—1461no—
426C2×C4—1461no—
427C2×C4—1461no—
428C2×C4—1461no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—416no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—2921no—
452C22—2921no—
453C22—2921no—
454C22—2921no—
455C22—1462no—
456C22—1462no—
457C22—1462no—
458C22C2×D4×D7311yescharacteristic
459C22C2×#1192402711yescharacteristic
460C22C2×#1192402811yescharacteristic
461C22#1455663611yescharacteristic
462C22#1455663611yescharacteristic
463C22#1455663611yescharacteristic
464C22#1455663611yescharacteristic
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—2921no—
470C4—2921no—
471C4—2921no—
472C4—2921no—
473C4—2921no—
474C4—2921no—
475C4—1462no—
476C2—42no—
477C2—42no—
478C2—42no—
479C2—2922no—
480C2#1798914711yescharacteristic
481C2#1798917211yescharacteristic
482C2#1798917511yescharacteristic
483C2#1798922411yescharacteristic
484C2#1798922711yescharacteristic
485C2#1798926311yescharacteristic
486C2#1798933011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#379×C73C2
hypercenter#379D73
hypocenterC73#2684
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#14556577C2semidirect
3. #17988515C2semidirect
4. #17988512C2semidirect
5. #17988503C2semidirect
6. #17988502C2semidirect
7. #17988499C2semidirect
8. #17988499C2semidirect
9. #17988481C2semidirect
10. #17988480C2semidirect
11. #17988463C2semidirect
12. #17988463C2semidirect
13. #17988463C2semidirect
14. #17988443C2semidirect
15. #379×C73C2semidirect
16. C22×Dic146C22semidirect
20. C22×C4×D73C22semidirect
23. C2×C4⋊Dic73C22semidirect
24. C2×#11924007C22semidirect
34. C2×#11924005C22semidirect
35. C2×#11924005C22semidirect
36. C2×#11924005C22semidirect
37. C2×C4×Dic73C22semidirect
38. #14556498C22semidirect
39. #14556498C22semidirect
40. #14556498C22semidirect
41. #14556498C22semidirect
42. #14556498C22semidirect
43. #14556498C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
244. C73#2684semidirect
259. #379D73semidirect