Finite Group Databasebeta

← #22613313

Subgroups — #22613313

Order 9344.

786 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556573C211yesmaximal, characteristic, complemented
2C2×#14556559C211yesmaximal, characteristic
3C2×#14556548C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D73C211yesmaximal, characteristic, complemented
5#17988510C211yesmaximal, characteristic, complemented
6#17988509C211yesmaximal, characteristic, complemented
7#17988502C211yesmaximal, characteristic, complemented
8#17988501C211yesmaximal, characteristic, complemented
9#17988487C211yesmaximal, characteristic, complemented
10#17988481C211yesmaximal, characteristic, complemented
11#17988478C211yesmaximal, characteristic, complemented
12#17988463C211yesmaximal, characteristic, complemented
13#17988458C211yesmaximal, characteristic, complemented
14#17988442C211yesmaximal, characteristic, complemented
15#390×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20C22×C4×D73C2211yescharacteristic
21#14556573—24no—
22#14556559—24no—
23#14556548—24no—
24C2×C4⋊Dic73C2211yescharacteristic, complemented
25C2×#11924007C2211yescharacteristic, complemented
26C2×#11924007C2211yescharacteristic, complemented
27C2×#11924007C2211yescharacteristic, complemented
28C2×#11924007C2211yescharacteristic, complemented
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic, complemented
33C2×C22⋊Dic73C2211yescharacteristic, complemented
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic
39C2×#11924005C2211yescharacteristic
40C2×#11924005C2211yescharacteristic
41C2×#11924005C2211yescharacteristic
42C22⋊C4×D73—24no—
43C2×C4×Dic73C2211yescharacteristic, complemented
44#14556498C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46#14556498C2211yescharacteristic, complemented
47#14556498C2211yescharacteristic, complemented
48C22×D4×C73C2211yescharacteristic
49C2×C4⋊C4×C73C2211yescharacteristic, complemented
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C22⋊C4×C73C2211yescharacteristic, complemented
53C2×C22⋊C4×C73C2211yescharacteristic, complemented
54C2×C42×C73C2211yescharacteristic, complemented
55C23×D73—22no—
56C23×D73—22no—
57C23×D73—22no—
58C23×D73—22no—
59C23×D73—22no—
60C23×D73—41no—
61C23×D73—41no—
62C23×D73C2311yescharacteristic
63C23×D73C2311yescharacteristic
64C2×C22⋊D73—22no—
65C2×C22⋊D73—22no—
66C2×C22⋊D73—22no—
67C2×C22⋊D73—22no—
68C2×C22⋊D73—22no—
69C2×C22⋊D73—41no—
70C22×Dic73C2311yescharacteristic
71C22×Dic73C2311yescharacteristic
72C22×Dic73C2311yescharacteristic
73C22×Dic73C2311yescharacteristic
74C22×Dic73C2311yescharacteristic
75C22×Dic73C2311yescharacteristic
76C2×C4×D73—22no—
77C2×C4×D73—22no—
78C2×C4×D73—22no—
79C2×C4×D73—41no—
80C2×C4×D73—41no—
81C2×C4×D73D414yescomplemented
82C4⋊Dic73—22no—
83#11924007—22no—
84#11924007—22no—
85#11924007—22no—
86#11924007—41no—
87C22⋊Dic73—22no—
88C22⋊Dic73—22no—
89C22⋊Dic73—22no—
90C22⋊Dic73—22no—
91C22⋊Dic73—41no—
92#11924005—22no—
93#11924005—22no—
94#11924005—22no—
95#11924005—22no—
96#11924005—22no—
97#11924005—22no—
98#11924005—41no—
99#11924005D414yes—
100C4×Dic73—22no—
101C24×C73C2311yescharacteristic
102C24×C73C2311yescharacteristic
103C2×D4×C73—22no—
104C2×D4×C73—22no—
105C2×D4×C73—41no—
106C22×C4×C73C2311yescharacteristic
107C22×C4×C73C2311yescharacteristic
108C22×C4×C73C2311yescharacteristic
109C22×C4×C73C2311yescharacteristic
110C22×C4×C73C2311yescharacteristic
111C4⋊C4×C73—41no—
112C22⋊C4×C73—22no—
113C22⋊C4×C73—22no—
114C22⋊C4×C73—41no—
115C22⋊C4×C73—41no—
116C42×C73—22no—
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—21no—
130C23×C73#4112yes—
131C23×C73C2411yescharacteristic
132C22×D73—21no—
133C22×D73—21no—
134C22×D73—21no—
135C22×D73—21no—
136C22×D73—28no—
137C22×D73—21no—
138C22×D73—21no—
139C22×D73—21no—
140C22×D73—21no—
141C22×D73—21no—
142C22×D73—21no—
143C22×D73—44no—
144C22×D73—44no—
145C22×D73—44no—
146C22×D73—44no—
147C22×D73—44no—
148C22×D73—44no—
149C22×D73C2×D412yes—
150C22×D73C2×D412yes—
151C22×D73#4112yes—
152C22×D73#4112yes—
153D4×C73—44no—
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×C73—21no—
163C2×C4×C73—21no—
164C2×C4×C73—21no—
165C2×C4×C73—21no—
166C2×C4×C73—21no—
167C2×C4×C73C2×D412yes—
168C2×C4×C73C2×D412yes—
169C22⋊D73—44no—
170C22⋊D73—44no—
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×Dic73—21no—
183C2×Dic73—21no—
184C2×Dic73—21no—
185C2×Dic73—21no—
186C2×Dic73—21no—
187C2×Dic73C2×D412yes—
188C2×Dic73C2×D412yes—
189C4×D73—28no—
190C4×D73—44no—
191C22×C73—22no—
192C22×C73—22no—
193C22×C73—22no—
194C22×C73—41no—
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×C73C22×D411yescharacteristic
206C22×C73C22×D411yescharacteristic
207C22×C73C2×#4111yescharacteristic
208C22×C73C2×#4111yescharacteristic
209C22×C73C2×#4111yescharacteristic
210C22×C73H(5,𝔽2)11yescharacteristic
211C22×C73H(5,𝔽2)11yescharacteristic
212C2×D73—22no—
213C2×D73—22no—
214C2×D73—22no—
215C2×D73—22no—
216C2×D73—22no—
217C2×D73—22no—
218C2×D73—22no—
219C2×D73—22no—
220C2×D73—22no—
221C2×D73—416no—
222C2×D73—41no—
223C2×D73—41no—
224C2×D73—41no—
225C2×D73—41no—
226C2×D73#12114yes—
227C4×C73—22no—
228C4×C73—22no—
229C4×C73—41no—
230C4×C73—41no—
231C4×C73—41no—
232Dic73—22no—
233Dic73—22no—
234Dic73—41no—
235Dic73—41no—
236Dic73—41no—
237Dic73—41no—
238C2×C73—42no—
239C2×C73—81no—
240C2×C73C2×#12111yescharacteristic
241C2×C73#52511yescharacteristic
242C2×C73#53511yescharacteristic
243C2×C73#54611yescharacteristic
244C2×C73#54611yescharacteristic
245C2×C73#55111yescharacteristic
246C2×C73#55111yescharacteristic
247D73—24no—
248D73—42no—
249#2411—731nomaximal, Sylow
250C73#241111yescharacteristic, complemented, Sylow
251C2×#123—731no—
252C2×#120—731no—
253C2×#117—731no—
254C22×C22⋊C4—731no—
255#396—731no—
256#396—731no—
257#394—731no—
258#394—731no—
259#390—731no—
260#390D7311yescharacteristic, complemented
261#388—731no—
262#388—731no—
263#386—731no—
264#385—731no—
265#379—731no—
266C25—731no—
267C22×D4—731no—
268C22×D4—731no—
269C22×D4C2×D7311yescharacteristic
270C23×C4—731no—
271C23×C4—731no—
272#123—1464no—
273#120—1464no—
274#117—1464no—
275C2×C4⋊C4—731no—
276C2×C4⋊C4—731no—
277C2×C4⋊C4—731no—
278C2×C4⋊C4—731no—
279C2×C4⋊C4—731no—
280C2×C4⋊C4C2×D7311yescharacteristic, complemented
281C2×C22⋊C4—731no—
282C2×C22⋊C4—731no—
283C2×C22⋊C4—731no—
284C2×C22⋊C4—731no—
285C2×C22⋊C4—731no—
286C2×C22⋊C4—731no—
287C2×C22⋊C4—731no—
288C2×C22⋊C4—731no—
289C2×C22⋊C4—731no—
290C2×C22⋊C4—731no—
291C2×C22⋊C4—731no—
292C2×C22⋊C4—731no—
293C2×C22⋊C4—731no—
294C2×C22⋊C4—1464no—
295C2×C22⋊C4C2×D7311yescharacteristic
296C2×C22⋊C4C2×D7311yescharacteristic
297C2×C22⋊C4C2×D7311yescharacteristic, complemented
298C2×C22⋊C4C2×D7311yescharacteristic, complemented
299C2×C42—731no—
300C2×C42C2×D7311yescharacteristic, complemented
301#95—731no—
302#95—731no—
303#95—731no—
304#95—731no—
305C24—2921no—
306C24—2921no—
307C24—731no—
308C24—731no—
309C24—1462no—
310C24—1462no—
311C24—1462no—
312C24—1462no—
313C24—1462no—
314C24C22×D7311yescharacteristic
315C24C22×D7311yescharacteristic
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—41no—
319C2×D4—2921no—
320C2×D4—1462no—
321C2×D4—1462no—
322C2×D4—1462no—
323C2×D4—1462no—
324C2×D4—1462no—
325C22×C4—2921no—
326C22×C4—2921no—
327C22×C4—731no—
328C22×C4—731no—
329C22×C4—734no—
330C22×C4—731no—
331C22×C4—731no—
332C22×C4—731no—
333C22×C4—731no—
334C22×C4—1462no—
335C22×C4—1462no—
336C22×C4—1462no—
337C22×C4C22×D7311yescharacteristic
338C22×C4C22×D7311yescharacteristic
339C22×C4C22×D7311yescharacteristic
340C22×C4C22×D7311yescharacteristic
341C22×C4C22×D7311yescharacteristic
342C4⋊C4—41no—
343C4⋊C4—2921no—
344C4⋊C4—1462no—
345C4⋊C4—1462no—
346C4⋊C4—1462no—
347C4⋊C4—1462no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—2921no—
353C22⋊C4—2921no—
354C22⋊C4—734no—
355C22⋊C4—1462no—
356C22⋊C4—1462no—
357C22⋊C4—1462no—
358C22⋊C4—1462no—
359C22⋊C4—1462no—
360C22⋊C4—1462no—
361C22⋊C4—1462no—
362C22⋊C4—1462no—
363C22⋊C4—1462no—
364C22⋊C4—1462no—
365C42—22no—
366C42—1462no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—2924no—
381C23—2924no—
382C23—2924no—
383C23—2924no—
384C23—2924no—
385C23—2924no—
386C23—732no—
387C23—732no—
388C23—732no—
389C23—732no—
390C23—1468no—
391C23—1461no—
392C23—1461no—
393C23—1461no—
394C23—1461no—
395C23—1461no—
396C23—1461no—
397C23—1461no—
398C23—1461no—
399C23—1461no—
400C23—1461no—
401C23#1192402812yes—
402C23C23×D7311yescharacteristic
403D4—44no—
404D4—2924no—
405D4—2924no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—2924no—
420C2×C4—732no—
421C2×C4—732no—
422C2×C4—1468no—
423C2×C4—1461no—
424C2×C4—1461no—
425C2×C4—1461no—
426C2×C4—1461no—
427C2×C4—1461no—
428C2×C4—1461no—
429C2×C4—1461no—
430C2×C4—1461no—
431C2×C4—1461no—
432C2×C4—1461no—
433C2×C4—1461no—
434C2×C4—1461no—
435C2×C4—1461no—
436C2×C4—1461no—
437C2×C4—1461no—
438C2×C4—1461no—
439C2×C4D4×D7312yes—
440C2×C4D4×D7312yes—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—29216no—
456C22—2921no—
457C22—2921no—
458C22—2921no—
459C22—2921no—
460C22—734no—
461C22—1462no—
462C22—1462no—
463C22—1462no—
464C22—1462no—
465C22—1462no—
466C22—1462no—
467C22—1462no—
468C22—1462no—
469C22—1462no—
470C22C2×D4×D7311yescharacteristic
471C22C2×D4×D7311yescharacteristic
472C22#41×D7311yescharacteristic
473C22#41×D7311yescharacteristic
474C22C2×#1192402811yescharacteristic
475C22#1455663611yescharacteristic
476C22#1455663611yescharacteristic
477C4—22no—
478C4—22no—
479C4—41no—
480C4—41no—
481C4—41no—
482C4—2921no—
483C4—2921no—
484C4—2921no—
485C4—2921no—
486C4—1462no—
487C4—1462no—
488C2—42no—
489C2—81no—
490C2—2922no—
491C2—1464no—
492C2#121×D7311yescharacteristic
493C2#1798909611yescharacteristic
494C2#1798915011yescharacteristic
495C2#1798922711yescharacteristic
496C2#1798923411yescharacteristic
497C2#1798926611yescharacteristic
498C2#1798926711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#390×C73C2
hypercenter#390D73
hypocenterC73#2411
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14556573C2semidirect
3. C2×#14556548C2semidirect
4. C2×C22⋊C4×D73C2semidirect
5. #17988510C2semidirect
6. #17988509C2semidirect
7. #17988502C2semidirect
8. #17988501C2semidirect
9. #17988487C2semidirect
10. #17988481C2semidirect
11. #17988478C2semidirect
12. #17988463C2semidirect
13. #17988458C2semidirect
14. #17988442C2semidirect
15. #390×C73C2semidirect
24. C2×C4⋊Dic73C22semidirect
25. C2×#11924007C22semidirect
26. C2×#11924007C22semidirect
27. C2×#11924007C22semidirect
28. C2×#11924007C22semidirect
32. C2×C22⋊Dic73C22semidirect
33. C2×C22⋊Dic73C22semidirect
43. C2×C4×Dic73C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
46. #14556498C22semidirect
47. #14556498C22semidirect
49. C2×C4⋊C4×C73C22semidirect
52. C2×C22⋊C4×C73C22semidirect
53. C2×C22⋊C4×C73C22semidirect
54. C2×C42×C73C22semidirect
81. C2×C4×D73D4semidirect
250. C73#2411semidirect
260. #390D73semidirect
280. C2×C4⋊C4C2×D73semidirect
297. C2×C22⋊C4C2×D73semidirect
298. C2×C22⋊C4C2×D73semidirect
300. C2×C42C2×D73semidirect