Finite Group Databasebeta

← #22614822

Subgroups — #22614822

Order 9344.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556576C211yesmaximal, characteristic, complemented
2C2×#14556561C211yesmaximal, characteristic
3C2×#14556553C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D73C211yesmaximal, characteristic, complemented
5#17988509C211yesmaximal, characteristic, complemented
6#17988504C211yesmaximal, characteristic, complemented
7#17988503C211yesmaximal, characteristic, complemented
8#17988481C211yesmaximal, characteristic, complemented
9#17988477C211yesmaximal, characteristic, complemented
10#17988465C211yesmaximal, characteristic, complemented
11#17988463C211yesmaximal, characteristic, complemented
12#17988449C211yesmaximal, characteristic, complemented
13#17988444C211yesmaximal, characteristic, complemented
14#17988442C211yesmaximal, characteristic, complemented
15#396×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C22×D292C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic
20C22×C4×D73C2211yescharacteristic
21C22×C4×D73C2211yescharacteristic
22C22×C4×D73C2211yescharacteristic, complemented
23#14556576—24no—
24#14556561—24no—
25#14556553—24no—
26C2×C4⋊Dic73C2211yescharacteristic, complemented
27C2×#11924007C2211yescharacteristic, complemented
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic, complemented
39C2×#11924005C2211yescharacteristic, complemented
40C2×#11924005C2211yescharacteristic, complemented
41C22⋊C4×D73—24no—
42C2×C4×Dic73C2211yescharacteristic, complemented
43#14556498C2211yescharacteristic, complemented
44#14556498C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46#14556498C2211yescharacteristic, complemented
47#14556498C2211yescharacteristic, complemented
48C2×C4⋊C4×C73C2211yescharacteristic, complemented
49C2×C4⋊C4×C73C2211yescharacteristic, complemented
50C2×C4⋊C4×C73C2211yescharacteristic, complemented
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C22⋊C4×C73C2211yescharacteristic
53C2×C22⋊C4×C73C2211yescharacteristic
54#95×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
64C23×D73C2311yescharacteristic
65C2×D292—22no—
66C2×D292—22no—
67C2×D292—22no—
68C2×D292—22no—
69C2×D292—41no—
70C2×D292D414yes—
71C2×C22⋊D73—22no—
72C2×C22⋊D73—22no—
73C2×C22⋊D73—41no—
74C22×Dic73C2311yescharacteristic
75C22×Dic73C2311yescharacteristic
76C22×Dic73C2311yescharacteristic
77C22×Dic73C2311yescharacteristic
78C22×Dic73C2311yescharacteristic
79C2×C4×D73—22no—
80C2×C4×D73—22no—
81C2×C4×D73—22no—
82C2×C4×D73—22no—
83C2×C4×D73—41no—
84C2×C4×D73—41no—
85C2×C4×D73—41no—
86C2×C4×D73—41no—
87C2×C4×D73D414yescomplemented
88C4⋊Dic73—41no—
89#11924007—22no—
90C22⋊Dic73—22no—
91C22⋊Dic73—22no—
92#11924005—22no—
93#11924005—22no—
94#11924005—22no—
95#11924005—22no—
96#11924005—22no—
97#11924005—22no—
98#11924005—22no—
99#11924005—22no—
100#11924005—22no—
101#11924005—22no—
102#11924005—41no—
103C4×Dic73—22no—
104C24×C73C2311yescharacteristic
105C22×C4×C73C2311yescharacteristic
106C22×C4×C73C2311yescharacteristic
107C22×C4×C73C2311yescharacteristic
108C22×C4×C73C2311yescharacteristic
109C22×C4×C73C2311yescharacteristic
110C22×C4×C73C2311yescharacteristic
111C4⋊C4×C73—22no—
112C4⋊C4×C73—22no—
113C4⋊C4×C73—41no—
114C22⋊C4×C73—22no—
115C22⋊C4×C73—22no—
116C22⋊C4×C73—41no—
117C23×C73—21no—
118C23×C73—21no—
119C23×C73—21no—
120C23×C73—21no—
121C23×C73—21no—
122C23×C73—21no—
123C23×C73#4112yes—
124C23×C73C2411yescharacteristic
125C22×D73—21no—
126C22×D73—21no—
127C22×D73—21no—
128C22×D73—21no—
129C22×D73—28no—
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—21no—
139C22×D73—21no—
140C22×D73—21no—
141C22×D73—21no—
142C22×D73—44no—
143C22×D73—44no—
144C22×D73—44no—
145C22×D73—44no—
146C22×D73—44no—
147C22×D73—44no—
148C22×D73C2×D412yes—
149C22×D73C2×D412yes—
150C22×D73C2×D412yes—
151C22×D73#4112yes—
152C22×D73#4112yes—
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×C73—21no—
163C2×C4×C73—21no—
164C2×C4×C73—21no—
165C2×C4×C73—21no—
166C2×C4×C73—21no—
167C2×C4×C73—21no—
168C2×C4×C73—21no—
169C2×C4×C73C2×D412yes—
170C2×C4×C73C2×D412yes—
171C22⋊D73—44no—
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×Dic73C2×D412yes—
187D292—28no—
188D292—44no—
189C4×D73—44no—
190C4×D73—44no—
191C4×D73—44no—
192C22×C73—22no—
193C22×C73—22no—
194C22×C73—22no—
195C22×C73—41no—
196C22×C73—41no—
197C22×C73—41no—
198C22×C73—41no—
199C22×C73C22×D411yescharacteristic
200C22×C73C22×D411yescharacteristic
201C22×C73C2×#4111yescharacteristic
202C22×C73C2×#4111yescharacteristic
203C22×C73C2×#4111yescharacteristic
204C22×C73H(5,𝔽2)11yescharacteristic
205C22×C73H(5,𝔽2)11yescharacteristic
206C2×D73—22no—
207C2×D73—22no—
208C2×D73—22no—
209C2×D73—22no—
210C2×D73—22no—
211C2×D73—22no—
212C2×D73—22no—
213C2×D73—22no—
214C2×D73—22no—
215C2×D73—22no—
216C2×D73—22no—
217C2×D73—22no—
218C2×D73—416no—
219C2×D73—41no—
220C2×D73—41no—
221C2×D73—41no—
222C2×D73—41no—
223C2×D73—41no—
224C2×D73—41no—
225C2×D73—41no—
226C2×D73—41no—
227C2×D73#12114yes—
228C4×C73—22no—
229C4×C73—22no—
230C4×C73—41no—
231C4×C73—41no—
232C4×C73—41no—
233C4×C73—41no—
234Dic73—22no—
235Dic73—41no—
236Dic73—41no—
237Dic73—41no—
238Dic73—41no—
239C2×C73—42no—
240C2×C73C2×#12111yescharacteristic
241C2×C73#52511yescharacteristic
242C2×C73#53411yescharacteristic
243C2×C73#54611yescharacteristic
244C2×C73#54611yescharacteristic
245C2×C73#55111yescharacteristic
246C2×C73#55111yescharacteristic
247D73—24no—
248D73—42no—
249D73—42no—
250#2534—731nomaximal, Sylow
251C73#253411yescharacteristic, complemented, Sylow
252C2×#123—731no—
253C2×#120—731no—
254C2×C4×D4—731no—
255C22×C22⋊C4—731no—
256#396—731no—
257#396D7311yescharacteristic, complemented
258#394—731no—
259#394—731no—
260#388—731no—
261#388—731no—
262#386—731no—
263#386—731no—
264#381—731no—
265#380—731no—
266#379—731no—
267C25—731no—
268C22×D4—731no—
269C22×D4—731no—
270C22×D4—731no—
271C23×C4—731no—
272C23×C4—731no—
273C23×C4—731no—
274#123—1464no—
275#120—1464no—
276C4×D4—1464no—
277C2×C4⋊C4—731no—
278C2×C4⋊C4—731no—
279C2×C4⋊C4C2×D7311yescharacteristic, complemented
280C2×C4⋊C4C2×D7311yescharacteristic, complemented
281C2×C4⋊C4C2×D7311yescharacteristic, complemented
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—731no—
295C2×C22⋊C4—1464no—
296C2×C22⋊C4C2×D7311yescharacteristic
297C2×C22⋊C4C2×D7311yescharacteristic
298C2×C22⋊C4C2×D7311yescharacteristic
299C2×C42—731no—
300#95—731no—
301#95—731no—
302#95—731no—
303#95—731no—
304#95—731no—
305#95C2×D7311yescharacteristic, complemented
306C24—2921no—
307C24—2921no—
308C24—731no—
309C24—731no—
310C24—731no—
311C24—1462no—
312C24—1462no—
313C24—1462no—
314C24—1462no—
315C24—1462no—
316C24C22×D7311yescharacteristic
317C2×D4—2921no—
318C2×D4—2921no—
319C2×D4—734no—
320C2×D4—1462no—
321C2×D4—1462no—
322C2×D4—1462no—
323C2×D4—1462no—
324C2×D4—1462no—
325C2×D4—1462no—
326C22×C4—2921no—
327C22×C4—2921no—
328C22×C4—2921no—
329C22×C4—2921no—
330C22×C4—734no—
331C22×C4—731no—
332C22×C4—731no—
333C22×C4—731no—
334C22×C4—731no—
335C22×C4—731no—
336C22×C4—1462no—
337C22×C4—1462no—
338C22×C4—1462no—
339C22×C4—1462no—
340C22×C4C22×D7311yescharacteristic
341C22×C4C22×D7311yescharacteristic
342C22×C4C22×D7311yescharacteristic
343C22×C4C22×D7311yescharacteristic
344C22×C4C22×D7311yescharacteristic
345C22×C4C22×D7311yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—41no—
349C4⋊C4—2921no—
350C4⋊C4—1462no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—41no—
354C22⋊C4—2921no—
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—
365C22⋊C4—1462no—
366C22⋊C4—1462no—
367C42—1462no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—2924no—
375C23—2924no—
376C23—2924no—
377C23—2924no—
378C23—2924no—
379C23—2924no—
380C23—732no—
381C23—732no—
382C23—732no—
383C23—732no—
384C23—732no—
385C23—1468no—
386C23—1461no—
387C23—1461no—
388C23—1461no—
389C23—1461no—
390C23—1461no—
391C23—1461no—
392C23—1461no—
393C23—1461no—
394C23—1461no—
395C23—1461no—
396C23—1461no—
397C23—1461no—
398C23—1461no—
399C23—1461no—
400C23—1461no—
401C23—1461no—
402C23#1192402912yes—
403C23C23×D7311yescharacteristic
404D4—2924no—
405D4—2924no—
406D4—1468no—
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—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—2924no—
424C2×C4—2924no—
425C2×C4—2924no—
426C2×C4—732no—
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×C4—1461no—
440C2×C4—1461no—
441C2×C4D4×D7312yes—
442C2×C4D4×D7312yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—29216no—
451C22—2921no—
452C22—2921no—
453C22—2921no—
454C22—2921no—
455C22—2921no—
456C22—2921no—
457C22—2921no—
458C22—2921no—
459C22—734no—
460C22—1462no—
461C22—1462no—
462C22—1462no—
463C22—1462no—
464C22—1462no—
465C22—1462no—
466C22—1462no—
467C22—1462no—
468C22—1462no—
469C22—1462no—
470C22—1462no—
471C22—1462no—
472C22C2×D4×D7311yescharacteristic
473C22C2×D4×D7311yescharacteristic
474C22#41×D7311yescharacteristic
475C22#41×D7311yescharacteristic
476C22C2×#1192402911yescharacteristic
477C22#1455663611yescharacteristic
478C22#1455663711yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—2921no—
486C4—2921no—
487C4—2921no—
488C4—2921no—
489C4—1462no—
490C2—42no—
491C2—2922no—
492C2—2922no—
493C2—1464no—
494C2#121×D7311yescharacteristic
495C2#1798910011yescharacteristic
496C2#1798914511yescharacteristic
497C2#1798922811yescharacteristic
498C2#1798923411yescharacteristic
499C2#1798926211yescharacteristic
500C2#1798926411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#396×C73C2
hypercenter#396D73
hypocenterC73#2534
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#14556576C2semidirect
3. C2×#14556553C2semidirect
4. C2×C22⋊C4×D73C2semidirect
5. #17988509C2semidirect
6. #17988504C2semidirect
7. #17988503C2semidirect
8. #17988481C2semidirect
9. #17988477C2semidirect
10. #17988465C2semidirect
11. #17988463C2semidirect
12. #17988449C2semidirect
13. #17988444C2semidirect
14. #17988442C2semidirect
15. #396×C73C2semidirect
22. C22×C4×D73C22semidirect
26. C2×C4⋊Dic73C22semidirect
27. C2×#11924007C22semidirect
38. C2×#11924005C22semidirect
39. C2×#11924005C22semidirect
40. C2×#11924005C22semidirect
42. C2×C4×Dic73C22semidirect
43. #14556498C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
46. #14556498C22semidirect
47. #14556498C22semidirect
48. C2×C4⋊C4×C73C22semidirect
49. C2×C4⋊C4×C73C22semidirect
50. C2×C4⋊C4×C73C22semidirect
54. #95×C73C22semidirect
87. C2×C4×D73D4semidirect
251. C73#2534semidirect
257. #396D73semidirect
279. C2×C4⋊C4C2×D73semidirect
280. C2×C4⋊C4C2×D73semidirect
281. C2×C4⋊C4C2×D73semidirect
305. #95C2×D73semidirect