Finite Group Databasebeta

← #22616366

Subgroups — #22616366

Order 9344.

626 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556563C211yesmaximal, characteristic, complemented
2C2×#14556562C211yesmaximal, characteristic, complemented
3#17988529C211yesmaximal, characteristic, complemented
4#17988515C211yesmaximal, characteristic, complemented
5#17988512C211yesmaximal, characteristic, complemented
6#17988503C211yesmaximal, characteristic, complemented
7#17988495C211yesmaximal, characteristic, complemented
8#17988467C211yesmaximal, characteristic, complemented
9#17988467C211yesmaximal, characteristic, complemented
10#17988467C211yesmaximal, characteristic, complemented
11#17988464C211yesmaximal, characteristic, complemented
12#17988463C211yesmaximal, characteristic, complemented
13#17988462C211yesmaximal, characteristic, complemented
14#17988449C211yesmaximal, characteristic, complemented
15#392×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C23×Dic73C2211yescharacteristic
20C23×Dic73C2211yescharacteristic
21C22×C4×D73C2211yescharacteristic
22#14556563—24no—
23#14556562—24no—
24C2×C4⋊Dic73C2211yescharacteristic
25C2×C4⋊Dic73C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33C2×C22⋊Dic73C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C22×D4×C73C2211yescharacteristic
47C22×D4×C73C2211yescharacteristic
48C22×D4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C2×C22⋊D73—22no—
55C2×C22⋊D73—22no—
56C2×C22⋊D73—22no—
57C2×C22⋊D73—41no—
58C2×C22⋊D73—41no—
59C2×C22⋊D73—41no—
60C2×C22⋊D73—41no—
61C2×C22⋊D73—41no—
62C2×C22⋊D73D414yescomplemented
63C22×Dic73—22no—
64C22×Dic73—41no—
65C22×Dic73—41no—
66C22×Dic73—41no—
67C22×Dic73—41no—
68C22×Dic73—41no—
69C22×Dic73C2311yescharacteristic
70C22×Dic73C2311yescharacteristic
71C22×Dic73C2311yescharacteristic
72C22×Dic73C2311yescharacteristic
73C22×Dic73C2311yescharacteristic
74C22×Dic73C2311yescharacteristic
75C22×Dic73C2311yescharacteristic
76C2×C4×D73—22no—
77C2×C4×D73—22no—
78C2×C4×D73—41no—
79C4⋊Dic73—22no—
80C4⋊Dic73—41no—
81#11924007—22no—
82C22⋊Dic73—22no—
83C22⋊Dic73—22no—
84C22⋊Dic73—22no—
85C22⋊Dic73—41no—
86C22⋊Dic73—41no—
87C22⋊Dic73—41no—
88C22⋊Dic73—41no—
89#11924005—22no—
90#11924005—41no—
91#11924005—41no—
92C24×C73C2311yescharacteristic
93C24×C73C2311yescharacteristic
94C24×C73C2311yescharacteristic
95C2×D4×C73—22no—
96C2×D4×C73—22no—
97C2×D4×C73—22no—
98C2×D4×C73—22no—
99C2×D4×C73—22no—
100C2×D4×C73—41no—
101C2×D4×C73—41no—
102C2×D4×C73—41no—
103C2×D4×C73—41no—
104C22×C4×C73C2311yescharacteristic
105C22×C4×C73C2311yescharacteristic
106C22×C4×C73C2311yescharacteristic
107C22×C4×C73C2311yescharacteristic
108C22⋊C4×C73—22no—
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—21no—
130C23×C73C2×D412yes—
131C23×C73#4112yes—
132C23×C73C2411yescharacteristic
133C22×D73—21no—
134C22×D73—21no—
135C22×D73—21no—
136C22×D73—21no—
137C22×D73—21no—
138C22×D73—21no—
139C22×D73C2×D412yes—
140D4×C73—44no—
141D4×C73—44no—
142D4×C73—44no—
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×C73—21no—
151C2×C4×C73—21no—
152C2×C4×C73—21no—
153C2×C4×C73—21no—
154C2×C4×C73#4112yes—
155C22⋊D73—44no—
156C22⋊D73—44no—
157C22⋊D73—44no—
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—
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—44no—
179C2×Dic73—44no—
180C2×Dic73C2×D412yes—
181C4×D73—44no—
182C22×C73—22no—
183C22×C73—22no—
184C22×C73—22no—
185C22×C73—22no—
186C22×C73—22no—
187C22×C73—22no—
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×C73—41no—
198C22×C73—41no—
199C22×C73—41no—
200C22×C73—41no—
201C22×C73—41no—
202C22×C73—41no—
203C22×C73C22×D411yescharacteristic
204C22×C73C2×#4111yescharacteristic
205C22×C73C2×#4111yescharacteristic
206C22×C73H(5,𝔽2)11yescharacteristic
207C22×C73H(5,𝔽2)11yescharacteristic
208C22×C73H(5,𝔽2)11yescharacteristic
209C22×C73H(5,𝔽2)11yescharacteristic
210C2×D73—22no—
211C2×D73—22no—
212C2×D73—22no—
213C2×D73—41no—
214C2×D73—41no—
215C2×D73—41no—
216C2×D73—41no—
217C4×C73—22no—
218C4×C73—41no—
219C4×C73—41no—
220C4×C73—41no—
221Dic73—22no—
222Dic73—41no—
223Dic73—41no—
224Dic73—41no—
225Dic73—41no—
226Dic73—41no—
227Dic73—41no—
228C2×C73—42no—
229C2×C73—42no—
230C2×C73—81no—
231C2×C73#53411yescharacteristic
232C2×C73#53811yescharacteristic
233C2×C73#54011yescharacteristic
234C2×C73#54611yescharacteristic
235C2×C73#54611yescharacteristic
236C2×C73#55311yescharacteristic
237C2×C73#56011yescharacteristic
238D73—42no—
239#2688—731nomaximal, Sylow
240C73#268811yescharacteristic, complemented, Sylow
241C2×#121—731no—
242C2×#121—731no—
243#400—731no—
244#397—731no—
245#397—731no—
246#394—731no—
247#392—731no—
248#392D7311yescharacteristic, complemented
249#386—731no—
250#386—731no—
251#386—731no—
252#386—731no—
253#386—731no—
254#385—731no—
255#381—731no—
256C22×D4—731no—
257C22×D4—731no—
258C22×D4—731no—
259C22×D4C2×D7311yescharacteristic
260C22×D4C2×D7311yescharacteristic
261C22×D4C2×D7311yescharacteristic
262C23×C4—731no—
263C23×C4—731no—
264C23×C4—731no—
265#121—1464no—
266#121—1464no—
267C2×C4⋊C4—731no—
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⋊C4C2×D7311yescharacteristic
281C2×C22⋊C4C2×D7311yescharacteristic
282C2×C22⋊C4C2×D7311yescharacteristic
283#95—731no—
284#95—731no—
285#95—731no—
286#95—731no—
287#95—731no—
288#95—731no—
289#95—731no—
290#95—731no—
291#95—731no—
292#95C2×D7311yescharacteristic
293C24—731no—
294C24C22×D7311yescharacteristic
295C24C22×D7311yescharacteristic
296C24C22×D7311yescharacteristic
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—2921no—
307C2×D4—2921no—
308C2×D4—2921no—
309C2×D4—2921no—
310C2×D4—2921no—
311C2×D4—734no—
312C2×D4—1462no—
313C2×D4—1462no—
314C2×D4—1462no—
315C22×C4—2921no—
316C22×C4—2921no—
317C22×C4—2921no—
318C22×C4—2921no—
319C22×C4—2921no—
320C22×C4—2921no—
321C22×C4—731no—
322C22×C4—731no—
323C22×C4—731no—
324C22×C4—731no—
325C22×C4—731no—
326C22×C4—731no—
327C22×C4—731no—
328C22×C4—1462no—
329C22×C4—1462no—
330C22×C4—1462no—
331C22×C4C22×D7311yescharacteristic
332C22×C4C22×D7311yescharacteristic
333C22×C4C22×D7311yescharacteristic
334C22×C4C22×D7311yescharacteristic
335C4⋊C4—2921no—
336C4⋊C4—1462no—
337C4⋊C4—1462no—
338C22⋊C4—22no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—2921no—
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—
351C23—21no—
352C23—21no—
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—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—732no—
371C23—1461no—
372C23—1461no—
373C23—1461no—
374C23—1461no—
375C23—1461no—
376C23—1461no—
377C23D4×D7312yes—
378C23#1192402712yes—
379C23C23×D7311yescharacteristic
380D4—44no—
381D4—44no—
382D4—44no—
383D4—2924no—
384D4—2924no—
385D4—2924no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—2924no—
398C2×C4—2924no—
399C2×C4—2924no—
400C2×C4—732no—
401C2×C4—1461no—
402C2×C4—1461no—
403C2×C4—1461no—
404C2×C4—1461no—
405C2×C4—1461no—
406C2×C4—1461no—
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#1192402712yes—
422C22—22no—
423C22—22no—
424C22—22no—
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—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—2921no—
444C22—2921no—
445C22—2921no—
446C22—2921no—
447C22—1462no—
448C22—1462no—
449C22—1462no—
450C22C2×D4×D7311yescharacteristic
451C22C2×#1192402711yescharacteristic
452C22C2×#1192402711yescharacteristic
453C22#1455663611yescharacteristic
454C22#1455663611yescharacteristic
455C22#1455663611yescharacteristic
456C22#1455663711yescharacteristic
457C4—22no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—2921no—
462C4—2921no—
463C4—2921no—
464C4—2921no—
465C4—2921no—
466C4—2921no—
467C4—1462no—
468C2—42no—
469C2—42no—
470C2—81no—
471C2—2922no—
472C2#1798914511yescharacteristic
473C2#1798917211yescharacteristic
474C2#1798919111yescharacteristic
475C2#1798922411yescharacteristic
476C2#1798922411yescharacteristic
477C2#1798928911yescharacteristic
478C2#1798932511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#392×C73C2
hypercenter#392D73
hypocenterC73#2688
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14556563C2semidirect
2. C2×#14556562C2semidirect
3. #17988529C2semidirect
4. #17988515C2semidirect
5. #17988512C2semidirect
6. #17988503C2semidirect
7. #17988495C2semidirect
8. #17988467C2semidirect
9. #17988467C2semidirect
10. #17988467C2semidirect
11. #17988464C2semidirect
12. #17988463C2semidirect
13. #17988462C2semidirect
14. #17988449C2semidirect
15. #392×C73C2semidirect
62. C2×C22⋊D73D4semidirect
240. C73#2688semidirect
248. #392D73semidirect