Finite Group Databasebeta

← #22615087

Subgroups — #22615087

Order 9344.

672 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556569C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D73C211yesmaximal, characteristic
3#17988516C211yesmaximal, characteristic, complemented
4#17988515C211yesmaximal, characteristic, complemented
5#17988500C211yesmaximal, characteristic, complemented
6#17988499C211yesmaximal, characteristic, complemented
7#17988481C211yesmaximal, characteristic, complemented
8#17988478C211yesmaximal, characteristic, complemented
9#17988477C211yesmaximal, characteristic, complemented
10#17988449C211yesmaximal, characteristic, complemented
11#17988449C211yesmaximal, characteristic, complemented
12#17988442C211yesmaximal, characteristic
13#17988442C211yesmaximal, characteristic
14C4×#11924005C211yesmaximal, characteristic, complemented
15#388×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×Dic146C2211yescharacteristic, complemented
18C22×C4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20#14556569—24no—
21C2×#11924007C2211yescharacteristic, complemented
22C2×#11924007C2211yescharacteristic, complemented
23C2×C22⋊Dic73C2211yescharacteristic
24C2×C22⋊Dic73C2211yescharacteristic
25C2×C22⋊Dic73C2211yescharacteristic
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C22⋊C4×D73—24no—
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
46C2×C4⋊C4×C73C2211yescharacteristic, complemented
47C2×C22⋊C4×C73C2211yescharacteristic
48C2×C22⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C42×C73C2211yescharacteristic, complemented
51#95×C73C2211yescharacteristic, complemented
52#95×C73C2211yescharacteristic, complemented
53C23×D73—22no—
54C23×D73—22no—
55C23×D73—22no—
56C23×D73—22no—
57C23×D73—22no—
58C23×D73—41no—
59C23×D73—41no—
60C23×D73C2311yescharacteristic
61C23×D73C2311yescharacteristic
62C2×Dic146—22no—
63C2×Dic146—41no—
64C2×Dic146—41no—
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C22×Dic73C2311yescharacteristic
71C2×C4×D73—22no—
72C2×C4×D73—22no—
73C2×C4×D73—22no—
74C2×C4×D73—41no—
75C2×C4×D73—41no—
76C2×C4×D73D414yes—
77#11924007—22no—
78#11924007—22no—
79C22⋊Dic73—22no—
80C22⋊Dic73—22no—
81C22⋊Dic73—41no—
82#11924005—22no—
83#11924005—22no—
84#11924005—22no—
85#11924005—22no—
86#11924005—22no—
87#11924005—22no—
88#11924005—22no—
89#11924005—22no—
90#11924005—41no—
91#11924005—41no—
92C4×Dic73—41no—
93C24×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96C22×C4×C73C2311yescharacteristic
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C4⋊C4×C73—22no—
101C22⋊C4×C73—22no—
102C22⋊C4×C73—22no—
103C22⋊C4×C73—41no—
104C42×C73—41no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73#4112yes—
112C23×C73C2411yescharacteristic
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—28no—
118C22×D73—21no—
119C22×D73—21no—
120C22×D73—21no—
121C22×D73—21no—
122C22×D73—21no—
123C22×D73—21no—
124C22×D73—44no—
125C22×D73—44no—
126C22×D73—44no—
127C22×D73—44no—
128C22×D73—44no—
129C22×D73—44no—
130C22×D73C2×D412yes—
131C22×D73#4112yes—
132C22×D73#4112yes—
133C22×D73#4112yes—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
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×C73C2×D412yes—
152C2×Dic73—21no—
153C2×Dic73—21no—
154C2×Dic73—21no—
155C2×Dic73—21no—
156C2×Dic73—21no—
157C2×Dic73—21no—
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×Dic73C2×D412yes—
170C4×D73—44no—
171C4×D73—44no—
172Dic146—44no—
173C22×C73—22no—
174C22×C73—22no—
175C22×C73—22no—
176C22×C73—41no—
177C22×C73—41no—
178C22×C73—41no—
179C22×C73—41no—
180C22×C73C22×D411yescharacteristic
181C22×C73C2×#4111yescharacteristic
182C22×C73C2×#4111yescharacteristic
183C22×C73C2×#4111yescharacteristic
184C22×C73C2×#4111yescharacteristic
185C22×C73H(5,𝔽2)11yescharacteristic
186C22×C73H(5,𝔽2)11yescharacteristic
187C2×D73—22no—
188C2×D73—22no—
189C2×D73—22no—
190C2×D73—22no—
191C2×D73—22no—
192C2×D73—22no—
193C2×D73—22no—
194C2×D73—22no—
195C2×D73—22no—
196C2×D73—416no—
197C2×D73—41no—
198C2×D73—41no—
199C2×D73—41no—
200C2×D73—41no—
201C2×D73#12414yes—
202C4×C73—22no—
203C4×C73—41no—
204C4×C73—41no—
205C4×C73—41no—
206C4×C73—41no—
207C4×C73—41no—
208Dic73—22no—
209Dic73—41no—
210Dic73—41no—
211Dic73—41no—
212Dic73—41no—
213Dic73—41no—
214C2×C73—42no—
215C2×C73#52511yescharacteristic
216C2×C73C2×#12411yescharacteristic
217C2×C73#53411yescharacteristic
218C2×C73#55111yescharacteristic
219C2×C73#55111yescharacteristic
220C2×C73#55111yescharacteristic
221C2×C73#55111yescharacteristic
222D73—24no—
223D73—42no—
224#2561—731nomaximal, Sylow
225C73#256111yescharacteristic, complemented, Sylow
226C2×C22⋊Q8—731no—
227C22×C22⋊C4—731no—
228#397—731no—
229#397—731no—
230#393—731no—
231#393—731no—
232#388—731no—
233#388—731no—
234#388—731no—
235#388D7311yescharacteristic, complemented
236#381—731no—
237#381—731no—
238#379—731no—
239#379—731no—
240C4×C22⋊C4—731no—
241C25—731no—
242C22×Q8—731no—
243C23×C4—731no—
244C23×C4—731no—
245C22⋊Q8—1464no—
246C2×C4⋊C4—731no—
247C2×C4⋊C4—731no—
248C2×C4⋊C4C2×D7311yescharacteristic, complemented
249C2×C22⋊C4—731no—
250C2×C22⋊C4—731no—
251C2×C22⋊C4—731no—
252C2×C22⋊C4—731no—
253C2×C22⋊C4—731no—
254C2×C22⋊C4—731no—
255C2×C22⋊C4—731no—
256C2×C22⋊C4—731no—
257C2×C22⋊C4—731no—
258C2×C22⋊C4—731no—
259C2×C22⋊C4—731no—
260C2×C22⋊C4—731no—
261C2×C22⋊C4—731no—
262C2×C22⋊C4—1464no—
263C2×C22⋊C4C2×D7311yescharacteristic
264C2×C22⋊C4C2×D7311yescharacteristic
265C2×C22⋊C4C2×D7311yescharacteristic
266C2×C42—731no—
267C2×C42C2×D7311yescharacteristic, complemented
268#95—731no—
269#95—731no—
270#95—731no—
271#95—731no—
272#95—731no—
273#95—731no—
274#95—731no—
275#95—731no—
276#95C2×D7311yescharacteristic, complemented
277#95C2×D7311yescharacteristic, complemented
278C24—2921no—
279C24—2921no—
280C24—731no—
281C24—731no—
282C24—1462no—
283C24—1462no—
284C24—1462no—
285C24—1462no—
286C24—1462no—
287C24C22×D7311yescharacteristic
288C2×Q8—2921no—
289C2×Q8—2921no—
290C2×Q8—1462no—
291C22×C4—2921no—
292C22×C4—2921no—
293C22×C4—734no—
294C22×C4—731no—
295C22×C4—731no—
296C22×C4—731no—
297C22×C4—731no—
298C22×C4—731no—
299C22×C4—731no—
300C22×C4—1462no—
301C22×C4—1462no—
302C22×C4—1462no—
303C22×C4C22×D7311yescharacteristic
304C22×C4C22×D7311yescharacteristic
305C22×C4C22×D7311yescharacteristic
306C22×C4C22×D7311yescharacteristic
307C22×C4C22×D7311yescharacteristic
308C22×C4C22×D7311yescharacteristic
309C4⋊C4—22no—
310C4⋊C4—1462no—
311C4⋊C4—1462no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—41no—
315C22⋊C4—2921no—
316C22⋊C4—2921no—
317C22⋊C4—2921no—
318C22⋊C4—1462no—
319C22⋊C4—1462no—
320C22⋊C4—1462no—
321C22⋊C4—1462no—
322C22⋊C4—1462no—
323C22⋊C4—1462no—
324C22⋊C4—1462no—
325C22⋊C4—1462no—
326C22⋊C4—1462no—
327C22⋊C4—1462no—
328C42—41no—
329C42—2921no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—2924no—
337C23—2924no—
338C23—2924no—
339C23—2924no—
340C23—2924no—
341C23—2924no—
342C23—732no—
343C23—732no—
344C23—732no—
345C23—732no—
346C23—1468no—
347C23—1461no—
348C23—1461no—
349C23—1461no—
350C23—1461no—
351C23—1461no—
352C23—1461no—
353C23—1461no—
354C23—1461no—
355C23—1461no—
356C23—1461no—
357C23#1192402812yes—
358C23C23×D7311yescharacteristic
359Q8—2924no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—2924no—
378C2×C4—2924no—
379C2×C4—732no—
380C2×C4—1461no—
381C2×C4—1461no—
382C2×C4—1461no—
383C2×C4—1461no—
384C2×C4—1461no—
385C2×C4—1461no—
386C2×C4—1461no—
387C2×C4—1461no—
388C2×C4—1461no—
389C2×C4—1461no—
390C2×C4—1461no—
391C2×C4—1461no—
392C2×C4—1461no—
393C2×C4—1461no—
394C2×C4—1461no—
395C2×C4—1461no—
396C2×C4—1461no—
397C2×C4D4×D7312yes—
398C22—22no—
399C22—22no—
400C22—22no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—29216no—
406C22—2921no—
407C22—2921no—
408C22—2921no—
409C22—2921no—
410C22—734no—
411C22—1462no—
412C22—1462no—
413C22—1462no—
414C22—1462no—
415C22—1462no—
416C22—1462no—
417C22—1462no—
418C22—1462no—
419C22—1462no—
420C22C2×D4×D7311yescharacteristic
421C22#41×D7311yescharacteristic
422C22#41×D7311yescharacteristic
423C22#41×D7311yescharacteristic
424C22C2×#1192402811yescharacteristic
425C22#1455663611yescharacteristic
426C22#1455663711yescharacteristic
427C4—22no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—2921no—
434C4—2921no—
435C4—2921no—
436C4—2921no—
437C4—2921no—
438C4—1462no—
439C2—42no—
440C2—2922no—
441C2—1464no—
442C2#1798909611yescharacteristic
443C2#124×D7311yescharacteristic
444C2#1798914511yescharacteristic
445C2#1798926111yescharacteristic
446C2#1798926211yescharacteristic
447C2#1798926511yescharacteristic
448C2#1798926611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#388×C73C2
hypercenter#388D73
hypocenterC73#2561
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14556569C2semidirect
3. #17988516C2semidirect
4. #17988515C2semidirect
5. #17988500C2semidirect
6. #17988499C2semidirect
7. #17988481C2semidirect
8. #17988478C2semidirect
9. #17988477C2semidirect
10. #17988449C2semidirect
11. #17988449C2semidirect
14. C4×#11924005C2semidirect
15. #388×C73C2semidirect
17. C22×Dic146C22semidirect
21. C2×#11924007C22semidirect
22. C2×#11924007C22semidirect
37. C2×C4×Dic73C22semidirect
38. #14556498C22semidirect
39. #14556498C22semidirect
40. #14556498C22semidirect
41. #14556498C22semidirect
42. #14556498C22semidirect
43. #14556498C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
46. C2×C4⋊C4×C73C22semidirect
50. C2×C42×C73C22semidirect
51. #95×C73C22semidirect
52. #95×C73C22semidirect
225. C73#2561semidirect
235. #388D73semidirect
248. C2×C4⋊C4C2×D73semidirect
267. C2×C42C2×D73semidirect
276. #95C2×D73semidirect
277. #95C2×D73semidirect