Finite Group Databasebeta

← #22614053

Subgroups — #22614053

Order 9344.

786 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×#14556567C211yesmaximal, characteristic, complemented
2C2×#14556559C211yesmaximal, characteristic
3C2×C22⋊C4×D73C211yesmaximal, characteristic, complemented
4#17988515C211yesmaximal, characteristic, complemented
5#17988503C211yesmaximal, characteristic, complemented
6#17988501C211yesmaximal, characteristic, complemented
7#17988498C211yesmaximal, characteristic, complemented
8#17988487C211yesmaximal, characteristic, complemented
9#17988480C211yesmaximal, characteristic, complemented
10#17988478C211yesmaximal, characteristic, complemented
11#17988463C211yesmaximal, characteristic, complemented
12#17988463C211yesmaximal, characteristic, complemented
13#17988442C211yesmaximal, characteristic, complemented
14C4×#11924005C211yesmaximal, characteristic, complemented
15C2×#124×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20C22×C4×D73C2211yescharacteristic
21#14556567—24no—
22#14556559—24no—
23C2×C4⋊Dic73C2211yescharacteristic, complemented
24C2×#11924007C2211yescharacteristic, complemented
25C2×#11924007C2211yescharacteristic, complemented
26C2×C22⋊Dic73C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic, complemented
30C2×C22⋊Dic73C2211yescharacteristic, complemented
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic
39C22⋊C4×D73—24no—
40C2×C4×Dic73C2211yescharacteristic, complemented
41#14556498C2211yescharacteristic, complemented
42#14556498C2211yescharacteristic, complemented
43#14556498C2211yescharacteristic, complemented
44#14556498C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46#14556498C2211yescharacteristic, complemented
47C22×Q8×C73C2211yescharacteristic, complemented
48C22×D4×C73C2211yescharacteristic
49#124×C73—24no—
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—22no—
80C2×C4×D73—41no—
81C2×C4×D73—41no—
82C4⋊Dic73—22no—
83#11924007—22no—
84#11924007—22no—
85C22⋊Dic73—22no—
86C22⋊Dic73—22no—
87C22⋊Dic73—41no—
88C22⋊Dic73—41no—
89C22⋊Dic73—41no—
90#11924005—22no—
91#11924005—22no—
92#11924005—22no—
93#11924005—22no—
94#11924005—22no—
95#11924005—22no—
96#11924005—41no—
97#11924005D414yes—
98C4×Dic73—41no—
99C24×C73C2311yescharacteristic
100C24×C73C2311yescharacteristic
101C2×Q8×C73—22no—
102C2×Q8×C73—22no—
103C2×Q8×C73—41no—
104C2×D4×C73—22no—
105C2×D4×C73—22no—
106C2×D4×C73—41no—
107C22×C4×C73C2311yescharacteristic
108C22×C4×C73C2311yescharacteristic
109C22×C4×C73C2311yescharacteristic
110C22×C4×C73C2311yescharacteristic
111C22×C4×C73C2311yescharacteristic
112C22⋊C4×C73—22no—
113C22⋊C4×C73—22no—
114C22⋊C4×C73—22no—
115C22⋊C4×C73D414yescomplemented
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×C73C2×D412yes—
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×D73#4112yes—
151C22×D73#4112yes—
152C22×D73#4112yes—
153Q8×C73—44no—
154D4×C73—44no—
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—
169C2×C4×C73C2×D412yes—
170C22⋊D73—44no—
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×Dic73—21no—
187C2×Dic73—21no—
188C2×Dic73—21no—
189C2×Dic73C2×D412yes—
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×C73—41no—
200C22×C73—41no—
201C22×C73—41no—
202C22×C73—41no—
203C22×C73—41no—
204C22×C73—41no—
205C22×C73—41no—
206C22×C73C22×D411yescharacteristic
207C22×C73C22×D411yescharacteristic
208C22×C73C2×#4111yescharacteristic
209C22×C73C2×#4111yescharacteristic
210C22×C73C2×#4111yescharacteristic
211C22×C73H(5,𝔽2)11yescharacteristic
212C22×C73H(5,𝔽2)11yescharacteristic
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—22no—
222C2×D73—416no—
223C2×D73—41no—
224C2×D73—41no—
225C2×D73—41no—
226C2×D73—41no—
227C2×D73#12414yescomplemented
228C4×C73—22no—
229C4×C73—22no—
230C4×C73—22no—
231C4×C73—41no—
232C4×C73—41no—
233Dic73—22no—
234Dic73—41no—
235Dic73—41no—
236Dic73—41no—
237Dic73—41no—
238Dic73—41no—
239C2×C73—42no—
240C2×C73—81no—
241C2×C73#52511yescharacteristic
242C2×C73C2×#12411yescharacteristic
243C2×C73#53811yescharacteristic
244C2×C73D4211yescharacteristic
245C2×C73#54611yescharacteristic
246C2×C73#54611yescharacteristic
247C2×C73#55111yescharacteristic
248D73—24no—
249D73—42no—
250#2472—731nomaximal, Sylow
251C73#247211yescharacteristic, complemented, Sylow
252C2×#124D7311yescharacteristic, complemented
253C2×C22⋊Q8—731no—
254C2×#120—731no—
255C22×C22⋊C4—731no—
256#397—731no—
257#394—731no—
258#394—731no—
259#393—731no—
260#390—731no—
261#388—731no—
262#388—731no—
263#386—731no—
264#386—731no—
265#379—731no—
266C4×C22⋊C4—731no—
267C25—731no—
268C22×Q8C2×D7311yescharacteristic, complemented
269C22×D4—731no—
270C22×D4—731no—
271C22×D4C2×D7311yescharacteristic
272C23×C4—731no—
273C23×C4—731no—
274#124—24no—
275C22⋊Q8—1464no—
276#120—1464no—
277C2×C4⋊C4—731no—
278C2×C4⋊C4—731no—
279C2×C4⋊C4—731no—
280C2×C22⋊C4—731no—
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—1464no—
294C2×C22⋊C4C2×D7311yescharacteristic
295C2×C22⋊C4C2×D7311yescharacteristic
296C2×C22⋊C4C2×D7311yescharacteristic, complemented
297C2×C22⋊C4C2×D7311yescharacteristic, complemented
298C2×C42—731no—
299C2×C42C2×D7311yescharacteristic, complemented
300#95—731no—
301#95—731no—
302#95—731no—
303#95—731no—
304#95—731no—
305#95—731no—
306C24—2921no—
307C24—2921no—
308C24—731no—
309C24—731no—
310C24—1462no—
311C24—1462no—
312C24—1462no—
313C24—1462no—
314C24—1462no—
315C24C22×D7311yescharacteristic
316C24C22×D7311yescharacteristic
317C2×Q8—22no—
318C2×Q8—22no—
319C2×Q8—41no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—41no—
323C2×D4—2921no—
324C2×D4—1462no—
325C2×D4—1462no—
326C2×D4—1462no—
327C2×D4—1462no—
328C2×D4—1462no—
329C22×C4—2921no—
330C22×C4—2921no—
331C22×C4—731no—
332C22×C4—731no—
333C22×C4—731no—
334C22×C4—731no—
335C22×C4—731no—
336C22×C4—731no—
337C22×C4—1462no—
338C22×C4—1462no—
339C22×C4—1462no—
340C22×C4—1462no—
341C22×C4C22×D7311yescharacteristic
342C22×C4C22×D7311yescharacteristic
343C22×C4C22×D7311yescharacteristic
344C22×C4C22×D7311yescharacteristic
345C22×C4C22×D7311yescharacteristic
346C4⋊C4—1462no—
347C4⋊C4—1462no—
348C4⋊C4—1462no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—2921no—
353C22⋊C4—2921no—
354C22⋊C4—2921no—
355C22⋊C4—2921no—
356C22⋊C4—734no—
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⋊C4C22⋊D7314yescomplemented
366C42—22no—
367C42—2921no—
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—21no—
381C23—2924no—
382C23—2924no—
383C23—2924no—
384C23—2924no—
385C23—2924no—
386C23—2924no—
387C23—732no—
388C23—732no—
389C23—732no—
390C23—732no—
391C23—1468no—
392C23—1461no—
393C23—1461no—
394C23—1461no—
395C23—1461no—
396C23—1461no—
397C23—1461no—
398C23—1461no—
399C23—1461no—
400C23—1461no—
401C23—1461no—
402C23C2×C22⋊D7312yes—
403C23C23×D7311yescharacteristic
404Q8—44no—
405D4—44no—
406D4—2924no—
407D4—2924no—
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—2924no—
421C2×C4—2924no—
422C2×C4—732no—
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×C4—1461no—
440C2×C4D4×D7312yes—
441C2×C4C2×C22⋊D7312yes—
442C2×C4C2×C22⋊D7312yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—29216no—
458C22—2921no—
459C22—2921no—
460C22—2921no—
461C22—2921no—
462C22—734no—
463C22—1462no—
464C22—1462no—
465C22—1462no—
466C22—1462no—
467C22—1462no—
468C22—1462no—
469C22—1462no—
470C22—1462no—
471C22—1462no—
472C22C2×D4×D7311yescharacteristic
473C22C22×C22⋊D7311yescharacteristic
474C22#41×D7311yescharacteristic
475C22#41×D7311yescharacteristic
476C22#41×D7311yescharacteristic
477C22#1455663611yescharacteristic
478C22#1455663711yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—2921no—
485C4—2921no—
486C4—2921no—
487C4—2921no—
488C4—2921no—
489C4—1462no—
490C2—42no—
491C2—81no—
492C2—2922no—
493C2—1464no—
494C2#1798909411yescharacteristic
495C2#124×D7311yescharacteristic
496C2#1798917111yescharacteristic
497C2D4×C22⋊D7311yescharacteristic
498C2#1798922511yescharacteristic
499C2#1798923011yescharacteristic
500C2#1798926711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#124×C73C2
hypercenterC2×#124D73
hypocenterC73#2472
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14556567C2semidirect
3. C2×C22⋊C4×D73C2semidirect
4. #17988515C2semidirect
5. #17988503C2semidirect
6. #17988501C2semidirect
7. #17988498C2semidirect
8. #17988487C2semidirect
9. #17988480C2semidirect
10. #17988478C2semidirect
11. #17988463C2semidirect
12. #17988463C2semidirect
13. #17988442C2semidirect
14. C4×#11924005C2semidirect
15. C2×#124×C73C2semidirect
23. C2×C4⋊Dic73C22semidirect
24. C2×#11924007C22semidirect
25. C2×#11924007C22semidirect
29. C2×C22⋊Dic73C22semidirect
30. C2×C22⋊Dic73C22semidirect
40. C2×C4×Dic73C22semidirect
41. #14556498C22semidirect
42. #14556498C22semidirect
43. #14556498C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
46. #14556498C22semidirect
47. C22×Q8×C73C22semidirect
52. C2×C22⋊C4×C73C22semidirect
53. C2×C22⋊C4×C73C22semidirect
54. C2×C42×C73C22semidirect
115. C22⋊C4×C73D4semidirect
227. C2×D73#124semidirect
251. C73#2472semidirect
252. C2×#124D73semidirect
268. C22×Q8C2×D73semidirect
296. C2×C22⋊C4C2×D73semidirect
297. C2×C22⋊C4C2×D73semidirect
299. C2×C42C2×D73semidirect
365. C22⋊C4C22⋊D73semidirect