Finite Group Databasebeta

← #22619188

Subgroups — #22619188

Order 9344.

754 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D73C211yesmaximal, characteristic
2C2×#14556623C211yesmaximal, characteristic, complemented
3C2×#14556620C211yesmaximal, characteristic, complemented
4C22⋊Q8×D73C211yesmaximal, characteristic, complemented
5#17988751C211yesmaximal, characteristic, complemented
6#17988749C211yesmaximal, characteristic, complemented
7#17988747C211yesmaximal, characteristic, complemented
8#17988744C211yesmaximal, characteristic, complemented
9#17988741C211yesmaximal, characteristic, complemented
10#17988739C211yesmaximal, characteristic, complemented
11#17988736C211yesmaximal, characteristic, complemented
12#17988587C211yesmaximal, characteristic, complemented
13#17988585C211yesmaximal, characteristic, complemented
14#17988549C211yesmaximal, characteristic, complemented
15#452×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×#11924028—21no—
18C2×#11924028C2211yescharacteristic
19C2×#11924027—21no—
20C2×#11924027C2211yescharacteristic
21#41×D73—24no—
22#41×D73—24no—
23C2×Q8×D73C2211yescharacteristic
24C2×Q8×D73C2211yescharacteristic, complemented
25C2×D4×D73—21no—
26C2×D4×D73C2211yescharacteristic
27C22×C4×D73—21no—
28C22×C4×D73C2211yescharacteristic
29#14556623—24no—
30#14556620—24no—
31C2×Dic292C2211yescharacteristic, complemented
32C2×#11924018C2211yescharacteristic, complemented
33C2×#11924018C2211yescharacteristic, complemented
34C2×#11924017C2211yescharacteristic, complemented
35C2×#11924016C2211yescharacteristic, complemented
36C2×#11924015C2211yescharacteristic, complemented
37C2×#11924011C2211yescharacteristic, complemented
38C2×#11924011C2211yescharacteristic, complemented
39#14556571C2211yescharacteristic
40#14556570C2211yescharacteristic, complemented
41#14556569—21no—
42#14556568—21no—
43#14556567C2211yescharacteristic
44C4⋊C4×D73—21no—
45C4⋊C4×D73C2211yescharacteristic, complemented
46C22⋊C4×D73—21no—
47#14556516C2211yescharacteristic, complemented
48#14556515C2211yescharacteristic, complemented
49#14556514C2211yescharacteristic, complemented
50#14556513C2211yescharacteristic, complemented
51#14556512C2211yescharacteristic, complemented
52#14556511C2211yescharacteristic, complemented
53C22⋊#10596831C2211yescharacteristic, complemented
54#14556503C2211yescharacteristic
55#14556503C2211yescharacteristic
56C2×#41×C73C2211yescharacteristic
57C2×Q16×C73C2211yescharacteristic, complemented
58C2×SD16×C73C2211yescharacteristic, complemented
59C22⋊Q8×C73C2211yescharacteristic, complemented
60#103×C73C2211yescharacteristic, complemented
61#102×C73C2211yescharacteristic, complemented
62C22⋊C8×C73C2211yescharacteristic, complemented
63C23×D73—21no—
64C23×D73D411yescharacteristic
65#11924029—22no—
66#11924029D414yes—
67#11924028—28no—
68#11924028—22no—
69#11924028—22no—
70#11924027—28no—
71#11924027—22no—
72#11924027D414yes—
73C2×Dic146—21no—
74C2×Dic146—21no—
75C2×Dic146C2311yescharacteristic
76C2×Dic146C2311yescharacteristic
77Q8×D73—22no—
78Q8×D73—22no—
79Q8×D73—22no—
80Q8×D73—22no—
81C2×D292—21no—
82C2×D292C2311yescharacteristic
83C2×C22⋊D73—21no—
84C2×C22⋊D73—21no—
85C2×C22⋊D73—21no—
86D4×D73—28no—
87D4×D73—22no—
88D4×D73—22no—
89C22×Dic73—21no—
90C22×Dic73D411yescharacteristic
91C2×C4×D73—28no—
92C2×C4×D73—21no—
93C2×C4×D73—21no—
94C2×C4×D73—21no—
95C2×C4×D73—22no—
96C2×C4×D73—22no—
97C2×C4×D73—21no—
98C2×C4×D73—21no—
99C2×C4×D73D411yescharacteristic
100C2×C4×D73D411yescharacteristic
101C2×C4×D73C2311yescharacteristic
102C2×C4×D73C2311yescharacteristic
103Dic292—22no—
104#11924018—22no—
105#11924018—22no—
106#11924017—22no—
107#11924016—22no—
108#11924015—22no—
109#11924011—22no—
110#11924011—22no—
111C2×#10596831C2311yescharacteristic
112C2×#10596831C2311yescharacteristic
113C4⋊Dic73—21no—
114C4⋊Dic73C2311yescharacteristic
115#11924007—21no—
116#11924007—21no—
117#11924007—21no—
118C22⋊Dic73—21no—
119#11924005—21no—
120#11924005—21no—
121#41×C73—22no—
122#41×C73—22no—
123C2×Q8×C73C2311yescharacteristic
124C2×Q8×C73C2311yescharacteristic
125C2×D4×C73—21no—
126C2×D4×C73C2311yescharacteristic
127C22×C4×C73—21no—
128C22×C4×C73C2311yescharacteristic
129Q16×C73—22no—
130SD16×C73—22no—
131C2×C8×C73C2311yescharacteristic
132C2×C8×C73C2311yescharacteristic
133C4⋊C4×C73—21no—
134C4⋊C4×C73C2311yescharacteristic
135C22⋊C4×C73—21no—
136C23×C73—21no—
137C23×C73C2×D411yescharacteristic
138C22×D73—24no—
139C22×D73—21no—
140C22×D73—22no—
141C22×D73—22no—
142C22×D73—41no—
143C22×D73—42no—
144C22×D73—42no—
145C22×D73C2×D411yescharacteristic
146C22×D73C2×D411yescharacteristic
147Q8×C73—21no—
148Q8×C73—21no—
149Q8×C73—21no—
150Q8×C73C2×D412yes—
151D4×C73—24no—
152D4×C73—21no—
153D4×C73C2×D412yes—
154C2×C4×C73—24no—
155C2×C4×C73—21no—
156C2×C4×C73—21no—
157C2×C4×C73—21no—
158C2×C4×C73—21no—
159C2×C4×C73—21no—
160C2×C4×C73C2×D411yescharacteristic
161C2×C4×C73C2411yescharacteristic
162C22⋊D73—24no—
163C22⋊D73—24no—
164C22⋊D73—24no—
165C2×Dic73—21no—
166C2×Dic73—24no—
167C2×Dic73—22no—
168C2×Dic73—21no—
169C2×Dic73—21no—
170C2×Dic73C2×D411yescharacteristic
171C2×Dic73C2×D411yescharacteristic
172D292—24no—
173D292—21no—
174D292C2×D412yes—
175C4×D73—24no—
176C4×D73—24no—
177C4×D73—22no—
178C4×D73—21no—
179C4×D73—21no—
180C4×D73—22no—
181C4×D73—24no—
182C4×D73—42no—
183C4×D73—42no—
184C4×D73C2×D412yes—
185C4×D73C2×D412yes—
186Dic146—24no—
187Dic146—21no—
188Dic146—21no—
189Dic146—21no—
190Dic146—42no—
191Dic146C2×D412yes—
192C8×C73—21no—
193C8×C73—21no—
194#10596831—21no—
195#10596831—21no—
196C22×C73—21no—
197C22×C73—22no—
198C22×C73—21no—
199C22×C73—21no—
200C22×C73—41no—
201C22×C73—41no—
202C22×C73C22×D411yescharacteristic
203C2×D73—21no—
204C2×D73—21no—
205C2×D73—21no—
206C2×D73—21no—
207C2×D73—22no—
208C2×D73—44no—
209C2×D73—48no—
210C2×D73—41no—
211C2×D73—41no—
212C2×D73#12012yes—
213C2×D73#13712yescomplemented
214C4×C73—22no—
215C4×C73—21no—
216C4×C73—41no—
217C4×C73—41no—
218C4×C73C22×D411yescharacteristic
219C4×C73C22×D411yescharacteristic
220Dic73—21no—
221Dic73—22no—
222Dic73—41no—
223Dic73—41no—
224Dic73#12012yes—
225C2×C73—41no—
226C2×C73—42no—
227C2×C73C2×#12011yescharacteristic
228C2×C73C2×#13711yescharacteristic
229C2×C73#57511yescharacteristic
230D73—22no—
231D73—22no—
232D73—42no—
233#3007—731nomaximal, Sylow
234C73#300711yescharacteristic, complemented, Sylow
235C22×#41—731no—
236C2×#137—731no—
237C2×#137—731no—
238C2×C22⋊Q8—731no—
239#452—731no—
240#452—731no—
241#452—731no—
242#452D7311yescharacteristic, complemented
243#451—731no—
244#451—731no—
245#450—731no—
246#450—731no—
247#417—731no—
248#417—731no—
249#407—731no—
250C2×#41—731no—
251C2×#41—731no—
252C2×#41—731no—
253C2×#41—1461no—
254C2×#41—1461no—
255C2×#41—1464no—
256C2×#41—1464no—
257C2×#41C2×D7311yescharacteristic
258C22×Q8—731no—
259C22×Q8—731no—
260C22×D4—731no—
261C22×D4—1461no—
262C23×C4—731no—
263C23×C4—1461no—
264#137—1464no—
265#137—1464no—
266C2×Q16—731no—
267C2×Q16—731no—
268C2×Q16—731no—
269C2×Q16C2×D7311yescharacteristic, complemented
270C2×SD16—731no—
271C2×SD16—731no—
272C2×SD16—731no—
273C2×SD16C2×D7311yescharacteristic, complemented
274C2×M16—731no—
275C2×M16—731no—
276C22⋊Q8—731no—
277C22⋊Q8—731no—
278C22⋊Q8—731no—
279C22⋊Q8—1461no—
280C22⋊Q8—1461no—
281C22⋊Q8C2×D7311yescharacteristic, complemented
282C2×C4⋊C4—731no—
283C2×C4⋊C4—1461no—
284C2×C22⋊C4—1461no—
285#103—731no—
286#103—731no—
287#103—731no—
288#103C2×D7311yescharacteristic, complemented
289#102—731no—
290#102—731no—
291#102—731no—
292#102C2×D7311yescharacteristic, complemented
293C22⋊C8—731no—
294C22⋊C8—731no—
295C22⋊C8—731no—
296C22⋊C8C2×D7311yescharacteristic, complemented
297C24—731no—
298C24—1461no—
299#41—22no—
300#41—22no—
301#41—734no—
302#41—734no—
303#41—1462no—
304#41—1462no—
305#41—1468no—
306#41—1462no—
307#41—1462no—
308#41—1468no—
309C2×Q8—731no—
310C2×Q8—731no—
311C2×Q8—1461no—
312C2×Q8—1461no—
313C2×Q8—1462no—
314C2×Q8—1462no—
315C2×Q8—1462no—
316C2×Q8—1462no—
317C2×Q8C22×D7311yescharacteristic
318C2×Q8C22×D7311yescharacteristic
319C2×D4—21no—
320C2×D4—731no—
321C2×D4—1461no—
322C2×D4—1461no—
323C2×D4—1462no—
324C2×D4—1468no—
325C2×D4—1461no—
326C2×D4—1461no—
327C2×D4—1462no—
328C2×D4C22×D7311yescharacteristic
329C22×C4—21no—
330C22×C4—731no—
331C22×C4—731no—
332C22×C4—731no—
333C22×C4—731no—
334C22×C4—731no—
335C22×C4—1461no—
336C22×C4—1461no—
337C22×C4—1462no—
338C22×C4—1462no—
339C22×C4—1461no—
340C22×C4—1461no—
341C22×C4—1468no—
342C22×C4—1461no—
343C22×C4—1461no—
344C22×C4C22×D7311yescharacteristic
345Q16—22no—
346Q16—1462no—
347Q16—1462no—
348Q16—1462no—
349SD16—22no—
350SD16—1462no—
351SD16—1462no—
352SD16—1462no—
353M16—1462no—
354M16—1462no—
355C2×C8—731no—
356C2×C8—731no—
357C2×C8C22×D7311yescharacteristic
358C2×C8C22×D7311yescharacteristic
359C4⋊C4—21no—
360C4⋊C4—731no—
361C4⋊C4—1461no—
362C4⋊C4—1461no—
363C4⋊C4—1461no—
364C4⋊C4—1461no—
365C4⋊C4C22×D7311yescharacteristic
366C22⋊C4—21no—
367C22⋊C4—1461no—
368C22⋊C4—1461no—
369C22⋊C4—1461no—
370C23—21no—
371C23—2921no—
372C23—2922no—
373C23—2922no—
374C23—731no—
375C23—731no—
376C23—1462no—
377C23—1462no—
378C23—1464no—
379C23—1461no—
380C23D4×D7311yescharacteristic
381Q8—21no—
382Q8—21no—
383Q8—21no—
384Q8—2922no—
385Q8—732no—
386Q8—1464no—
387Q8—1461no—
388Q8—1461no—
389Q8—1461no—
390Q8D4×D7312yes—
391D4—24no—
392D4—21no—
393D4—732no—
394D4—1464no—
395D4—1464no—
396D4—1464no—
397D4—1464no—
398D4—1461no—
399D4D4×D7312yes—
400C2×C4—24no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—2922no—
407C2×C4—2922no—
408C2×C4—731no—
409C2×C4—732no—
410C2×C4—732no—
411C2×C4—731no—
412C2×C4—1462no—
413C2×C4—1464no—
414C2×C4—1462no—
415C2×C4—1464no—
416C2×C4—1464no—
417C2×C4—1461no—
418C2×C4—1461no—
419C2×C4—1462no—
420C2×C4—1464no—
421C2×C4—1461no—
422C2×C4—1461no—
423C2×C4—1461no—
424C2×C4D4×D7311yescharacteristic
425C2×C4C23×D7311yescharacteristic
426C8—21no—
427C8—21no—
428C8—1461no—
429C8—1461no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—22no—
434C22—41no—
435C22—41no—
436C22—2928no—
437C22—2924no—
438C22—2921no—
439C22—2921no—
440C22—732no—
441C22—732no—
442C22—1462no—
443C22—1461no—
444C22—1461no—
445C22—1461no—
446C22—1461no—
447C22C2×D4×D7311yescharacteristic
448C4—21no—
449C4—22no—
450C4—41no—
451C4—41no—
452C4—2921no—
453C4—2921no—
454C4—732no—
455C4—1461no—
456C4—1462no—
457C4C2×D4×D7311yescharacteristic
458C4C2×D4×D7311yescharacteristic
459C2—41no—
460C2—42no—
461C2—2922no—
462C2—1462no—
463C2—1462no—
464C2#120×D7311yescharacteristic
465C2#137×D7311yescharacteristic
466C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#452×C73C2
socleC22×C73C22×D4
hypercenter#452D73
hypocenterC73#3007
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. C2×#14556623C2semidirect
3. C2×#14556620C2semidirect
4. C22⋊Q8×D73C2semidirect
5. #17988751C2semidirect
6. #17988749C2semidirect
7. #17988747C2semidirect
8. #17988744C2semidirect
9. #17988741C2semidirect
10. #17988739C2semidirect
11. #17988736C2semidirect
12. #17988587C2semidirect
13. #17988585C2semidirect
14. #17988549C2semidirect
15. #452×C73C2semidirect
24. C2×Q8×D73C22semidirect
31. C2×Dic292C22semidirect
32. C2×#11924018C22semidirect
33. C2×#11924018C22semidirect
34. C2×#11924017C22semidirect
35. C2×#11924016C22semidirect
36. C2×#11924015C22semidirect
37. C2×#11924011C22semidirect
38. C2×#11924011C22semidirect
40. #14556570C22semidirect
45. C4⋊C4×D73C22semidirect
47. #14556516C22semidirect
48. #14556515C22semidirect
49. #14556514C22semidirect
50. #14556513C22semidirect
51. #14556512C22semidirect
52. #14556511C22semidirect
53. C22⋊#10596831C22semidirect
57. C2×Q16×C73C22semidirect
58. C2×SD16×C73C22semidirect
59. C22⋊Q8×C73C22semidirect
60. #103×C73C22semidirect
61. #102×C73C22semidirect
62. C22⋊C8×C73C22semidirect
213. C2×D73#137semidirect
234. C73#3007semidirect
242. #452D73semidirect
269. C2×Q16C2×D73semidirect
273. C2×SD16C2×D73semidirect
281. C22⋊Q8C2×D73semidirect
288. #103C2×D73semidirect
292. #102C2×D73semidirect
296. C22⋊C8C2×D73semidirect