Finite Group Databasebeta

← #2175×D73 #33239269

Subgroups — #2175×D73 #33239269

Order 18688.

734 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD32×D73C211yesmaximal, characteristic
2C4×Q16×D73C211yesmaximal, characteristic, complemented
3C4×D8×D73C211yesmaximal, characteristic
4#22611798C211yesmaximal, characteristic, complemented
5#22611797C211yesmaximal, characteristic, complemented
6#22611796C211yesmaximal, characteristic, complemented
7#22611795C211yesmaximal, characteristic, complemented
8#22611794C211yesmaximal, characteristic, complemented
9#22611793C211yesmaximal, characteristic, complemented
10#22611792C211yesmaximal, characteristic, complemented
11#366×D73C211yesmaximal, characteristic, complemented
12#358×D73C211yesmaximal, characteristic, complemented
13#357×D73C211yesmaximal, characteristic
14#346×D73C211yesmaximal, characteristic, complemented
15C73×#2175C211yesmaximal, characteristic, complemented
16C2×Q16×D73C2211yescharacteristic
17C2×D8×D73C2211yescharacteristic
18C4×Q8×D73—21no—
19C4×D4×D73—21no—
20C2×#14556536C2211yescharacteristic
21C2×#14556535C2211yescharacteristic
22C2×#14556534C2211yescharacteristic
23SD32×D73C418yescomplemented
24C2×C16×D73C2211yescharacteristic
25C2×C16×D73C2211yescharacteristic
26C4×Dic292C2211yescharacteristic, complemented
27Q16×Dic73C2211yescharacteristic, complemented
28#17988681C2211yescharacteristic, complemented
29C4×#11924018—21no—
30#17988679—21no—
31C4×D584C2211yescharacteristic
32D8×Dic73C2211yescharacteristic
33#17988669C2211yescharacteristic
34C4×#11924013—21no—
35#17988667—21no—
36#107×D73C2211yescharacteristic
37#107×D73C2211yescharacteristic
38#103×D73—21no—
39#102×D73—21no—
40C4×C8×D73C2211yescharacteristic
41#17988413C2211yescharacteristic, complemented
42#17988412C2211yescharacteristic, complemented
43#17988412C2211yescharacteristic, complemented
44#17988392C2211yescharacteristic, complemented
45#17988391C2211yescharacteristic, complemented
46#17988390C2211yescharacteristic, complemented
47#17988389C2211yescharacteristic
48#17988388C2211yescharacteristic
49#17988387C2211yescharacteristic
50#17988363C2211yescharacteristic, complemented
51#17988362C2211yescharacteristic, complemented
52#17988362C2211yescharacteristic, complemented
53C2×SD32×C73C2211yescharacteristic
54C4×Q16×C73C2211yescharacteristic, complemented
55C4×D8×C73C2211yescharacteristic
56#366×C73C2211yescharacteristic, complemented
57#358×C73C2211yescharacteristic, complemented
58#357×C73C2211yescharacteristic
59#346×C73C2211yescharacteristic, complemented
60C2×Q8×D73—21no—
61C2×D4×D73—21no—
62C22×C4×D73—41no—
63C2×Dic292C2311yescharacteristic
64C2×#11924018—21no—
65Q16×D73—22no—
66Q16×D73C2×C414yescomplemented
67C2×D584C2311yescharacteristic
68C2×#11924013—21no—
69D8×D73—22no—
70D8×D73C2×C414yes—
71C2×C8×D73D411yescharacteristic
72C2×C8×D73C2311yescharacteristic
73Q8×Dic73—21no—
74C4×Dic146—21no—
75C4×Dic146—41no—
76#14556556—21no—
77#14556556—41no—
78C4×D292—21no—
79D4×Dic73—21no—
80#14556553—21no—
81C4×C22⋊D73—41no—
82#14556551—41no—
83C4⋊C4×D73—21no—
84C4⋊C4×D73—21no—
85C4⋊C4×D73—41no—
86C22⋊C4×D73—41no—
87C42×D73—41no—
88C42×D73D411yescharacteristic
89#14556536C2×C414yescomplemented
90#14556535C2×C414yescomplemented
91#14556534C2×C414yescomplemented
92C2×#11924003C2311yescharacteristic
93C2×#11924003C2311yescharacteristic
94C16×D73—22no—
95C16×D73C2×C414yescomplemented
96#14556525C2311yescharacteristic
97#14556525C2311yescharacteristic
98#14556524—21no—
99#14556524—21no—
100#14556516—21no—
101#14556515—21no—
102#14556514—21no—
103#14556513—21no—
104#14556512—21no—
105#14556511—21no—
106C4×#10596831D411yescharacteristic
107C8×Dic73D411yescharacteristic
108C8×Dic73C2311yescharacteristic
109C2×Q16×C73C2311yescharacteristic
110C2×D8×C73C2311yescharacteristic
111C4×Q8×C73—21no—
112C4×D4×C73—21no—
113SD32×C73C2×C414yescomplemented
114C2×C16×C73C2311yescharacteristic
115C2×C16×C73C2311yescharacteristic
116#107×C73C2311yescharacteristic
117#107×C73C2311yescharacteristic
118#103×C73—21no—
119#102×C73—21no—
120C4×C8×C73C2311yescharacteristic
121C23×D73—41no—
122C2×Dic146—21no—
123C2×Dic146—41no—
124Q8×D73—24no—
125Q8×D73—42no—
126C2×D292—21no—
127C2×C22⋊D73—41no—
128D4×D73—24no—
129D4×D73—42no—
130C22×Dic73—41no—
131C2×C4×D73—41no—
132C2×C4×D73—41no—
133C2×C4×D73—41no—
134C2×C4×D73—41no—
135C2×C4×D73—41no—
136C2×C4×D73—84no—
137C2×C4×D73D811yescharacteristic
138C2×C4×D73D811yescharacteristic
139C2×C4×D73C2×D411yescharacteristic
140Dic292—21no—
141Dic292C22×C412yescomplemented
142#11924018—24no—
143D584—21no—
144D584C22×C412yes—
145#11924013—24no—
146C2×#10596831C2×D411yescharacteristic
147C2×#10596831C2×D411yescharacteristic
148C8×D73—22no—
149C8×D73C22×C412yes—
150C8×D73#4112yes—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—41no—
154#11924007—41no—
155#11924007—41no—
156#11924007—41no—
157#11924007—41no—
158C22⋊Dic73—41no—
159#11924005—41no—
160#11924005—41no—
161C4×Dic73—41no—
162C4×Dic73—41no—
163C4×Dic73—41no—
164C4×Dic73D811yescharacteristic
165C4×Dic73D811yescharacteristic
166C4×Dic73C2×D411yescharacteristic
167#11924003—21no—
168#11924003C22×C412yescomplemented
169C2×Q8×C73—21no—
170C2×D4×C73—21no—
171C22×C4×C73—41no—
172Q16×C73—21no—
173Q16×C73C22×C412yescomplemented
174D8×C73—21no—
175D8×C73C22×C412yes—
176C2×C8×C73C2×D411yescharacteristic
177C2×C8×C73C2411yescharacteristic
178C4⋊C4×C73—21no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—41no—
181C22⋊C4×C73—41no—
182C42×C73—41no—
183C42×C73C2×D411yescharacteristic
184C16×C73—21no—
185C16×C73C22×C412yescomplemented
186C23×C73—41no—
187C22×D73—41no—
188C22×D73—44no—
189C22×D73—82no—
190C22×D73—82no—
191C22×D73C2×D811yescharacteristic
192Q8×C73—22no—
193Q8×C73—41no—
194D4×C73—22no—
195D4×C73—41no—
196C2×C4×C73—41no—
197C2×C4×C73—41no—
198C2×C4×C73—41no—
199C2×C4×C73—82no—
200C2×C4×C73C2×D811yescharacteristic
201C2×C4×C73C2×D811yescharacteristic
202C2×C4×C73C22×D411yescharacteristic
203C22⋊D73—44no—
204C2×Dic73—41no—
205C2×Dic73—41no—
206C2×Dic73—41no—
207C2×Dic73—82no—
208C2×Dic73C2×D811yescharacteristic
209C2×Dic73C2×D811yescharacteristic
210C2×Dic73C2×D811yescharacteristic
211D292—22no—
212D292—41no—
213C4×D73—22no—
214C4×D73—22no—
215C4×D73—44no—
216C4×D73—82no—
217C4×D73—82no—
218C4×D73—82no—
219C4×D73—82no—
220C4×D73C4×D412yes—
221C4×D73#13512yes—
222Dic146—22no—
223Dic146—41no—
224Dic146—44no—
225C8×C73—21no—
226C8×C73C23×C411yescharacteristic
227C8×C73C2×#4111yescharacteristic
228#10596831—21no—
229#10596831C4×D412yes—
230C22×C73—42no—
231C22×C73—81no—
232C22×C73—81no—
233C22×C73C22×D811yescharacteristic
234C2×D73—42no—
235C2×D73—81no—
236C2×D73—81no—
237C2×D73—88no—
238C2×D73C4×D812yes—
239C2×D73#50912yes—
240C2×D73#51012yes—
241C4×C73—21no—
242C4×C73—21no—
243C4×C73—42no—
244C4×C73—81no—
245C4×C73—81no—
246C4×C73C2×C4×D411yescharacteristic
247C4×C73C2×#13511yescharacteristic
248Dic73—21no—
249Dic73—21no—
250Dic73—42no—
251Dic73—81no—
252Dic73—81no—
253Dic73C4×D812yes—
254C2×#2175—731nomaximal, Sylow
255C2×C73—82no—
256C2×C73C2×C4×D811yescharacteristic
257C2×C73C2×#50911yescharacteristic
258C2×C73C2×#51011yescharacteristic
259D73—82no—
260D73#217514yesdirect product factor
261C22×SD32—731no—
262C2×C4×Q16—731no—
263C2×C4×D8—731no—
264#2175—731no—
265#2175—731no—
266#2175—731no—
267#2175—731no—
268#2175—731no—
269#2175—731no—
270#2175—731no—
271#2175D7311yescharacteristic, direct product factor
272C2×#366—731no—
273C2×#358—731no—
274C2×#357—731no—
275C2×#346—731no—
276C73C2×#217511yescharacteristic, complemented, Sylow
277C22×Q16—731no—
278C22×D8—731no—
279C2×C4×Q8—1461no—
280C2×C4×D4—1461no—
281C2×SD32—731no—
282C2×SD32—731no—
283C2×SD32—738no—
284C2×SD32—731no—
285C2×SD32C2×D7311yescharacteristic
286C22×C16—731no—
287C22×C16—731no—
288C4×Q16—731no—
289C4×Q16—731no—
290C4×Q16—731no—
291C4×Q16—1461no—
292C4×Q16—1461no—
293C4×Q16C2×D7311yescharacteristic, complemented
294C4×D8—731no—
295C4×D8—731no—
296C4×D8—731no—
297C4×D8—1461no—
298C4×D8—1461no—
299C4×D8C2×D7311yescharacteristic
300C2×#107—731no—
301C2×#107—731no—
302C2×#103—1461no—
303C2×#102—1461no—
304C2×C4×C8—731no—
305#366—731no—
306#366—731no—
307#366—731no—
308#366C2×D7311yescharacteristic, complemented
309#358—731no—
310#358—731no—
311#358—731no—
312#358C2×D7311yescharacteristic, complemented
313#357—731no—
314#357—731no—
315#357—731no—
316#357C2×D7311yescharacteristic
317#346—731no—
318#346—731no—
319#346—731no—
320#346C2×D7311yescharacteristic, complemented
321C22×Q8—1461no—
322C22×D4—1461no—
323C23×C4—2921no—
324C2×Q16—734no—
325C2×Q16—731no—
326C2×Q16—1462no—
327C2×Q16—1461no—
328C2×Q16C22×D7311yescharacteristic
329C2×D8—734no—
330C2×D8—731no—
331C2×D8—1462no—
332C2×D8—1461no—
333C2×D8C22×D7311yescharacteristic
334C22×C8—731no—
335C22×C8—731no—
336C4×Q8—21no—
337C4×Q8—2921no—
338C4×Q8—2921no—
339C4×Q8—1461no—
340C4×Q8—1461no—
341C4×Q8—1461no—
342C4×D4—21no—
343C4×D4—2921no—
344C4×D4—2921no—
345C4×D4—1461no—
346C4×D4—1461no—
347C4×D4—1461no—
348C2×C4⋊C4—2921no—
349C2×C4⋊C4—1461no—
350C2×C4⋊C4—1461no—
351C2×C22⋊C4—2921no—
352C2×C42—2921no—
353C2×C42—731no—
354SD32—734no—
355SD32—734no—
356SD32—734no—
357SD32C4×D7314yescomplemented
358C2×C16—731no—
359C2×C16—734no—
360C2×C16—731no—
361C2×C16—1462no—
362C2×C16C22×D7311yescharacteristic
363C2×C16C22×D7311yescharacteristic
364#107—731no—
365#107—731no—
366#107—1461no—
367#107—1461no—
368#107C22×D7311yescharacteristic
369#107C22×D7311yescharacteristic
370#103—21no—
371#103—1461no—
372#103—1461no—
373#103—1461no—
374#102—21no—
375#102—1461no—
376#102—1461no—
377#102—1461no—
378C4×C8—731no—
379C4×C8—731no—
380C4×C8—731no—
381C4×C8C22×D7311yescharacteristic
382C24—2921no—
383C2×Q8—21no—
384C2×Q8—2921no—
385C2×Q8—2922no—
386C2×Q8—1464no—
387C2×Q8—1461no—
388C2×D4—21no—
389C2×D4—2922no—
390C2×D4—2921no—
391C2×D4—1464no—
392C2×D4—1461no—
393C22×C4—41no—
394C22×C4—2921no—
395C22×C4—2921no—
396C22×C4—2921no—
397C22×C4—2921no—
398C22×C4—2921no—
399C22×C4—2921no—
400C22×C4—5844no—
401C22×C4—731no—
402C22×C4—731no—
403C22×C4—731no—
404Q16—21no—
405Q16—732no—
406Q16—1464no—
407Q16—1461no—
408Q16C2×C4×D7312yescomplemented
409D8—21no—
410D8—732no—
411D8—1464no—
412D8—1461no—
413D8C2×C4×D7312yes—
414C2×C8—731no—
415C2×C8—732no—
416C2×C8—732no—
417C2×C8—731no—
418C2×C8—1462no—
419C2×C8D4×D7311yescharacteristic
420C2×C8C23×D7311yescharacteristic
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—41no—
424C4⋊C4—2921no—
425C4⋊C4—2921no—
426C4⋊C4—2921no—
427C4⋊C4—2921no—
428C4⋊C4—2921no—
429C4⋊C4—1461no—
430C4⋊C4—1461no—
431C22⋊C4—41no—
432C22⋊C4—2921no—
433C22⋊C4—2921no—
434C22⋊C4—2921no—
435C42—41no—
436C42—2921no—
437C42—2921no—
438C42—2921no—
439C42—731no—
440C42—731no—
441C42—731no—
442C42D4×D7311yescharacteristic
443C16—21no—
444C16—732no—
445C16—1461no—
446C16C2×C4×D7312yescomplemented
447C23—41no—
448C23—2924no—
449C23—2921no—
450C23—5842no—
451C23—5842no—
452C23—731no—
453Q8—22no—
454Q8—41no—
455Q8—2924no—
456Q8—2921no—
457Q8—1462no—
458D4—22no—
459D4—41no—
460D4—2924no—
461D4—2921no—
462D4—1462no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—82no—
467C2×C4—2924no—
468C2×C4—2921no—
469C2×C4—2921no—
470C2×C4—2921no—
471C2×C4—5842no—
472C2×C4—5842no—
473C2×C4—5842no—
474C2×C4—5842no—
475C2×C4—5842no—
476C2×C4—731no—
477C2×C4—732no—
478C2×C4—732no—
479C2×C4—731no—
480C2×C4—731no—
481C2×C4—1462no—
482C2×C4—1462no—
483C2×C4D8×D7311yescharacteristic
484C2×C4D8×D7311yescharacteristic
485C2×C4C2×D4×D7311yescharacteristic
486C8—21no—
487C8—732no—
488C8—1461no—
489C8C22×C4×D7311yescharacteristic
490C8#41×D7311yescharacteristic
491C22—42no—
492C22—81no—
493C22—81no—
494C22—2922no—
495C22—5848no—
496C22—5841no—
497C22—5841no—
498C22—732no—
499C22—732no—
500C22—732no—
501C22C2×D8×D7311yescharacteristic
502C4—21no—
503C4—21no—
504C4—42no—
505C4—81no—
506C4—81no—
507C4—2922no—
508C4—5841no—
509C4—5841no—
510C4—732no—
511C4—1461no—
512C4—1461no—
513C4C4×D4×D7311yescharacteristic
514C4#135×D7311yescharacteristic
515C2—82no—
516C2—5842no—
517C2—734no—
518C2C4×D8×D7311yescharacteristic
519C2#509×D7311yescharacteristic
520C2#510×D7311yescharacteristic
subgroupG/H
centerC22C2×D8×D73
commutatorC8×C73C23×C4
FrattiniC2×C8C23×D73
FittingC73×#2175C2
socleC22×C73C22×D8
prime radicalC2×D8×D73C22
cosocleC2×C8×C73C24
hypercenter#2175D73
hypocenterC73C2×#2175
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
2. C4×Q16×D73C2semidirect
4. #22611798C2semidirect
5. #22611797C2semidirect
6. #22611796C2semidirect
7. #22611795C2semidirect
8. #22611794C2semidirect
9. #22611793C2semidirect
10. #22611792C2semidirect
11. #366×D73C2semidirect
12. #358×D73C2semidirect
14. #346×D73C2semidirect
15. C73×#2175C2semidirect
23. SD32×D73C4semidirect
26. C4×Dic292C22semidirect
27. Q16×Dic73C22semidirect
28. #17988681C22semidirect
41. #17988413C22semidirect
42. #17988412C22semidirect
43. #17988412C22semidirect
44. #17988392C22semidirect
45. #17988391C22semidirect
46. #17988390C22semidirect
50. #17988363C22semidirect
51. #17988362C22semidirect
52. #17988362C22semidirect
54. C4×Q16×C73C22semidirect
56. #366×C73C22semidirect
57. #358×C73C22semidirect
59. #346×C73C22semidirect
66. Q16×D73C2×C4semidirect
89. #14556536C2×C4semidirect
90. #14556535C2×C4semidirect
91. #14556534C2×C4semidirect
95. C16×D73C2×C4semidirect
113. SD32×C73C2×C4semidirect
141. Dic292C22×C4semidirect
168. #11924003C22×C4semidirect
173. Q16×C73C22×C4semidirect
185. C16×C73C22×C4semidirect
260. D73#2175direct (N × H)
271. #2175D73direct (N × H)
276. C73C2×#2175semidirect
293. C4×Q16C2×D73semidirect
308. #366C2×D73semidirect
312. #358C2×D73semidirect
320. #346C2×D73semidirect
357. SD32C4×D73semidirect
408. Q16C2×C4×D73semidirect
446. C16C2×C4×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×SD32×D732
C4×Q16×D732
C4×D8×D732
#226117982
#226117972
#226117962
#226117952
#226117942
#226117932
#226117922
#366×D732
#358×D732
#357×D732
#346×D732
C73×#21752
C2×#217573