Finite Group Databasebeta

← #2084×D73 #33114956

Subgroups — #2084×D73 #33114956

Order 18688.

1086 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×#106×D73C212yesmaximal
2#389×D73C211yesmaximal, characteristic
3#384×D73C211yesmaximal, characteristic
4#22611411C212yesmaximal, complemented
5#22611410C212yesmaximal, complemented
6#22611409C211yesmaximal, characteristic, complemented
7#22611408C211yesmaximal, characteristic, complemented
8#22611407C211yesmaximal, characteristic, complemented
9#340×D73C212yesmaximal
10#336×D73C211yesmaximal, characteristic
11C73×#2084C211yesmaximal, characteristic, complemented
12C22×C8×D73C2212yes—
13C2×C4⋊C4×D73—21no—
14C2×C4⋊C4×D73—21no—
15C2×C4⋊C4×D73—21no—
16C2×C4⋊C4×D73C2212yes—
17C2×C4⋊C4×D73C2211yescharacteristic
18C2×C4⋊C4×D73C2211yescharacteristic
19C2×C42×D73C2211yescharacteristic
20C2×#14556523C2212yes—
21C2×#14556522C2212yes—
22C2×#14556522C2212yes—
23#106×D73—28no—
24#17988486C2211yescharacteristic
25#17988485C2211yescharacteristic
26#17988484—21no—
27#17988483C2211yescharacteristic
28#17988482—21no—
29#17988457C2211yescharacteristic
30#17988456—21no—
31#17988456—21no—
32#17988456C2212yes—
33#95×D73—21no—
34#17988350C2212yes—
35#17988349C2212yes—
36#17988349C2212yes—
37#17988342C2211yescharacteristic
38#17988341C2212yes—
39C2×#106×C73C2212yes—
40#389×C73C2211yescharacteristic
41#384×C73C2211yescharacteristic
42#340×C73C2212yes—
43#336×C73C2211yescharacteristic
44C22×C4×D73—21no—
45C22×C4×D73—21no—
46C22×C4×D73—22no—
47C22×C4×D73D411yescharacteristic
48C22×C4×D73D411yescharacteristic
49C22×C4×D73C2311yescharacteristic
50C22×#10596831C2312yes—
51C2×C8×D73—24no—
52C2×C8×D73—24no—
53C2×C8×D73Q818yes—
54C2×C4⋊Dic73—21no—
55C2×C4⋊Dic73—21no—
56C2×C4⋊Dic73—21no—
57C2×C4⋊Dic73C2312yes—
58C2×C4⋊Dic73C2311yescharacteristic
59C2×C4⋊Dic73C2311yescharacteristic
60C2×#11924007—21no—
61C2×#11924007—22no—
62C2×#11924007—22no—
63C2×#11924007—22no—
64C2×#11924007—21no—
65C2×#11924007—21no—
66C2×#11924007—21no—
67C4⋊C4×D73—22no—
68C4⋊C4×D73—24no—
69C4⋊C4×D73—24no—
70C4⋊C4×D73—24no—
71C4⋊C4×D73—44no—
72C4⋊C4×D73—44no—
73C4⋊C4×D73—44no—
74C4⋊C4×D73D414yes—
75C2×C4×Dic73D411yescharacteristic
76C2×C4×Dic73D411yescharacteristic
77C2×C4×Dic73C2311yescharacteristic
78C42×D73—24no—
79#14556523—24no—
80#14556522—24no—
81#14556522—24no—
82#14556498—21no—
83#14556498—21no—
84#14556498—21no—
85C22×C8×C73C2312yes—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73C2312yes—
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C42×C73C2311yescharacteristic
93#106×C73—24no—
94#95×C73—21no—
95C23×D73C2×D411yescharacteristic
96C22×Dic73—21no—
97C22×Dic73—21no—
98C22×Dic73—22no—
99C22×Dic73C2×D411yescharacteristic
100C22×Dic73C2×D411yescharacteristic
101C22×Dic73C2×D411yescharacteristic
102C2×C4×D73—22no—
103C2×C4×D73—22no—
104C2×C4×D73—22no—
105C2×C4×D73—22no—
106C2×C4×D73—24no—
107C2×C4×D73—42no—
108C2×C4×D73—42no—
109C2×C4×D73—44no—
110C2×C4×D73—42no—
111C2×C4×D73—44no—
112C2×C4×D73—42no—
113C2×C4×D73—44no—
114C2×C4×D73—42no—
115C2×C4×D73SD1614yes—
116C2×C4×D73SD1614yes—
117C2×C4×D73C2×D412yes—
118C2×C4×D73C2×Q814yes—
119C2×C4×D73#4114yes—
120C2×C4×D73#4112yes—
121C2×#10596831—22no—
122C2×#10596831—22no—
123C2×#10596831C2×Q814yes—
124C8×D73—216no—
125C4⋊Dic73—21no—
126C4⋊Dic73—22no—
127C4⋊Dic73—22no—
128C4⋊Dic73—22no—
129C4⋊Dic73—42no—
130C4⋊Dic73—42no—
131C4⋊Dic73—42no—
132C4⋊Dic73C2×D412yes—
133#11924007—24no—
134#11924007—44no—
135#11924007—42no—
136#11924007—44no—
137#11924007—42no—
138#11924007—42no—
139#11924007—44no—
140C4×Dic73—22no—
141C4×Dic73—22no—
142C4×Dic73—22no—
143C22×C4×C73—21no—
144C22×C4×C73—21no—
145C22×C4×C73—22no—
146C22×C4×C73C2×D411yescharacteristic
147C22×C4×C73C2×D411yescharacteristic
148C22×C4×C73C2411yescharacteristic
149C2×C8×C73—22no—
150C2×C8×C73—22no—
151C2×C8×C73C2×Q814yes—
152C4⋊C4×C73—21no—
153C4⋊C4×C73—22no—
154C4⋊C4×C73—22no—
155C4⋊C4×C73—22no—
156C4⋊C4×C73—42no—
157C4⋊C4×C73—42no—
158C4⋊C4×C73—42no—
159C4⋊C4×C73C2×D412yes—
160C42×C73—22no—
161C23×C73C22×D411yescharacteristic
162C22×D73#12112yes—
163C22×D73#12312yes—
164C22×D73C4⋊Q812yes—
165C22×D73C2×SD1612yes—
166C22×D73C2×SD1612yes—
167C22×D73AGL(1,ℤ/8)12yes—
168C22×D73#13712yes—
169C2×C4×C73—21no—
170C2×C4×C73—21no—
171C2×C4×C73—21no—
172C2×C4×C73—21no—
173C2×C4×C73—22no—
174C2×C4×C73—41no—
175C2×C4×C73—41no—
176C2×C4×C73—42no—
177C2×C4×C73—41no—
178C2×C4×C73—41no—
179C2×C4×C73—42no—
180C2×C4×C73—42no—
181C2×C4×C73—41no—
182C2×C4×C73C2×SD1612yes—
183C2×C4×C73C2×SD1612yes—
184C2×C4×C73C22×D411yescharacteristic
185C2×C4×C73C22×Q812yes—
186C2×C4×C73C2×#4112yes—
187C2×C4×C73C2×#4111yescharacteristic
188C2×Dic73—21no—
189C2×Dic73—21no—
190C2×Dic73—21no—
191C2×Dic73—21no—
192C2×Dic73—22no—
193C2×Dic73—41no—
194C2×Dic73—41no—
195C2×Dic73—42no—
196C2×Dic73—41no—
197C2×Dic73—41no—
198C2×Dic73—42no—
199C2×Dic73—42no—
200C2×Dic73—41no—
201C2×Dic73#12112yes—
202C2×Dic73#12312yes—
203C2×Dic73C4⋊Q812yes—
204C2×Dic73C2×SD1612yes—
205C2×Dic73C2×SD1612yes—
206C4×D73—28no—
207C4×D73—28no—
208C4×D73—48no—
209C4×D73—88no—
210C4×D73—84no—
211C4×D73C22⋊Q818yes—
212C4×D73#12518yes—
213C8×C73—24no—
214#10596831—24no—
215C22×C73C2×#12111yescharacteristic
216C22×C73C2×#12311yescharacteristic
217C22×C73C2×C4⋊Q811yescharacteristic
218C22×C73C22×SD1611yescharacteristic
219C22×C73C22×SD1611yescharacteristic
220C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
221C22×C73C2×#13711yescharacteristic
222C2×D73#39814yes—
223C2×D73#46014yes—
224C2×D73#46114yes—
225C2×D73#48114yes—
226C2×D73#48314yes—
227C2×D73#49814yes—
228C2×D73#50114yes—
229C4×C73—22no—
230C4×C73—22no—
231C4×C73—42no—
232C4×C73—81no—
233C4×C73—82no—
234C4×C73C2×C22⋊Q812yes—
235C4×C73C2×#12512yes—
236Dic73—22no—
237Dic73—22no—
238Dic73—42no—
239Dic73—81no—
240Dic73—82no—
241Dic73#39814yes—
242C2×#2084—731nomaximal, Sylow
243C2×C73C2×#39811yescharacteristic
244C2×C73C2×#46111yescharacteristic
245C2×C73C2×#46011yescharacteristic
246C2×C73C2×#48311yescharacteristic
247C2×C73C2×#48111yescharacteristic
248C2×C73C2×#49811yescharacteristic
249C2×C73C2×#50111yescharacteristic
250D73#208418yesdirect product factor
251C22×#106—732no—
252C2×#389—731no—
253C2×#384—731no—
254#2084—732no—
255#2084—731no—
256#2084—731no—
257#2084—732no—
258#2084—731no—
259#2084D7311yescharacteristic, direct product factor
260C2×#340—732no—
261C2×#336—731no—
262C73C2×#208411yescharacteristic, complemented, Sylow
263C23×C8—732no—
264C22×C4⋊C4—731no—
265C22×C4⋊C4—732no—
266C22×C4⋊C4—731no—
267C22×C4⋊C4—1461no—
268C22×C4⋊C4—1461no—
269C22×C4⋊C4—1461no—
270C22×C42—731no—
271C2×#106—732no—
272C2×#106—732no—
273C2×#106—732no—
274C2×#106—1468no—
275C2×#106C2×D7312yes—
276#389—731no—
277#389—731no—
278#389—731no—
279#389—1461no—
280#389—1461no—
281#389C2×D7311yescharacteristic
282#384—732no—
283#384—731no—
284#384—1461no—
285#384—1461no—
286#384C2×D7311yescharacteristic
287C2×#95—1461no—
288#340—732no—
289#340—732no—
290#340—732no—
291#340C2×D7312yes—
292#336—732no—
293#336—731no—
294#336C2×D7311yescharacteristic
295C23×C4—731no—
296C23×C4—731no—
297C23×C4—731no—
298C23×C4—1462no—
299C23×C4—1461no—
300C23×C4—1461no—
301C22×C8—732no—
302C22×C8—738no—
303C22×C8—1464no—
304C22×C8—1464no—
305C22×C8C22×D7312yes—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—2924no—
310C2×C4⋊C4—2924no—
311C2×C4⋊C4—2924no—
312C2×C4⋊C4—731no—
313C2×C4⋊C4—734no—
314C2×C4⋊C4—731no—
315C2×C4⋊C4—732no—
316C2×C4⋊C4—1464no—
317C2×C4⋊C4—1464no—
318C2×C4⋊C4—1464no—
319C2×C4⋊C4—1462no—
320C2×C4⋊C4—1462no—
321C2×C4⋊C4—1461no—
322C2×C4⋊C4—1462no—
323C2×C4⋊C4—1462no—
324C2×C4⋊C4—1461no—
325C2×C4⋊C4—1461no—
326C2×C4⋊C4—1461no—
327C2×C4⋊C4—1461no—
328C2×C4⋊C4—1461no—
329C2×C4⋊C4—1461no—
330C2×C4⋊C4C22×D7311yescharacteristic
331C2×C4⋊C4C22×D7312yes—
332C2×C4⋊C4C22×D7311yescharacteristic
333C2×C42—731no—
334C2×C42—731no—
335C2×C42—731no—
336C2×C42—1464no—
337C2×C42C22×D7311yescharacteristic
338#106—24no—
339#106—1464no—
340#106—1464no—
341#106—1464no—
342#95—21no—
343#95—1461no—
344#95—1461no—
345#95—1461no—
346C24—731no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—2922no—
351C22×C4—2922no—
352C22×C4—2924no—
353C22×C4—2922no—
354C22×C4—2924no—
355C22×C4—2924no—
356C22×C4—2922no—
357C22×C4—2922no—
358C22×C4—731no—
359C22×C4—732no—
360C22×C4—734no—
361C22×C4—734no—
362C22×C4—732no—
363C22×C4—731no—
364C22×C4—731no—
365C22×C4—734no—
366C22×C4—734no—
367C22×C4—1464no—
368C22×C4—1462no—
369C22×C4—1462no—
370C22×C4—1462no—
371C22×C4—1462no—
372C22×C4—1461no—
373C22×C4—1462no—
374C22×C4—1461no—
375C22×C4D4×D7311yescharacteristic
376C22×C4D4×D7311yescharacteristic
377C22×C4C23×D7311yescharacteristic
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—734no—
381C2×C8—14616no—
382C2×C8—1462no—
383C2×C8—1462no—
384C2×C8Q8×D7314yes—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—42no—
390C4⋊C4—42no—
391C4⋊C4—42no—
392C4⋊C4—2922no—
393C4⋊C4—2922no—
394C4⋊C4—2924no—
395C4⋊C4—2924no—
396C4⋊C4—2922no—
397C4⋊C4—2922no—
398C4⋊C4—2924no—
399C4⋊C4—2922no—
400C4⋊C4—2922no—
401C4⋊C4—732no—
402C4⋊C4—1464no—
403C4⋊C4—1462no—
404C4⋊C4—1462no—
405C4⋊C4—1462no—
406C4⋊C4—1461no—
407C4⋊C4D4×D7312yes—
408C42—22no—
409C42—1462no—
410C42—1462no—
411C42—1462no—
412C23—732no—
413C23—732no—
414C23—732no—
415C23—732no—
416C23—732no—
417C23—732no—
418C23—732no—
419C23C2×D4×D7311yescharacteristic
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—2928no—
434C2×C4—2921no—
435C2×C4—2921no—
436C2×C4—2922no—
437C2×C4—2921no—
438C2×C4—2921no—
439C2×C4—2922no—
440C2×C4—2922no—
441C2×C4—2921no—
442C2×C4—5844no—
443C2×C4—5848no—
444C2×C4—732no—
445C2×C4—732no—
446C2×C4—732no—
447C2×C4—738no—
448C2×C4—738no—
449C2×C4—732no—
450C2×C4—732no—
451C2×C4—1468no—
452C2×C4—1468no—
453C2×C4—1462no—
454C2×C4—1461no—
455C2×C4—1461no—
456C2×C4—1461no—
457C2×C4—1461no—
458C2×C4SD16×D7312yes—
459C2×C4SD16×D7312yes—
460C2×C4C2×D4×D7311yescharacteristic
461C2×C4C2×Q8×D7312yes—
462C2×C4#41×D7312yes—
463C2×C4#41×D7311yescharacteristic
464C8—24no—
465C8—1464no—
466C22—734no—
467C22—734no—
468C22—734no—
469C22—734no—
470C22—734no—
471C22—734no—
472C22—734no—
473C22#121×D7311yescharacteristic
474C22#123×D7311yescharacteristic
475C22C4⋊Q8×D7311yescharacteristic
476C22C2×SD16×D7311yescharacteristic
477C22C2×SD16×D7311yescharacteristic
478C22AGL(1,ℤ/8)×D7311yescharacteristic
479C22#137×D7311yescharacteristic
480C4—22no—
481C4—22no—
482C4—42no—
483C4—81no—
484C4—82no—
485C4—2922no—
486C4—5841no—
487C4—5842no—
488C4—734no—
489C4—1462no—
490C4—1462no—
491C4C22⋊Q8×D7312yes—
492C4#125×D7312yes—
493C2—738no—
494C2#398×D7311yescharacteristic
495C2#461×D7311yescharacteristic
496C2#460×D7311yescharacteristic
497C2#483×D7311yescharacteristic
498C2#481×D7311yescharacteristic
499C2#498×D7311yescharacteristic
500C2#501×D7311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2084C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
hypercenter#2084D73
hypocenterC73C2×#2084
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
4. #22611411C2semidirect
5. #22611410C2semidirect
6. #22611409C2semidirect
7. #22611408C2semidirect
8. #22611407C2semidirect
11. C73×#2084C2semidirect
250. D73#2084direct (N × H)
259. #2084D73direct (N × H)
262. C73C2×#2084semidirect

Maximal subgroups

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

subgroupindex
C2×#106×D732
#389×D732
#384×D732
#226114112
#226114102
#226114092
#226114082
#226114072
#340×D732
#336×D732
C73×#20842
C2×#208473