Finite Group Databasebeta

← #1920×D73 #33088116

Subgroups — #1920×D73 #33088116

Order 18688.

1086 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#106×D73C211yesmaximal, characteristic
2#389×D73C211yesmaximal, characteristic
3C4×C4⋊C4×D73C211yesmaximal, characteristic
4#22610519C211yesmaximal, characteristic, complemented
5#22610518C211yesmaximal, characteristic, complemented
6#22610517C211yesmaximal, characteristic, complemented
7#22610516C211yesmaximal, characteristic, complemented
8#22610515C211yesmaximal, characteristic, complemented
9#22610514C211yesmaximal, characteristic, complemented
10#22610513C211yesmaximal, characteristic, complemented
11#340×D73C211yesmaximal, characteristic
12#340×D73C211yesmaximal, characteristic
13#340×D73C211yesmaximal, characteristic
14#336×D73C211yesmaximal, characteristic
15C73×#1920C211yesmaximal, characteristic, complemented
16C22×C8×D73C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×C4⋊C4×D73—21no—
19C2×C4⋊C4×D73C2211yescharacteristic
20C2×C4⋊C4×D73C2211yescharacteristic
21C2×C4⋊C4×D73C2211yescharacteristic
22C2×C4⋊C4×D73C2211yescharacteristic
23C2×C42×D73—21no—
24C2×C42×D73C2211yescharacteristic
25C2×#14556523C2211yescharacteristic
26C2×#14556522C2211yescharacteristic
27C2×#14556522C2211yescharacteristic
28#106×D73C418yescomplemented
29#17988486C2211yescharacteristic
30#17988485C2211yescharacteristic
31#17988484—21no—
32#17988483C2211yescharacteristic
33#17988482—21no—
34C4⋊C4×Dic73C2211yescharacteristic
35C4⋊C4×Dic73C2211yescharacteristic
36C4×#11924007—21no—
37C4×C4⋊Dic73C2211yescharacteristic
38#17988438—21no—
39#95×D73—21no—
40#95×D73—21no—
41#17988350C2211yescharacteristic
42#17988350C2211yescharacteristic
43#17988350C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988342C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53C2×#106×C73C2211yescharacteristic
54#389×C73C2211yescharacteristic
55C4×C4⋊C4×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60C22×C4×D73—21no—
61C22×C4×D73—21no—
62C22×C4×D73—21no—
63C22×C4×D73—21no—
64C22×C4×D73D411yescharacteristic
65C22×C4×D73D411yescharacteristic
66C22×C4×D73C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C2×C8×D73—22no—
70C2×C8×D73—22no—
71C2×C8×D73—22no—
72C2×C8×D73—22no—
73C2×C8×D73—22no—
74C2×C8×D73C2×C414yes—
75C2×C4⋊Dic73—21no—
76C2×C4⋊Dic73C2311yescharacteristic
77C2×C4⋊Dic73C2311yescharacteristic
78C2×C4⋊Dic73C2311yescharacteristic
79C2×C4⋊Dic73C2311yescharacteristic
80C2×#11924007—21no—
81C2×#11924007—21no—
82C2×#11924007—21no—
83C2×#11924007—21no—
84C2×#11924007—21no—
85C2×#11924007—21no—
86C4⋊C4×D73—22no—
87C4⋊C4×D73—22no—
88C4⋊C4×D73—22no—
89C4⋊C4×D73—22no—
90C4⋊C4×D73—22no—
91C4⋊C4×D73—44no—
92C4⋊C4×D73C2×C414yes—
93C4⋊C4×D73C2×C414yes—
94C4⋊C4×D73Q814yes—
95C2×C4×Dic73—21no—
96C2×C4×Dic73—21no—
97C2×C4×Dic73—21no—
98C2×C4×Dic73D411yescharacteristic
99C2×C4×Dic73D411yescharacteristic
100C2×C4×Dic73C2311yescharacteristic
101C42×D73—22no—
102C42×D73—22no—
103C42×D73—44no—
104#14556523C2×C414yescomplemented
105#14556522C2×C414yescomplemented
106#14556522C2×C414yescomplemented
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110#14556498—21no—
111#14556498—21no—
112#14556498—21no—
113C22×C8×C73C2311yescharacteristic
114C22×C8×C73C2311yescharacteristic
115C2×C4⋊C4×C73—21no—
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C42×C73—21no—
121C2×C42×C73C2311yescharacteristic
122#106×C73C2×C414yescomplemented
123#95×C73—21no—
124#95×C73—21no—
125C23×D73C2×D411yescharacteristic
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73C2×D411yescharacteristic
131C22×Dic73C2×D411yescharacteristic
132C22×Dic73C2×D411yescharacteristic
133C2×C4×D73—22no—
134C2×C4×D73—22no—
135C2×C4×D73—24no—
136C2×C4×D73—24no—
137C2×C4×D73—24no—
138C2×C4×D73—22no—
139C2×C4×D73—22no—
140C2×C4×D73—22no—
141C2×C4×D73—42no—
142C2×C4×D73—42no—
143C2×C4×D73—42no—
144C2×C4×D73—42no—
145C2×C4×D73—42no—
146C2×C4×D73—42no—
147C2×C4×D73—42no—
148C2×C4×D73—42no—
149C2×C4×D73—42no—
150C2×C4×D73SD1614yes—
151C2×C4×D73C22×C412yes—
152C2×C4×D73C2×Q812yes—
153C2×C4×D73#4112yes—
154C2×C4×D73#4112yes—
155C2×C4×D73#4112yes—
156C2×C4×D73#4112yes—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831C22×C412yes—
163C8×D73—28no—
164C8×D73—44no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73—42no—
171C4⋊Dic73C22×C412yes—
172C4⋊Dic73C22×C412yes—
173C4⋊Dic73C2×Q812yes—
174#11924007—24no—
175#11924007—24no—
176#11924007—24no—
177#11924007—42no—
178#11924007—42no—
179#11924007—42no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—22no—
183C4×Dic73—22no—
184C4×Dic73—42no—
185C4×Dic73—42no—
186C4×Dic73—42no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73C2×D411yescharacteristic
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73C2411yescharacteristic
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73C22×C412yes—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—42no—
206C4⋊C4×C73C22×C412yes—
207C4⋊C4×C73C22×C412yes—
208C4⋊C4×C73C2×Q812yes—
209C42×C73—21no—
210C42×C73—21no—
211C42×C73—42no—
212C23×C73C22×D411yescharacteristic
213C22×D73C4×D412yes—
214C22×D73C22⋊Q812yes—
215C22×D73#12312yes—
216C22×D73C2×SD1612yes—
217C22×D73#13512yes—
218C22×D73AGL(1,ℤ/8)12yes—
219C22×D73#13712yes—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—22no—
223C2×C4×C73—22no—
224C2×C4×C73—22no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73C2×SD1612yes—
238C2×C4×C73C23×C411yescharacteristic
239C2×C4×C73C22×Q811yescharacteristic
240C2×C4×C73C2×#4111yescharacteristic
241C2×C4×C73C2×#4111yescharacteristic
242C2×C4×C73C2×#4111yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—22no—
247C2×Dic73—22no—
248C2×Dic73—22no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—21no—
252C2×Dic73—41no—
253C2×Dic73—41no—
254C2×Dic73—41no—
255C2×Dic73—41no—
256C2×Dic73—41no—
257C2×Dic73—41no—
258C2×Dic73—41no—
259C2×Dic73—41no—
260C2×Dic73—41no—
261C2×Dic73C4×D412yes—
262C2×Dic73C22⋊Q812yes—
263C2×Dic73#12312yes—
264C2×Dic73C2×SD1612yes—
265C4×D73—28no—
266C4×D73—48no—
267C4×D73—48no—
268C4×D73—48no—
269C4×D73—44no—
270C4×D73—84no—
271C4×D73#11714yes—
272C4×D73C4×Q814yes—
273C4×D73#12514yes—
274C4×D73#12614yes—
275C8×C73—22no—
276C8×C73—41no—
277#10596831—22no—
278#10596831—41no—
279C22×C73C2×C4×D411yescharacteristic
280C22×C73C2×C22⋊Q811yescharacteristic
281C22×C73C2×#12311yescharacteristic
282C22×C73C22×SD1611yescharacteristic
283C22×C73C2×#13511yescharacteristic
284C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C73C2×#13711yescharacteristic
286C2×D73#38714yes—
287C2×D73C4×SD1614yes—
288C2×D73#44014yes—
289C2×D73#47614yes—
290C2×D73#47914yes—
291C2×D73#48214yes—
292C2×D73#48314yes—
293C4×C73—22no—
294C4×C73—41no—
295C4×C73—42no—
296C4×C73—42no—
297C4×C73—42no—
298C4×C73—81no—
299C4×C73C2×#11711yescharacteristic
300C4×C73C2×C4×Q811yescharacteristic
301C4×C73C2×#12511yescharacteristic
302C4×C73C2×#12611yescharacteristic
303Dic73—22no—
304Dic73—41no—
305Dic73—42no—
306Dic73—42no—
307Dic73—42no—
308Dic73—81no—
309Dic73#38714yes—
310C2×#1920—731nomaximal, Sylow
311C2×C73C2×#38711yescharacteristic
312C2×C73C2×C4×SD1611yescharacteristic
313C2×C73C2×#44011yescharacteristic
314C2×C73C2×#47611yescharacteristic
315C2×C73C2×#47911yescharacteristic
316C2×C73C2×#48311yescharacteristic
317C2×C73C2×#48211yescharacteristic
318D73#192018yesdirect product factor
319C22×#106—731no—
320C2×#389—731no—
321C2×C4×C4⋊C4—731no—
322#1920—731no—
323#1920—731no—
324#1920—731no—
325#1920—731no—
326#1920—731no—
327#1920—731no—
328#1920—731no—
329#1920D7311yescharacteristic, direct product factor
330C2×#340—731no—
331C2×#340—731no—
332C2×#340—731no—
333C2×#336—731no—
334C73C2×#192011yescharacteristic, complemented, Sylow
335C23×C8—731no—
336C23×C8—731no—
337C22×C4⋊C4—731no—
338C22×C4⋊C4—731no—
339C22×C4⋊C4—731no—
340C22×C4⋊C4—731no—
341C22×C4⋊C4—1461no—
342C22×C42—731no—
343C22×C42—1461no—
344C2×#106—731no—
345C2×#106—731no—
346C2×#106—731no—
347C2×#106—738no—
348C2×#106C2×D7311yescharacteristic
349#389—731no—
350#389—731no—
351#389—731no—
352#389—1461no—
353#389—1461no—
354#389C2×D7311yescharacteristic
355C4×C4⋊C4—731no—
356C4×C4⋊C4—731no—
357C4×C4⋊C4—731no—
358C4×C4⋊C4—1461no—
359C4×C4⋊C4—1461no—
360C4×C4⋊C4C2×D7311yescharacteristic
361C2×#95—1461no—
362C2×#95—1461no—
363#340—731no—
364#340—731no—
365#340—731no—
366#340—731no—
367#340—731no—
368#340—731no—
369#340—731no—
370#340—731no—
371#340—731no—
372#340C2×D7311yescharacteristic
373#340C2×D7311yescharacteristic
374#340C2×D7311yescharacteristic
375#336—731no—
376#336—731no—
377#336—731no—
378#336C2×D7311yescharacteristic
379C23×C4—731no—
380C23×C4—731no—
381C23×C4—731no—
382C23×C4—1461no—
383C23×C4—1461no—
384C23×C4—1461no—
385C23×C4—1461no—
386C22×C8—731no—
387C22×C8—734no—
388C22×C8—731no—
389C22×C8—1462no—
390C22×C8—1462no—
391C22×C8—1462no—
392C22×C8—1462no—
393C22×C8—1462no—
394C22×C8C22×D7311yescharacteristic
395C22×C8C22×D7311yescharacteristic
396C2×C4⋊C4—21no—
397C2×C4⋊C4—2924no—
398C2×C4⋊C4—731no—
399C2×C4⋊C4—731no—
400C2×C4⋊C4—731no—
401C2×C4⋊C4—734no—
402C2×C4⋊C4—734no—
403C2×C4⋊C4—734no—
404C2×C4⋊C4—731no—
405C2×C4⋊C4—1462no—
406C2×C4⋊C4—1462no—
407C2×C4⋊C4—1462no—
408C2×C4⋊C4—1462no—
409C2×C4⋊C4—1462no—
410C2×C4⋊C4—1461no—
411C2×C4⋊C4—1461no—
412C2×C4⋊C4—1461no—
413C2×C4⋊C4—1461no—
414C2×C4⋊C4—1461no—
415C2×C4⋊C4—1461no—
416C2×C4⋊C4—1461no—
417C2×C4⋊C4C22×D7311yescharacteristic
418C2×C4⋊C4C22×D7311yescharacteristic
419C2×C4⋊C4C22×D7311yescharacteristic
420C2×C4⋊C4C22×D7311yescharacteristic
421C2×C42—21no—
422C2×C42—2924no—
423C2×C42—731no—
424C2×C42—731no—
425C2×C42—731no—
426C2×C42—1462no—
427C2×C42—1462no—
428C2×C42—1461no—
429C2×C42—1461no—
430C2×C42—1461no—
431C2×C42C22×D7311yescharacteristic
432#106—734no—
433#106—734no—
434#106—734no—
435#106C4×D7314yescomplemented
436#95—21no—
437#95—21no—
438#95—1461no—
439#95—1461no—
440#95—1461no—
441#95—1461no—
442#95—1461no—
443#95—1461no—
444C24—731no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—2922no—
450C22×C4—2922no—
451C22×C4—2922no—
452C22×C4—2922no—
453C22×C4—2922no—
454C22×C4—2922no—
455C22×C4—2922no—
456C22×C4—2922no—
457C22×C4—2922no—
458C22×C4—731no—
459C22×C4—732no—
460C22×C4—732no—
461C22×C4—732no—
462C22×C4—732no—
463C22×C4—732no—
464C22×C4—732no—
465C22×C4—731no—
466C22×C4—734no—
467C22×C4—731no—
468C22×C4—1462no—
469C22×C4—1462no—
470C22×C4—1464no—
471C22×C4—1464no—
472C22×C4—1464no—
473C22×C4—1462no—
474C22×C4—1462no—
475C22×C4—1462no—
476C22×C4—1461no—
477C22×C4—1461no—
478C22×C4—1461no—
479C22×C4—1461no—
480C22×C4D4×D7311yescharacteristic
481C22×C4D4×D7311yescharacteristic
482C22×C4C23×D7311yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—2924no—
489C2×C8—732no—
490C2×C8—1468no—
491C2×C8—1461no—
492C2×C8—1461no—
493C2×C8—1461no—
494C2×C8—1461no—
495C2×C8—1461no—
496C2×C8C2×C4×D7312yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—2922no—
504C4⋊C4—2922no—
505C4⋊C4—2922no—
506C4⋊C4—2922no—
507C4⋊C4—732no—
508C4⋊C4—732no—
509C4⋊C4—732no—
510C4⋊C4—1464no—
511C4⋊C4—1464no—
512C4⋊C4—1464no—
513C4⋊C4—1461no—
514C4⋊C4—1461no—
515C4⋊C4—1461no—
516C4⋊C4—1461no—
517C4⋊C4—1461no—
518C4⋊C4C2×C4×D7312yes—
519C4⋊C4C2×C4×D7312yes—
520C4⋊C4Q8×D7312yes—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—2922no—
525C42—2922no—
526C42—2922no—
527C42—1462no—
528C42—1462no—
529C42—1461no—
530C42—1461no—
531C23—732no—
532C23—732no—
533C23—732no—
534C23—732no—
535C23—732no—
536C23—732no—
537C23—732no—
538C23C2×D4×D7311yescharacteristic
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—2928no—
557C2×C4—2928no—
558C2×C4—2928no—
559C2×C4—2924no—
560C2×C4—2921no—
561C2×C4—2921no—
562C2×C4—2921no—
563C2×C4—2921no—
564C2×C4—2921no—
565C2×C4—2921no—
566C2×C4—2921no—
567C2×C4—2921no—
568C2×C4—2921no—
569C2×C4—5844no—
570C2×C4—732no—
571C2×C4—732no—
572C2×C4—732no—
573C2×C4—734no—
574C2×C4—734no—
575C2×C4—734no—
576C2×C4—734no—
577C2×C4—732no—
578C2×C4—1468no—
579C2×C4—1462no—
580C2×C4—1462no—
581C2×C4—1462no—
582C2×C4—1461no—
583C2×C4—1461no—
584C2×C4—1461no—
585C2×C4—1461no—
586C2×C4—1461no—
587C2×C4SD16×D7312yes—
588C2×C4C22×C4×D7311yescharacteristic
589C2×C4C2×Q8×D7311yescharacteristic
590C2×C4#41×D7311yescharacteristic
591C2×C4#41×D7311yescharacteristic
592C2×C4#41×D7311yescharacteristic
593C2×C4#41×D7311yescharacteristic
594C8—22no—
595C8—41no—
596C8—2921no—
597C8—1462no—
598C22—734no—
599C22—734no—
600C22—734no—
601C22—734no—
602C22—734no—
603C22—734no—
604C22—734no—
605C22C4×D4×D7311yescharacteristic
606C22C22⋊Q8×D7311yescharacteristic
607C22#123×D7311yescharacteristic
608C22C2×SD16×D7311yescharacteristic
609C22#135×D7311yescharacteristic
610C22AGL(1,ℤ/8)×D7311yescharacteristic
611C22#137×D7311yescharacteristic
612C4—22no—
613C4—42no—
614C4—42no—
615C4—42no—
616C4—41no—
617C4—81no—
618C4—2922no—
619C4—2922no—
620C4—2922no—
621C4—2921no—
622C4—5841no—
623C4—734no—
624C4—1462no—
625C4#117×D7311yescharacteristic
626C4C4×Q8×D7311yescharacteristic
627C4#125×D7311yescharacteristic
628C4#126×D7311yescharacteristic
629C2—738no—
630C2#387×D7311yescharacteristic
631C2C4×SD16×D7311yescharacteristic
632C2#440×D7311yescharacteristic
633C2#476×D7311yescharacteristic
634C2#479×D7311yescharacteristic
635C2#483×D7311yescharacteristic
636C2#482×D7311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1920C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
cosocleC22×C4×C73C24
hypercenter#1920D73
hypocenterC73C2×#1920
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
4. #22610519C2semidirect
5. #22610518C2semidirect
6. #22610517C2semidirect
7. #22610516C2semidirect
8. #22610515C2semidirect
9. #22610514C2semidirect
10. #22610513C2semidirect
15. C73×#1920C2semidirect
28. #106×D73C4semidirect
104. #14556523C2×C4semidirect
105. #14556522C2×C4semidirect
106. #14556522C2×C4semidirect
122. #106×C73C2×C4semidirect
318. D73#1920direct (N × H)
329. #1920D73direct (N × H)
334. C73C2×#1920semidirect
435. #106C4×D73semidirect

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
C4×C4⋊C4×D732
#226105192
#226105182
#226105172
#226105162
#226105152
#226105142
#226105132
#340×D732
#336×D732
C73×#19202
C2×#192073