Finite Group Databasebeta

← #1809×D73 #33085553

Subgroups — #1809×D73 #33085553

Order 18688.

1662 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D73C211yesmaximal, characteristic
2C2×#107×D73C211yesmaximal, characteristic, complemented
3C2×#106×D73C211yesmaximal, characteristic, complemented
4#380×D73C212yesmaximal
5#22609965C211yesmaximal, characteristic, complemented
6#22609964C211yesmaximal, characteristic, complemented
7#22609963C212yesmaximal, complemented
8#22609962C212yesmaximal, complemented
9#22609961C211yesmaximal, characteristic, complemented
10#340×D73C212yesmaximal, complemented
11C73×#1809C211yesmaximal, characteristic, complemented
12C23×C4×D73C2211yescharacteristic
13C22×#11924012C2211yescharacteristic
14C22×#11924011C2211yescharacteristic
15C22×#11924011C2211yescharacteristic
16C2×M16×D73—24no—
17C2×M16×D73—24no—
18C2×M16×D73C418yescomplemented
19C22×C8×D73C2211yescharacteristic
20C22×C8×D73C2211yescharacteristic
21C2×C4⋊C4×D73C2212yes—
22C2×C4⋊C4×D73C2212yes—
23C2×C22⋊C4×D73—22no—
24C2×#14556525C2211yescharacteristic, complemented
25C2×#14556524C2212yescomplemented
26#107×D73—24no—
27C2×#14556523C2211yescharacteristic, complemented
28C2×#14556522C2212yescomplemented
29#106×D73—24no—
30#17988447C2212yes—
31#17988446—22no—
32#17988445—22no—
33#17988444C2212yes—
34#17988444C2212yes—
35#95×D73—22no—
36#17988350C2212yescomplemented
37#17988349C2212yescomplemented
38#17988349C2212yescomplemented
39C22×M16×C73C2211yescharacteristic
40C2×#107×C73C2211yescharacteristic, complemented
41C2×#106×C73C2211yescharacteristic, complemented
42#380×C73C2212yes—
43#340×C73C2212yescomplemented
44C24×D73D411yescharacteristic
45C23×Dic73D411yescharacteristic
46C22×C4×D73—22no—
47C22×C4×D73—22no—
48C22×C4×D73—22no—
49C22×C4×D73—22no—
50C22×C4×D73—22no—
51C22×C4×D73—22no—
52C22×C4×D73C2×C414yes—
53C22×C4×D73D411yescharacteristic
54C22×C4×D73D411yescharacteristic
55C22×C4×D73Q814yes—
56C22×C4×D73C2311yescharacteristic
57C22×C4×D73C2311yescharacteristic
58C2×#11924012—22no—
59C2×#11924012—22no—
60C2×#11924012C2×C414yescomplemented
61C2×#11924011—22no—
62C2×#11924011—22no—
63C2×#11924011—22no—
64C2×#11924011—22no—
65C2×#11924011C2×C414yescomplemented
66C2×#11924011C2×C414yescomplemented
67M16×D73—232no—
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C2×C8×D73—22no—
71C2×C8×D73—22no—
72C2×C8×D73C2×C414yes—
73C2×C8×D73C2×C414yes—
74C2×C8×D73D414yes—
75C2×C8×D73D414yes—
76C2×C4⋊Dic73C2312yes—
77C2×C4⋊Dic73C2312yes—
78C2×#11924007—22no—
79C2×#11924007—22no—
80C4⋊C4×D73—24no—
81C4⋊C4×D73—24no—
82C4⋊C4×D73—24no—
83C4⋊C4×D73—24no—
84C2×C22⋊Dic73—22no—
85C2×#11924005—22no—
86C2×#11924005—22no—
87C22⋊C4×D73—48no—
88#14556525—22no—
89#14556524—24no—
90#14556523—22no—
91#14556522—24no—
92#14556498—22no—
93#14556498—22no—
94#14556498—22no—
95C23×C4×C73C2311yescharacteristic
96C2×M16×C73—22no—
97C2×M16×C73—22no—
98C2×M16×C73C2×C414yescomplemented
99C22×C8×C73C2311yescharacteristic
100C22×C8×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2312yes—
102C2×C4⋊C4×C73C2312yes—
103C2×C22⋊C4×C73—22no—
104#107×C73—22no—
105#106×C73—22no—
106#95×C73—22no—
107C23×D73—22no—
108C23×D73—22no—
109C23×D73—24no—
110C23×D73—24no—
111C23×D73C4⋊C414yes—
112C23×D73C2×D411yescharacteristic
113C23×D73C2×D411yescharacteristic
114C22×Dic73—22no—
115C22×Dic73—22no—
116C22×Dic73—22no—
117C22×Dic73—22no—
118C22×Dic73C4⋊C414yes—
119C22×Dic73C2×D411yescharacteristic
120C22×Dic73C2×D411yescharacteristic
121C2×C4×D73—22no—
122C2×C4×D73—22no—
123C2×C4×D73—21no—
124C2×C4×D73—21no—
125C2×C4×D73—21no—
126C2×C4×D73—21no—
127C2×C4×D73—22no—
128C2×C4×D73—22no—
129C2×C4×D73—28no—
130C2×C4×D73—28no—
131C2×C4×D73—28no—
132C2×C4×D73—28no—
133C2×C4×D73—44no—
134C2×C4×D73—44no—
135C2×C4×D73—44no—
136C2×C4×D73—44no—
137C2×C4×D73—44no—
138C2×C4×D73—44no—
139C2×C4×D73C4⋊C414yes—
140C2×C4×D73C4⋊C414yes—
141C2×C4×D73C22×C412yes—
142C2×C4×D73C22×C412yes—
143C2×C4×D73C2×D412yes—
144C2×C4×D73C2×D412yes—
145C2×C4×D73C2×Q812yes—
146C2×C4×D73C2×Q812yes—
147C2×C4×D73#4112yes—
148C2×C4×D73#4112yes—
149#11924012—28no—
150#11924011—28no—
151#11924011—28no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831C22×C412yes—
155C2×#10596831C22×C412yes—
156C2×#10596831C2×D412yes—
157C2×#10596831C2×D412yes—
158C8×D73—28no—
159C8×D73C22⋊C4116yescomplemented
160C4⋊Dic73—22no—
161C4⋊Dic73—22no—
162C4⋊Dic73—22no—
163C4⋊Dic73—22no—
164#11924007—44no—
165#11924007—44no—
166C22⋊Dic73—44no—
167#11924005—44no—
168#11924005—44no—
169C24×C73C2×D411yescharacteristic
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—22no—
175C22×C4×C73—22no—
176C22×C4×C73C22×C412yes—
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×Q812yes—
179C22×C4×C73C2411yescharacteristic
180M16×C73—28no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73C22×C412yes—
184C2×C8×C73C22×C412yes—
185C2×C8×C73C2×D412yes—
186C2×C8×C73C2×D412yes—
187C4⋊C4×C73—22no—
188C4⋊C4×C73—22no—
189C4⋊C4×C73—22no—
190C4⋊C4×C73—22no—
191C22⋊C4×C73—44no—
192C23×C73—21no—
193C23×C73—21no—
194C23×C73—22no—
195C23×C73—22no—
196C23×C73C2×C4⋊C412yes—
197C23×C73C22×D411yescharacteristic
198C22×D73—21no—
199C22×D73—21no—
200C22×D73—22no—
201C22×D73—22no—
202C22×D73—28no—
203C22×D73—216no—
204C22×D73—48no—
205C22×D73—44no—
206C22×D73—44no—
207C22×D73C2×C4⋊C412yes—
208C22×D73C2×C4⋊C412yes—
209C22×D73#12112yes—
210C22×D73#12112yes—
211C22×D73AGL(1,ℤ/8)14yes—
212C22×D73#13714yes—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—22no—
216C2×C4×C73—22no—
217C2×C4×C73—22no—
218C2×C4×C73—22no—
219C2×C4×C73—42no—
220C2×C4×C73—42no—
221C2×C4×C73—42no—
222C2×C4×C73—42no—
223C2×C4×C73—42no—
224C2×C4×C73—42no—
225C2×C4×C73C2×C4⋊C412yes—
226C2×C4×C73C23×C411yescharacteristic
227C2×C4×C73C22×D411yescharacteristic
228C2×C4×C73C22×D411yescharacteristic
229C2×C4×C73C22×Q811yescharacteristic
230C2×C4×C73C2×#4111yescharacteristic
231C2×C4×C73C2×#4111yescharacteristic
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—28no—
235C2×Dic73—42no—
236C2×Dic73—42no—
237C2×Dic73—42no—
238C2×Dic73—42no—
239C2×Dic73—42no—
240C2×Dic73—42no—
241C2×Dic73C2×C4⋊C412yes—
242C2×Dic73C2×C4⋊C412yes—
243C2×Dic73#12112yes—
244C2×Dic73#12112yes—
245C4×D73—28no—
246C4×D73—22no—
247C4×D73—22no—
248C4×D73—22no—
249C4×D73—22no—
250C4×D73—28no—
251C4×D73—88no—
252C4×D73—88no—
253C4×D73C2×C22⋊C414yes—
254C4×D73#11714yes—
255C4×D73C22⋊Q814yes—
256C4×D73C22⋊Q814yes—
257C8×C73—22no—
258C8×C73C2×C22⋊C414yescomplemented
259#10596831—22no—
260#10596831C2×C22⋊C414yescomplemented
261C22×C73—24no—
262C22×C73—22no—
263C22×C73—42no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73C22×C4⋊C411yescharacteristic
267C22×C73C2×#12111yescharacteristic
268C22×C73C2×#12111yescharacteristic
269C22×C73C2×AGL(1,ℤ/8)12yes—
270C22×C73C2×#13712yes—
271C2×D73—24no—
272C2×D73—22no—
273C2×D73—42no—
274C2×D73—41no—
275C2×D73—41no—
276C2×D73—416no—
277C2×D73#38014yes—
278C2×D73#42818yes—
279C2×D73#46818yes—
280C2×D73#46914yes—
281C2×D73#47014yes—
282C4×C73—22no—
283C4×C73—82no—
284C4×C73—82no—
285C4×C73C22×C22⋊C411yescharacteristic
286C4×C73C2×#11711yescharacteristic
287C4×C73C2×C22⋊Q811yescharacteristic
288C4×C73C2×C22⋊Q811yescharacteristic
289Dic73—22no—
290Dic73—82no—
291Dic73—82no—
292Dic73#38014yes—
293C2×#1809—731nomaximal, Sylow
294C2×C73—42no—
295C2×C73C2×#38011yescharacteristic
296C2×C73C2×#42812yes—
297C2×C73C2×#46812yes—
298C2×C73C2×#46911yescharacteristic
299C2×C73C2×#47011yescharacteristic
300D73—42no—
301D73#180918yesdirect product factor
302C23×M16—731no—
303C22×#107—731no—
304C22×#106—731no—
305C2×#380—732no—
306#1809—731no—
307#1809—731no—
308#1809—732no—
309#1809—732no—
310#1809—731no—
311#1809D7311yescharacteristic, direct product factor
312C2×#340—732no—
313C73C2×#180911yescharacteristic, complemented, Sylow
314C24×C4—731no—
315C22×M16—731no—
316C22×M16—738no—
317C22×M16—731no—
318C22×M16—731no—
319C22×M16—1464no—
320C22×M16—1464no—
321C22×M16C2×D7311yescharacteristic
322C23×C8—731no—
323C23×C8—731no—
324C22×C4⋊C4—732no—
325C22×C4⋊C4—732no—
326C22×C22⋊C4—1462no—
327C2×#107—731no—
328C2×#107—732no—
329C2×#107—1464no—
330C2×#107C2×D7311yescharacteristic, complemented
331C2×#106—731no—
332C2×#106—732no—
333C2×#106—1464no—
334C2×#106C2×D7311yescharacteristic, complemented
335#380—732no—
336#380—732no—
337#380—732no—
338#380—1462no—
339#380—1462no—
340#380C2×D7312yes—
341C2×#95—1462no—
342#340—732no—
343#340—732no—
344#340—732no—
345#340C2×D7312yescomplemented
346C25—731no—
347C23×C4—731no—
348C23×C4—731no—
349C23×C4—734no—
350C23×C4—731no—
351C23×C4—731no—
352C23×C4—734no—
353C23×C4—731no—
354C23×C4—1462no—
355C23×C4—1462no—
356C23×C4—1462no—
357C23×C4—1462no—
358C23×C4—1462no—
359C23×C4—1462no—
360C23×C4C22×D7311yescharacteristic
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—734no—
364C2×M16—734no—
365C2×M16—734no—
366C2×M16—1462no—
367C2×M16—1462no—
368C2×M16—14632no—
369C2×M16—1462no—
370C2×M16—1462no—
371C2×M16—1462no—
372C2×M16—1462no—
373C2×M16C4×D7314yescomplemented
374C22×C8—731no—
375C22×C8—734no—
376C22×C8—734no—
377C22×C8—734no—
378C22×C8—731no—
379C22×C8—734no—
380C22×C8—1462no—
381C22×C8—1462no—
382C22×C8C22×D7311yescharacteristic
383C22×C8C22×D7311yescharacteristic
384C2×C4⋊C4—732no—
385C2×C4⋊C4—732no—
386C2×C4⋊C4—1464no—
387C2×C4⋊C4—1464no—
388C2×C4⋊C4—1464no—
389C2×C4⋊C4—1464no—
390C2×C4⋊C4—1462no—
391C2×C4⋊C4—1462no—
392C2×C4⋊C4C22×D7312yes—
393C2×C4⋊C4C22×D7312yes—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—2928no—
396C2×C22⋊C4—1462no—
397C2×C22⋊C4—1462no—
398C2×C22⋊C4—1462no—
399#107—22no—
400#107—1464no—
401#107—1462no—
402#106—22no—
403#106—1464no—
404#106—1462no—
405#95—22no—
406#95—1462no—
407#95—1462no—
408#95—1462no—
409C24—731no—
410C24—734no—
411C24—731no—
412C24—1464no—
413C24—1462no—
414C24—1462no—
415C24—1464no—
416C24D4×D7311yescharacteristic
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—2924no—
424C22×C4—2924no—
425C22×C4—2924no—
426C22×C4—2924no—
427C22×C4—2924no—
428C22×C4—2924no—
429C22×C4—731no—
430C22×C4—732no—
431C22×C4—732no—
432C22×C4—732no—
433C22×C4—732no—
434C22×C4—732no—
435C22×C4—732no—
436C22×C4—734no—
437C22×C4—731no—
438C22×C4—734no—
439C22×C4—734no—
440C22×C4—732no—
441C22×C4—732no—
442C22×C4—1468no—
443C22×C4—1462no—
444C22×C4—1462no—
445C22×C4—1468no—
446C22×C4—1468no—
447C22×C4—1468no—
448C22×C4—1462no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4—1462no—
452C22×C4—1462no—
453C22×C4—1462no—
454C22×C4—1461no—
455C22×C4—1461no—
456C22×C4—1461no—
457C22×C4—1461no—
458C22×C4C2×C4×D7312yes—
459C22×C4D4×D7311yescharacteristic
460C22×C4Q8×D7312yes—
461C22×C4C23×D7311yescharacteristic
462M16—28no—
463M16—1468no—
464M16—1468no—
465M16—1468no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—732no—
469C2×C8—732no—
470C2×C8—732no—
471C2×C8—7316no—
472C2×C8—732no—
473C2×C8—1468no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8C2×C4×D7312yes—
477C2×C8C2×C4×D7312yes—
478C2×C8D4×D7312yes—
479C2×C8D4×D7312yes—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—2924no—
485C4⋊C4—2924no—
486C4⋊C4—1462no—
487C4⋊C4—1462no—
488C4⋊C4—1462no—
489C4⋊C4—1462no—
490C22⋊C4—44no—
491C22⋊C4—2924no—
492C22⋊C4—2924no—
493C22⋊C4—2924no—
494C23—22no—
495C23—21no—
496C23—21no—
497C23—22no—
498C23—2928no—
499C23—2924no—
500C23—2924no—
501C23—734no—
502C23—732no—
503C23—732no—
504C23—732no—
505C23—734no—
506C23—732no—
507C23—1468no—
508C23—14616no—
509C23—1462no—
510C23—1461no—
511C23—1461no—
512C23—1462no—
513C23C4⋊C4×D7312yes—
514C23C2×D4×D7311yescharacteristic
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—2922no—
528C2×C4—2922no—
529C2×C4—2922no—
530C2×C4—2922no—
531C2×C4—2922no—
532C2×C4—2922no—
533C2×C4—5848no—
534C2×C4—5848no—
535C2×C4—732no—
536C2×C4—732no—
537C2×C4—732no—
538C2×C4—734no—
539C2×C4—734no—
540C2×C4—734no—
541C2×C4—734no—
542C2×C4—732no—
543C2×C4—1468no—
544C2×C4—1468no—
545C2×C4—1468no—
546C2×C4—1461no—
547C2×C4—1461no—
548C2×C4—1462no—
549C2×C4—1462no—
550C2×C4—1462no—
551C2×C4—1462no—
552C2×C4C4⋊C4×D7312yes—
553C2×C4C22×C4×D7311yescharacteristic
554C2×C4C2×D4×D7311yescharacteristic
555C2×C4C2×D4×D7311yescharacteristic
556C2×C4C2×Q8×D7311yescharacteristic
557C2×C4#41×D7311yescharacteristic
558C2×C4#41×D7311yescharacteristic
559C8—22no—
560C8—734no—
561C8—1462no—
562C8C22⋊C4×D7314yescomplemented
563C22—22no—
564C22—24no—
565C22—42no—
566C22—41no—
567C22—41no—
568C22—29216no—
569C22—2922no—
570C22—2921no—
571C22—2921no—
572C22—734no—
573C22—738no—
574C22—734no—
575C22—734no—
576C22—738no—
577C22—1462no—
578C22—1464no—
579C22C2×C4⋊C4×D7311yescharacteristic
580C22#121×D7311yescharacteristic
581C22#121×D7311yescharacteristic
582C22AGL(1,ℤ/8)×D7312yes—
583C22#137×D7312yes—
584C4—22no—
585C4—82no—
586C4—82no—
587C4—5842no—
588C4—5842no—
589C4—734no—
590C4—1462no—
591C4C2×C22⋊C4×D7311yescharacteristic
592C4#117×D7311yescharacteristic
593C4C22⋊Q8×D7311yescharacteristic
594C4C22⋊Q8×D7311yescharacteristic
595C2—42no—
596C2—2922no—
597C2—738no—
598C2#380×D7311yescharacteristic
599C2#428×D7312yes—
600C2#468×D7312yes—
601C2#469×D7311yescharacteristic
602C2#470×D7311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1809C2
socleC23×C73C22×D4
prime radicalC24×D73D4
cosocleC22×C4×C73C24
hypercenter#1809D73
hypocenterC73C2×#1809
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#107×D73C2semidirect
3. C2×#106×D73C2semidirect
5. #22609965C2semidirect
6. #22609964C2semidirect
7. #22609963C2semidirect
8. #22609962C2semidirect
9. #22609961C2semidirect
10. #340×D73C2semidirect
11. C73×#1809C2semidirect
18. C2×M16×D73C4semidirect
24. C2×#14556525C22semidirect
25. C2×#14556524C22semidirect
27. C2×#14556523C22semidirect
28. C2×#14556522C22semidirect
36. #17988350C22semidirect
37. #17988349C22semidirect
38. #17988349C22semidirect
40. C2×#107×C73C22semidirect
41. C2×#106×C73C22semidirect
43. #340×C73C22semidirect
60. C2×#11924012C2×C4semidirect
65. C2×#11924011C2×C4semidirect
66. C2×#11924011C2×C4semidirect
98. C2×M16×C73C2×C4semidirect
159. C8×D73C22⋊C4semidirect
258. C8×C73C2×C22⋊C4semidirect
260. #10596831C2×C22⋊C4semidirect
301. D73#1809direct (N × H)
311. #1809D73direct (N × H)
313. C73C2×#1809semidirect
330. C2×#107C2×D73semidirect
334. C2×#106C2×D73semidirect
345. #340C2×D73semidirect
373. C2×M16C4×D73semidirect
562. C8C22⋊C4×D73semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D732
C2×#107×D732
C2×#106×D732
#380×D732
#226099652
#226099642
#226099632
#226099622
#226099612
#340×D732
C73×#18092
C2×#180973