Finite Group Databasebeta

← #33051906

Subgroups — #33051906

Order 18688.

1206 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
1C2×#17989068C211yesmaximal, characteristic
2#22618970C212yesmaximal, complemented
3#22608268C212yesmaximal, complemented
4#22608267C212yesmaximal, complemented
5#22608261C211yesmaximal, characteristic, complemented
6#22608259C212yesmaximal, complemented
7#22608253C212yesmaximal, complemented
8#22608244C212yesmaximal, complemented
9C73×#1463C211yesmaximal, characteristic, complemented
10C22×#11924028C411yescharacteristic
11#17989068—24no—
12#17989068—24no—
13C2×#14556556C411yescharacteristic
14C2×#14556556C2211yescharacteristic
15C2×#14556553C411yescharacteristic
16C2×#14556553C2211yescharacteristic
17C2×C4×C22⋊D73C411yescharacteristic
18C2×C4×C22⋊D73C411yescharacteristic
19C2×C4×C22⋊D73C2211yescharacteristic
20C2×C4×C22⋊D73C2211yescharacteristic
21C2×#14556550C411yescharacteristic
22C2×#14556549C411yescharacteristic
23C2×#14556549C2211yescharacteristic
24C2×C4⋊C4×D73C411yescharacteristic
25C2×C4⋊C4×D73C2211yescharacteristic
26#17988663—24no—
27#17988662—24no—
28#17988637C2214yes—
29#17988551C2212yes—
30#17988549C2214yes—
31#17988313C2212yes—
32#17988313C2212yes—
33#17988312C2214yes—
34#17988310C2214yes—
35C22×C4⋊C4×C73C2211yescharacteristic
36#407×C73C2212yes—
37#324×C73C2212yes—
38#324×C73C2212yes—
39C2×#11924028—24no—
40C2×#11924028—22no—
41C2×#11924028—22no—
42C2×#11924028—24no—
43C22×Dic146C2×C411yescharacteristic
44C22×D292C2×C411yescharacteristic
45C22×C22⋊D73C2×C411yescharacteristic
46C22×C22⋊D73C2×C411yescharacteristic
47C22×C4×D73C2×C411yescharacteristic
48C22×C4×D73C2×C411yescharacteristic
49C22×C4×D73C2×C411yescharacteristic
50C22×C4×D73C2×C411yescharacteristic
51C22×C4×D73C2×C411yescharacteristic
52C22×C4×D73C2311yescharacteristic
53C2×#11924012—22no—
54C2×#11924011—24no—
55#14556556—24no—
56#14556556—24no—
57#14556553—24no—
58#14556553—24no—
59C4×C22⋊D73—22no—
60C4×C22⋊D73—22no—
61C4×C22⋊D73—22no—
62C4×C22⋊D73—22no—
63C4×C22⋊D73—22no—
64C4×C22⋊D73—22no—
65C4×C22⋊D73D414yes—
66C4×C22⋊D73D414yes—
67#14556550—22no—
68#14556550—22no—
69#14556549—24no—
70#14556549—24no—
71C2×C4⋊Dic73C2×C411yescharacteristic
72C2×C4⋊Dic73C2×C411yescharacteristic
73C2×#11924007C2×C411yescharacteristic
74C2×#11924007C2×C411yescharacteristic
75C2×#11924007C2×C411yescharacteristic
76C2×#11924007C2311yescharacteristic
77C4⋊C4×D73—24no—
78C4⋊C4×D73—24no—
79C2×C22⋊Dic73C2×C411yescharacteristic
80C2×C22⋊Dic73C2×C411yescharacteristic
81C2×#11924005C2×C411yescharacteristic
82C2×#11924005C2×C411yescharacteristic
83C2×#11924005C2×C411yescharacteristic
84C2×#11924005C2311yescharacteristic
85C2×C4×Dic73C2×C411yescharacteristic
86C2×C4×Dic73C2×C411yescharacteristic
87C2×C4×Dic73C2×C411yescharacteristic
88C2×C4×Dic73C2×C411yescharacteristic
89C2×C4×Dic73C2×C411yescharacteristic
90C2×C4×Dic73C2311yescharacteristic
91#14556520—24no—
92C22⋊#10596831—22no—
93C22⋊#10596831C2314yes—
94#14556503—24no—
95C8×Dic73—24no—
96C23×C4×C73C2×C411yescharacteristic
97C23×C4×C73C2×C411yescharacteristic
98C23×C4×C73C2311yescharacteristic
99C2×M16×C73—22no—
100C2×C4⋊C4×C73—22no—
101C2×C4⋊C4×C73—22no—
102C2×C4⋊C4×C73C2×C411yescharacteristic
103C2×C4⋊C4×C73C2×C411yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C22⋊C8×C73—22no—
107C22⋊C8×C73C2314yes—
108C23×D73C22×C411yescharacteristic
109C23×D73C22×C411yescharacteristic
110#11924028—216no—
111#11924028—216no—
112C2×Dic146—22no—
113C2×Dic146—22no—
114C2×Dic146M1614yescomplemented
115C2×D292—22no—
116C2×D292—22no—
117C2×D292—22no—
118C2×C22⋊D73—21no—
119C2×C22⋊D73—21no—
120C2×C22⋊D73—22no—
121C2×C22⋊D73—22no—
122C2×C22⋊D73—22no—
123C2×C22⋊D73—22no—
124C2×C22⋊D73C22⋊C412yes—
125C2×C22⋊D73C22⋊C412yes—
126C22×Dic73C22×C411yescharacteristic
127C22×Dic73C22×C411yescharacteristic
128C22×Dic73C22×C411yescharacteristic
129C22×Dic73C22×C411yescharacteristic
130C22×Dic73C22×C411yescharacteristic
131C22×Dic73C22×C411yescharacteristic
132C2×C4×D73—22no—
133C2×C4×D73—22no—
134C2×C4×D73—22no—
135C2×C4×D73—22no—
136C2×C4×D73—22no—
137C2×C4×D73—22no—
138C2×C4×D73—22no—
139C2×C4×D73—22no—
140C2×C4×D73—81no—
141C2×C4×D73—81no—
142C2×C4×D73—81no—
143C2×C4×D73—81no—
144C2×C4×D73M1614yescomplemented
145C2×C4×D73C2×D414yes—
146#11924012—82no—
147#11924011—84no—
148C2×#10596831—24no—
149C4⋊Dic73—22no—
150C4⋊Dic73—22no—
151#11924007—22no—
152#11924007—22no—
153#11924007—22no—
154#11924007C22⋊C414yes—
155C22⋊Dic73—21no—
156C22⋊Dic73—21no—
157C22⋊Dic73C22⋊C412yes—
158C22⋊Dic73C22⋊C412yes—
159#11924005—22no—
160#11924005—22no—
161#11924005—22no—
162#11924005C22⋊C414yes—
163C4×Dic73—22no—
164C4×Dic73—22no—
165C4×Dic73—22no—
166C4×Dic73—22no—
167C4×Dic73—22no—
168C4×Dic73C2×D414yes—
169C24×C73C22×C411yescharacteristic
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—22no—
173C22×C4×C73—22no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—81no—
177C22×C4×C73—81no—
178C22×C4×C73C22×C411yescharacteristic
179C22×C4×C73C22×C411yescharacteristic
180C22×C4×C73C22×C411yescharacteristic
181C22×C4×C73C22×C411yescharacteristic
182C22×C4×C73C22×C411yescharacteristic
183C22×C4×C73C2×D412yes—
184C22×C4×C73C2×D412yes—
185C22×C4×C73C2411yescharacteristic
186M16×C73—82no—
187C2×C8×C73—24no—
188C4⋊C4×C73—22no—
189C4⋊C4×C73—22no—
190C4⋊C4×C73—22no—
191C4⋊C4×C73—22no—
192C23×C73—21no—
193C23×C73—21no—
194C23×C73—41no—
195C23×C73—41no—
196C23×C73C2×C22⋊C411yescharacteristic
197C23×C73C2×C22⋊C411yescharacteristic
198C23×C73C23×C411yescharacteristic
199C22×D73—21no—
200C22×D73—21no—
201C22×D73—21no—
202C22×D73—21no—
203C22×D73—41no—
204C22×D73—41no—
205C22×D73—41no—
206C22×D73—41no—
207C22×D73C2×C22⋊C412yes—
208C22×D73C2×M1612yes—
209C2×C4×C73—24no—
210C2×C4×C73—24no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—42no—
218C2×C4×C73—41no—
219C2×C4×C73—42no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73—81no—
224C2×C4×C73—81no—
225C2×C4×C73C2×C22⋊C412yes—
226C2×C4×C73C2×M1612yes—
227C2×C4×C73C2×M1612yes—
228C2×C4×C73C22×D412yes—
229C22⋊D73—24no—
230C22⋊D73—24no—
231C22⋊D73—24no—
232C22⋊D73—24no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—41no—
238C2×Dic73—41no—
239C2×Dic73—41no—
240C2×Dic73—41no—
241C2×Dic73C2×C22⋊C412yes—
242C2×Dic73C2×C22⋊C412yes—
243C2×Dic73C2×C22⋊C412yes—
244C2×Dic73C2×M1612yes—
245C2×Dic73C2×M1612yes—
246C2×Dic73C2×M1612yes—
247D292—28no—
248C4×D73—28no—
249C4×D73—28no—
250C4×D73—44no—
251C4×D73—82no—
252C4×D73—82no—
253C4×D73—82no—
254Dic146—28no—
255C8×C73—44no—
256#10596831—44no—
257C22×C73—21no—
258C22×C73—21no—
259C22×C73—21no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—21no—
263C22×C73—21no—
264C22×C73—21no—
265C22×C73—42no—
266C22×C73—42no—
267C22×C73C22×C22⋊C411yescharacteristic
268C22×C73C22×M1611yescharacteristic
269C22×C73C22×M1611yescharacteristic
270C2×D73—22no—
271C2×D73—22no—
272C2×D73—22no—
273C2×D73—22no—
274C2×D73—42no—
275C2×D73—42no—
276C2×D73—42no—
277C2×D73—41no—
278C2×D73—41no—
279C2×D73—42no—
280C4×C73—22no—
281C4×C73—22no—
282C4×C73—22no—
283C4×C73—22no—
284C4×C73—41no—
285C4×C73—41no—
286Dic73—22no—
287Dic73—22no—
288Dic73—22no—
289Dic73—41no—
290Dic73—41no—
291Dic73#40714yes—
292#17370—731nomaximal, Sylow
293C2×C73—21no—
294C2×C73—21no—
295C2×C73—41no—
296C2×C73—41no—
297C2×C73C2×#40711yescharacteristic
298C2×C73#288311yescharacteristic
299C2×C73#288911yescharacteristic
300D73—42no—
301D73—42no—
302C2×#520—731no—
303#2975—732no—
304#1465—732no—
305#1465—732no—
306#1463—732no—
307#1463—731no—
308#1463D7311yescharacteristic, complemented
309#1461—732no—
310#1458—732no—
311C73#1737011yescharacteristic, complemented, Sylow
312C22×#41—731no—
313#520—1464no—
314#520—1464no—
315C2×C4×Q8—731no—
316C2×C4×Q8—731no—
317C2×C4×D4—731no—
318C2×C4×D4—731no—
319C2×C4×D4—731no—
320C2×C4×D4—731no—
321C2×C4×D4—731no—
322C2×C4×D4—731no—
323C2×#117—731no—
324C2×#117—731no—
325C2×#117—731no—
326C22×C4⋊C4—731no—
327C22×C4⋊C4—731no—
328C22×C4⋊C4C2×D7311yescharacteristic
329#436—1464no—
330#436—1464no—
331#431—734no—
332#407—732no—
333#407—734no—
334#407C2×D7312yes—
335#324—732no—
336#324—732no—
337#324—734no—
338#324C2×D7312yes—
339#324C2×D7312yes—
340#323—734no—
341C2×#41—1464no—
342C2×#41—1462no—
343C2×#41—1462no—
344C2×#41—1464no—
345C22×Q8—731no—
346C22×D4—731no—
347C22×D4—731no—
348C22×D4—731no—
349C23×C4—731no—
350C23×C4—731no—
351C23×C4—731no—
352C23×C4—731no—
353C23×C4—731no—
354C23×C4—731no—
355C23×C4C4×D7311yescharacteristic
356C23×C4C4×D7311yescharacteristic
357C23×C4C22×D7311yescharacteristic
358C2×M16—22no—
359C2×M16—1464no—
360C2×M16—1462no—
361C4×Q8—1464no—
362C4×Q8—1464no—
363C4×D4—734no—
364C4×D4—734no—
365C4×D4—1464no—
366C4×D4—1462no—
367C4×D4—1462no—
368C4×D4—1464no—
369C4×D4—1462no—
370C4×D4—1462no—
371C4×D4—1462no—
372C4×D4—1462no—
373#117—1464no—
374#117—1464no—
375#117—1462no—
376#117—1462no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—731no—
380C2×C4⋊C4—731no—
381C2×C4⋊C4—731no—
382C2×C4⋊C4—731no—
383C2×C4⋊C4—731no—
384C2×C4⋊C4—731no—
385C2×C4⋊C4—1464no—
386C2×C4⋊C4—1464no—
387C2×C4⋊C4C4×D7311yescharacteristic
388C2×C4⋊C4C4×D7311yescharacteristic
389C2×C4⋊C4C22×D7311yescharacteristic
390C2×C4⋊C4C22×D7311yescharacteristic
391C2×C22⋊C4—731no—
392C2×C22⋊C4—731no—
393C2×C22⋊C4—731no—
394C2×C22⋊C4—731no—
395C2×C22⋊C4—731no—
396C2×C22⋊C4—731no—
397C2×C42—731no—
398C2×C42—731no—
399C2×C42—731no—
400C2×C42—731no—
401C2×C42—731no—
402C2×C42—731no—
403C4⋊C8—1464no—
404C22⋊C8—22no—
405C22⋊C8—734no—
406C22⋊C8—1464no—
407C22⋊C8—1462no—
408C22⋊C8C22×D7314yes—
409C4×C8—1464no—
410C24—731no—
411C24—731no—
412C24C2×C4×D7311yescharacteristic
413#41—14616no—
414#41—14616no—
415C2×Q8—734no—
416C2×Q8—1462no—
417C2×Q8—1462no—
418C2×D4—732no—
419C2×D4—732no—
420C2×D4—1462no—
421C2×D4—1462no—
422C2×D4—1462no—
423C2×D4—1462no—
424C2×D4—1462no—
425C2×D4—1462no—
426C2×D4—1461no—
427C2×D4—1461no—
428C2×D4—1462no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—81no—
436C22×C4—81no—
437C22×C4—5841no—
438C22×C4—5841no—
439C22×C4—5841no—
440C22×C4—5841no—
441C22×C4—731no—
442C22×C4—731no—
443C22×C4—734no—
444C22×C4—731no—
445C22×C4—731no—
446C22×C4—731no—
447C22×C4—731no—
448C22×C4—734no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4—1462no—
452C22×C4—1462no—
453C22×C4—1462no—
454C22×C4—1462no—
455C22×C4—1462no—
456C22×C4—1462no—
457C22×C4C2×C4×D7311yescharacteristic
458C22×C4C2×C4×D7311yescharacteristic
459C22×C4C2×C4×D7311yescharacteristic
460C22×C4C2×C4×D7311yescharacteristic
461C22×C4C2×C4×D7311yescharacteristic
462C22×C4D4×D7312yes—
463C22×C4D4×D7312yes—
464C22×C4C23×D7311yescharacteristic
465M16—82no—
466M16—5844no—
467M16—5842no—
468C2×C8—24no—
469C2×C8—1464no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—734no—
475C4⋊C4—1462no—
476C4⋊C4—1462no—
477C4⋊C4—1462no—
478C4⋊C4—1462no—
479C4⋊C4—1462no—
480C22⋊C4—732no—
481C22⋊C4—732no—
482C22⋊C4—734no—
483C22⋊C4—1462no—
484C22⋊C4—1462no—
485C22⋊C4—1461no—
486C22⋊C4—1461no—
487C22⋊C4—1462no—
488C42—734no—
489C42—1462no—
490C42—1462no—
491C42—1462no—
492C42—1462no—
493C42—1462no—
494C23—21no—
495C23—21no—
496C23—41no—
497C23—41no—
498C23—2921no—
499C23—2921no—
500C23—2921no—
501C23—2921no—
502C23—732no—
503C23—732no—
504C23—1461no—
505C23—1461no—
506C23—1461no—
507C23—1461no—
508C23C22⋊C4×D7311yescharacteristic
509C23C22⋊C4×D7311yescharacteristic
510C23C22×C4×D7311yescharacteristic
511Q8—1468no—
512D4—1468no—
513D4—1464no—
514D4—1464no—
515D4—1464no—
516D4—1464no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—2924no—
534C2×C4—2921no—
535C2×C4—2921no—
536C2×C4—2921no—
537C2×C4—2921no—
538C2×C4—5842no—
539C2×C4—5842no—
540C2×C4—5842no—
541C2×C4—732no—
542C2×C4—732no—
543C2×C4—732no—
544C2×C4—732no—
545C2×C4—732no—
546C2×C4—732no—
547C2×C4—1468no—
548C2×C4—1468no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4C22⋊C4×D7312yes—
554C2×C4M16×D7312yes—
555C2×C4M16×D7312yes—
556C2×C4C2×D4×D7312yes—
557C8—44no—
558C8—2924no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—42no—
568C22—42no—
569C22—2922no—
570C22—2922no—
571C22—2922no—
572C22—2922no—
573C22—2921no—
574C22—2921no—
575C22—1462no—
576C22—1462no—
577C22—1462no—
578C22—1462no—
579C22C2×C22⋊C4×D7311yescharacteristic
580C22C2×M16×D7311yescharacteristic
581C22C2×M16×D7311yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—2921no—
589C4—2921no—
590C4—734no—
591C4—1462no—
592C4—1462no—
593C4—1462no—
594C2—21no—
595C2—21no—
596C2—41no—
597C2—41no—
598C2—2922no—
599C2—2922no—
600C2#407×D7311yescharacteristic
601C2#2261838911yescharacteristic
602C2#2261841111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D73
commutatorC23×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1463C2
socleC22×C73C22×C22⋊C4
prime radicalC22×#11924028C4
cosocleC22×C4×C73C24
hypercenter#1463D73
hypocenterC73#17370
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. #22618970C2semidirect
3. #22608268C2semidirect
4. #22608267C2semidirect
5. #22608261C2semidirect
6. #22608259C2semidirect
7. #22608253C2semidirect
8. #22608244C2semidirect
9. C73×#1463C2semidirect
114. C2×Dic146M16semidirect
144. C2×C4×D73M16semidirect
308. #1463D73semidirect
311. C73#17370semidirect

Maximal subgroups

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

subgroupindex
C2×#179890682
#226189702
#226082682
#226082672
#226082612
#226082592
#226082532
#226082442
C73×#14632
#1737073