Finite Group Databasebeta

← #33088390

Subgroups — #33088390

Order 18688.

1218 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988627C211yesmaximal, characteristic, complemented
2C2×#17988586C211yesmaximal, characteristic
3C2×#17988586C211yesmaximal, characteristic
4#22612421C211yesmaximal, characteristic
5#22610572C212yesmaximal, complemented
6#22610565C212yesmaximal, complemented
7#22610558C212yesmaximal, complemented
8#22610551C212yesmaximal, complemented
9#22609650C211yesmaximal, characteristic, complemented
10#22609625C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C73C211yesmaximal, characteristic, complemented
12C22×#11924028C2211yescharacteristic
13C22×#11924012C2211yescharacteristic
14C22×#11924012C2211yescharacteristic
15C2×#14556550C2211yescharacteristic
16#17988627—24no—
17C2×#14556524C2212yes—
18C2×#14556522C2212yes—
19#17988586—24no—
20#17988586C418yescomplemented
21C2×#14556514C2212yes—
22C2×#14556514C2212yes—
23C2×#14556511C2212yes—
24C2×#14556511C2212yes—
25#17988493C2211yescharacteristic
26#17988493C2211yescharacteristic
27#17988489C2211yescharacteristic
28#17988489C2211yescharacteristic
29#17988466—21no—
30#17988466—21no—
31C4×#11924005—21no—
32C4×#11924005—21no—
33#17988349C2212yes—
34#17988349C2212yes—
35#17988342C2212yes—
36#17988342C2212yes—
37C22×C4⋊C4×C73C2211yescharacteristic
38C22×C4⋊C4×C73C2211yescharacteristic
39C22×C42×C73—21no—
40C22×C42×C73C2211yescharacteristic
41C4×C4⋊C4×C73—21no—
42C4×C4⋊C4×C73—21no—
43C4×C4⋊C4×C73C2212yes—
44C4×C4⋊C4×C73C2212yes—
45C2×#95×C73—21no—
46C2×#11924028—22no—
47C2×#11924028—22no—
48C2×#11924028—22no—
49C2×#11924028—22no—
50C2×#11924028—22no—
51C2×#11924028C2×C414yes—
52C22×Dic146C2311yescharacteristic
53C22×D292C2311yescharacteristic
54C22×C22⋊D73—21no—
55C22×C4×D73—21no—
56C2×#11924012—22no—
57C2×#11924012—22no—
58C2×#11924012—22no—
59C2×#11924012—22no—
60C2×#11924012—22no—
61C2×#11924012C2×C414yes—
62C22×#10596831C2312yes—
63C22×#10596831C2312yes—
64#14556550—22no—
65#14556550—22no—
66C2×C4⋊Dic73C2311yescharacteristic
67C2×C4⋊Dic73C2311yescharacteristic
68C2×C22⋊Dic73—21no—
69C2×#11924005—21no—
70C2×#11924005—21no—
71C2×#11924005—21no—
72C2×#11924005—21no—
73C2×C4×Dic73—21no—
74#14556524—24no—
75#14556522—24no—
76#14556514—24no—
77#14556514C2×C418yescomplemented
78#14556511—24no—
79#14556511C2×C418yescomplemented
80#14556498—21no—
81#14556498—21no—
82#14556498—21no—
83#14556498—21no—
84C23×C4×C73—21no—
85C23×C4×C73—21no—
86C23×C4×C73D411yescharacteristic
87C23×C4×C73D411yescharacteristic
88C23×C4×C73C2311yescharacteristic
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—22no—
92C2×C4⋊C4×C73—22no—
93C2×C4⋊C4×C73C2×C414yes—
94C2×C4⋊C4×C73D414yes—
95C2×C4⋊C4×C73C2312yes—
96C2×C4⋊C4×C73C2312yes—
97C2×C42×C73—22no—
98C2×C42×C73—22no—
99C2×C42×C73—22no—
100C2×C42×C73—22no—
101C2×C42×C73—44no—
102C2×C42×C73D411yescharacteristic
103C2×C42×C73D411yescharacteristic
104C2×C42×C73C2311yescharacteristic
105C2×C42×C73C2311yescharacteristic
106#95×C73—22no—
107#95×C73—22no—
108C23×D73—21no—
109#11924028—28no—
110#11924028—28no—
111#11924028—44no—
112#11924028—44no—
113C2×Dic146—21no—
114C2×Dic146—21no—
115C2×Dic146—21no—
116C2×Dic146—21no—
117C2×Dic146—21no—
118C2×Dic146C22×C412yes—
119C2×D292—21no—
120C2×D292—21no—
121C2×D292—21no—
122C2×D292—21no—
123C2×D292—21no—
124C2×D292C22×C412yes—
125C2×C22⋊D73—24no—
126C2×C22⋊D73—42no—
127C2×C22⋊D73—42no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—21no—
131C2×C4×D73—24no—
132C2×C4×D73—42no—
133C2×C4×D73—42no—
134#11924012—28no—
135#11924012—44no—
136C2×#10596831—22no—
137C2×#10596831—22no—
138C2×#10596831—22no—
139C2×#10596831—22no—
140C2×#10596831—22no—
141C2×#10596831C22×C414yes—
142C4⋊Dic73—21no—
143C4⋊Dic73—21no—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C22⋊Dic73—42no—
147#11924005—42no—
148#11924005—42no—
149#11924005—42no—
150#11924005—42no—
151C4×Dic73—42no—
152C24×C73C2×D411yescharacteristic
153C22×C4×C73—22no—
154C22×C4×C73—22no—
155C22×C4×C73—22no—
156C22×C4×C73—24no—
157C22×C4×C73—24no—
158C22×C4×C73—22no—
159C22×C4×C73—22no—
160C22×C4×C73—22no—
161C22×C4×C73—41no—
162C22×C4×C73—41no—
163C22×C4×C73—42no—
164C22×C4×C73—42no—
165C22×C4×C73—42no—
166C22×C4×C73—42no—
167C22×C4×C73C22×C412yes—
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D412yes—
174C22×C4×C73#4112yes—
175C22×C4×C73#4112yes—
176C22×C4×C73#4112yes—
177C22×C4×C73#4112yes—
178C22×C4×C73C2411yescharacteristic
179C4⋊C4×C73—24no—
180C4⋊C4×C73—24no—
181C4⋊C4×C73—22no—
182C4⋊C4×C73—22no—
183C4⋊C4×C73C22×C414yes—
184C4⋊C4×C73C2×D414yes—
185C42×C73—22no—
186C42×C73—22no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73—44no—
192C42×C73—44no—
193C23×C73—21no—
194C23×C73—21no—
195C23×C73—21no—
196C23×C73—21no—
197C23×C73C4×D412yes—
198C23×C73#12112yes—
199C23×C73#12312yes—
200C23×C73C22×D411yescharacteristic
201C22×D73—22no—
202C22×D73—41no—
203C22×D73—41no—
204C22×D73—41no—
205C22×D73—41no—
206C22×D73—41no—
207C22×D73—41no—
208C2×C4×C73—28no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—24no—
214C2×C4×C73—24no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—44no—
222C2×C4×C73—48no—
223C2×C4×C73—48no—
224C2×C4×C73—42no—
225C2×C4×C73—42no—
226C2×C4×C73—42no—
227C2×C4×C73—42no—
228C2×C4×C73#11714yes—
229C2×C4×C73C4×D412yes—
230C2×C4×C73C4×D414yes—
231C2×C4×C73#12112yes—
232C2×C4×C73#12312yes—
233C2×C4×C73#12414yes—
234C2×C4×C73#12614yes—
235C2×C4×C73AGL(1,ℤ/8)12yes—
236C2×C4×C73#13712yes—
237C2×C4×C73C23×C411yescharacteristic
238C2×C4×C73C22×D411yescharacteristic
239C2×C4×C73C2×#4111yescharacteristic
240C2×C4×C73C2×#4111yescharacteristic
241C2×C4×C73C2×#4111yescharacteristic
242C2×C4×C73C2×#4111yescharacteristic
243C22⋊D73—48no—
244C2×Dic73—22no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73—41no—
253D292—22no—
254D292—22no—
255D292—41no—
256D292—41no—
257C4×D73—48no—
258Dic146—22no—
259Dic146—22no—
260Dic146—41no—
261Dic146—41no—
262#10596831—24no—
263#10596831—42no—
264C22×C73—22no—
265C22×C73—22no—
266C22×C73—22no—
267C22×C73—22no—
268C22×C73—22no—
269C22×C73—22no—
270C22×C73#38814yes—
271C22×C73C2×C4×D411yescharacteristic
272C22×C73C2×#12111yescharacteristic
273C22×C73C2×#12311yescharacteristic
274C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C73C2×#13711yescharacteristic
276C22×C73#57511yescharacteristic
277C22×C73#57511yescharacteristic
278C2×D73—42no—
279C2×D73—42no—
280C2×D73—42no—
281C2×D73—81no—
282C2×D73—81no—
283C2×D73—81no—
284C2×D73—81no—
285C4×C73—22no—
286C4×C73—22no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73—44no—
290C4×C73—44no—
291C4×C73#38814yes—
292C4×C73C2×#11711yescharacteristic
293C4×C73C2×C4×D411yescharacteristic
294C4×C73C2×#12411yescharacteristic
295C4×C73C2×#12611yescharacteristic
296Dic73—42no—
297Dic73—81no—
298Dic73—81no—
299#21059—731nomaximal, Sylow
300C2×C73—24no—
301C2×C73C2×#38811yescharacteristic
302C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
303C2×C73C4×#13711yescharacteristic
304C2×C73#303611yescharacteristic
305C2×C73#303711yescharacteristic
306C2×C73#309211yescharacteristic
307C2×C73#309311yescharacteristic
308D73—82no—
309C2×#428—731no—
310C2×#417—731no—
311C2×#417—731no—
312#2297—731no—
313C2×C4×C4⋊C4D7311yescharacteristic, complemented
314#1928—732no—
315#1927—732no—
316#1926—732no—
317#1925—732no—
318#1736—731no—
319#1728—731no—
320C73#2105911yescharacteristic, complemented, Sylow
321C22×#41—731no—
322C22×M16—731no—
323C22×M16—731no—
324C2×#117—731no—
325C22×C4⋊C4C2×D7311yescharacteristic
326C22×C4⋊C4C2×D7311yescharacteristic
327C22×C42—21no—
328C22×C42C2×D7311yescharacteristic
329#428—1464no—
330C2×#107—732no—
331C2×#106—732no—
332#417—738no—
333#417—1464no—
334C2×#103—732no—
335C2×#103—732no—
336C2×#102—732no—
337C2×#102—732no—
338#391—731no—
339#391—731no—
340#390—731no—
341#390—731no—
342#386—1461no—
343#386—1461no—
344C4×C4⋊C4—21no—
345C4×C4⋊C4—21no—
346C4×C4⋊C4C2×D7312yes—
347C4×C4⋊C4C2×D7312yes—
348C4×C22⋊C4—1461no—
349C4×C22⋊C4—1461no—
350C2×#95—21no—
351#340—732no—
352#340—732no—
353#336—732no—
354#336—732no—
355C2×#41—734no—
356C2×#41—1462no—
357C2×#41—1462no—
358C2×#41—1462no—
359C2×#41—1462no—
360C2×#41—1462no—
361C22×Q8—731no—
362C22×D4—731no—
363C22×D4—1461no—
364C23×C4—21no—
365C23×C4—21no—
366C23×C4—1461no—
367C23×C4C22⋊D7311yescharacteristic
368C23×C4C22⋊D7311yescharacteristic
369C23×C4C22×D7311yescharacteristic
370C2×M16—734no—
371C2×M16—1462no—
372C2×M16—1462no—
373C2×M16—1462no—
374C2×M16—1462no—
375C2×M16—1462no—
376C22×C8—732no—
377C22×C8—732no—
378#117—1462no—
379#117—1462no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—731no—
385C2×C4⋊C4—731no—
386C2×C4⋊C4C4×D7314yes—
387C2×C4⋊C4D29214yes—
388C2×C4⋊C4C22×D7312yes—
389C2×C4⋊C4C22×D7312yes—
390C2×C22⋊C4—1461no—
391C2×C22⋊C4—1461no—
392C2×C22⋊C4—1461no—
393C2×C22⋊C4—1461no—
394C2×C22⋊C4—1461no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—44no—
400C2×C42—1461no—
401C2×C42C22⋊D7311yescharacteristic
402C2×C42C22⋊D7311yescharacteristic
403C2×C42C22×D7311yescharacteristic
404C2×C42C22×D7311yescharacteristic
405#107—1464no—
406#106—1464no—
407#103—738no—
408#103—1464no—
409#102—738no—
410#102—1464no—
411#95—22no—
412#95—22no—
413#95—1461no—
414#95—1461no—
415#95—1461no—
416#95—1461no—
417C24—1461no—
418C24C2×C22⋊D7311yescharacteristic
419#41—2924no—
420#41—2924no—
421#41—1468no—
422#41—1468no—
423C2×Q8—732no—
424C2×Q8—1461no—
425C2×Q8—1461no—
426C2×Q8—1461no—
427C2×Q8—1461no—
428C2×Q8—1461no—
429C2×D4—2922no—
430C2×D4—2922no—
431C2×D4—732no—
432C2×D4—1464no—
433C2×D4—1461no—
434C2×D4—1461no—
435C2×D4—1461no—
436C2×D4—1461no—
437C2×D4—1461no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—2922no—
453C22×C4—2922no—
454C22×C4—1461no—
455C22×C4—1461no—
456C22×C4—1461no—
457C22×C4—1464no—
458C22×C4C2×C4×D7312yes—
459C22×C4C2×C22⋊D7311yescharacteristic
460C22×C4C2×C22⋊D7311yescharacteristic
461C22×C4C2×C22⋊D7311yescharacteristic
462C22×C4C2×C22⋊D7311yescharacteristic
463C22×C4C2×C22⋊D7311yescharacteristic
464C22×C4C2×D29212yes—
465C22×C4#1192402812yes—
466C22×C4#1192402812yes—
467C22×C4#1192402812yes—
468C22×C4#1192402812yes—
469C22×C4C23×D7311yescharacteristic
470M16—2924no—
471M16—1468no—
472C2×C8—734no—
473C2×C8—1462no—
474C2×C8—1462no—
475C2×C8—1462no—
476C2×C8—1462no—
477C2×C8—1462no—
478C4⋊C4—24no—
479C4⋊C4—24no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—1461no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C4⋊C4—1461no—
486C4⋊C4C2×C4×D7314yes—
487C4⋊C4C2×D29214yes—
488C22⋊C4—2922no—
489C22⋊C4—2922no—
490C22⋊C4—2922no—
491C22⋊C4—2922no—
492C22⋊C4—2922no—
493C42—22no—
494C42—22no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—44no—
500C42—44no—
501C42—2922no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—2921no—
507C23—2921no—
508C23—2921no—
509C23—2921no—
510C23—2921no—
511C23—2921no—
512C23—1462no—
513C23C4×C22⋊D7312yes—
514C23#1455656512yes—
515C23#1455657412yes—
516C23C22×C22⋊D7311yescharacteristic
517Q8—2921no—
518Q8—2921no—
519Q8—1462no—
520Q8—1462no—
521D4—2928no—
522D4—2921no—
523D4—2921no—
524D4—1462no—
525D4—1462no—
526C2×C4—28no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—48no—
540C2×C4—48no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—2921no—
547C2×C4—2921no—
548C2×C4—2928no—
549C2×C4—2921no—
550C2×C4—2921no—
551C2×C4—2921no—
552C2×C4—2921no—
553C2×C4—2921no—
554C2×C4—2921no—
555C2×C4—1462no—
556C2×C4#1455654814yes—
557C2×C4C4×C22⋊D7312yes—
558C2×C4C4×D29214yes—
559C2×C4#1455656512yes—
560C2×C4#1455657412yes—
561C2×C4#1455657914yes—
562C2×C4#1455658514yes—
563C2×C4#1455661712yes—
564C2×C4#1455662212yes—
565C2×C4C22×C4×D7311yescharacteristic
566C2×C4C22×D29211yescharacteristic
567C2×C4C2×#1192402811yescharacteristic
568C2×C4C2×#1192402811yescharacteristic
569C2×C4C2×#1192402811yescharacteristic
570C2×C4C2×#1192402811yescharacteristic
571C8—2922no—
572C8—1464no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—2922no—
580C22—2922no—
581C22—2922no—
582C22—5841no—
583C22—5841no—
584C22—5841no—
585C22—5841no—
586C22#1798847814yes—
587C22C2×C4×C22⋊D7311yescharacteristic
588C22C2×#1455656511yescharacteristic
589C22C2×#1455657411yescharacteristic
590C22C2×#1455661711yescharacteristic
591C22C2×#1455662211yescharacteristic
592C22#1798938511yescharacteristic
593C22#1798938511yescharacteristic
594C4—22no—
595C4—22no—
596C4—44no—
597C4—44no—
598C4—41no—
599C4—41no—
600C4—2922no—
601C4—5841no—
602C4—5841no—
603C4#1798847814yes—
604C4C2×#1455654811yescharacteristic
605C4C2×C4×D29211yescharacteristic
606C4C2×#1455657911yescharacteristic
607C4C2×#1455658511yescharacteristic
608C2—24no—
609C2—5842no—
610C2C2×#1798847811yescharacteristic
611C2C4×#1455661711yescharacteristic
612C2C4×#1455662211yescharacteristic
613C2#2261939511yescharacteristic
614C2#2261940311yescharacteristic
615C2#2261985411yescharacteristic
616C2#2261986211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×C4×C4⋊C4×C73C2
socleC23×C73C22×D4
prime radicalC22×#11924028C22
cosocleC22×C4×C73C24
hypercenterC2×C4×C4⋊C4D73
hypocenterC73#21059
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#17988627C2semidirect
5. #22610572C2semidirect
6. #22610565C2semidirect
7. #22610558C2semidirect
8. #22610551C2semidirect
9. #22609650C2semidirect
10. #22609625C2semidirect
11. C2×C4×C4⋊C4×C73C2semidirect
20. #17988586C4semidirect
77. #14556514C2×C4semidirect
79. #14556511C2×C4semidirect
313. C2×C4×C4⋊C4D73semidirect
320. C73#21059semidirect

Maximal subgroups

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

subgroupindex
C2×#179886272
C2×#179885862
#226124212
#226105722
#226105652
#226105582
#226105512
#226096502
#226096252
C2×C4×C4⋊C4×C732
#2105973