Finite Group Databasebeta

← #33115940

Subgroups — #33115940

Order 18688.

782 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22612556C211yesmaximal, characteristic
2#22612546C211yesmaximal, characteristic
3#22611504C211yesmaximal, characteristic, complemented
4#22611501C211yesmaximal, characteristic, complemented
5#22611498C211yesmaximal, characteristic, complemented
6#22611497C211yesmaximal, characteristic, complemented
7#22611495C211yesmaximal, characteristic, complemented
8#22611491C211yesmaximal, characteristic, complemented
9#22611489C211yesmaximal, characteristic, complemented
10#22609649C211yesmaximal, characteristic
11#22609649C211yesmaximal, characteristic
12#22609646C211yesmaximal, characteristic
13#340×D73C211yesmaximal, characteristic
14#22609626C211yesmaximal, characteristic
15C73×#2101C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×#14556549C2211yescharacteristic
19C2×#14556549C2211yescharacteristic
20C2×#14556548C2211yescharacteristic
21C2×C4⋊C4×D73C2211yescharacteristic
22C2×C4⋊C4×D73C2211yescharacteristic
23#17988486C2211yescharacteristic
24#17988485C2211yescharacteristic
25#17988484—21no—
26#17988484—21no—
27#17988484—21no—
28#17988483C2211yescharacteristic
29#17988482—21no—
30#17988461—21no—
31#17988461—21no—
32#17988457C2211yescharacteristic
33#17988456C2211yescharacteristic
34#17988452C2211yescharacteristic
35#17988446—21no—
36#17988444—21no—
37#17988350C2211yescharacteristic
38#17988350C2211yescharacteristic
39#17988350C2211yescharacteristic
40#17988350C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#389×C73C2211yescharacteristic
53#382×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×C4×D73—21no—
60C22×C4×D73—21no—
61C22×C4×D73C2311yescharacteristic
62C2×#11924011—22no—
63C2×#11924011—22no—
64C2×#11924011—22no—
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C2×C8×D73—22no—
68C2×C8×D73—22no—
69C2×C8×D73—22no—
70#14556549—22no—
71#14556549—22no—
72#14556549—22no—
73#14556549—22no—
74#14556548—22no—
75#14556548—22no—
76C2×C4⋊Dic73—21no—
77C2×C4⋊Dic73—21no—
78C2×C4⋊Dic73—21no—
79C2×C4⋊Dic73C2311yescharacteristic
80C2×C4⋊Dic73C2311yescharacteristic
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×#11924007—21no—
84C2×#11924007—21no—
85C2×#11924007—21no—
86C2×#11924007—21no—
87C2×#11924007—21no—
88C2×#11924007—21no—
89C2×#11924007D411yescharacteristic
90C2×#11924007D411yescharacteristic
91C4⋊C4×D73—22no—
92C4⋊C4×D73—22no—
93C4⋊C4×D73—22no—
94C4⋊C4×D73Q814yes—
95C2×#11924005—21no—
96C2×#11924005—21no—
97C2×#11924005D411yescharacteristic
98C2×#11924005D411yescharacteristic
99C2×C4×Dic73—21no—
100C2×C4×Dic73—21no—
101C2×C4×Dic73C2311yescharacteristic
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107C22×C8×C73C2311yescharacteristic
108C22×C8×C73C2311yescharacteristic
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73C2311yescharacteristic
111C2×C4⋊C4×C73C2311yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115#95×C73—21no—
116#95×C73—21no—
117#95×C73—21no—
118C23×D73C2×D411yescharacteristic
119C22×Dic73—21no—
120C22×Dic73—21no—
121C22×Dic73—21no—
122C22×Dic73—21no—
123C22×Dic73C2×D411yescharacteristic
124C22×Dic73C2×D411yescharacteristic
125C22×Dic73C2×D411yescharacteristic
126C2×C4×D73—24no—
127C2×C4×D73—42no—
128C2×C4×D73—81no—
129C2×C4×D73—81no—
130C2×C4×D73—81no—
131C2×C4×D73—81no—
132C2×C4×D73C2×Q812yes—
133C2×C4×D73#4112yes—
134C2×C4×D73#4112yes—
135C2×C4×D73#4112yes—
136C2×C4×D73#4112yes—
137C2×C4×D73#4112yes—
138#11924011—44no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C8×D73—44no—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—81no—
154C4⋊Dic73—81no—
155C4⋊Dic73—81no—
156C4⋊Dic73C2×Q812yes—
157#11924007—24no—
158#11924007—22no—
159#11924007—22no—
160#11924007—42no—
161#11924007—81no—
162#11924007—81no—
163#11924007—81no—
164#11924007—81no—
165#11924005—22no—
166#11924005—22no—
167#11924005—42no—
168#11924005—42no—
169C4×Dic73—21no—
170C4×Dic73—21no—
171C4×Dic73—42no—
172C4×Dic73—42no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2411yescharacteristic
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—81no—
194C4⋊C4×C73C2×Q812yes—
195C42×C73—21no—
196C42×C73—21no—
197C23×C73C22×D411yescharacteristic
198C22×D73—21no—
199C22×D73—21no—
200C22×D73—21no—
201C22×D73—21no—
202C22×D73C22⋊Q812yes—
203C22×D73#12312yes—
204C22×D73#12412yes—
205C2×C4×C73—22no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—41no—
213C2×C4×C73—41no—
214C2×C4×C73—41no—
215C2×C4×C73—41no—
216C2×C4×C73—41no—
217C2×C4×C73—41no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73C22×Q811yescharacteristic
224C2×C4×C73C2×#4111yescharacteristic
225C2×C4×C73C2×#4111yescharacteristic
226C2×C4×C73C2×#4111yescharacteristic
227C2×C4×C73C2×#4111yescharacteristic
228C2×C4×C73C2×#4111yescharacteristic
229C2×Dic73—22no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—41no—
237C2×Dic73—41no—
238C2×Dic73—41no—
239C2×Dic73—41no—
240C2×Dic73—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73C22⋊Q812yes—
248C2×Dic73#12312yes—
249C2×Dic73#12412yes—
250C4×D73—84no—
251C4×D73—84no—
252C4×D73#12514yes—
253C4×D73#12514yes—
254C4×D73#12614yes—
255C4×D73#12614yes—
256C8×C73—41no—
257C8×C73—41no—
258#10596831—41no—
259#10596831—41no—
260C22×C73C2×C22⋊Q811yescharacteristic
261C22×C73C2×#12311yescharacteristic
262C22×C73C2×#12411yescharacteristic
263C22×C73#57611yescharacteristic
264C22×C73#57711yescharacteristic
265C22×C73#57711yescharacteristic
266C22×C73#57811yescharacteristic
267C2×D73—22no—
268C2×D73—22no—
269C2×D73—22no—
270C2×D73—22no—
271C2×D73—22no—
272C2×D73—22no—
273C2×D73#40014yes—
274C4×C73—42no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—81no—
278C4×C73—81no—
279C4×C73—81no—
280C4×C73C2×#12511yescharacteristic
281C4×C73C2×#12511yescharacteristic
282C4×C73C2×#12611yescharacteristic
283C4×C73C2×#12611yescharacteristic
284Dic73—42no—
285Dic73—41no—
286Dic73—41no—
287Dic73—81no—
288Dic73—81no—
289Dic73—81no—
290Dic73#40014yes—
291#23749—731nomaximal, Sylow
292C2×C73C2×#40011yescharacteristic
293C2×C73#308111yescharacteristic
294C2×C73#308211yescharacteristic
295C2×C73#309811yescharacteristic
296C2×C73#309911yescharacteristic
297C2×C73#313611yescharacteristic
298C2×C73#313711yescharacteristic
299D73—24no—
300#2317—731no—
301#2316—731no—
302#2101—731no—
303#2101—731no—
304#2101—731no—
305#2101D7311yescharacteristic, complemented
306#2100—731no—
307#2100—731no—
308#2099—731no—
309#2099—731no—
310#1736—731no—
311#1736—731no—
312#1735—731no—
313C2×#340—731no—
314#1729—731no—
315C73#2374911yescharacteristic, complemented, Sylow
316C22×M16—731no—
317C23×C8—731no—
318C2×#117—731no—
319C2×#117—731no—
320C2×#117—731no—
321C22×C4⋊C4—731no—
322C22×C4⋊C4—731no—
323#389—731no—
324#389—731no—
325#389—731no—
326#389—1461no—
327#389—1461no—
328#389—1461no—
329#389—1461no—
330#389C2×D7311yescharacteristic
331#385—1461no—
332#385—1461no—
333#384—731no—
334#384—731no—
335#382—731no—
336#382C2×D7311yescharacteristic
337#380—1461no—
338#380—1461no—
339#340—731no—
340#340—731no—
341#340—731no—
342#340—731no—
343#340—731no—
344#340—731no—
345#340—731no—
346#340—731no—
347#340—731no—
348#340—731no—
349#340—731no—
350#340—731no—
351#340C2×D7311yescharacteristic
352#340C2×D7311yescharacteristic
353#340C2×D7311yescharacteristic
354#340C2×D7311yescharacteristic
355#336—731no—
356#336—731no—
357#336—731no—
358#336C2×D7311yescharacteristic
359C23×C4—731no—
360C23×C4—1461no—
361C23×C4—1461no—
362C2×M16—1462no—
363C2×M16—1462no—
364C2×M16—1462no—
365C22×C8—731no—
366C22×C8—731no—
367C22×C8—1462no—
368C22×C8—1462no—
369C22×C8—1462no—
370C22×C8C22×D7311yescharacteristic
371C22×C8C22×D7311yescharacteristic
372#117—1462no—
373#117—1462no—
374#117—1462no—
375#117—1462no—
376#117—1462no—
377#117—1462no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—731no—
380C2×C4⋊C4—734no—
381C2×C4⋊C4—731no—
382C2×C4⋊C4—731no—
383C2×C4⋊C4—731no—
384C2×C4⋊C4—731no—
385C2×C4⋊C4—731no—
386C2×C4⋊C4—1462no—
387C2×C4⋊C4—1462no—
388C2×C4⋊C4—1462no—
389C2×C4⋊C4—1461no—
390C2×C4⋊C4—1461no—
391C2×C4⋊C4—1461no—
392C2×C4⋊C4—1461no—
393C2×C4⋊C4—1461no—
394C2×C4⋊C4—1461no—
395C2×C4⋊C4—1461no—
396C2×C4⋊C4—1461no—
397C2×C4⋊C4—1461no—
398C2×C4⋊C4C22×D7311yescharacteristic
399C2×C4⋊C4C22×D7311yescharacteristic
400C2×C4⋊C4C22×D7311yescharacteristic
401C2×C4⋊C4C22×D7311yescharacteristic
402C2×C22⋊C4—731no—
403C2×C22⋊C4—731no—
404C2×C22⋊C4—1461no—
405C2×C22⋊C4—1461no—
406C2×C42—731no—
407C2×C42—1461no—
408C2×C42—1461no—
409C2×C42C22×D7311yescharacteristic
410#95—21no—
411#95—21no—
412#95—21no—
413#95—1461no—
414#95—1461no—
415#95—1461no—
416#95—1461no—
417#95—1461no—
418C24—731no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—2922no—
424C22×C4—5841no—
425C22×C4—5841no—
426C22×C4—5841no—
427C22×C4—5841no—
428C22×C4—731no—
429C22×C4—732no—
430C22×C4—732no—
431C22×C4—732no—
432C22×C4—732no—
433C22×C4—732no—
434C22×C4—732no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—1464no—
438C22×C4—1461no—
439C22×C4—1461no—
440C22×C4—1461no—
441C22×C4—1461no—
442C22×C4D4×D7311yescharacteristic
443C22×C4D4×D7311yescharacteristic
444C22×C4C23×D7311yescharacteristic
445M16—2924no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—2924no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—81no—
467C4⋊C4—2922no—
468C4⋊C4—5841no—
469C4⋊C4—5841no—
470C4⋊C4—5841no—
471C4⋊C4—5841no—
472C4⋊C4—5841no—
473C4⋊C4—5841no—
474C4⋊C4—5841no—
475C4⋊C4—732no—
476C4⋊C4—1464no—
477C4⋊C4—1462no—
478C4⋊C4—1462no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C4⋊C4—1461no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C4⋊C4—1461no—
486C4⋊C4Q8×D7312yes—
487C22⋊C4—2922no—
488C22⋊C4—2922no—
489C22⋊C4—1462no—
490C22⋊C4—1462no—
491C42—21no—
492C42—21no—
493C42—2922no—
494C42—2922no—
495C42—1461no—
496C42—1461no—
497C23—732no—
498C23—732no—
499C23—732no—
500C23—1461no—
501C23—1461no—
502C23—1461no—
503C23—1461no—
504C23C2×D4×D7311yescharacteristic
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—2921no—
524C2×C4—2921no—
525C2×C4—2921no—
526C2×C4—2921no—
527C2×C4—2921no—
528C2×C4—2921no—
529C2×C4—2921no—
530C2×C4—2921no—
531C2×C4—2921no—
532C2×C4—2921no—
533C2×C4—2921no—
534C2×C4—5844no—
535C2×C4—5844no—
536C2×C4—732no—
537C2×C4—732no—
538C2×C4—732no—
539C2×C4—734no—
540C2×C4—734no—
541C2×C4—734no—
542C2×C4—734no—
543C2×C4—1461no—
544C2×C4—1461no—
545C2×C4—1461no—
546C2×C4—1461no—
547C2×C4—1462no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4C2×Q8×D7311yescharacteristic
551C2×C4#41×D7311yescharacteristic
552C2×C4#41×D7311yescharacteristic
553C2×C4#41×D7311yescharacteristic
554C2×C4#41×D7311yescharacteristic
555C2×C4#41×D7311yescharacteristic
556C8—41no—
557C8—41no—
558C8—2921no—
559C8—2921no—
560C22—734no—
561C22—1462no—
562C22—1462no—
563C22—1462no—
564C22—1462no—
565C22—1462no—
566C22—1462no—
567C22C22⋊Q8×D7311yescharacteristic
568C22#123×D7311yescharacteristic
569C22#124×D7311yescharacteristic
570C22#1798939111yescharacteristic
571C22#1798939411yescharacteristic
572C22#1798939611yescharacteristic
573C22#1798940111yescharacteristic
574C4—41no—
575C4—41no—
576C4—42no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—2921no—
581C4—2921no—
582C4—2922no—
583C4—5841no—
584C4—5841no—
585C4—5841no—
586C4—734no—
587C4#125×D7311yescharacteristic
588C4#125×D7311yescharacteristic
589C4#126×D7311yescharacteristic
590C4#126×D7311yescharacteristic
591C2—1464no—
592C2#400×D7311yescharacteristic
593C2#2261976111yescharacteristic
594C2#2261977211yescharacteristic
595C2#2261990611yescharacteristic
596C2#2261991711yescharacteristic
597C2#2262028211yescharacteristic
598C2#2262029511yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2101C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
hypercenter#2101D73
hypocenterC73#23749
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2101

Complements

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

NH ≅ G/Ntype
3. #22611504C2semidirect
4. #22611501C2semidirect
5. #22611498C2semidirect
6. #22611497C2semidirect
7. #22611495C2semidirect
8. #22611491C2semidirect
9. #22611489C2semidirect
15. C73×#2101C2semidirect
305. #2101D73semidirect
315. C73#23749semidirect

Maximal subgroups

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

subgroupindex
#226125562
#226125462
#226115042
#226115012
#226114982
#226114972
#226114952
#226114912
#226114892
#226096492
#226096462
#340×D732
#226096262
C73×#21012
#2374973