Finite Group Databasebeta

← #33056038

Subgroups — #33056038

Order 18688.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619978C211yesmaximal, characteristic
2#22619076C211yesmaximal, characteristic, complemented
3#22618955C211yesmaximal, characteristic, complemented
4#22608792C211yesmaximal, characteristic, complemented
5#22608785C211yesmaximal, characteristic, complemented
6#22608764C211yesmaximal, characteristic, complemented
7#22608757C211yesmaximal, characteristic, complemented
8#22608752C211yesmaximal, characteristic, complemented
9#22608740C211yesmaximal, characteristic, complemented
10#22608734C211yesmaximal, characteristic, complemented
11#22608723C211yesmaximal, characteristic, complemented
12#22608722C211yesmaximal, characteristic, complemented
13#22608340C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#1486C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17#17988922C411yescharacteristic
18#17988905C411yescharacteristic
19#17988887C411yescharacteristic
20#17988887C411yescharacteristic
21#17988802C411yescharacteristic
22#17988802C411yescharacteristic
23#17988738C411yescharacteristic
24#17988721C411yescharacteristic
25#17988714C2211yescharacteristic, complemented
26#17988711C2211yescharacteristic, complemented
27C4×#11924016C2211yescharacteristic
28C4×#11924016C2211yescharacteristic
29C4×#11924013C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31#17988664C2211yescharacteristic, complemented
32#17988663—21no—
33#17988656—21no—
34D4×#10596831—21no—
35D4×#10596831—21no—
36D4×#10596831C2211yescharacteristic
37D4×#10596831C2211yescharacteristic
38D4×#10596831C2211yescharacteristic
39D4×#10596831C2211yescharacteristic
40#17988652C2211yescharacteristic, complemented
41#17988647—21no—
42#17988640C2211yescharacteristic
43#17988640C2211yescharacteristic
44#17988640C2211yescharacteristic
45#17988612—21no—
46C2×C22⋊#10596831—21no—
47C2×C22⋊#10596831—21no—
48#17988339C2211yescharacteristic, complemented
49#17988339C2211yescharacteristic, complemented
50#17988337C2211yescharacteristic, complemented
51#17988337C2211yescharacteristic, complemented
52#17988319C2211yescharacteristic, complemented
53#17988319C2211yescharacteristic, complemented
54#17988316C2211yescharacteristic, complemented
55#17988316C2211yescharacteristic, complemented
56#17988309C2211yescharacteristic, complemented
57#17988309C2211yescharacteristic, complemented
58#17988308C2211yescharacteristic, complemented
59C8×#10596831C2211yescharacteristic, complemented
60C2×C4×D4×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62#423×C73C2211yescharacteristic
63D4⋊C8×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66D4⋊C8×C73C2211yescharacteristic
67C2×#11924016C2×C411yescharacteristic
68C2×#11924016C2×C411yescharacteristic
69C2×#11924013C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924011—21no—
72C22×#10596831—21no—
73C22×#10596831—21no—
74C22×#10596831—21no—
75C22×#10596831—21no—
76C2×C8×D73—21no—
77#14556585—21no—
78#14556583C2×C411yescharacteristic
79#14556579C2×C411yescharacteristic
80#14556574—21no—
81#14556570C2×C411yescharacteristic
82#14556565C2×C411yescharacteristic
83C4×Dic146C2311yescharacteristic
84C4×D292C2311yescharacteristic
85C4×C22⋊D73—21no—
86#14556548—21no—
87#14556524C2×C411yescharacteristic
88#14556524C2×C411yescharacteristic
89#14556522C2×C411yescharacteristic
90#14556522C2×C411yescharacteristic
91C4⋊#10596831C2×C411yescharacteristic
92C4⋊#10596831C2×C411yescharacteristic
93C4⋊#10596831D411yescharacteristic
94C4⋊#10596831D411yescharacteristic
95C4⋊#10596831C2311yescharacteristic
96C4⋊#10596831C2311yescharacteristic
97#14556520—21no—
98#14556520—21no—
99#14556514C2×C411yescharacteristic
100#14556514C2×C411yescharacteristic
101#14556512C2×C411yescharacteristic
102#14556512C2×C411yescharacteristic
103#14556512C2×C411yescharacteristic
104#14556512C2×C411yescharacteristic
105#14556511C2×C411yescharacteristic
106#14556511C2×C411yescharacteristic
107C22⋊#10596831—21no—
108C22⋊#10596831—21no—
109C22⋊#10596831—21no—
110C22⋊#10596831—21no—
111C22⋊#10596831—21no—
112C22⋊#10596831C2×C411yescharacteristic
113C22⋊#10596831C2×C411yescharacteristic
114C22⋊#10596831D411yescharacteristic
115C22⋊#10596831D411yescharacteristic
116#14556503—21no—
117#14556503—21no—
118#14556501—21no—
119C4×#10596831—21no—
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C8×Dic73—21no—
125C22×D4×C73C2×C411yescharacteristic
126C23×C4×C73—21no—
127C2×M16×C73—21no—
128C4×D4×C73—21no—
129C4×D4×C73—21no—
130C4×D4×C73C2×C411yescharacteristic
131C4×D4×C73C2×C411yescharacteristic
132C4×D4×C73C2311yescharacteristic
133C4×D4×C73C2311yescharacteristic
134C2×C4⋊C4×C73C2×C411yescharacteristic
135C2×C22⋊C4×C73—21no—
136C2×C42×C73C2311yescharacteristic
137C4⋊C8×C73—21no—
138C4⋊C8×C73—21no—
139C4⋊C8×C73C2311yescharacteristic
140C4⋊C8×C73C2311yescharacteristic
141C22⋊C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146C22×C411yescharacteristic
145C2×D292C22×C411yescharacteristic
146C2×C22⋊D73—21no—
147C2×C4×D73—21no—
148#11924016—22no—
149#11924016—22no—
150#11924013—22no—
151#11924013—22no—
152#11924011—81no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—81no—
156C2×#10596831—81no—
157C2×#10596831—81no—
158C2×#10596831—81no—
159C2×#10596831C22×C411yescharacteristic
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C2×D411yescharacteristic
164C2×#10596831C2×D411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C8×D73—81no—
168C4⋊Dic73C22×C411yescharacteristic
169C4⋊Dic73C22×C411yescharacteristic
170#11924007—21no—
171#11924007—21no—
172#11924007—21no—
173#11924007—21no—
174C22⋊Dic73—21no—
175#11924005—21no—
176#11924005—21no—
177#11924005—21no—
178#11924005—21no—
179C4×Dic73—21no—
180C24×C73—21no—
181C2×D4×C73—22no—
182C2×D4×C73—22no—
183C2×D4×C73—21no—
184C2×D4×C73C22×C411yescharacteristic
185C2×D4×C73C22×C411yescharacteristic
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—81no—
192C22×C4×C73—81no—
193C22×C4×C73C22×C411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73#4111yescharacteristic
196M16×C73—81no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73C22×C411yescharacteristic
203C4⋊C4×C73C22×C411yescharacteristic
204C22⋊C4×C73—21no—
205C22⋊C4×C73—21no—
206C22⋊C4×C73—21no—
207C22⋊C4×C73—21no—
208C42×C73C22×C411yescharacteristic
209C42×C73C2×D411yescharacteristic
210C42×C73#4111yescharacteristic
211C42×C73C2411yescharacteristic
212C23×C73—24no—
213C23×C73—21no—
214C23×C73—21no—
215C23×C73—81no—
216C23×C73—81no—
217C23×C73C4×D411yescharacteristic
218C22×D73—21no—
219D4×C73—24no—
220D4×C73—21no—
221D4×C73—21no—
222D4×C73#13112yes—
223D4×C73#13112yes—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—81no—
236C2×C4×C73—81no—
237C2×C4×C73—81no—
238C2×C4×C73C4×D411yescharacteristic
239C2×C4×C73C4×D411yescharacteristic
240C2×C4×C73C4×D411yescharacteristic
241C2×C4×C73C23×C411yescharacteristic
242C2×C4×C73C22×D411yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C22⋊D73—81no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248D292—21no—
249D292—21no—
250C4×D73—41no—
251C4×D73—41no—
252Dic146—21no—
253Dic146—21no—
254C8×C73—41no—
255C8×C73—41no—
256C8×C73—41no—
257C8×C73—41no—
258#10596831—21no—
259#10596831—21no—
260#10596831—21no—
261#10596831—21no—
262#10596831—21no—
263#10596831—21no—
264#10596831—21no—
265#10596831—21no—
266#10596831—41no—
267#10596831—41no—
268C22×C73—21no—
269C22×C73—22no—
270C22×C73—22no—
271C22×C73—21no—
272C22×C73—21no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—84no—
278C22×C73C2×C4×D411yescharacteristic
279C2×D73—41no—
280C2×D73—41no—
281C2×D73—41no—
282C4×C73—21no—
283C4×C73—21no—
284C4×C73—21no—
285C4×C73—21no—
286C4×C73—41no—
287C4×C73—41no—
288C4×C73C2×#13111yescharacteristic
289C4×C73C2×#13111yescharacteristic
290C4×C73#57611yescharacteristic
291C4×C73#57711yescharacteristic
292Dic73—41no—
293Dic73—41no—
294Dic73—41no—
295#17918—731nomaximal, Sylow
296C2×C73—41no—
297C2×C73—42no—
298C2×C73—42no—
299C2×C73#292911yescharacteristic
300C2×C73#294611yescharacteristic
301C2×C73#295711yescharacteristic
302D73—81no—
303#3105—731no—
304#2993—731no—
305#2972—731no—
306#1586—731no—
307#1585—731no—
308#1582—731no—
309#1581—731no—
310#1580—731no—
311SD16⋊C8—731no—
312C8×SD16—731no—
313C8×D8—731no—
314#1574—731no—
315#1486D7311yescharacteristic, complemented
316#1482—731no—
317#1454—731no—
318C73#1791811yescharacteristic, complemented, Sylow
319#529—731no—
320C2×C4×D4C2×D7311yescharacteristic
321#484—731no—
322#481—731no—
323#478—731no—
324#478—731no—
325#463—731no—
326#463—731no—
327#450—731no—
328#447—731no—
329#446—731no—
330C8×Q8—731no—
331C4×SD16—731no—
332C4×SD16—731no—
333C4×D8—731no—
334C4×D8—731no—
335#436—731no—
336#436—1461no—
337#435—1461no—
338C8×D4—731no—
339C8×D4—731no—
340C8×D4—731no—
341C8×D4—731no—
342C8×D4—731no—
343C8×D4—1461no—
344C8×D4—1461no—
345#433—1461no—
346#431—731no—
347#431—731no—
348#431—731no—
349#431C2×D7311yescharacteristic
350#424—1461no—
351#423C2×D7311yescharacteristic
352C2×C22⋊C8—1461no—
353C2×C22⋊C8—1461no—
354#335—731no—
355#335—731no—
356#334—731no—
357#334—731no—
358Q8⋊C8—731no—
359Q8⋊C8—731no—
360D4⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8C2×D7311yescharacteristic
363D4⋊C8C2×D7311yescharacteristic
364D4⋊C8C2×D7311yescharacteristic
365D4⋊C8C2×D7311yescharacteristic
366#322—731no—
367#322—731no—
368#322—731no—
369C82—731no—
370C22×D4C4×D7311yescharacteristic
371C23×C4—21no—
372C2×SD16—731no—
373C2×SD16—731no—
374C2×D8—731no—
375C2×D8—731no—
376C2×M16—21no—
377C2×M16—1461no—
378C22×C8—1461no—
379C22×C8—1461no—
380C22×C8—1461no—
381C22×C8—1461no—
382C22×C8—1461no—
383#126—1461no—
384#125—731no—
385#124—731no—
386#123—1461no—
387C22⋊Q8—731no—
388#121—731no—
389C4×Q8—731no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—731no—
393C4×D4—1461no—
394C4×D4C4×D7311yescharacteristic
395C4×D4C4×D7311yescharacteristic
396C4×D4C22×D7311yescharacteristic
397C4×D4C22×D7311yescharacteristic
398#117—1461no—
399C2×C4⋊C4C4×D7311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C42C22×D7311yescharacteristic
402#107—731no—
403#107—731no—
404#106—731no—
405#106—731no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—731no—
412C4⋊C8—731no—
413C4⋊C8—731no—
414C4⋊C8—1461no—
415C4⋊C8—1461no—
416C4⋊C8C22×D7311yescharacteristic
417C4⋊C8C22×D7311yescharacteristic
418#103—731no—
419#103—731no—
420#102—731no—
421#102—731no—
422#102—731no—
423#102—731no—
424#102—731no—
425#102—731no—
426C22⋊C8—21no—
427C22⋊C8—731no—
428C22⋊C8—731no—
429C22⋊C8—731no—
430C22⋊C8—731no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435C22⋊C8—1461no—
436C22⋊C8—1461no—
437C22⋊C8—1461no—
438#97—1461no—
439C4×C8—731no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—731no—
443C4×C8—1461no—
444C4×C8—1461no—
445C4×C8C22×D7311yescharacteristic
446C4×C8C22×D7311yescharacteristic
447C24—21no—
448C2×Q8—731no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—731no—
453C2×D4—1461no—
454C2×D4C2×C4×D7311yescharacteristic
455C2×D4C2×C4×D7311yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—81no—
462C22×C4—81no—
463C22×C4—1461no—
464C22×C4C2×C4×D7311yescharacteristic
465C22×C4D4×D7311yescharacteristic
466C22×C4#1192402711yescharacteristic
467SD16—1462no—
468SD16—1462no—
469D8—1462no—
470D8—1462no—
471M16—81no—
472M16—5841no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—5841no—
478C2×C8—5841no—
479C2×C8—5841no—
480C2×C8—5841no—
481C2×C8—5841no—
482C2×C8—731no—
483C2×C8—731no—
484C2×C8—731no—
485C2×C8—731no—
486C2×C8—731no—
487C2×C8—731no—
488C2×C8—731no—
489C2×C8—731no—
490C2×C8—1461no—
491C2×C8—1461no—
492C4⋊C4—21no—
493C4⋊C4—731no—
494C4⋊C4—731no—
495C4⋊C4—1461no—
496C4⋊C4—1461no—
497C4⋊C4—1461no—
498C4⋊C4—1461no—
499C4⋊C4C2×C4×D7311yescharacteristic
500C4⋊C4C2×C4×D7311yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C22⋊C4—1461no—
510C42—1461no—
511C42C2×C4×D7311yescharacteristic
512C42D4×D7311yescharacteristic
513C42#1192402711yescharacteristic
514C42C23×D7311yescharacteristic
515C23—24no—
516C23—21no—
517C23—21no—
518C23—81no—
519C23—81no—
520C23—1461no—
521C23#1455655111yescharacteristic
522Q8—1461no—
523Q8—1461no—
524D4—24no—
525D4—21no—
526D4—21no—
527D4—5841no—
528D4—1461no—
529D4—1461no—
530D4#1455659912yes—
531D4#1455659912yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—2921no—
547C2×C4—2921no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4#1455655111yescharacteristic
552C2×C4#1455655111yescharacteristic
553C2×C4#1455655111yescharacteristic
554C2×C4C22×C4×D7311yescharacteristic
555C2×C4C2×D4×D7311yescharacteristic
556C2×C4C2×#1192402711yescharacteristic
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—2921no—
562C8—2921no—
563C8—1461no—
564C8—1461no—
565C8—1461no—
566C8—1461no—
567C8—1461no—
568C8—1461no—
569C8—1461no—
570C8—1461no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—22no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—84no—
581C22—2921no—
582C22—2921no—
583C22—2921no—
584C22C2×#1455655111yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—2921no—
592C4—2921no—
593C4—2921no—
594C4C2×#1455659911yescharacteristic
595C4C2×#1455659911yescharacteristic
596C4#1798938811yescharacteristic
597C4#1798939311yescharacteristic
598C2—41no—
599C2—42no—
600C2—42no—
601C2—5841no—
602C2#2261862111yescharacteristic
603C2#2261875711yescharacteristic
604C2#2261884411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1486C2
socleC22×C73C2×C4×D4
prime radical#17988721C4
cosocleC42×C73C24
hypercenter#1486D73
hypocenterC73#17918
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #22619076C2semidirect
3. #22618955C2semidirect
4. #22608792C2semidirect
5. #22608785C2semidirect
6. #22608764C2semidirect
7. #22608757C2semidirect
8. #22608752C2semidirect
9. #22608740C2semidirect
10. #22608734C2semidirect
11. #22608723C2semidirect
12. #22608722C2semidirect
13. #22608340C2semidirect
14. #22608231C2semidirect
15. C73×#1486C2semidirect
25. #17988714C22semidirect
26. #17988711C22semidirect
31. #17988664C22semidirect
40. #17988652C22semidirect
48. #17988339C22semidirect
49. #17988339C22semidirect
50. #17988337C22semidirect
51. #17988337C22semidirect
52. #17988319C22semidirect
53. #17988319C22semidirect
54. #17988316C22semidirect
55. #17988316C22semidirect
56. #17988309C22semidirect
57. #17988309C22semidirect
58. #17988308C22semidirect
59. C8×#10596831C22semidirect
315. #1486D73semidirect
318. C73#17918semidirect

Maximal subgroups

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

subgroupindex
#226199782
#226190762
#226189552
#226087922
#226087852
#226087642
#226087572
#226087522
#226087402
#226087342
#226087232
#226087222
#226083402
#226082312
C73×#14862
#1791873