Finite Group Databasebeta

← #33056044

Subgroups — #33056044

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#22619082C211yesmaximal, characteristic, complemented
3#22608795C211yesmaximal, characteristic, complemented
4#22608788C211yesmaximal, characteristic, complemented
5#22608767C211yesmaximal, characteristic, complemented
6#22608760C211yesmaximal, characteristic, complemented
7#22608753C211yesmaximal, characteristic, complemented
8#22608743C211yesmaximal, characteristic, complemented
9C8×#11924016C211yesmaximal, characteristic, complemented
10C8×#11924013C211yesmaximal, characteristic, complemented
11#22608719C211yesmaximal, characteristic, complemented
12#22608356C211yesmaximal, characteristic, complemented
13#22608337C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#2972C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17#17988922C411yescharacteristic
18#17988905C411yescharacteristic
19#17988887C411yescharacteristic
20#17988887C411yescharacteristic
21#17988802C411yescharacteristic
22#17988802C411yescharacteristic
23#17988738C411yescharacteristic
24#17988721C411yescharacteristic
25#17988717C2211yescharacteristic, complemented
26C8×Dic146C2211yescharacteristic, complemented
27C4×#11924016C2211yescharacteristic
28C4×#11924016C2211yescharacteristic
29C4×#11924013C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31#17988666C2211yescharacteristic, complemented
32#17988662—21no—
33#17988661—21no—
34C8×D292C2211yescharacteristic, complemented
35#17988647—21no—
36#17988640C2211yescharacteristic
37#17988640C2211yescharacteristic
38#17988612—21no—
39#17988611C2211yescharacteristic
40#17988339C2211yescharacteristic, complemented
41#17988339C2211yescharacteristic, complemented
42#17988337C2211yescharacteristic, complemented
43#17988337C2211yescharacteristic, complemented
44#17988317C2211yescharacteristic, complemented
45#17988317C2211yescharacteristic, complemented
46D4⋊#10596831C2211yescharacteristic
47D4⋊#10596831C2211yescharacteristic
48D4⋊#10596831C2211yescharacteristic
49D4⋊#10596831C2211yescharacteristic
50#17988314C2211yescharacteristic, complemented
51#17988314C2211yescharacteristic, complemented
52#17988309C2211yescharacteristic, complemented
53#17988309C2211yescharacteristic, complemented
54#17988308C2211yescharacteristic, complemented
55C8×#10596831C2211yescharacteristic, complemented
56C2×C4×D4×C73C2211yescharacteristic
57C8×D4×C73—21no—
58C8×D4×C73—21no—
59C8×D4×C73C2211yescharacteristic
60C8×D4×C73C2211yescharacteristic
61C8×D4×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#431×C73C2211yescharacteristic
64#431×C73C2211yescharacteristic
65C2×C22⋊C8×C73—21no—
66C2×C22⋊C8×C73—21no—
67C2×#11924016C2×C411yescharacteristic
68C2×#11924016C2×C411yescharacteristic
69C2×#11924013C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924012—21no—
72C2×#11924011—21no—
73C2×C8×D73—21no—
74#14556585—21no—
75#14556583C2×C411yescharacteristic
76#14556579C2×C411yescharacteristic
77#14556574—21no—
78#14556570C2×C411yescharacteristic
79#14556565C2×C411yescharacteristic
80C4×Dic146C2311yescharacteristic
81C4×D292C2311yescharacteristic
82C4×C22⋊D73—21no—
83#14556548—21no—
84#14556524C2×C411yescharacteristic
85#14556524C2×C411yescharacteristic
86#14556522C2×C411yescharacteristic
87#14556522C2×C411yescharacteristic
88C4⋊#10596831—21no—
89C4⋊#10596831—21no—
90C4⋊#10596831C2×C411yescharacteristic
91C4⋊#10596831C2×C411yescharacteristic
92C4⋊#10596831C2311yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94#14556520—21no—
95#14556520—21no—
96#14556514C2×C411yescharacteristic
97#14556514C2×C411yescharacteristic
98#14556512C2×C411yescharacteristic
99#14556512C2×C411yescharacteristic
100#14556512C2×C411yescharacteristic
101#14556512C2×C411yescharacteristic
102#14556511C2×C411yescharacteristic
103#14556511C2×C411yescharacteristic
104C22⋊#10596831—21no—
105C22⋊#10596831C2×C411yescharacteristic
106C22⋊#10596831C2×C411yescharacteristic
107#14556503—21no—
108#14556503—21no—
109#14556501—21no—
110C4×#10596831C2311yescharacteristic
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C4×#10596831C2311yescharacteristic
114C8×Dic73—21no—
115C22×D4×C73C2×C411yescharacteristic
116C23×C4×C73—21no—
117C22×C8×C73—21no—
118C22×C8×C73—21no—
119C22×C8×C73—21no—
120C22×C8×C73—21no—
121C4×D4×C73—21no—
122C4×D4×C73—21no—
123C4×D4×C73C2×C411yescharacteristic
124C4×D4×C73C2×C411yescharacteristic
125C4×D4×C73C2311yescharacteristic
126C4×D4×C73C2311yescharacteristic
127C2×C4⋊C4×C73C2×C411yescharacteristic
128C2×C22⋊C4×C73—21no—
129C2×C42×C73C2311yescharacteristic
130C4⋊C8×C73D411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73C2311yescharacteristic
133C4⋊C8×C73C2311yescharacteristic
134C22⋊C8×C73—21no—
135C22⋊C8×C73—21no—
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73—21no—
139C22⋊C8×C73D411yescharacteristic
140C22⋊C8×C73D411yescharacteristic
141C4×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#11924012—81no—
153#11924011—81no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831C22×C411yescharacteristic
159C2×#10596831C22×C411yescharacteristic
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C22×C411yescharacteristic
162C8×D73—81no—
163C4⋊Dic73C22×C411yescharacteristic
164C4⋊Dic73C22×C411yescharacteristic
165#11924007—21no—
166#11924007—21no—
167#11924007—21no—
168#11924007—21no—
169C22⋊Dic73—21no—
170#11924005—21no—
171#11924005—21no—
172#11924005—21no—
173#11924005—21no—
174C4×Dic73—21no—
175C24×C73—21no—
176C2×D4×C73—22no—
177C2×D4×C73—22no—
178C2×D4×C73—21no—
179C2×D4×C73C22×C411yescharacteristic
180C2×D4×C73C22×C411yescharacteristic
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—81no—
187C22×C4×C73—81no—
188C22×C4×C73C22×C411yescharacteristic
189C22×C4×C73C2×D411yescharacteristic
190C22×C4×C73#4111yescharacteristic
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—81no—
194C2×C8×C73—81no—
195C2×C8×C73—81no—
196C2×C8×C73—81no—
197C2×C8×C73C2×D411yescharacteristic
198C2×C8×C73C2×D411yescharacteristic
199C2×C8×C73C2×D411yescharacteristic
200C2×C8×C73C2×D411yescharacteristic
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—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—41no—
259C8×C73—41no—
260#10596831—21no—
261#10596831—21no—
262#10596831—21no—
263#10596831—21no—
264#10596831—41no—
265#10596831—41no—
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#2972D7311yescharacteristic, complemented
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#1486—731no—
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—21no—
339C8×D4—21no—
340C8×D4—731no—
341C8×D4C2×D7311yescharacteristic
342C8×D4C2×D7311yescharacteristic
343C8×D4C2×D7311yescharacteristic
344C8×D4C2×D7311yescharacteristic
345#433—1461no—
346#431—731no—
347#431—731no—
348#431C2×D7311yescharacteristic
349#431C2×D7311yescharacteristic
350#424—1461no—
351#423—731no—
352C2×C22⋊C8—21no—
353C2×C22⋊C8—21no—
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⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8—731no—
365D4⋊C8—731no—
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—1461no—
377C2×M16—1461no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
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—731no—
407C4⋊C8—731no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—1461no—
411C4⋊C8—1461no—
412C4⋊C8—1461no—
413C4⋊C8—1461no—
414C4⋊C8C22⋊D7311yescharacteristic
415C4⋊C8C22⋊D7311yescharacteristic
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—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—731no—
432C22⋊C8—731no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435C22⋊C8—1461no—
436C22⋊C8C22⋊D7311yescharacteristic
437C22⋊C8C22⋊D7311yescharacteristic
438#97—1461no—
439C4×C8—21no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—731no—
443C4×C8—731no—
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×C4C2×C22⋊D7311yescharacteristic
466C22×C4#1192402811yescharacteristic
467SD16—1462no—
468SD16—1462no—
469D8—1462no—
470D8—1462no—
471M16—5841no—
472M16—5841no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—81no—
479C2×C8—5841no—
480C2×C8—731no—
481C2×C8—731no—
482C2×C8—731no—
483C2×C8—731no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8C2×C22⋊D7311yescharacteristic
489C2×C8C2×C22⋊D7311yescharacteristic
490C2×C8C2×C22⋊D7311yescharacteristic
491C2×C8C2×C22⋊D7311yescharacteristic
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
512C42C2×C22⋊D7311yescharacteristic
513C42#1192402811yescharacteristic
514C42C23×D7311yescharacteristic
515C23—24no—
516C23—21no—
517C23—21no—
518C23—81no—
519C23—81no—
520C23—1461no—
521C23C4×C22⋊D7311yescharacteristic
522Q8—1461no—
523Q8—1461no—
524D4—24no—
525D4—21no—
526D4—21no—
527D4—5841no—
528D4—1461no—
529D4—1461no—
530D4#1455659712yes—
531D4#1455659712yes—
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×C4C4×C22⋊D7311yescharacteristic
552C2×C4C4×C22⋊D7311yescharacteristic
553C2×C4C4×C22⋊D7311yescharacteristic
554C2×C4C22×C4×D7311yescharacteristic
555C2×C4C22×C22⋊D7311yescharacteristic
556C2×C4C2×#1192402811yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—2921no—
564C8—2921no—
565C8—2921no—
566C8—2921no—
567C8—1461no—
568C8—1461no—
569C8—1461no—
570C8—1461no—
571C22—21no—
572C22—22no—
573C22—22no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—84no—
581C22—2921no—
582C22—2921no—
583C22—2921no—
584C22C2×C4×C22⋊D7311yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—2921no—
592C4—2921no—
593C4—2921no—
594C4C2×#1455659711yescharacteristic
595C4C2×#1455659711yescharacteristic
596C4#1798939011yescharacteristic
597C4#1798939811yescharacteristic
598C2—41no—
599C2—42no—
600C2—42no—
601C2—5841no—
602C2#2261862511yescharacteristic
603C2#2261876311yescharacteristic
604C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2972C2
socleC22×C73C2×C4×D4
prime radical#17988721C4
cosocleC42×C73C24
hypercenter#2972D73
hypocenterC73#17918
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #22619082C2semidirect
3. #22608795C2semidirect
4. #22608788C2semidirect
5. #22608767C2semidirect
6. #22608760C2semidirect
7. #22608753C2semidirect
8. #22608743C2semidirect
9. C8×#11924016C2semidirect
10. C8×#11924013C2semidirect
11. #22608719C2semidirect
12. #22608356C2semidirect
13. #22608337C2semidirect
14. #22608231C2semidirect
15. C73×#2972C2semidirect
25. #17988717C22semidirect
26. C8×Dic146C22semidirect
31. #17988666C22semidirect
34. C8×D292C22semidirect
40. #17988339C22semidirect
41. #17988339C22semidirect
42. #17988337C22semidirect
43. #17988337C22semidirect
44. #17988317C22semidirect
45. #17988317C22semidirect
50. #17988314C22semidirect
51. #17988314C22semidirect
52. #17988309C22semidirect
53. #17988309C22semidirect
54. #17988308C22semidirect
55. C8×#10596831C22semidirect
305. #2972D73semidirect
318. C73#17918semidirect

Maximal subgroups

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

subgroupindex
#226199782
#226190822
#226087952
#226087882
#226087672
#226087602
#226087532
#226087432
C8×#119240162
C8×#119240132
#226087192
#226083562
#226083372
#226082312
C73×#29722
#1791873