Finite Group Databasebeta

← #33056101

Subgroups — #33056101

Order 18688.

678 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619929C211yesmaximal, characteristic
2#22619005C211yesmaximal, characteristic, complemented
3#22618952C211yesmaximal, characteristic, complemented
4#22608796C211yesmaximal, characteristic, complemented
5#22608794C211yesmaximal, characteristic, complemented
6#22608763C211yesmaximal, characteristic, complemented
7#22608757C211yesmaximal, characteristic, complemented
8#22608756C211yesmaximal, characteristic, complemented
9C8×#11924013C211yesmaximal, characteristic, complemented
10C8×#11924013C211yesmaximal, characteristic, complemented
11#22608708C211yesmaximal, characteristic, complemented
12#22608372C211yesmaximal, characteristic, complemented
13#22608346C211yesmaximal, characteristic, complemented
14#22608227C211yesmaximal, characteristic, complemented
15C73×#1580C211yesmaximal, characteristic, complemented
16#17989134C2211yescharacteristic
17C4×D4×D73C2211yescharacteristic
18#17988902C411yescharacteristic
19#17988899C411yescharacteristic
20#17988866C411yescharacteristic
21#17988865C411yescharacteristic
22#17988781C411yescharacteristic
23#17988780C411yescharacteristic
24#17988722C411yescharacteristic
25#17988719C411yescharacteristic
26C4×D584C2211yescharacteristic
27C4×#11924013C2211yescharacteristic
28C4×#11924013C2211yescharacteristic
29#17988665C2211yescharacteristic, complemented
30#17988664C2211yescharacteristic, complemented
31#17988661—21no—
32#17988658—21no—
33C8×D292C2211yescharacteristic
34C8×D292C2211yescharacteristic, complemented
35D4×#10596831C2211yescharacteristic
36#17988652C2211yescharacteristic
37C8×C22⋊D73—21no—
38#17988650—21no—
39#17988643C2211yescharacteristic
40#17988639C2211yescharacteristic
41#17988638C2211yescharacteristic
42#17988638C2211yescharacteristic
43#17988553—21no—
44#17988552—21no—
45C2×#14556503—21no—
46C22⋊C8×D73—21no—
47C4×#11924011C2211yescharacteristic
48#17988339C2211yescharacteristic, complemented
49#17988339C2211yescharacteristic, complemented
50#17988338C2211yescharacteristic, complemented
51#17988316C2211yescharacteristic
52#17988316C2211yescharacteristic, complemented
53D4⋊#10596831C2211yescharacteristic
54D4⋊#10596831C2211yescharacteristic, complemented
55#17988314C2211yescharacteristic
56#17988314C2211yescharacteristic, complemented
57#17988309C2211yescharacteristic, complemented
58#17988309C2211yescharacteristic, complemented
59C8×#10596831C2211yescharacteristic, complemented
60C4×D8×C73C2211yescharacteristic
61C8×D4×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic, complemented
63#334×C73C2211yescharacteristic, complemented
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic, complemented
66#322×C73C2211yescharacteristic, complemented
67C2×#11924028—21no—
68C2×D4×D73C2×C411yescharacteristic
69C22×C4×D73—21no—
70C2×D584C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72C2×#11924013C2×C411yescharacteristic
73C2×#11924012—21no—
74C2×#11924011—21no—
75C2×#11924011—21no—
76C22×#10596831—21no—
77C2×C8×D73—21no—
78C2×C8×D73—21no—
79C2×C8×D73—21no—
80#14556590C2×C411yescharacteristic
81#14556587C2×C411yescharacteristic
82#14556577—21no—
83#14556566C2×C411yescharacteristic
84#14556564—21no—
85#14556562C2×C411yescharacteristic
86C4×D292C2311yescharacteristic
87C4×D292C2311yescharacteristic
88D4×Dic73C2×C411yescharacteristic
89#14556553C2×C411yescharacteristic
90C4×C22⋊D73—21no—
91C4×C22⋊D73—21no—
92#14556551—21no—
93C4⋊C4×D73C2×C411yescharacteristic
94C22⋊C4×D73—21no—
95C42×D73C2311yescharacteristic
96#14556525C2×C411yescharacteristic
97#14556524C2×C411yescharacteristic
98#14556524C2×C411yescharacteristic
99C4⋊#10596831C2311yescharacteristic
100C4⋊#10596831C2311yescharacteristic
101#14556520C2×C411yescharacteristic
102#14556520C2×C411yescharacteristic
103#14556520D411yescharacteristic
104#14556520D411yescharacteristic
105#14556513C2×C411yescharacteristic
106#14556513C2×C411yescharacteristic
107#14556512C2×C411yescharacteristic
108#14556512C2×C411yescharacteristic
109#14556511C2×C411yescharacteristic
110#14556511C2×C411yescharacteristic
111C22⋊#10596831—21no—
112C22⋊#10596831—21no—
113#14556503—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503—21no—
118#14556503—21no—
119#14556503C2×C411yescharacteristic
120#14556503C2×C411yescharacteristic
121#14556503D411yescharacteristic
122#14556503D411yescharacteristic
123#14556501—21no—
124#14556501—21no—
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C4×#10596831C2311yescharacteristic
128C8×Dic73—21no—
129C2×D8×C73C2×C411yescharacteristic
130C22×C8×C73—21no—
131C22×C8×C73—21no—
132C4×D4×C73C2311yescharacteristic
133C4×D4×C73C2311yescharacteristic
134#107×C73C2×C411yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#102×C73C2×C411yescharacteristic
138#102×C73C2×C411yescharacteristic
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C23×D73—21no—
145#11924028—81no—
146#11924028—81no—
147C2×Dic146—21no—
148C2×D292—21no—
149C2×D292C22×C411yescharacteristic
150C2×D292C22×C411yescharacteristic
151C2×C22⋊D73—21no—
152C2×C22⋊D73—21no—
153C2×C22⋊D73—21no—
154C2×C22⋊D73—21no—
155D4×D73—22no—
156D4×D73—22no—
157C22×Dic73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—21no—
161C2×C4×D73—21no—
162C2×C4×D73—81no—
163C2×C4×D73—81no—
164C2×C4×D73C22×C411yescharacteristic
165C2×C4×D73C2×D411yescharacteristic
166C2×C4×D73#4111yescharacteristic
167D584—22no—
168#11924013—22no—
169#11924013—22no—
170#11924012—81no—
171#11924011—42no—
172#11924011—81no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—81no—
177C2×#10596831C22×C411yescharacteristic
178C2×#10596831C22×C411yescharacteristic
179C2×#10596831C2×D411yescharacteristic
180C2×#10596831C2×D411yescharacteristic
181C8×D73—81no—
182C8×D73—81no—
183C8×D73—81no—
184C4⋊Dic73C22×C411yescharacteristic
185C4⋊Dic73C22×C411yescharacteristic
186#11924007—21no—
187#11924007—21no—
188C22⋊Dic73—21no—
189C22⋊Dic73—21no—
190#11924005—21no—
191#11924005—21no—
192#11924005—21no—
193#11924005—21no—
194C4×Dic73C22×C411yescharacteristic
195C4×Dic73C2×D411yescharacteristic
196C4×Dic73#4111yescharacteristic
197C2×D4×C73C22×C411yescharacteristic
198C2×D4×C73C22×C411yescharacteristic
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201D8×C73—22no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—81no—
206C2×C8×C73—81no—
207C2×C8×C73C22×C411yescharacteristic
208C2×C8×C73C22×C411yescharacteristic
209C2×C8×C73C2×D411yescharacteristic
210C2×C8×C73C2×D411yescharacteristic
211C4⋊C4×C73C22×C411yescharacteristic
212C4⋊C4×C73C22×C411yescharacteristic
213C22⋊C4×C73—21no—
214C22⋊C4×C73—21no—
215C42×C73C2411yescharacteristic
216C23×C73—21no—
217C23×C73—21no—
218C22×D73—21no—
219C22×D73—24no—
220C22×D73—21no—
221C22×D73—81no—
222C22×D73—81no—
223C22×D73C4×D411yescharacteristic
224D4×C73—21no—
225D4×C73—21no—
226D4×C73—21no—
227D4×C73#13112yes—
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×C73C23×C411yescharacteristic
235C2×C4×C73C22×D411yescharacteristic
236C2×C4×C73C2×#4111yescharacteristic
237C22⋊D73—24no—
238C22⋊D73—81no—
239C22⋊D73—81no—
240C22⋊D73—81no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—81no—
244C2×Dic73C4×D411yescharacteristic
245C2×Dic73C4×D411yescharacteristic
246C2×Dic73C4×D411yescharacteristic
247D292—21no—
248D292—21no—
249D292—21no—
250D292—81no—
251D292#13112yes—
252C4×D73—21no—
253C4×D73—21no—
254C4×D73—21no—
255C4×D73—21no—
256C4×D73—41no—
257C4×D73—41no—
258C4×D73—41no—
259C4×D73—41no—
260C4×D73—41no—
261C4×D73—81no—
262C4×D73—81no—
263Dic146—81no—
264C8×C73—21no—
265C8×C73—21no—
266C8×C73—21no—
267C8×C73—21no—
268C8×C73—41no—
269C8×C73—41no—
270C8×C73—41no—
271#10596831—22no—
272#10596831—21no—
273#10596831—21no—
274#10596831—21no—
275#10596831—21no—
276#10596831—41no—
277#10596831—41no—
278C22×C73—22no—
279C22×C73—41no—
280C22×C73—41no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73—41no—
284C22×C73C2×C4×D411yescharacteristic
285C2×D73—21no—
286C2×D73—22no—
287C2×D73—21no—
288C2×D73—21no—
289C2×D73—41no—
290C2×D73—41no—
291C2×D73—41no—
292C2×D73—41no—
293C2×D73—41no—
294C2×D73—84no—
295C4×C73—21no—
296C4×C73—41no—
297C4×C73—41no—
298C4×C73C2×#13111yescharacteristic
299C4×C73C2×#13111yescharacteristic
300C4×C73#57611yescharacteristic
301C4×C73#57611yescharacteristic
302Dic73—21no—
303Dic73—21no—
304Dic73—21no—
305Dic73—41no—
306Dic73—41no—
307#17922—731nomaximal, Sylow
308C2×C73—42no—
309C2×C73—81no—
310C2×C73#292911yescharacteristic
311C2×C73#294811yescharacteristic
312C2×C73#295611yescharacteristic
313D73—41no—
314D73—42no—
315D73—81no—
316#3100—731no—
317#2981—731no—
318#2972—731no—
319#1586—731no—
320#1586—731no—
321#1581—731no—
322#1581—731no—
323#1580—731no—
324#1580D7311yescharacteristic, complemented
325C8×D8—731no—
326C8×D8—731no—
327#1572—731no—
328#1490—731no—
329#1484—731no—
330#1453—731no—
331C73#1792211yescharacteristic, complemented, Sylow
332#532—731no—
333C2×C4×D4—731no—
334#480—731no—
335#480—731no—
336#474—731no—
337#474—731no—
338#459—731no—
339#459—731no—
340#447—731no—
341#447—731no—
342C4×D8—731no—
343C4×D8—731no—
344C4×D8—731no—
345C4×D8C2×D7311yescharacteristic
346#436—731no—
347#436—731no—
348#435—1461no—
349#435—1461no—
350C8×D4—731no—
351C8×D4—731no—
352C8×D4—731no—
353C8×D4—731no—
354C8×D4—1461no—
355C8×D4—1461no—
356C8×D4C2×D7311yescharacteristic
357C8×D4C2×D7311yescharacteristic, complemented
358#432—731no—
359#431—731no—
360#431—731no—
361#431—731no—
362#408—1461no—
363#408—1461no—
364C2×C22⋊C8—1461no—
365C2×C22⋊C8—1461no—
366C4×M16—731no—
367#335—731no—
368#335—731no—
369#334—731no—
370#334C2×D7311yescharacteristic, complemented
371D4⋊C8—731no—
372D4⋊C8—731no—
373D4⋊C8—731no—
374D4⋊C8—731no—
375D4⋊C8—731no—
376D4⋊C8—731no—
377D4⋊C8C2×D7311yescharacteristic
378D4⋊C8C2×D7311yescharacteristic, complemented
379#322—731no—
380#322—731no—
381#322C2×D7311yescharacteristic, complemented
382C82—731no—
383C2×#41—1461no—
384C22×D4—731no—
385C23×C4—1461no—
386C2×D8—731no—
387C2×D8—731no—
388C2×D8—731no—
389C2×D8C4×D7311yescharacteristic
390C2×M16—1461no—
391C2×M16—1461no—
392C2×M16—1461no—
393C22×C8—21no—
394C22×C8—21no—
395C22×C8—1461no—
396C22×C8—1461no—
397C22×C8—1461no—
398C22×C8—1461no—
399C4⋊Q8—731no—
400#127—731no—
401#124—1461no—
402#121—731no—
403#121—731no—
404#121—1461no—
405C4×D4—731no—
406C4×D4—731no—
407C4×D4—731no—
408C4×D4—731no—
409C4×D4—1461no—
410C4×D4—1461no—
411C4×D4—1461no—
412C4×D4C22×D7311yescharacteristic
413C4×D4C22×D7311yescharacteristic
414C2×C4⋊C4—731no—
415C2×C22⋊C4—1461no—
416C2×C42—731no—
417#107—731no—
418#107—731no—
419#107—731no—
420#107C4×D7311yescharacteristic
421C4⋊C8—731no—
422C4⋊C8—731no—
423C4⋊C8—731no—
424C4⋊C8—731no—
425C4⋊C8—731no—
426C4⋊C8—731no—
427C4⋊C8C22×D7311yescharacteristic
428C4⋊C8C22×D7311yescharacteristic
429#102—731no—
430#102—731no—
431#102—731no—
432#102—731no—
433#102—731no—
434#102—731no—
435#102C4×D7311yescharacteristic
436#102C4×D7311yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—731no—
440C22⋊C8—731no—
441C22⋊C8—731no—
442C22⋊C8—731no—
443C22⋊C8—1461no—
444C22⋊C8—1461no—
445C22⋊C8—1461no—
446C22⋊C8—1461no—
447C22⋊C8—1461no—
448C22⋊C8—1461no—
449C22⋊C8—1461no—
450C22⋊C8—1461no—
451#97—1461no—
452#97—1461no—
453C4×C8—731no—
454C4×C8—731no—
455C4×C8—731no—
456C4×C8—1461no—
457C4×C8C22×D7311yescharacteristic
458C4×C8C22×D7311yescharacteristic
459C4×C8C22×D7311yescharacteristic
460C24—1461no—
461#41—5841no—
462#41—5841no—
463C2×Q8—1461no—
464C2×D4—731no—
465C2×D4—731no—
466C2×D4—1461no—
467C2×D4—1461no—
468C2×D4—1461no—
469C2×D4—1461no—
470C2×D4—1462no—
471C2×D4—1461no—
472C2×D4—1462no—
473C2×D4C2×C4×D7311yescharacteristic
474C2×D4C2×C4×D7311yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—5841no—
478C22×C4—5841no—
479C22×C4—731no—
480C22×C4—731no—
481C22×C4—731no—
482C22×C4—1461no—
483C22×C4—1461no—
484C22×C4—1461no—
485C22×C4—1461no—
486C22×C4—1461no—
487D8—22no—
488D8—1462no—
489D8—1462no—
490D8—1462no—
491M16—2922no—
492M16—5841no—
493M16—5841no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—81no—
498C2×C8—81no—
499C2×C8—5841no—
500C2×C8—5841no—
501C2×C8—5841no—
502C2×C8—5841no—
503C2×C8—731no—
504C2×C8—731no—
505C2×C8—731no—
506C2×C8—731no—
507C2×C8—1461no—
508C2×C8—1461no—
509C2×C8—1461no—
510C2×C8C2×C4×D7311yescharacteristic
511C2×C8C2×C4×D7311yescharacteristic
512C2×C8D4×D7311yescharacteristic
513C2×C8D4×D7311yescharacteristic
514C4⋊C4—731no—
515C4⋊C4—731no—
516C4⋊C4—1461no—
517C4⋊C4—1461no—
518C4⋊C4C2×C4×D7311yescharacteristic
519C4⋊C4C2×C4×D7311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—1461no—
523C22⋊C4—1461no—
524C22⋊C4—1461no—
525C22⋊C4—1461no—
526C22⋊C4—1461no—
527C22⋊C4—1461no—
528C42—731no—
529C42—731no—
530C42—731no—
531C42C23×D7311yescharacteristic
532C23—21no—
533C23—21no—
534C23—5841no—
535C23—5841no—
536C23—731no—
537C23—1464no—
538C23—1461no—
539C23—1461no—
540Q8—5841no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—5841no—
545D4—5841no—
546D4—5841no—
547D4—5841no—
548D4—732no—
549D4—1464no—
550D4—1461no—
551D4—1461no—
552D4—1461no—
553D4#1455659712yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—2921no—
561C2×C4—2921no—
562C2×C4—2921no—
563C2×C4—2921no—
564C2×C4—2921no—
565C2×C4—5841no—
566C2×C4—5841no—
567C2×C4—5841no—
568C2×C4—731no—
569C2×C4—731no—
570C2×C4—731no—
571C2×C4—1461no—
572C2×C4—1461no—
573C2×C4—1461no—
574C2×C4—1461no—
575C2×C4—1461no—
576C2×C4—1461no—
577C2×C4C22×C4×D7311yescharacteristic
578C2×C4C2×D4×D7311yescharacteristic
579C2×C4#41×D7311yescharacteristic
580C8—21no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—2921no—
588C8—2921no—
589C8—1462no—
590C8—1461no—
591C8—1461no—
592C8—1461no—
593C8—1461no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—2921no—
601C22—2921no—
602C22—2921no—
603C22—2921no—
604C22—2921no—
605C22—5844no—
606C22—1461no—
607C22—1461no—
608C22—1461no—
609C22—1462no—
610C22C4×D4×D7311yescharacteristic
611C4—21no—
612C4—41no—
613C4—41no—
614C4—2921no—
615C4—2921no—
616C4—1461no—
617C4—1461no—
618C4—1461no—
619C4#131×D7311yescharacteristic
620C4C2×#1455659711yescharacteristic
621C4#1798939111yescharacteristic
622C4#1798939111yescharacteristic
623C2—42no—
624C2—81no—
625C2—2922no—
626C2—2921no—
627C2—5841no—
628C2#2261862011yescharacteristic
629C2#2261878011yescharacteristic
630C2#2261883911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1580C2
socleC22×C73C2×C4×D4
prime radical#22619929C2
cosocleC42×C73C24
hypercenter#1580D73
hypocenterC73#17922
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

Complements

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

NH ≅ G/Ntype
2. #22619005C2semidirect
3. #22618952C2semidirect
4. #22608796C2semidirect
5. #22608794C2semidirect
6. #22608763C2semidirect
7. #22608757C2semidirect
8. #22608756C2semidirect
9. C8×#11924013C2semidirect
10. C8×#11924013C2semidirect
11. #22608708C2semidirect
12. #22608372C2semidirect
13. #22608346C2semidirect
14. #22608227C2semidirect
15. C73×#1580C2semidirect
29. #17988665C22semidirect
30. #17988664C22semidirect
34. C8×D292C22semidirect
48. #17988339C22semidirect
49. #17988339C22semidirect
50. #17988338C22semidirect
52. #17988316C22semidirect
54. D4⋊#10596831C22semidirect
56. #17988314C22semidirect
57. #17988309C22semidirect
58. #17988309C22semidirect
59. C8×#10596831C22semidirect
62. C8×D4×C73C22semidirect
63. #334×C73C22semidirect
65. D4⋊C8×C73C22semidirect
66. #322×C73C22semidirect
324. #1580D73semidirect
331. C73#17922semidirect
357. C8×D4C2×D73semidirect
370. #334C2×D73semidirect
378. D4⋊C8C2×D73semidirect
381. #322C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226199292
#226190052
#226189522
#226087962
#226087942
#226087632
#226087572
#226087562
C8×#119240132
#226087082
#226083722
#226083462
#226082272
C73×#15802
#1792273