Finite Group Databasebeta

← #33056048

Subgroups — #33056048

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#22619980C211yesmaximal, characteristic
2#22619082C211yesmaximal, characteristic, complemented
3#22618954C211yesmaximal, characteristic, complemented
4#22608797C211yesmaximal, characteristic, complemented
5#22608790C211yesmaximal, characteristic, complemented
6#22608769C211yesmaximal, characteristic, complemented
7#22608762C211yesmaximal, characteristic, complemented
8#22608756C211yesmaximal, characteristic, complemented
9#22608745C211yesmaximal, characteristic, complemented
10C8×#11924017C211yesmaximal, characteristic, complemented
11C8×D584C211yesmaximal, characteristic, complemented
12#22608720C211yesmaximal, characteristic, complemented
13#22608357C211yesmaximal, characteristic, complemented
14#22608340C211yesmaximal, characteristic, complemented
15C73×#1454C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18#17988923C411yescharacteristic
19#17988906C411yescharacteristic
20#17988888C411yescharacteristic
21#17988888C411yescharacteristic
22#17988803C411yescharacteristic
23#17988803C411yescharacteristic
24#17988740C411yescharacteristic
25#17988723C411yescharacteristic
26#17988717C2211yescharacteristic, complemented
27C8×Dic146C2211yescharacteristic, complemented
28C4×#11924017C2211yescharacteristic
29C4×#11924017C2211yescharacteristic
30C4×D584C2211yescharacteristic
31C4×D584C2211yescharacteristic
32#17988666C2211yescharacteristic, complemented
33#17988662—21no—
34#17988661—21no—
35C8×D292C2211yescharacteristic
36C8×D292C2211yescharacteristic
37C8×D292C2211yescharacteristic
38C8×D292C2211yescharacteristic
39C8×D292C2211yescharacteristic, complemented
40#17988652—21no—
41#17988652—21no—
42#17988647—21no—
43#17988640C2211yescharacteristic
44#17988612—21no—
45#17988611C2211yescharacteristic
46C22⋊C8×D73—21no—
47C22⋊C8×D73—21no—
48#17988340C2211yescharacteristic, complemented
49#17988340C2211yescharacteristic, complemented
50#17988338C2211yescharacteristic, complemented
51#17988338C2211yescharacteristic, complemented
52#17988319C2211yescharacteristic, complemented
53#17988319C2211yescharacteristic, complemented
54#17988316C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988316C2211yescharacteristic
57#17988316C2211yescharacteristic
58#17988316C2211yescharacteristic, complemented
59#17988316C2211yescharacteristic, complemented
60#431×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63#322×C73C2211yescharacteristic, complemented
64#322×C73C2211yescharacteristic, complemented
65#322×C73C2211yescharacteristic, complemented
66C82×C73C2211yescharacteristic, complemented
67C22×D292C2×C411yescharacteristic
68C22×C4×D73—21no—
69C2×#11924017C2×C411yescharacteristic
70C2×#11924017C2×C411yescharacteristic
71C2×D584C2×C411yescharacteristic
72C2×D584C2×C411yescharacteristic
73C2×#11924012—21no—
74C2×#11924011—21no—
75C2×C8×D73—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78C2×C8×D73—21no—
79C2×C8×D73—21no—
80#14556585—21no—
81#14556583C2×C411yescharacteristic
82#14556579C2×C411yescharacteristic
83#14556574—21no—
84#14556570C2×C411yescharacteristic
85#14556565C2×C411yescharacteristic
86C4×Dic146C2311yescharacteristic
87C4×D292—21no—
88C4×D292—21no—
89C4×D292C2×C411yescharacteristic
90C4×D292C2×C411yescharacteristic
91C4×D292C2311yescharacteristic
92C4×D292C2311yescharacteristic
93C4×D292C2311yescharacteristic
94C4×C22⋊D73—21no—
95#14556548—21no—
96C2×C4⋊Dic73C2×C411yescharacteristic
97C2×#11924005—21no—
98#14556525C2×C411yescharacteristic
99#14556525C2×C411yescharacteristic
100#14556523C2×C411yescharacteristic
101#14556523C2×C411yescharacteristic
102C4⋊#10596831—21no—
103C4⋊#10596831C2311yescharacteristic
104C4⋊#10596831C2311yescharacteristic
105C4⋊#10596831C2311yescharacteristic
106C4⋊#10596831C2311yescharacteristic
107#14556520—21no—
108#14556520—21no—
109#14556516C2×C411yescharacteristic
110#14556516C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556513C2×C411yescharacteristic
113#14556513C2×C411yescharacteristic
114#14556513C2×C411yescharacteristic
115#14556513C2×C411yescharacteristic
116#14556513C2×C411yescharacteristic
117C22⋊#10596831—21no—
118#14556503—21no—
119#14556503—21no—
120#14556503—21no—
121#14556503—21no—
122#14556503—21no—
123#14556503—21no—
124#14556501—21no—
125C4×#10596831—21no—
126C8×Dic73—21no—
127C2×C42×C73C2311yescharacteristic
128C4⋊C8×C73—21no—
129C4⋊C8×C73C2×C411yescharacteristic
130C4⋊C8×C73C2×C411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73D411yescharacteristic
133C22⋊C8×C73—21no—
134C22⋊C8×C73C2×C411yescharacteristic
135C22⋊C8×C73C2×C411yescharacteristic
136C22⋊C8×C73D411yescharacteristic
137C22⋊C8×C73D411yescharacteristic
138C4×C8×C73C2311yescharacteristic
139C4×C8×C73C2311yescharacteristic
140C4×C8×C73C2311yescharacteristic
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C23×D73—21no—
145C2×Dic146C22×C411yescharacteristic
146C2×D292—21no—
147C2×D292—22no—
148C2×D292—22no—
149C2×D292C22×C411yescharacteristic
150C2×D292C22×C411yescharacteristic
151C2×D292C22×C411yescharacteristic
152C2×C22⋊D73—21no—
153C22×Dic73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—81no—
160C2×C4×D73—81no—
161#11924017—22no—
162#11924017—22no—
163D584—22no—
164D584—22no—
165#11924012—81no—
166#11924011—81no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C8×D73—81no—
172C8×D73—81no—
173C8×D73—81no—
174C8×D73—81no—
175C8×D73—81no—
176C4⋊Dic73—21no—
177C4⋊Dic73C22×C411yescharacteristic
178C4⋊Dic73C22×C411yescharacteristic
179C4⋊Dic73C22×C411yescharacteristic
180C4⋊Dic73C22×C411yescharacteristic
181#11924007—21no—
182#11924007—21no—
183#11924007—21no—
184#11924007—21no—
185C22⋊Dic73—21no—
186#11924005—21no—
187#11924005—21no—
188#11924005—21no—
189#11924005—21no—
190#11924005—21no—
191#11924005—21no—
192#11924005—21no—
193#11924005—21no—
194C4×Dic73—21no—
195C22×C4×C73C22×C411yescharacteristic
196C22×C4×C73C2×D411yescharacteristic
197C22×C4×C73#4111yescharacteristic
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73C22×C411yescharacteristic
201C2×C8×C73C22×C411yescharacteristic
202C2×C8×C73C22×C411yescharacteristic
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C2×D411yescharacteristic
205C2×C8×C73C2×D411yescharacteristic
206C2×C8×C73C2×D411yescharacteristic
207C2×C8×C73C2×D411yescharacteristic
208C42×C73C22×C411yescharacteristic
209C42×C73C2×D411yescharacteristic
210C42×C73#4111yescharacteristic
211C42×C73C2411yescharacteristic
212C23×C73C4×D411yescharacteristic
213C22×D73—21no—
214C22×D73—21no—
215C22×D73—24no—
216C22×D73—21no—
217C22×D73—81no—
218C22×D73—81no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—41no—
224C2×C4×C73C4×D411yescharacteristic
225C2×C4×C73C4×D411yescharacteristic
226C2×C4×C73C4×D411yescharacteristic
227C2×C4×C73C23×C411yescharacteristic
228C2×C4×C73C22×D411yescharacteristic
229C2×C4×C73C2×#4111yescharacteristic
230C22⋊D73—81no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—81no—
237D292—24no—
238D292—21no—
239D292—21no—
240D292—21no—
241D292—21no—
242D292#13112yes—
243D292#13112yes—
244C4×D73—41no—
245C4×D73—41no—
246C4×D73—41no—
247C4×D73—41no—
248C4×D73—41no—
249C4×D73—41no—
250C4×D73—81no—
251C4×D73—81no—
252Dic146—21no—
253Dic146—21no—
254C8×C73—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—21no—
259C8×C73—21no—
260C8×C73—21no—
261C8×C73—21no—
262C8×C73—41no—
263C8×C73—41no—
264#10596831—41no—
265#10596831—41no—
266#10596831—41no—
267#10596831—41no—
268C22×C73—21no—
269C22×C73—21no—
270C22×C73—21no—
271C22×C73C2×C4×D411yescharacteristic
272C2×D73—22no—
273C2×D73—22no—
274C2×D73—41no—
275C2×D73—41no—
276C2×D73—41no—
277C2×D73—41no—
278C2×D73—41no—
279C2×D73—41no—
280C2×D73—41no—
281C2×D73—84no—
282C4×C73—21no—
283C4×C73—21no—
284C4×C73—21no—
285C4×C73—21no—
286C4×C73C2×#13111yescharacteristic
287C4×C73C2×#13111yescharacteristic
288C4×C73#57611yescharacteristic
289C4×C73#57711yescharacteristic
290Dic73—41no—
291Dic73—41no—
292Dic73—41no—
293Dic73—41no—
294Dic73—41no—
295#17918—731nomaximal, Sylow
296C2×C73—41no—
297C2×C73#292911yescharacteristic
298C2×C73#294611yescharacteristic
299C2×C73#295711yescharacteristic
300D73—42no—
301D73—42no—
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#1486—731no—
316#1482—731no—
317#1454D7311yescharacteristic, complemented
318C73#1791811yescharacteristic, complemented, Sylow
319#529—731no—
320C2×C4×D4—731no—
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#431C2×D7311yescharacteristic
348#431C2×D7311yescharacteristic
349#431C2×D7311yescharacteristic
350#424—1461no—
351#423—731no—
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⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8—731no—
365D4⋊C8—731no—
366#322C2×D7311yescharacteristic, complemented
367#322C2×D7311yescharacteristic, complemented
368#322C2×D7311yescharacteristic, complemented
369C82C2×D7311yescharacteristic, complemented
370C22×D4—731no—
371C23×C4—1461no—
372C2×SD16—731no—
373C2×SD16—731no—
374C2×D8—731no—
375C2×D8—731no—
376C2×M16—1461no—
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—731no—
391C4×D4—731no—
392C4×D4—731no—
393C4×D4—731no—
394C4×D4—731no—
395C4×D4—1461no—
396C4×D4—1461no—
397C4×D4—1461no—
398#117—1461no—
399C2×C4⋊C4—731no—
400C2×C22⋊C4—1461no—
401C2×C42C22×D7311yescharacteristic
402#107—731no—
403#107—731no—
404#106—731no—
405#106—731no—
406C4⋊C8—21no—
407C4⋊C8—731no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—1461no—
412C4⋊C8—1461no—
413C4⋊C8—1461no—
414C4⋊C8C4×D7311yescharacteristic
415C4⋊C8C4×D7311yescharacteristic
416C4⋊C8D29211yescharacteristic
417C4⋊C8D29211yescharacteristic
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—1461no—
428C22⋊C8—1461no—
429C22⋊C8—1461no—
430C22⋊C8—1461no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8C4×D7311yescharacteristic
435C22⋊C8C4×D7311yescharacteristic
436C22⋊C8D29211yescharacteristic
437C22⋊C8D29211yescharacteristic
438#97—1461no—
439C4×C8—1461no—
440C4×C8—1461no—
441C4×C8C22×D7311yescharacteristic
442C4×C8C22×D7311yescharacteristic
443C4×C8C22×D7311yescharacteristic
444C4×C8C22×D7311yescharacteristic
445C4×C8C22×D7311yescharacteristic
446C4×C8C22×D7311yescharacteristic
447C24—1461no—
448C2×Q8—731no—
449C2×D4—731no—
450C2×D4—731no—
451C2×D4—731no—
452C2×D4—1462no—
453C2×D4—1462no—
454C2×D4—1461no—
455C2×D4—1461no—
456C22×C4—5841no—
457C22×C4—5841no—
458C22×C4—1461no—
459C22×C4—1461no—
460C22×C4—1461no—
461C22×C4—1461no—
462C22×C4—1461no—
463C22×C4—1461no—
464C22×C4C2×C4×D7311yescharacteristic
465C22×C4C2×D29211yescharacteristic
466C22×C4#1192402811yescharacteristic
467SD16—1462no—
468SD16—1462no—
469D8—1462no—
470D8—1462no—
471M16—5841no—
472M16—5841no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—5841no—
476C2×C8—5841no—
477C2×C8—5841no—
478C2×C8—5841no—
479C2×C8—5841no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1461no—
483C2×C8—1461no—
484C2×C8C2×C4×D7311yescharacteristic
485C2×C8C2×C4×D7311yescharacteristic
486C2×C8C2×C4×D7311yescharacteristic
487C2×C8C2×C4×D7311yescharacteristic
488C2×C8C2×D29211yescharacteristic
489C2×C8C2×D29211yescharacteristic
490C2×C8C2×D29211yescharacteristic
491C2×C8C2×D29211yescharacteristic
492C4⋊C4—731no—
493C4⋊C4—731no—
494C4⋊C4—731no—
495C4⋊C4—731no—
496C4⋊C4—1461no—
497C4⋊C4—1461no—
498C4⋊C4—1461no—
499C4⋊C4—1461no—
500C4⋊C4—1461no—
501C22⋊C4—1461no—
502C22⋊C4—1461no—
503C22⋊C4—1461no—
504C22⋊C4—1461no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C22⋊C4—1461no—
510C42—1461no—
511C42C2×C4×D7311yescharacteristic
512C42C2×D29211yescharacteristic
513C42#1192402811yescharacteristic
514C42C23×D7311yescharacteristic
515C23—5841no—
516C23—5841no—
517C23—1464no—
518C23—1461no—
519C23—1461no—
520C23—1461no—
521C23C4×D29211yescharacteristic
522Q8—1461no—
523Q8—1461no—
524D4—5841no—
525D4—732no—
526D4—732no—
527D4—1464no—
528D4—1461no—
529D4—1461no—
530D4—1461no—
531D4—1461no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—2921no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—5841no—
544C2×C4—5841no—
545C2×C4—5841no—
546C2×C4—1461no—
547C2×C4—1461no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4C4×D29211yescharacteristic
552C2×C4C4×D29211yescharacteristic
553C2×C4C4×D29211yescharacteristic
554C2×C4C22×C4×D7311yescharacteristic
555C2×C4C22×D29211yescharacteristic
556C2×C4C2×#1192402811yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—21no—
565C8—41no—
566C8—41no—
567C8—2921no—
568C8—2921no—
569C8—2921no—
570C8—2921no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—2921no—
575C22—2921no—
576C22—2921no—
577C22—2921no—
578C22—2921no—
579C22—2921no—
580C22—2921no—
581C22—5844no—
582C22—1462no—
583C22—1462no—
584C22C2×C4×D29211yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—2921no—
590C4—2921no—
591C4—2921no—
592C4—2921no—
593C4—2921no—
594C4#131×D7311yescharacteristic
595C4#131×D7311yescharacteristic
596C4#1798939211yescharacteristic
597C4#1798939911yescharacteristic
598C2—41no—
599C2—2922no—
600C2—2922no—
601C2—5841no—
602C2#2261862711yescharacteristic
603C2#2261876511yescharacteristic
604C2#2261884911yescharacteristic
subgroupG/H
centerC2×C4C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1454C2
socleC22×C73C2×C4×D4
prime radical#17988723C4
cosocleC42×C73C24
hypercenter#1454D73
hypocenterC73#17918
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #22619082C2semidirect
3. #22618954C2semidirect
4. #22608797C2semidirect
5. #22608790C2semidirect
6. #22608769C2semidirect
7. #22608762C2semidirect
8. #22608756C2semidirect
9. #22608745C2semidirect
10. C8×#11924017C2semidirect
11. C8×D584C2semidirect
12. #22608720C2semidirect
13. #22608357C2semidirect
14. #22608340C2semidirect
15. C73×#1454C2semidirect
26. #17988717C22semidirect
27. C8×Dic146C22semidirect
32. #17988666C22semidirect
39. C8×D292C22semidirect
48. #17988340C22semidirect
49. #17988340C22semidirect
50. #17988338C22semidirect
51. #17988338C22semidirect
52. #17988319C22semidirect
53. #17988319C22semidirect
58. #17988316C22semidirect
59. #17988316C22semidirect
63. #322×C73C22semidirect
64. #322×C73C22semidirect
65. #322×C73C22semidirect
66. C82×C73C22semidirect
317. #1454D73semidirect
318. C73#17918semidirect
366. #322C2×D73semidirect
367. #322C2×D73semidirect
368. #322C2×D73semidirect
369. C82C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226199802
#226190822
#226189542
#226087972
#226087902
#226087692
#226087622
#226087562
#226087452
C8×#119240172
C8×D5842
#226087202
#226083572
#226083402
C73×#14542
#1791873