Finite Group Databasebeta

← #33056042

Subgroups — #33056042

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#22619076C211yesmaximal, characteristic, complemented
3#22618954C211yesmaximal, characteristic, complemented
4#22608794C211yesmaximal, characteristic, complemented
5#22608787C211yesmaximal, characteristic, complemented
6#22608766C211yesmaximal, characteristic, complemented
7#22608759C211yesmaximal, characteristic, complemented
8#22608754C211yesmaximal, characteristic, complemented
9#22608742C211yesmaximal, characteristic, complemented
10#22608730C211yesmaximal, characteristic, complemented
11#22608725C211yesmaximal, characteristic, complemented
12#22608355C211yesmaximal, characteristic, complemented
13#22608337C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#1574C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18#17988923C411yescharacteristic
19#17988906C411yescharacteristic
20#17988888C411yescharacteristic
21#17988888C411yescharacteristic
22#17988803C411yescharacteristic
23#17988803C411yescharacteristic
24#17988740C411yescharacteristic
25#17988723C411yescharacteristic
26#17988714C2211yescharacteristic, complemented
27#17988711C2211yescharacteristic, complemented
28C4×#11924017C2211yescharacteristic
29C4×#11924017C2211yescharacteristic
30C4×D584C2211yescharacteristic
31C4×D584C2211yescharacteristic
32#17988664C2211yescharacteristic, complemented
33#17988663—21no—
34#17988656—21no—
35C8×D292—21no—
36C8×D292—21no—
37#17988652C2211yescharacteristic
38#17988652C2211yescharacteristic
39#17988652C2211yescharacteristic
40#17988652C2211yescharacteristic
41#17988652C2211yescharacteristic, complemented
42#17988647—21no—
43#17988640C2211yescharacteristic
44#17988640C2211yescharacteristic
45#17988612—21no—
46C22⋊C8×D73—21no—
47C22⋊C8×D73—21no—
48#17988317C2211yescharacteristic, complemented
49#17988317C2211yescharacteristic, complemented
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988314C2211yescharacteristic
53#17988314C2211yescharacteristic
54#17988314C2211yescharacteristic, complemented
55#17988314C2211yescharacteristic, complemented
56#17988309C2211yescharacteristic, complemented
57#17988309C2211yescharacteristic, complemented
58#17988308C2211yescharacteristic, complemented
59C8×#10596831C2211yescharacteristic, complemented
60#431×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62#423×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic, complemented
64#335×C73C2211yescharacteristic, complemented
65#334×C73C2211yescharacteristic, complemented
66#334×C73C2211yescharacteristic, complemented
67C22×D292C2×C411yescharacteristic
68C22×C4×D73—21no—
69C2×#11924017C2×C411yescharacteristic
70C2×#11924017C2×C411yescharacteristic
71C2×D584C2×C411yescharacteristic
72C2×D584C2×C411yescharacteristic
73C2×#11924011—21no—
74C2×C8×D73—21no—
75C2×C8×D73—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78C2×C8×D73—21no—
79#14556585—21no—
80#14556583C2×C411yescharacteristic
81#14556579C2×C411yescharacteristic
82#14556574—21no—
83#14556570C2×C411yescharacteristic
84#14556565C2×C411yescharacteristic
85C4×Dic146C2311yescharacteristic
86C4×D292—21no—
87C4×D292—21no—
88C4×D292C2×C411yescharacteristic
89C4×D292C2×C411yescharacteristic
90C4×D292C2311yescharacteristic
91C4×D292C2311yescharacteristic
92C4×D292C2311yescharacteristic
93C4×C22⋊D73—21no—
94#14556548—21no—
95C2×C4⋊Dic73C2×C411yescharacteristic
96C2×#11924005—21no—
97#14556525C2×C411yescharacteristic
98#14556525C2×C411yescharacteristic
99#14556523C2×C411yescharacteristic
100#14556523C2×C411yescharacteristic
101C4⋊#10596831—21no—
102C4⋊#10596831D411yescharacteristic
103C4⋊#10596831D411yescharacteristic
104#14556520—21no—
105#14556520—21no—
106#14556516C2×C411yescharacteristic
107#14556516C2×C411yescharacteristic
108#14556513C2×C411yescharacteristic
109#14556513C2×C411yescharacteristic
110#14556513C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556513C2×C411yescharacteristic
113#14556513C2×C411yescharacteristic
114C22⋊#10596831—21no—
115C22⋊#10596831D411yescharacteristic
116C22⋊#10596831D411yescharacteristic
117#14556503—21no—
118#14556503—21no—
119#14556503—21no—
120#14556503—21no—
121#14556503—21no—
122#14556503—21no—
123#14556501—21no—
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C4×#10596831C2311yescharacteristic
128C8×Dic73—21no—
129C2×M16×C73—21no—
130C2×C42×C73C2311yescharacteristic
131C4⋊C8×C73—21no—
132C4⋊C8×C73C2×C411yescharacteristic
133C4⋊C8×C73C2×C411yescharacteristic
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137C4⋊C8×C73C2311yescharacteristic
138C22⋊C8×C73—21no—
139C22⋊C8×C73C2×C411yescharacteristic
140C22⋊C8×C73C2×C411yescharacteristic
141C4×C8×C73—21no—
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#11924011—81no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831C2×D411yescharacteristic
169C2×#10596831C2×D411yescharacteristic
170C2×#10596831C2×D411yescharacteristic
171C2×#10596831C2×D411yescharacteristic
172C8×D73—81no—
173C8×D73—81no—
174C8×D73—81no—
175C8×D73—81no—
176C8×D73—81no—
177C4⋊Dic73—21no—
178C4⋊Dic73C22×C411yescharacteristic
179C4⋊Dic73C22×C411yescharacteristic
180C4⋊Dic73C22×C411yescharacteristic
181C4⋊Dic73C22×C411yescharacteristic
182#11924007—21no—
183#11924007—21no—
184#11924007—21no—
185#11924007—21no—
186C22⋊Dic73—21no—
187#11924005—21no—
188#11924005—21no—
189#11924005—21no—
190#11924005—21no—
191#11924005—21no—
192#11924005—21no—
193#11924005—21no—
194#11924005—21no—
195C4×Dic73—21no—
196C22×C4×C73C22×C411yescharacteristic
197C22×C4×C73C2×D411yescharacteristic
198C22×C4×C73#4111yescharacteristic
199M16×C73—81no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C22×C411yescharacteristic
206C2×C8×C73C22×C411yescharacteristic
207C2×C8×C73C22×C411yescharacteristic
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—41no—
259C8×C73—41no—
260C8×C73—41no—
261C8×C73—41no—
262#10596831—21no—
263#10596831—21no—
264#10596831—21no—
265#10596831—21no—
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#1574D7311yescharacteristic, complemented
315#1486—731no—
316#1482—731no—
317#1454—731no—
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#431—731no—
348#431C2×D7311yescharacteristic
349#431C2×D7311yescharacteristic
350#424—1461no—
351#423C2×D7311yescharacteristic
352C2×C22⋊C8—1461no—
353C2×C22⋊C8—1461no—
354#335C2×D7311yescharacteristic, complemented
355#335C2×D7311yescharacteristic, complemented
356#334C2×D7311yescharacteristic, complemented
357#334C2×D7311yescharacteristic, complemented
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×D4—731no—
371C23×C4—1461no—
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—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—1461no—
410C4⋊C8—1461no—
411C4⋊C8—1461no—
412C4⋊C8C4×D7311yescharacteristic
413C4⋊C8C4×D7311yescharacteristic
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—731no—
428C22⋊C8—731no—
429C22⋊C8—1461no—
430C22⋊C8—1461no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435C22⋊C8—1461no—
436C22⋊C8C4×D7311yescharacteristic
437C22⋊C8C4×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—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×C4D4×D7311yescharacteristic
466C22×C4#1192402911yescharacteristic
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—1461no—
487C2×C8—1461no—
488C2×C8C2×C4×D7311yescharacteristic
489C2×C8C2×C4×D7311yescharacteristic
490C2×C8C2×C4×D7311yescharacteristic
491C2×C8C2×C4×D7311yescharacteristic
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
512C42D4×D7311yescharacteristic
513C42#1192402911yescharacteristic
514C42C23×D7311yescharacteristic
515C23—5841no—
516C23—5841no—
517C23—1464no—
518C23—1461no—
519C23—1461no—
520C23—1461no—
521C23#1455655311yescharacteristic
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×C4#1455655311yescharacteristic
552C2×C4#1455655311yescharacteristic
553C2×C4#1455655311yescharacteristic
554C2×C4C22×C4×D7311yescharacteristic
555C2×C4C2×D4×D7311yescharacteristic
556C2×C4C2×#1192402911yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—2921no—
566C8—2921no—
567C8—1461no—
568C8—1461no—
569C8—1461no—
570C8—1461no—
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×#1455655311yescharacteristic
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#1798939111yescharacteristic
597C4#1798939611yescharacteristic
598C2—41no—
599C2—2922no—
600C2—2922no—
601C2—5841no—
602C2#2261862411yescharacteristic
603C2#2261876111yescharacteristic
604C2#2261884711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1574C2
socleC22×C73C2×C4×D4
prime radical#17988723C4
cosocleC42×C73C24
hypercenter#1574D73
hypocenterC73#17918
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
2. #22619076C2semidirect
3. #22618954C2semidirect
4. #22608794C2semidirect
5. #22608787C2semidirect
6. #22608766C2semidirect
7. #22608759C2semidirect
8. #22608754C2semidirect
9. #22608742C2semidirect
10. #22608730C2semidirect
11. #22608725C2semidirect
12. #22608355C2semidirect
13. #22608337C2semidirect
14. #22608231C2semidirect
15. C73×#1574C2semidirect
26. #17988714C22semidirect
27. #17988711C22semidirect
32. #17988664C22semidirect
41. #17988652C22semidirect
48. #17988317C22semidirect
49. #17988317C22semidirect
54. #17988314C22semidirect
55. #17988314C22semidirect
56. #17988309C22semidirect
57. #17988309C22semidirect
58. #17988308C22semidirect
59. C8×#10596831C22semidirect
63. #335×C73C22semidirect
64. #335×C73C22semidirect
65. #334×C73C22semidirect
66. #334×C73C22semidirect
314. #1574D73semidirect
318. C73#17918semidirect
354. #335C2×D73semidirect
355. #335C2×D73semidirect
356. #334C2×D73semidirect
357. #334C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226199802
#226190762
#226189542
#226087942
#226087872
#226087662
#226087592
#226087542
#226087422
#226087302
#226087252
#226083552
#226083372
#226082312
C73×#15742
#1791873