Finite Group Databasebeta

← #33055025

Subgroups — #33055025

Order 18688.

666 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619050C211yesmaximal, characteristic
2#22619045C211yesmaximal, characteristic
3C4×#14556599C211yesmaximal, characteristic
4#22608698C211yesmaximal, characteristic, complemented
5#22608697C211yesmaximal, characteristic, complemented
6#22608695C211yesmaximal, characteristic, complemented
7#22608693C211yesmaximal, characteristic, complemented
8#22608692C211yesmaximal, characteristic, complemented
9#22608686C211yesmaximal, characteristic, complemented
10#22608685C211yesmaximal, characteristic, complemented
11#22608682C211yesmaximal, characteristic, complemented
12#22608680C211yesmaximal, characteristic, complemented
13#22608678C211yesmaximal, characteristic, complemented
14#334×D73C211yesmaximal, characteristic, complemented
15C73×#1569C211yesmaximal, characteristic, complemented
16C2×#14556599C411yescharacteristic
17C2×#14556599C411yescharacteristic
18C4×#11924028C2211yescharacteristic
19#17988716—21no—
20#17988715—21no—
21#17988663—21no—
22#17988662—21no—
23#17988661—21no—
24#17988660—21no—
25#17988657—21no—
26#17988656—21no—
27#17988644C2211yescharacteristic
28#17988643C2211yescharacteristic
29#17988643C2211yescharacteristic
30#17988639C2211yescharacteristic
31#17988639C2211yescharacteristic
32#17988611C2211yescharacteristic
33#17988609C2211yescharacteristic
34#17988609C2211yescharacteristic
35C4⋊C8×D73C2211yescharacteristic
36C4⋊C8×D73C2211yescharacteristic
37#17988545C411yescharacteristic
38#17988545C411yescharacteristic
39#17988544C411yescharacteristic
40#17988544C411yescharacteristic
41#17988544C411yescharacteristic
42#17988544C411yescharacteristic
43C4×#11924011C2211yescharacteristic
44C4×#11924011C2211yescharacteristic
45C2×C4×#10596831C2211yescharacteristic
46C4×C8×D73C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988340C2211yescharacteristic
50#17988339C2211yescharacteristic
51#17988339C2211yescharacteristic
52#17988338C2211yescharacteristic
53#17988338C2211yescharacteristic
54#17988337C2211yescharacteristic
55#17988337C2211yescharacteristic
56#17988337C2211yescharacteristic
57#17988337C2211yescharacteristic
58#17988337C2211yescharacteristic
59#17988337C2211yescharacteristic
60#432×C73C2211yescharacteristic
61#423×C73C2211yescharacteristic
62C4×M16×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64#335×C73C2211yescharacteristic
65#334×C73C2211yescharacteristic
66#334×C73C2211yescharacteristic
67C2×#11924028C2×C411yescharacteristic
68#14556599—24no—
69#14556599—24no—
70C2×#11924012—21no—
71C2×#11924011—21no—
72C2×#11924011—21no—
73C2×#11924011C2×C411yescharacteristic
74C2×#11924011C2×C411yescharacteristic
75C2×#11924011C2×C411yescharacteristic
76C2×#11924011C2×C411yescharacteristic
77C22×#10596831C2×C411yescharacteristic
78C22×#10596831C2×C411yescharacteristic
79C2×C8×D73—21no—
80C2×C8×D73—21no—
81C2×C8×D73C2×C411yescharacteristic
82C2×C8×D73C2×C411yescharacteristic
83C2×C8×D73C2×C411yescharacteristic
84C2×C8×D73C2×C411yescharacteristic
85C4×Dic146D411yescharacteristic
86C4×Dic146Q811yescharacteristic
87C4×D292D411yescharacteristic
88C4×D292Q811yescharacteristic
89C4×C22⋊D73D411yescharacteristic
90C4×C22⋊D73D411yescharacteristic
91C4×C22⋊D73Q811yescharacteristic
92C4×C22⋊D73Q811yescharacteristic
93#14556550C2×C411yescharacteristic
94#14556548C2×C411yescharacteristic
95#14556548C2×C411yescharacteristic
96C42×D73C2311yescharacteristic
97C42×D73C2311yescharacteristic
98C4⋊#10596831—21no—
99C4⋊#10596831C2311yescharacteristic
100C4⋊#10596831C2311yescharacteristic
101C4⋊#10596831C2311yescharacteristic
102C4⋊#10596831C2311yescharacteristic
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556520—21no—
107C22⋊#10596831—21no—
108#14556503—21no—
109#14556503—21no—
110#14556503—21no—
111#14556503—21no—
112#14556502—21no—
113#14556501—21no—
114#14556501—21no—
115#14556501C2×C411yescharacteristic
116#14556501C2×C411yescharacteristic
117#14556501C2×C411yescharacteristic
118#14556501C2×C411yescharacteristic
119C4×#10596831C2×C411yescharacteristic
120C4×#10596831C2×C411yescharacteristic
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C8×Dic73—21no—
124C8×Dic73—21no—
125C8×Dic73C2×C411yescharacteristic
126C8×Dic73C2×C411yescharacteristic
127C8×Dic73C2×C411yescharacteristic
128C8×Dic73C2×C411yescharacteristic
129C2×M16×C73—21no—
130C2×M16×C73C2×C411yescharacteristic
131C2×M16×C73C2×C411yescharacteristic
132C2×C42×C73C2311yescharacteristic
133C4⋊C8×C73—21no—
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137C4⋊C8×C73C2311yescharacteristic
138C22⋊C8×C73—21no—
139#97×C73—21no—
140#97×C73C2×C411yescharacteristic
141#97×C73C2×C411yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—22no—
145#11924028—22no—
146C2×Dic146C4⋊C411yescharacteristic
147C2×D292C4⋊C411yescharacteristic
148C2×C22⋊D73C4⋊C411yescharacteristic
149C2×C22⋊D73C4⋊C411yescharacteristic
150C2×C4×D73C22×C411yescharacteristic
151C2×C4×D73C22×C411yescharacteristic
152C2×C4×D73C2×D411yescharacteristic
153C2×C4×D73C2×D411yescharacteristic
154C2×C4×D73C2×Q811yescharacteristic
155C2×C4×D73C2×Q811yescharacteristic
156#11924012—81no—
157#11924011—22no—
158#11924011—22no—
159#11924011—22no—
160#11924011—81no—
161#11924011—81no—
162#11924011M1614yescomplemented
163C2×#10596831—22no—
164C2×#10596831—22no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831C22×C411yescharacteristic
170C2×#10596831C22×C411yescharacteristic
171C2×#10596831C22×C411yescharacteristic
172C2×#10596831C22×C411yescharacteristic
173C8×D73—22no—
174C8×D73—22no—
175C8×D73—22no—
176C8×D73—81no—
177C8×D73—81no—
178C8×D73M1614yescomplemented
179C4⋊Dic73C4⋊C411yescharacteristic
180C4⋊Dic73C4⋊C411yescharacteristic
181#11924007C4⋊C411yescharacteristic
182#11924007C4⋊C411yescharacteristic
183#11924007C4⋊C411yescharacteristic
184#11924007C4⋊C411yescharacteristic
185C22⋊Dic73C4⋊C411yescharacteristic
186C22⋊Dic73C4⋊C411yescharacteristic
187#11924005C4⋊C411yescharacteristic
188#11924005C4⋊C411yescharacteristic
189#11924005C4⋊C411yescharacteristic
190#11924005C4⋊C411yescharacteristic
191C4×Dic73C22×C411yescharacteristic
192C4×Dic73C22×C411yescharacteristic
193C4×Dic73C2×D411yescharacteristic
194C4×Dic73C2×D411yescharacteristic
195C4×Dic73C2×Q811yescharacteristic
196C4×Dic73C2×Q811yescharacteristic
197C22×C4×C73C22×C411yescharacteristic
198C22×C4×C73C2×D411yescharacteristic
199C22×C4×C73C2×Q811yescharacteristic
200M16×C73—22no—
201M16×C73—22no—
202M16×C73—81no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73C22×C411yescharacteristic
208C2×C8×C73C22×C411yescharacteristic
209C2×C8×C73C22×C411yescharacteristic
210C2×C8×C73C22×C411yescharacteristic
211C42×C73C22×C411yescharacteristic
212C42×C73C2×D411yescharacteristic
213C42×C73C2×Q811yescharacteristic
214C42×C73C2411yescharacteristic
215C23×C73C2×C4⋊C411yescharacteristic
216C22×D73C2×C4⋊C411yescharacteristic
217C22×D73C2×C4⋊C411yescharacteristic
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—41no—
223C2×C4×C73C2×C4⋊C411yescharacteristic
224C2×C4×C73C2×C4⋊C411yescharacteristic
225C2×C4×C73C2×C4⋊C411yescharacteristic
226C2×C4×C73C23×C411yescharacteristic
227C2×C4×C73C22×D411yescharacteristic
228C2×C4×C73C22×Q811yescharacteristic
229C22⋊D73—22no—
230C22⋊D73—22no—
231C2×Dic73C2×C4⋊C411yescharacteristic
232C2×Dic73C2×C4⋊C411yescharacteristic
233C2×Dic73C2×C4⋊C411yescharacteristic
234C2×Dic73C2×C4⋊C411yescharacteristic
235C2×Dic73C2×C4⋊C411yescharacteristic
236C2×Dic73C2×C4⋊C411yescharacteristic
237D292—22no—
238C4×D73—21no—
239C4×D73—21no—
240C4×D73—21no—
241C4×D73—21no—
242C4×D73—21no—
243C4×D73—21no—
244C4×D73—41no—
245C4×D73—41no—
246C4×D73C2×M1612yes—
247C4×D73C2×M1612yes—
248Dic146—22no—
249C8×C73—21no—
250C8×C73—21no—
251C8×C73—41no—
252C8×C73—41no—
253C8×C73—41no—
254C8×C73—41no—
255C8×C73C2×M1612yes—
256C8×C73C2×M1612yes—
257#10596831—21no—
258#10596831—21no—
259#10596831—41no—
260#10596831—41no—
261#10596831—41no—
262#10596831—41no—
263#10596831C2×M1612yes—
264#10596831C2×M1612yes—
265C22×C73—21no—
266C22×C73—21no—
267C22×C73—21no—
268C22×C73C22×C4⋊C411yescharacteristic
269C2×D73—21no—
270C2×D73—21no—
271C2×D73—21no—
272C2×D73—21no—
273C2×D73—21no—
274C2×D73#42312yes—
275C4×C73—21no—
276C4×C73—21no—
277C4×C73—21no—
278C4×C73—21no—
279C4×C73C22×M1611yescharacteristic
280C4×C73C22×M1611yescharacteristic
281C4×C73#57711yescharacteristic
282C4×C73#57711yescharacteristic
283Dic73—21no—
284Dic73—21no—
285Dic73—21no—
286Dic73—21no—
287Dic73—21no—
288Dic73#42312yes—
289#17798—731nomaximal, Sylow
290C2×C73—41no—
291C2×C73C2×#42311yescharacteristic
292C2×C73#291211yescharacteristic
293C2×C73#291611yescharacteristic
294D73—22no—
295D73—41no—
296#2989—731no—
297#2989—731no—
298C4×#131—731no—
299#1569—731no—
300#1569—731no—
301#1569—731no—
302#1569D7311yescharacteristic, complemented
303#1568—731no—
304#1568—731no—
305#1566—731no—
306#1566—731no—
307#1565—731no—
308#1565—731no—
309#1564—731no—
310C2×#334—731no—
311C73#1779811yescharacteristic, complemented, Sylow
312C2×#131—731no—
313C2×#131—731no—
314C4×#41—731no—
315#446—1461no—
316#446—1461no—
317#436—1461no—
318#436—1461no—
319#435—1461no—
320#435—1461no—
321#435—1461no—
322#435—1461no—
323#432—731no—
324#432—731no—
325#432—731no—
326#432C2×D7311yescharacteristic
327#431—731no—
328#431—731no—
329#423—731no—
330#423—731no—
331#423—731no—
332#423C2×D7311yescharacteristic
333C2×C4⋊C8—731no—
334C2×C4⋊C8—731no—
335#405—731no—
336#405—731no—
337#405—731no—
338#405—731no—
339#405—731no—
340#405—731no—
341C4×M16—731no—
342C4×M16—731no—
343C4×M16C2×D7311yescharacteristic
344C2×C4×C8—731no—
345C2×C4×C8—731no—
346C2×C4×C8—731no—
347#335—731no—
348#335—731no—
349#335—731no—
350#335—731no—
351#335C2×D7311yescharacteristic
352#335C2×D7311yescharacteristic
353#334—731no—
354#334—731no—
355#334—731no—
356#334—731no—
357#334—731no—
358#334—731no—
359#334—731no—
360#334—731no—
361#334C2×D7311yescharacteristic
362#334C2×D7311yescharacteristic
363C2×#41—731no—
364#131—1464no—
365#131—1464no—
366C2×M16—21no—
367C2×M16—731no—
368C2×M16—731no—
369C2×M16—731no—
370C2×M16—731no—
371C2×M16—1461no—
372C2×M16—1461no—
373C2×M16—1461no—
374C2×M16C4×D7311yescharacteristic
375C2×M16C4×D7311yescharacteristic
376C22×C8—731no—
377C22×C8—731no—
378C22×C8—731no—
379C22×C8—731no—
380C22×C8—731no—
381C22×C8—731no—
382C22×C8—1461no—
383C22×C8—1461no—
384C4×Q8—731no—
385C4×Q8—731no—
386C4×D4—731no—
387C4×D4—731no—
388C4×D4—731no—
389C4×D4—731no—
390C4×D4—731no—
391C4×D4—731no—
392#117—731no—
393#117—731no—
394#117—731no—
395C2×C42—731no—
396C2×C42—731no—
397C2×C42C22×D7311yescharacteristic
398C4⋊C8—21no—
399C4⋊C8—731no—
400C4⋊C8—731no—
401C4⋊C8—731no—
402C4⋊C8—731no—
403C4⋊C8—1461no—
404C4⋊C8—1461no—
405C4⋊C8—1461no—
406C4⋊C8—1461no—
407C4⋊C8—1461no—
408C4⋊C8C22×D7311yescharacteristic
409C4⋊C8C22×D7311yescharacteristic
410C4⋊C8C22×D7311yescharacteristic
411C4⋊C8C22×D7311yescharacteristic
412C22⋊C8—21no—
413C22⋊C8—1461no—
414C22⋊C8—1461no—
415C22⋊C8—1461no—
416C22⋊C8—1461no—
417C22⋊C8—1461no—
418#97—21no—
419#97—731no—
420#97—731no—
421#97—731no—
422#97—731no—
423#97—1461no—
424#97—1461no—
425#97—1461no—
426#97C4×D7311yescharacteristic
427#97C4×D7311yescharacteristic
428C4×C8—731no—
429C4×C8—731no—
430C4×C8—731no—
431C4×C8—731no—
432C4×C8—731no—
433C4×C8—731no—
434C4×C8—731no—
435C4×C8—731no—
436C4×C8—1461no—
437C4×C8—1461no—
438C4×C8C22×D7311yescharacteristic
439C4×C8C22×D7311yescharacteristic
440#41—1462no—
441#41—1462no—
442C2×Q8—731no—
443C2×D4—731no—
444C2×D4—731no—
445C2×D4—731no—
446C22×C4—731no—
447C22×C4—731no—
448C22×C4—731no—
449C22×C4—731no—
450C22×C4—731no—
451C22×C4—731no—
452C22×C4C2×C4×D7311yescharacteristic
453C22×C4D4×D7311yescharacteristic
454C22×C4Q8×D7311yescharacteristic
455M16—22no—
456M16—22no—
457M16—81no—
458M16—5841no—
459M16—5841no—
460M16—5841no—
461M16—734no—
462M16—1462no—
463M16—1462no—
464M16—1462no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—5841no—
470C2×C8—5841no—
471C2×C8—731no—
472C2×C8—731no—
473C2×C8—734no—
474C2×C8—731no—
475C2×C8—731no—
476C2×C8—1462no—
477C2×C8—1462no—
478C2×C8—1461no—
479C2×C8—1461no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1462no—
483C2×C8—1462no—
484C2×C8—1462no—
485C2×C8C2×C4×D7311yescharacteristic
486C2×C8C2×C4×D7311yescharacteristic
487C2×C8C2×C4×D7311yescharacteristic
488C2×C8C2×C4×D7311yescharacteristic
489C4⋊C4—731no—
490C4⋊C4—731no—
491C4⋊C4—731no—
492C4⋊C4—731no—
493C4⋊C4—731no—
494C4⋊C4—731no—
495C22⋊C4—731no—
496C22⋊C4—731no—
497C22⋊C4—731no—
498C22⋊C4—731no—
499C22⋊C4—731no—
500C22⋊C4—731no—
501C42—731no—
502C42—731no—
503C42—731no—
504C42—731no—
505C42—731no—
506C42—731no—
507C42C2×C4×D7311yescharacteristic
508C42D4×D7311yescharacteristic
509C42Q8×D7311yescharacteristic
510C42C23×D7311yescharacteristic
511C23—731no—
512C23—731no—
513C23C4⋊C4×D7311yescharacteristic
514Q8—1462no—
515D4—1462no—
516D4—1462no—
517D4—1462no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—2921no—
524C2×C4—2921no—
525C2×C4—731no—
526C2×C4—732no—
527C2×C4—732no—
528C2×C4—731no—
529C2×C4—731no—
530C2×C4—731no—
531C2×C4—731no—
532C2×C4—731no—
533C2×C4—1461no—
534C2×C4—1461no—
535C2×C4—1461no—
536C2×C4—1461no—
537C2×C4—1461no—
538C2×C4—1461no—
539C2×C4C4⋊C4×D7311yescharacteristic
540C2×C4C4⋊C4×D7311yescharacteristic
541C2×C4C4⋊C4×D7311yescharacteristic
542C2×C4C22×C4×D7311yescharacteristic
543C2×C4C2×D4×D7311yescharacteristic
544C2×C4C2×Q8×D7311yescharacteristic
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—2921no—
552C8—2921no—
553C8—2921no—
554C8—2921no—
555C8—732no—
556C8—732no—
557C8—1461no—
558C8—1461no—
559C8M16×D7312yes—
560C8M16×D7312yes—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—732no—
565C22—1461no—
566C22—1461no—
567C22—1461no—
568C22—1461no—
569C22—1461no—
570C22C2×C4⋊C4×D7311yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—732no—
576C4—1461no—
577C4—1461no—
578C4—1461no—
579C4—1461no—
580C4—1461no—
581C4C2×M16×D7311yescharacteristic
582C4C2×M16×D7311yescharacteristic
583C4#1798939611yescharacteristic
584C4#1798939711yescharacteristic
585C2—41no—
586C2—2921no—
587C2—1462no—
588C2#423×D7311yescharacteristic
589C2#2261852511yescharacteristic
590C2#2261854111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1569C2
socleC22×C73C22×C4⋊C4
prime radicalC2×#11924028C2×C4
cosocleC42×C73C24
hypercenter#1569D73
hypocenterC73#17798
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
4. #22608698C2semidirect
5. #22608697C2semidirect
6. #22608695C2semidirect
7. #22608693C2semidirect
8. #22608692C2semidirect
9. #22608686C2semidirect
10. #22608685C2semidirect
11. #22608682C2semidirect
12. #22608680C2semidirect
13. #22608678C2semidirect
14. #334×D73C2semidirect
15. C73×#1569C2semidirect
162. #11924011M16semidirect
178. C8×D73M16semidirect
302. #1569D73semidirect
311. C73#17798semidirect

Maximal subgroups

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

subgroupindex
#226190502
#226190452
C4×#145565992
#226086982
#226086972
#226086952
#226086932
#226086922
#226086862
#226086852
#226086822
#226086802
#226086782
#334×D732
C73×#15692
#1779873