Finite Group Databasebeta

← #32009529

Subgroups — #32009529

Order 18176.

796 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
1C2×#17986296C211yesmaximal, characteristic
2#22590804C211yesmaximal, characteristic
3#22589298C211yesmaximal, characteristic, complemented
4#22589106C211yesmaximal, characteristic, complemented
5#22589070C211yesmaximal, characteristic, complemented
6#22589065C211yesmaximal, characteristic, complemented
7#22589022C211yesmaximal, characteristic
8#22589022C211yesmaximal, characteristic
9#22588967C211yesmaximal, characteristic
10#22588960C211yesmaximal, characteristic
11#22588932C211yesmaximal, characteristic, complemented
12#22588925C211yesmaximal, characteristic, complemented
13#22588347C211yesmaximal, characteristic
14C4×C4⋊(C71⋊C8)C211yesmaximal, characteristic, complemented
15C4×#125×C71C211yesmaximal, characteristic, complemented
16C2×C4×D284C2211yescharacteristic
17C2×#14556085—21no—
18#17986296C418yescomplemented
19C2×#14556061C2211yescharacteristic
20C2×#14556061C2211yescharacteristic
21C2×#14556059C2211yescharacteristic
22C2×#14556059C2211yescharacteristic
23C2×C4⋊(C71⋊C8)C2211yescharacteristic
24C2×C4⋊(C71⋊C8)C2211yescharacteristic
25C2×#14556048C2211yescharacteristic
26C2×#14556048C2211yescharacteristic
27C2×#14556048C2211yescharacteristic
28C2×#14556048C2211yescharacteristic
29C2×C4×C71⋊C8C2211yescharacteristic
30C2×C4×C71⋊C8C2211yescharacteristic
31#17985901C2211yescharacteristic
32#17985901C2211yescharacteristic
33#17985897C2211yescharacteristic
34#17985897C2211yescharacteristic
35#17985890—21no—
36#17985890—21no—
37C4×C4⋊Dic71C2211yescharacteristic
38C4×(C2×D71)⋊C4—21no—
39#17985761C2211yescharacteristic
40#17985761C2211yescharacteristic
41#17985761C2211yescharacteristic
42#17985761C2211yescharacteristic
43#17985761C2211yescharacteristic
44#17985761C2211yescharacteristic
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985754C2211yescharacteristic
48#17985754C2211yescharacteristic
49C2×#125×C71C2211yescharacteristic
50#389×C71C2211yescharacteristic
51#389×C71C2211yescharacteristic
52#387×C71—21no—
53#387×C71—21no—
54#382×C71C2211yescharacteristic
55C4×C4⋊C4×C71—21no—
56C4×C4⋊C4×C71—21no—
57C4×C4⋊C4×C71C2211yescharacteristic
58C4×C4⋊C4×C71C2211yescharacteristic
59C43×C71C2211yescharacteristic
60C22×D284C2311yescharacteristic
61C22×C4×D71—21no—
62C22×C71⋊C8C2311yescharacteristic
63C22×C71⋊C8C2311yescharacteristic
64C22×C71⋊C8C2311yescharacteristic
65C22×C71⋊C8C2311yescharacteristic
66C4×D284—22no—
67C4×D284C2×C414yes—
68#14556085—44no—
69C2×C4⋊Dic71C2311yescharacteristic
70C2×C4⋊Dic71C2311yescharacteristic
71C2×C4⋊Dic71C2311yescharacteristic
72C2×Dic71⋊C4—21no—
73C2×Dic71⋊C4—21no—
74C2×(C2×D71)⋊C4—21no—
75C2×(C2×D71)⋊C4—21no—
76C2×(C2×D71)⋊C4—21no—
77C2×(C2×D71)⋊C4—21no—
78C2×(C2×D71)⋊C4—21no—
79C2×C4×Dic71—21no—
80#14556061—41no—
81#14556061C2×C414yes—
82#14556059—41no—
83#14556059C2×C414yes—
84C4⋊(C71⋊C8)—22no—
85C4⋊(C71⋊C8)C2×C414yes—
86#14556048—41no—
87#14556048—41no—
88#14556048C2×C414yes—
89#14556048C2×C414yes—
90C4×C71⋊C8—41no—
91C4×C71⋊C8—41no—
92C71⋊#95—21no—
93C71⋊#95—21no—
94C71⋊#95—21no—
95#125×C71—22no—
96#125×C71C2×C414yes—
97C2×C4⋊C4×C71—21no—
98C2×C4⋊C4×C71—21no—
99C2×C4⋊C4×C71—21no—
100C2×C4⋊C4×C71—21no—
101C2×C4⋊C4×C71C2311yescharacteristic
102C2×C4⋊C4×C71C2311yescharacteristic
103C2×C4⋊C4×C71C2311yescharacteristic
104C2×C4⋊C4×C71C2311yescharacteristic
105C2×C42×C71—21no—
106C2×C42×C71—21no—
107C2×C42×C71D411yescharacteristic
108C2×C42×C71D411yescharacteristic
109C2×C42×C71D411yescharacteristic
110C2×C42×C71D411yescharacteristic
111C2×C42×C71C2311yescharacteristic
112C2×C42×C71C2311yescharacteristic
113C2×C42×C71C2311yescharacteristic
114#95×C71—21no—
115#95×C71—21no—
116#95×C71—21no—
117#95×C71—21no—
118#95×C71—21no—
119#95×C71—21no—
120C23×D71—21no—
121C2×D284—21no—
122C2×D284—21no—
123C2×D284—21no—
124C2×D284—21no—
125C2×D284—21no—
126C2×D284C22×C412yes—
127C22×Dic71—21no—
128C22×Dic71—21no—
129C22×Dic71—21no—
130C2×C4×D71—24no—
131C2×C4×D71—42no—
132C2×C4×D71—42no—
133C2×C71⋊C8—21no—
134C2×C71⋊C8—21no—
135C2×C71⋊C8—21no—
136C2×C71⋊C8—21no—
137C2×C71⋊C8—21no—
138C2×C71⋊C8—21no—
139C2×C71⋊C8—21no—
140C2×C71⋊C8—21no—
141C2×C71⋊C8—21no—
142C2×C71⋊C8—21no—
143C2×C71⋊C8C22×C412yes—
144C2×C71⋊C8C22×C412yes—
145C4⋊Dic71—21no—
146C4⋊Dic71—21no—
147C4⋊Dic71—21no—
148C4⋊Dic71—21no—
149C4⋊Dic71—21no—
150C4⋊Dic71C22×C412yes—
151Dic71⋊C4—42no—
152Dic71⋊C4—42no—
153(C2×D71)⋊C4—24no—
154(C2×D71)⋊C4—42no—
155(C2×D71)⋊C4—42no—
156(C2×D71)⋊C4—42no—
157(C2×D71)⋊C4—42no—
158C4×Dic71—42no—
159C22×C4×C71—21no—
160C22×C4×C71—21no—
161C22×C4×C71—21no—
162C22×C4×C71—21no—
163C22×C4×C71C2×D411yescharacteristic
164C22×C4×C71C2×D411yescharacteristic
165C22×C4×C71C2×D411yescharacteristic
166C22×C4×C71C2×D411yescharacteristic
167C22×C4×C71C2×D411yescharacteristic
168C22×C4×C71C2×D411yescharacteristic
169C22×C4×C71C2411yescharacteristic
170C4⋊C4×C71—24no—
171C4⋊C4×C71—24no—
172C4⋊C4×C71—21no—
173C4⋊C4×C71—21no—
174C4⋊C4×C71—21no—
175C4⋊C4×C71—21no—
176C4⋊C4×C71—21no—
177C4⋊C4×C71—21no—
178C4⋊C4×C71—42no—
179C4⋊C4×C71—42no—
180C4⋊C4×C71C22×C412yes—
181C4⋊C4×C71C22×C412yes—
182C42×C71—22no—
183C42×C71—22no—
184C42×C71—22no—
185C42×C71—21no—
186C42×C71—21no—
187C42×C71—21no—
188C42×C71—21no—
189C42×C71—41no—
190C42×C71—42no—
191C42×C71—42no—
192C42×C71C22×C412yes—
193C42×C71#4112yes—
194C23×C71C22×D411yescharacteristic
195C22×D71—22no—
196C22×D71—41no—
197C22×D71—41no—
198C22×D71—41no—
199C22×D71—41no—
200C22×D71—41no—
201C22×D71—41no—
202C2×C4×C71—21no—
203C2×C4×C71—21no—
204C2×C4×C71—21no—
205C2×C4×C71—21no—
206C2×C4×C71—21no—
207C2×C4×C71—21no—
208C2×C4×C71—21no—
209C2×C4×C71—21no—
210C2×C4×C71—21no—
211C2×C4×C71—21no—
212C2×C4×C71—22no—
213C2×C4×C71—22no—
214C2×C4×C71—21no—
215C2×C4×C71—21no—
216C2×C4×C71—21no—
217C2×C4×C71—41no—
218C2×C4×C71—41no—
219C2×C4×C71—41no—
220C2×C4×C71—41no—
221C2×C4×C71—41no—
222C2×C4×C71—41no—
223C2×C4×C71—41no—
224C2×C4×C71—41no—
225C2×C4×C71—41no—
226C2×C4×C71—41no—
227C2×C4×C71C4×D412yes—
228C2×C4×C71C4×D412yes—
229C2×C4×C71#13512yes—
230C2×C4×C71#13512yes—
231C2×C4×C71AGL(1,ℤ/8)12yes—
232C2×C4×C71C23×C411yescharacteristic
233C2×C4×C71C2×#4111yescharacteristic
234C2×C4×C71H(5,𝔽2)11yescharacteristic
235C2×C4×C712−1+411yescharacteristic
236C2×C4×C712−1+411yescharacteristic
237C2×C4×C712−1+411yescharacteristic
238C2×Dic71—22no—
239C2×Dic71—41no—
240C2×Dic71—41no—
241C2×Dic71—41no—
242C2×Dic71—41no—
243C2×Dic71—41no—
244C2×Dic71—41no—
245C2×Dic71—41no—
246C2×Dic71—41no—
247D284—22no—
248D284—22no—
249D284—41no—
250D284—41no—
251C4×D71—48no—
252C71⋊C8—22no—
253C71⋊C8—22no—
254C71⋊C8—41no—
255C71⋊C8—41no—
256C22×C71C2×C4×D411yescharacteristic
257C22×C71#53611yescharacteristic
258C22×C71#53711yescharacteristic
259C22×C71C2×#13511yescharacteristic
260C22×C71C2×#13511yescharacteristic
261C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C71#57511yescharacteristic
263C2×D71—42no—
264C2×D71—42no—
265C2×D71—42no—
266C2×D71—81no—
267C2×D71—81no—
268C2×D71—81no—
269C2×D71—81no—
270C4×C71—22no—
271C4×C71—22no—
272C4×C71—22no—
273C4×C71—22no—
274C4×C71—22no—
275C4×C71—42no—
276C4×C71—42no—
277C4×C71—41no—
278C4×C71—81no—
279C4×C71—81no—
280C4×C71#51911yescharacteristic
281C4×C71#52011yescharacteristic
282C4×C71#54111yescharacteristic
283C4×C71#54211yescharacteristic
284Dic71—42no—
285Dic71—81no—
286Dic71—81no—
287#22114—711nomaximal, Sylow
288C2×C71#232311yescharacteristic
289C2×C71C4×#13511yescharacteristic
290C2×C71C4×AGL(1,ℤ/8)11yescharacteristic
291C2×C71#322811yescharacteristic
292C2×C71#323211yescharacteristic
293C2×C71#324711yescharacteristic
294C2×C71#325011yescharacteristic
295D71—82no—
296C2×#478—711no—
297C4×#125D7111yescharacteristic, complemented
298#2293—711no—
299#1989—711no—
300#1949—711no—
301#1942—711no—
302#1941—711no—
303#1934—711no—
304#1934—711no—
305#1926—711no—
306#1925—711no—
307#1921—711no—
308#1920—711no—
309#1804—711no—
310C4×C4⋊C8—711no—
311C71#2211411yescharacteristic, complemented, Sylow
312C2×#125C2×D7111yescharacteristic
313C2×C4×D4—711no—
314C2×#117—1421no—
315#478—718no—
316C2×#107—711no—
317C2×#107—711no—
318C2×#106—711no—
319C2×#106—711no—
320C2×C4⋊C8—711no—
321C2×C4⋊C8—711no—
322C2×#102—711no—
323C2×#102—711no—
324C2×#102—711no—
325C2×#102—711no—
326C2×C4×C8—711no—
327C2×C4×C8—711no—
328#390—711no—
329#390—711no—
330#389—711no—
331#389—711no—
332#389C2×D7111yescharacteristic
333#389C2×D7111yescharacteristic
334#388—1421no—
335#388—1421no—
336#387—21no—
337#387—21no—
338#382C2×D7111yescharacteristic
339C4×C4⋊C4—21no—
340C4×C4⋊C4—21no—
341C4×C4⋊C4—711no—
342C4×C4⋊C4C2×D7111yescharacteristic
343C4×C4⋊C4C2×D7111yescharacteristic
344C4×C22⋊C4—1421no—
345C43C2×D7111yescharacteristic
346#340—711no—
347#340—711no—
348#340—711no—
349#340—711no—
350#340—711no—
351#340—711no—
352#340—711no—
353#340—711no—
354#336—711no—
355#336—711no—
356C22×D4—711no—
357C23×C4—1421no—
358C22×C8—711no—
359C22×C8—711no—
360C22×C8—711no—
361C22×C8—711no—
362#125—22no—
363#125C4×D7114yes—
364C4×D4—714no—
365C4×D4—1422no—
366#117—2844no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—711no—
372C2×C4⋊C4—711no—
373C2×C4⋊C4—711no—
374C2×C4⋊C4—1421no—
375C2×C4⋊C4—1421no—
376C2×C4⋊C4C22×D7111yescharacteristic
377C2×C4⋊C4C22×D7111yescharacteristic
378C2×C4⋊C4C22×D7111yescharacteristic
379C2×C4⋊C4C22×D7111yescharacteristic
380C2×C22⋊C4—1421no—
381C2×C22⋊C4—1421no—
382C2×C22⋊C4—1421no—
383C2×C22⋊C4—1421no—
384C2×C22⋊C4—1421no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—1421no—
388C2×C42C22⋊D7111yescharacteristic
389C2×C42C22⋊D7111yescharacteristic
390C2×C42C22⋊D7111yescharacteristic
391C2×C42C22⋊D7111yescharacteristic
392C2×C42C22×D7111yescharacteristic
393C2×C42C22×D7111yescharacteristic
394C2×C42C22×D7111yescharacteristic
395#107—2841no—
396#107—714no—
397#106—2841no—
398#106—714no—
399C4⋊C8—714no—
400C4⋊C8—1422no—
401#102—2841no—
402#102—2841no—
403#102—714no—
404#102—714no—
405C4×C8—2841no—
406C4×C8—2841no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—1421no—
414#95—1421no—
415#95—1421no—
416C24—1421no—
417C2×D4—712no—
418C2×D4—1421no—
419C2×D4—1421no—
420C2×D4—1421no—
421C2×D4—1421no—
422C2×D4—1421no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—2842no—
428C22×C4—2842no—
429C22×C4—1421no—
430C22×C4—1421no—
431C22×C4—1421no—
432C22×C4—1424no—
433C22×C4C2×C22⋊D7111yescharacteristic
434C22×C4C2×C22⋊D7111yescharacteristic
435C22×C4C2×C22⋊D7111yescharacteristic
436C22×C4C2×C22⋊D7111yescharacteristic
437C22×C4C2×C22⋊D7111yescharacteristic
438C22×C4C2×C22⋊D7111yescharacteristic
439C22×C4C23×D7111yescharacteristic
440C2×C8—712no—
441C2×C8—712no—
442C2×C8—1421no—
443C2×C8—1421no—
444C2×C8—1421no—
445C2×C8—1421no—
446C2×C8—1421no—
447C2×C8—1421no—
448C2×C8—1421no—
449C2×C8—1421no—
450C2×C8—1421no—
451C2×C8—1421no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—24no—
455C4⋊C4—24no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—2842no—
463C4⋊C4—2842no—
464C4⋊C4—712no—
465C4⋊C4—1421no—
466C4⋊C4—1421no—
467C4⋊C4—1421no—
468C4⋊C4—1421no—
469C4⋊C4—1421no—
470C4⋊C4C2×C4×D7112yes—
471C4⋊C4C2×C4×D7112yes—
472C22⋊C4—2842no—
473C22⋊C4—2842no—
474C22⋊C4—2842no—
475C22⋊C4—2842no—
476C22⋊C4—1424no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—22no—
482C42—22no—
483C42—22no—
484C42—41no—
485C42—42no—
486C42—42no—
487C42—2842no—
488C42C2×C4×D7112yes—
489C42#1176586512yes—
490C23—2841no—
491C23—2841no—
492C23—2841no—
493C23—2841no—
494C23—2841no—
495C23—2841no—
496C23—1422no—
497C23C22×C22⋊D7111yescharacteristic
498D4—2841no—
499D4—2841no—
500D4—1422no—
501D4—1422no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—2848no—
528C2×C4—2841no—
529C2×C4—2841no—
530C2×C4—2841no—
531C2×C4—2841no—
532C2×C4—2841no—
533C2×C4—2841no—
534C2×C4—2841no—
535C2×C4—2841no—
536C2×C4—1422no—
537C2×C4C4×C22⋊D7112yes—
538C2×C4C4×C22⋊D7112yes—
539C2×C4#1455614812yes—
540C2×C4#1455614812yes—
541C2×C4#1455615312yes—
542C2×C4C22×C4×D7111yescharacteristic
543C2×C4C2×#1176586511yescharacteristic
544C2×C4#1455617411yescharacteristic
545C2×C4#1455617511yescharacteristic
546C2×C4#1455617611yescharacteristic
547C2×C4#1455617611yescharacteristic
548C8—2841no—
549C8—2841no—
550C8—1422no—
551C8—1422no—
552C22—2842no—
553C22—2842no—
554C22—2842no—
555C22—5681no—
556C22—5681no—
557C22—5681no—
558C22—5681no—
559C22C2×C4×C22⋊D7111yescharacteristic
560C22#1798657311yescharacteristic
561C22#1798657711yescharacteristic
562C22C2×#1455614811yescharacteristic
563C22C2×#1455614811yescharacteristic
564C22C2×#1455615311yescharacteristic
565C22#1798679711yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—42no—
572C4—41no—
573C4—42no—
574C4—81no—
575C4—81no—
576C4—2842no—
577C4—5681no—
578C4—5681no—
579C4#1798647511yescharacteristic
580C4#1798648111yescharacteristic
581C4#1798660711yescharacteristic
582C4#1798662111yescharacteristic
583C2—5682no—
584C2#2259101611yescharacteristic
585C2C4×#1455614811yescharacteristic
586C2C4×#1455615311yescharacteristic
587C2#2259947611yescharacteristic
588C2#2259950811yescharacteristic
589C2#2259966611yescharacteristic
590C2#2259968711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC4×#125×C71C2
socleC23×C71C22×D4
prime radicalC22×D284C23
cosocleC22×C4×C71C24
hypercenterC4×#125D71
hypocenterC71#22114
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C43 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
3. #22589298C2semidirect
4. #22589106C2semidirect
5. #22589070C2semidirect
6. #22589065C2semidirect
11. #22588932C2semidirect
12. #22588925C2semidirect
14. C4×C4⋊(C71⋊C8)C2semidirect
15. C4×#125×C71C2semidirect
18. #17986296C4semidirect
297. C4×#125D71semidirect
311. C71#22114semidirect

Maximal subgroups

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

subgroupindex
C2×#179862962
#225908042
#225892982
#225891062
#225890702
#225890652
#225890222
#225889672
#225889602
#225889322
#225889252
#225883472
C4×C4⋊(C71⋊C8)2
C4×#125×C712
#2211471