Finite Group Databasebeta

← #24987119

Subgroups — #24987119

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582788C211yesmaximal, characteristic
2#19134359C211yesmaximal, characteristic, complemented
3C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
4C2×#14582622C211yesmaximal, characteristic
5C2×#14582622C211yesmaximal, characteristic
6#19132438C211yesmaximal, characteristic, complemented
7C43×#1280C211yesmaximal, characteristic, complemented
8C22×Dic43⋊C4C411yescharacteristic
9C22×(C2×D43)⋊C4C411yescharacteristic
10C22×(C2×D43)⋊C4C411yescharacteristic
11C22×(C2×D43)⋊C4C2211yescharacteristic
12C22×C4×Dic43C2211yescharacteristic
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15C2×#13063235—21no—
16C2×C8×Dic43—21no—
17#14582788—21no—
18#14582788—21no—
19#14582788—21no—
20#14582788—21no—
21C2×C43⋊#95C411yescharacteristic
22#14582653—21no—
23#14582653—21no—
24#14582622C414yescomplemented
25#14582622C414yescomplemented
26C2×C22⋊C8×C43C2211yescharacteristic
27C2×C22⋊C8×C43C2211yescharacteristic
28C2×#95×C43C2211yescharacteristic
29C24×D43C2×C411yescharacteristic
30C23×Dic43C2×C411yescharacteristic
31C23×Dic43C2×C411yescharacteristic
32C23×Dic43C2×C411yescharacteristic
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—42no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—42no—
47C2×(C2×D43)⋊C4—42no—
48C2×(C2×D43)⋊C4C2×C412yes—
49C2×(C2×D43)⋊C4C2×C412yes—
50C2×C4×Dic43—42no—
51C2×C4×Dic43D411yescharacteristic
52C2×C4×Dic43D411yescharacteristic
53C2×C4×Dic43D411yescharacteristic
54C2×C4×Dic43D411yescharacteristic
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)C2×C412yes—
58C22⋊(C43⋊C8)C2×C412yes—
59#13063235—42no—
60C8×Dic43—42no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C23×C4×C43C2×C411yescharacteristic
64C23×C4×C43C2×C411yescharacteristic
65C23×C4×C43C2311yescharacteristic
66C22×C8×C43—21no—
67C22×C8×C43—21no—
68C22⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70C22⋊C8×C43C2×C412yes—
71C22⋊C8×C43C2×C412yes—
72#95×C43—21no—
73#95×C43—21no—
74C24×C43C22×C411yescharacteristic
75C23×D43—21no—
76C23×D43—21no—
77C23×D43—21no—
78C23×D43—21no—
79C23×D43—21no—
80C23×D43—21no—
81C23×D43—41no—
82C23×D43—41no—
83C23×D43—41no—
84C23×D43—41no—
85C23×D43C4212yes—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43C22×C411yescharacteristic
99C22×C4×C43C22×C411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43#4111yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×Dic43—22no—
105C22×Dic43—22no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43—21no—
109C22×Dic43—21no—
110C22×Dic43—21no—
111C22×Dic43—21no—
112C22×Dic43—41no—
113C22×Dic43—41no—
114C22×Dic43—41no—
115C22×Dic43—41no—
116C22×Dic43C4212yes—
117C22×Dic43C22⋊C411yescharacteristic
118C22×Dic43C22⋊C411yescharacteristic
119C22×Dic43C22⋊C411yescharacteristic
120C22×Dic43C22⋊C411yescharacteristic
121C2×C8×C43—22no—
122C2×C8×C43—22no—
123C2×C8×C43—41no—
124C2×C8×C43—41no—
125C2×C8×C43—41no—
126C2×C8×C43—41no—
127(C2×D43)⋊C4—22no—
128(C2×D43)⋊C4—22no—
129(C2×D43)⋊C4—22no—
130(C2×D43)⋊C4—22no—
131(C2×D43)⋊C4—42no—
132(C2×D43)⋊C4—42no—
133(C2×D43)⋊C4—42no—
134(C2×D43)⋊C4—42no—
135Dic43⋊C4—42no—
136Dic43⋊C4—42no—
137C4×Dic43—22no—
138C4×Dic43—22no—
139C4×Dic43—41no—
140C4×Dic43—41no—
141C2×C43⋊C8—22no—
142C2×C43⋊C8—22no—
143C2×C43⋊C8—41no—
144C2×C43⋊C8—41no—
145C2×C43⋊C8—41no—
146C2×C43⋊C8—41no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43C2×C4211yescharacteristic
152C23×C43C2×C22⋊C411yescharacteristic
153C23×C43#11711yescharacteristic
154C23×C43#13111yescharacteristic
155C23×C43#13111yescharacteristic
156C23×C43#13111yescharacteristic
157C23×C43#13111yescharacteristic
158C22×D43—22no—
159C22×D43—22no—
160C22×D43—22no—
161C22×D43—42no—
162C22×D43—42no—
163C22×D43—41no—
164C22×D43—41no—
165C22×D43—41no—
166C22×D43—41no—
167C22×D43—41no—
168C22×D43—41no—
169C22×D43—41no—
170C22×D43—41no—
171C22×D43—42no—
172C22×D43—42no—
173C22×D43—81no—
174C22×D43—81no—
175C22×D43—81no—
176C22×D43—81no—
177C22×D43—81no—
178C22×D43—81no—
179C22×D43—81no—
180C22×D43—81no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—21no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—81no—
196C2×C4×C43—81no—
197C2×C4×C43—81no—
198C2×C4×C43—81no—
199C2×C4×C43C4×D411yescharacteristic
200C2×C4×C43C4×D411yescharacteristic
201C2×C4×C43C4×D411yescharacteristic
202C2×C4×C43C4×D411yescharacteristic
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—22no—
208C2×Dic43—21no—
209C2×Dic43—21no—
210C2×Dic43—21no—
211C2×Dic43—21no—
212C2×Dic43—21no—
213C2×Dic43—21no—
214C2×Dic43—42no—
215C2×Dic43—42no—
216C2×Dic43—42no—
217C2×Dic43—42no—
218C2×Dic43—42no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43—42no—
222C2×Dic43#9912yes—
223C2×Dic43#10012yes—
224C8×C43—42no—
225C8×C43—42no—
226C43⋊C8—42no—
227C43⋊C8—42no—
228#8155—431nomaximal, Sylow
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—21no—
239C22×C43—21no—
240C22×C43—21no—
241C22×C43C4×C22⋊C411yescharacteristic
242C22×C43#40511yescharacteristic
243C22×C43#40511yescharacteristic
244C22×C43#40811yescharacteristic
245C22×C43#40811yescharacteristic
246C22×C43C2×#9911yescharacteristic
247C22×C43#41011yescharacteristic
248C22×C43C2×#10011yescharacteristic
249C22×C43#41311yescharacteristic
250C22×C43#43311yescharacteristic
251C22×C43#43311yescharacteristic
252C2×D43—42no—
253C2×D43—42no—
254C2×D43—42no—
255C2×D43—82no—
256C2×D43—82no—
257C2×D43—81no—
258C2×D43—81no—
259C2×D43—81no—
260C2×D43—81no—
261C2×D43—82no—
262C2×D43—82no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—81no—
268C4×C43—81no—
269Dic43—22no—
270Dic43—22no—
271Dic43—41no—
272Dic43—41no—
273Dic43—42no—
274C2×#388—431no—
275#1749—431no—
276C4×C22⋊C8—431no—
277C2×#323—431no—
278C2×#323—431no—
279#1280—431no—
280#1280D4311yescharacteristic, complemented
281C2×C43—21no—
282C2×C43—21no—
283C2×C43—21no—
284C2×C43—21no—
285C2×C43#146811yescharacteristic
286C2×C43#146911yescharacteristic
287C2×C43#147111yescharacteristic
288C2×C43#147311yescharacteristic
289C2×C43#175011yescharacteristic
290C2×C43C4×#9911yescharacteristic
291C2×C43C4×#10011yescharacteristic
292D43—82no—
293C22×C4⋊C4—431no—
294C22×C22⋊C4—431no—
295C22×C22⋊C4—431no—
296C22×C22⋊C4—431no—
297C22×C42—431no—
298C2×C22⋊C8—431no—
299C2×C22⋊C8—431no—
300C2×C22⋊C8C2×D4311yescharacteristic
301C2×C22⋊C8C2×D4311yescharacteristic
302C2×#97—861no—
303C2×C4×C8—861no—
304#388—861no—
305#388—861no—
306#388—861no—
307#388—861no—
308C2×#95—431no—
309C2×#95C2×D4311yescharacteristic
310#336—861no—
311#336—861no—
312#323—434no—
313#323—434no—
314C43#815511yescharacteristic, complemented, Sylow
315C25—431no—
316C23×C4—431no—
317C23×C4—431no—
318C23×C4—431no—
319C23×C4C4×D4311yescharacteristic
320C23×C4C4×D4311yescharacteristic
321C23×C4C22×D4311yescharacteristic
322C22×C8—21no—
323C22×C8—21no—
324C22×C8—861no—
325C22×C8—861no—
326C2×C4⋊C4—861no—
327C2×C4⋊C4—861no—
328C2×C4⋊C4—1722no—
329C2×C22⋊C4—432no—
330C2×C22⋊C4—432no—
331C2×C22⋊C4—861no—
332C2×C22⋊C4—861no—
333C2×C22⋊C4—861no—
334C2×C22⋊C4—861no—
335C2×C22⋊C4—861no—
336C2×C22⋊C4—861no—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339C2×C22⋊C4—1722no—
340C2×C22⋊C4—1722no—
341C2×C42—431no—
342C2×C42—431no—
343C2×C42—431no—
344C2×C42—431no—
345C2×C42—1722no—
346C22⋊C8—21no—
347C22⋊C8—21no—
348C22⋊C8—432no—
349C22⋊C8—432no—
350C22⋊C8—861no—
351C22⋊C8—861no—
352C22⋊C8C4×D4312yes—
353C22⋊C8C4×D4312yes—
354#97—1722no—
355C4×C8—1722no—
356#95—21no—
357#95—21no—
358#95—861no—
359#95—861no—
360C24—432no—
361C24—861no—
362C24—861no—
363C24—861no—
364C24—861no—
365C24—861no—
366C24—861no—
367C24—1721no—
368C24—1721no—
369C24—1721no—
370C24—1721no—
371C24C2×C4×D4311yescharacteristic
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—431no—
385C22×C4—431no—
386C22×C4—431no—
387C22×C4—431no—
388C22×C4—432no—
389C22×C4—862no—
390C22×C4—862no—
391C22×C4—861no—
392C22×C4—861no—
393C22×C4—861no—
394C22×C4—861no—
395C22×C4—861no—
396C22×C4—861no—
397C22×C4—1721no—
398C22×C4—1721no—
399C22×C4—1721no—
400C22×C4—1721no—
401C22×C4C2×C4×D4311yescharacteristic
402C22×C4C2×C4×D4311yescharacteristic
403C22×C4D4×D4311yescharacteristic
404C22×C4D4×D4311yescharacteristic
405C22×C4#1062190011yescharacteristic
406C22×C4#1062190211yescharacteristic
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—41no—
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—862no—
414C2×C8—862no—
415C2×C8—1721no—
416C2×C8—1721no—
417C2×C8—1721no—
418C2×C8—1721no—
419C4⋊C4—1722no—
420C4⋊C4—1722no—
421C22⋊C4—862no—
422C22⋊C4—862no—
423C22⋊C4—862no—
424C22⋊C4—862no—
425C22⋊C4—1722no—
426C22⋊C4—1722no—
427C22⋊C4—1722no—
428C22⋊C4—1722no—
429C42—862no—
430C42—862no—
431C42—1721no—
432C42—1721no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—862no—
438C23—862no—
439C23—862no—
440C23—3441no—
441C23—3441no—
442C23—3441no—
443C23—3441no—
444C23—3441no—
445C23—3441no—
446C23—3441no—
447C23—3441no—
448C23—1722no—
449C23—1722no—
450C23—1722no—
451C23—1722no—
452C23—1721no—
453C23—1721no—
454C23—1721no—
455C23—1721no—
456C23—1721no—
457C23—1721no—
458C23—1721no—
459C23—1721no—
460C23C42×D4311yescharacteristic
461C23C22⋊C4×D4311yescharacteristic
462C23#1306328311yescharacteristic
463C23#1306333111yescharacteristic
464C23#1306333111yescharacteristic
465C23#1306333311yescharacteristic
466C23#1306333311yescharacteristic
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—81no—
482C2×C4—81no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—432no—
486C2×C4—432no—
487C2×C4—861no—
488C2×C4—861no—
489C2×C4—861no—
490C2×C4—861no—
491C2×C4—861no—
492C2×C4—861no—
493C2×C4—861no—
494C2×C4—861no—
495C2×C4—861no—
496C2×C4—861no—
497C2×C4—862no—
498C2×C4—1722no—
499C2×C4—1722no—
500C2×C4—1722no—
501C2×C4—1722no—
502C2×C4—1722no—
503C2×C4—1721no—
504C2×C4—1721no—
505C2×C4—1722no—
506C2×C4(C22⋊D43)⋊C411yescharacteristic
507C2×C4(C22⋊D43)⋊C411yescharacteristic
508C2×C4#1306328711yescharacteristic
509C2×C4#1306328711yescharacteristic
510C8—42no—
511C8—42no—
512C8—1722no—
513C8—1722no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—3442no—
527C22—3442no—
528C22—3442no—
529C22—3442no—
530C22—3441no—
531C22—3441no—
532C22—3441no—
533C22—3441no—
534C22—1722no—
535C22—1722no—
536C22—1722no—
537C22#1458274611yescharacteristic
538C22#1458285311yescharacteristic
539C22#1458285611yescharacteristic
540C22#1458286411yescharacteristic
541C22#1458286411yescharacteristic
542C22#99×D4311yescharacteristic
543C22#1458287111yescharacteristic
544C22#100×D4311yescharacteristic
545C22#1458288211yescharacteristic
546C22#1458295911yescharacteristic
547C22#1458295911yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—81no—
553C4—81no—
554C4—862no—
555C4—862no—
556C4—1721no—
557C4—1721no—
558C4—1722no—
559C2—21no—
560C2—21no—
561C2—21no—
562C2—21no—
563C2—3442no—
564C2#1913294211yescharacteristic
565C2#1913294511yescharacteristic
566C2#1913295311yescharacteristic
567C2#1913296311yescharacteristic
568C2#1913436011yescharacteristic
569C2#1913438211yescharacteristic
570C2#1913438611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC23×C43C2×C42
FrattiniC23×C4C22×D43
FittingC43×#1280C2
socleC23×C43C2×C22⋊C4
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1280D43
hypocenterC43#8155
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
2. #19134359C2semidirect
3. C22⋊C8×Dic43C2semidirect
6. #19132438C2semidirect
7. C43×#1280C2semidirect
24. #14582622C4semidirect
25. #14582622C4semidirect
280. #1280D43semidirect
314. C43#8155semidirect

Maximal subgroups

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

subgroupindex
C2×#145827882
#191343592
C22⋊C8×Dic432
C2×#145826222
#191324382
C43×#12802
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