Finite Group Databasebeta

← #24999880

Subgroups — #24999880

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140337C211yesmaximal, characteristic
2#19134910C211yesmaximal, characteristic
3#19134790C211yesmaximal, characteristic, complemented
4C2×#14582634C211yesmaximal, characteristic
5#19132848C211yesmaximal, characteristic, complemented
6#19132475C211yesmaximal, characteristic, complemented
7C2×C43×#324C211yesmaximal, characteristic, complemented
8C2×#13063308—21no—
9C2×#13063299C2211yescharacteristic
10C22×C4⋊Dic43C2211yescharacteristic
11C2×#13063257—21no—
12C2×#13063247—21no—
13#14582829—21no—
14#14582821—21no—
15#14582821—21no—
16#14582816—21no—
17#14582778—21no—
18#14582759C2211yescharacteristic
19C2×C43⋊#95—21no—
20C2×C43⋊#95—21no—
21C2×C43⋊#95C2211yescharacteristic
22#14582662—21no—
23#14582662—21no—
24#14582634—22no—
25C22×C4⋊C4×C43C2211yescharacteristic
26C2×C22⋊C8×C43C2211yescharacteristic
27C2×C22⋊C8×C43C2211yescharacteristic
28C43×#324—22no—
29C22×D172D411yescharacteristic
30C22×C22⋊D43—21no—
31C23×Dic43—21no—
32C23×Dic43—21no—
33#13063308—42no—
34#13063308—42no—
35#13063299—21no—
36#13063299—21no—
37#13063299—21no—
38#13063299—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—42no—
42C2×C4⋊Dic43D411yescharacteristic
43C2×C4⋊Dic43D411yescharacteristic
44C2×C4⋊Dic43D411yescharacteristic
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4—21no—
47C2×C22⋊Dic43—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—21no—
52C2×(C2×D43)⋊C4—21no—
53#13063257—42no—
54#13063247—42no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—42no—
61C43⋊#95—42no—
62C23×C4×C43D411yescharacteristic
63C23×C4×C43D411yescharacteristic
64C23×C4×C43C2311yescharacteristic
65C22×C8×C43—21no—
66C22×C8×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43D412yes—
77C24×C43C2×D411yescharacteristic
78C23×D43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43SD1612yes—
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C22×C4×C43#4111yescharacteristic
98C22×C4×C43#4111yescharacteristic
99C2×C22⋊D43—41no—
100C2×C22⋊D43—41no—
101C2×C22⋊D43—41no—
102C2×C22⋊D43—41no—
103C2×C22⋊D43—41no—
104C2×C22⋊D43—41no—
105C22×Dic43—22no—
106C22×Dic43—22no—
107C22×Dic43—21no—
108C22×Dic43—21no—
109C22×Dic43—21no—
110C22×Dic43—41no—
111C22×Dic43—41no—
112C22×Dic43—41no—
113C22×Dic43—41no—
114C22×Dic43—41no—
115C22×Dic43—41no—
116C22×Dic43—41no—
117C22×Dic43—41no—
118C22×Dic43—41no—
119C22×Dic43—41no—
120C22×Dic43—41no—
121C22×Dic43—41no—
122C2×D172—21no—
123C2×D172—21no—
124C2×D172—41no—
125C2×D172—41no—
126C2×C8×C43—22no—
127C2×C8×C43—41no—
128C2×C8×C43—41no—
129C2×C8×C43—41no—
130C2×C8×C43—41no—
131C2×C8×C43—41no—
132C4⋊C4×C43—41no—
133C4⋊C4×C43—41no—
134C4⋊C4×C43—41no—
135C4⋊C4×C43—41no—
136C22⋊Dic43—41no—
137C22⋊Dic43—41no—
138(C2×D43)⋊C4—42no—
139(C2×D43)⋊C4—42no—
140(C2×D43)⋊C4—41no—
141(C2×D43)⋊C4—41no—
142(C2×D43)⋊C4—81no—
143(C2×D43)⋊C4—81no—
144C4⋊Dic43—22no—
145C4⋊Dic43—22no—
146C4⋊Dic43—21no—
147C4⋊Dic43—21no—
148C4⋊Dic43—41no—
149C4⋊Dic43—41no—
150C4⋊Dic43—41no—
151C4⋊Dic43—41no—
152Dic43⋊C4—42no—
153Dic43⋊C4—42no—
154C23×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43—21no—
158C23×C43#12011yescharacteristic
159C23×C43#12111yescharacteristic
160C23×C43#12311yescharacteristic
161C23×C43C2×SD1611yescharacteristic
162C23×C43#13511yescharacteristic
163C23×C43AGL(1,ℤ/8)11yescharacteristic
164C23×C43AGL(1,ℤ/8)11yescharacteristic
165C22×D43—41no—
166C22×D43—41no—
167C22×D43—41no—
168C22×D43—41no—
169C22×D43—41no—
170C22×D43—41no—
171C22×D43—41no—
172C2×C4×C43—21no—
173C2×C4×C43—21no—
174C2×C4×C43—21no—
175C2×C4×C43—21no—
176C2×C4×C43—22no—
177C2×C4×C43—22no—
178C2×C4×C43—22no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—42no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—81no—
192C2×C4×C43#12111yescharacteristic
193C2×C4×C43#12111yescharacteristic
194C2×C4×C43#12311yescharacteristic
195C2×C4×C43#12411yescharacteristic
196C22⋊D43—81no—
197C22⋊D43—81no—
198C22⋊D43—81no—
199C22⋊D43—81no—
200C2×Dic43—42no—
201C2×Dic43—42no—
202C2×Dic43—42no—
203C2×Dic43—42no—
204C2×Dic43—42no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—42no—
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43—81no—
216C2×Dic43—81no—
217C2×Dic43—81no—
218C2×Dic43—81no—
219C2×Dic43—81no—
220C2×Dic43—81no—
221C2×Dic43—81no—
222C2×Dic43—81no—
223D172—42no—
224D172—81no—
225C8×C43—42no—
226C8×C43—81no—
227#10396—431nomaximal, Sylow
228C22×C43—21no—
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#39411yescharacteristic
241C22×C43#44911yescharacteristic
242C22×C43#45011yescharacteristic
243C22×C43#45411yescharacteristic
244C22×C43#45611yescharacteristic
245C22×C43B(4,𝔽2)11yescharacteristic
246C22×C43#45811yescharacteristic
247C22×C43#46511yescharacteristic
248C22×C43#46911yescharacteristic
249C22×C43#48111yescharacteristic
250C22×C43#48211yescharacteristic
251C2×D43—81no—
252C2×D43—81no—
253C2×D43—81no—
254C2×D43—81no—
255C2×D43—81no—
256C2×D43—81no—
257C2×D43—81no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—42no—
263C4×C43—81no—
264Dic43—82no—
265Dic43—82no—
266Dic43—81no—
267Dic43—81no—
268Dic43—81no—
269#2618—431no—
270#1874—431no—
271#1853—431no—
272C2×#327—431no—
273C2×#324D4311yescharacteristic, complemented
274#1441—431no—
275#1294—431no—
276C2×C43—21no—
277C2×C43—21no—
278C2×C43—21no—
279C2×C43—21no—
280C2×C43#159711yescharacteristic
281C2×C43#160411yescharacteristic
282C2×C43#160911yescharacteristic
283C2×C43#161611yescharacteristic
284C2×C43#203411yescharacteristic
285C2×C43#203811yescharacteristic
286C2×C43#204411yescharacteristic
287D43—161no—
288C2×#123—861no—
289C2×#121—431no—
290C22×C4⋊C4—431no—
291C22×C4⋊C4C2×D4311yescharacteristic
292C2×#106—861no—
293C2×#102—861no—
294C2×C22⋊C8C2×D4311yescharacteristic
295C2×C22⋊C8C2×D4311yescharacteristic
296#398—861no—
297#396—861no—
298#396—861no—
299#394—861no—
300#386—861no—
301#380—431no—
302C2×#95—431no—
303C2×#95—861no—
304C2×#95—861no—
305#340—861no—
306#340—861no—
307#327—862no—
308#324—22no—
309C43#1039611yescharacteristic, complemented, Sylow
310C22×D4—431no—
311C22×D4—861no—
312C23×C4—861no—
313C23×C4—861no—
314C23×C4D17211yescharacteristic
315C23×C4D17211yescharacteristic
316C23×C4C22×D4311yescharacteristic
317C22×C8—21no—
318C22×C8—21no—
319#123—1722no—
320#123—1722no—
321#121—861no—
322#121—861no—
323#121—861no—
324#121—861no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—431no—
332C2×C4⋊C4—431no—
333C2×C4⋊C4—431no—
334C2×C4⋊C4—861no—
335C2×C4⋊C4—861no—
336C2×C4⋊C4—861no—
337C2×C4⋊C4—861no—
338C2×C4⋊C4—1722no—
339C2×C22⋊C4—861no—
340C2×C22⋊C4—861no—
341C2×C22⋊C4—861no—
342C2×C22⋊C4—861no—
343C2×C22⋊C4—861no—
344C2×C22⋊C4—861no—
345#106—1722no—
346#102—1722no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8C22⋊D4312yes—
351#95—861no—
352#95—861no—
353#95—861no—
354#95—861no—
355#95—861no—
356#95—1722no—
357#95—1722no—
358C24—861no—
359C24C2×D17211yescharacteristic
360C2×D4—861no—
361C2×D4—861no—
362C2×D4—1721no—
363C2×D4—1721no—
364C2×D4—1721no—
365C2×D4—1721no—
366C2×D4—1721no—
367C2×D4—1721no—
368C2×D4—1721no—
369C2×D4—1721no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—862no—
384C22×C4—862no—
385C22×C4—861no—
386C22×C4—861no—
387C22×C4—861no—
388C22×C4—1721no—
389C22×C4—1721no—
390C22×C4—1721no—
391C22×C4—1721no—
392C22×C4—1721no—
393C22×C4—1721no—
394C22×C4—1721no—
395C22×C4—1721no—
396C22×C4—1721no—
397C22×C4—1721no—
398C22×C4—1721no—
399C22×C4—1721no—
400C22×C4#1062187312yes—
401C22×C4#1062189811yescharacteristic
402C22×C4D4×D4311yescharacteristic
403C22×C4D4×D4311yescharacteristic
404C22×C4#1062190011yescharacteristic
405C22×C4#1062190011yescharacteristic
406C22×C4C2×C22⋊D4311yescharacteristic
407C2×C8—22no—
408C2×C8—41no—
409C2×C8—41no—
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—862no—
418C4⋊C4—862no—
419C4⋊C4—861no—
420C4⋊C4—861no—
421C4⋊C4—1721no—
422C4⋊C4—1721no—
423C4⋊C4—1721no—
424C4⋊C4—1721no—
425C4⋊C4—1722no—
426C4⋊C4—1722no—
427C22⋊C4—3441no—
428C22⋊C4—3441no—
429C22⋊C4—1722no—
430C22⋊C4—1722no—
431C22⋊C4—1721no—
432C22⋊C4—1721no—
433C22⋊C4—1721no—
434C22⋊C4—1721no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—1721no—
440C23—1721no—
441C23—1721no—
442C23—1721no—
443C23—1721no—
444C23—1721no—
445C23—1721no—
446C23#1306329511yescharacteristic
447C23#1306329911yescharacteristic
448C23#1306330911yescharacteristic
449C23C2×#1062187311yescharacteristic
450C23#1306334711yescharacteristic
451C23#1306335311yescharacteristic
452C23#1306335311yescharacteristic
453D4—3441no—
454D4—3441no—
455D4—3441no—
456D4—3441no—
457D4—3441no—
458D4—1722no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—81no—
479C2×C4—3441no—
480C2×C4—3441no—
481C2×C4—3441no—
482C2×C4—3441no—
483C2×C4—3441no—
484C2×C4—3441no—
485C2×C4—3441no—
486C2×C4—3441no—
487C2×C4—1722no—
488C2×C4—1722no—
489C2×C4—1722no—
490C2×C4—1722no—
491C2×C4—1722no—
492C2×C4—1721no—
493C2×C4—1721no—
494C2×C4—1721no—
495C2×C4—1721no—
496C2×C4—1721no—
497C2×C4—1721no—
498C2×C4—1721no—
499C2×C4—1721no—
500C2×C4—1722no—
501C2×C4—1721no—
502C2×C4#1306329611yescharacteristic
503C2×C4#1306329711yescharacteristic
504C2×C4#1306330711yescharacteristic
505C2×C4#1306331111yescharacteristic
506C8—42no—
507C8—81no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—3441no—
521C22—3441no—
522C22—3441no—
523C22—3441no—
524C22—3441no—
525C22—3441no—
526C22—3441no—
527C22#1458281511yescharacteristic
528C22#1458304611yescharacteristic
529C22#1458305211yescharacteristic
530C22#1458307411yescharacteristic
531C22#1458308411yescharacteristic
532C22#1458308711yescharacteristic
533C22#1458309011yescharacteristic
534C22#1458312811yescharacteristic
535C22#1458315211yescharacteristic
536C22#1458321811yescharacteristic
537C22#1458322411yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—42no—
543C4—81no—
544C4—3442no—
545C4—3441no—
546C4—3442no—
547C4—3441no—
548C4—3441no—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—21no—
553C2—6881no—
554C2#1913352611yescharacteristic
555C2#1913356611yescharacteristic
556C2#1913359411yescharacteristic
557C2#1913363411yescharacteristic
558C2#1913578511yescharacteristic
559C2#1913581311yescharacteristic
560C2#1913584511yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC2×C43×#324C2
socleC23×C43#120
prime radicalC2×#13063299C22
hypercenterC2×#324D43
hypocenterC43#10396
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. #19134790C2semidirect
5. #19132848C2semidirect
6. #19132475C2semidirect
7. C2×C43×#324C2semidirect
273. C2×#324D43semidirect
309. C43#10396semidirect

Maximal subgroups

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

subgroupindex
#191403372
#191349102
#191347902
C2×#145826342
#191328482
#191324752
C2×C43×#3242
#1039643