Finite Group Databasebeta

← #24999930

Subgroups — #24999930

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140529C211yesmaximal, characteristic
2#19134910C211yesmaximal, characteristic
3#19134903C211yesmaximal, characteristic, complemented
4C2×#14582632C211yesmaximal, characteristic
5#19132852C211yesmaximal, characteristic, complemented
6#19132437C211yesmaximal, characteristic, complemented
7C2×C43×#328C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C22×C4⋊Dic43C2211yescharacteristic
10C2×#13063249—21no—
11C2×#13063247—21no—
12C2×C22⋊(C43⋊C8)C2211yescharacteristic
13#14582838—21no—
14#14582825—21no—
15#14582816—21no—
16#14582810—21no—
17#14582776—21no—
18#14582776—21no—
19C2×C43⋊#95—21no—
20C2×C43⋊#95—21no—
21C2×C43⋊#95C2211yescharacteristic
22#14582662—21no—
23#14582661—21no—
24#14582632—22no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×C22⋊C8×C43C2211yescharacteristic
27C2×#95×C43C2211yescharacteristic
28C43×#328—22no—
29C22×D172D411yescharacteristic
30C22×C22⋊D43—21no—
31C23×Dic43—21no—
32C23×Dic43D411yescharacteristic
33C23×Dic43D411yescharacteristic
34C22×C43⋊C8—21no—
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×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48#13063249—42no—
49#13063247—42no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—42no—
59C43⋊#95—42no—
60C22×Q8×C43D411yescharacteristic
61C23×C4×C43—21no—
62C23×C4×C43C2311yescharacteristic
63C22×C8×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66C22⋊Q8×C43—21no—
67C22⋊Q8×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43D411yescharacteristic
70C2×C22⋊C4×C43—21no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73#95×C43—21no—
74#95×C43D412yes—
75C24×C43C2×D411yescharacteristic
76C23×D43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—21no—
79C2×Q8×C43—41no—
80C2×Q8×C43—41no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—22no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43#4111yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C22×C4×C43#4111yescharacteristic
98C2×C22⋊D43—41no—
99C2×C22⋊D43—41no—
100C2×C22⋊D43—41no—
101C2×C22⋊D43—41no—
102C2×C22⋊D43—41no—
103C2×C22⋊D43—41no—
104C22×Dic43—22no—
105C22×Dic43—21no—
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×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—41no—
127C2×C8×C43—41no—
128C2×C8×C43—41no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—41no—
132C4⋊C4×C43—41no—
133C22⋊C4×C43—41no—
134C22⋊C4×C43—41no—
135(C2×D43)⋊C4—41no—
136(C2×D43)⋊C4—41no—
137(C2×D43)⋊C4—81no—
138(C2×D43)⋊C4—81no—
139(C2×D43)⋊C4—81no—
140(C2×D43)⋊C4—81no—
141C4⋊Dic43—22no—
142C4⋊Dic43—22no—
143C4⋊Dic43—21no—
144C4⋊Dic43—21no—
145C4⋊Dic43—41no—
146C4⋊Dic43—41no—
147C2×C43⋊C8—41no—
148C2×C43⋊C8—41no—
149C2×C43⋊C8—41no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—21no—
153C23×C43—21no—
154C23×C43#12011yescharacteristic
155C23×C43#12111yescharacteristic
156C23×C43#12411yescharacteristic
157C23×C43#13511yescharacteristic
158C23×C43#13511yescharacteristic
159C23×C43AGL(1,ℤ/8)11yescharacteristic
160C23×C43#13711yescharacteristic
161C22×D43—41no—
162C22×D43—41no—
163C22×D43—41no—
164C22×D43—41no—
165C22×D43—41no—
166C22×D43—41no—
167C22×D43—41no—
168Q8×C43—42no—
169Q8×C43—81no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—21no—
173C2×C4×C43—21no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—42no—
179C2×C4×C43—42no—
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—42no—
187C2×C4×C43—81no—
188C2×C4×C43—81no—
189C2×C4×C43—81no—
190C2×C4×C43—81no—
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43#12111yescharacteristic
193C2×C4×C43#12311yescharacteristic
194C2×C4×C43#12311yescharacteristic
195C22⋊D43—81no—
196C22⋊D43—81no—
197C22⋊D43—81no—
198C22⋊D43—81no—
199C2×Dic43—42no—
200C2×Dic43—42no—
201C2×Dic43—42no—
202C2×Dic43—42no—
203C2×Dic43—41no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—42no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—81no—
214C2×Dic43—81no—
215C2×Dic43—81no—
216C2×Dic43—81no—
217C2×Dic43—81no—
218C2×Dic43—81no—
219D172—42no—
220D172—81no—
221C8×C43—81no—
222C43⋊C8—81no—
223#10404—431nomaximal, Sylow
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—21no—
227C22×C43—21no—
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#39411yescharacteristic
237C22×C43#44911yescharacteristic
238C22×C43#45211yescharacteristic
239C22×C43#45411yescharacteristic
240C22×C43#45511yescharacteristic
241C22×C43B(4,𝔽2)11yescharacteristic
242C22×C43#45811yescharacteristic
243C22×C43#46311yescharacteristic
244C22×C43#46411yescharacteristic
245C22×C43#48811yescharacteristic
246C22×C43#48911yescharacteristic
247C2×D43—81no—
248C2×D43—81no—
249C2×D43—81no—
250C2×D43—81no—
251C2×D43—81no—
252C2×D43—81no—
253C2×D43—81no—
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—82no—
259C4×C43—81no—
260C4×C43—81no—
261Dic43—82no—
262Dic43—81no—
263Dic43—81no—
264Dic43—81no—
265#2639—431no—
266#1874—431no—
267#1872—431no—
268C2×#328D4311yescharacteristic, complemented
269C2×#327—431no—
270#1442—431no—
271#1280—431no—
272C2×C43—21no—
273C2×C43—21no—
274C2×C43—21no—
275C2×C43—21no—
276C2×C43#159711yescharacteristic
277C2×C43#160611yescharacteristic
278C2×C43#161211yescharacteristic
279C2×C43#161511yescharacteristic
280C2×C43#204011yescharacteristic
281C2×C43#204211yescharacteristic
282C2×C43#204411yescharacteristic
283D43—161no—
284C2×C22⋊Q8C2×D4311yescharacteristic
285C2×#121—431no—
286C22×C4⋊C4—431no—
287C2×#103—861no—
288C2×#102—861no—
289C2×C22⋊C8—431no—
290C2×C22⋊C8C2×D4311yescharacteristic
291#400—861no—
292#397—861no—
293#394—861no—
294#393—861no—
295#386—861no—
296#386—861no—
297C2×#95—431no—
298C2×#95—861no—
299C2×#95—861no—
300C2×#95C2×D4311yescharacteristic
301#340—861no—
302#340—861no—
303#328—22no—
304#327—862no—
305C43#1040411yescharacteristic, complemented, Sylow
306C22×Q8D17211yescharacteristic
307C22×D4—431no—
308C22×D4—861no—
309C23×C4—21no—
310C23×C4—431no—
311C23×C4—431no—
312C23×C4—861no—
313C23×C4C22×D4311yescharacteristic
314C22×C8—21no—
315C22×C8—861no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320#121—861no—
321#121—861no—
322#121—861no—
323#121—861no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—431no—
326C2×C4⋊C4—861no—
327C2×C4⋊C4—861no—
328C2×C4⋊C4—1722no—
329C2×C4⋊C4D17211yescharacteristic
330C2×C22⋊C4—21no—
331C2×C22⋊C4—861no—
332C2×C22⋊C4—861no—
333C2×C22⋊C4—861no—
334C2×C22⋊C4—861no—
335C2×C22⋊C4—861no—
336#103—1722no—
337#102—1722no—
338C22⋊C8—21no—
339C22⋊C8—21no—
340C22⋊C8—861no—
341C22⋊C8—861no—
342#95—21no—
343#95—861no—
344#95—861no—
345#95—861no—
346#95—861no—
347#95—861no—
348#95—861no—
349#95—1722no—
350#95—1722no—
351#95C22⋊D4312yes—
352C24—861no—
353C24D4×D4311yescharacteristic
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—41no—
357C2×Q8—41no—
358C2×D4—861no—
359C2×D4—861no—
360C2×D4—1721no—
361C2×D4—1721no—
362C2×D4—1721no—
363C2×D4—1721no—
364C2×D4—1721no—
365C2×D4—1721no—
366C2×D4—1721no—
367C2×D4—1721no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—861no—
380C22×C4—861no—
381C22×C4—862no—
382C22×C4—861no—
383C22×C4—861no—
384C22×C4—861no—
385C22×C4—861no—
386C22×C4—861no—
387C22×C4—1721no—
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×C4C2×D17211yescharacteristic
398C22×C4#1062189811yescharacteristic
399C22×C4D4×D4311yescharacteristic
400C22×C4#1062190011yescharacteristic
401C22×C4#1062190011yescharacteristic
402C22×C4C2×C22⋊D4311yescharacteristic
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—1721no—
407C2×C8—1721no—
408C2×C8—1721no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—862no—
414C4⋊C4—862no—
415C4⋊C4—861no—
416C4⋊C4—861no—
417C4⋊C4—1721no—
418C4⋊C4—1721no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—3441no—
422C22⋊C4—3441no—
423C22⋊C4—3441no—
424C22⋊C4—3441no—
425C22⋊C4—1721no—
426C22⋊C4—1721no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—1721no—
432C23—1721no—
433C23—1721no—
434C23—1721no—
435C23—1721no—
436C23—1721no—
437C23—1721no—
438C23#1306329511yescharacteristic
439C23#1306329711yescharacteristic
440C23#1306331111yescharacteristic
441C23#1306334611yescharacteristic
442C23#1306334811yescharacteristic
443C23#1306335211yescharacteristic
444C23#1306335711yescharacteristic
445Q8—42no—
446Q8—81no—
447D4—3441no—
448D4—3441no—
449D4—3441no—
450D4—3441no—
451D4—3441no—
452D4—1722no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—3441no—
475C2×C4—3441no—
476C2×C4—3441no—
477C2×C4—3441no—
478C2×C4—3441no—
479C2×C4—3441no—
480C2×C4—1722no—
481C2×C4—1722no—
482C2×C4—1722no—
483C2×C4—1722no—
484C2×C4—1721no—
485C2×C4—1721no—
486C2×C4—1721no—
487C2×C4—1721no—
488C2×C4—1721no—
489C2×C4—1721no—
490C2×C4—1721no—
491C2×C4—1721no—
492C2×C4—1722no—
493C2×C4—1721no—
494C2×C4#1306329611yescharacteristic
495C2×C4#1306329911yescharacteristic
496C2×C4#1306330711yescharacteristic
497C2×C4#1306330911yescharacteristic
498C8—81no—
499C8—3441no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—3441no—
513C22—3441no—
514C22—3441no—
515C22—3441no—
516C22—3441no—
517C22—3441no—
518C22—3441no—
519C22#1458281511yescharacteristic
520C22#1458304711yescharacteristic
521C22#1458306411yescharacteristic
522C22#1458307311yescharacteristic
523C22#1458307811yescharacteristic
524C22#1458308711yescharacteristic
525C22#1458309011yescharacteristic
526C22#1458311611yescharacteristic
527C22#1458312311yescharacteristic
528C22#1458325511yescharacteristic
529C22#1458326011yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—82no—
535C4—81no—
536C4—81no—
537C4—3442no—
538C4—3441no—
539C4—3441no—
540C4—3441no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—6881no—
546C2#1913352711yescharacteristic
547C2#1913357811yescharacteristic
548C2#1913361211yescharacteristic
549C2#1913362911yescharacteristic
550C2#1913582311yescharacteristic
551C2#1913583311yescharacteristic
552C2#1913584511yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC2×C43×#328C2
socleC23×C43#120
prime radicalC2×#13063299C22
hypercenterC2×#328D43
hypocenterC43#10404
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
3. #19134903C2semidirect
5. #19132852C2semidirect
6. #19132437C2semidirect
7. C2×C43×#328C2semidirect
268. C2×#328D43semidirect
305. C43#10404semidirect

Maximal subgroups

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

subgroupindex
#191405292
#191349102
#191349032
C2×#145826322
#191328522
#191324372
C2×C43×#3282
#1040443