Finite Group Databasebeta

← #24990602

Subgroups — #24990602

Order 11008.

692 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#19137192C211yesmaximal, characteristic
2#19134790C211yesmaximal, characteristic, complemented
3#19134782C211yesmaximal, characteristic, complemented
4C2×#14582622C211yesmaximal, characteristic
5#19132841C211yesmaximal, characteristic
6#19132474C211yesmaximal, characteristic, complemented
7C43×#1294C211yesmaximal, characteristic, complemented
8C22×C4⋊Dic43C2211yescharacteristic
9C22×(C2×D43)⋊C4—21no—
10C22×(C2×D43)⋊C4C2211yescharacteristic
11C2×#13063258—21no—
12C2×#13063257—21no—
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14#14582791—21no—
15#14582791—21no—
16#14582789—21no—
17#14582789—21no—
18#14582759C2211yescharacteristic
19#14582754—21no—
20C22⋊C4×Dic43—21no—
21C2×C43⋊#95—21no—
22#14582662—21no—
23#14582661—21no—
24#14582622C414yescomplemented
25C2×C22⋊C8×C43C2211yescharacteristic
26C43×#380C2211yescharacteristic
27C2×#95×C43C2211yescharacteristic
28C24×D43D411yescharacteristic
29C23×Dic43—21no—
30C23×Dic43D411yescharacteristic
31C22×C43⋊C8—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—42no—
35C2×C4⋊Dic43D411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×C22⋊Dic43—21no—
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)⋊C4—42no—
49C2×(C2×D43)⋊C4C2×C412yes—
50C2×(C2×D43)⋊C4Q812yes—
51C2×C4×Dic43—21no—
52C2×C4×Dic43—21no—
53#13063258—42no—
54#13063257—42no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)C2×C412yes—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—42no—
61C23×C4×C43—21no—
62C23×C4×C43C2311yescharacteristic
63C22×C8×C43—21no—
64C2×C4⋊C4×C43D411yescharacteristic
65C2×C4⋊C4×C43D411yescharacteristic
66C2×C22⋊C4×C43—21no—
67C22⋊C8×C43—21no—
68C22⋊C8×C43C2×C412yes—
69#95×C43—21no—
70#95×C43—21no—
71#95×C43—21no—
72C24×C43C2×D411yescharacteristic
73C23×D43—21no—
74C23×D43—21no—
75C23×D43—21no—
76C23×D43—21no—
77C23×D43—21no—
78C23×D43—21no—
79C23×D43—41no—
80C23×D43—41no—
81C23×D43—41no—
82C23×D43—41no—
83C23×D43C4⋊C412yes—
84C22×C4×C43—22no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43C22×C411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×Q811yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C22×C4×C43#4111yescharacteristic
101C22×Dic43—22no—
102C22×Dic43—21no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—41no—
107C22×Dic43—41no—
108C22×Dic43—41no—
109C22×Dic43—41no—
110C22×Dic43—41no—
111C22×Dic43—41no—
112C22×Dic43—41no—
113C22×Dic43—41no—
114C22×Dic43C4⋊C412yes—
115C2×C8×C43—22no—
116C2×C8×C43—41no—
117C2×C8×C43—41no—
118C4⋊C4×C43—41no—
119C4⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C22⋊Dic43—41no—
123C22⋊Dic43—41no—
124(C2×D43)⋊C4—22no—
125(C2×D43)⋊C4—22no—
126(C2×D43)⋊C4—22no—
127(C2×D43)⋊C4—22no—
128(C2×D43)⋊C4—48no—
129(C2×D43)⋊C4—81no—
130(C2×D43)⋊C4—81no—
131(C2×D43)⋊C4—81no—
132(C2×D43)⋊C4—81no—
133C4⋊Dic43—22no—
134C4⋊Dic43—22no—
135C4⋊Dic43—41no—
136C4⋊Dic43—41no—
137C4⋊Dic43—41no—
138C4⋊Dic43—41no—
139C4×Dic43—81no—
140C4×Dic43—81no—
141C2×C43⋊C8—22no—
142C2×C43⋊C8—41no—
143C2×C43⋊C8—41no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43—21no—
148C23×C43C2×C4⋊C411yescharacteristic
149C23×C43#12011yescharacteristic
150C23×C43#12311yescharacteristic
151C23×C43#13511yescharacteristic
152C23×C43#13511yescharacteristic
153C23×C43AGL(1,ℤ/8)11yescharacteristic
154C23×C43#13711yescharacteristic
155C22×D43—22no—
156C22×D43—22no—
157C22×D43—22no—
158C22×D43—42no—
159C22×D43—42no—
160C22×D43—42no—
161C22×D43—42no—
162C22×D43—42no—
163C22×D43—42no—
164C22×D43—41no—
165C22×D43—41no—
166C22×D43—41no—
167C22×D43—41no—
168C22×D43—41no—
169C22×D43—41no—
170C22×D43—41no—
171C22×D43—41no—
172C22×D43—81no—
173C22×D43—81no—
174C22×D43—81no—
175C22×D43—81no—
176C22×D43—81no—
177C22×D43—81no—
178C2×C4×C43—21no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—21no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—42no—
187C2×C4×C43—42no—
188C2×C4×C43—42no—
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×C43C22⋊Q811yescharacteristic
202C2×C4×C43C22⋊Q811yescharacteristic
203C2×Dic43—22no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—42no—
207C2×Dic43—42no—
208C2×Dic43—42no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—42no—
214C2×Dic43—41no—
215C2×Dic43—41no—
216C2×Dic43—81no—
217C2×Dic43—81no—
218C2×Dic43—81no—
219C2×Dic43—81no—
220C2×Dic43—81no—
221C8×C43—42no—
222C43⋊C8—42no—
223#8858—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#38511yescharacteristic
237C22×C43#42711yescharacteristic
238C22×C43#42811yescharacteristic
239C22×C43#44911yescharacteristic
240C22×C43#45211yescharacteristic
241C22×C43#45311yescharacteristic
242C22×C43#45511yescharacteristic
243C22×C43B(4,𝔽2)11yescharacteristic
244C22×C43#45811yescharacteristic
245C22×C43#48211yescharacteristic
246C22×C43#48511yescharacteristic
247C2×D43—44no—
248C2×D43—42no—
249C2×D43—42no—
250C2×D43—42no—
251C2×D43—82no—
252C2×D43—82no—
253C2×D43—81no—
254C2×D43—81no—
255C2×D43—81no—
256C2×D43—81no—
257C2×D43—82no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—82no—
263C4×C43—81no—
264C4×C43—81no—
265Dic43—42no—
266Dic43—82no—
267Dic43—81no—
268Dic43—81no—
269#2312—431no—
270#1853—431no—
271#1852—431no—
272C2×#323—431no—
273#1439—431no—
274#1294—431no—
275#1294D4311yescharacteristic, complemented
276C2×C43—21no—
277C2×C43—21no—
278C2×C43—21no—
279C2×C43—21no—
280C2×C43#160011yescharacteristic
281C2×C43#160611yescharacteristic
282C2×C43#161211yescharacteristic
283C2×C43#161811yescharacteristic
284C2×C43#185411yescharacteristic
285C2×C43#185611yescharacteristic
286C2×C43#186711yescharacteristic
287D43—82no—
288C22×C4⋊C4—431no—
289C22×C22⋊C4—431no—
290C22×C22⋊C4—861no—
291C2×#107—861no—
292C2×#106—861no—
293C2×C22⋊C8—431no—
294C2×C22⋊C8C2×D4311yescharacteristic
295#388—861no—
296#388—861no—
297#388—861no—
298#388—861no—
299#380—431no—
300#380C2×D4311yescharacteristic
301#379—861no—
302C4×C22⋊C4—861no—
303C2×#95—861no—
304C2×#95C2×D4311yescharacteristic
305#340—861no—
306#340—861no—
307#323—434no—
308C43#885811yescharacteristic, complemented, Sylow
309C25—431no—
310C23×C4—21no—
311C23×C4—431no—
312C23×C4—861no—
313C23×C4C22×D4311yescharacteristic
314C22×C8—21no—
315C22×C8—861no—
316C2×C4⋊C4—431no—
317C2×C4⋊C4—431no—
318C2×C4⋊C4—861no—
319C2×C4⋊C4—861no—
320C2×C4⋊C4—1722no—
321C2×C4⋊C4D17211yescharacteristic
322C2×C4⋊C4D17211yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—432no—
325C2×C22⋊C4—432no—
326C2×C22⋊C4—861no—
327C2×C22⋊C4—861no—
328C2×C22⋊C4—861no—
329C2×C22⋊C4—861no—
330C2×C22⋊C4—861no—
331C2×C22⋊C4—861no—
332C2×C22⋊C4—861no—
333C2×C22⋊C4—861no—
334C2×C22⋊C4—861no—
335C2×C22⋊C4—1722no—
336C2×C22⋊C4—1722no—
337C2×C22⋊C4—1722no—
338C2×C42—861no—
339C2×C42—861no—
340#107—1722no—
341#106—1722no—
342C22⋊C8—21no—
343C22⋊C8—432no—
344C22⋊C8—861no—
345C22⋊C8C4×D4312yes—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—861no—
350#95—861no—
351#95—861no—
352#95—1722no—
353C24—432no—
354C24—861no—
355C24—861no—
356C24—861no—
357C24—861no—
358C24—861no—
359C24—861no—
360C24—1721no—
361C24—1721no—
362C24—1721no—
363C24—1721no—
364C24D4×D4311yescharacteristic
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—432no—
377C22×C4—861no—
378C22×C4—861no—
379C22×C4—862no—
380C22×C4—861no—
381C22×C4—861no—
382C22×C4—1721no—
383C22×C4—1721no—
384C22×C4—1721no—
385C22×C4—1721no—
386C22×C4—1721no—
387C22×C4—1721no—
388C22×C4—1721no—
389C22×C4—1721no—
390C22×C4C2×C4×D4311yescharacteristic
391C22×C4C2×D17211yescharacteristic
392C22×C4#1062189811yescharacteristic
393C22×C4D4×D4311yescharacteristic
394C22×C4#1062190011yescharacteristic
395C22×C4Q8×D4311yescharacteristic
396C2×C8—22no—
397C2×C8—41no—
398C2×C8—41no—
399C2×C8—862no—
400C2×C8—1721no—
401C2×C8—1721no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—862no—
405C4⋊C4—862no—
406C4⋊C4—1721no—
407C4⋊C4—1721no—
408C4⋊C4—1721no—
409C4⋊C4—1721no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—862no—
413C22⋊C4—862no—
414C22⋊C4—862no—
415C22⋊C4—862no—
416C22⋊C4—3441no—
417C22⋊C4—3441no—
418C22⋊C4—3441no—
419C22⋊C4—3441no—
420C22⋊C4—1728no—
421C22⋊C4—1721no—
422C22⋊C4—1721no—
423C42—3441no—
424C42—3441no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—862no—
430C23—862no—
431C23—862no—
432C23—3441no—
433C23—3441no—
434C23—3441no—
435C23—3441no—
436C23—3441no—
437C23—3441no—
438C23—1722no—
439C23—1722no—
440C23—1722no—
441C23—1722no—
442C23—1722no—
443C23—1722no—
444C23—1721no—
445C23—1721no—
446C23—1721no—
447C23—1721no—
448C23—1721no—
449C23—1721no—
450C23—1721no—
451C23—1721no—
452C23C4⋊C4×D4311yescharacteristic
453C23#1306329511yescharacteristic
454C23#1306330711yescharacteristic
455C23#1306334611yescharacteristic
456C23#1306334611yescharacteristic
457C23#1306334911yescharacteristic
458C23#1306335711yescharacteristic
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—862no—
481C2×C4—3441no—
482C2×C4—3441no—
483C2×C4—3441no—
484C2×C4—3441no—
485C2×C4—3441no—
486C2×C4—1722no—
487C2×C4—1722no—
488C2×C4—1721no—
489C2×C4—1721no—
490C2×C4—1721no—
491C2×C4—1721no—
492C2×C4—1721no—
493C2×C4—1722no—
494C2×C4—1721no—
495C2×C4—1721no—
496C2×C4—1721no—
497C2×C4—1722no—
498C2×C4(C22⋊D43)⋊C411yescharacteristic
499C2×C4C4×D17211yescharacteristic
500C2×C4#1306330311yescharacteristic
501C2×C4#1306330511yescharacteristic
502C8—42no—
503C8—1722no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—3442no—
517C22—3442no—
518C22—3442no—
519C22—3441no—
520C22—3441no—
521C22—3441no—
522C22—3441no—
523C22—1724no—
524C22—1722no—
525C22—1722no—
526C22—1722no—
527C22#1458277311yescharacteristic
528C22#1458293411yescharacteristic
529C22#1458294011yescharacteristic
530C22#1458304511yescharacteristic
531C22#1458306411yescharacteristic
532C22#1458306811yescharacteristic
533C22#1458307811yescharacteristic
534C22#1458308711yescharacteristic
535C22#1458309011yescharacteristic
536C22#1458322211yescharacteristic
537C22#1458323811yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—82no—
543C4—81no—
544C4—81no—
545C4—3442no—
546C4—3441no—
547C4—3441no—
548C4—1722no—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—21no—
553C2—3442no—
554C2#1913354211yescharacteristic
555C2#1913357811yescharacteristic
556C2#1913361011yescharacteristic
557C2#1913364611yescharacteristic
558C2#1913479511yescharacteristic
559C2#1913480611yescharacteristic
560C2#1913487711yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1294C2
socleC23×C43#120
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1294D43
hypocenterC43#8858
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. #19134790C2semidirect
3. #19134782C2semidirect
6. #19132474C2semidirect
7. C43×#1294C2semidirect
24. #14582622C4semidirect
275. #1294D43semidirect
308. C43#8858semidirect

Maximal subgroups

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

subgroupindex
#191371922
#191347902
#191347822
C2×#145826222
#191328412
#191324742
C43×#12942
#885843